Heating of nanoparticles and their environment by laser radiation and applications

Measuring single-particle heat generation using a 2D phospholipid bilayer assay. (a) Temperature profile of a gold nanoparticle (NP) irradiated at a laser intensity of P = 2.7 × 10⁶ W/cm²; the temperature decays with increasing distance from the particle center. (b) Biological assay used to map the temperature profile as shown in (c), which shows representative melted footprints for three different NPs at the same laser intensity of P = 4.3 × 10⁶ W/cm². The fluorescent images were recorded by acquiring an emission bandwidth of 496–587 nm, and the NPs were imaged by recording 594-nm laser light reflected from them. The scale bar corresponds to 2 μm. (d) Surface temperature as a function of laser intensity for all three NPs derived from the size of the melted footprints. Adapted from Ref. 23, which was licensed under a Creative Commons Attribution 4.0 International License.

Experimental and theoretical studies have been carried out to assess the PT efficiency of NPs with several different morphologies, including spherical GNPs and gold nanorods and nano-urchins, as well as spherical conjugates of GNPs, in which 20-nm GNPs were functionalized with dyes.²⁴ The efficiency of PT conversion was obtained from experimental results for the heating of nanostructures with an IR laser with a wavelength of 808 nm. Functionalizing the surfaces of the spherical 20-nm GNPs increased their PT efficiency by a factor of four, making them promising candidates for hyperthermia treatment along with gold nanorods and nanoshells. Note especially that surface functionalization is key for increased efficiency and temperature and can be used to determine the temperatures reached by NPs.

A set of studies investigated the pulsed heating of GNPs.^25–27 The possibility of heating NPs was evaluated by experimenting with modifying the surface of a polycarbonate substrate on which the particles were deposited,²⁵ and GNPs with diameters of 40 and 100 nm were irradiated with nanosecond pulses with a fluence of up to 25 mJ/cm². The results showed that particle heating could modify the substrate surface, and the heat-affected zone was estimated to be approximately twice the particle diameter. This effect can be used to determine the temperature of NPs and is also applied in in vitro PT therapy of human HeLa cancer cells.

Femtosecond and nanosecond laser excitation of metal NPs has been performed experimentally.^26,27 To determine the temperatures of the NPs and their environment indirectly, x-ray scattering and laser spectroscopy were used together with computer simulation. While x-ray scattering is an excellent method for determining nanoscale structure, it unfortunately requires a large-scale facility that is not always available for daily experiments. By contrast, laser spectroscopy is used widely for NP spectroscopy and the recording of dynamics. Structural information is indirect in many cases, but with proper modeling of the optical response, one can get good insights into the structure. Ultrafast laser spectroscopy has been used to investigate picosecond dynamics, typically electron relaxation and ultrafast particle vibrations.

The simplest approach—at nanosecond scale at least—is to examine the spectral response directly with a fast detector and oscilloscope, using the high sensitivity of plasmon resonance to changes in the temperature or dielectric medium. Two setups have been used for optical probing of particle excitation. One is the steady-liquid single-shot method, which allows the use of multiple probe colors simultaneously [Fig. 2(b)]. A 10-ns Nd:YAG laser pulse was used, the frequency of which was doubled, and this setup allowed semi-quantitative observation of the overall spectral behavior. Better control over the fluence and exposed volume can be achieved with a perpendicular setup [Fig. 2(a)]. The pump laser—a triple-frequency Nd:YAG laser with a pulse width of 3 ns—was collimated into a linear focus across a capillary that enclosed the flowing gold hydrosol. Perpendicular to this, a probe laser beam [cw laser at 532 nm (Nd:YAG) or 632 nm (He–Ne)] crossed the laser-excited volume. The probing of the multiwave setup was carried out using fast photodiodes and a digital storage oscilloscope (1 GHz), and single shots were recorded by the combination of a solid-state laser and a conventional laser diode at 405, 488, 635, and 660 nm.

FIG. 2.

Sketches of setups for probing nanosol dynamics by (a) perpendicular optical probing of a continuously flowing sample in a capillary, (b) collinear optical pumping and probing with multiple wavelengths (only one probe laser is shown), and (c) x-ray probing in an x-ray capillary in either wide-angle geometry or small angle (SAXS) geometry (with larger detector distance). Adapted from Ref. 27, which was published under a CC BY (Creative Commons Attribution) license.

An increase in the temperature of the water phase causes a weakening and a slight blue shift of the resonance, which is very weak at 100 °C but can be sharp if the water phase is close to the critical temperature. In Fig. 3, the measured expansion transients are superimposed on the corresponding calculated cooling curves.

FIG. 3.

Lattice temperature transients of different-sized gold nanoparticles (GNPs) as determined by lattice expansion in time-resolved x-ray scattering after femtosecond laser irradiation. The black solid lines on top of the scattered experimental data are the results of numerical simulations using the two-temperature model. The temperature change of the adjacent water layer is taken from the heat transfer calculation of temperature for water adjacent to the GNP (lower blue lines: bold for 100 nm, dashed for 36 nm, and dotted for 14 nm). Adapted from Ref. 27, which was published under a CC BY (Creative Commons Attribution) license.

SNPs are very attractive for chemical and technological applications and biophysical and medical investigations because of their unique physicochemical properties with plasmon resonance in the wavelength range of 400–450 nm. Experimental studies have been carried out of the heating processes that occur with SNPs.^28–34 Aqueous solutions of metal-based NPs (SNPs with a size of ∼27.5 nm and copper oxide NPs with a size of ∼80 nm) were exposed to a cw NIR laser (λ = 1064 nm) at powers of 2.2 and 4.5 W for 5 min,²⁸ and differential heating of a bulk aqueous suspension of NPs with different physicochemical properties revealed a maximum temperature of 67 °C and different heating kinetics of different NPs excited by NIR.

Various experimental studies of laser interaction with SNPs have been carried out, including laser heating of NPs. Note that laser methods for synthesizing and controlling the parameters of SNPs have become widespread in recent years and play a prominent role in the development of general physicochemical methods. The laser method has been used to obtain silver nanospheres by selective laser heating of silver nanocolloids,²⁹ and the results of laser heating and annealing of metal NPs synthesized in glasses by ion implantation have been analyzed.³⁰ The growth of metal NPs with wide size distribution leads to specific optical properties of implanted materials, and the modification of SNPs by an excimer laser has been considered.

Plasmonic nanostructures including aggregated SNPs have been irradiated with multiple overlapping femtosecond laser pulses with a very low fluence (∼7.2 mJ/cm²) and heated efficiently without attendant damage to the surrounding material.³¹ Improved coupling and efficient heating were found to be strongly dependent on the geometry of these NPs and the polarization of the laser radiation. It was found that this effect of selective heating is most evident in clusters of two, three, four, and seven SNPs. Under these conditions, the heating efficiency is such that the temperature of 50-nm SNPs can be raised from room temperature to their melting point. Selective femtosecond laser heating of SNPs was concentrated in certain clusters of two, three, four, and seven SNPs, where the laser pulse energy absorption was enhanced by localized surface plasmon (LSP)-induced hotspots and depended on the polarization of the incident laser radiation.

Temperature plays the most important role in the outcome of the thermal sintering of metal NPs and in the selection of a suitable substrate.³² The temperature field during the pulsed laser sintering of inkjet-printed SNPs on glass substrates has been estimated using a three-dimensional numerical model, in which the temperature-dependent thermal conductivity of SNPs was assumed. A maximum temperature of ∼204 °C over the line of SNPs was obtained at a laser power of 276 mW and a scanning speed of 135 m/s. Accordingly, the laser heating of SNPs immersed in glass³³ and in liquid³⁴ has been considered.

NIR light has a relatively large penetration depth into biological tissue, and its absorption by metal NPs can cause extreme heating for cancer treatment. With this purpose in mind, the laser heating of other NPs has been studied. Cuvettes containing platinum NP solutions were irradiated with an NIR diode laser (λ = 1064 nm) and at a constant laser power in the range of 0.5–5 W, and the heating characteristics of the sample were measured with an IR camera.³⁵ Individual irradiated NPs with a diameter of 50–70 nm easily reached surface temperatures of up to 900 K, which was estimated by direct measurements based on a biological matrix under the action of laser radiation. Platinum particles remain stable at these extreme temperatures, unlike the gold nanoshells that are often used for PT purposes.

In Ref. 36, how thermal effects and the laser fluence affect the structural and chemical stability of individual magnetic NPs excited by single femtosecond laser pulses was estimated. The energy transfer from a femtosecond laser pulse into an NP is limited by the Rayleigh scattering cross section, and combined with the absorption of light by the supporting substrate and protective layers, this determines the NP temperature increase. Individual cobalt NPs (8–20 nm in size) were studied as a prototype of a model system, using x-ray photoemission electron microscopy and scanning electron microscopy upon excitation by single femtosecond laser pulses of various intensity and polarization.

The main difference between the heating of NPs by cw radiation and laser pulses should be noted. During cw radiation, the thermal losses of NPs due to thermal conduction determine the heating dynamics and maximum temperature of NPs. When exposed to laser pulses with a duration of more than 10 ns, the thermal losses of NPs due to thermal conduction affect their heating dynamics and maximum temperature to a lesser or greater extent, depending on the pulse duration. Under the action of ultrashort laser pulses with a pulse duration of the order of 10 ps or less, the effect of thermal losses of NPs due to heat conduction is very small.

B. Numerical modeling of heating of nanoparticles by laser pulses

The heating of NPs by laser radiation is the first and main process that determines a whole set of subsequent processes and the results of laser–NP interactions. Investigating this process is a significant task, and accuracy and reliability of its theoretical description are very important. Heat dissipation from the surface of a heated NP has a few important features that determine the subsequent processes arising inside and around the NP, and describing this process correctly is very important for any applications of heated NPs. The presence of a possible surface problem for heat dissipation (thermal resistivity) from the surface of an NP immersed in an ambient liquid or solid has been noted in the literature, and how this affects NP heating is discussed in Sec. II E. On the other hand, in many situations, NP surface resistivity has no significant effect, and the condition of “ideal” heat contact between the NP surface and the ambient medium is used.^37–39 This means that the heat flux from a heated NP spreads through the NP surface to the environment without any resistance, and this approach is used below.

It is valid to apply the diffusive heat equation to nanoscale thermal processes if the mean free path of the heat carriers (electrons and phonons) in the NPs and the molecules and phonons in the ambient medium is much smaller than the characteristic NP size.⁴⁰ The mean free path of carriers (molecules) in amorphous surrounding solids and liquids is very short at ∼0.1 nm, and this is much smaller than the characteristic NP radius r₀ of 10–100 nm. Consequently, the heat flow in NPs surrounded by liquids and amorphous solids can be described well by the diffusive heat equation when nanometer length scales are involved. For a metal nanosphere in a homogeneous medium, the typical temporal and spatial scales for the observed heat transfer match the requirements for purely diffusive thermal transport in the surrounding medium.

When laser pulses act on an NP, the thermal processes are described by the following system of heat conduction equations for the NP and its surrounding medium for a spherical geometry with the given initial conditions:³⁷

c_{i} ρ_{i} \frac{\partial T_{i}}{\partial t} = \frac{1}{r^{2}} \frac{\partial}{\partial r} (r^{2} k_{i} \frac{\partial T_{i}}{\partial r}) + q_{i}, T_{i} (r, t = 0) = T_{\infty},

(1)

where for the two-component system, i = 0, 1 denotes the parameters of the NP (i = 0) or its surrounding medium (i = 1), T_i is the temperature, and t is time. The terms c_i, ρ_i, and k_i are the heat capacity, density, and thermal conductivity, respectively, and r is the radial coordinate of the spherical coordinate system whose origin is fixed at the NP center; the NP parameters are determined for r ≤ r₀ (i = 0), and those of the ambient medium are determined for r > r₀ (i = 1). The term q₀ (i.e., q_i with i = 0) is the power density of heat sources inside the NP (r ≤ r₀) and is given by

q_{0} = I_{0} K_{abs} π {r_{0}}^{2} / V_{0}

⁠, where I₀ is the radiation intensity, K_abs(r₀, λ, T₀) is the efficiency factor for absorption of radiation with wavelength λ by a spherical particle of radius r₀,⁴¹ and V₀ = 4/3πr₀³ is the NP volume. For r > r₀, we have q₁ = 0. Finally, T_∞ is the initial temperature of the NP and medium, and ideal thermal contact is assumed by fulfilling the following conditions:

k_{0} \frac{\partial T_{0}}{\partial r} |r_{0} = k_{1} \frac{\partial T_{1}}{\partial r} |r_{0}, T_{0} |r_{0} = T_{1} |r_{0} .

(2)

The pressure in a medium containing NPs is usually assumed to be constant during radiation–NP interaction. Currently, it is very difficult to determine experimentally the value or temporal dependence of T₀ during short laser pulse action on an NP by nonperturbative methods. Therefore, theoretical determination of T₀(r, t) is very important for understanding the experimental results and dependences.

Numerous studies have carried out numerical modeling of NP heating by laser radiation. The process of heating a spherical GNP by nanosecond laser pulses and the heat transfer between the particle and the surrounding medium without mass transfer have been modeled by the finite element method.⁴² For an NP radius of r₀ = 25 nm and a radiation wavelength of λ = 532 nm in liquid water in the temperature range of 20–100 °C and a gaseous suspension in the range of 100–400 °C, it was noted that the temperature-induced change in dielectric properties led to a temperature-dependent change in the absorption efficiency factor. Such changes significantly affect the temperature reached by the particle and the surrounding microenvironment, so to determine the temperature increase correctly, it is necessary to know the thermal and dielectric properties of the medium. For nanosecond pulses, it was found that the temperature distribution in the external medium around an NP becomes spatially quasi-stationary. An increase in pulse duration t_P in a wide range does not lead to a significant change in the spatial temperature profile, which means the establishment of a quasi-stationary distribution in time, which is important for describing the heating of the NP.

Computational modeling of the pulsed laser-induced heating of GNPs in water has taken into account the numerical two-temperature model, the spatiotemporal evolution of the water temperature, the diameter-dependent behavior of the maximum GNP temperature, the refractive index gradient, and the dielectric function of gold.⁴³ The temperature evolution of the electron and lattice systems is modeled well by the two-temperature model with its two coupled partial differential equations. The model was extended to media in which radial heat conduction is assumed to occur, and the equation for the medium coupling the electron and lattice systems is the boundary condition at the NP−water interface. Given that heat conduction in a GNP is much faster than that in water, the electron and lattice equations can be simplified. For nanosecond pulse durations, the heat flux into the surrounding medium leads to particle cooling during energy deposition, and heat transfer to the surrounding medium creates a local temperature gradient in the water adjacent to a GNP.

The temperature evolutions of a single GNP and an ensemble of GNPs both embedded in a polystyrene matrix and irradiated with a nanosecond laser at 532 nm have been modeled numerically.⁴⁴ The temporal and spatial temperature distributions were calculated by solving the heat diffusion equations with appropriate initial and boundary conditions. The temperature evolution and the dynamics of the NP system are influenced by the distribution of GNPs in the polymer matrix, which plays a significant role in the temperature dependence and in the dynamics of the system toward reaching thermal equilibrium.

The spatiotemporal dependences of T₀ on t_P have been calculated numerically and analytically for the heating of a GNP by cw and pulsed irradiation.^39,45 Figure 4 shows the spatiotemporal distributions of the temperature T inside and around a spherical GNP in water and with r₀ = 25 nm for different time instants. The results describe the formation of the temperature distributions inside an NP and outside in the environment during radiation action and NP cooling. Note that the action of a femtosecond pulse with t_P of the order of 10–100 fs for implementing thermal processes inside the whole NP is actually equivalent to that of a pulse with t_P = 1 × 10⁻¹² s, this being because the release of absorbed energy into the lattice from the electronic system as a result of electron–phonon equalization over a time of ∼1 × 10⁻¹² s (see Ref. 47) is equal to the simple absorption of energy by the NP as a whole from a pulse with a duration of t_P = 1 × 10⁻¹² s. Therefore, the description of the laser heating of a whole NP by femtosecond pulses can be started from t_P = 1 × 10⁻¹² s. For t_P = 1 × 10⁻⁸ s and longer, the formation of a vapor nanobubble is possible under the action of pulses with this duration, so the maximum temperature for the numerical solution is limited to 373 K. However, for t_P = 1 × 10⁻¹⁰ s and especially 1 × 10⁻¹² s, it is assumed that a vapor nanobubble cannot form during the pulse duration, so the maximum temperature for the numerical solution is limited to 600 K.

FIG. 4.

Computer (solid black lines) and analytical [dashed red lines; see Eq. (1)] dependences of temperature T along radius r for time instants t/t_P (left column) and temporal dependences of T_max (r = 0) (right column) on t for GNP with r₀ = 25 nm placed in water: (a) for cw irradiation with I_n = 0.75 MW/cm² at t = 1 × 10⁻⁸ s (1), 1 × 10⁻⁶ s (2), 1 × 10⁻³ s (3), 5 × 10⁻³ s (4), and 1 × 10⁻² s (5); (b) for pulsed irradiation with t_P = 1 × 10⁻⁸ s and I_n = 1.13 MW/cm² at t/t_P = 0.1 (1), 0.5 (2), 1 (3), 2.0 (4), 5.0 (5), and 10.0 (6); (c) for pulsed irradiation with t_P = 1 × 10⁻¹⁰ s and I_n = 42 MW/cm² at t/t_P = 0.1 (1), 0.5 (2), 1.0 (3), 5.0 (4), and 100 (5); (d) for pulsed irradiation with t_P = 1 × 10⁻¹² s and I_n = 2.5 GW/cm² at t/t_P = 0.1 (1), 0.5 (2), 1.0 (3), 5.0 (4), 100.0 (5), and 300.0 (6). The vertical line in the left column represents the boundary of the NP, and the normalized radiation intensity is I_n = I₀K_abs. Adapted from Refs. 39 and 45.

When an NP absorbs laser radiation, it is heated intensively.^39,45 For the variants presented in Fig. 4, the distribution of T(r) inside an NP for various values of t_P is practically independent of r because the electron thermal diffusivity of metals is very high.⁴⁶ A feature for cw irradiation and pulses with t_P ≥ 1 × 10⁻⁸ s is the development of heat transfer from the NPs to the environment when exposed to radiation. Numerical distributions of temperature versus r outside the NP [Figs. 4(a) and 4(b)] correspond qualitatively to quasi-stationary forms with some repeatable T(r) for several moments of time. On the other hand, the emerging nonstationary nature of the heat exchange of the NP with the surrounding medium (water) is confirmed by computer simulation for short laser pulses with t_P between 1 × 10⁻¹⁰ and 1 × 10⁻¹² s. This indicates the practically absent or weak heat exchange of the NP with the environment and the thermal localization of the absorbed laser pulse energy in the NP, which leads to its significant heating above the environment. The heating of an NP by cw irradiation to its maximum temperature is achieved because the energy absorption is compensated by heat losses due to thermal conductivity. The maximum NP temperature under the action of laser pulses is achieved at the end of the pulse at t_P. After the laser pulse is turned off, the NP emits energy to the medium, and its temperature T₀ decreases and tends to the initial temperature T_∞ (Fig. 4, right column).

Numerical calculations have been used to ascertain how laser wavelength and particle size affect the absorption factor for colloidal SNPs with a radius of 5–50 nm under irradiation by 30-ns laser pulses with a wavelength of 248, 266, 355, 532, and 1064 nm, and the final temperatures for all particles were obtained.⁴⁸ To analyze numerically the interaction between a nanosecond pulse-width laser beam and SNPs, a simulation was carried out.⁴⁹ The effects of a laser pulse width of 4, 36, 64, and 100 ns with a wavelength of 1070 nm on a water-encapsulated SNP with a diameter of 100 nm and NP temperature distribution were simulated numerically, and the results showed that most of the irradiated energy was absorbed by the several-nanometers-thick surface layer of the NP.

C. Analytical study of heating of single nanoparticles by laser pulses

There have been many analytical studies of the heating of NPs by laser pulses. Compared to computer results, analytical solutions are much simpler and more useful for describing the thermal processes, but they are less accurate. Analytical temperature solutions have been derived by modeling a nanorod as a prolate spheroid for both cw and pulsed lasers.⁵⁰ For the cw case, an exact analytical solution for the steady-state heat transfer was presented using integer-degree Legendre function expansions in prolate spheroidal coordinates, and the maximum temperature and temperature profiles as functions of laser power and nanorod geometry were obtained. Also, a theoretical study of the heating of a solid ellipsoidal NP in a medium by short laser pulses has been carried out.⁵¹

Computer modeling^39,42,45 has established two main results that can be used to create an analytical model: (i) the approximate uniform temperature inside the NP volume at various times t during irradiation and cooling for a wide range of t_P values (Fig. 4, left column), and (ii) the computer-derived quasi-stationary distributions of T for r > r₀ and t_P ≥ 1 × 10⁻⁸ s. Assuming a uniform temperature T₀ inside the NP volume during heating and cooling of the NP as confirmed by computer simulation, and after integration over the NP volume for the spherically symmetric case, the equation that describes the heating of an NP and results from Eq. has the form^5,45,52

c_{0} ρ_{0} V_{0} \frac{d T_{0}}{d t} = \frac{1}{4} I_{0} K_{abs} S_{0} - J_{ε} S_{0}

(3)

with the initial condition

T_{0} (t = 0) = T_{\infty},

(4)

where

S_{0} = 4 π {r_{0}^{2}}_{\infty}

is the surface area of a spherical NP of radius r₀, I₀ is the intensity of the laser radiation, and J_ε is the energy flux density from the NP. The quantity J_ε near the particle surface comprises the energy losses due to heat conduction (J_C) and radiation cooling (J_R), i.e.,

J_{ε} = J_{C} + J_{R}, J_{C} = - k_{1 T} (T_{1}) {\frac{d T_{1}}{d r}|}_{r_{0}}, J_{R} = ε σ (T_{0}^{4} - T_{\infty}^{4}) .

(5)

The value of J_C is determined at the NP surface, k_1T(T₁) is the heat conduction coefficient of the environment and depends on its temperature, the particle surface emissivity is approximately unity, ε is the coefficient of emissivity, and σ is the Stefan–Boltzmann constant.⁴⁶ Estimations of J_C in water and J_R based on Eq. using the characteristic temperature of T₀ = 4 × 10³ K give J_C ≫ J_R, and for the temperature interval of T_∞ < T₀ < 4 × 10³ K, the value of J_R can be neglected.

Next, for constant K_abs = K_∞ and the temperature dependence

k_{1 T} = k_{1} {(T_{1} / T_{\infty})}^{a}

with

k_{1} = k_{1 T} (T_{1} = T_{\infty})

⁠,⁴⁶ Eqs. and can be solved in a spherical coordinate system whose origin is at the NP center for the quasi-stationary temperature distribution around the NP under the conditions of

\frac{\partial T_{1}}{\partial t} = 0

and q₁ = 0 for r ≥ r₀. For a ≠ −1, we have

T_{1} (r) = T_{\infty} {[1 + \frac{r_{0}}{r} ({(\frac{T_{0}}{T_{\infty}})}^{a + 1} - 1)]}^{\frac{1}{a + 1}},

J_{C} = - k_{1} (T_{0}) {\frac{d T}{d r}|}_{r_{0}} = \frac{k_{1} T_{\infty}}{(a + 1) r_{0}} [{(\frac{T_{0}}{T_{\infty}})}^{\frac{1}{a + 1}} - 1],

(6)

and for a = 0 we have

T (r) = T_{\infty} + \frac{r_{0}}{r} (T_{0} - T_{\infty}), J_{C} = \frac{k_{1}}{r_{0}} (T_{0} - T_{\infty}) .

(7)

The characteristic time t_T1 for forming a quasi-stationary temperature distribution in the space r > r₀ for the distance r ∼ r₀ is t_T1 ∼ r₀²/4χ₁, where χ₁ = k₁/c₁ρ₁ is the thermal diffusivity of the ambient medium. The temperature T in the medium outside the spherical particle under the condition of constant T₀ can be described spatiotemporally as³⁷

T (r, t) = T_{\infty} + \frac{(T_{0} - T_{\infty}) r_{0}}{r} e r f (\frac{r - r_{0}}{2 \sqrt{χ_{1} t}}) .

This solution is transformed into Eq. under the condition of

r - r_{0} ≪ 2 \sqrt{χ_{1} t}

and can be considered as a quasi-stationary distribution. The temporal dependence T₀(t) from Eqs. , , and for time 0 ≤ t ≤ t_P is⁵²

T_{0} = T_{\infty} + \frac{I_{0} K_{abs} r_{0}}{4 k_{1}} [1 - \exp (- t / τ_{0})], τ_{0} = \frac{c_{0} ρ_{0} {r_{0}}^{2}}{3 k_{1}} .

(8)

The cooling of an NP is described by the following expression, which can be derived from Eqs. and under I₀ = 0, T₀(t = t_P) = T_max, and t > t_P: for a = 0, we have

T_{0} = T_{\infty} + (T_{\max} - T_{\infty}) \exp (- (t - t_{P}) / τ_{0}),

(9)

where T_max is the maximum NP temperature at the end of the laser pulse at t = t_P.

The characteristic time τ₀ determines the temporal dependencies of T₀ during NP heating, heat exchange between a single spherical NP and the surrounding medium, and NP cooling, and it can be compared with the laser pulse duration t_P. The characteristic time is $τ_{0} = \frac{c_{0} ρ_{0} {r_{0}}^{2}}{3 k_{1 \infty}}$ with k₁ = 6 × 10⁻³ W/cm K at T_∞ = 300 K (see Ref. 46), and for GNPs with radius r₀ = 5–100 nm, it is equal τ₀ =1.4 × 10⁻¹⁰–1.4 × 10⁻⁸ s (see Fig. 5).

FIG. 5.

Dependence of τ0 on radius r0 of GNPs immersed in water. Adapted from Ref. 53.

Dependence of τ₀ on radius r₀ of GNPs immersed in water. Adapted from Ref. 53.

Note that analytical descriptions of the heat flow in an infinite medium heated by a sphere for some special boundary conditions have been investigated.^37,38 Unfortunately, these solutions are presented in complicated forms that are difficult to use for concrete situations.

The characteristic times t_T1 and τ₀ describe the formation of a quasi-steady spatial distribution of the temperature around an NP at $t_{T 1} = \frac{c_{1} ρ_{1} {r_{0}}^{2}}{4 k_{1}}$ and NP heating and cooling in $τ_{0} = \frac{c_{0} ρ_{0} {r_{0}}^{2}}{3 k_{1}}$ ⁠. It is interesting to note that we have ρ₀c₀ = 2.49 for gold and 2.48 for silver, and Fig. 5 can be used approximately for both metal NPs. These characteristic times depend quadratically on r₀, but t_T1 depends on only the thermal parameters of the medium, whereas τ₀ depends on the parameters of both the NP and the medium. Experimental data⁵⁴ confirm a quadratic (parabolic) dependence of the characteristic time for energy dissipation versus NP radius, i.e., τ₀ ∼ r₀².

Comparing τ₀ with the laser pulse duration t_P leads to two possible time regimes. “Long” laser pulses with pulse duration t_P > τ₀ or cw irradiation (which essentially exceeds the characteristic time τ₀) cause the heating of both the NP and the surrounding medium as heat diffuses across the NP boundary, and this case can be used for intensive heat exchange from NPs to the ambient medium. From Eq. , the stationary value of T₀ for t_P > τ₀ is given by

t_{P} > τ_{0} T_{0} \approx T_{\infty} + \frac{I_{0} K_{abs} r_{0}}{4 k_{1}} .

(10)

For t_P < τ₀, we have “short” laser pulses during which there is practically no heat exchange between an NP and its environment, and the laser energy is thermally confined within the NP during the pulse action, causing rapid heating of the NP itself and its conservation. If the condition t < τ₀ for time interval 0 ≤ t ≤ t_p is obeyed, the expansion of the exponent in gives the dependence T₀ on t. For t_P < τ₀, we have

t_{P} < τ_{0} T_{0} \approx T_{\infty} + \frac{3 I_{0} K_{abs} t}{4 ρ_{0} c_{0} r_{0}} .

(11)

The case of t_P ∼ τ₀ is the transition regime for pulse durations between thermal confinement in the NP and heat diffusion from the NP.

Analytical spatiotemporal dependences based on the solutions in Eqs. (8) and (9) are shown in Fig. 4. The analytical and numerical temperature distributions versus r outside the NP are practically close [Fig. 4(a)] and match qualitatively [Figs. 4(b) and 4(c)] for a few time instants. This means the formation of quasi-stationary spatial temperature profiles for cw and pulsed irradiation with t_P ≥ 1 × 10⁻⁸ s > τ₀. Computer simulation has confirmed the possibility of using the analytical model to describe the temporal dependence of NP temperature T₀ and the outward distribution T(r) with sufficient accuracy for the ranges t_P ≥ 10⁻⁸ s and 10⁻¹² s ≤ t_P ≤ 10⁻⁸ s with errors of ±20%–30% for NP heating and cooling. Note the absolute coincidence between the analytical and numerical values of T_0max, which means good accuracy for the solution in Eqs. (8) and (11) for pulse durations between 1 × 10⁻¹⁰ and 1 × 10⁻¹² s due to the practical absence of heat exchange with the ambient environment.

Analysis of the thermo-optical characteristics of the interaction processes of laser radiation with SNPs has been carried out on the basis of the developed theory taking into account the absorption of laser radiation by NPs and their thermo-optical and other properties.⁵⁵

Very high cooling rates due to intensive cooling of NPs can be realized in the case of absorbing NPs embedded in a transparent solid (liquid) medium with high thermal conduction, where energy deposited by the ultrashort laser pulse in an NP can be followed by high heat fluxes due to an effective three-dimensional heat transfer into the medium. The cooling rate for microparticles and NPs is estimated as [see Ref. 56 and also Eq. ]

\frac{d T_{0}}{d t} = - \frac{3}{r_{0} c_{0} ρ_{0}} J_{C} = \frac{3 k_{1}}{r_{0}^{2} c_{0} ρ_{0}} (T_{0} - T_{\infty}),

(12)

and simple evaluation of the NP cooling rate from Eq. gives a value of ∼10¹² K/s for the first 100 ps and for r₀ = 25 nm. Highly heated metal NPs injected into a cold liquid environment can be rapidly undercooled and undergo rapid transformation into nonequilibrium structures.⁵⁷

Analytical modeling of NP heating by laser radiation¹⁷ is actually based on a stationary-state situation using only the energy conservation equation, when equality exists between the heat input to an NP by the conversion of energy absorbed by the NP and the outward heat flux by conduction at thermal equilibrium. This approach can be applied only for cw irradiation and pulses with long durations. The theoretical model¹⁸ used for the analytical description of NP heating in the stationary stage is based on the balance between laser energy absorbed by NPs and energy spent for phase transitions such as heating, melting, and evaporation without taking into account the heat loss due to thermal conduction, radiation cooling, and convective heat transfer. It has been noted that this heat loss can reach 80%–90% of the energy absorbed during nanosecond laser pulses and that the aforementioned models have rather low levels of correctness.

D. Thermal resistance at NP metal–environment (liquid) interface

In Subsection II C, perfect thermal contact between a metal NP and its host medium was considered. However, the NP can have poor contact with its environment, and an interfacial thermal resistance may occur on the metal surface of the NP because of the contact discontinuity between the two materials with different thermophysical and chemical properties, surface nanoscale roughness with different protrusions, holes, porosity, poor wettability of the solvent or the hydrophobic coating of the NP surface by some liquids in the case of a colloidal solution, etc. The result of all of this is known as “Kapitza thermal resistance.” These origins are considered together in the definition of the interfacial thermal resistance 1/G, where G is the thermal conductance. These facts can play an important role in a possible thermal resistivity for heat dissipation from the surface of a heated NP immersed in a liquid or solid ambient, as was mentioned by Cahill et al.^58–60 Essentially, mathematical modeling is used to obtain the value of G by fitting a theoretical expression to experimental data, rather than to independently describe the experiment.

Heat dissipation from an NP of radius r₀ has two components: (i) heat transfer across the interface between the NP and its surroundings, and (ii) heat diffusion in the surroundings. The finite thermal conductance forms a temperature jump $T_{0} (t) - T_{1} (r_{0}, t)$ at the NP interface, and the heat flux density from the NP surface is determined by $J_{K} = G (T_{0} - T_{1} (r_{0}))$ ⁠, where $T_{1} (r_{0})$ is the surrounding temperature at the NP surface.

Heat dissipation during NP cooling is described by a system of two equations that determine the heat transfer through the NP surface at r = r₀ and the heat diffusion into the surrounding medium (see also Refs. 26 and 60, and 61), i.e.,

\frac{d T_{0} (t)}{d t} = - \frac{3 G}{r_{0} c_{0}} (T_{0} (t) - T_{1} (r_{0}, t)),

(13a)

ρ_{1} c_{1} \frac{\partial T_{1}}{\partial t} = \frac{k_{1}}{r} \frac{\partial^{2}}{\partial r^{2}} (r T_{1}) .

(13b)

Equations and can be solved together using a Laplace transform and numerical techniques to determine the rate of cooling of the particle, with G treated as an adjustable parameter.

Studies have been carried out of plasmonic sensing of heat transport at solid−liquid interfaces⁶² and ultrafast thermo-optical dynamics of a single metal nano-object.^63–66 There was a study of a system of gold nanodisks supported on fused silica and other substrates and immersed in various solutions as prospective nano-objects for different applications.⁶² Gold nanodisks with a diameter of 60 nm, a thickness of 20 nm, and coated with hydrophilic self-assembled monolayers in water and in water–glucoside mixtures showed the values of G = 190 and 130 MW m⁻² K⁻¹, respectively. Comprehensive analytical and numerical thermo-optical models were developed by the Del Fatti group, linking the optical signals measured by ultrafast transient spectroscopy on metal nano-objects in dielectric environments to their thermal dynamics.⁶³ Ultrafast time-resolved measurements to study photoexcited transport at the metal–liquid interfaces of colloidal GNPs were carried out experimentally.⁶⁴ Perturbations of the energy states on both sides of the interfaces within a nanoscale distance were measured simultaneously by using transient absorption spectroscopy together with the stimulated emission depletion of fluorescence molecules. Evidence was shown of ultrafast coupling between GNPs and their surrounding solvent molecules on the picosecond time scale, which can be represented by a small contact resistance.

The cooling dynamics of single nanodisks (made of gold and 60−190 nm in diameter and 18−40 nm in thickness) supported on a sapphire substrate were investigated quantitatively using optical pump–probe spectroscopy combined with a spatial modulation microscope.⁶⁵ The measured cooling kinetics depended mainly on the nanodisk thickness and to a much lesser extent on the diameter, in agreement with numerical simulations based on Fourier’s law of heat diffusion, also accounting for the presence of a thermal resistance at the interface between the nanodisks and their substrate. The transient optical response associated with the internal thermalization of a single gold nanodisk (occurring on the timescale of a few picoseconds) was investigated quantitatively by time-resolved spectroscopy experiments, and the measured signals were compared with a model accounting for the effects of both electron and ionic lattice heating.⁶⁶ Perfect contact and thermal conductance G were assumed at their interface.

Molecular dynamics (MD) simulations have been carried out to calculate the thermal transport and Kapitza resistance at fluid–solid interfaces.^67–69 MD simulations were performed to model the interfacial thermal conductance G from bare GNPs (icosahedral, cuboctahedral, and spherical) to a hexane solvent.⁶⁷ The computed conductance was found to depend on not only the NP shape but also the size, particularly for nanospheres. Particle morphology has a significant effect on interfacial thermal conductance from bare particles to the surrounding solvent. A new and reliable linear response method was introduced to calculate the interfacial thermal resistance or Kapitza resistance in fluid–solid interfaces with the use of equilibrium MD simulations.⁶⁸ MD simulations are carried out in a Lennard-Jones system with fluid confined between two solid slabs. Different types of interfaces are tested by varying the fluid–solid interactions (wetting coefficient) at the interface. This method allows us to directly determine the Kapitza length from MD simulations by considering the temperature fluctuation and heat flux fluctuations at the interface. It was observed that the Kapitza length decreases monotonically with an increasing wetting coefficient as expected. Heat transfer and the thermal conductance at the interface between an SNP and surrounding water were studied using MD simulations.⁶⁹ Interfacial heat transfer between a solid NP and water with a discontinuity between the temperatures of two bodies was related to the difference in acoustic impedance at the two sides of the interface.

On the other hand, the joint effect of the heat fluxes due to the thermal conductance J_K and heat conduction J_C can be determined based on the analytical model in Eqs. and , i.e.,

c_{0} ρ_{0} V_{0} \frac{d T_{0}}{d t} = \frac{1}{4} I_{0} K_{abs} S_{0} - J_{K} S_{0},

(14)

{J_{K}|}_{r_{0}} = {J_{C}|}_{r_{0}} .

(15)

Equation is presented in general form for NP heating and cooling processes [in Eq. , J_ε is replaced by J_K). The condition of heat flow continuity on the NP surface should be fulfilled, and the process of heat conduction [Eq. ] is solved in the stationary state. The condition in Eq. allows us to obtain the expression for

T_{1} (r_{0})

at the NP boundary, i.e.,

{J_{K}|}_{r_{0}} = G (T_{0} - T_{1} (r_{0})) = {J_{C}|}_{r_{0}} = \frac{k_{1}}{r_{0}} (T_{1} (r_{0}) - T_{\infty})

T_{1} (r_{0}) = \frac{T_{0} + \frac{k_{1}}{G r_{0}} T_{\infty}}{1 + \frac{k_{1}}{G r_{0}}}, {J_{K}|}_{r_{0}} = {J_{C}|}_{r_{0}} = G \frac{(T_{0} - T_{\infty})}{1 + \frac{G r_{0}}{k_{1}}} .

(16)

The use of these relations makes it possible to obtain solutions for the dependences of NP temperatures on time for the stages of heating and cooling, i.e.,

T_{0} = T_{\infty} + \frac{I K_{abs} r_{0}}{4 k_{1}} (1 + \frac{k_{1}}{G r_{0}}) [1 - \exp (- \frac{t}{τ_{0} (1 + \frac{k_{1}}{G r_{0}})})],

(17)

T_{0} = T_{\infty} + (T_{\max} - T_{\infty}) \exp (- \frac{(t - t_{P})}{τ_{0} (1 + \frac{k_{1}}{G r_{0}})}) .

(18)

These solutions make it possible to estimate the contributions of thermal conductivity and interfacial thermal conductance in the case of their joint action. The characteristic time $τ_{0} (1 + \frac{k_{\infty}}{G r_{0}})$ determines the dynamics of NP heating and cooling. The interfacial thermal conductance G is determined empirically by comparing the experimental and theoretical dependences; it depends on the accuracy of those data, and moreover they differ in experiments with similar conditions. The experimental values of G for GNPs immersed in water in different publications are in the range of 20–200 MW m⁻² K⁻¹.^58–60 Several experimental studies have reported values of G for GNPs in different surroundings.^26,61 For example, spherical GNPs with r₀ = 9 nm exhibited G = 110 ± 10 and 40 ± 5 MW m⁻² K⁻¹ in water and ethanol, respectively,⁶¹ and G = 105 ± 15 MW m⁻² K⁻¹ in water for with r₀ = 50 nm.²⁶ Perfect contact between a metal NP and its host medium means neglecting any thermal resistance on the interface, or equivalently setting the interfacial conductance G to infinity. The solutions in Eqs. (16)–(18) for the limit G ≫ k_∞/r₀ are transformed into the solutions for ideal thermal contact [Eqs. (8) and (9)]. In water with k_∞ ≈ 6 × 10⁻¹ W m⁻¹ K⁻¹ (see Ref. 46), the value G ∼ 100 MW m⁻² K⁻¹ > k_∞/r₀ is obtained for r₀ > 6 nm. This means that the effect of thermal conductance (resistivity) on the NP surface is significant for small NPs. The advantages of analytical calculations over the numerical approach for describing the interfacial thermal conductivity on the NP surface lie in the simplicity and reliability of the approach, with the use of only independent determinable and verifiable parameters.

The problem of describing correctly the heat exchange of a hot NP with its surrounding medium is evident, and the many mentioned obstacles prevent this situation from being described correctly and entirely in a mathematical context. The nature and the regions of existence of interfacial thermal resistivity (conductance) should be clarified and confirmed by direct experiments together with complicated computer modeling of the processes on a real NP surface in different ambient media, and studies should be continued into how G depends on NP material (metal), size, morphology, and different surroundings, etc.

E. Laser thresholds for initiation of photothermal processes

As mentioned above, the initiation of thermal processes inside and around NPs has a threshold nature, i.e., it begins when certain values of the parameters of the NPs, radiation, etc. are reached. Experimental and theoretical determination of the threshold parameters is very important for implementing various processes in nanotechnology. In laser nanomedicine and biology, it is especially important to avoid undesirable damage to the target or its surrounding tissues in the case of over-threshold laser exposure. Theoretical investigation of the threshold parameters of the laser radiation is based on the energy conservation law for the processes of laser–NP interaction, and it includes the integral energies that characterize the interaction of laser radiation with an NP from the beginning of irradiation at t = 0 to the considered time t. These integral energies are the quantity of radiation energy Q_abs absorbed by an NP, and the quantities of heat Q_PR spent for some processes that are initiated by achieving the relevant threshold temperatures under laser action inside the NP, such as the NP melting energy (Q_M), the energy removed from an NP by heat conduction (Q_C), and the initial (Q_T∞) and current (Q_T0) NP thermal energies, i.e.,

Q_{abs} (t) = π r_{0}^{2} \int_{0}^{t} I_{0} (t) K_{abs} d t, Q_{C} = 4 π r_{0}^{2} \int_{0}^{t} J_{C} d t,

(19)

Q_{T \infty} = ρ_{0} c_{0} V_{0} T_{\infty}, Q_{T 0} = ρ_{0} c_{0} V_{0} T_{0} .

It is assumed that the NP radius does not change in these processes under consideration, i.e., r₀ is a constant. For constant I₀ and K_abs, the energy Q_abs is given by Q_abs = πr₀²I₀K_abst = πr₀²K_absE for t ≤ t_P, where E = I₀t is the laser fluence.

The energy conservation law for NP–laser interaction is

Q_{abs} + Q_{T \infty} = Q_{T 0} + Q_{C} + Q_{PR},

(20)

which can be used for determining the threshold parameters and controlling the energy conservation during the laser action on the NP. In conventional use are femtosecond and picosecond laser pulses (known as short pulses) and nanosecond pulses (known as long pulses).

The energy Q_C can be calculated analytically using the expressions for J_C [Eq. ] and T₀ [Eq. ] for the time period t_P ≥ t ≥ 0 (heating) and T₀ [Eqs. and ] for t_P ≥ t ≥ 0 (heating) and t ≥ t_P (cooling):⁷⁰

Q_{C} (t) = Q_{abs} (t) [1 - \frac{τ_{0}}{t} (1 - \exp (- \frac{t}{τ_{0}}))] (t_{P} \geq t \geq 0),

\begin{align} Q_{C} (t) & = Q_{abs} (t_{P}) [1 + \frac{τ_{0}}{t_{P}} \exp (- \frac{t}{τ_{0}}) (1 - \exp (\frac{t_{P}}{τ_{0}}))] t \geq t_{P} . \end{align}

(21)

For long (t_P > τ₀) and short (t_P < τ₀) pulses, the energy Q_C can be simplified for the time period [0, t_P] as follows:

t_{p} > τ_{0} : Q_{C} (t_{P}) \approx Q_{abs} (t_{P}) [1 - \frac{τ_{0}}{t_{P}}]; t_{p} < τ_{0} : Q_{C} (t_{P}) \approx 0 .

(22)

It is interesting to know how much of the energy absorbed by the NP (Q_abs) is used for heat conduction exchange with the ambient medium (Q_C) at times t_P and 2t_P. Figure 6 shows how the following ratios depend on t_P/τ₀ for t_P/τ₀ = 0.1–10:

\frac{Q_{C} (t_{P})}{Q_{abs} (t_{P})} = [1 - \frac{τ_{0}}{t_{P}} (1 - \exp (- \frac{t_{P}}{τ_{0}}))],

(23)

\frac{Q_{C} (2 t_{P})}{Q_{abs} (t_{P})} = [1 + \frac{τ_{0}}{t_{P}} \exp (- \frac{2 t_{P}}{τ_{0}}) (1 - \exp (\frac{t_{P}}{τ_{0}}))]

FIG. 6.

Dependences of QC(tP)/Qabs(tP) (solid line) and QC(2tP)/Qabs(tP) (dashed line) on tP/τ0. Adapted from Ref. 70.

Dependences of Q_C(t_P)/Q_abs(t_P) (solid line) and Q_C(2t_P)/Q_abs(t_P) (dashed line) on t_P/τ₀. Adapted from Ref. 70.

These dependences allow us to estimate the influence of the parameter t_P/τ₀ on the heat conduction exchange of the NP with the ambient medium. For t_P/τ₀ = 1 and 2, the values of Q_C(t_P) and Q_C(2t_P) are accordingly Q_C(t_P) = 0.37Q_abs(t_P) and Q_C(2t_P) = 0.78Q_abs(t_P). This means that most of the laser energy absorbed by the NP is spent on heating the surrounding water in a time equal to one or two pulse durations.

The threshold laser fluence E_TH at t = t_P for some thermal process of laser–NP interaction can be determined from Eq. , i.e.,

Q_{abs} (t_{P}) + Q_{T \infty} = Q_{T 0} (t_{P}) + Q_{C} (t_{P}) + Q_{PR} (t_{P}),

(24)

and taking into account Eq. for Q_C, we have E_TH as^53,70

E_{TH} = \frac{4 k_{1} t_{P}}{K_{abs} r_{0} (1 - \exp (- \frac{t_{P}}{τ_{0}}))} (T_{TH} - T_{\infty} + \frac{Q_{PR}}{c_{0} ρ_{0} V_{0}}) .

(25)

Here, T_TH is some characteristic threshold temperature of the NP, and reaching T_TH initiates a certain thermal process. Obviously, achieving T_TH at the end of the laser pulse at t_P is necessary to minimize the value of the laser fluence, and in this case T_TH is equal to the maximum NP temperature

T_{0}^{\max}

achieved at t_P, i.e.,

T_{TH} = T_{0}^{\max}

⁠. The value of T_TH can be determined either theoretically or experimentally, and

T_{0}^{\max}

can be estimated for a specific experimental fluence E_EXP based on the following equation:^53,70

T_{0}^{\max} = T_{\infty} + \frac{E_{EXP} K_{abs} r_{0} (1 - \exp (- \frac{t_{P}}{τ_{0}}))}{4 k_{1} t_{P}} - \frac{Q_{PR}}{c_{0} ρ_{0} V_{0}} .

(26)

For t_P ≫ τ₀ and t_P ≪ τ₀, simplified equations for E_TH and

T_{0}^{\max}

can be obtained from Eqs. and , i.e.,

t_{P} ≫ τ_{0} : E_{TH} = \frac{4 k_{1} t_{P}}{K_{abs} r_{0}} (T_{TH} - T_{\infty} + \frac{Q_{PR}}{c_{0} ρ_{0} V_{0}}),

(27)

T_{0}^{\max} = T_{\infty} + \frac{E_{EXP} K_{abs} r_{0}}{4 k_{1} t_{P}} - \frac{Q_{PR}}{c_{0} ρ_{0} V_{0}},

t_{P} ≪ τ_{0} : E_{TH} = \frac{4 c_{0} ρ_{0} r_{0}}{3 K_{abs}} (T_{TH} - T_{\infty} + \frac{Q_{PR}}{c_{0} ρ_{0} V_{0}}),

(28)

T_{0}^{\max} = T_{\infty} + \frac{3 E_{EXP} K_{abs}}{4 c_{0} ρ_{0} r_{0}} - \frac{Q_{PR}}{c_{0} ρ_{0} V_{0}} .

It is interesting that for t_P ≪ τ₀ in Eq. , E_TH and

T_{0}^{\max}

do not depend on t_P. Equation gives approximately accurate values of

T_{0}^{\max}

for t_P > 10⁻⁸ s, and the values of

T_{0}^{\max}

from Eq. for t_P < τ₀ are precisely equal to the computer calculated values of

T_{0}^{\max}

because of the practical absence of NP heat losses during laser pulse action. Equation is useful for estimating

T_{0}^{\max}

from the experimental values of E_EXP. Comparing

T_{0}^{\max}

with a fixed value of T_TH allows estimation and checking the correctness and accuracy of experimental results and controlling the initiation of possible processes. In the absence of internal processes in the NP, Q_PR in Eqs. and – disappears. Q_C is an inevitable companion to NP heating and cooling. For melting and vaporizing, Q_C is a parasitic process of energy loss. For bubble formation, Q_C is a process that provides thermal bubble formation, and therefore it is a useful process.

The main problem in direct comparison of experimental and theoretical results for the heating dynamics and achieving the maximum NP temperatures is the impossibility of direct experimental measurement of the NP temperature during and immediately after short pulses, and in many cases the complicated schemes of experiments including the placement of NPs on substrates, etc. A real comparison of theory with experimental results can be carried out only for the calculated and experimental threshold laser densities, which makes it possible to achieve melting and evaporation of NPs, and only after that can the threshold NP temperature be estimated. These comparisons were made in Refs. 53, 70, and 71, and suitable accuracies were achieved. This fact confirms the correctness of the analytical heating model.^39,45,52 On the other hand, the accuracy of the analytical model can be confirmed by comparison with numerical calculations; this was done in Fig. 4, and satisfactory agreement was obtained.

F. Effect of temperature on optical properties and heating of gold nanoparticles by laser pulses

Usually, theoretical studies of laser heating of NPs and estimates of the threshold laser fluencies for melting and evaporation of NPs^18,53,70,71 were carried out using constant optical refractive indices of NP metals.⁷² On the other hand, the optical parameters of metals and metal NPs heated by laser pulses may depend on their temperature. Experimental data for the temperature dependence of the refractive indices of gold and other metals for some optical wavelengths were presented.⁷³ An analysis of the influence of the temperature dependences of the optical parameters of NPs on their heating by laser pulses was presented.⁷⁴ An analysis is made of the theoretical time dependences of the NP temperature and threshold laser fluencies for short and long laser pulses, taking into account the dependence of NP absorption on its temperature during laser exposure.

The dependence of K_abs on NP temperature can be presented for some NPs and wavelengths in the following form^74–78 for approximating the real dependence of the NP absorption factor

K_{abs}^{T} (T_{0})

⁠:

K_{abs}^{T} (T_{0}) = K_{abs} {(T_{\infty} / T_{0})}^{b},

(29)

where

K_{abs}^{T} (T_{\infty}) = K_{abs}

is constant and b is variable. The correct analytical solution of Eqs. , , and together with the dependence in Eq. was obtained only for b = −1.⁷⁵ For b > 0, the simplified analytical solution of Eqs. , , , and can be obtained for short and long pulse action on an NP.

The action of short pulses with duration t_P < τ₀ on an NP without the heat losses due to thermal conduction from the NP surface to the ambient medium during laser pulse action is described by

ρ_{0} c_{0} V_{0} \frac{d T_{0}}{d t} = \frac{1}{4} I_{0} K_{abs}^{T} (T_{0}) S_{0} .

(30)

The solutions of Eq. taking into account the constant value of K_abs and, on the other hand, the dependence

K_{abs}^{T} (T_{0})

in Eq. have the following forms:

T_{0} = T_{\infty} + \frac{3 I K_{abs}}{4 c_{0} ρ_{0} r_{0}} t,

(31a)

T_{0} = T_{\infty} {[1 + \frac{3 (1 + b) I_{0} K_{abs}}{4 T_{\infty} ρ_{0} c_{0} r_{0}} t]}^{\frac{1}{1 + b}},

(31b)

with the maximum value of

T_{0 \max} = T_{0} (t_{P})

⁠. The energy conservation law for an NP during short laser action allows us to obtain the threshold laser fluence E_TH for

K_{abs}^{T} (T_{0})

[Eq. ]:

E_{TH} = \frac{4 c_{0} ρ_{0} r_{0}}{3 (1 + b) K_{abs}} [{(T_{TH} + \frac{Q_{PR}}{c_{0} ρ_{0} V_{0}})}^{b + 1} T_{\infty}^{- b} - T_{\infty}],

(32)

where T_TH is the threshold temperature of the actual process. The solution of Eq. is transformed into Eq. under b = 0.

The action of long pulses with t_P > τ₀ on an NP is accompanied by thermal conduction from the NP surface to the ambient medium. The maximum value of T_0 max for the NP at the end of the laser pulse action and the threshold fluence E_TH are determined on the basis of equality of the thermal losses from the NP and the energy released due to the absorption of laser pulse energy during one unit of time. The maximum NP temperature T_0max = T_TH and the threshold fluence E_TH with

K_{abs}^{T} (T_{0 \max})

are determined as follows:

\frac{d T_{0}}{d t} = 0, T_{0 \max} = T_{\infty} + \frac{E_{0} K_{abs}^{T} (T_{0 \max}) r_{0}}{4 k_{1} t_{P}},

(33a)

E_{TH} = \frac{4 k_{1} t_{P}}{K_{abs}^{T} (T_{0 \max}) r_{0}} (T_{TH} - T_{\infty} + \frac{Q_{PR}}{c_{0} ρ_{0} V_{0}}) .

(33b)

In this case, the ratio between E_TH with

K_{abs}^{T} (T_{0 \max})

[Eq. ] and E_TH with K_abs [Eq. ] is determined by the ratio between

K_{abs}^{T} (T_{0 \max})

and K_abs. Thus, this change in

K_{abs}^{T} (T_{0})

with increase from T_∞ to T_0max can affect the determination of the laser threshold parameters for NP transformations (melting, evaporation, etc.).

The dependences of K_abs on r₀ for a solid GNP with the selected temperatures T₀ = 273, 843, and 1336 K and for the melted NP with T₀ = 1336 K for a wavelength of 532 nm are presented in Fig. 7(a), calculated on the basis of the values of refractive indices from Ref. 73 and Mie theory.⁴¹ An increase in T₀ leads to a decrease in all values of K_abs(r₀), including the maximum value of K_abs, and a shift in its position toward larger values of r₀ on the r₀ axis. Figures 7(b) and 7(c) show the analytical and numerical dependences of NP temperature T₀ on t for 532-nm laser action on a GNP with radius r₀ = 30 nm for short and long pulses. Analytical and numerical calculations were carried out simultaneously with K_abs and with $K_{abs}^{T} (T_{0})$ ⁠. The choice of the intensity I is based on reaching T₀ = T_M =1336 K for the GNP at the end of the short and long pulses accordingly for the case of K_abs.

FIG. 7.

(a) Calculated dependences of efficiency factor Kabs of absorption of radiation with wavelength 532 nm by GNP with temperature T0 = 273 K (1, green), 843 K (2, brown), 1336 K (3, red; solid state), and 1336 K (4, orange; melted state) on r0. (b) and (c) Dependences of NP temperature T0 on t for 532-nm laser action on GNP with radius r0 = 30 nm for (b) short pulses with intensity I = 2.67 × 107 W/cm2 and tP = 1 × 10−10 s [analytical solutions of Eq. (31a) with Kabs (green dashed line) and Eq. (31b) with KabsT(T0) (blue solid line), and numerical calculation of Eq. (3) with KabsT(T0) (red dotted line)] and (c) long pulses with intensity I = 2.24 × 106 W/cm2 and tP = 5 × 10−9 s [analytical solution of Eq. (8) with Kabs (green dashed line) and numerical calculation of Eq. (3) with KabsT(T0) (red dotted line)]. In both cases, the horizontal orange line indicates the value of TM = 1336 K, and the vertical line indicates the time t = tP. Adapted from Ref. 74.

(a) Calculated dependences of efficiency factor K_abs of absorption of radiation with wavelength 532 nm by GNP with temperature T₀ = 273 K (1, green), 843 K (2, brown), 1336 K (3, red; solid state), and 1336 K (4, orange; melted state) on r₀. (b) and (c) Dependences of NP temperature T₀ on t for 532-nm laser action on GNP with radius r₀ = 30 nm for (b) short pulses with intensity I = 2.67 × 10⁷ W/cm² and t_P = 1 × 10⁻¹⁰ s [analytical solutions of Eq. (31a) with K_abs (green dashed line) and Eq. (31b) with $K_{abs}^{T} (T_{0})$ (blue solid line), and numerical calculation of Eq. (3) with $K_{abs}^{T} (T_{0})$ (red dotted line)] and (c) long pulses with intensity I = 2.24 × 10⁶ W/cm² and t_P = 5 × 10⁻⁹ s [analytical solution of Eq. (8) with K_abs (green dashed line) and numerical calculation of Eq. (3) with $K_{abs}^{T} (T_{0})$ (red dotted line)]. In both cases, the horizontal orange line indicates the value of T_M = 1336 K, and the vertical line indicates the time t = t_P. Adapted from Ref. 74.

Actually, at t = t_P for short and long pulses, the analytical solution of Eq. (31a) with K_abs reaches the gold melting temperature of T_M = 1336 K. However, the analytical solution of Eq. (31b) and the numerical calculations of Eq. (3) with $K_{abs}^{T} (T_{0})$ [Figs. 7(b) and 7(c)] reach a temperature of T_0max ∼ 1100 K at t_P, and the difference between them and the analytical solution of Eq. (31a) with K_abs is equal to ΔT₀ ∼ 200 K. This means that a decrease of $K_{abs}^{T} (T_{0})$ during laser NP heating leads to a noticeable decrease of the temperature T_0max reached at t_P, which should be taken into account in the laser processing of metal NPs. On the other hand, it means that reaching T₀ = T_M with $K_{abs}^{T} (T_{0})$ at fixed duration t_P requires the increase of I₀ (threshold fluence E_M) in comparison with the value of I₀ when K_abs is used. This increase of laser intensity for the action of short and long pulses on a GNP for the presented data is ∼30%. The dependences T₀(t) calculated numerically and analytically with $K_{abs}^{T} (T_{0})$ practically coincide with each other, thereby confirming the good accuracy of the analytical dependences.

The dependence of $K_{abs}^{T} (T_{0})$ for GNPs with r₀ = 10–40 nm and a wavelength of 532 nm [Fig. 7(a)] can be approximated by Eq. (29) with b = 1/4 with an accuracy of ∼5%–20%. The optimum absorption factor of radiation with a wavelength of 532 nm by GNPs decreases significantly with increasing temperature in the range of 300–1336 K including NP melting. This influence determines the temporal behavior of NP temperature and the maximum temperature achieved at t_P. The decrease of $K_{abs}^{T} (T_{0})$ for 532 nm in comparison with its initial value K_abs during NP laser heating leads makes it necessary to increase the laser fluence (intensity) in order to reach the maximum temperature at the end of laser action at t_P.

III. LASER HEATING OF ENSEMBLE OF NANOPARTICLES

In Sec. II, results were presented for the laser heating of single NPs. However, these results can be used to explain the laser heating of an ensemble of NPs if (i) the relevant processes happen only during the pulse duration and (ii) the latter is shorter than the characteristic time for the onset of thermal interaction between neighboring NPs. On the other hand, it necessary to know the processes of both the heating of a single NP as well as the global temperature as a result of irradiation of an ensemble of NPs. The transition between single-particle and ensemble heating under the influence of collective effects is discussed and the resulting theoretical expressions are presented below, which are useful for predicting the temperature dynamics in NP suspensions with different densities. These results close the gap between single particles and collective thermal effects of an ensemble of NPs. In experiments on heating with an ensemble, the temperature is determined in two spatial regions: the temperature inside an NP and in the nanoscale region surrounding it, and the global temperature of the liquid medium.

A. Experimental studies of heating an ensemble of nanoparticles by laser radiation

The PT properties of NPs and their ability to convert absorbed light into heat have been studied experimentally since the beginning of the new millennium. The laser light absorbed by the ensemble of NPs is converted into thermal energy, which leads to an increase in the temperature of the NPs, and then the released heat is transferred to the environment (water).

Visible radiation at resonant frequencies is transduced to thermal energy by GNPs. In a reported study, the temperature in aqueous suspensions of 20-nm GNPs resonantly irradiated by a cw argon laser at a wavelength 514 nm with a nominal fluence of 2.4 W/cm² increased to a maximum equilibrium value.⁷⁹ This value of temperature increased in proportion to the incident laser power and the NP content at low concentration. The heat input to the system by NP transduction of resonant irradiation equaled the heat flux outward by conduction and radiation at thermal equilibrium. The efficiency of transducing incident resonant light to heat by microvolume suspensions of GNPs was determined by applying an energy balance to obtain a microscale heat-transfer time constant from the transient temperature profile. The measured transduction efficiency was increased from 3.4% to 9.9% by modulating the incident cw irradiation.

A set of experiments on photoheating in a water droplet containing GNPs was performed.⁸⁰ The efficiency of light-to-heat conversion due to collective photoheating—which turns out to be remarkable close to unity—was determined using photocalorimetry. Detailed studies revealed a complex character of heat transfer in an optically stimulated droplet, with the main mechanism of equilibration being convectional flow. These studies are crucial for understanding PT effects in NPs and for their potential and current applications in nanotechnologies and biotechnologies.

A comparative study of the laser heating of GNPs, SNPs, and silver nanowires was conducted to search for a suitable frequency and material for hyperthermia application in cancer treatment.⁸¹ It was found that GNPs with r₀ = 2.5–25 nm are photothermally efficient at 300 mW for a wavelength of 450 nm and at 500 mW for 532 nm, with each sample illuminated for 10 min. GNPs showed more thermal efficacy in the production of heat in comparison with SNPs and nanowires.

PT properties and heat-elevation experimental measurement of the absorption coefficient of spherical (GNS) and urchin-shaped (GNU) GNPs of different sizes and suspended in water were studied regarding different parameters such as GNP concentration, laser excitation intensity, and exposure time.⁸² Aqueous solutions of GNPs with different diameters (50, 80, and 90 nm) were introduced in a quartz cuvette and irradiated with an 808-nm cw laser at different laser irradiances (0.5, 1, 2, and 3 W/cm²) for 15 min at an initial room temperature of 296 K. For each type of GNP, the temperature increased linearly from t = 0 to ∼5 min. The deviation of the lines from linear fits of the temperature elevation curves is determined by the heat exchange of the heated volume in the quartz cuvette with the outer medium. Beyond 5 min, it stabilizes and reaches a maximum and constant level [Figs. 8(a) and 8(b)]. The temperature elevation increases linearly with the GNP concentration, reaching tens of degrees [Fig. 8(c)].

FIG. 8.

Temperature elevation ΔT(t) = T(t) − T_∞ (T_∞ = 296 K) versus time in solutions of 50-pM GNPs (the dashed lines are linear fits of the temperature elevation curves) excited with a laser power density of (a) 1 W/cm² and (b) 2 W/cm². (c) Temperature elevation of water after 15 min of excitation at different excitation power densities (0.5, 1, 2, and 3 W/cm²) for different GNP concentrations (10–60 pM) for 80-nm GNS. The red line denotes the minimum temperature for PT therapy. Adapted with permission from Ref. 82. Copyright (2019) American Chemical Society.

The generation and transfer of heat when laser irradiation is applied to water containing a suspension of gold nanorods coated with different polyelectrolytes have been examined.⁸³ It was found that relatively high fluences must be applied in order to generate relevant changes in temperature. This is due to the significant lateral heat transfer from the sides of the well, which strongly limits the temperature that can be achieved. A 650-mW cw laser with a wavelength 635 nm—which is similar to the longitudinal plasmon resonance peak of the gold nanorods—can deliver heat with an overall efficiency of up to 3%. Small volumes were irradiated in a clear plastic well plate, and at least 97% of the laser energy was lost as a result of conduction or convection to the environment or transmission through the sample, and only 3% was retained in the fluid. This is double the efficiency achievable without the nanorods. An increase in temperature of up to 15 °C can be achieved, which is suitable for inducing cell death by hyperthermia (Fig. 9).

FIG. 9.

(a) Schematic of spherical coordinate system for a single NP, where r is the radial coordinate with the origin fixed at the center of the NP of radius r₀, and r_C is the radius of the cell. (b) For the NP ensemble, the cylindrical coordinates are R and Z, where R_b is the characteristic radius of the radiation beam; the small solid circles present NPs, the dashed circles present the boundaries of cells, and the Z axis corresponds to the direction of radiation propagation represented by the dashed arrows. Adapted from Ref. 39.

The temperature changes in the vicinity of a single optically trapped spherical GNP encapsulated in a thermoresponsive shell have been studied in detail.⁸⁴ Individual beads were trapped in a counter-propagating optical tweezers setup at various laser powers, which allowed the overall particle size to be tuned through the phase transition of the thermoresponsive shell. The experimentally obtained sizes measured at different irradiation powers were compared with the average size values obtained by dynamic light scattering from an ensemble of beads at different temperatures. The results showed that variations in the thermal conductivity of the polymer, the viscosity of the aqueous solution, and the absorption cross section of the coated GNP must be taken into account when considering local laser heating experiments in aqueous solution at the nanoscale.

The dynamics of PT conversion and the related nonlinear optical response from water-soluble nano-eggs consisting of a gold nanocrystal ensemble trapped in a water-soluble shell of ferrite nanocrystals of ∼250–300 nm in size have been studied.⁸⁵ Different metal concentrations were analyzed by means of ultrafast pump–probe spectroscopy and semiclassical modeling of PT dynamics from the onset of hot-carrier photogeneration (picosecond time scale) to the heating of the matrix ligands in the suprastructure core (hundreds of nanoseconds). The results showed the possibility of designing and tailoring the PT properties of the nano-eggs by acting on the core size, and they indicated superior performances compared to conventional nanoheaters of comparable size and chemical compositions.

Optothermal ensemble techniques to manipulate and assemble individual NPs both in solution and on solid substrates have been developed by exploiting optothermal conversion and controlling optothermal−matter interactions.⁸⁶ The optothermoelectric ensemble of colloidal particles into superstructures by coordinating thermophoresis and interparticle depletion bonding in the solution was studied. Localized laser heating generates a temperature gradient field, where the thermal migration of ions creates a thermoelectric field to trap charged particles, which provides strong interparticle bonding to stabilize colloidal superstructures with precisely controlled configurations and interparticle distances.

B. Model of heating an ensemble of nanoparticles and the environment by laser radiation

The following definitions are used below: the environment (surrounding) is a medium (liquid) around an NP, and a heterogeneous system defines an ensemble of NPs immersed in a liquid. Below, a model is considered for heating an ensemble of NPs irradiated by a laser and the environment due to the heat transfer of the NPs. An ensemble of NPs affects thermal processes in the case of a high concentration, which leads to the activation of synergetic processes in comparison with the heating of single NPs.

Usually, under experimental conditions, a cylindrical laser beam propagates through a layer of a heterogeneous two-component system containing NPs immersed in some liquid (water, soft tissue) or solid material. Two coordinate systems were introduced. The first is the cylindrical coordinate system (R, Z), where the R axis corresponds to the radius of the radiation beam with characteristic radius R_B, and the Z axis corresponds to the direction of laser beam propagation. The characteristic distance Z_ext is defined as the length at which the radiation is attenuated by a factor of e = 2.71. The second coordinate system is the spherical one with radial coordinate r, the origin of which is fixed at the center of each NP and cell.

For simplicity, spherical NPs are assumed to be monodisperse with a characteristic radius r₀. The ensemble of ordered NPs was studied on the basis of a cell approximation with regular placement of NPs at the center of each cell with radius r_C. Such a model with acceptable accuracy represents a real heterogeneous system loaded with NPs.⁸⁷ The processes of light-to-heat conversion under the action of radiation pulses of duration t_P on an ensemble of NPs are described by the following characteristic times associated with thermal processes around single NPs and inside the volume of a heterogeneous system illuminated by a radiation beam:³⁹

t_{T 1} \sim \frac{{r_{0}}^{2}}{4 χ_{1}}, t_{TN} \sim \frac{{N_{0}}^{- 2 / 3}}{16 χ_{1}}, t_{TR} \sim \frac{{R_{b}}^{2}}{4 χ_{1}}, t_{TZ} \sim \frac{{Z_{ext}}^{2}}{4 χ_{1}},

(34)

where χ₁ is the thermal diffusivity of the medium and N₀ is the concentration of NPs. It is assumed that the temperatures inside the NPs are equalized. The characteristic time t_T1 in Eq. describes the formation of quasi-stationary temperature distributions around single spherical NPs. The cell radius r_C is equal to r_C = 0.5N₀^−1/3. The characteristic overlap time of temperature fields between adjacent NPs is t_TN, and when a common temperature is formed in the medium, this is equal to

t_{TN} \sim \frac{{r_{c}}^{2}}{4 χ_{1}} = \frac{{N_{0}}^{- 2 / 3}}{16 χ_{1}}

[see Eq. ]. The value of the irradiated volume is obviously determined by the characteristic dimensions R_b and Z_ext, which are ∼0.1–0.2 cm.^81–86 The values of t_TR and t_TZ are the characteristic times describing the development of heat transfer from the volume of heated medium illuminated by the radiation beam to the neighboring environment along the R and Z coordinates. For spherical GNPs with r₀ = 25 nm in water, the estimate of t_T1 gives t_T1 ∼ 1 × 10⁻⁹ s, and for a heterogeneous medium with an NP concentration of N₀ = 1 × 10⁹ or 1 × 10¹² cm⁻³, t_TN is equal to ∼4.4 × 10⁻⁵ or 4.4 × 10⁻⁷ s, respectively. The characteristic times for heat removal from the heated volume are given approximately as t_TR, t_TZ ∼ 1 s. The approximate values of the presented characteristic times satisfy the following inequalities: t_TR, t_TZ ≫ t_TN ≫ t_T1.

The duration of radiation exposure t_P for irradiating an ensemble of NPs usually varies in a wide range from short pulses with t_P ∼ 10⁻⁸–10⁻¹² s to cw exposure. Taking into account the indicated inequalities, several characteristic time intervals can be distinguished for the implementation of various thermal processes. Here, four characteristic stages of the interaction of radiation with pulse duration t_P with an NP ensemble in a medium can be distinguished: (a) t_P is less than t_T1, (b) t_P is greater than t_T1 but less than t_TN; (c) t_P is greater than t_T1 and t_TN but less than t_TR and t_TZ; (d) t_P is greater than t_TR, t_TZ, t_TN, and t_T1:

t_{T 1} > t_{P}

(35a)

t_{TN} > t_{P} > t_{T 1}

(35b)

t_{TR}, t_{TZ} > t_{P} > t_{TN}, t_{T 1}

(35c)

t_{P} > t_{TR}, t_{TZ}, t_{TN}, t_{T 1}

(35d)

Figure 10 shows the qualitative dependences of the temperature T on r inside two neighboring cells for the time t_P satisfying cases (a)–(c); case (d) is not shown in Fig. 10. Satisfying condition (35a) means that at t_T1 > t_P, quasi-stationary temperature distributions around the NPs have not formed and there is practically no heat exchange between the NPs and the environment; the situation is as for single NPs that do not interact thermally. When condition (35b) is satisfied, quasi-stationary temperature distributions around the NPs are formed and heat exchange occurs between the NPs and the environment, but without heat transfer between neighboring cells during the time t_P and without the formation of a common temperature distribution in the medium between the NPs [Fig. 10(b)]. When condition (35c) is satisfied, heat exchange occurs between neighboring cells, the medium is heated, and a distribution of general temperature in the medium between NPs is formed over time t_P [Fig. 10(c)]. Fulfilling condition (35d) means that a temperature field has formed inside and around the illuminated volume, and a developed heat exchange of the heated volume with the external environment has been established.

FIG. 10.

Qualitative representation of spatial dependences of temperature T on r inside two adjacent cells for time t_P such that (a) t_T1 > t_P, (b) t_TN > t_P > t_T1, and (c) t_P > t_TN, t_T1. The vertical dashed lines indicate the boundaries of the spherical cells with (−r_C, r_C), and the vertical dashed-dotted lines indicate the centers of the NPs and cells. In (c), the horizontal dashed line indicates the temperature level of the medium. The scale marks at (−r₀, r₀) indicate the radii of the NPs. The colors from green through yellow to red show qualitatively the rise in temperature. Adapted from Ref. 39.

C. Analytical study of heating of an ensemble of nanoparticles and the environment by laser radiation

Describing the heating of an NP ensemble by radiation with t_P such that t_TN > t_P > t_T1 can be done in the framework of the heating of single NPs (see Sec. II). Considering case (i.e., t_TR, t_TZ > t_P > t_TN), t_T1 is based on the following system of equations without taking into account heat conduction inside and outside the illuminated (heated) volume of the heterogeneous system for a = 0 (see Ref. 45):

c_{0} ρ_{0} V_{0} \frac{d T_{0}}{d t} = I_{0} K_{abs} π {r_{0}}^{2} - 4 π r_{0} k_{1} (T_{0} - T_{1}) - Q_{PR 0},

(36)

c_{1} ρ_{1} \frac{d T_{1}}{d t} = N_{0} 4 π r_{0} k_{1} (T_{0} - T_{1}) - Q_{PR 1} - Q_{C}

with the initial conditions

T_{0} (t = 0) = T_{\infty}, T_{1} (t = 0) = T_{\infty} .

(37)

This is a two-temperature model involving the NP temperature T₀ and the surrounding temperature T₁, and it is somewhat analogous to the two-temperature model of the electron and lattice temperatures when ultrashort pulses act on metals or metal NPs. The terms Q_PR0 (T₀) and Q_PR1 (T₁) describe the heat losses due to the occurrence of thermal processes inside the NPs or inside the volume of the medium occupied by the NP ensemble, and Q_C is the heat loss due to heat conduction to the outer environment. Let us consider for simplicity the stage of heating the NPs and medium by laser radiation under Q_PR0 = Q_PR1 = 0 and for t_TR, t_TZ > t_P > t_TN, t_T1, i.e., Q_C = 0 and the solutions of Eqs. and have the forms

\begin{array}{l} T_{0} & = T_{\infty} + \frac{I_{0} K_{abs} π {r_{0}}^{2} t N_{0}}{c ρ} \\ + \frac{I_{0} K_{abs} r_{0} {(c_{1} ρ_{1})}^{2}}{4 k_{1} {(c ρ)}^{2}} [1 - \exp \{- \frac{t}{τ_{01}}\}] \end{array}

\begin{align} T_{1} & = T_{\infty} + \frac{I_{0} K_{abs} π {r_{0}}^{2} t N_{0}}{c ρ} \\ - \frac{I_{0} K_{abs} r_{0} c_{1} ρ_{1} N_{0} c_{0} ρ_{0} V_{0}}{4 k_{1} {(c ρ)}^{2}} [1 - \exp \{- \frac{t}{τ_{01}}\}], \end{align}

(38)

where

c ρ = c_{1} ρ_{1} + 4 π {r_{0}}^{3} c_{0} ρ_{0} N_{0} / 3

is the heat capacity of the heterogeneous medium per 1 g of medium, and

I_{0} K_{abs} π {r_{0}}^{2} t N_{0} = Q_{abs} (t) N_{0}

⁠. The characteristic time

τ_{01} = \frac{c_{0} ρ_{0} c_{1} ρ_{1} {r_{0}}^{2}}{3 k_{1} c ρ} = τ_{0} \frac{c_{1} ρ_{1}}{c ρ}

determines the dependences of temperatures T₀ and T₁ on time t. The value of τ₀₁ is equal τ₀ when N₀ = 0, and the influence of the NP ensemble on τ₀₁ is negligible up to extremely high values of the NP concentration (N₀ > 10¹⁵ cm⁻³ for GNPs with r₀ = 25 nm) because of the small contribution of the NPs to the thermodynamical properties (heat capacity) of the heterogeneous medium.

If the condition t_P ≫ τ₀₁ is satisfied for “long” radiation exposure, then the heat transfer of the NPs to the environment determines the temperature values, i.e.,

T_{0} \approx T_{\infty} + \frac{I_{0} K_{abs} π {r_{0}}^{2} t N_{0}}{c ρ} + \frac{I_{0} K_{abs} r_{0} {(c_{1} ρ_{1})}^{2}}{4 k_{1} {(c ρ)}^{2}},

(39)

T_{1} \approx T_{\infty} + \frac{I_{0} K_{abs} π {r_{0}}^{2} t N_{0}}{c ρ} - \frac{I_{0} K_{abs} r_{0} c_{1} ρ_{1} N_{0} c_{0} ρ_{0} V_{0}}{4 k_{1} {(c ρ)}^{2}} .

In this case, the temperatures T₀ and T₁ increase with time t and do not have stationary maximum values in the time interval 0 < t < t_P. The stationary overheating T₀−T₁ of the NPs is constant compared to the medium under radiation exposure, i.e.,

T_{0} - T_{1} = \frac{I_{0} K_{abs} r_{0} c_{1} ρ_{1}}{4 k_{1} c ρ} .

Thermal confinement of the irradiated volume of a heterogeneous system can be performed under the condition t_TN < t_P < τ₀₁ for short pulses and a high NP concentration in the medium. Expanding the exponential function in Eq. gives the values of T₀ on t and T₁, i.e.,

T_{0} \approx T_{\infty} + \frac{3 I_{0} t K_{abs}}{4 ρ_{0} c_{0} r_{0}}, T_{1} \sim T_{\infty}, T_{0} - T_{1} \approx \frac{3 I_{0} t K_{abs}}{4 ρ_{0} c_{0} r_{0}} .

(40)

For “short” radiation pulses, the heat exchange of the NPs with the environment can be practically ignored, and T₀ is proportional to t and the medium temperature T₁ ≈ T_∞. The expression for T₀ is equal to Eq. for the heating of a single NP.

The NP cooling after the pulse action is determined by the expressions for t > t_P from Eq. , i.e.,

T_{0} = T_{0 M} - (T_{0 M} - T_{1 M}) \frac{c_{1} ρ_{1}}{c ρ} [1 - \exp (- \frac{(t - t_{P})}{τ_{01}})],

T_{1} = T_{1 M} + (T_{0 M} - T_{1 M}) \frac{N_{0} c_{0} ρ_{0} V_{0}}{c ρ} [1 - \exp (- \frac{(t - t_{P})}{τ_{01}})],

(41)

where T_0M and T_1M are the values of the NP and medium temperatures at t = t_P, and for t → ∞, the stationary values of the NP and medium temperatures will be equal to each other, i.e.,

{T_{0}}_{S} = {T_{1}}_{S} = \frac{T_{0 M} N_{0} c_{0} ρ_{0} V_{0} + {T_{1}}_{M} c_{1} ρ_{1}}{c ρ} .

Note that the NP cooling is carried out only by transferring the NP energy into the energy of the surrounding liquid without heat exchange with the external environment.

The intensity of the radiation pulses I_n in Fig. 11 was chosen such that it would be possible to heat the NPs up to a temperature of 373 K and avoid boiling of the surrounding water. The time dependences of T₀ on t have significant features for different values of t_P. Energy release in NPs and heat exchange lead to a rapid increase in temperatures T₀ and T₁ with time with a small difference between them at t_P = 1 × 10⁻² and 1 × 10⁻⁴ s [see Figs. 11(a) and 11(b)]. The impact of radiation pulses with a pulse duration of t_P = 1 × 10⁻⁵ s and 1 × 10⁻⁶ s leads to moderate heating of the medium because of a reduction in the pulse duration and a decrease in the heat exchange of the NPs with the medium. The temperature T₀ reaches between 0.7T_max and 0.9T_max by the time t ∼ 1 × 10⁻²t_P. After that, the heat release in the NPs is approximately compensated for by heat exchange with the environment, and during the remaining part of t_p, T₀ slowly reaches T_max at t = t_p. The stationary overheating of the NP ensemble, as compared with the medium, is constant under radiation exposure.

FIG. 11.

Dependences of temperatures T0 (dashed-dotted) of NPs and T1 (solid) of medium on t/tP for r0 = 25 nm and N0 = 1 × 1012 cm−3 for (a) tP = 1 × 10−2 s and In = 2.1 × 103 W/cm2, (b) tP = 1 × 10−4 s and In = 1.75 × 105 W/cm2, (c) tP = 1 × 10−5 s and In = 6.5 × 105 W/cm2, and (d) tP = 1 × 10−6 s and In = 9.0 × 105 W/cm2 determined based on the analytical equations (38) and (41). The normalized radiation intensity is In = I0Kabs. Adapted from Ref. 39.

Dependences of temperatures T₀ (dashed-dotted) of NPs and T₁ (solid) of medium on t/t_P for r₀ = 25 nm and N₀ = 1 × 10¹² cm⁻³ for (a) t_P = 1 × 10⁻² s and I_n = 2.1 × 10³ W/cm², (b) t_P = 1 × 10⁻⁴ s and I_n = 1.75 × 10⁵ W/cm², (c) t_P = 1 × 10⁻⁵ s and I_n = 6.5 × 10⁵ W/cm², and (d) t_P = 1 × 10⁻⁶ s and I_n = 9.0 × 10⁵ W/cm² determined based on the analytical equations (38) and (41). The normalized radiation intensity is I_n = I₀K_abs. Adapted from Ref. 39.

When the pulse duration t_P is less than between 10⁻⁷ and 10⁻⁸ s, the heat transfer mode switches to heating only the NPs without significant heating of the medium for the given values of N₀. NPs give off thermal energy to the medium in a time of ∼1 × 10⁻⁸ s after the end of the pulse with t_P = 1 × 10⁻⁶ s, and their temperature T₀ decreases and becomes equal to some stationary temperature. The cooling process in a heterogeneous system after the termination of the action of radiation is carried out during the formation of the general distribution T₁(R, Z, t) and subsequent heat exchange with the environment.

Consider the case in which thermal equilibrium is realized under the action of cw laser radiation on a medium and heat exchange of its heated volume with the environment. Consideration of the case when T₀ and T₁ have achieved their own maximum stationary temperatures is based on fulfilling condition , i.e., t_P > t_R, t_Z, t_TN, t_T1 with the formation of a temperature field in the medium and heat exchange of its heated volume with the environment. In this situation, we have Q_C ≠ 0 and stationary thermal equality when energy release in the NPs in the irradiated volume of the medium is compensated for by heat losses due to internal processes and heat exchange with the external environment. The situation is described by the solutions of Eq. for

\frac{d T_{0}}{d t} = 0

and

\frac{d T_{1}}{d t} = 0

⁠, and at the stationary temperatures of the NPs (T_0S) and the environment (T_1S), the overheating of the NPs compared to the liquid and Q_C are equal under Q_PR0 = 0 and Q_PR1 = 0, i.e.,

\begin{gathered} T_{0 S} - T_{1 S} = \frac{I_{0} K_{abs} r_{0}}{4 k_{1}}, \\ T_{0 S} - T_{1 S} = \frac{Q_{C}}{4 π r_{0} k_{1} N_{0}}, \\ Q_{C} = N_{0} I_{0} K_{abs} π r_{0}^{2} . \end{gathered}

(42)

This means that the heat Q_C is determined by the heat release inside the heterogeneous medium due to the absorption of laser radiation by the NPs. For a general description of the light-to-heat conversion processes in this case, the system of equations in Eq. (36) must be solved numerically with the corresponding boundary and initial conditions.

IV. NANOTHERMOMETRY OF NANOPARTICLES UNDER LASER HEATING

The main problem in the study and application of NPs in high-temperature laser and photonic nanotechnologies is the determination of the temperature of NPs during and after exposure to radiation, especially for short laser pulses. Several applications require reliable characterization of the PT response and heat dissipation of nanosized particles, which remains a challenge for both modeling and experimental measurements. Devices such as thermocouples and thermal imaging cameras are used widely for temperature evaluation. However, thermocouples and thermal cameras have limited performance due to their low accuracy (no better than 0.1 °C) and long response times in estimating temperature dynamics. However, many of the existing techniques are limited by such disadvantages as low sensitivity and systematic errors associated with the local environment or the optical properties of NPs and the environment.

Nanothermometry—a challenging and complex field that can range from biology and medicine to material sciences—is still in its infancy and is evolving rapidly. Various methods based on phase transitions in the surroundings under heating from NPs, Raman scattering by NPs, and changes in the optical properties of the NPs and their surrounding medium are analyzed briefly below. The techniques based on optical detection have a spatial resolution that is limited by the diffraction limit of visible light (200−300 nm). Thermal methods using wavefront distortion, particle position, the spectrum of thermal radiation, and the change in the spectra of scattered radiation achieve an accuracy of 1–5 °C but are limited to temperatures up to 600–700 K. To assess the correctness and range of nanothermometry methods, direct comparative tests of individual methods on identical nanostructures under identical conditions and with theoretical results will be required. The contradiction of various data and large temperature fluctuations have led to serious doubts about the accuracy of the intracellular thermometry methods used. All of the above emphasizes the need for nanothermometry methods to be independently and carefully calibrated and designed to quantify temperature under specific conditions. The first task is to significantly expand the temperature and spatial resolutions to describe the temporal behavior of the NP temperature in the heating and cooling stages of high-temperature and high-speed processes. Methods based on temperature-induced optical shifts in NPs and in their environment and the detection of Raman scattering and thermal radiation are considered, leaving aside fluorescent molecular probes and nanoprobes.

A. Changes in refractive indices of metals and environment and spectral thermometry of optical scattering of nanoparticles

Intense laser action on NPs leads to them being heated to high temperatures because of the absorption of radiation energy, which in turn leads to the transfer of NP thermal energy into the environment and its heating. The increase of the temperatures of the NPs and medium affects their optical refractive indices. Detection techniques developed before 2006 led to studies of individual metal NPs (1–100 nm in diameter) in the optical far field.⁸⁸ All methods are based on detecting a scattered wave emitted by either a particle or its close environment. Direct absorption and interference techniques rely on the particle’s scattering and have similar limits in their signal-to-noise ratio. To study the properties of the particle itself, it is convenient to detect the wave scattered directly by the particle, and it is particularly important to access its response at picosecond and shorter timescales.

The importance of taking into account the temperature dependences of the optical parameters of the NP and its environment is due to the influence of these dependences on the dynamics, efficiency, and results of the interaction of the radiation with NPs in various media, as was noted previously. The temperature dependences of the optical parameters (refractive indices) of various metals (gold, silver, copper, tungsten) and surrounding media (water, SiO₂, Al₂O₃, etc.) have been presented in various publications, and the calculated optical absorption and scattering properties were presented.⁷⁸ Unfortunately, note that currently the available data are completely insufficient for the current demand from high-temperature laser nanotechnologies.

Under the action of short pulses with t_P < τ₀, there is no heat exchange of NPs with their surroundings, and only the changes of the refractive index and optical properties of the NPs should be taken into account. This refractive-index variation changes the scattering and absorption optical signals from heated NPs and can be used to measure the temperatures of resonant metal (gold) NPs. These signals should be detected at times t < τ₀ for determining the NP temperature during pulse action and thereafter. The temperatures can be determined by comparing the peak positions of experimentally obtained absorption, scattering, or extinction spectra with temperature-dependent spectra calculated by Mie theory. Light scattering spectra are detected by dark-field microscopy, which is a powerful tool for studying LSP resonances of single noble metal NPs and for developing novel methods for determining NP temperature.

The effects of temperature on the spectral absorption characteristics of NPs with an average diameter of 20 nm (GNPs) in the temperature range of 17–915 °C and of 24 nm (SNPs) in the range of 17–700 °C in a host silica matrix have been studied experimentally,⁸⁹ and their evolution is shown in Figs. 12(a) and 12(b). An increase in temperature (not above the melting temperature) leads to a noticeable red shift and broadening of the SPR in GNPs and SNPs, and the scattering and extinction characteristics demonstrate analogous behavior. Thermal expansion has been shown to be the main mechanism responsible for the temperature-induced red shift of SPR in NPs. Meanwhile, the increase in electron–phonon scattering rate with increasing temperature should be the dominant mechanism for the broadening of the SPR in the GNPs.⁸⁹

FIG. 12.

Top row: evolutions of experimental absorption spectra (optical density) of (a) GNPs with a mean size of 20 nm and (b) SNPs with a mean size of 24 nm in silica with gradual increase in temperature (a) from 19 to 915 °C and (b) from 17 to 670 °C. Adapted from Ref. 89 under an open-access license. Bottom row: dependences of efficiency factors of (c) scattering (K_sca) and (d) extinction (K_ext) of radiation with wavelength 532 nm by GNPs with temperatures T₀ = 273 K (1, green), 843 K (2, brown), 1336 K (3, red; solid state), and 1336 K (4, orange; melted state) on r₀. Adapted from Ref. 74.

The dependences on r₀ of the efficiency factors of scattering (K_sca) and extinction (K_ext) of radiation with wavelength 532 nm by GNPs in water with various temperatures T₀ have been presented.⁷⁴ The wavelength shifts associated with maximum absorption [Fig. 7(a)], scattering [Fig. 12(c)], and extinction [Fig. 12(d)] can be used for determining NP temperatures, and the features presented above can possibly be used for determining NP temperatures based on the selective detection of the dependences of the absorption, scattering, and extinction (transmittance) properties of NPs on temperature.

B. Raman spectroscopy for determining temperature of nanoparticles

Surface-enhanced Raman scattering (SERS) is the inelastic scattering of photons by nanoscatterers, whose exchange energy corresponds to the vibrational modes of the scattering molecules. In Raman scattering, the energy of the scattered photon is given by hν′ = hν − hν_m, where ν is the frequency of the incident light and ν_m is the oscillation frequency of the excited state. There is also a second opposite process given by hν′ = hν + hν_m, and this is called the anti-Stokes (AS) mechanism. Therefore, in the SERS spectrum, the energy positions of the corresponding Stokes and AS peaks are symmetrical with respect to the energy of the excitation photon.

The intensity ratio between the AS and Stokes peaks is related to the ratio between the occupation numbers of the ground state and the excited state, which obey Fermi statistics. The idea of using the AS radiation of NPs themselves (without the emission of the surrounding molecules) as a method of thermometry was proposed in 2016 by Cahill et al.⁹⁰ The temperature dependence of the AS radiation was explained, and the Bose–Einstein statistics corresponding to its profile were considered. A series of measurements was carried out at different laser powers, and using an iterative algorithm, a sequential (linear) evolution of the temperature rise as a function of the laser power was obtained. SERS can be used for temperature measurements and has been applied successfully to GNPs,⁹¹ their aggregates,^92–94 etc.

The optical properties of plasmonic NPs depend strongly on the interaction with other NPs, which complicates the analysis of systems consisting of several particles. Heat dissipation in aggregated NPs and its effect on SERS have been studied using correlated PT heterodyne imaging, electron microscopy, and SERS measurements.⁹² Absorption cross sections for dimers per particle are indicative of light interaction between particles and strong field enhancement, which are important for SERS. The total absorption for larger aggregates is simply proportional to the volume of the aggregate. This observation allows us to model the absorption of light and heating in aggregates, assuming that the particles act as independent heat sources. Very high temperatures can be generated at the surfaces of NPs, and the temperature decreases as the thermal conductivity of the environment increases, which is consistent with SERS measurements.

A new implementation of AS thermometry has been made, which makes it possible to determine the PT characteristics of individual NPs in situ from a single hyperspectral photoluminescence confocal image.⁹³ The method is label-free, applicable to any type of NP with detectable AS emission, and does not require any prior information about the NP itself or the environment. The PT responses of spherical GNPs with four different diameters (48, 64, 80, and 103 nm) deposited on glass, sapphire, and graphene substrates and immersed in water have been studied, as was the role of the substrate (Fig. 13). The PT coefficient β was determined experimentally at least 40 times for each NP size, and for r₀ = 80 nm it was equal to β = 62.5 K μm²/mW. Also, theoretical calculations were carried out using a finite-element solver.

FIG. 13.

Experimental and calculated photothermal coefficient β of spherical GNPs as a function of diameter. The error bars for the diameter represent the standard deviation of NP size as measured by transmission electron microscopy. Adapted with permission from Ref. 93. Copyright (2021) American Chemical Society.

Note that increase in the NP temperature should be proportional to the laser intensity. This simple limitation allowed the authors of Ref. 93 to take temperature measurements without prior calibration or the use of another laser, making their approach more direct and simpler than existing methods. For cw laser radiation, NP temperature increases linearly with excitation intensity, i.e., T₀ = T_∞ + βI₀, and β is equal to

β = \frac{K_{abs} r_{0}}{4 k_{1}} .

The estimate gives β = 60.6 K μm²/mW, which is in accordance with the value presented above.⁹³ This method makes it possible to measure the PT coefficient β of single NPs and obtain it with an optimal precision of 4% from a single hyperspectral photoluminescent image. Alternatively, if β is known or has been determined previously, then this method allows NPs to be used as nanothermometers to measure the ambient temperature.

Gold nanorods and NPs are excellent candidates for nanoprobes because they are sufficiently bright emitters when excited by a monochromatic source. The AS emission spectrum of gold nanorods irradiated at resonance was used by Orrit et al. to measure the absolute temperature of NPs and their environment without the need for preliminary calibration.^94,95 This approach requires another shorter-wavelength laser to excite and record the NP PL spectra. Using this method, the authors achieved consistent temperature measurements The accuracy of 4 K of determining the medium temperature was established in spectral measurements with an integration time of 180 s. This procedure can be easily implemented in any microscope capable of recording emission spectra, and it is not limited to any specific NP shape. The application range of AS thermometry in plasmonics was extended by the use of temperature measurements under picosecond pulsed illumination.⁹⁵ In this case, transient increase in the electron temperature can reach ∼1000 K, as expected under pulsed illumination. In a recent review, Baffou et al.⁹⁶ presented and discussed advances in the development of efficient and reliable thermometry techniques for nanoplasmonic systems, including devices based on the spectral measurement of AS emission of plasmonic NPs and fluorescent approaches. AS Raman thermometry proves to be more powerful in many aspects and also allows subdiffraction spatial resolution to be achieved. The major difference between fluorescence and AS thermometry is that they do not measure the same physical quantity: fluorescence measures the temperature in the environment of NPs, while AS thermometry provides the internal temperature of NPs. Fluorescence and AS thermometry complement each other, and the ideal approach to nanothermometry in plasmonics has yet to be found, making this field of research still very active. Currently, AS Raman thermometry has been used only for conventional (mainly gold) NPs, and its use for other materials could help find alternatives for applications in plasmonics.

C. Thermal distortion of refractive index of environment heated by a nanoparticle

The PT method for determining NP and environment temperatures uses a photo-induced change in the refractive index of the environment as an additional step to scatter a wave with a different wavelength.⁸⁸ This leads to a considerable improvement in signal-to-background ratio and thus to a much higher sensitivity. PT methods enhance the scattered wave through an accumulated change of the index of refraction in a volume larger than that of the particle itself. For long-pulse (t_P > τ₀) or cw irradiation and a low intensity level, the change in the optical properties of the environment can be used. With significant heating of NPs, it is necessary to solve a combined problem that takes into account the change in the optical properties of NPs and, at the same time, changes in the optical properties of the environment. When an NP is heated, the heat dissipates into its surroundings, potentially changing their physical properties in a detectable manner. For example, any liquid changes its refractive index when heated. Thus, upon local heating of NPs in a solvent, this change makes it possible to optically study the local temperature change. As detailed below, temperature-induced phase transitions are also detectable shifts in the environment from which the temperature of the plasmonic NP can be inferred. Exposing a gold nanosphere to a focused laser beam creates a temperature distribution in the surrounding medium due to its heating caused by heat dissipation. This temperature distribution can be converted into a function of the refractive index, which depends on both the GNP temperature and the distance to the NP surface.

Based on the temperature-induced change in the refractive index, an optical microscopy technique for nanothermometry based on four-wave shear interferometry has been used.⁹⁷ The principle of this method is that as the temperature rises, the liquid changes its refractive index. A plane wave was distorted by thermally induced variations in the refractive index of the liquid, and this wavefront distortion was measured by a wavefront analyzer and then processed using an inversion algorithm to determine the temperature increase. This method has a high acquisition speed (∼10 μs) and a sensitivity of ∼1 K. However, the main advantage is that the range of measured temperature is arbitrarily large compared to other methods.

The temperature around a heated NP decreases with inverse distance, and the temperature profile T(r) creates a refractive-index profile n(r) surrounding the NP as shown below:

T (r) = T_{\infty} + Δ T \frac{r_{0}}{r}, n (r) = n_{\infty} + \frac{d n}{d T} Δ T (r) = n_{\infty} + Δ n \frac{r_{0}}{r},

where

Δ T = (T_{0} - T_{\infty})

⁠, n_∞ is the unperturbed refractive index of the medium at T_∞, and dn/dT is the thermorefractive coefficient of the medium. Although the refractive-index profile extends over an infinite distance, at r = 2r₀ the refractive-index perturbation decays to half of its maximum and acts as a nanoscopic thermal lens.

The PT contrast theory was developed^98,99 for focused laser beams (without plane-wave approximation), and it predicts a two-lobed (positive and negative) PT signal detection volume. The action of a nanoscopic spherically symmetric refractive-index profile on a focused Gaussian beam can easily be represented as the action of a phase-modifying lens. Rays crossing the inhomogeneous field of the refractive index n(r) collect an additional phase along their trajectory, which advances or retards their phase with respect to the unperturbed ray. This approach was extended to a full ab initio model and showed for the first time that the mechanism behind the signal—despite its nanoscopic origin—is also a lens-like action of the induced refractive-index profile, only hidden under a complex mask of the generalized Mie-like framework. The diffraction model provides concise analytical expressions for the shape and magnitude of the axial PT signal and its angular distribution, phase, and shape as a function of experimental and sample parameters, all of which exhibit a clear lens signature. The advantages and limitations of various models have been summarized,⁹⁹ which allows choosing the right basis for future studies using single-absorber PT microscopy.

PT microscopy allows the detection of individual nano-absorbers among strong scatterers and bypasses many fluorescence-based detection limitations.¹⁰⁰ PT detection is based on the absorption of a heating beam by a small sample, up to a single metal NP. This thermal lens is then visualized by scattering the probe beam, typically at a wavelength different from that of the heating beam, to facilitate the rejection of the intense heating light by spectral filters. Over the past two decades, various implementations of PT microscopy and spectroscopy, as well as an all-optical detection method, have achieved single-particle and molecule sensitivities, which have been developed for a wide range of applications in biology and material science. PT imaging has been used to detect tiny nano-objects such as single metal NPs down to 1.4 nm in diameter, semiconductor nanocrystals, single nonabsorbing proteins, and even single organic dye molecules. The maximum power of the probe laser beam was produced, the optimal optical and thermal properties of the medium in which the absorber was located were selected, and the absorber was thermally isolated from the glass substrate. GNPs, which have high photostability and biocompatibility, became ideal probes for cell imaging and PT microscopy, which was demonstrated on biomolecules labeled with GNPs down to 5 nm in size. The PT signal arises from a change of refractive index surrounding an NP and is therefore proportional to the heating intensity.

PT spectro-microscopy—as a reference tool for characterizing and optimizing optoplasmonic biodetection methods—was used by the Orrit group to investigate the response of plasmonic nanostructures to changes in their dielectric environment.¹⁰¹ Accurate detection of nano-objects such as viral particles, micelles, and proteins requires optimization of many experimental parameters. Changes in the optical properties caused by heating lead to changes in the scattered light, which are detected as changes in the intensity of the probe beam illuminating the sample. Because these changes are very small, their detection is facilitated if the intensity of the heating beam is modulated at a fixed frequency, which allows subsequent phase-sensitive demodulation with a lock-in amplifier. Here, a deviation from this scheme was used by probing gold nanorods at wavelengths close to their LSP resonance and their response to thermal changes in the refractive index. However, for applications in soft matter and biological systems, the maximum heating power is limited to much lower values because of boiling of surrounding liquids or thermal damage to biomolecules such as protein denaturation.

The use of various laser wavelengths for PT imaging in combination with dark-field scattering and electron microscopy has been carried out to separate the radiative and nonradiative properties of single NPs and their ensembles and to develop PT spectroscopy in a wide range of wavelengths.¹⁰² The experimental characterization was consistent with the trend of Mie theory and in terms of its predictions regarding the intensity of absorption and scattering at 532 nm as a function of size. High-resolution electron microscopy, dark-field spectroscopy, and PT imaging have been combined with numerical methods capable of modeling arbitrary NP geometry and evaluating nonradiative and radiative contributions to the surface plasmon.

The use of highly sensitive thermometric methods is essential for evaluating nanoplatforms for PT therapy. The thermal lens technique was introduced to evaluate optically induced temperature changes in colloidal samples of GNPs.¹⁰³ Measurements using a thermal lens also made it possible to obtain the value of the NP absorption cross section, regardless of knowledge about the scattering properties of the nanostructure. The developed thermometric system had a sensitivity of 0.2 °C⁻¹ and made it possible to measure temperature fluctuations of metal colloidal samples with a resolution of 0.01 °C. Measurement of changes in colloidal temperature makes it possible to estimate the local temperature variation achieved by each nanoheater before thermalization of the excitation volume. These results established a practical and efficient method for evaluating optically induced temperature changes in metal colloids.

The absorption of laser energy by an NP and the dissipation of the absorbed energy into the environment causes heating of the NP and a change in its optical properties and temperature gradient, which in turn changes the optical properties of the medium and NP. The behavior of ultrahigh-resolution mid-IR PT microscopy has a great advantage for the chemical characterization of specimens, especially for biological applications.

D. Thermochemical phase transitions in lipid bilayers surrounding a heated nanoparticle

An assay based on a lipid bilayer undergoing a phase transition upon heating from an NP was developed by the Oddershede group.¹⁰⁴ The idea of this method is to place an NP on a lipid with a well-defined phase transition temperature and keep it below that temperature. Then, the size of the melted region around the NP following irradiation should be measured after irradiation. The lipid bilayer consisted of saturated lipids with a phase transition temperature of T_m = 33.8 °C, which was several degrees above the ambient temperature. During irradiation of the NP, the surrounding bilayer formed a circular region of fluid phase. The radius D_m of the liquid region is equal to the distance r_m from the NP center to the molten region of the melted region where T = T_m. Recently, this methodology was used to quantify the extreme PT heating of platinum NPs.³⁵ The experimental features of this process were discussed in Sec. II B. The accuracy of the methods based on the phase transition of the lipid bilayer is limited by the accuracy of determining the well-defined phase transition temperature and the transition width. The advantage of the lipid-based method is that it is a direct experimental estimate of the temperature, which does not rely on knowledge of the viscosity of the medium or thermal conductivity, for example. Also, the measurements can be carried out at a distance from the irradiated NP in both 2D and 3D environments. The disadvantages are that not all nanoscopic systems are compatible with lipid bilayers and the selected lipid bilayer may be sensitive to osmotic pressure and solution conditions. Unfortunately, there are no data on the laser fluence (intensity) used in experiments³⁵ (only general laser power), which limits the possibility of checking theoretically the correctness of the results and their applicability. On the other hand, the SPR of platinum NPs is located in the range of 400–450 nm, and the possible use of platinum NPs in biomedical treatment is limited by their very low absorptivity in the NIR spectral interval.

Nanothermometry is a nanoscale temperature measurement technique that is emerging as an important tool in science and applications in biology, solid-matter physics, and materials science. The ideal nanothermometer must be not only accurate but also applicable over a wide temperature range, reliable under various environmental conditions, and the readout time must be short enough to detect rapid temperature changes. A number of competing methods are currently being developed, each with distinct advantages and disadvantages. Estimating the temperature of optically heated colloids is essential for the development of efficient materials and procedures for laser thermotherapy. In the future, this wide variety of methods may evolve into a toolbox of several well-calibrated methods for use in a large variety of nanometric applications.

V. APPLICATIONS OF LASER HEATING OF NANOPARTICLES IN NANOTECHNOLOGY

In this section, applications of the laser heating of NPs in various areas of nanotechnology are discussed. The thermal processes inside NPs causing their melting, evaporation, reduction, etc. are not considered, nor are vapor bubble generation, optical breakdown, and hydrodynamic and acoustic processes in the environment.

A. Thermochemical reactions and selective nanophotothermolysis initiated in environment by nanoparticles heated by a laser

Efficient heat generation by plasmon-resonant NPs under laser irradiation and intensive heat exchange with the environment and its heating lead to possible thermochemical processes and reactions that can be used for various applications. One of these processes is thermochemical transformation in the environment: heating the material (tissue) surrounding a GNP may provide its thermochemical transformation as the heat-induced breakdown of this structure. The degree of thermal transformation is described by the following kinetic equation:^105,106

\frac{\partial f}{\partial t} = - \frac{k_{B} T}{ℏ} \exp (- \frac{Δ H - T Δ S}{R_{g} T}) f

(43)

with the initial condition f(t = 0) = 1, where f is the degree of thermo-transformed molecules, k_B and h are the Boltzmann and Planck constants, respectively, ∆H and ∆S are the differences in enthalpies and entropies, respectively, of the initial and activated states, and R_g is the universal gas constant.

Heating the material (tissue) surrounding a GNP may also provide thermal denaturation phenomena as the heat-induced breakdown of the structure of a protein macromolecule leading to the loss by protein of natural functional properties. The degree of thermal denaturation of protein in tissue is described by the kinetic equation in Eq. (43). Laser-induced local thermal denaturation of tissue proteins around NPs without forming significant thermodenaturation in tissue can be achieved by selecting the laser parameters for the NPs in question.^14,107 Radiation pulses with t_p = 1 × 10⁻⁶ and 1 × 10⁻⁹ s cause intensive heating and heat localization of laser pulse energy in GNPs. Heating and cooling of a GNP is accompanied by the propagation of heat and thermal denaturation from its surface to the surrounding tissues during heat transfer, which leads to its significant heating above the surrounding tissue. The existence of a sharp temperature gradient near the particle surface (see Fig. 14) confirms the possibility of realizing the selective denaturation of tissue proteins. The denaturation reaction rate depends strongly on temperature [see Eq. (43)], and cooling the tissue below 330–340 K causes an abrupt retardation of the reaction and furthermore a cessation of the expansion of the denaturation region during the aforementioned time intervals. Therefore, such irradiation regimes can obviously be realized by selecting pulse energies (intensities) such that denaturation nanoregions around GNPs can be formed that do not overlap with one another because of the strong temperature dependence of the protein denaturation rate [see Eq. (43)]. In these cases (Fig. 14), proteins undergo complete denaturation in a 5–20-nm-thick spherical layer directly adjacent to the GNP for t_p ranging from 1 ps to 1 μs. In the remaining volume of the cell, virtually no protein denaturation is observed.

FIG. 14.

Computer distributions of temperature T (solid lines) and degree f of protein molecules that did not undergo thermodenaturation (dashed lines) along radius r for (a) pulse duration t_p = 1 × 10⁻⁶ s and normalized intensity I_n = 2.6 × 10⁶ W/cm² at time instants t = 0 (0), 1 × 10⁻⁷ s (1), 1 × 10⁻⁶ s (2), 1.1 × 10⁻⁶ s (3) and (b) t_p = 1 × 10⁻⁹ s and I_n = 1.1 × 10⁷ W/cm² at t = 0 (0), 5 × 10⁻¹⁰ s (1), 1 × 10⁻⁹ s (2), 5 × 10⁻⁹ s (3). The results are for a spherical GNP with radius r₀ = 30 nm. Adapted from Ref. 107.

The selective thermodenaturation of proteins around GNPs can have advantages such as nanosized precision of localized damage for 1 × 10⁻⁹ s ≤ t_p ≤ 1 × 10⁻⁶ s (larger damage zone for different mechanisms) and lower laser fluence in comparison with other modes described below. PT therapy—which involves the application of plasmonic NPs as light-triggered thermal transducers—has emerged as a promising cancer treatment because due to the temperatures generated upon laser irradiation of plasmonic NPs surrounding tissue containing cancer cells become irreversibly damaged or immediately ablate. Experimental studies of the selective degradation of proteins by laser irradiation onto GNPs in solution¹⁰⁸ and variation of protein corona composition of GNPs following plasmonic heating¹⁰⁹ have been carried out to investigate protein transformations under laser pulses.

Precise control of protein activity in a living system is a challenging but long-pursued problem in the biomedical sciences. On the other hand, thermal denaturation of proteins is the main method of thermal treatment of degenerative biocells and human organs. Thermal denaturation of egg protein in the presence of GNPs via their heating at the plasmon resonance wavelength by the pulsed radiation of the second harmonic of an Nd:YAG laser (532 nm) has been investigated.¹¹⁰ The heating temperature of the medium with GNPs was calculated, and the numerical estimates of the temperature of the heated medium containing protein and GNPs (45.3 °C at the moment of protein denaturation) agreed well with the literature data on its thermal denaturation and with the data of pyrometric measurements (42.0 ± 1.5 °C). Egg protein can be used successfully to investigate the specific features of laser heating of proteins in the presence of metal NPs under their excitation at the plasmon resonance wavelength. The proposed experimental approach to studying the laser heating of a biomedium using the protein from chicken eggs as a model medium is easily implementable and may serve as a convenient research tool.

Hyperthermia has been used to photo-inactivate protein activity without genetic modification, with nanosecond laser pulses used to create nanoscale heating around plasmonic NPs to inactivate adjacent protein in live cells. A numerical model was studied to investigate the important parameters affecting efficient inactivation of proteins at the nanoscale by NP localized heating.¹¹¹ The impact zone is influenced by laser pulse duration, temperature-dependent thermal conductivity, and nonspherical NP geometry, but it is insensitive to temperature-dependent material density and specific heat, as well as to thermal interface resistance based on reported data in the literature. Different proteins with various Arrhenius kinetic parameters have significantly different impact zones, and the study reported in Ref. 111 provides guidelines for designing the protein PT inactivation process.

Plasmonic NPs inserted into the bulk of a transparent medium lead to modification of nano-composites consisting of a typical polymer matrix and metal NPs under femtosecond laser pulses.¹¹² A photochemical reaction initiated by the two-photon absorption of light near a plasmonic NP within the matrix products of such a reaction changes the symmetry of the material, resulting in the appearance of anisotropy in the initially isotropic material. The efficiency of a thermally activated chemical reaction at the surface of a plasmonic particle and the distribution of the product of such a reaction near the metal NP irradiated by an ultrashort laser pulse were studied.

Investigations have been carried out of gold and gold–zinc oxide nanocrystals encapsulated in a metal-organic matrix upon plasmonic heating with nanosecond laser pulses.¹¹³ Irradiation of the composite particles leads to heating of the gold core, and decomposition of the surrounding matrix acts as a temperature probe. Cavities inside the matrix were found in transmission electron microscopy (TEM) images after irradiation, and their size depended on the laser energy density and the heat generated at the gold core after absorption of a laser pulse. The matrix surrounding the gold core can be heated to decomposition over a distance of up to 60 nm, and this represents a method for visualizing the heat transfer from the gold cores to the ZIF-8 matrix in three dimensions.

B. Applications of laser heating of nanoparticle ensembles in laser nanomedicine

The results of applications of lasers and NPs in nanomedicine achieved prior to 2016–2017 have been presented.^114,115 The successful synthesis and characterization of high-quality and biocompatible plasmonic colloidal NPs has contributed to numerous and expanding applications in biomedicine.¹¹⁴ Such particles are highly promising for cancer treatment, drug delivery, and future nanomedicine applications. Nanodiagnostics and NP-mediated drug delivery are recognized as complementary theranostic technologies that combine diagnostic and therapeutic effects into one entity, are promising for precision medicine, and can lead to unprecedented advances in medicine. NPs play a key role in the efficient transport and delivery of imaging probes, therapeutic agents, or biological materials to target sites such as a specific organ, tissue, or even underlying cell. In addition, some of them have active functions that facilitate their use as nanoprobes for imaging/sensing or agents for novel therapies. The major advantage of approaches with plasmonic NPs is remote local control of NP heating, which has a tremendous impact on the thermal response of biological materials and manipulation with soft materials. Plasmonic NPs have shown potential in medical applications such as PT cancer therapy with reduced side effects. The rapid heating and cooling cycles, which can be performed by modern lasers and NPs, have shown very high spatial confinement and selectivity.

Emerging areas of micro- and nanoscale technologies in medicine have been discussed, starting with fundamental discoveries and ending with their implementation.¹¹⁵ The consideration focused on several areas of growing interest. Combined use of micro- and nanotechnologies to provide smart diagnostic solutions for the identification and separation of circulating tumor cells and cost-effective diagnosis of infectious diseases was discussed. New contributions of micro- and nanotechnologies to the solution of the main therapeutic problems were considered, such as the creation of therapeutic cancer vaccines based on materials with micro- and nanoscale characteristics, the use of NP carriers for targeted drug release, and the integration of micro- and nanotechnologies in tissue engineering applications. Lab-on-chip systems were used for drug testing/development with a particular focus on the latest advances in the fabrication of vascularized tissues for drug testing/screening. The integration of micro- and nanotechnologies will continue to improve the diagnosis and treatment of infectious and chronic diseases and provide new platforms to study diseases at the tissue and cellular levels.

Short laser pulses and NPs have been used for the manipulation of small objects such as membranes, cells, vesicles, and aggregates. Irradiation of plasmonic NPs provides an excellent tool for NP-mediated membrane heating and manipulation of lipid membranes including the plasma membrane surrounding cells.¹⁵ Membranes respond strongly to thermal changes, in particular near phase transitions from the gel to fluid state. Optical trapping combined with plasmonic heating of GNPs has been used to locally melt membranes and study the permeability of lipid membranes near the gel-to-fluid phase transition of the artificial and cellular plasma membranes is feasible by irradiation of plasmonic NPs. The photothermally induced rupture of laser-irradiated plasmonic NPs on artificial membranes and cellular plasma membranes has been used to inject GNPs into the cytoplasm of cells using both pulsed¹¹⁶ and cw¹¹⁷ lasers. This strategy—which can be termed optothermal injection—is a less invasive alternative to optoporation in which pulsed lasers are used to puncture cell membranes for optimized molecule diffusion and can have detrimental effects on the cell, such as cell death.¹¹⁸ The mechanism behind optothermal injection using cw lasers was explained by plasmonic heating, which disrupts the plasma membrane and allows a particle to move into the cellular cytoplasm. The approach of using optically induced heating to pass the endosome or plasma membrane of cells has great potential. In particular, the combination of a noninvasive cw NIR laser with an NIR resonant NP will only perturb the cell within a volume of ∼100 nm in size. In contrast, a pulsed UV laser will penetrate the whole cell and cause photodamage, e.g., within the nucleus. However, the effect of the heating on the chemically attached molecules has to be further validated, for instance by using the injected NPs as DNA carriers to transfect cells and subsequently measure the transfection efficiency.

Also, cell membranes respond to local heating by increased permeability of ions, as demonstrated with a patch clamp technique combined with local plasmonic heating.¹¹⁹ This optothermal injection strategy is a less invasive alternative to optoporation in which pulsed lasers are used to puncture cell membranes for optimized molecular diffusion. The mechanism behind optothermal injection using cw lasers was explained by plasmonic heating that disrupts the plasma membrane and an optical radiation pressure pushing the particle into the cellular cytoplasm. Laser-assisted NP injection can potentially be used to inject molecules into the cell cytoplasm, provided that the temperature increase on the NP surface does not degrade the attached molecules. The combination of a noninvasive NIR laser with an NIR resonant NP will only perturb the cell within a nanovolume.

Highly localized membrane heating can be used for controlled fusion of selected cells or vesicles.¹⁵ Irradiation of plasmonic NPs at the contact area between two vesicles or two cells results in immediate full fusion of the two. Fusion can be triggered with both pulsed and cw lasers as long as the irradiated NPs are in close proximity to both membranes of the entities to be fused. This approach has great potential for hybrid cell formation, for controlled mixing of proteins and buffers in biophysical applications, and vesicle fusion, and it will pave the way for a number of novel future applications.

Aggregation of proteins is a prominent hallmark of virtually all neurodegenerative disorders including Alzheimer’s, Parkinson’s, and Huntington’s diseases. A label-free, laser-based PT treatment of aggregates in huntingtin-like aggregation has been introduced.¹²⁰ Nanosecond laser pulse-induced local PT heating was demonstrated that directly disrupted the aggregates so as can delay their accumulation, maintain motility, and extend the lifespan of treated nematodes. These beneficial effects were validated by confocal PT, fluorescence, and video imaging. The results demonstrated that the used theranostics platform, integrating PT therapy without drugs or other chemicals, and combined with advanced imaging to monitor PT ablation of aggregates, initiates systemic recovery and thus validates the concept of aggregate-disruption treatments for neurodegenerative diseases in humans. Also, the PT inactivation of universal viral particles by an LSP-resonance-mediated heating filter membrane has been studied.¹²¹

Plasmonic PT therapy has been successfully developed for various types of cancer. Cancer cells are more sensitive to temperature increase than are healthy cells, and temperature increase seems to aid the effect of chemotherapy. Therefore, raising the temperature appears to be a useful strategy for targeting most types of cancer, in particular if the treatment can be localized, thus calling for the use of laser-induced heating of plasmonic NPs. The relationship between treatment time and temperature is of great importance for the clinical hyperthermia of cancer cells.

The development of new effective cancer treatment methods has attracted much attention, mainly because of the limited efficacy and considerable side effects of currently used cancer treatment methods such as radiation therapy and chemotherapy. PT therapy based on the use of plasmonically resonant metal NPs has emerged as a promising technique for eradicating cancer cells selectively. In this method, plasmonic NPs are preferentially absorbed by a tumor and then selectively heated by exposure to laser radiation with a specific plasmonic resonant wavelength, to destroy the tumor while minimizing damage to adjacent normal tissue. PT therapy is a minimally invasive technique for cancer treatment, using laser-activated photoabsorbers to convert photon energy into heat sufficient to induce cell destruction via apoptosis, necroptosis, and/or necrosis. A major challenge is the delivery and accumulation of particles at the tumor site with the aim of minimizing the delivery of particles to distant organs of the organism while still homogeneously distributing the particles within the tumor. One option is delivery via enhanced permeability and retention, which arises from the fact that angiogenesis leads to the formation of blood vessels within and surrounding the tumor that are different from vessels in normal tissue; the tumor vessels have the distinct property that they act as a sieve for NPs with diameters between 60 and 100 nm. PET is emerging as a novel tool for evaluating the efficiency of thermoplasmonic cancer therapy, and PET can be used to monitor cell viability within a tumor (or other tissues) in a noninvasive manner.

PT cancer therapy based on plasmonic NPs has the advantage that the particles remain in the tissue after treatment and so the therapy can be repeated using the same particles. It is important to select the right particles for plasmonic NP-based therapy, this choice being based on (i) optimal size for high absorption in the NIR biological transparency window and efficient delivery to the target, (ii) nontoxicity in the relevant concentrations and biocompatibility, and (iii) thermal stability. Solid gold, platinum, and titanium NPs are examples of NIR-resonant NPs that are nontoxic with very high thermal stability, and laser irradiation in extracorporeal or intravenous mode can be used to activate NP agents with selectivity in the target tissue. Plasmonic NPs for PT therapy can be exploited as a contrast agent in PT and photoacoustic imaging at nanometer and micrometer resolution. This combination should therefore optimally be used to combine treatment with detailed information about the location of NPs in the organism. Biophotonic therapy modalities comprise very promising alternative techniques for cancer treatment with minimal invasiveness and side-effects.

During the past decade, PT therapy has attracted increased interest because it can be combined with customized functionalized NPs.¹²² Recent advances in nanotechnology have given rise to various types of NPs, such as GNPs, designed to act both as radiosensitizers and PT sensitizing agents because of their unique optical and electrical properties, i.e., functioning in dual mode. Functionalized GNPs can be employed in combination with nonionizing and ionizing radiation to significantly improve the efficacy of cancer treatment while at the same time sparing normal tissues.

Heat transfer from NPs for the targeted destruction of infectious organisms has been studied and analyzed.¹²³ Whereas the application of optically or magnetically heated NPs to destroy tumors is now well established, examination is ongoing to extend this concept to target pathogens and explore the issues of power density and heat transfer. Depending on the rate of heating, either hyperthermia or thermoablation may occur, which implies very different sources of excitation and heat transfer for the two modes, and different strategies for their clinical application. Heating by isolated NPs and by agglomerates of NPs is compared: hyperthermia is much more readily achieved with agglomerates and for large target volumes, a factor that favors magnetic excitation and moderate power densities. In contrast, destruction of planktonic pathogens is best achieved by localized thermoablation and high power density by pulsed optical excitation.

The combination of an NIR laser and plasmonic NPs is compelling for the PT treatment of brain cancer, this being due to the efficient light-to-heat conversion and biocompatibility and the possibility of minimizing the damage of the surrounding brain tissue.¹²⁴ The temperature change in three different porcine cerebral tissues (i.e., the stem, the cerebrum, and the cerebellum) under laser treatment was tested; the different tissues have different optical and thermal properties and confirm the enhancement of heating with the addition of plasmonic NPs, balancing the effect and side effects of plasmonic PT therapy.

Sophisticated technologies have been developed in cancer nanomedicine, such as PT therapy and photodynamic therapy. However, single-mode phototherapy cannot completely treat persistent tumors, with the challenges of relapse or metastasis remaining. The development of strategies combining other therapeutic methods including chemotherapy, immunotherapy, gene therapy, and radiotherapy has been discussed, along with future directions,¹²⁵ and phototheranostic materials for imaging-guided cancer therapy targeted by GNPs and the optical properties of NP aggregates have been discussed in recent articles.^126–128 Activatable phototheranostic materials have been developed to simultaneously and specifically turn on their diagnostic signals (fluorescence/self-luminescence/photoacoustic signals) and PT/photodynamic effects in response to cancer hallmarks.¹²⁶ GNPs are of increasing interest for their unique properties, and their biocompatability, minimal toxicity, multivalency, and size tunability make them exciting drug carriers. The functionalization of GNPs with targeting moieties allow their selective delivery to cancers, with antibodies, proteins, peptides, and aptamers all exploited. The recent advances in targeted GNPs for the treatment of cancer have been analyzed, with a particular focus on these classes of targeting ligands, their benefits, and the potential drawbacks of each ligand class.¹²⁷ The optical properties of NP aggregates depend on their dimensions and shape as well as the proximity of the NPs within the near-field limit, leading to a shift of the resonance peak in the optical spectrum, and their influence on the therapeutic outcome has been discussed.¹²⁸ This will be useful in moving toward the practical application of various therapeutic modalities utilizing the optical characteristics of NPs. The recent progress, current challenges, and future perspectives in the design, synthesis, and proof-of-concept applications of activatable NPs have been summarized.

Note that not only can GNPs be used for PT therapy, but other NPs are also possible effective agents. Recently, silica NPs entered clinical trials for a variety of biomedical applications, including oral drug delivery, diagnostics, plasmonic resonance, and PT ablation therapy.¹²⁹ Preliminary results indicate the safety, efficacy, and viability of silica NPs, and by modulating their structural and physiochemical properties, such as size, charge, surface functionality, and shape, silica NPs can deliver drugs across biological barriers. Based on their performance in clinical trials, silica NPs are emerging as a promising diagnostic and delivery platform and could play a key role in the development of next-generation theranostics, nanovaccines, and formulations to orally deliver peptides and proteins. Also, viability studies have demonstrated that platinum NPs are nontoxic at therapeutically relevant concentrations and can efficiently kill human cancer cells.³⁵ Plasmonic platinum superstructures with boosted NIR absorption and PT conversion efficiency in the second biowindow can be used for cancer therapy.¹³⁰ They are highly promising candidates for thermoplasmonic applications in the life sciences, in nanomedicine, and for biomedical engineering.

In an analysis of the PT effect and its mechanism, antitumor therapy and other technological and biomedical applications of the PT effect were discussed, paying particular attention to PT materials based on gold.¹³¹ Most of these results were obtained by irradiating at 808 nm (a wavelength well placed inside the biotransparent window), which is the wavelength of commonly available NIR laser sources, but obviously a good match between the maximum absorption of a given NP and the irradiation wavelength can optimize the PT conversion efficiency. In turn, the wavelength of the maximum absorption of an NP is tuned by not only its composition but also its dimensions and shape. The ability to tailor the composition, shape dimensions, and coating of NPs, and consequently their optical properties, PT response, and stability, allows sophisticated, high-technology techniques to be applied successfully.

Although various latest technologies are currently available to treat cancer, there is a need for more developed and novel technologies to combat this deadly condition. NP-based cancer therapeutics offer a promising approach to treating cancer effectively while minimizing adverse events. After two decades of preclinical development, NPs are being investigated for treating specific disorders and are slowly but steadily moving into clinical trials, where they can be used to treat a wide range of diseases. The first pilot clinical trials appeared in 2019, when the treatment of prostate cancer with silica–gold nanoshells and an optical-fiber directed NIR laser was reported to be successful on 46 subjects.¹³² Potential NP toxicity and accumulation, the need for high NP concentrations, the high irradiances used in research papers, and the bodily deepness of most tumors are all obstacles in the translation of PT through-tissue treatments from lab benches to clinics.

Clinical translation of GNPs and perspectives of next-generation engineered nanogold for multimodal cancer therapy and imaging have been discussed.^133,134 Among various NPs, GNPs are biocompatible and have proved their efficiency in treating cancer because they can reach tumors via enhanced permeability and retention, which can facilitate the active targeting of GNPs to the tumor tissue. In addition to PT therapy, GNP-based nanoplatforms have been investigated for combinational multimodal therapies in the past few years, including photodynamic therapy, chemotherapy, radiotherapy, immunotherapy, etc., to ablate cancer cells. In the current clinical landscape of therapeutic metal (gold) NPs, the shared characteristics that allowed for their transition from bench to bedside were analyzed, and existing hurdles that need to be overcome before they can be approved for clinical use were examined. In any case, PT cancer therapy has huge potential because it will be able to reach tumors of any cancer type at sites that are not accessible for surgery, and it should be able to knock down even cancer stem cells.

C. Thermal radiation emission by nanoparticles and laser-induced incandescence

NPs heated by laser radiation emit thermal radiation from their surfaces presumably in the NIR range because of their characteristic temperature of 1-5 thousand K. IR thermal imaging determines the temperature of the peak intensity of an nano-object by measuring the intensity of IR radiation on its surface without contact.¹³⁵ This technology is particularly suitable for measuring the instantaneous temperature distribution of high-temperature objects heated by laser irradiation in relatively low-temperature backgrounds. Most of the thermal imaging methods have response times of a few milliseconds, which may not be fast enough for the monitoring of rapid transient temperature changes in laser micro-nanofabrication processes, which significantly limits the possible uses of this method. Thermal (blackbody) radiation has a spectrum that depends entirely on the temperature of the particle, and the spectral distribution of the emission intensity for a specific wavelength can be calculated from Planck’s law with the peak intensity¹³⁶

λ_{\max} = \frac{B}{T}

(44)

(B = const.) and energy losses due to radiation cooling (J_R) [see Eq. ]. The use of thermal radiation is possible for determining the high temperature T₀ of heat-resistant particles with radius r₀ ∼ 1 μm and more in a gaseous or liquid medium under the specified conditions. Let us consider the latest achievements in this area and the possibilities of application to determine the temperature of NPs in various situations.

A measurement technique that can provide important characteristics such as particle concentrations, sizes, and temperatures is LII, which was developed and is used widely as a diagnostic tool for in situ measurements of particle sizes, volume fractions, and temperature in flames, exhaust gases, and other high-temperature processes. There are two variants of LII: one is based on pulsed laser excitation and is used mainly in combustion diagnostics and emissions measurements; the other relies on cw lasers and has become increasingly popular in environmental applications. A typical LII setup consists of two systems: (i) a pulsed laser for exciting the NPs in the aerosol (colloid) probe volume and (ii) a system for detecting the laser-induced emission, usually at multiple wavelengths and with high temporal resolution. One such system is a pyrometer, which is a noncontact device for measuring temperature remotely. The pyrometer’s optical system collects the thermal radiation signal and focuses it on the photosensitive detector (semiconductor photodiode) with an electronic circuit to amplify the signals. The output signal of the detector determines the temperature of an object based on the amount of heat radiation emitted from its surface.

Soot and other carbonaceous particles are especially suitable for LII application because of their high sublimation temperature of ∼4000 K and the appreciable imaginary part of their refractive index. These two properties allow for high peak particle temperatures, resulting in a pronounced thermal emission in the visible spectral range with convenient detection.^135,137,138 On the other hand, metal microparticles comprise another class targeted for LII investigations, and studies performed so far have covered a wide range of them.^139–141 The peak temperatures of laser-heated metal NPs are typically below 3000 K, so this temperature translates into a significantly lower intensity and consequently a lower signal-to-noise ratio.

Although LII is commonly linked to the measurement of NPs in a gas, there are many investigations that deal with the properties of nanosized particles in a liquid (condensed) phase. Significant studies employing LII for particles suspended in liquids are very important for their applications in biomedical and other fields.^137,142,143 Many studies used dispersions of metal particles to investigate the change of the refractive index of a colloid during and after a nanosecond laser pulse.

Recent studies of oxide NPs (TiO₂, Fe₂O₃, etc.) by LII have been carried out,^140,144,145 and a method has been developed to verify the possibility of measuring the LII signal from TiO₂ NPs.¹⁴⁴ The optical system for LII was validated on flame-generated soot particles, then spectrally resolved measurements of the laser-induced emission of a TiO₂ NP aerosol were performed. At a laser wavelength of 355 nm, the laser-induced emission spectrum presents a response to laser fluence and detection gate delay typical of blackbody radiation, i.e., dependent on the particle temperature. It is concluded that LII can be used to characterize noncarbonaceous TiO₂ NPs.

A typical LII setup is shown in Fig. 15 and has been discussed in some detail.¹⁴⁰ The system consists of two subsystems: (i) a pulsed laser and associated optics for exciting the NPs in the aerosol probe volume and (ii) a system for detecting the consequent laser-induced emission, usually at multiple wavelengths and often with high temporal resolution. The excitation system typically includes an Nd:YAG laser and optics needed to focus the beam. It is also commonplace to condition the beam to produce a time-averaged spatially uniform fluence profile, e.g., through relay imaging, and also to vary the laser fluence. Planck’s law offers an appealing relation between the absolute temperature of the system under interrogation and the thermal spectrum. Therefore, by balancing the absorbed power with the emission power and the heat dissipation, the particle temperature can be extracted. Unfortunately, standard thermal imaging, which is often used to measure the heating of microparticles in suspension,¹⁴⁶ is problematic for nanothermometry because of its poor spatial wavelength resolution of several micrometers of peak intensity given by Planck’s law [see Eq. (44)] for T₀ ∼ (1–3) × 10³ K.¹⁴⁷ Thermal radiation spectroscopy is unsuitable for far-field nanothermometry, primarily because of the power loss in the near surroundings. On the other hand, an improved method has been developed of monitoring surface temperature changes subjected to external stimulation by dynamic IR thermography.¹⁴⁸ The method is based on the careful analysis of an IR image sequence recorded before, during, and after the stimulation that allows one to evaluate the temporal behavior of the surface temperature. The developed method can produce a quantitative analysis of the changes in the surface temperature distribution of a gold hydrosol, as well as characterizing the PT properties of the NPs. Lock-in thermography, a technique where temperature changes are obtained by means of an IR camera mounted on a standard microscope stand, was used to measure efficiently and noninvasively the heat generated by plasmonic NP solutions exposed to a modulated light source.¹⁴⁹ A multi-wavelength (525 and 660 nm with consequent power densities of 74.2 and 136 mW/cm²) light source was used to excite GNP dispersions, and the data showed how the amplitude of the temperature response increased linearly with the gold concentration and was almost independent of the investigated particle size.

FIG. 15.

Schematic of a typical setup for time-resolved laser-induced incandescence (LII) detection (TiRe-LII), including a two-color photomultiplier assembly, a spectrometer, and an attenuator to control the laser fluence, in this case via a polarizer and a half-wave plate. Adapted from Ref. 140 on the basis of the open CC BY license.

The transient PT process of GNPs capped with different molecules (citrate, etc.) has been investigated by time-resolved IR emission spectroscopy monitored with a step-scan Fourier-transform spectrometer.¹⁵⁰ Upon photoexcitation of the GNPs with a 532-nm nanosecond pulsed laser, the transient IR emission was observed within ∼1 μs, referring to the duration of the laser heating and thermalization of the GNPs. Comparing the IR emission contours with the blackbody radiation spectra at different temperatures revealed that the temperature reached 400 ± 100 °C in 90–120 ns as the 24-nm GNPs were excited by a peak fluence of 25 m J cm⁻² from a 5-ns pulsed laser at 532 nm. This was the first time that the transient broadband thermal IR emission of photoexcited GNPs had been recorded within a submicrosecond timeframe. The duplexity in the temporal capability and broadband spectroscopic window of the time-resolved emission IR spectroscopy provides a promising noncontact thermometer to illustrate the PT process and quantify the transient temperatures of miscellaneous metal nanostructures upon photoexcitation.

Size measurement of iron NPs by LII has been carried out,^138,141,151 and application of the LII method for instant size measurements of NPs has been considered.¹⁴¹ The process of laser energy absorption by NPs in the Rayleigh limit was analyzed, taking into account the spatiotemporal energy distribution in the laser beam, as well as the cooling of NPs by collisions with ambient gas molecules in the free molecular regime and in the course of evaporation. Software was created for analyzing and interpreting the heat radiation signals of laser-heated NPs (LII) obtained in experiments, as well as for determining their sizes. Data were obtained on the sizes of carbon NPs and the time profiles of iron NPs, and these agreed well with TEM data.

Numerous existing and emerging applications of aerosolized metal NPs in materials science are strongly size-dependent. Recently, time-resolved LII (TiRe-LII) was investigated as a candidate for sizing aerosolized metal NPs, which requires an accurate model of the heat transfer. A model was developed that can be used to analyze experimental TiRe-LII data from aerosols of molybdenum NPs in helium, argon, nitrogen, and carbon dioxide.¹⁵¹ TiRe-LII is increasingly being used to characterize noncarbonaceous NPs. In this technique, a nanosecond laser pulse heats the NPs within a sample volume of aerosol, and the subsequent emission (assumed to be purely incandescence) is collected at one or more wavelengths. However, there are several measured phenomena (particularly with metal NPs) that cannot be explained using traditional models. Some measurement phenomena can be explained by combining Mie theory with a polydisperse particle size distribution or by considering the change in the refractive index as the NPs melt.¹⁵² The possibility of determining the primary particle size distribution in fractal-like aggregates through TiRe-LII under the influence of thermal shielding of polydispersed aggregates was investigated for two typical measurement situations: in-flame measurements at high temperature and a soot-laden aerosol at room temperature.¹³⁸ It is crucial to use the full duration of the usable LII signal trace to recover the width of the size distribution with small uncertainties.

The excessive absorption and anomalous cooling phenomena reported in LII measurements on metal NPs by considering the effects of aggregate structure and sintering have been studied.¹⁵³ Experimental investigations were conducted on iron and molybdenum aerosols, which have different melting points and thus respond differently to the laser pulse. The enhancement of the absorption cross section of the NPs due to aggregation did not fully explain the observed excessive absorption. When the molybdenum aggregates cool, they may sinter through gradual grain boundary diffusion. This change in structure alters their absorption cross section, noted as a rapid drop in the pyrometric temperature, which could explain the anomalous cooling reported for this metal.

A recent overview of the main results of LII was presented along with associated uncertainties, as well as open research challenges and new opportunities arising from the application of LII to various classes of materials, including metal, oxide and nitride, and other manufactured particles.¹⁴⁰ At higher fluences, atoms and molecules evaporated from NPs produce atomic emission lines that can be used to determine the temperature and composition of NPs, as well as other properties. Advancements in optoelectronic detector systems, streak cameras, and picosecond pulsed lasers, and their combinations with complementary optical techniques, elastic and inelastic scattering, and plasma signals related to laser-induced breakdown spectroscopy, can help develop more-sensitive LII systems. In combination with additional techniques such as light scattering, probe sampling, and molecular-beam techniques and other instruments, new directions for research and applications with LII continue to materialize.

D. Electron and ion emission from heated nanoparticles

Understanding plasmon-mediated electron emission and energy transfer is critical for controlling light−matter interactions at nanoscale dimensions. The emission of photoelectrons from plasmonic NPs into a surrounding matrix due to surface and volume mechanisms has been studied.^154,155 Models have been used that take into account a step potential at the surface of a spherical NP and the hot electron cooling, giving analytical results for the photoelectron emission rate from an NP.¹⁵⁴ The discontinuity of the dielectric permittivity at the NP boundary in the surface mechanism leads to a substantial (by ∼five times) increase in the internal photoelectron emission rate from an NP compared to the case when such a discontinuity is absent. Generally, the surface photoeffect is larger than the volume one, and its predominance is based on two factors: (i) effective cooling of hot carriers during their propagation from the volume of the NP to its surface in the scenario of the volume mechanism and (ii) strengthening of the surface mechanism through the effect of the discontinuity of the dielectric permittivity at the NP boundary. The latter is stronger at lower photon energies and so is more substantial for internal photoemission than for an external one. It is essential to take both mechanisms into account in the development of devices based on the photoelectric effect and when considering hot electron emission from a plasmonic nanoantenna.

The contribution of “transition absorption” (i.e., the loss of energy of electrons passing through the boundary between different materials) to the surface mechanism of photoemission has been analyzed.¹⁵⁵ The photoemission rate and transition absorption for NPs surrounded by various media with a broad range of permittivities were calculated, and it was shown that the photoemission rate and transition absorption follow the same dependence on the permittivity. Transition absorption is responsible for the enhancement of photoemission in the surface scenario, and the ratio of photoemission cross section for a gold nanosphere embedded in different materials such as silicon, zinc oxide, and titanium dioxide was calculated. The surface mechanism in the total photoemission dominates in the NIR wavelength range.

The observation of emission from a hot gas of free electrons in a metal with a cold lattice has been reported.¹⁵⁶ The emission was observed upon irradiation of the metal with femtosecond laser pulses, and the distinctive feature of this emission as compared to the case of equilibrium heating is the dependence of the emission quantum yield on the parameters of the electron–phonon interaction. Upon the nonequilibrium heating of electrons and the lattice, the emission quantum yield will differ from the case of equilibrium heating. The thermal emission of hot electrons coexisting with a cold lattice is a phenomenon of fundamental interest. In continuation of previous research, the photoemission of electrons from a metal needle under the action of radiation from a femtosecond IR laser with a wavelength of 1240 nm was studied.¹⁵⁷ Diagnostics of electron bunches using a Faraday cup and the time-of-flight method showed the possibility of obtaining electron pulses with a charge of 40 pC at a laser pulse energy of 45 μJ. The dependence of the electron pulse charge, which is proportional to the sixth power of the laser pulse energy, indicated a multiphoton mechanism of electron emission.

Thermionic emission has been applied to calculate the current emitted from laser-heated NPs and to interpret TiRe-LII signals.¹⁵⁸ This adjusted form of thermionic emission predicts significantly lower values of emitted current compared to the commonly used Richardson–Dushman equation, this being because the buildup of positive charge in a laser-heated NP increases the energy barrier for further emission of electrons. Thermionic emission influences the particle’s energy balance equation, which can influence TiRe-LII signals.

A review of the emission properties of metal NPs as of 2016 was presented in Ref. 159, covering the emission of electrons and photons from NPs due to excitation by electron injection via electric current, electromagnetic radiation via microwave fields, laser radiation in the IR, visible, and synchrotron (x-ray) ranges, and electron and ion bombardment. In each case, the emission mechanism depends on the characteristic length scales of the NPs, and the NPs may demonstrate properties that are absent in bulk material.

Mapping local electron emission and energy transfer with nanometer resolution from plasmonic nano-antennas excited by femtosecond laser pulses and chemical transformations in two different high-resolution electron-beam lithography resists has been studied.¹⁶⁰ Exposure of the electron-beam resists was observed in regions on the surface of the nano-antennas where the local field was significantly enhanced, and it was consistent with previously reported optical-field-controlled electron emission from plasmonic hotspots. Exposure at the center of nanorods resulted from the emission of hot electrons produced via plasmon decay in the nanorods. These results provide a means to map both optical-field-controlled electron emission and hot-electron transfer from NPs via chemical transformations produced locally in lithographic materials.

A semi-analytical model for calculating the bulk internal emission of photoelectrons from metal NPs into a semiconductor matrix has been proposed.¹⁶¹ The jump of the effective electron mass at the metal−semiconductor interface and cooling of the hot electrons because of electron−electron and electron−NP surface collisions in the metal were taken into account. The interplay between the plasmonic electric dipole and quadrupole resonances was studied, and the optimum parameters for different geometrical shapes of NPs with respect to the photoemission cross section were revealed. The absorption cross section predicts well the optimum size of the dipolar NPs, and this opens the possibility for the fast optimization and design of photoelectric devices.

Modification of a previously developed blade-type planar structure by using plasmonic gold nanostars in order to stimulate photofield emission and provide efficient laser control of the electron current has been studied.¹⁶² Localization and enhancement of the field at the tips of the gold nanostars provided a significant increase in the tunneling electron current in the experimental sample (both electrical field and photofield emission). Irradiation at a wavelength near the plasmon resonance (red laser) provided a gain in the photoresponse value of up to five times compared to irradiation far from the resonance (green laser). The kinetics of the energy density of photoinduced hot and thermalized electrons were estimated, and the proposed laser-controlled matrix current source is promising for use in x-ray computed tomography systems.

It has been reported that thermionic emission can dominate over multiphoton ionization in GNPs under femtosecond laser irradiation.¹⁶³ The brightness of individual particles observed with photoemission electron microscopy increased steeply for laser power above 200 mW, which is reproduced well by the Richardson–Dushman equation. The temperature estimated by fitting the equation is ∼1 eV. The difference in brightness among the NPs as large as a few orders of magnitude was attributed to variation in the defect density. The particles having a similar temperature despite exhibiting largely varying brightness levels can be explained by slow energy transfer from the defects to the ambient electron gas. The observed results suggest that thermionic emission can be a useful diagnostic tool for characterizing NPs.

Plasmon-enhanced photoemission from GNPs covered with a cesium film in the microwave electron gun of a free electron laser has been studied.¹⁶⁴ The cesium film was found to be effective for exciting photoelectrons from the GNPs under visible light (at 532 nm).

The presented results confirm the feasibility of applying the proposed metal NPs and ultrashort laser pulses to the creation of high-brightness electron sources acting during short time intervals. They are of great interest for the development, design, and optimization of photoelectric devices and accessible nanoscale coherent electron sources with potential applications in microscopy, spectroscopy, sensing, and signal processing. Thermo-electron emission can play a major role in the generation of optical breakdown initiated by metal NPs under ultrashort laser action.

E. Optothermal chemical catalysis

Metal NPs are used as commercial catalysts for many chemical reactions, including ammonia synthesis, hydrocarbon reforming, and oxidation and hydrogenation reactions, which proceed through one of two general mechanisms: phonon driven or charge-carrier driven.^165–167 Phonon-driven chemical reactions are triggered by the thermal heating of catalyst NPs, which excites the phonon modes of the NPs, which in turn couple with the vibrational modes of the reacting adsorbates, etc. This coupling results in the evolution of the adsorbate from the reactant to the product state in the ground state. These reactions usually require relatively high temperatures, and the distribution of the products is governed by the ground-state free-energy landscape. Charge-carrier-driven reactions on metal surfaces can also be activated in an alternative mechanism whereby external light is used to excite charge carriers (electrons and/or holes) on the metal surface, and they are based on coupling between excited electronic and vibrational states of the adsorbate–NP complex. The energized charge carriers transiently populate otherwise unpopulated electronic states centered on the adsorbate molecule, thereby forming transient ions or excited states. The adsorbate (the whole adsorbate–NP system) moves to another potential energy surface, and forces that are induced on the atoms in the adsorbate lead to nuclear motion of atoms, which can lead to the activation of chemical bonds and transformations. External light used to excite charge carriers can also be absorbed by the lattice, and the heating of NPs by optical radiation (see Secs. II and III) is also realized and should be taken into account.

Photochemical transformations and photochemical catalysis on plasmonic metal NPs including a number of opportunities in the field of selective chemical synthesis have been analyzed.¹⁶⁵ These opportunities in the field of selective chemical synthesis are based on photophysical processes and optically excited plasmonic NPs, which can also activate chemical transformations directly on their surfaces. Two mechanisms were discussed by which reactions on metal NPs can be triggered: either by excited NP phonons or by energetic charge carriers. Also discussed were the physical characteristics of optically excited plasmonic metal NPs and the mechanisms through which these physical properties can lead to chemical transformations. The oxidation state of atoms on the surface of copper NPs can be changed when the particles are illuminated with resonant light under hydrocarbon partial-oxidation operating conditions. This change had a significant effect on the outcome of the chemical oxidation reaction taking place on these structures. The light-induced reduction of copper oxide to copper metal changed the dominant chemical pathway from one leading to the complete combustion of the hydrocarbon (propylene was used in this case) to one resulting in the desired partial oxidation (propylene oxide) product. Light illumination led to copper undergoing localized SPR-supported electron transfer from bonding to antibonding states associated with the Cu–O chemical bond, which resulted in the reduction of copper oxide.

Substantial light-induced reduction of the thermal activation barrier has been reported for ammonia decomposition on a plasmonic photocatalyst, which was introduced to account simultaneously for the effects of light illumination on electronic and thermal excitations.¹⁶⁶ The specific role of hot carriers in plasmon-mediated photochemistry was underlined, which is critically important for designing energy-efficient plasmonic photocatalysts. Hot carriers produced by nonradiative decay of LSPs can be more energetic than those generated by direct photoexcitation. A supralinear intensity dependence of photocatalytic reaction rates was observed in multiple plasmonic photocatalytic reactions, demonstrating higher quantum yields with increasing photon flux. For plasmon-mediated O₂ dissociation on silver cubes, the photocatalytic reaction rate increased exponentially with temperature under constant white-light illumination. The apparent activation barrier for thermal catalysis can be decreased by illumination of a plasmonic photocatalyst, and its characterization must be studied to examine the mechanism of hot-carrier-induced activation barrier reduction. Experimental practices required to isolate thermal effects in plasmonic photocatalysis taking into account the lessons from recent experiments were considered.¹⁶⁷

Fabrication of highly efficient plasmonic nanostructures has been considered, including plasmonic metal nanostructures and metal/semiconductor heterostructures.¹⁶⁸ Plasmon-driven photochemical reactions (coupling reactions, O₂ dissociation and oxidation reactions, H₂ dissociation and hydrogenation reactions, N₂ fixation, NH₃ decomposition, and CO₂ reduction) and plasmon-enhanced electrocatalytic reactions (hydrogen evolution reaction, oxygen reduction reaction, oxygen evolution reaction, alcohol oxidation reaction, and CO₂ reduction) were analyzed. A perspective was given on the remaining challenges and future opportunities for plasmonic nanomaterials and plasmon-related chemistry in the field of energy conversion and storage.

Most modern chemical reactors make use of catalysts to increase their conversion yields, but their operation at steady-state temperatures limits their rate, selectivity, and energy efficiency. Short light pulses and PT NP arrays can modulate the temperature of catalytic sites at timescales typical of chemical processes using heat dissipation and time-dependent microkinetic reactions.¹⁶⁹ It has been demonstrated that pulsed PT catalysis can result in a favorable dynamic mode of operation with higher energy efficiency, higher catalyst activity than for any steady-state temperature, reactor operation at room temperature, resilience against catalyst poisons, and access to adsorbed reagent distributions that are normally out of reach. The key experimental parameters controlling reaction rates in pulsed heterogeneous catalysis were discussed, and specific recommendations were made for exploring its potential in real experiments, paving the way to a more energy-efficient and process-intensive operation of chemical reactors.

Air pollution has always been a hot issue of public concern, and substantial work has gone into air pollution control for decades. Volatile organic compounds (VOCs) have extensive sources, mainly from industrial and traffic exhaust emissions, and the research progress of PT catalytic removal of VOCs by nanocatalysts in recent years has been reviewed.¹⁷⁰ PT catalysis is a new coupling technology in recent years and has developed rapidly; it can simultaneously solve the high-energy consumption of thermal catalysis and the low efficiency of photocatalysis. PT catalysis realizes the synergistic effect of optical energy and thermochemistry, which also has the potential to improve the reaction rate and optimize the selectivity. The fundamentals of PT catalysis and the fabrication of catalysts were described, a design strategy for optimizing PT catalysis performance was proposed, and the performance of VOC degradation with PT catalysis was evaluated. Finally, the future limitations and challenges were discussed, and potential research directions and priorities were highlighted.

Plasmonic nanomaterials coupled with catalytically active surfaces offer unique opportunities for various catalysis applications, where surface plasmons produced upon proper light excitation can be used to drive and/or facilitate various chemical reactions. Photocatalysis based on plasmonic metal NPs has emerged as a promising approach to facilitate light-driven chemical conversions under far milder conditions than thermal catalysis but without understanding of the relation between thermal and electronic excitations. Numerous recent demonstrations of hot-carrier-driven photocatalysis by metal NPs that support surface plasmons have greatly stimulated current research activity, and recent progress in the field of photochemical catalysis on plasmonic metal nanostructures was summarized.

F. Application of results of laser heating of NPs for their laser processing

The experimental and theoretical results for the laser heating of NPs presented in the previous sections have been used successfully for the laser processing of NPs in laser nanotechnologies. The ability to manufacture NPs with well-defined sizes (larger or smaller than the original NPs) and spherical shapes, especially from any initial shape or size, greatly helps to accelerate the use of NPs in various nano-applications. One of the first laser nanotechnologies was developed based on the melting and subsequent spheroidization of NPs. Pulsed laser melting in liquid is a technique that selectively heats raw particles to produce spherical particles of various sizes.

The Barchikowski group have carried out numerous studies of laser ablation and the generation of NPs and their subsequent heating and processing by laser radiation.^171–175 These studies included special topics such as the laser synthesis of germanium submicrometer spheres by picosecond pulsed laser melting in liquids¹⁷¹ and the alloying of NPs by laser ablation of compacted micropowder mixtures.¹⁷² Laser fragmentation of colloidal GNPs was studied with high-intensity nanosecond pulses driven by a single-step fragmentation mechanism.¹⁷³ The sequence of thermal processes of heating–melting–evaporation–condensation is realized when the particle temperature practically reaches the melting and evaporation temperatures. The evaporated atoms and clusters undergo subsequent nucleation growth with the formation of new small particles. The formation of particles from the vapor phase is consecutively influenced by two main phenomena: nucleation (condensation) and particle growth. To understand the results, the energy balance was used. The results of experimental studies were considered and analyzed in reviews that present the results to date.^174,175

The Amendola group has used NP heating to fragment large NPs to produce very small ones.^176–180 Laser fragmentation of colloidal GNPs by laser pulses was studied as a process in which, as a result of laser action on large NPs, many much smaller ones are generated.¹⁷⁶ The average size of GNPs was reduced to a few nanometers by laser processing using various strategies. TEM analysis carried out on the original GNP solution fully confirmed the significant reduction in the NP size. Synthesis of GNPs in a liquid medium by laser ablation to improve size control and productivity was carried out using geometrically confined configurations.¹⁷⁷ A review of SPR in GNPs has been published.¹⁷⁸ A very interesting topic of theoretical and experimental studies is the generation of alloyed NPs, the production of which is either very difficult or impossible by methods other than laser ones. Easy synthesis of nonequilibrium cobalt–silver NPs with magnetic and plasmonic properties by laser ablation in liquid was carried out.¹⁷⁹ The latest developments in the field of plasmonic alloyed NPs were presented, taking into account their synthesis, modelling, properties, and applications.¹⁸⁰

Pulsed laser melting in liquid has emerged as a facile approach to the synthesis of submicrometer spheres for various applications. When melting with a long pulse duration, the energy absorbed by a particle will be dissipated immediately after laser–matter interaction, following a decrease in temperature for tens of nanoseconds, which limits the efficiency of the process. Pulsed laser melting in liquid is a technique that realizes the selective heating of raw particles to produce spherical particles of various sizes including submicrometer particles (SMPs). The heating, melting, and coalescing of small nonspherical NPs to generate large spherical ones under the action of laser radiation have been investigated experimentally by the Koshizaki group.^18,181–185 In this approach, the initial raw NPs dispersed in a liquid are irradiated with a pulsed laser and heated beyond the melting point to generate molten droplets, followed by fusion and quenching to form SMPs. Single-crystalline spherical ZnO particles were formed by pulsed laser irradiation of commercial ZnO NPs in water.¹⁸¹ Spherical gold and iron SMPs can be fabricated by pulsed-laser melting in a liquid using a mixture of gold and iron oxide NPs as initial particles dispersed in ethanol.¹⁸² The size-dependent GNP agglomeration mechanism is applicable for improving the efficiency of growing gold SMPs by laser melting using GNPs obtained by laser ablation in liquids with a wide size distribution. This result confirms that reducing the proportion of GNPs with low agglomeration efficiency in the colloidal solution increases the gold SMP size. The effects of stabilizer concentration on the size of spherical gold SMPs prepared by laser-induced agglomeration and melting of colloidal NPs¹⁸⁴ and the effect of viscosity on the process of formation of spherical SMPs¹⁸⁵ have been studied.

Theoretical studies of laser heating and the interaction of laser pulses by numerical methods based on the equations of fluid mechanics and molecular dynamics have been carried out by Zhigilei et al.^186–189 Numerical simulations of the interaction of a short laser pulse with a GNP surrounded by water and the effect of a liquid environment on the single-pulse generation of laser-induced periodic surface structures and NPs have been carried out.^186,187 A computational model has been developed that can realistically consider many interrelated processes that occur during the fragmentation of NPs by short-pulse laser irradiation.¹⁸⁸ The explosive phase decomposition of an overheated NP and the nucleation and collapse of a nanobubble in a liquid environment lead to two channels for the formation of fragmentation products. Fragmentation mechanisms depending on the energy density deposited by the laser pulse were investigated in atomistic simulation.¹⁸⁹ Two different modes of NP fragmentation were studied, leading to the formation of a large central NP surrounded by smaller satellite fragments.

Note that the absorption of laser radiation by NPs and their heating during laser action are the main and initial processes of all the subsequent processes of melting, evaporation, fragmentation, and ablation of NPs, which are used and will be used more widely in the future in laser micro- and nano-engineering of metal NPs¹⁹⁰ and other nanostructures.¹⁹¹ In this regard, the need for continuous studies of the processes of laser heating of NPs and their cooling after the end of laser exposure is very important and relevant.

VI. CONCLUSION

Reviewed herein were the fundamental processes involved in the laser heating of a single NP or an ensemble thereof by cw and pulsed laser radiation, the energy dissipation of NPs due to heat transfer by the thermal conduction to the environment, and the cooling after completion of the laser action on the NPs. The dependences and values of the temperatures of the NPs and the environment, their time scales, and estimates of laser fluence thresholds for initiation of subsequent PT processes were analyzed. Experimental results of studying the heating of single and ensemble metal NPs by laser pulses were discussed.

An analytical model for describing the heating, heat dissipation, and exchange with the environment of the NPs was presented. Comparison and definite agreement of analytical results with computer and some experimental results for NP heating in the range of pulse durations from cw to femtosecond pulses validated the correctness of the developed analytical model. The presented analytical model gives a quantitatively (in certain time intervals) and qualitatively correct description of the time dependences of the NP temperature T₀ and the outward distribution T(r) and the heating and cooling dynamics of single and ensemble NPs and the environment. The heating of NPs to high temperatures—in some cases exceeding the melting point of the NP material—leads to the necessity of taking into account the dependences of the absorbing and thermal properties of NPs and the environment on temperature. The temperature dependence of the optical absorption factor of metal (gold) NPs can significantly affect their laser heating and other subsequent thermal processes. A decrease in the value of the absorption factor during laser heating of NPs leads to a corresponding increase in the threshold laser fluence, which leads to the achievement of characteristic NP temperatures at the end of the laser pulse and the beginning of various processes. This circumstance must be taken into account when studying the threshold thermal processes of laser–NP interactions, especially in laser nanomedicine, because of the high sensitivity of the results of laser exposure to threshold parameters. Analytical modeling has a number of advantages over computer simulations, because its results are much simpler and more convenient and can be used for direct quantitative description of various experiments based on simple equations. The reviewed analytical models demonstrate the advantages of a complete description of the processes of heating, heat transfer, and cooling for a single NP, an ensemble of NPs, and the medium. They can be useful theoretical tools for describing various NPs and environments and can be used to understand, evaluate, and interpret experimental results.

Nanothermometry methods for NPs under laser heating to determine their temperature dynamics under the action of laser radiation were considered. These include changes in the refractive indices of NP metals and an environment heated by an NP, Raman spectroscopy, and thermochemical transitions in a medium surrounding a heated NP. Characterization of radiation absorption and heating dynamics of NPs using nanothermometry determines a sequence of thermal phenomena that can be used in many applications of heated NPs. It seems that developing methods for nanothermometry of NPs under laser heating with short pulses is the main problem that must be solved for a correct understanding and interpretation of experiments. Of particular interest is the use of laser heating of NPs for laser nanobiomedicine, which requires highly precise laser and NP parameters, taking into account the danger of tissue damage. The next problem could be the use of not monodisperse but polydisperse ensembles of NPs for laser absorption of laser radiation for the controlled heating of tissues.

This review dealt with concepts related to many areas of application of the laser heating of NPs in science and technology, including thermochemical reactions and selective nanophotothermolysis initiated in the environment by laser-heated NPs, emission of thermal radiation by NPs and LII, electron and ion emission of heated NPs, and optothermal chemical catalysis. The proposed models can be used to estimate the parameters of a laser and NPs during laser–NP interactions in various fields of thermal application of laser heating of NPs in PT nanotechnologies, nanoenergy, laser nanomedicine, laser processing of NPs, nonlinear optical diagnostics, etc. In general, this review has presented a fairly complete modern picture of the heating of single and ensemble NPs by laser radiation, the characterization of their processes by nanothermometry methods, and various applications.

ACKNOWLEDGMENTS

The author is deeply grateful to his colleagues L. Astafyeva, A. Chumakov, and A. Smetannikov for their cooperation.

AUTHOR DECLARATIONS

Conflict of Interest

The author has no conflicts to disclose.

DATA AVAILABILITY

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

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