Hot electron and thermal effects in plasmonic photocatalysis

At the beginning of the 20th century, the rise in the world population was depleting the deposits of KNO₃ that constituted the natural supplies of nitrogen-based fertilizers, thus endangering the planet of starvation. This serious threat was prevented by the advent of heterogeneous catalysis and, in particular, by the development of the nitrogen fixation process to ammonia,

Although this process is spontaneous, i.e., the variation of the Gibbs free energy associated to the reaction is negative, it does not proceed at a detectable rate due to the high energy required to break the triple bond in the N₂ molecule. Fritz Haber realized the synthesis of ammonia from its elements in 1909 using an Os-based catalyst, for which he was awarded the Nobel Prize in Chemistry in 1918. In the meantime, Carl Bosch scaled it up to the industrial level (the first plant opened in 1913) by introducing high-pressure chemistry in the catalytic process, for which he received the Nobel Prize in Chemistry in 1931. The process is indeed known as the Haber–Bosch process. However, its large-scale development was possible thanks to Alwin Mittasch, who discovered the possibility of using an Fe-based catalyst for this reaction (still in use today).¹ 

Today, an additional rise in the world population is once more posing a threat to the global supplies of food. To make matters worse, modern society has to face the unprecedented challenge of pollution and climate change. The need for using clean and renewable energy to produce sustainable fuels and chemicals is thus becoming more and more urgent. Solar energy is regarded as the ideal option since the Sun deposits 120 000 TW of radiation on the Earth's surface, several orders of magnitude more than that needed by the whole humanity.² As a consequence, the scientific community has started to investigate the possibility of using solar energy in the field of catalysis. The field of heterogeneous photocatalysis already emerged in the 1950s; nevertheless, it has not reached large-scale application yet mainly due to the limitations of semiconductors employed in this field.^3,4

More recently, scientists have devoted their attention back to metal nanostructures as catalysts, but having the additional feature of exhibiting plasmonic properties, which have found traditional application in surface-enhanced Raman spectroscopy (SERS) for the detection of molecules.⁵ The nascent field of plasmonic photocatalysis aims thus at driving catalytic reactions employing solar light instead of external heating provided by non-renewable sources.^6,7 The possible advantages include lowering the reactor temperatures by localizing the heat only in proximity to the reactive molecules, and increasing the efficiency of catalytic reactions by providing a control on selectivity thanks to peculiar non-thermal effects related to the plasmon resonance of nanoparticles (NPs).^8–11 These ambitious goals, justified by exciting early results in the field, require, though, a deeper understanding of the basic mechanisms involved in the coupling between plasmon decay and the chemical reactions occurring at metal NP surfaces. Specifically, the heating of the metal NPs upon plasmon decay, the transfer of charge carriers from the former to adsorbed molecules, or the local field enhancement may enhance the reaction rates, thus acting synergistically. Nevertheless, only carrier-mediated and local field-enhanced processes offer the possibility of tuning the reaction pathways.^8–10 As a consequence, recent investigations are making an effort to shed more light on the fundamental principles underlying these catalytic processes, with the aim of enabling the realization of efficient and scalable plasmonic photocatalysts.

This tutorial aims first at giving a basic introduction about the field of plasmonic photocatalysis, explaining the differences and similarities with “traditional” catalysis and photocatalysis; second, at describing the basic physical–chemical mechanisms involved in plasmonic nanoparticles in contact with molecules; and third, at discussing examples of plasmonic photocatalysis in colloidal systems and at the solid/gas interphase in solid pellet catalysts through the identification of thermal and non-thermal mechanisms in these two cases. In particular, the case of solid catalysts (in contact with molecular gases) is discussed in more detail because of the greater challenges in discerning the underlying mechanisms as well as due to its relevance in industrial processes. Finally, a summary concerning the main advancements reached in the field of plasmonic photocatalysis and the main open issues to fully distinguish thermal and non-thermal effects is presented. The readers interested in further knowledge in the field and in other aspects that have not been included here are referred to systematic reviews.^{8–10,12–14}

Catalysis is defined as the process by which the rate of a chemical reaction can increase by adding a catalyst, a substance that is not consumed in the reaction. In particular, heterogeneous catalysis (i.e., the catalyst is in a different phase than the reactants, on the contrary to the homogeneous case) has enormous importance in everyday life. Common examples are the Haber–Bosch process for NH₃ production, the Fischer–Tropsch process for the production of hydrocarbons,¹⁵ or the abatement of dangerous gases in the catalytic converter of cars.¹⁶ Figure 1(a) schematically illustrates a reactor for NH₃ synthesis, which operates at high temperatures (400–500 °C) and pressures (150–250 atm) and contains a catalyst bed that is exposed to the gas mixture. At the microscopic level, the reactant molecules bind with surface atoms of the catalyst (chemisorption), thus forming new bonds (dissociative chemisorption), and the new species formed at the surface can move to new sites and react with each other, eventually leading to new molecules that may leave the surface (desorption). These elementary steps are common for all the catalytic reactions. Typical catalytic materials are transition metals such as Pd, Pt, Rh, Co, and Fe, which can be supported on an inert oxide, such as Al₂O₃.¹⁷ 

On the other hand, photocatalysis is a process whereby a chemical reaction is induced by light absorption on a solid material, called a photocatalyst, which is not consumed in the reaction (similarly to a catalyst).^3,4 Figure 1(b) shows this concept in the case of photocatalytic water splitting, which has been extensively investigated by worldwide research: an aqueous suspension of semiconductor nanoparticles is illuminated with solar radiation, and H₂O molecules are decomposed into gaseous H₂ and O₂,

The role of the photocatalyst is that of producing electron–hole pairs upon photoexcitation, with light energy greater than its bandgap (E_g); subsequently, these charge carriers drive the reduction (electrons) and oxidation (holes) half-reactions of water at the surface of the photocatalyst. Some applications of photocatalysis have been developed to the industrial scale, for example, self-cleaning coatings on windows and tiles of buildings, photocatalytic coatings with antibacterial properties, and devices to remove ethylene, preventing early fruit and vegetable maturation.¹⁸ Typical photocatalysts are semiconductor metal oxides, such as TiO₂, Fe₂O₃, ZnO, BiVO₄, and WO₃, and their bandgaps usually range between 2 and 3 eV, meaning that all the light energy lower than E_g is not absorbed.¹⁹ 

Plasmonic photocatalysis is a concept that has been introduced only recently,^8–10 and it is based on the idea of taking advantage of the efficient light absorption of metals NPs in the UV-visible region and on the exploitation of their characteristic localized surface plasmon resonance (LSPR). The latter consists in a resonant collective oscillation of free electrons in response to an external electromagnetic field²⁰ and whose decay leads to potentially useful effects to drive or enhance a catalytic process. Figure 1(c) illustrates the example of ethylene epoxidation reaction on plasmonic Ag NPs supported on Al₂O₃,²¹ 

In this case, the LSPR excitation on plasmonic Ag NPs favors the cleavage of a specific bond in a molecule (such as the O–O bond in this specific example), enabling to drive the desired reaction at lower temperature than in traditional thermal catalysis and, in some cases, providing a better selectivity toward the desired product. Typical plasmonic materials are coinage metals, such as Au, Ag, and Cu, but due to their cost, chemical stability, and scarcity, alternative materials have been proposed, such as Al,²² doped and non-stoichiometric metal oxides,^23,24 and transition metal nitrides (TiN, ZrN, and HfN).^25–27 Traditional catalytic metals, such as Rh or Pd, can also be used as plasmonic catalysts, but they typically exhibit weak and broad plasmonic resonances due to their high optical losses in the visible range. Thus, they can be combined with “good” plasmonic metals forming multi-component catalysts, where the energy harvested by the plasmonic NP is transferred to the catalytic material, which drives the reaction of interest. Typical examples are the so-called antenna–reactor hybrids²⁸ or core–shell systems.^29,30 Finally, it should be noted that the use of plasmonic metals has also been proposed to improve the properties of wide bandgap semiconductor photocatalysts or photoanodes, as a sort of visible-light sensitization. A thorough discussion on such systems can be found in the literature, and it will not be discussed here.^14,31–38

A catalyst essentially lowers the activation energy E_a of a reaction by allowing the formation of intermediate compounds with the reactants, providing an alternate (faster) reaction pathway, without altering the chemical equilibrium of the reaction. The overall mechanism may consist of several intermediate steps: the one with the highest E_a is also the slowest one, and it is called the rate-determining step (RDS). Figure 2 schematically illustrates the potential energy of a system in which the reagents in state A are transformed into the products in state B overcoming the RDS. This is called the potential energy surface (PES), and it is typically represented for simplicity as a 2D function with respect to significant geometrical or vibrational parameters, i.e., the reaction coordinate. In traditional heterogeneous catalysis, the reactor containing the catalyst is typically heated to overcome E_a, because the reaction rate R increases with temperature (T) according to the Arrhenius equation

where A is a reaction-dependent pre-exponential factor, T is the absolute temperature (in K), and k_B is the Boltzmann constant (1.38 ⋅ 10^–23 J K^–1). Heating promotes molecular vibrations of the reactants, thus moving to higher vibrational levels at the ground electronic state. Subsequently, the transformation into the products can take place.

Figure 2 also represents the possible additional reaction pathways provided by a plasmonic photocatalyst under irradiation. In this case, the light energy can provide heat to drive the catalytic reaction along the ground state PES, similar to the conventional case. More interestingly, the plasmon dissipation can excite an electronic transition from the ground state to the excited state of the reactants–catalyst system (A* in Fig. 2), thus moving along a new PES. Such a transition requires an electron (or hole) transfer process upon photon absorption, and it was already discovered by Ertl and co-workers on single crystal metal surfaces.³⁹ This mechanism is referred to as desorption induced by electronic transitions (DIET).⁴⁰ The transient state can undergo the catalytic reaction reaching the products state B* by overcoming the new activation energy E_a*, which may be smaller than the corresponding one in the ground state (as shown in Fig. 2). Moreover, if several possible reaction pathways are available, a different potential energy minimum leading to different products may be found (C* in Fig. 2). This aspect is crucial because it may enable improved product selectivity compared with traditional thermal catalysis. Finally, the product in the excited state decays back to the ground state by back-transferring the electron (or hole) to the plasmonic catalyst (B or D in Fig. 2).

While the strategy of driving the catalytic reaction along an excited state PES is impractical on single crystalline metal surfaces because it requires high-intensity laser pulses, it is much more convenient by exciting plasmonic NPs under continuous wave illumination, thus promoting a substantial number of excited charge carriers upon plasmon decay.^9,10 Therefore, Sec. III describes the basic physical principles of plasmon oscillation and the most relevant decay mechanisms in terms of their application to catalytic reactions, i.e., hot carrier generation/injection and thermal effects.

The optical properties of bulk conductive materials can be generally described by the Drude–Lorentz model for the complex relative permittivity or dielectric function,^41,42

where $ε1(ω)$ and $ε2(ω)$ are the real and imaginary parts of the dielectric function, respectively, and $ε∞$ is a constant $(ε∞>1)$⁠. The Drude term is characterized by the plasma frequency/energy,

where $ℏ$ is the reduced Planck’s constant, n is the number density of conduction electrons, e is the elementary charge, $ε0$ is the vacuum permittivity, and m* is the electron effective mass. The Drude oscillator accounts for the intraband transitions, i.e., electron excitations from occupied states (below the Fermi level) to unoccupied states (above the Fermi level) within the same band upon photon absorption. In correspondence of the plasma frequency $ωp$⁠, electrons longitudinally oscillate in a collective motion, termed volume plasmon, with a damping factor $γ∞=1/τD$⁠, where $τD$ is the relaxation time (fs). On the other hand, one or more Lorentz oscillators account for interband transitions, i.e., electron excitations occurring between two different bands upon photon absorption. Each jth Lorentz term is described by the energy position $ℏω0,j$⁠, the strength $fj$⁠, and the damping factor $Υj$⁠.

To take into account the nm-sized dimension of the material, i.e., a NP with radius R_NP, the dielectric function can be re-written as²⁰ 

where the size-dependent damping factor additionally includes a surface scattering term,

with Λ being a phenomenological constant and $vF$ the Fermi velocity.

Experimental data on the dielectric functions of noble metals (Au, Ag, and Cu) have been available for decades.⁴³ Nowadays, the dielectric function is typically retrieved by spectroscopic ellipsometry.^44,45 The latter can also be performed during thermal treatments (i.e., in situ spectroscopic ellipsometry), providing valuable information on the optical behavior of plasmonic materials at temperatures as high as those employed for catalytic reactions.^46–48 The measured data, then, are usually fitted using a proper software by the Drude–Lorentz model or alternative ones depending on the material. On the other hand, the theoretical modeling of the dielectric functions is still an active area of research for both thin films and nanoparticles, especially for materials with strong interband transitions in the UV-visible range (such as Au) or for alloys.^134,135 For example, a library of dielectric functions calculated by the density functional theory (DFT) of several binary alloys of common plasmonic materials (such as Au–Cu or Ag–Au) has been recently reported.⁴⁹ 

The knowledge of the dielectric function allows us to predict the conditions for occurrence of surface plasmons, i.e., collective electron oscillation in metal structures in response to the incoming electromagnetic field. Surface plasmons can be classified in surface plasmon polaritons (SPPs), propagating plasmons along the interface between a metal and a dielectric, and localized surface plasmons (LSPs), non-propagating plasmons in nanostructures, which are more relevant in the field of plasmonic photocatalysis. Considering for simplicity a small spherical NP (with $RNP≪λ$⁠, i.e., quasi-static approximation), the polarizability $α$ exhibits a resonance when²⁰ 

where $εm$ is the dielectric permittivity of the medium. A LSPR is thus expected when $ε1(ω)≈2εm$ and $ε2≈0$⁠, which produces a sharp peak in the extinction cross section,

where $σabs$ and $σscat$ are the absorption and scattering cross sections, respectively. In this simple approximation, the LSPR occurs at the frequency

The quasi-static approximation, however, becomes increasingly inaccurate by increasing the NP dimension; thus, the extinction cross section for spherical NPs of arbitrary size can be computed by the Mie theory.⁵⁰ For example, Fig. 3(a) shows the extinction cross section of some common plasmonic materials, computed as isolated 50 nm-sized NP in air, and compared to the standard AM 1.5G solar spectrum. Ag exhibits a very sharp peak in the UV region, Au and TiN in the visible region (around 550 nm), and Al in the NIR region. The Mie theory also predicts the size dependence of the resonant wavelength, i.e., a redshift by increasing the size [Fig. 3(b)].⁵¹ On the other hand, a similar effect can be obtained by incapsulating the nanostructure in a medium with high dielectric constant, as evidenced by the simple quasi-static approximation [Eq. (11)]. To take into account different shapes of NPs, instead, finite element modeling (FEM) or finite-difference time-domain (FDTD) methods can be employed, which also allow us to compute the electromagnetic field around the nanostructure.⁵² For example, Fig. 3(c) shows that by engineering the shape of Au nanostructures into the so-called “nanostars,”^53–55 it is possible to tune the LSPR peak in the red–NIR region and, consequently, the spectral dependence of hot electron generation.⁵³ The latter is promoted by the stronger electromagnetic field enhancement at the spikes of nanostars as compared, for example, with spheres and nanorods (NRs).⁵³ Moreover, the injection of non-thermal electrons from Au nanostars to a TiO₂ shell was reported,⁵⁴ which is highly desirable to exploit such carriers for chemical reactions. As a consequence, such a high degree of tunability allows the design of optimal plasmonic nanostructures based on the specific spectral region of interest.

Figures 3(d)–3(g) give more insights into the intraband and interband transitions that in general occur upon photoexcitation in metals (either surfaces or nanostructures).⁵⁷ Interband transitions [Fig. 3(d)] involve an electron excitation from a filled state (below the Fermi level, E_F) in the d band to an empty state (above E_F) in the s band without changing the momentum (k₁ = k₂) as a consequence of the Fermi golden rule. The resulting excited electrons, however, typically have a slightly higher energy than E_F. Charge carriers with higher energies, useful in terms of catalytic reactions, can be excited via intraband transitions, i.e., from a filled state to an empty state in the same band, i.e., the s band, which require a change in momentum (from k₁ to k₂). The additional momentum can be provided by a lattice phonon [Fig. 3(e)], by a reciprocal lattice vector (electron–electron assisted transition, which generates two electron–hole pairs, not shown), or is not required due to the breaking of the momentum conservation rule at the metal surface [surface scattering or Landau damping, Fig. 3(f)]. A different pathway has been further proposed in the case of a metal–adsorbate system [Fig. 3(g)]: a direct excitation mechanism from a filled state in the s band of the metal to an empty state in the hybridized levels by conserving the momentum k₁.^59–61 The distribution of the excited carriers in the metal is thus affected by the prevalence of either interband or intraband transitions and can be computed using different degrees of approximation.^58,62–66 For example, Fig. 3(h) shows the energy distributions of such carriers upon decay of SPPs in common plasmonic metals from ab initio calculations using a relativistic density functional theory (DFT + U) approach with a Wannier representation.⁵⁸ According to this model, the SPP mainly decays via intraband excitations in Ag, producing hot electrons and holes with relatively equal energies, thus yielding an almost flat distribution. On the contrary, in Al, Au, and Cu, the contribution of interband transitions is particularly relevant. Such transitions dominate at high energy (small wavelengths) and are thus strongly material-dependent. For Au and Cu, in particular, an asymmetric distribution of charge carriers can be observed, since low-energy electrons and high-energy holes are produced. For Al, conversely, a relatively flat distribution of hot electrons and holes was found. The distributions of hot carriers excited by SPPs have been experimentally measured only recently for the first time, showing the predominance of Landau damping [Fig. 3(f)] as an intraband excitation mechanism in thin Au films; this led to a symmetric energy distribution of hot electrons and hot holes, contrarily to the calculated distributions in Fig. 3(h).⁶⁷ 

We now discuss the time-evolution of the LSPR decay in a plasmonic metal NP–adsorbate system. Figure 4 illustrates the density of states for a metal NP (according to the Fermi–Dirac statistics) and for a molecule adsorbed on its surface. The excitation of the LSPR produces strong electromagnetic fields around the NP [Fig. 4(a)], which can couple with the electronic degrees of freedom of the adsorbate. In other words, the local field enhancement can directly affect the adsorbate concomitantly with the LSPR oscillation.⁶⁸ Plasmon decay occurs in the range of tens of fs^69,70 either radiatively, by re-emission of photons (scattering, not discussed here), or non-radiatively. The former pathway is favored for relatively large NPs (i.e., >50 nm), since $σscat∝R6$⁠, while the latter for smaller NPs, since $σabs∝R3$⁠.⁵¹ Non-radiative decay produces hot electrons and holes with a non-thermal distribution [Fig. 4(b1)], which then relax to a thermal (Fermi–Dirac) distribution via electron–electron scattering within 100 fs–1 ps [Fig. 4(c1)].^71–76 The typical energy of such carriers is about ±1 eV around the Fermi level, corresponding to an electronic temperature (T_e) of thousands of K, which is not attainable by conventional heating.⁷⁷ If this energy is not sufficient to reach the adsorbate unoccupied states, excited carriers further relax via electron–phonon scattering in the range of 1–10 ps, leading to a heating of the lattice [Fig. 4(d)].^75,76 Eventually, heat is dissipated toward the surrounding medium in 100 ps–10 ns proportionally to ɛ₂(ω)|E_in|², where E_in is the electric field inside the material.^78,79 However, if the energy of the hot carriers matches the empty levels of the adsorbate, the so-called indirect transfer can occur [Fig. 4(c2)], which must be sufficiently fast to compete with electron–electron and electron–phonon scattering. Since most of the hot carriers have energy close to the Fermi level, the charge transfer will mostly occur toward adsorbate states close to E_F. Recently, an alternative pathway has been shown, also known as direct transfer, which implies the generation of hot electrons (holes) in the unoccupied (occupied) orbitals of the adsorbate [Fig. 4(b2)].⁵⁹ This process is also known as chemical interface damping (CID) and requires a strong hybridization between the adsorbate and the surface of the plasmonic NP.^80,81 The direct transfer has also been reported on plasmonic/semiconductor composites, such as CdSe nanorods functionalized with Au NPs.⁸² The nomenclature DIET introduced in Sec. I does not explicitly discern between the direct and the indirect electron transfer processes since it was introduced before the discovery of the former.⁴⁰ Apart from the specific electron transfer mechanism, the nuclear motion of the adsorbate evolves then on the excited state PES (Sec. II A). On longer time scales (1 ps–1 ns), the adsorbate reacts and the excess charge is transferred back from the adsorbate to the plasmonic NP (not shown).

The simultaneous occurrence of electric field enhancements, hot electron transfer and photothermal heating effects under typical experimental conditions, i.e., under CW illumination, implies that suitable theoretical and/or experimental procedures must be employed to correctly distinguish these mechanisms. Typically, the burden of proof resides in showing an actual involvement of hot carriers, which means that thermal effects should be either excluded or clearly quantified.

The photothermal effects arising in a system of plasmonic NPs under illumination can be numerically evaluated as follows. The power absorbed by a NP under irradiation can be evaluated as⁸³ 

where q(r) is the heat power density inside the NP, V_NP is the NP volume, and I is the irradiance of the incident radiation. In case of a plane wave, the latter reads

where n_m is the refractive index of the surrounding medium (considered a real number), c₀ is the speed of light, and E(r) is the electric field. By considering that heat originates from the Joule effect, it is possible to show that

Equation (14) clearly shows that the heat power density in the NP is proportional to the imaginary part (ɛ₂) of the dielectric function and to the electric field inside the plasmonic material. At the steady state, the heat generated by the irradiated NP propagates in the surrounding medium by conduction, convection, and radiation,⁸⁴ 

where $κm$ is the thermal conductivity of the medium, A is the area normal to the direction of heat transfer, dT/dx is the temperature gradient, h is the heat transfer coefficient for convection, T_s is the surface temperature of the NP, T_m is the temperature of the surrounding medium, $ε(λ,T)$ is the emissivity of the hot material, and σ is the Stefan–Boltzmann constant (σ = 5.67 ⋅ 10^–8 W m^–2 K^–4). By using the radial coordinate r > R_NP, where R_NP is the nanoparticle radius, and solving Eq. (15), the temperature distribution outside of the NP can be found as^83,85–87

A similar expression can be found for particles of different geometries other than spherical.⁸⁸ This represents a local contribution due to the heating of the NP itself, and it is illustrated in Fig. 5(a), which shows that the temperature in a single Au NP in water is uniform and it rises of only few K compared to the liquid.

In a system of N nanoparticles, the contribution of all the other N − 1 ones must be taken into account,⁸⁸ 

where the subscript j refers to the NP under consideration in the position r_j and k to all the other NPs, located at r_k. Both Eqs. (16) and (17) show that the thermal conductivity of the medium $κm$ affects the temperature increase at the surface of the nanoparticle, i.e., the temperature will be lower for particles suspended in liquids than at the interface with a gas. In the limit of a very large number of NPs, the general expression of the total temperature increase reads^85,87

where ΔT(R_NP) is the single-particle contribution evaluated by Eq. (16) with r = R_NP, d is the average inter-particle distance and m is the dimensionality of the system. This expression is valid in the 2D case (m = 2) and in the 3D case (m = 3). Equation (18) shows that the temperature increase associated with collective heating effects is typically orders of magnitude higher than the local one, due to the proportionality factor N^1/2 (in the 2D case) and N^2/3 (in the 3D case). Figure 5(b), for example, shows the temperature variation in the center of a 4 × 4 array of Au NPs on a polymeric surface at the interface with water: even for such a low number of particles, the temperature increase in correspondence of the LSPR wavelength associated with collective effects is clearly higher than that for the single-particle case. Figure 5(c) shows instead the situation for an infinite square array illuminated by a 2 μm beam monochromatic light (532 nm); in this case, the temperature increase associated with collective effects [$ΔT0ext$⁠, Eq. (17)] is ∼20 K, while the single-particle contribution [$ΔT0s$⁠, Eq. (16)] is lower than 2 K. The opposite situation occurs in Fig. 5(d): as the case depicted in Fig. 5(b), the number of NPs is very low (5 × 5 array), but due to their high inter-particle distance and very small diameter, they heat up mostly as isolated particles.

The discussion above has great importance in terms of the typical laboratory experiments of plasmon-assisted catalysis. In the case of plasmonic photocatalysis dispersed in colloidal suspension, no localized thermal “hot spots” can be found around the single NPs due to the high value of the thermal conductivity of the medium κ_m (∼0.6 W m^–1 K^–1 for water)⁸⁴ as well as of the heat transfer coefficient h, especially under stirring (10²–10³ W m^–2 K^–1 for free convection and 500–10⁴ W m^–2 K^–1 for forced convection for water).⁸⁴ In addition, the temperature of the liquid medium is limited by evaporation, which means that the radiative contribution to heat transfer in Eq. (15) can be neglected. Equation (16) thus leads to gross underestimations (by orders of magnitude) of the actual temperature increase in the system. Rather, collective effects give rise to a homogeneous temperature rise,^85,89,90 which can be evaluated by Eq. (18) (with m = 3) and can also be experimentally measured with a thermocouple placed in the liquid, T_m, which approximates well the surface temperature of NPs, T_s, i.e., T_m = T_s.

In the case of solid catalysts for gas-phase reactions, the situation is more complex because plasmonic NPs are typically dispersed in a dielectric matrix (such as SiO₂ or Al₂O₃), forming a porous powdered solid, which entirely absorbs the incoming radiation. In addition, the heat exchange with the gas is limited due to the lower value of κ_m. As a consequence, a substantial heating of the sample is expected, which must be accurately measured taking into account also the radiative loss term in Eq. (15). In particular, the emissivity of the material can be retrieved by measuring the optical absorbance in the IR region $α(λ,T)$ by Fourier transform infrared spectroscopy (FTIR) and applying Kirchhoff's law of thermal radiation,

Ideally, the measurement should be done at the same temperature as that of the plasmonic photocatalysis experiments due to the dependence on T of the emissivity. A precise knowledge of $ε(λ,T)$ then allows a reliable measurement of the surface temperature of the sample by non-contact techniques, such as by an IR pyrometer or a thermal camera. However, the use of thermocouples embedded in the catalyst bed is also suggested due to the presence of thermal gradients along the thickness of the material (see Sec. VI).

From the experimental point of view, plasmonic photocatalysis is claimed when an enhancement of the reaction rate or, accordingly, of the turnover frequency (TOF), is observed. The TOF is defined as

where R is the reaction rate, t is the time, N_A is the Avogadro constant, and n_cat is the number of moles of the catalyst. A higher TOF or reaction rate under irradiation with light intensity H, thus, can translate in a lower E_a compared to the thermal process [Fig. 6(a)]. This claim can be justified only if the temperature measured in the illuminated system can be accurately evaluated and reproduced in the dark experiment. By performing catalytic runs under illumination at different light intensities and in the dark at different temperatures (generated under a specific light intensity), the reaction rates can be plot using the Arrhenius equation, thus enabling the determination of E_a both in the dark and under illumination conditions.^91–93 

In parallel to the numerical evaluation of photothermal heating effects discussed in Sec. IV A, some experimental procedures allow us to highlight the involvement of electron-driven processes.^94,95

A first strategy consists in evaluating the difference between the overall TOF/reaction rate under light intensity H, TOF_photo(H), and that in the dark at the same temperature as that measured under H, TOF_therm(H), thus extracting the contribution attributed to hot electrons,

A second approach consists in measuring the reaction rate under different wavelengths by keeping constant the light intensity and comparing it with the optical absorption spectrum of the plasmonic catalyst [Fig. 6(b)]. If these quantities follow the same trend, heating effects alone are not sufficient, but also electric field enhancements and/or hot electron transfer must be considered.

Third, the observation of a linear dependence of the reaction rate on the photon flux has been typically ascribed to electron-driven processes [Fig. 6(c)].^21,96 A super-linear dependence due to multi-photon absorption may be instead observed under high power⁹⁶ or fs-pulsed laser illumination,⁹⁷ while an Arrhenius-like (exponential) dependence [Eq. (4)] would imply a photothermal process [Fig. 6(d)]. However, if the light power is varied across a limited experimental window, an apparently linear trend may occur also for a photothermal process. In other words, the light power should be varied to achieve a change in the reaction rate of orders of magnitude, thus allowing a reliable fit of the data excluding an Arrhenius dependence. This may not always be feasible due to instrumental limitations and due to the risk of damaging the sample under high irradiation conditions.

Finally, a conclusive evidence of hot electron transfer can be obtained by studying the kinetic isotope effect (KIE). This consists in the change of the reaction rate when isotopically substituted molecules are used instead of the “regular” ones, i.e., by replacing ¹⁶O with ¹⁸O or ¹H with ²H (deuterium). The reaction rate using a light isotope (R_light or TOF_light) is higher than that using the heavy one (R_heavy or TOF_heavy); thus, the KIE is defined as

In the case of hot carrier-driven processes, higher KIEs have been reported with respect to phonon-driven ones.^39,98 As a consequence, a higher KIE measured under illumination (KIE_photo) with respect to the standard value in the dark (KIE_dark) would confirm the active involvement of hot carriers rather than solely thermal effects,

It should be noted that further experimental techniques for discriminating between thermal and hot electron-driven effects are available, such as thermal microscopy techniques,⁷⁹ anti-Stokes photoluminescence (PL) emission,⁹⁹ and dark-field microscopy combined with an electrochemical setup to study reactions at the single-particle level.¹⁰⁰ Such techniques are, however, more advanced and thus their description goes beyond the scope of this tutorial.

The different approaches presented above have been employed by several research groups focusing on plasmonic catalysis to show the involvement of hot electrons and to exploit their effect to activate unconventional pathways in industrially relevant examples. Some examples will be thus discussed below, classified into chemical reactions occurring in the liquid phase for colloidal systems (Sec. V) and at the solid/gas interphase for solid pellet catalysts (Sec. VI) according to their strongly different thermal constraints.

Plasmonic photocatalysis experiments in colloidal systems typically involve a transparent reactor enclosing an aqueous suspension of plasmonic NPs or nanostructures illuminated by a CW source, with a gas outlet line going through a septum preventing contaminations from the atmosphere, and a thermocouple measuring the temperature of the liquid T_m [Fig. 7(a)]. In these conditions, the surface temperature T_s of the NPs is also known, i.e., T_m = T_s (Sec. IV A), and the issue of correctly evaluating photothermal heating effects can be conveniently accounted for by performing a control experiment.¹⁰¹ The latter consists in performing the same reaction without light irradiation while heating the liquid at the same temperature T_m measured under illumination [Fig. 7(b)]. As a consequence, non-thermal plasmonic effects can be assessed following the procedures described in Sec. IV B. Although typical catalytic reactions at the industrial level occur in the gas phase in contact with the surface of the catalyst (Sec. II), other processes in the liquid phase (e.g., H₂ production, CO₂ photoreduction, biomass valorization, etc.) are emerging and have a great relevance in the quest for reaching a sustainable energy system. Experiments in the liquid phase also play an important role from a fundamental point of view to gain knowledge on promising plasmonic photocatalysts for applications to gas-phase reactions.

Some groups have investigated the role of thermal and hot electron effects by LSPR decay to selectively drive dehydrogenation reactions. These hold a great importance in the technological development of proton-exchange membrane or polymer electrolyte membrane fuel cells (PEMFCs), which require an on demand flow of pure H₂ without CO contaminations. Zheng et al.¹⁰² studied the photocatalytic dehydrogenation of formic acid (HCOOH),¹⁰³ 

which competes with the dehydration reaction,

In particular, they observed the dehydrogenation reaction [Eq. (25)] at temperatures as low as 5 °C by employing antenna–reactor Au nanorods (NRs)-Pd, with Pd covering the tips of the rods [Fig. 8(a)].¹⁰² While the purely thermocatalytic reaction (i.e., under dark) at 5 °C was greatly suppressed, upon light irradiation, the H₂ generation increased to values comparable to those in dark at 40 °C. To demonstrate the role of plasmonically generated carriers, the authors compared the H₂ evolution action spectrum to the extinction spectrum of Pd-tipped Au NRs, showing a very good agreement between the two trends [Fig. 8(b)]. Moreover, the decrease of photoluminescence (PL) signal for Pd-tipped Au NRs compared to bare Au NRs indicated an effective charge transfer from Au to Pd. The authors also considered that heat generation mostly occurred in the center of NRs; as a consequence, the higher activity of Pd-tipped Au NRs compared to fully Pd-covered Au NRs further confirmed the prevalence of hot carrier transfer rather than the thermoplasmonic effect.

Rej et al.⁹³ instead, considered the dehydrogenation of ammonia borane (NH₃BH₃), an intriguing reaction that can be triggered on demand to release H₂ according to¹⁰⁴ 

The authors employed antenna–reactor TiN–Pt nanohybrids, made of TiN nanocubes (∼41 nm size) and Pt nanocrystals (∼3 nm) attached on the nanocubes to synergistically exploit hot electron injection and thermal effects [Fig. 8(c)]. The so-obtained TiN–Pt nanohybrids were first tested in photocatalytic experiments under monochromatic light with low intensity (2 mW cm^–2), to avoid any photothermal contribution. In such conditions, the apparent quantum yield (AQY, number of molecules generated per photon) followed the absorption spectrum trend [Fig. 8(d)], demonstrating that the only mechanism involved was hot electron mediated. In contrast, when NH₃BH₃ dehydrogenation experiments were performed under solar simulated light from 1 to 10 Suns [Fig. 8(e)], both photothermal and hot electron effects were observed. In this case, a non-linear increase of TOF_photo [Eq. (21)] by increasing the light intensity was found, but the relative contribution of TOF_therm decreased with the intensity: as a consequence, the hot electron effect was increasingly relevant at higher light intensity. This is also illustrated by the calculation of the AQYs [Fig. 8(f)]: the hot electron contribution ranged from 2% (with a total AQY of ∼9%) at 1 Sun to 4% (with a total AQY of ∼7%) at 10 Suns illumination. Furthermore, it was hypothesized that the rate-determining step in the overall mechanism was the rupture of the O–H bond of an adsorbed water molecule,

where * indicates a molecule adsorbed at the surface of the catalyst. To confirm that, KIE experiments with deuterated water were performed, and they showed a larger KIE under 8 Suns illumination (5.57) than that obtained in the dark (5.10). In addition, a decrease of E_a for the reaction in Eq. (28) from 0.8 eV in the dark to 0.5 eV under light illumination was found. All these observations supported the claimed mechanism of hot electron injection from TiN nanocubes to Pt nanocrystals, which then catalyze the O–H bond breaking of adsorbed water, leading then to the subsequent steps of the reaction.⁹³ 

Other groups employed photoelectrochemical techniques to distinguish thermal from non-thermal effects. A photoelectrochemical setup, indeed, allowed the discovery of the hot electron injection mechanism for the Au/TiO₂ system in the pioneering work by Tian and Tatsuma, who excluded any role of thermal effects due to the relatively high Schottky barrier (∼1 eV) between Au and TiO₂.¹⁰⁵ More recently, Zhan et al. prepared a plasmonic electrode made of a bowtie Au array by lithographic methods [Fig. 9(a)] and tested it in a three-electrode cell at neutral pH (0.2M Na₂SO₄) under visible-light irradiation (λ > 420 nm).¹⁰⁶ First, such a plasmonic electrode could work either as a photoanode or a photocathode, contrarily to conventional semiconductor-based photoelectrodes. In addition, by performing chronoamperometry measurements at different applied potentials, the authors found two main components in the photocurrent [Fig. 9(b)]: a rapid response current (RRC, 0.05 s) and a slow response current (SRC, 10 s). The RRC exhibited a super-linear dependence on the incident power, while the SRC a linear one [Fig. 9(c)]; moreover, the RRC as a function of the incident wavelength showed a good agreement with the extinction spectrum of the plasmonic electrode, on the contrary of the SRC [Fig. 9(d)]. As a consequence, the authors attributed the RRC to the hot electron transfer process, which is maximum in correspondence of the LSPR peak, and the SRC to the thermal effects, which are stronger at low wavelengths where interband transitions take place. However, attribution of the super-linear dependence of the RRC to electron transfer effects is in contrast with previous studies on plasmonic photocatalysis showing a linear increase of the reaction rate vs incident power.^21,96

A photoelectrochemical approach was also reported by Rodio et al. by employing an Au NPs/ITO (In-doped SnO₂) electrode in hydroxide (OH^–) adsorption and glucose (C₆H₁₂O₆) oxidation experiments.¹⁰⁷ In alkaline electrolyte, OH^– ions can be adsorbed at the surface of Au and those species can further promote glucose oxidation to gluconic acid:

After determining the potential for this reaction (+0.3 V vs Ag/Ag⁺), the authors evaluated the photocurrent (I_ph = I_light − I_dark) spectra both with and without glucose in the electrolyte at +0.3 V, finding a maximum in correspondence of the LSPR resonance [Fig. 9(e)]. However, the authors pointed out that the photocurrent should be normalized by the absorbed power (I_ph/P_abs) in order to clearly distinguish the underlying mechanism. In particular, I_ph/P_abs showed the same peak as I_ph [Fig. 9(e)], which is a strong indication of transfer of non-thermalized hot carriers. On the other hand, a flat trend of I_ph/P_abs vs wavelength would suggest a main role of thermal effects or of transfer of thermalized electrons, while a monotonic increase of I_ph/P_abs vs wavelength would suggest an electric field enhancement effect. The linear trend of I_ph vs P_abs for different excitation wavelengths [Fig. 9(f)] also indicated non-thermal effects, contrarily to the conclusion provided by Zhan et al.¹⁰⁶ [Fig. 9(c)] and accordingly to the procedure reported in Sec. IV B.

Jain and co-workers employed instead a different strategy: they reported plasmon-driven redox reactions produced by carrier extraction from colloidal polyvynilpyrrolidone (PVP)-coated Au NPs, thus not feasible by solely thermal effects. In particular, multi-electron transfer from Au NPs to adsorbed molecules was reported under sufficiently intense light irradiation in the presence of various alcohols as hole scavengers. For example, Au NPs in the presence of isopropanol (IPA) were employed to reduce CO₂ into methane (CH₄) and propane (C₂H₆) under laser light irradiation [Fig. 10(a)].¹⁰⁸ CO₂ reduction is a hot topic in the current research due to its potentiality of sustainably producing hydrocarbons while reversing greenhouse gas emissions (i.e., zero or negative carbon footprint process).¹⁰⁹ By using Au as an electrocatalyst, however, CO and H₂ are typically obtained, while only Cu is able to further reduce CO into CH₄ and other hydrocarbons.¹¹⁰ Yu et al.¹⁰⁸ however, observed CH₄ production at 488 and 532 nm irradiation with a reaction rate increasing with the light intensity. Moreover, C₂H₆ was evolved under 488 nm irradiation with a threshold light intensity of 300 mW cm^–2. Under light irradiation in the presence of a hole scavenger, indeed, a build-up of electron population in Au NPs occurs, leading to an increase of the Fermi level with respect to the dark conditions [Fig. 10(b)]. As a consequence, hot electrons have sufficiently high energy to be transferred to the LUMO of CO₂ molecules adsorbed on Au NPs surface. At the same time, photogenerated holes are extracted by the hole scavenger. At sufficiently high light intensity, the electron–hole generation in Au NPs is fast enough to enable a multi-electron transfer process, leading to an abrupt increase in the reaction rate after the threshold light intensity [Fig. 10(a)]. In such conditions, two CO₂ molecules are simultaneously adsorbed on a single Au NP and reduced to the intermediate CO₂^•– (having the high energetic cost of 1.9 eV), which is the rate-determining step [Fig. 10(c)]. C–C coupling leading to C₂H₆ is then possible under high electron transfer rates only under high intensity 488 nm light, which generates relatively long-lived (1 ps) separated charge carriers by interband transitions.

Another example reported by the same group consisted in the transition from one-electron to two-electron transfer in the reduction of [Fe(CN)₆]^3– (ferricyanide) to [Fe(CN)₆]^4– (ferrocyanide) with Au NPs under laser light irradiation [Fig. 10(d)].¹¹¹ Hot electrons had sufficiently high energy to drive the reduction reaction, while hot holes drove the slow water oxidation in the absence of ethanol,

As a consequence, by increasing the laser light power, a saturation in the reaction rate occurred [Fig. 10(d)]. On the contrary, by employing ethanol (C₂H₅OH) or other alcohols, an abrupt increase in the reaction rate for high laser powers was observed thanks to the fast hole scavenging [Fig. 10(d)]. This was also related to the fact that ethanol has a more favorable oxidation potential than water (0.22 V vs SHE instead of 1.23 V vs SHE). In particular, a two-electron transfer process occurred, where hot electrons reduced [Fe(CN)₆]^3– to [Fe(CN)₆]^4– and hot holes reduced C₂H₅OH to C₂H₅O^• (ethoxy radical) and, subsequently, to CH₃CHO (acetaldehyde):

Moreover, the action spectrum for the reaction did not follow the LSPR resonance, but the rate increased by decreasing the irradiation wavelength [Fig. 10(e)], somehow similarly to traditional photocatalysis experiments with semiconductors. This effect was attributed to the longer lifetime of hot charge carriers produced by interband transitions (under 488 nm irradiation). Finally, the production of [Fe(CN)₆]^4– was observed also in the dark but with one order of magnitude lower rate, thus pointing out the main role of hot electron transfer.

Despite the intriguing results on multi-electron transfer processes, it has been argued that the thermodynamic efficiency of these reactions should be carefully assessed since they imply the use of hole scavengers.⁸ This has been recently reported again by Jain and co-workers for CO₂ reduction assisted by imidazolium salts^112,113 and, earlier, for water splitting by Moskovits and co-workers by employing Au nanorod photosynthetic devices.^114,115 In the water splitting community, for example, the solar-to-hydrogen (STH) efficiency is defined in the absence of hole or electron scavengers, because the only reagent should be water and the only products should be hydrogen and oxygen according to Eq. (2).¹¹⁶ Thus, an ultimate aim of plasmonic photocatalysis in the liquid phase consists in exploiting the input energy of solar radiation to drive a thermodynamically uphill reaction, i.e., photosynthetic processes, like CO₂ reduction or water splitting without the assistance of any additional scavenger in solution.

Plasmonic photocatalysis experiments for gas-phase reactions are typically performed using powdered catalysts in pellets, as in the case of conventional heterogeneous catalysis, but the reactor design is more complex (Fig. 11). A mm-thick porous pellet is enclosed in a cup and a mesh and contained in a small vacuum cell. The latter is equipped with a viewport allowing light irradiation (by a laser, a LED, or a solar simulator) and, optionally, temperature reading by an IR pyrometer or a thermal camera. Reactive and carrier gases are flown through the porous catalyst bed, and the reaction is monitored by gas chromatography (GC) or by a mass spectrometer. A critical point is the temperature measurement: temperature gradients typically occur along the thickness z of the catalyst, such that, for the same average temperature T_e, the top temperature will be higher than the bottom under illumination without external heating, while the opposite will occur in the dark under external heating. For this reason, not only the default thermocouple controlling the heater is necessary (T₀) but also additional thermocouples at the bottom (T₁) and at the surface (T₂) of the catalyst (the latter should not be directly exposed to light to prevent self-heating) should be included in the experimental setup. Additionally, non-contact measurement by IR pyrometer or thermal camera can give reliable information on the surface temperature of the catalyst provided the emissivity of the sample is known (Sec. IV A). Nevertheless, the opposite sign of thermal gradients generally prevents an exact replica in the dark of the plasmonic catalysis experiment under irradiation and require more complex control experiments, contrarily to the case of colloidal suspensions (Sec. V), as discussed in the following.

The first examples of plasmonic photocatalysis on solid systems were reported by Linic and co-workers, who employed plasmonic Ag nanocubes on an Al₂O₃ support for the ethylene epoxidation reaction [Eq. (3)],^21,96 followed other reports on H₂ dissociation.^117,118 These reports triggered the interest of the scientific community, and various groups addressed the possibility of tuning the product selectivity by the action of plasmon excitation, which represents one of (if not) the critical advantages for the large-scale exploitation of plasmonic photocatalysis.

The epoxidation of propylene to propylene oxide (PO), for example,

is performed industrially at ∼400–500 K with Cu-based catalysts. However, in such conditions, the surface of Cu is oxidized and exhibits a low selectivity to PO, while other products are observed, such as acrolein (C₃H₄O) and CO₂. Linic and co-workers were able to tune the selectivity of ∼40 nm Cu NPs supported on SiO₂ from ∼20% in the dark to ∼50% under light irradiation with intensities higher than 550 mW cm^–2 at 473 K [Fig. 12(a)].¹¹⁹ At this threshold value, on the other hand, the reaction rate exhibited a net drop, but then increased again by further increasing the light intensity, while the selectivity slightly decreased. In addition, the selectivity at controlled reaction rate for the thermal process (in the dark) was systematically lower than that for the photothermal process under 550 mW cm^–2 light irradiation [Fig. 12(b)]. The increase in selectivity was ascribed to the reduction of the surface oxide layer (Cu₂O) to metallic Cu at light intensities >550 mW cm^–2 mediated by hot electron effects. In particular, the decay of the LSPR in the Cu core could excite hot electrons toward the conduction band of the oxide shell, thus weakening the Cu–O bond, leading to its reduction. A purely thermal mechanism was instead excluded, because no selectivity threshold was observed by increasing the catalyst temperature in the dark, contrarily to Fig. 12(a).

In another case study, Halas and co-workers employed Al nanocrystals decorated with small Pd islands realizing antenna–reactor Al–Pd hybrids for the dissociation of H₂ and for the selective hydrogenation of acetylene to ethylene,²⁸ 

This reaction is important for polyethylene production and the further hydrogenation of ethylene to ethane must be avoided,¹²⁰ 

By irradiating the Al–Pd catalyst under white light with increasing light intensity, an increase of selectivity to ethylene was found, with a C₂H₄/C₂H₆ ratio rising from ∼7 to ∼37. On the other hand, by increasing the temperature in dark conditions, the selectivity decreased [Fig. 12(c)]. These observations were explained by the rapid desorption of H₂ induced by hot electrons generated by the antenna mode on Pd, the latter measured by electron energy loss spectroscopy and calculated by FDTD simulations [Fig. 12(d)]. The depletion of H₂ on the surface of Pd thus prevented the additional hydrogenation of ethylene to ethane.

Multi-component plasmonic photocatalysts were also proposed by Linic and co-workers, who reported 75 nm-Ag nanocubes covered by 1 nm-Pt shell to exploit the direct excitation of electrons after the LSPR decay in Ag to Pt to catalyze the preferential CO oxidation in excess of H₂ (PROX),²⁹ 

which competes with the combustion of hydrogen,

and which is important to prevent the poisoning of PEMFCs by CO.¹²¹ Linic and co-workers found that the Pt shell modified the plasmon decay pathway, favoring absorption over scattering, which mostly occurred in the Pt shell [Fig. 12(e)]. The authors hypothesized a selective activation of CO molecules on the core–shell catalyst surface, enhancing the reaction rate and the product selectivity to CO₂.

A further example of important reaction in the field of energy storage is the hydrogenation of CO₂, which generally occurs through two competitive mechanisms:¹²² the methanation of CO₂,

and the reverse water gas shift reaction (RWGS),

Liu and colleagues employed supported Rh NPs as catalytic metals with plasmonic resonance.¹²³ In particular, they synthesized Rh nanocubes (37 nm) on Al₂O₃ NPs, having LSPR in the UV, to drive the selective CO₂ methanation against the RWGS under LED illumination [Fig. 12(f)]. While CH₄ and CO were produced at comparable rates in the dark at 623 K, by shining UV light, a sevenfold increase in the rate of CH₄ production was observed. In particular, the selectivity to CH₄ in the dark reaction reached the maximum of ∼60% at 600 K, while it increased to >80% and >90% at all temperatures under blue and UV LED illumination, respectively [Fig. 12(g)]. The authors explained the observed results in terms of hot electron transfer based on the change from linear to super-linear dependence of the reaction rate on light intensity at ∼1 W cm^–2 and by DFT calculations, showing the overlap between the anti-bonding orbitals of adsorbed CHO and Rh d orbitals on the Rh(100) surface. As a consequence, hot electrons generated by plasmon decay could be injected selectively to CHO anti-bonding orbitals, breaking the C–O bonds and reducing the apparent activation energy for CH₄ production.

Although the studies presented above shed light on the possibility of exploiting hot electron transfer from plasmonic metals to enhance the reaction rate or the product selectivity compared to purely thermal mechanisms, the scientific community realized only recently that an unequivocal distinction between thermal and non-thermal effects is actually more subtle than expected, mainly due to the challenge of properly measuring the surface temperature and the thermal gradients forming in the catalyst bed (Fig. 11). As such, a recent debate has emerged among the scientific community concerning this topic.

A “hot paper” in this regard is the one reported by Halas and co-workers in 2018, in which the distinction between thermal and non-thermal effects contributing to the enhancement in ammonia decomposition,

by an antenna–reactor Cu–Ru photocatalyst was reported.⁹² Cu–Ru NPs supported on MgO exhibited a substantial increase in the H₂ production rate under broadband light illumination at 9.6 W cm^–2 without external heating compared to the experiments in the dark at 482 °C [Fig. 13(a)]. On the contrary, pure Cu NPs exhibited only a moderate activity under light and none in the dark, while pure Ru NPs were almost inactive without substantial change from dark to light conditions. The reaction rate R was fitted with an Arrhenius law,

where R₀ is a constant and both the activation energy E_a and the surface temperature T_s of the catalyst depend on the light intensity (I_inc) and wavelength (λ). By measuring R and T_s at various I_inc and λ, the authors calculated several values of E_a under light illumination, which decreased up to 0.27 eV compared to the value in the dark, $Eadark=1.21eV$ [Fig. 13(b)]. Such a remarkable decrease in the activation energy was thus attributed to the activation of adsorbed N atoms and the consequent desorption of N₂ molecules by hot electrons injected to Ru atoms upon the decay of Cu LSPR. Sivan et al., however, criticized the reliability of the temperature measurement, specifically the choice of the emissivity value for the Cu-Ru/MgO catalyst surface (which was taken from the literature and not measured by FTIR spectroscopy, see Sec. IV A) and the positioning of the thermocouple (only one thermocouple T₀ was employed, see Fig. 11), leading to 3%–5% mismatch in the temperature value measured by the two instruments.^124,125 Indeed, a rather moderate 5% error in the temperature measurement would greatly affect the purely thermal reaction rate due to the exponential dependence by Arrhenius law. Thus, Sivan et al. suggested a standard formulation of the Arrhenius law,

where the activation energy would not depend on the light intensity (thus not showing any decrease related to hot electron effects), i.e., $Ea=Eadark$⁠, and where

would be the effective temperature of the reactor. As a consequence, Sivan et al. argued that the results presented in Ref. 92, as well as in previous works,^96,117,118 may be merely explained by thermal effects.^124,126 However, Jain pointed out that the same form of the Arrhenius equation can be obtained both for a purely photochemical model [Eq. (42)], where, for the sake of simplicity, the activation energy linearly depends on the incident light intensity,

and for a purely thermal model, as in Eqs. (43) and (44).¹²⁷ Figure 13(c) shows the superposition between the Arrhenius plots obtained by Eqs. (42) and (45) with B = 0.1 eV cm² W^–1 (red dots) and Eqs. (42) and (44) with a(λ) = 54 K cm² W^–1. This shows that the use of the Arrhenius equation with a(λ) as a fit parameter does not provide a conclusive evidence for a rate enhancement related to either hot electron injection or purely thermal effect (increase of surface temperature).

In a similar example, Halas and co-workers employed Cu–Ru single-atom alloy NPs as antenna–reactor plasmonic catalysts to drive the methane dry reforming (MDR) reaction,¹²⁸ which is considered an environmentally friendly reaction to convert greenhouse gases into syngas,¹²⁹ 

Such an antenna–reactor plasmonic catalyst enabled the MDR reaction at lower temperature than the traditional thermocatalysis. Importantly, the authors upgraded the temperature measurement compared to their previous study (adding a thermocouple as T₂ in Fig. 11, which was in exact agreement with the reading from a thermal camera) and found a strongly different behavior for the catalyst under light irradiation compared to the dark conditions. In particular, a longer stability due to the absence of coke (i.e., carbon deposits deactivating the catalyst) and higher selectivity to H₂ by increasing the light intensity were found.

A possible approach to address the problem of evaluating non-thermal effects was proposed by the group of Liu and Everitt.^130–132 In particular, they employed two 0.25 mm-thick type K thermocouples T₁ and T₂ as in Fig. 11 and calculated an equivalent temperature of the catalyst T_eq, assuming a linear vertical gradient under steady state conditions, with the recursive equation

This equation was used first to retrieve T_eq by using as input the measured T₁ and T₂ and the activation energy E_a obtained by fitting the reaction rate data vs either T₁ or T₂ in some specific conditions, for example, in the dark. Afterward, the same equation was used to extract a more accurate value of E_a by using T₁, T₂, and T_eq as input. These steps were repeated until convergence. To reproduce the same thermal gradients in the dark and under illumination, moreover, the authors proposed to coat the catalyst with a 1 mm-thick overlayer of Ti₂O₃, a very efficient photothermal material with broadband light absorption¹³³ and negligible catalytic activity [Fig. 13(d)]. In this way, it was possible to measure the thermal reaction rate R_t,m under these “indirect illumination” conditions and subtract it to the overall reaction rate under illumination R_tot, both measured with identical thermal gradients, to retrieve the non-thermal contribution R_nt. This approach was applied to study the ammonia synthesis [Eq. (1)] with a Ru–Cs/MgO catalyst.¹³⁰ At the same T_eq = 325 °C in the dark and under blue LED illumination, very similar reaction rates were found in both cases for equivalent thermal gradients, thus ruling out significant contributions from non-thermal effects. On the contrary, the enhancement of NH₃ production under illumination was ascribed to the strong negative thermal gradient (T₂ > T₁) by photothermal heating. Temperature gradients into the solid pellet catalyst indeed may introduce different adsorption/desorption kinetics and thus boost the products’ formation rate to reach the chemical equilibrium. This aspect has profound implications into the fundamental steps occurring during a chemical reaction and should be investigated more in detail. The same strategy was applied to study the CO₂ hydrogenation by Rh/TiO₂ NPs,¹³² which was already investigated by the same group by employing Rh nanocubes [Figs. 12(f) and 12(g)].¹²³ In this case, the authors found that the dependence of the non-thermal reaction rate R_nt on the light intensity was not univocal: by increasing the value of T₁ (bottom temperature of the catalyst), the dependence changed from super-linear to linear and then further to sub-linear, the latter due to diffusion limitations and to the reverse CH₄ reforming reaction. Moreover, the non-thermal apparent quantum efficiency (AQE_nt) was extracted and plot as a function of T₁ for several incident light intensities [Fig. 13(e)]. Interestingly, AQE_nt became greater than zero at T₁ ∼ 200 °C, the same initiation temperature for the dark experiments. The dependence on temperature for the non-thermal AQE should not be considered a paradox, because also light-induced mechanisms, such as the reduction of the activation barrier for the RDS, can exhibit a temperature dependence. The linear relationship between AQE_nt and T₁ shows a deviation around 350 °C, due to the onset of the reverse reaction by heating. Overall, the authors found a strong synergy between the actions of light and heat to enhance the reaction rate and provided interesting insights into the possibility of disentangling thermal and non-thermal effects by an accurate design of the reactor.

After the initial wave of reports showing the potential advantages of the new class of plasmonic photocatalysts, especially the possibility of tuning the product selectivity, the scientific community has recently realized the subtle difficulty in properly accounting for non-thermal effects and their distinction from thermal ones. These and other plasmon-related phenomena, such as the localization of strong electric fields in the proximity of nanoparticles, can act synergistically in increasing the product yield/selectivity of chemical reactions. Nevertheless, their proper understanding and distinction is of interest both from the fundamental point of view as well as from the practical one, to realize more efficient photocatalysts that may operate at moderate temperatures. While this aspect is less critical for experiments in colloidal systems, in which the liquid effectively removes heat from the surface of nanoparticles, the same does not hold at the solid/gas interphase in solid pellet systems.

In general, several aspects must be considered to prevent any underestimation of thermal effects, including the correct evaluation of collective heating effects, a suitable reactor design, the appropriate positioning of thermocouples and/or the use of non-contact thermometry techniques (and the adoption of temperature-dependent optical properties to set the instruments), and the knowledge of thermal gradients within the catalyst in both dark and light-on conditions. An aspect often overlooked in plasmonic photocatalysis is the detailed characterization of the photocatalysts after reaction. Any small change in material composition, morphology, and surface properties may significantly affect the optical properties, the preferential plasmon decay pathway, and thus the reactivity of plasmonic catalysts. Therefore, more investigation in this direction would help the development of the field.

The contribution of hot electrons to catalysis can be instead proved by various experimental approaches, such as by evaluating the reaction rate under various light intensities and wavelengths, and by performing KIE tests. Insights from theory are invaluable, thanks to the possibility of modeling the hybridized orbitals of metal and adsorbed molecules, elucidating the possibility of electron transfer from the former to the latter. For example, DFT simulations are critical to gain further knowledge on the direct electron transfer effect, which could allow a relatively high efficiency of plasmonic photocatalysts despite the short lifetime of hot carriers. Conversely, FEM or FDTD methods can be used to compute the electric field enhancement and the temperature rise around the nanostructure, thus allowing us to understand the relative magnitude of non-thermal or thermal effects. On the other hand, advanced experimental techniques such as super-resolution fluorescence microscopy/spectroscopy could be used to follow in real time the kinetics of fundamental catalytic steps (i.e., adsorption/desorption of molecular species onto the surface of the plasmonic photocatalysts).

Such tools can also guide researchers in the design of innovative plasmonic photocatalysts targeting the desired chemical bonds of reactants, such as employing antenna–reactor complexes or non-traditional materials, for example, transition metal nitrides instead of coinage metals. All these efforts have been already undertaken by the scientific community and a further development of the field is expected, with the aim of both changing the paradigm of traditional catalytic reactions, such as nitrogen fixation or methane dry reforming, as well as addressing uphill reactions for solar fuels generation, such as water splitting and CO₂ reduction. We hope that this tutorial may inspire other scientists to perform new experiments in this field, not only warning them of the hidden dangers in correctly evaluating the plasmonic effects underlying the measured results but also illustrating the potential appeal of new advancements in this growing sector of research.

The authors gratefully acknowledge the support from the Ministry of Education, Youth and Sports through Project No. ERC_CZ LL1903 and the Operational Programme Research, Development and Education-European Regional Development Fund through Project No. CZ.02.1.01/0.0/0.0/15_003/0000416. A.N. also acknowledges the support from the Czech Science Foundation (GACR) through Project No. 20-17636S.

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