Synthesis of nanomaterials by electrode erosion using discharges in liquids

Discharge–liquid interactions were studied for the first time by Fizeau and Foucault in 1844.¹ They reported light emission from an electrode immersed into an electro-conductive medium. The use of discharges in contact with liquids dates back to 1887, when Gubkin² used a glow-discharge cathode to reduce silver ions (Ag⁺) in an aqueous solution of AgNO₃. This was the beginning of “glow discharge electrolysis” (GDE),³ as it will be named tens of years later. Other seminal works in this vein followed.^4,5 Discharges in liquids were intensively studied at the end of the 19th century, when researchers wanted to clarify breakdown mechanisms in these media,⁶ an undertaking that is still running. Discharge-assisted electrochemistry inspired biologists who dreamt of creating conditions favorable to the emergence of life thanks to these non-faradic electrochemical reactions.⁷ 

In the middle of the 20th century, the so-called “electrode effect,” i.e., the glow discharge taking place at either electrode depending on the voltage polarity, originally observed in molten salts, was also observed in aqueous solutions.⁸ Hickling and Newns³ discovered that the chemical performances of the GDE processes were several times the values of Faraday's law of electrolysis. The chemical products were different from those of conventional electrolysis such as the release of large amounts of molecular hydrogen and hydrogen peroxide, as well as the H⋅ and OH⋅ radicals in the liquid phase, among other secondary reaction products.^9,10

Very early, erosion of submerged electrodes was noticed. Joseph Priestly described the phenomenon of material erosion by electric spark in 1878.¹¹ But it is only in 1930 that he patented the idea to exploit it for electrical discharge machining (EDM).¹² This process is among the earliest non-traditional manufacturing processes.¹³ Material removal by controlled erosion through a series of sparks was actually developed in the USSR during the 1940s. Boris R. and Natalie I. Lazarenko first applied it to a machine for stock removal.¹⁴ Full commercial exploitation started only in the 1960s. The production of particles by EDM was considered as a drawback, making the process drift. Powdery by-products were simply not considered as a potential subject of study.

Nairne was the first to make silver and copper wires explode in 1774.¹⁵ Apparently, the production of ultrafine powders by the exploding wire technique was begun by Abrams,¹⁶ who studied radioactive Al, U, and Pu aerosols. In this process, the breakage of the wire in the liquid state leads to the disintegration of the wire in the form of hot microdrops or clusters.¹⁷ Joncich and Reu in 1964 chose to make explosions in liquid nitrogen to produce metal nitride particles.¹⁸ The wires are most often placed in water.^19,20 This allows one to increase the energy deposition and to use the converging shock wave generated by the exploding wire array to reach high pressure on the axis of the implosion.²¹ The production of nanoparticles by this process is still the subject of active research.^20,22,23 Explosions in general imply the presence of a plasma phase and a liquid phase.

By comparing the explosive detonation parameters with the carbon phase diagram and performing thermodynamic calculations, it has been shown empirically and theoretically that free carbon in detonation products of powerful condensed carbon-containing individual explosives with a negative oxygen balance should condense in a diamond or liquid phase.²⁴ This applies to the synthesis of nanodiamonds discovered first in the USSR in 1963 by Volkov, Danilenko, and Elin.²⁵ 

The situation changed dramatically with the advent of laser-based processes. Maiman constructed in 1960 the first functional pulsed-laser using a ruby crystal and emitting at 694 nm,²⁶ enabling the development of pulse laser ablation shortly afterward by Smith and Turner.²⁷ Patil et al.²⁸ introduced the concept of pulsed laser ablation at the solid–liquid interface in 1987. This method, known as Liquid Phase Pulsed Laser Ablation (LP-PLA), Laser Ablation in Liquids (LAL), or Laser Ablation Synthesis in Solution (LASiS), is based on the erosion of a solid target immersed in a solution by a laser beam focused through the liquid onto the solid surface. Progress in laser technology led to ultrashort pulse lasers (i.e., picosecond in 1964^29,30 and femtosecond in 1981³¹), which brought considerable perspectives to ablation in liquids by affecting basically the mechanisms of the erosion of solids.³² Moreover, accessing to synthesis conditions that are far from thermodynamic equilibrium opened up new possibilities, among which is the synthesis of nanomaterials with original properties.³³ 

The idea of using discharges to create conditions for such a purpose made submerged discharges a possible alternative to lasers as sources of energy deposition. The first works mentioning the synthesis of “fine powders” by discharges in liquids were published by Ishibashi et al.³⁴ They proposed a spark discharge method, in which a spark discharge takes place at the contact points of pellets dipped in the liquid medium. There is no doubt that nanoparticles were also synthesized in these conditions. Dubovoy et al.³⁵ proposed a similar approach in 1985 and Sato et al.³⁶ in 1992. The first experiments mentioning the synthesis of nanomaterials were certainly carried out by Ishigami et al.³⁷ in the USA who wanted to propose a simplified synthesis method of carbon nanotubes by arc discharges. This strategy eliminates nearly all of the complex and expensive machinery associated with conventional nanotube growth techniques. Sano et al.³⁸ in the UK demonstrated 1 year later with a similar device the possibility of producing carbon onions. The topic starts taking off in 2004 likely because of the ease of running these processes. The idea of resorting to ultrasound assistance came up quickly³⁹ as it was studied to improve the material removal rate, to reduce the tool wear rate, and to optimize the surface quality of the machined workpieces in EDM.^40,41

The idea of locating the plasma outside the discharge came back in 2005 with an alternating current (AC) plasma source.⁴² Two years before, the generation of nanomaterials by melting and evaporation of a sacrificial metal electrode in a microplasma was demonstrated for the first time by Shimizu et al.⁴³ Next, other solutions of GDE-type processes were proposed.^44–46 Corona discharges usually employed in GDE were replaced by various atmospheric plasmas among which dielectric barrier discharges.⁴⁷ The concept was applied to surface functionalization of nanoparticles by Mariotti et al.⁴⁸ 

The formation of bubbles (or their pre-existence) in liquids, submitted to an injection current, was the most studied mechanism responsible for breakdown. The formation of pre-breakdown bubbles was examined in the 60s.^49,50 Discharges in bubbles injected on purpose in a liquid became a new process as such when Yamabe et al. proposed this concept in 1993.⁵¹ Their utilization for nanoparticles’ synthesis was proposed only very recently. Shin et al.⁵² produced carbon nanomaterials by discharges in Ar/O₂ gas bubbles injected in 1-hexanol and by Yamada et al. who used a gas−liquid slug flow reactor system.⁵³ 

A bubble in a liquid can be considered as the counterpart of a droplet in a gas. Both are submitted to discharge–liquid interactions in the processes we are interested in. This is especially the case of warm dense matter produced, for instance, by ultra-intense laser excitation of liquid fuel targets,⁵⁴ a domain far beyond the scope of this article. The technological importance of introducing droplets in discharges was first foreseen at the end of the 19th century by Schoop in Switzerland. He used flames to coat metal surfaces with lead and tin,^55,56 inventing plasma spray. The process was strongly improved in the 50s with the development of plasmatron systems.⁵⁷ Droplets in cold plasmas were studied much later because studies were for long devoted to the sole interaction between electric fields and droplets in neutral gas after the discovery by Taylor in 1964 of a condition for stable liquid cone existence.⁵⁸ Hager and Dovichi studied the behavior of microscopic liquid droplets near a strong electrostatic field and developed the droplet electrospray.⁵⁹ The repulsion was a result of droplet charging via the corona discharge created at the tip of the high-voltage probe. In a related study, Kim and Dunn investigated the formation of progeny droplets ejected from a parent droplet in the presence of an intense electric field.⁶⁰ However, investigation of the behavior of droplets in cold non-equilibrium discharges is much recent. The interest of using pulsed discharge to improve combustion in engines required to investigate this topic.^61,62 Ward et al.⁶³ used an ultrasonic nozzle to atomize the acrylic acid monomer into an atmospheric pressure glow discharge (APGD) to deposit polymeric coatings, opening up the way to several other processes alike.^64–66 

Aggregation in low-pressure activated vapor phases leads to ultra-small nanoparticles that can be collected in liquids with extremely low vapor pressure, like oils or ionic liquids, which enables the production of nanofluids. The vapor phase can be created by any physical source like evaporation⁶⁷ or sputtering.⁶⁸ The liquid can also be directly decomposed by an electron beam, for instance.⁶⁹ 

We shall not forget to mention that liquid droplets in discharges are also of primary importance for climatologists⁷⁰ and astrophysicists.⁷¹ For example, the atmosphere of Titan is constantly bombarded by galactic cosmic rays and Saturnian magnetospheric electrons causing the formation of free electrons and primary ions, which are then stabilized by ion cluster formation and charging of aerosols. These charged particles accumulate in drops in cloud regions of the troposphere.

The synthesis of nanoparticles by discharge–liquid interactions involves the presence of all states of matter. The previous history, because it is intentionally short, is biased to select some seminal works as breakthroughs in the topic. The following article is centered on nanoparticles’ synthesis. Other correlated aspects can be found with much detail in some reference review articles:

• For discharges in liquids, see Refs. 72–83.

• For discharges in contact with liquids, see Refs. 48 and 84–96.

• For laser in liquids, see Refs. 32, 33, and 97–104.

• For spray in discharges, see Refs. 105–110.

• For electrical wire explosion, see Refs. 22 and 111.

• For sputtering onto liquids, see Refs. 112–117.

or in books, see Refs. 6, 81, and 118–122.

To the best of our knowledge, no review or book is available about nanoparticles’ synthesis for discharges in bubbles.

There are two main ways to generate a direct current (DC) discharge in a liquid to synthesize nanoparticles. A low-voltage generator (typically below 1 kV) can be used, which requires to put the two electrodes in contact, the discharge being created when the gap between the electrodes increases, either by material erosion or by mechanical separation. The current^123,124 or the voltage¹²⁵ is, most often, used as closed-loop feedback signals to keep the inter-electrode gap distance, measured with a detector, as constant as possible. For instance, Bera et al.¹²⁶ developed an optoelectronic system made of three main components to maintain constant a preselected distance between the electrodes (Fig. 1): a photosensor for an optical emission diagnosis, a feedback loop that is composed of analog electronics and a computing unit, and a servo-unit for axis translation of the anode.

Resorting to high-voltage discharges (typically beyond 1 kV) enables breakdown at short gaps (i.e., from 100 μm to 1 mm typically, depending on the strength of the dielectric liquid). If one electrode is insulating, AC or radiofrequency (RF) excitation can also be used. Table I presents selected examples of discharges in liquids for the synthesis of nanoparticles of simple metals. It is useful to compare conditions and have practical values of parameters. For carbon materials, a thorough review is available.⁷² 

Experimentally, reactor designs are many (Fig. 2), even though it is relatively simple to set up a process, as only a power generator, two electrodes, and a vessel containing the liquid are required. Indeed, the power source can be used to generate a DC, AC (low frequency), radio frequency, microwave, unipolar pulsed discharge, or bipolar pulsed discharge. The electrodes can be a pin, a plate, or even material granules. The shape of the vessel can be a cylinder or a cone to prevent the drift of particles from the discharge zone. The process can be assisted by ultrasound.^151,152 One electrode can vibrate to facilitate electrical breakdown and mix the treated solution.¹⁵³ 

Discharges created within liquids are often close to the equilibrium,¹⁶¹ which takes only a few nanoseconds to reach. Orders of magnitude of key parameters of this kind of discharges are as follows:

• Electron density n_e = 10¹⁸–10¹⁹ cm⁻³;

• Initial pressure P₀ = ∼ 100–1000 bars;

• Initial temperatures T_r ∼ T_v ∼ T_e < 1 eV; and

• Current I ∼ 1–10 A.

The fastest voltage rise time used to generate discharges in liquids is around 150 ps.¹⁶² For the synthesis of nanoparticles, it is always beyond 2 ns (i.e., within the so-called short time scale) and can extend to the second time scale. This means that typical phenomena found in target ablation by femtosecond and even picosecond lasers (leading to the so-called ultra-short interactions) are beyond the scope of this work.

The synthesis of nanoparticles by electrode erosion using discharges in liquids can be described by the following simplified chronological sketch of events (Fig. 3).¹⁶³ 

Before plasma ignition, charges are injected into the liquid during the pre-breakdown phase. Either electrons are injected at the cathode or impurities (and even the liquid itself if it is aprotic) can be split into ion pairs of opposite charges at the anode. Charge injection drives the electrohydrodynamic movement of the liquid, possibly leading to turbulent flows. Once charges are injected in the liquid, breakdown occurs when the liquid density becomes low enough to enable charge multiplications. When the discharge ignites, if the dissipated power is high enough, a shockwave can be emitted. The current flows back and forth across the electrode–liquid interfaces. Both electrodes are submitted to these current oscillations that can be described by a damped RLC circuit. The discharge volume extends toward the ground electrode under the electric field, forming an ionized channel that crosses the inter-electrode gap, typically in several nanoseconds for sub-millimetric gap distances, a bit like streamers in dielectric barrier discharges. When the channel reaches the ground electrode, the voltage drops suddenly, transforming the discharge channel into an arc discharge. The electrodes, on contact with the high-temperature arc discharge, start melting after a few hundred nanoseconds, releasing a metallic vapor in the discharge. Once the metallic vapor is emitted, nanoparticles are synthesized by condensation. Other erosion processes may also be involved, depending on the conditions, leading to different size distributions. Produced particles are next transferred into the liquid phase. Once the discharge phase stops, the gas volume it occupied expands and collapses several times within the millisecond time scale, leading to bubble oscillations.

An energy balance is useful at this stage.¹⁶⁴ Basically, the largest part of the energy delivered by the source is used to create the plasma (∼95%). Electrode erosion consumes only about 1% of the total energy (∼1%), whereas the bubble dissipates a few percent (∼5%). The amount of energy spent in the shockwave is almost negligible (<0.1%). Of course, these figures are affected by the type of discharge used, the inter-electrode gap distance, the nature of the liquid, etc. However, we readily understand that the overall yield of nanoparticles production is a key issue in this kind of process, even though large quantities of nanoparticles can be produced because of high production rates (typically ∼100 mg h⁻¹ and up to 10 g h⁻¹).⁸⁹ 

Electrodes can be eroded by different mechanisms. This produces impacts with complex shapes. As mentioned previously, some recently identified ablation mechanisms in laser processes with an ultra-short time scale (from a few femtoseconds to a few picoseconds) will not be considered.^165,166

At short pulses, thermal processes must be considered, which is not true for ultra-short processes. The melting of the electrodes by the discharge is the most important mechanism that leads to particles’ synthesis. The modelling of the process is generally attuned to those developed for the description of arc−surface interaction in domains like welding or circuit-breakers.^167–169 However, several other mechanisms are possible depending on experimental conditions. Whatever the conditions, the mean energy of ions in these high-pressure discharges is too low to promote any sputtering effect as it is too often claimed.

The discharge pressure at ignition is typically beyond hundreds of bars. It is still around a few tens of bars 200–250 ns after ignition at the end of a nanosecond-pulsed discharge.¹⁷⁰ This means that the energy of most particles in the ionized gas is certainly too low for sputtering. The melting of metal electrodes is not due to the Joule effect either, the resistivity of the material being too low until dissolved gases start forming bubbles, which affects the material conductivity. Following Hamdan et al.,¹⁶³ electrodes melt essentially by irradiation from the blackbody emission of the high-temperature discharge. The maximum temperature reaches a fraction of eV (typically around 5000 K), discharges being close to local thermodynamic equilibrium. As radiation is emitted similarly on either side of the discharge channel, erosion spots are similar on either electrode. The time to melting is of the order of 100 ns for a micrometric erosion spot on an aluminum electrode.

Local melting of the electrode leads to the formation of a liquid well. The bottom of the well is in contact with a mushy region if the electrode is an alloy and not a simple metal. The interface between the surface of the liquid well and the discharge is not clearly described for several reasons: the time evolution of the pressure is not well known, the existence of a plasma sheath is contentious as it should be extremely thin, the surface is likely to be unstable, etc.

The heated electrode emits a vapor either by evaporation from the molten electrode or by sublimation from the solid electrode, and this vapor condensates in colder parts where nanoparticles form. This mechanism together with nucleation (described hereinafter) is responsible for the synthesis of the smallest particles generated by discharge in liquids. Vaporization at the surface of the molten pool can be estimated as follows.¹⁷¹ The rate of the atomic flux (m⁻² s⁻¹) leaving the surface during normal evaporation and due to a pressure gradient is given by the Knudsen–Langmuir equation,

where M is the molar mass of the evaporating molecule or atom. The factor α (<1 and depends on temperature) is called the efficiency coefficient. R is the ideal gas constant, P is the vapor phase pressure, and $Ps∞$ the saturation pressure at temperature T of the liquid surface. These quantities are related by the Rankine form of the Clausius–Clapeyron equation, assuming the latent heat of vaporization L_v constant,

where P₀ is the ambient pressure, T_b is the equilibrium boiling temperature at ambient pressure (the normal boiling temperature), and L_v is either the heat of sublimation or the heat of evaporation. If L_v cannot be considered as constant, other expressions (like Dupré or Riedel's formulas) are required.

Vaporization can also occur because of a concentration gradient.¹⁷² The diffusive vaporization rate $∙md$ is expressed in terms of a phase change at the surface and the subsequent transport of the vaporized species to the bulk gas phase through the mass transfer boundary layer surrounding the pool. The vaporization rate is then defined as

where K is the mass transfer coefficient given by similarity laws.

What is referred to as “spallation” corresponds to material ejection driven by relaxation of the stress induced by the treatment.^98,173 Basically, the spallation of a liquid phase in contact with its mother solid phase is due to a drift in the phase diagram where the following thermodynamic pathway crosses the liquid branch of a binodal domain and enters a metastable region. This leads to the nucleation, growth, and coalescence of voids. This induces the formation of a transient foamy structure of interconnected liquid regions, and eventual separation (or spallation) of a thin liquid layer from the bulk of the target. Material spallation occurs at the liquid–solid boundary, where the spall strength is lower than that in the solid phase. However, the tensile wave is strong enough to cause the cut-off in the liquid phase, according to the applied criteria of nucleation [Fig. 4(a)].

In a liquid, the situation under vacuum being different, the particles produced by this mechanism exhibit distribution sizes that are around 10 nm.¹⁶⁵ The foamy structure coarsens with time and eventually decomposes into individual droplets on the time scale of nanoseconds. The top liquid layer loses stability because of Rayleigh–Taylor instability and decomposes into large droplets, estimated to have diameters from hundreds of nanometers to tens of micrometers.¹⁷⁴ 

What is referred to as “phase explosion” or “explosive boiling” is a process where a superheated surface region, expanding rapidly, undergoes a fast decomposition into a mixture of vapor and liquid droplets [Fig. 4(b)]. Thermodynamically, it means that solid matter is rapidly superheated up to the thermodynamic critical temperature, at which the spinodal decomposition in vapor and liquid phase in the irradiated material occurs by homogeneous nucleation.

This is typically what can be observed when a very clean glass of water (i.e., without surface defects to promote nucleation of steam bubbles) is heated in a microwave oven without boiling. The superheated metastable liquid can undergo an explosive liquid–vapor phase transition when a massive homogeneous nucleation of vapor bubbles starts, by simply touching the surface of the liquid, for instance. This phenomenon appears at much higher energy than spallation and occurs within the nanosecond time scale.¹⁷⁵ As for spallation, on the time scale of nanoseconds, vapor, small nanoparticles (∼10 nm), and large liquid droplets are produced.

Non-homogeneous distribution of surface temperature is caused by radial temperature gradients in the discharge. It can also be amplified if the discharge channel is not oriented perpendicularly to the liquid well. Because of this non-homogeneous distribution, two driving forces responsible for expulsion of the molten liquid are generated: one emanating from the recoil pressure effect caused by evaporation and the other one from the Marangoni effect. Large (beyond 100 nm in diameters and up to hundreds of μm) droplets are produced by both mechanisms (sometimes called hydrodynamic splashing¹⁷⁶) and emitted radially [Fig. 4(c)].

Expulsion of large liquid droplets can be driven at sufficiently high power by the vapor recoil. This phenomenon induces a pressure that splashes the melt and residual recoil pressure redistributes the metallic melt.¹⁰⁰ The melt expulsion by the recoil pressure is caused by the spatial variation of the normal stress exerted by vapor pressure within the hot spot. The gradient of vapor pressure makes the melt flow outward from the high-pressure spot center to the low-pressure periphery.¹⁷⁷ 

The Marangoni or the thermocapillary effect creates a strong tangential stress on a surface submitted to large gradients. The liquid movement within the molten pool is affected by this boundary condition that is due to the dependence of the surface tension on temperature. The surface tension of liquid pure metals decreases with increasing temperature¹⁷⁸ and then Marangoni's force acts in the opposite direction of the surface temperature gradient. As the temperature usually peaks at the center of the well, the liquid flows from the center to the spot edge, which contributes to the expulsion of the melt. At high heating rates and small thicknesses of the molten layer, Marangoni's stresses can lead to the rupture of the molten layer,¹⁷⁹ melt spattering, and formation of droplets.¹⁸⁰ 

The emission of droplets from the molten well is possible via bursting of bubbles formed in the liquid. Bubbles within the molten well can be created from boiling of the liquid metal or from absorption of discharge gases.¹⁸¹ Blisters are thus formed on the surface of the well.¹⁸² A liquid film, covering the surface of the bubble, bursts and releases very fine droplets.¹⁸³ The subsequent collapse of the bubble forms a rising jet of liquid that pinches, according to the Rayleigh–Plateau instability, and produces a spray of micrometer-scale droplets within tens of microseconds. [Fig. 4(d)]. The effect of the electric field on the ejection of droplets from bubbles bursting at the liquid surface was considered by Holgate and Coppins.¹⁸⁴ 

The different shapes of eroded areas, produced by the mechanisms described previously, are depicted in Fig. 4. Of course, these mechanisms can combine over sufficiently large time scales and give more complex structures. However, most of the eroded areas exhibit these shapes that are the most commonly encountered. Roughly, the size of a crater is a linear function of the square root of the electrical charge dissipated during the discharge process.¹⁸⁵ 

It is possible to strongly limit electrode erosion by using materials with high melting points (usually tungsten) and low current density.^134,135 When nanoparticles are synthesized from a liquid precursor, this point is critical to keep the as-produced nanofluid with high purity.

When the size of a particle shrinks, its thermodynamic properties changes. The Gibbs free energy of nanoparticles, made of one element, is determined by the bulk free energy and the surface free energy for both the solid and liquid phases.¹⁸⁸ Surface atoms are dominant for the size effect on the thermodynamic properties of nanoparticles. On the basis of the Gibbs free energy, thermodynamic properties of nanoparticles, such as melting temperature, molar heat of fusion, molar entropy of fusion, and temperature dependences of entropy and specific heat capacity can be determined.

Thermodynamics of alloy nanoparticles is still under debate, as recent results showed the existence of multiple local energy minima submitted to local thermal fluctuations.¹⁸⁹ The way phases separate during ultrafast cooling is difficult to predict. In simple systems like, for instance, two-element alloys undergoing eutectic decomposition with a wide miscibility gap, several situations can be encountered:

• The boundaries of phase compositions as well as transition temperatures are changed. It is the case of the Sn–In system [Fig. 5(a)].¹⁹⁰ 

• The decomposition mechanism changes. In the Cu–Ag system, phase separation at the nanoscale occurs above 5 nm particle diameters in the 15 and 30 at. % Ag composition range.¹⁹¹ The separation into Cu-rich and Ag-rich domains takes place by spinodal decomposition. Phase separation no longer occurs at nucleation sites but through the whole particle at once [Fig. 5(b)].

• The decomposition follows a specific path that leads to metastable phases that cannot be described by the two previous approaches. For instance, supercooled Au–Si nanoparticles exhibit a unique metastable phase δ₁ that grows heteroepitaxially to Au.¹⁹² 

Then, resorting to metastable phase diagrams is a first approach, which cannot be considered as highly predictable. As an illustration, there are more than 20 metastable Au–Si crystalline phases that have been identified to date.

Eutectic and spinodal decompositions are not easy to distinguish in nanostructures. The Cahn–Hilliard approach predicts the critical wavelength λ_c over which fluctuations of compositions occurs in spinodal decomposition. This approach is based on the following equation:

where ρ_i is the volume density of atoms i in a binary mixture made of atoms i and j, $D~ij$ is the interdiffusion coefficient, x is the spatial coordinate, t is the time, and $f0′′$ is the second derivative by composition of the Helmholz free energy of a unit volume of homogeneous material [see Fig. 6(a)].

κ is the gradient energy coefficient. When the system is phase-separated into high and low composition regions, $κ=ξ2kT$⁠. ξ is a length that scales with the interface width. It depends on the crystal lattice. For an fcc structure, $ξ=a2Tc/(Tc−T)$⁠,

T_c is the maximum temperature of the miscibility gap and a is the lattice parameter. It is possible to show that the following solution:

satisfies Eq. (4), which leads by substitution to the so-called amplification factor R,

Here, $h=2πλ$ and A is the amplitude of concentration fluctuations with a wavelength of λ. $ρ¯$ is the average composition. The sign of R is given by the evolution of the amplitude of a concentration fluctuation with a given wavelength: if it increases, then R > 0. The critical wavelength λ_c corresponds to the condition R = 0. It reads

In Fig. 6(b), λ_c is plotted vs composition.¹⁹¹ The width of the miscibility gap is about 93% and the minimum of λ_c is about 6 nm at 30 at. % of Ag. With increasing Ag content, λ_c increases more and more rapidly and tends to infinity close to the spinodal composition $(f0′′=0)$⁠.

Consequently, we deduce from Fig. 6(b) that, below 5 nm typically, the nanoparticle cannot adopt the modulated structure of spinodal decomposition. This is observed experimentally: particles smaller than 5 nm in diameter grow as a solid solution whatever the composition [Fig. 6(c)]. This shows that spinodal decomposition is both size and composition dependent. It also demonstrates that non-equilibrium alloys exist at sufficiently small scale.

Proper conditions are sometimes encountered for particles to aggregate, which depends on physicochemical processes at stake. Then, particles may settle, as they get bigger, on the bottom of the vessel in which they are contained. Because water is often used as primary solvent, the specific case of oxidative processes in liquid has to be specifically emphasized. Indeed, the stability of solutions is a key point in the synthesis of nanofluids. It is usually estimated by resorting to the zeta potential that derives the electric double layer that forms around particles.

Aggregation of nanoparticles, which leads to the formation of highly porous structures, is of primary importance as it generates multi-modal distributions that can compromise the application of synthesis processes of nanoparticles.¹⁹⁴ Irreversible aggregation of nanoparticles is well understood. The fractal formation in colloidal aggregation and the general underlying mechanism have been extensively investigated. They are well known and they can be appropriately applied on the nanoscale. Conversely, reversible aggregation still deserves to be deepened and it is only touched upon in this article.

Irreversible aggregation will be described briefly since many reference works provide comprehensive pictures of this phenomenon.^195–198 

The formation of the colloidal structure and the irreversible nanoparticle aggregation are well described by the diffusion-limited cluster aggregation (DLCA) model,^199,200 a more accurate version of the diffusion-limited aggregation (DLA) model.²⁰¹ The latter considers the existence of a primary particle acting as a seed for the formation of a cluster, to which other individual particles diffuse and attach. The former describes how all particles bind to each other and diffuse as clusters that can also attach together when in contact.

To account for the compactness of the agglomerated structure, often estimated less dense than observed, the reaction-limited cluster aggregation (RLCA) model was proposed.^202,203 It relies on the idea that approaching particles aggregate with a probability less than one. This probability is defined by the distribution of situations where the strength of the repulsion between the particles is inferior to the strength of the attraction force at shorter distances, which enables aggregation. The repulsion force is given by the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory.^204,205 It accounts for van der Waals interactions and electrostatic forces arising between the double layers around the particles. This supplementary degree of freedom favors non-binding collisions between clusters, which increases their interpenetration and produces denser structure once binding occurs. This approach was used, for instance, by Ziashahabi et al.²⁰⁶ to study the formation mechanism of bead-chain-like ZnO nanostructures prepared via DC arc discharge in liquid.

In colloidal solutions, an appropriate change of the conditions destabilizes the nanoparticle suspension and induces the aggregation of particles. The particles interact differently because their surface state changed in the new situation.²⁰⁷ Forces exerted on a single particle are modified and the former balance is affected in such a way that aggregation is enabled. This results in chemical bonding, non-covalent bonding being conventionally restricted to self-assembly.

Aggregation of nanoparticles is expected to proceed reversibly, and the general macroscopic laws describing the irreversible network formation process are not directly useable on the nanoscale. Reversible network formation is a complex emerging topic, an example of which is as follows.

It is possible to account for the many-body van der Waals interactions on the nanoscale with so-called “many-body dispersion (MBD)” models.^208,209 Van der Waals forces between polarizable non-metallic nanostructures can be understood by collective interactions between wavelike charge density fluctuations. A simple summation over pairwise interactions between instantaneous particle- or fragment-like dipolar fluctuations is not as meaningful. The collective wavelike fluctuations are responsible for the emergence of nontrivial modifications of the power laws that govern non-covalent interactions.

Practically, there are several ways in which the modeling of the formation of nanoparticle networks is approached. A practical review on reversible network formation is available in Ref. 207. Nonetheless, a theoretical framework accounting for the reversibility of the clustering process is still pending.

Discharges are often created in liquids with different oxidation capabilities. Notoriously, water is more oxidizing than ethanol and ethanol than ethylene glycol.²¹⁰ In general, alcohols, glycols, and hydrazine can all serve as reductant sources. The choice of the liquid is also known to affect the shape of the nanoparticles.^86,145,211

Discharges in liquids make these effects even more complicated to explain than other processes as liquids are transformed by discharges. Indeed, by-products resulting from liquid–discharge interactions are likely to play a role on the nucleation and growth of nanoparticles.

In the case of water, where air gases dissolve, chemistry is extremely complicated. It includes as main species H₂O, O₂, N₂, OH•, H•, O•, N•, H₂O₂, NO_x, O₃, HNO₂, HNO₃, NO•, ONOOH, and ions.²¹² Species responsible for oxidation are likely to be several, but the way oxidation occurs is still unclear.

Simple description explaining how ethanol molecules scavenge OH radicals and generate reducing species (H and H₂),^213,214

is put forward to explain how non-oxidized metal nanoparticles can be produced by discharges in ethanol. Similar reasoning can be applied to ethylene glycol as metallic nanoparticles can be produced as well (see, e.g., Refs. 215 and 216).

More complex mechanisms are certainly at stake, as in the case of carbonaceous liquids or liquids containing carbonaceous additives like surfactants, where nanoparticles are often coated by a few layers of carbon.⁸⁶ Lee et al.²¹⁷ showed by dissolving WCl₆ in ethanol that they could synthesize spherical tungsten nanoparticles. By adding an anionic surfactant (SDS) at 30% and 50% (the surfactant/WCl₆ molar ratio), spherical particles are no longer agglomerated. A weak fraction of triangular and hexagonal-shaped nanoparticles is also found. The presence of carbon is not studied but is very likely. Generally, the balance between a too large quantity of surfactant, leading to carbon contamination and a too small quantity, leading to no effect, can only be determined by a trial and error procedure.

Because of the importance of nanofluids in many industrial applications, it is essential to ensure a high stability of dispersion in order to maintain the fluid properties constant in time. The physicochemistry of nanoparticles in liquids is a complex topic, and the examples of gold and silver will be taken to illustrate this aspect. Next, the concept of electrical double layer will be introduced to explain how the zeta-potential is defined, a useful quantity to evaluate the stability of dispersions.

The synthesis of gold nanoparticles by femtosecond laser ablation in aqueous solutions produces colloidal Au nanoparticles that are characterized by their surface hydroxylation.²¹⁸ Au–O compounds, followed by a proton loss to give surface Au–O^–, result in the negative charging of the nanoparticles. This increase in the net surface charge of particles limits their coalescence due to electrostatic repulsion. If n-propylamine is added to the solution, amine groups react with the nanoparticle surface. This is accompanied by the reduction of the particle size, which indicates that functionalization of Au nanoparticles is likely achieved during their formation by laser ablation.

On the contrary, for silver²¹⁹ (but also for iron,²²⁰ for instance), surface oxidation affects the stability of dispersion. Nanoparticles synthesized in solutions can be stabilized by adding sodium dodecyl sulfate (SDS) as a surfactant. The surfactant coverage and the charge state on the nanoparticle surface are closely related to the concentration of SDS, which finally determines the stability of the nanoparticles in the solutions. The nanoparticles tend to be aggregated when the coverage is less than unity, while they are very stable when the surface is covered with a double layer of the surfactant molecules. High stability can be achieved as well by using isopropanol in the absence of additional capping agents. The liquid undergoes a self-inhibited free radical chain mechanism, generating the organic stabilizing agent that covers particles and stabilize them.²²¹ 

The stability of the suspension can also be affected by the evolution of the solvent itself that may age or react with chemicals from the gas environment it is in contact with. Another possibility showed recently is water splitting during pulsed laser ablation of metal targets in water.^222,223

The electrical double layer on the surface of a nanoparticle is based on the Gouy–Chapman–Stern model explaining how a surface charge, created by dissociative ionization of surface molecules, is counterbalanced by ions in the electrolyte. Basically, the double layer is made of the Stern (inner) layer where the ions are strongly bound and the Gouy–Chapman diffuse (outer) layer where the ions are loosely bound. Within the diffuse layer, there is a virtual boundary below which ions and particles behave as a whole. This boundary, placed at the zeta potential, is known as the surface hydrodynamic shear or slipping plane. Consequently, when a particle moves in an electrolyte, ions below the slipping plane move along, contrary to ions beyond the plane.

Because a nanoparticle is surrounded by the electrical double layer that sizes one Debye length, its movement can be affected by electric fields.²²⁴ It turns out that the electric double layer (EDL) can be polarized under the influence of external fields. This plays an important role in the accurate evaluation of the electrophoretic motion of particles.²²⁵ 

There are three main polarization mechanisms: EDL, volume, and field polarizations.

The EDL polarizability of charged species can be calculated by the Maxwell–Wagner theory from the permittivities and conductivities of the species and the medium. For a colloid, the concept of surface conductivity must be introduced and its polarizability is given by the Maxwell–Wagner–O'Konski theory.^226,227 EDL polarization cannot be neglected when the Debye length is comparable to the colloidal size, the zeta potential is moderately high, and/or the applied frequency of the external electric field is of the same order as the rate of ionic diffusion over the colloidal size.

In volume polarization (Fig. 7), the positive and negative ions in the liquid are migrating under the influence of the external field. As these ions cannot penetrate the colloid, the volume of the particle acts as a physical obstacle, which hinders the migration. The subsequent accumulation of charges of opposite signs on either side of the particle induces a dipole moment anti-parallel to the external electric field.

Field polarization is due to the Coulombic attraction/repulsion between a charged colloidal particle and the clouds of surrounding ions. Counter-ions/co-ions tend to accumulate in the tail of the particle as they circumvent the particle, resulting in a dipole moment proportional to the external electric field. This effect is observed for highly charged particles with high zeta potential, the induced dipole moment being then proportional to the external electric field.

Particles' life starts by nucleation, nuclei become seeds, and seeds become nanocrystals. What is meant by seeds is an intermediate object between a nucleus and a nanocrystal, in which no structure fluctuation (i.e., changes of bond-orientational order)²²⁸ is possible. From their formation to their transfer into the liquid phase, nanoparticles are submitted to complex environments where huge gradients prevail. Even though discharges in liquids are often close to equilibrium, nanoparticles can adopt complex shapes.

The shape and structure of Au or Ag nanocrystals strongly affect their spectroscopic properties (like localized surface plasmon resonance,²²⁹ surface-enhanced Raman scattering,²³⁰ surface enhanced fluorescence,²³¹ plasmon-enhanced optically stimulated luminescence,²³² etc.), enabling enhanced spectroscopies, reviewed, for example, in the following contributions.^233–235 

Classical nucleation theory stipulates that the formation of nuclei in supersaturated homogeneous solution is governed by the balance between the bulk and surface energy of the new phase,

The first exponent (−E_a/k_BT) is related to the kinetic barriers with an overall activation energy E_a, while the second exponent (−ΔG_ex/k_BT) represents the thermodynamic barrier. The parameter A is a pre-exponential factor that depends on the properties of the investigated material. It is possible to predict nucleation rates from this equation for any material at a given level of supersaturation.

However, as discussed by Gebauer et al.,²³⁶ values calculated accordingly can differ by orders of magnitude from experimentally measured data. Non-classical nucleation theories are then needed but are beyond the scope of this work.

The shape of a single crystal at equilibrium in an inert gas at low temperature (rigorously 0 K) or vacuum can be determined by the Wulff construction. For an fcc metal, possible shapes correspond to polyhedrons (truncated octahedrons). However, the final shape adopted by an fcc nanocrystal can differ a lot from Wulff's shapes. This deviation can be attributed to several reasons:²¹⁰ 

• nucleation and/or growth are far from equilibrium;

• surface energies are modified by a capping agent, impurity, or solvent;

• twin defects affect nucleation and growth and lead to new shapes such as decahedron and icosahedron with a total free energy lower than that of Wulff's polyhedrons; and

• the synthesis temperature is high.

There are three main ways to control the shape of nanoparticles.

Discharges in liquids are often near thermodynamic equilibrium. The shape of nanoparticles is then controlled by the interfacial free energy, γ. It can be defined as the energy needed for creating a unit area of new surface,

where G is the free energy and S is the surface area. For a given surface, N_b is the number of broken bonds, ɛ is the bond strength, and ρ_s is the atom surface density. For an fcc structure with a lattice constant a, one finds easily that

Then, a single-crystal seed takes an octahedral or tetrahedral shape in order to maximize the expression of {111} facets and minimize the total surface energy. These inequalities can be modified by the introduction of twin defects. The strain energy caused by twin defects greatly increases as the seed grows in size. This critical dependence on size is also sensitive to reaction kinetics, which offers a possibility of control.

If the reaction that forms the atoms building the particle is slow, nuclei and seeds form through random hexagonal close packing (rhcp), together with the inclusion of stacking faults.²³⁷ This limitation by a kinetically controlled step makes seeds adopt shapes that depart from those favored by thermodynamics. Inclusion of stacking faults and/or twin planes can thus lead to the formation of plate-like seeds.

The key is to ensure an extremely low concentration of metal atoms, so the nuclei will not be able to grow auto-catalytically into polyhedral structures. Instead, the atoms will add to the edges of a planar cluster to generate a plate-like seed. This was observed (Refs. 130 and 202) by forming plate-like lead particles using discharges in liquid nitrogen (Fig. 8).

Hieda et al.¹³⁵ produced gold nanoparticles whose shape was progressively etched and decreased in size during the treatment beyond 5 min by changing the composition of the colloidal solution (initially water containing HAuCl₄ ⋅ 4H₂O and sodium dodecyl sulfonate). Successive discharges create H₂O₂ species and lower the pH value, leading to new conditions where nucleation stops, and etching is enabled. This is also what Saito et al.⁷⁹ observed in similar experiments (Fig. 9).

Xia et al.²¹⁰ give a more accurate view of oxidative etching. The distribution of single-crystal vs twinned seeds can be further modified by oxidative etching, in which zero-valent metal atoms are oxidized back to ions. If a ligand for the metal ion is also present in the same solution, a combination of the ligand and O₂ can result in a powerful etchant for both the nuclei and seeds.

Consequently, we can readily understand how discharges in colloidal dispersions contribute to the shaping of nanoparticles. As the discharge runs, the production of oxidizing species (among which H₂O₂) progressively modifies the liquid composition by reacting with ligands and by forming etching agents. However, these mechanisms have not been clarified yet in the case of discharges in liquids.

The condensation mechanism for the growth of nuclei, i.e., deposition of atoms or molecules on the surface of growing particles, the condensation rate can be approximated by the collision rate of monomers with the nucleus,²³⁹ 

The average thermal velocity of the monomers in the gas is given by $vth=(8kBT/πM)1/2$⁠, where ρ is the monomer density, and r₀ and r_n are the hard sphere equivalent radii of a monomer and a cluster. In this expression for the condensation rate, the cross section is taken as the surface area of a sphere of radius r_n and the sticking probability upon collision is equal to 1.

Consequently, if this probability is not 1 but dependent on facet orientation, the shape of a crystal can change if there is a mix of different facets on the surface. For example, when metal atoms add to the {100} faces of a nanocube, they migrate to the edges of the face resulting in the elongation of the {111} facets. Progressively, the cube transforms into a cuboctahedron and eventually an octahedron. This shape evolution process is known as overgrowth.

The introduction of a capping agent can alter the growth rates of the different facets, thus dramatically altering the final nanocrystal shape. In discharges in liquids, sodium citrate,^131,138 reverse micelle solution [sodium bis (2-ethylhexyl) sulfosuccinate in dodecane],²⁴⁰ sodium dodecyl sulfonate,¹³⁵ cetyltrimethylammonium bromide (CTAB),²⁴¹ among many other capping agents, are used from recipes developed for chemical processes.

It is important to mention that surfactants and capping agents are very difficult to decompose completely, which results in poor catalytic activities. Discharges in liquids are often presented as efficient methods to synthesize nanoparticles without any surfactant.

Nanoparticles within the discharge can melt, be vaporized or coalesce, leading to changes in size distributions.

The melting point of a spherically symmetric nanoparticle decreases as the radius decreases, which is only observed at very low radius (typically below 10 nm).²⁴² This effect can be described down to about 1 nm for gold²⁴² or nickel²⁴³ by using a continuum model (Fig. 10). Melting point depression is often accounted for by the generalized Gibbs–Thomson implicit relation,

L_m is the latent heat (J kg⁻¹); T_m is the temperature at which the phase change occurs (K); $Tm∗$ is the bulk phase change temperature (K); c_p is the specific heat (J kg⁻¹ K⁻¹); Δc_p = c_l − c_s, σ is the surface tension (N m⁻¹) and κ is the mean curvature; ρ is the density (kg m⁻³); and p is the pressure (Pa). Subscripts a, s, and l indicate ambient, solid, and liquid, respectively.

Surface atoms are less strongly bound to the cluster than the bulk atom. Then, melting proceeds by separation of surface atoms from the bulk. This separation is paid for with the latent heat. With a sufficiently large cluster, the energy required is relatively constant since each surface molecule is affected by the same quantity of bulk molecules. However, as the cluster decreases in size, surface molecules are less and less influenced by the bulk, and less and less energy is required for separation. The change in the ratio of surface to bulk energy may also lead to a structural transition and a reduction in surface tension.

Once the vapor is emitted from the electrode, it condensates farther in colder regions into droplets that are still prone to vaporization along their path. Vaporization of a nanodroplet is affected by the particle size. The equilibrium pressure at the surface of the droplet [Eq. (2)] must be corrected.^244,245 The correction is as follows:

where $Psr$ is the saturation pressure for a droplet of radius r, σ is the surface energy, and ρ is the density.

Coalescence affects the size distribution of nanoparticles by merging primary particles, i.e., those produced by condensation, into a larger single nanoparticle (see Fig. 11). This is a very complex phenomenon between nanocrystals that can be decomposed into elementary steps,²⁴⁶ 

1. Coagulation refers to the attraction and contact between primary particles. In the discharge, it is due to in-flight collisions after which particles remain stuck together. This phenomenon is often referred to as Smoluchowski ripening.²⁴⁷ 

2. Rigid body reorientation occurs once the primary particles are close enough to start interacting. An interface forms that is usually misoriented because of the randomness in coagulation geometry. Thus, a number of interface layers are shorn. Eventually, the particles rotate as rigid bodies, driven by mutual torques, maximizing the contact area. A more coherent interface with a larger area is then produced.

3. Formation of defects results from the very fast (few ps) reorientation stage. If primary particles cannot be perfectly aligned because of their geometry, which is the most probable situation, a twin boundary—commonly accompanied by the appearance of misfit dislocations—forms, as rotation is hindered by the newly formed bonds.

4. Heat release results from free-surface annihilation due to bond formation. As the surface/volume ratio decreases, the part of the surface energy remaining after the creation of the interface transforms into thermal energy.²⁴⁸ 

5. Temporary melting of interface has been proposed by Grammatikopoulos et al.²⁴⁹ If the heat release essentially contributes to the temperature rise of the child particle (case of an adiabatic system), it can be sufficient to reorganize it at the atomic level. A wave that originates at the interface between the primary particles propagates along the body of the child particle, resulting in its full crystallization. Concurrently, a temporary disordering of the atoms at the interface and a “softening” of their bonds is observed.

6. Neck growth is all the more fast as local curvature is high, which speeds up atomic surface diffusion. A neck is formed on either side of the interface when primary particles coagulate. However, the neck only reaches substantial dimensions if it is promoted by the temporary melting of the interface that enhances the transport of atoms from the core of primary particles to the neck.

7. Plastic deformation. Even after neck formation, the system can still behave within the elastic limit (∼0.8 nm after Averback and Zhu²⁵⁰) as a coupled oscillator (with possible rotation of the two primary particles). Thermal vibration makes each particle pulsate around the initial contact locus. Plastic deformation is then possible by relaxation of accumulated internal shear stress, possibly assisted by the heat, which enables the glide of misfit dislocations and their annihilation at the surface. Protrusions can thus be formed.

8. Consolidation. The neck thickens at a growth rate that slows down because the difference in curvature between the neck and the primary particles becomes smaller. The two-particle system gets stiffer, which hinders its pulsation, and makes it behave as a single particle. Consolidation takes about 100–200 ps. Free-surface annihilation becomes negligible, and so the heating it induces. Oftentimes, experimentally grown nanoparticles are trapped in a metastable steady state due to quenching upon deposition. Coalescence is often considered as achieved at this point in theoretical approaches.

9. Slow ageing, however, extends the coalescence process and favors a “sphericization” of the system, as referred to by Lewis et al.,²⁵¹ a process that lasts for hundreds of ns up to a few μs. This means that the ratio of the surface area of the particle tends toward the surface area of a sphere of the same volume as the particle. Here, the neck acts as a sink for diffusing atoms.

Except for gold, nanoparticles produced by submerged discharges are prone to be oxidized either in air, when they are floating on, or taken out of a non-oxidizing liquid. They can also be oxidized on purpose, but this aspect is deemed to be beyond the scope of this article. Oxidation of sub-micrometric objects has been studied thoroughly.²⁵² Only oxidation in dry air at room temperature is described here. This process changes the size of the pristine nanoparticles because of the change of molar volume between the metal and its oxides.

Basically, when the particle is less than 1 μm in diameter, electrical neutrality, assumed in Wagner's theory for thick films,²⁵³ within the oxide layer is not satisfied, and when less than 20 nm, the Nernst–Einstein relationship is no longer appropriate. Thus, theories of thin film growth must consider atom jumps in the presence of large electric fields and the possibility of large space charges.

Cabrera and Mott's theory assumes that electrons can freely pass from the metal to ionize adsorbed oxygen atoms or molecules at the oxide/gas interface, so that the electron electrochemical potential (Fermi level) is equal in the metal and the adsorbed gas layer.²⁵⁴ The general picture is based on the injection of defects into the oxide at one of the film interfaces (with gas or metal). This process is assumed to be rate-controlling. Using the Kröger–Vink notation and taking the example of chromium oxidation, one notices that depending on the temperature and O₂ partial pressure, either triply charged chromium vacancies are injected at the gas/oxide interface and diffuse inward,

or triply charged interstitial chromium atoms are created at the metal/oxide interface and diffuse outward,

In both cases, the accumulation of vacancies at the metal/oxide interface induces the development of Kirkendall porosity. Such a porosity is not observed if the oxide growth is driven by two other types of mechanisms, observed with other metals: oxygen atoms, injected at the gas/oxide interface, diffuse inward (p-type MO_1 + x) and oxygen vacancies, injected at the metal/oxide interface, diffuse outward (n-type M_1 + xO). This explains why oxidation of some nanoparticles leads to core–shell structures and/or hollow particles.

For very thin (i.e., where tunnelling can no longer be neglected) films, Fromhold showed that the assumption of electronic equilibrium is reasonable.²⁵⁵ In the case of nanoparticles, quantum confinement effects should also intervene, but to best of our knowledge, no study has been done on this topic yet.

Finally, it is also important to mention that reduction of nanoparticles after oxidation does not lead to a complete recovery of the initial metallic state. For instance, after oxidation in O₂, ZnCu clusters (<10 nm) transform into a polycrystalline cluster consisting of separate CuO and ZnO nanocrystals. Subsequent reduction in H₂ converts CuO into Cu with ZnO nanocrystal covering its surface. Then, H₂ dissociates onto metallic Cu to form H atoms that partially reduce ZnO into CuZn.²⁵⁶ 

These theories are based on point defects but oxidation is also affected by the presence of structural defects that play a tremendous role at low temperature, as volume diffusion is strongly limited because of high-energy barriers of jump processes. These barriers can be lowered by stress to a certain extent, which is also an important effect to take into account in order to predict correctly how oxidation occurs in these specific conditions. Finally, in air, not only oxygen but also water can intervene as oxidation agents. The reader is referred to a number of seminal papers illustrating these phenomena in the case of different elements: e.g., oxidation at room temperature of reduced iron oxide nanoparticles by Wang et al.,²⁵⁷ air oxidation of monodisperse cobalt nanoparticles by Varon et al.,²⁵⁸ the first stage of air oxidation by Chen et al.,²⁵⁹ or the evolution of the oxide thickness and oxidation rate of Si nanoparticles in air and at room temperature by Yang et al.²⁶⁰ 

The effect of the spherical geometry on metal oxidation driven by mobile charged point defect was also studied by Fromhold.²⁶¹ The electric potential developed across the oxide is the same as for planar geometry, but the time, for complete oxidation for spherical particles of a given diameter, can be as much as a factor of 3 shorter than that for planar samples of same thickness.

Discharges in liquids can be used to synthesize nanoparticles made of, at least, two different materials that can be organized in different structures depicted in Fig. 12. Both materials are made immiscible, either because thermodynamics imposes it [Figs. 12(a)–12(e)] or because they are synthesized successively [Figs. 12(a)–12(c)].

Bi-particles [Fig. 12(a)] have been synthesized by different groups, e.g., Pt–Pd,²⁶² Ni–Cu,²⁴¹ Ag–Pt,²⁶³ Ag–Cu,²⁶⁴ etc. This kind of structures results from coalescence of particles that are synthesized either simultaneously (from electrodes made of different materials) or separately (in space and/or time). Tsukanov et al.²⁶⁵ showed by molecular dynamics that immiscible nanoparticles can interpenetrate if they collide with sufficiently high relative velocities.

Core–shell structures [Fig. 12(b)] are usually obtained by chained treatments where seed nanoparticles of one material are coated by another material in a second step. The best way to coat nanoparticles already present in a liquid is to decompose a precursor that deposits onto the nanoparticles’ surface. This is easy to achieve by discharges in contact with liquids, for instance.

Conversely, discharges in liquids rather form attached nanoparticles in sequenced treatment. The expansion of the discharge repels nanoparticles added in the liquid from emitted species by the electrodes. Then, one-step synthesis is only possible by mixing intimately the two elements in a crucible: e.g., CuO@Ta₂O₅.¹²³ For a carbon shell, one-step synthesis is also possible with a carbonaceous liquid, like benzene or hexane: e.g., (Co, Ni, Fe)@C.^266–268 Then, using a liquid precursor (like HAuCl₄) in a aqueous colloidal dispersion containing nanoparticles, say Pt, should give Pt@Au nanoparticles in one step. But to the best of our knowledge, no experiment of that kind has ever been done yet.

Pulsed laser ablation also provides similar capabilities. For instance, the introduction of ad hoc solvents lead to the creation of carbon shell or structures.²⁶⁹ Even more interestingly, the possibility of using CO₂ sub-products in solution with NaOH was showed to be efficient for the production of gold–carbon nanocomposites.^270,271

Kabbara et al.²⁷² showed that it is also possible in two steps, by wrapping one type of particle (Cu) into an ultra-thin foil made of another one (Zn) synthesized beforehand, this mechanical way of forming core–shell nanoparticles requiring no deposition.

Decorated nanoparticles [Fig. 12(c)] are usually obtained by depositing one phase of small size onto another phase of large size. Usually, this is a two-step process. This has been achieved in one step by discharges in liquids for the Si–Sn system.²⁷³ The mechanism relies on grain detachment of a sintered Si–Sn electrode, where Si and Sn are well separated, leading to tin nanoparticles attached to silicon grains.

Nanoparticles with multiple domains [Fig. 12(d)] are either made of one phase inlaid into another or made of one phase segregated at the grain boundaries of another. These particles, as Janus particles [Fig. 12(e)]—a special type of nanoparticles with surfaces exhibiting two or more distinct physical properties—have only been synthesized by PLAL but not by discharges in liquids.

As discharges in liquids most often produce several size distributions, it is essential to describe how to measure them, which requires to master the techniques used in order to get convergent results. It is also possible to change size distributions by fragmenting nanoparticles.

Ashkarran et al.¹³⁰ (Table I) obtained almost monodisperse (i.e., with a geometric standard deviation of a log-normal distribution <1.25) gold colloidal dispersion (mean size: 8 ± 3 nm) by creating discharges between two titanium electrodes in a HAuCl₄ solution. This process behaves as an electrochemical process, similarly to discharges in contact with liquids. Submerged discharges in liquids where nanoparticles are produced by electrode erosion produce multimodal size distributions (Fig. 13).^145,274,275

At most, three distributions coexist. Large particles (i.e., >100 nm and up to tens of μm) are only a few and spread all over the substrate. Nanoparticles of intermediate size (i.e., from 20 to 100 nm) are found either as necklace-like or fractal agglomerated structures or as isolated particles. Nanoparticles of small size (i.e., from 2 to 10 nm) are primary particles.

However, this approach is not satisfactory as the various populations are not associated with their mechanisms of formation. From the list of erosion mechanisms established hereinabove, it is easy to understand that the origin of the largest population of nanoparticles is due to ejection of droplets from the liquid well, but there are several possible mechanisms that may be involved. The origin of the smallest distribution can only be due to the rapid condensation of the vapor phase. On the contrary, the origin of the intermediate-size population can be multiple. The smallest nanoparticles can continue growing if they stay within the discharge region, reacting with the emitted vapor that is not homogeneously distributed within the interelectrode gap. They can also grow by coarsening with other particles and then the distribution of the particles themselves also matters. Consequently, we could expect 4, 5, or even more contributions in a multimodal size distribution. This statement is corroborated by several works where trimodal distributions are proposed (see, for instance, Refs. 128 and 150; Table I) but with very different mode positions. The issue lies in the possibility for distinguishing accurately all the modes in a distribution of nanoparticles.

In LASiS, nanosecond pulsed laser ablation is known to give more or less narrow monomodal distributions that are described by a log-normal distribution, ablation being principally driven by thermal processes. On the other hand, pico- and femtosecond ablation may lead to multimodal distributions due to the multiple ablation mechanisms. In this latter case, size distributions can also be sometimes described by a log-normal distribution. Therefore, caution must be taken to interpret these size distributions.

Logically, the existence of several erosion mechanisms must lead to an identical number of distributions. However, one reads commonly that two populations are to be distinguished: small and large. In recent studies based on molecular dynamics simulation, Shih et al.^175,176 investigate the origin of bimodal nanoparticle size distributions produced by laser ablation in liquids. They establish that “three distinct nanoparticle generation mechanisms operating at different stages of the ablation process and in different parts of the emerging cavitation bubble” exist. Two of them produce large nanoparticles (spallation and explosive boiling) and one small nanoparticle (nucleation at the very front of the emerging cavitation bubble). They conclude that “the coexistence of the three distinct mechanisms of the nanoparticle formation at the initial stage of the ablation process can be related to the broad nanoparticle size distributions commonly observed in nanosecond PLAL experiments.” To the best of our knowledge, no attempt was made to fit with a multimodal approach, and size distributions of nanoparticles produced by ns laser pulses that can be described by a monomodal log-normal function.

The confusion also exists because only the smallest nanoparticles are collected for the analysis. For instance, it is possible to proceed as follows.²⁷⁶ In a discharge-based process, when heavy particles settle at the bottom of the vessel that contains the synthesized colloid suspension, this latter can be cleared from its sediments by pouring carefully the upper part of the solution into another beaker. Then, small quantities of the new solution containing only its lightest particles can be collected with a pipette for further characterization.

There are several techniques that can be used to evaluate the mean diameter of a set of well-defined nanospheres: dynamic light scattering (DLS), atomic force microscopy (AFM) in tapping mode, UV-visible spectroscopy, and two-color Surface Plasmon Resonance (SPR) spectroscopy. Several articles^277,278 showed that estimates of the mean diameter of well-controlled nanospheres synthesized by wet chemistry and evaluated by the previously cited techniques are very close, demonstrating the convergence of these methods for almost ideal spheres. On the other hand, for other types of nano-objects, caution must be taken to interpret results produced by these different diagnostics, as discussed by Tomaszewska et al.²⁷⁹ For example, differences between TEM and UV-Vis spectroscopy often arise due to

• possible agglomeration of nanoparticles during deposition on the grid, especially in colloidal dispersions in water;

• non-spherical shape of nanoparticles;

• a non-representative sampling of nanoparticles for the TEM analysis; and

• nanoparticles are oxidized, which affects the effective dielectric constant to be used in the Mie fit required by UV-Vis spectroscopy.

The existence of an intermediate size distribution is not clearly understood yet, likely because it probably results from distinct phenomena,

• the duration of the nucleation process may strongly vary if the vapor is emitted at the very beginning of the process, when the pressure is high, or much later, when it is reduced;

• it is also true for the vapors emitted by the cathode and by the anode;

• coalescence of particles certainly affects the size distribution, smear out transitions between modes, etc.

To conclude about size distribution, it is important to mention that even though it is a useful concept to describe the population of nanoparticles produced by a given process, it cannot be used usually to correlate observations on size modes with underlying growth mechanisms.

Until now, fragmentation of nanoparticles has not been observed with electric discharges, but this process might exist as well for sufficiently fast electric fields (picosecond-pulsed discharges). Indeed, Giammanco et al.²⁸⁰ fragmented Au nanoparticles by interaction with the second and the third harmonics of a Nd:YAG picosecond laser. However, laser and discharge treatments are already associated in that purpose.²⁸¹ 

The photothermal mechanism responsible for nanoparticle fragmentation relies on the way temperature rise in response to laser excitation. At moderate fluences, heating, melting, and evaporation of irradiated nanoparticles enable size reduction of primary nanoparticles, creating a new population of smaller ones by nucleation and growth from the evaporated atoms. At higher fluences, nanoparticles can be either fully evaporated or fragmented by explosive decomposition into vapor and liquid droplets when superheated up to the limit of thermodynamic stability of the molten material.²⁸² 

According to Huang and Zhigilei,²⁸³ the detailed analysis of the nanoparticle fragmentation mechanisms reveals two distinct pathways of the formation of the fragmentation products: (1) the direct generation within ∼100−200 ps of relatively large nanoparticles with diameters ranging from ∼2.5 to 4 nm and (2) the much more gradual growth of smaller nanoparticles formed by agglomeration and coalescence of atomic clusters on the timescale of tens of nanoseconds. These two pathways are responsible for the early appearance of a bimodal mass-weighted particle size distribution.

The discharge–liquid interface is very difficult to probe but interesting results could be obtained thanks to original experimental works. Sano et al.²⁸⁴ recorded under microgravity conditions the development of an arc discharge submerged in water. They notice, from images of the reactor falling freely in a column under vacuum for about 4 s, that a transparent gas film was generated in the gas phase zone adjacent to the gas–liquid interface. The authors concluded that chemical reactions involving water were possible inside the bubble and not only at the water–gas interface.

The behavior of nanoparticles in discharge bubbles is much better understood thanks to recent results obtained with synchrotron facilities on pulsed laser ablation in liquid.^285–287 It has been shown, with SAXS experiments, that the bubble interface is a quite impervious boundary for primary and secondary particles. In PLAL, they cross the interface barrier by jet-like emission after the collapse of the first rebound. These two statements must also apply for submerged discharges created between two electrodes. Indeed, bubble oscillations produce many different kinds of instabilities like Rayleigh–Taylor, Kelvin–Helmholtz, Landau–Darrieus, or Birkhoff, leading to jet-like emission (Fig. 14).²⁸⁸ 

Basically, the discharge–liquid barrier is rather nanoparticles tight. The transfer from one phase to other is limited. This is also the case of the liquid–air barrier.

Sano et al.^38,289 synthesized carbon nanomaterials by erosion of graphite electrodes submerged in water. They noticed that nano-onions (average diameter : 25–30 nm) were majorly present as floating powder on the water surface, and the other nanocarbons being rather found located on the bottom of the vessel.

Even though the liquid evaporates, this mechanism does not transport any nanoparticles in air.²⁹⁰ This is why the dewetting of a colloidal dispersion concentrates nanoparticles at the moving front of the liquid fingers that form upon demixing of the two phases.²⁹¹ However, evaporation is affected by the presence of nanoparticles.²⁹² 

As long as nanoparticles are left in the liquid, nanofluids in containers can be considered as safe. However, they also face public concerns about their safety in use as they can be spilled by accident. The lack of legal framework for their handling and recycling is a key issue.²⁹³ It would be prudent to pursue green designs by choosing nontoxic or biodegradable nanoparticles.²⁹⁴ 

Discharges in liquids or in contact with liquids can be used for appropriate post-treatments of colloidal dispersions. Sometimes, one-dimensional objects are also synthesized together with nanoparticles as their assembly can be driven by electric fields. Then, applying electric fields with proper strengths in a post-treatment is a way to form new one-dimensional objects.

Because of the difficulty to control the complex chemistry induced by the presence of additives in processes using submerged discharges, it is possible to resort to a plasma post-treatment, as developed by Mariotti et al.⁴⁸ It relies on the utilization of plasma jets in contact with liquids. In this configuration, electrons are injected into the liquid solution from the plasma phase. More efficiently than radicals formed in the gas phase and ultra-violet radiation, electrons are supposed to mainly contribute to a specific liquid chemistry for the surface engineering of pre-synthesized nanomaterials.

This post-processing results in considerable improvements in the stability of a colloidal dispersion, especially in the case of silicon nanocrystals in ethanol or water, which could not be observed with standard electrochemistry,^295,296 and carbon.²⁸⁶ Stable Si-ncs can be created with different surface functional groups. This physicochemical change affects the optical properties of the colloid, and its photoluminescence emission varies from 590 to 650 nm just by changing the oxygen-bonding configuration at the surface.²⁹⁷ 

Discharges in liquids can be used to activate physicochemical processes, for example, by enhancing the reactivity of metal particles. High-voltage electrical discharges in liquids⁷⁴ are capable of

• modifying the kinetics of the reaction between particles;

• decreasing the energy of formation of new phases and compounds;

• increasing surface and bulk diffusion of reacting compounds;

• modifying the morphology and the dimensional characteristics; and

• changing physical and mechanical properties of treated materials.

If these effects have been demonstrated, they are not very well documented and still to be investigated in detail. Nonetheless, these empirical post-treatments demonstrate clearly that discharges in liquids are also very promising for controlled modifications of nanoparticles and not only for their synthesis.

A particle moving in a liquid environment can be submitted to many contributions like gravity, van der Waals or multi-body interactions, electrothermal flows, Brownian motion, fluid dynamics, etc. In this work, because light is shed on discharges produced between submerged electrodes, a special attention is paid to the electrokinetic motion of particles lying in an electrolyte exposed to an externally applied electric field.

Electro-osmosis is responsible for the flow driven by the Coulomb force induced by an electric field on the net charge in the electrical double layer at the electrodes. Upon experiencing an electrical potential gradient, the mobile ions in the Gouy–Chapman layer move past the electrode surface and drag molecules of the solution, putting the fluid in motion. Nanoparticles, whatever their charge, are carried by the flow of the liquid and not because of their own electrical double layer.

The electro-osmotic flow is evaluated by solving the Navier–Stokes continuity and momentum equations coupled with Laplace's equation for the external electric field and Poisson's equation for the potential within the electric double layer.

Electro-osmosis exerts a long-range interaction and does not scale with the particle radius, contrary to dielectrophoresis (DEP; see next paragraph) that results from short-range interactions and scales with the particle volume. Both forces can be combined to trap and manipulate nanoparticles.²⁹⁸ 

The principal drawback with DC electro-osmosis is the need for high DC voltages (up to 1 kV) across a 1 cm gap typically to reach acceptable flow velocities (around 100 μm s⁻¹).²⁹⁹ This can lead to unwanted electrochemical reactions, electrode dissolution, gas bubble production, and/or hydrodynamic instability. Resorting to AC electro-osmosis with voltages of only a few volts by using planar periodic arrays of interdigitated, asymmetric electrodes can overcome these drawbacks.

It was shown by Gierhart et al.³⁰⁰ that particle motion by AC electro-osmosis greatly influences the morphology of resultant nanoparticle assemblies.³⁰¹ With frequencies ranging typically from 0.1 to 10 kHz, this phenomenon is likely to be considered in AC-excited submerged discharges (see Table I).

The motion of a submicrometer particle is influenced by the cloud of ions near the charged or the polarized particle induced by the external electric field.

The particle can be initially charged and possess an equilibrium surface charge, which need not be uniformly distributed over its surface. The interaction between the electric field and the surface charge corresponds to the linear electrophoresis (EP) problem, where the dynamic reaction experienced by the particle and the induced mobility are linear in the external electric field.

For a polarizable uncharged particle, the external electric field produces an additional space charge distribution in the electrolyte, which decays away from the particle. The corresponding induced-charge electrophoresis (ICEP) problem implies that the force and torque experienced by the particle are nonlinear (quadratic) in the electric field.

Dielectrophoresis can be utilized to assemble nanoparticles into wires. Alternating current fields allow assembly of particles without the interference of direct current effects like electro-osmotic and electrochemical effects. The dielectrophoretic force results from the interaction of particle dipoles in a non-uniform DC or AC field. It is conservative and oriented along the field gradient,

a is the particle radius and ℜ denotes the real part of the Clausius–Mossotti factor, which is an effective polarizability of the particle in the medium, and it depends on ω, the angular field frequency. It is expressed by the complex relative permittivities of the particle $ε~p$ and of the medium $ε~m$⁠,

ℜ is bounded between −1/2 and 1 and varies with the frequency of the applied field and the complex permittivity of the medium. $∇→|E→rms|2$ is the gradient of the square of the root-mean-square electrical field. Then, the strength of the force exerted on a particle depends on $∇→|E→rms|2$ and also on ℜ. The frequency dependence of ℜ is given by

At high frequency, when $ω≫τMW−1=σp+2σmεp+2εm$⁠, where σ_m denotes the electric conductivity,³⁰² $ℜ→ℜ∞=(εp(ω)−εmεp(ω)+2εm)$⁠. At low frequency, $ℜ→ℜ0=(σp(ω)−σmσp(ω)+2σm)$⁠.

Positive dielectrophoresis occurs when ℜ > 0; the force is in the direction of increasing field strength and the particles are attracted by the electrode edges. The opposite behavior is observed for negative values.

In the interelectrode gap, nanoparticles experience a large electric field that induces a dipole in each of them if they are not conductors. In the case of most metallic particles for instance, ℜ = 1 because the conduction band electrons redistribute continually to annul the internal electric field. The field frequency needed to keep charges separated on each side of a metallic nanoparticle should excess tens of THz. On the contrary, dielectric nanoparticles with diameters between 10 and 100 nm can be trapped by an ac field in the MHz range.³⁰³ 

However, in 2001, Hermanson et al.³⁰⁴ succeeded in synthesizing gold wires with millimeter length in an AC electric field from a suspension of gold nanoparticles by dielectrophoresis. They suggested some collective effect or complex electrohydrodynamic interactions to account for direct chaining of gold nanoparticles.

Barsotti et al.³⁰⁵ considered in addition to the dipole contribution to the DEP force, effects of higher-order polarization moments and forces.³⁰⁶ These higher-order corrections to the DEP force cannot be neglected for conductive particles in AC fields and introduced a non-conservative term proportional to the curl of the vector electromechanical potential $W→n$ and the imaginary part of Clausius–Mossotti factor,

In the general case where spatially non-uniform electric fields are encountered, both DEP and ICEP contribute to the particle movement. The combined non-linear electrokinetic effect is known as dipolophoresis (DPP).³⁰⁷ DEP and ICEP mechanisms act in different directions and their combination can either be additive or be subtractive. Under appropriate circumstances like a constant gradient field, the sum of the two contributions can be null and particle mobility turned to zero.

In this pedagogical review, emphasis is put on specificities of discharges in liquids in nanoparticles' synthesis. As colloids and nanofluids are generated by these processes, application related to these biphasic systems is extremely large. For instance, they can be used:

• to replace water and ethylene glycol as conventional coolants in an automotive car radiator;³⁰⁸ 

• to produce hydrogen via their use as working fluid in solar parabolic trough collectors;³⁰⁹ 

• to recover oil more efficiently in rock pores by depositing a wedge film making rock surfaces more dewettable;³¹⁰ 

• to decrease by several orders of magnitude bacterial activity including Gram-negative, Gram-positive, and spore bacteria;³¹¹ 

• to serve as a new reaction media in the preparation of chemicals, like amides via direct amidation of aliphatic carboxylic acids;³¹² 

• to enable sensing like, for instance, those magnetically polarizable nanoemulsions used for imaging internal defects in materials;³¹³ etc.

There is a number of challenges that deserve to be tackled:

• Recently, nanoalloys, i.e., single solid solution, made of immiscible elements have been synthesized by PLAL.^314,315 Producing them by discharges in liquids has been showed to be possible too.³¹⁶ Mechanisms leading to nanoalloying of immiscible elements are still to be clarified.

These new results open up the way to the study of optical properties of metallic nanoalloys.^315,317 Engineering of nanoalloys for optical properties consists in controlling defects, element distributions, oxidation, and surface functionalization processes.

• Chemistry driven by discharges in liquids is a very complex topic, still in its infancy. Discharges in carbonaceous liquids, for instance, are responsible for the deposit of a carbon layer onto nanoparticles, but they also produce unusual chemical by-products like polyynes.³¹⁸ This is also true for the synthesis of uncommon nitrogen polymer³¹⁹ or diamondoids.³²⁰ 

Chemistry driven by discharges in liquids is extremely complex and capable of producing rare by-products. The possibility of a better control of chemical reactions in the liquid phase is an important stake. It is a major challenge for discharges in contact with liquids³²¹ but also for discharges in liquids.

• Multimodal size distributions are still an issue for large-scale production of well-controlled nanoparticles, but huge progress made recently on erosion mechanisms gives promising outlook to achieve unimodal monodisperse size distributions.

The possibility of controlling size distributions in a one-step process is not an easy task. If unimodal distributions have been produced by several groups (see Table I), none of them achieved to get monodisperse distributions. Discharges in liquids containing precursors are more suited to this goal than processes based on electrodes erosion.

• Control of defects to control properties.

Engineering of defects (twin defects, vacancies, edges, doping, etc.) in nanoparticles is a key topic to better control optical³²² and catalytic properties.³²³ Controlling defects in nanoparticles by discharges in liquids remains hitherto a dare to take. This is could be a way to develop low-cost catalysts based on non-rare chemical elements or to tune non-linear effects in nanoparticles for optics.

• Control of surface physicochemical states.

Controlling the grafting of selected chemical functional groups on nanoparticles remains a challenge. It is essential anyway to set the stability of nanoparticles in colloidal dispersion. It also controls their activity, not only catalytically but also optically. It may even affect the chemical homogeneity of very small nanoparticles. As seen before, discharge-enhanced post-treatments can be used to functionalize nanoparticles, but resorting to these processes cannot be generalized to any situation.

The authors acknowledge the French PIA (programme d'investissements d'avenir) project Lorraine Université d’Excellence (Ref. No. ANR-15-IDEX-04-LUE) for financial support.

The data that support the findings of this study are available from the corresponding author upon reasonable request.