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Driving chemical reactions with plasmonic nanoparticles is a rapidly growing field of research, with potential applications of high economic and industrial impact. Localized surface plasmon resonances in metal nanoparticles can catalyze chemical reactions via optical near-field enhancement, heat generation, and hot-charge carrier injection1. The latter mechanism, based on the use of non-equilibrium electrons and holes to activate redox reactions, was initially proposed in 2004, paving the way to a very active branch of research in plasmonics2, 3. Photon absorption in plasmonic metal nanoparticles results in the excitation of non-equilibrium electron–hole pairs with an energy as high as a few eV. Such non-thermal, highly energetic charge carriers are termed hot carriers in solid-state physics because they markedly deviate from the thermalized Fermi–Dirac energy distribution of the free electrons in the metal. The transfer of these hot charge carriers from the nanoparticle to the surrounding molecular adsorbates or photocatalytic materials (such as TiO2) is capable of driving electronic and chemical processes in the nanoparticle vicinity. Since 2010, there has been a sudden rise in the number of publications related to hot-carrier plasmonics, driven by seminal work from the groups of Moskovits4, 5, Halas6 and Linic7, 8, among others, and forecasting applications in nanochemistry8, 9, water-splitting5, 7, 10, optoelectronics6, 11, and photovoltaics4, 12-14.
Depending on the application, different definitions of hot electrons in plasmonics have been used, and some clarification has to be made before going further to avoid confusion and ambiguity. After a photon is absorbed by a metal nanoparticle, a very energetic electron–hole pair is created, with an energy equal to the photon energy hν. This energy is shared between these two carriers with a ratio that depends on where the excited electron originates from within the conduction band15. These primary hot carriers are usually coined quasi-ballistic carriers15-17. Within a few tens of fs18, the primary hot carriers thermalize with the other electrons of the metal through electron–electron inelastic scattering events. These subsequent thermalized charge carriers have a strongly reduced energy compared with the primary hot electrons, less than a few tenths of eV. However, they have also been called "hot" by a large part of the community, especially those working with pulsed lasers, as such low energies still correspond to electronic temperatures on the order of a few thousands of K. These thermalized, "warm" electrons16 should be distinguished from the primary, quasi-ballistic hot electrons because of their lower energy and their longer lifetimes, of the order of picoseconds, dictated by multiple, sequential electron–phonon scattering processes. In hot-carrier-assisted plasmonic chemistry, only primary hot electrons have enough energy to contribute to chemical reactions.
The actual involvement of hot carriers in several chemistry experiments has been recently questioned, with the proposition of alternative mechanisms, such as direct photoexcitation of hybrid particle–adsorbate complexes19-21 or simple heat generation22-24. Indeed, the further thermalization of these excited carriers via electron–phonon scattering leads to heating of the entire nanoparticle and further heat diffusion to the surrounding reaction medium, suggesting that photothermal effects may also contribute to the observed reactivity enhancement25.
The main concern with primary hot carriers resides in their very short lifetime. They thermalize via electron–electron scattering within a time scale τe-e of a few tens of fs for gold18, making any interaction with the surrounding environment a low-probability event. The time-average number of primary hot electrons generated in a single nanoparticle under illumination can be quantified using this simple expression:
$$ \left\langle {N_{{\mathrm{hot}}\, {{e - }}}} \right\rangle = \frac{{\sigma _{{\mathrm{abs}}}I\tau _{{{e - e}}}}}{{h\nu }} $$ (1) where σabs is the absorption cross section of the nanoparticle, I is the irradiance (power per unit area) of light, τe-e~50 fs and hν are the photon energy. For a gold nanosphere, 50nm in radius (σabs=2×104nm2) illuminated at 530nm with I=5×104W/m2 (a typical value from the literature7-9, 26-28), the time-average number of hot electrons in the nanoparticle under steady-state illumination $ \left\langle {N_{{\mathrm{hot}}\, {{e - }}}} \right\rangle$ is ~10−4. This low number means that for irradiances typically used in plasmon-assisted photochemical experiments, primary hot-charge carriers are available for only ~0.01% of the time, i.e., on very brief occasions. Under continuous-wave (CW) illumination, a hot carrier always thermalizes before the absorption of the next photon, such that no primary hot-carrier population exists. A large population of primary hot carriers can exist only under pulsed illumination where thousands of photons can be absorbed during τe-e. However, under the conditions mentioned above, the nanoparticle still absorbs ~3 billion photons per second, generating 3 billion primary hot electron–hole pairs. Thus, the very small lifetime of the primary hot carriers is unfavorable but does not necessarily preclude detectable hot-carrier-assisted processes, a priori. The community is aware of this issue, and several recent studies directly analyze the respective contributions of hot electrons and photothermal effects, as shown in Fig. 1. Nevertheless, although plasmonic nanoparticles are excellent light-to-heat converters, the associated temperature increase is often difficult to predict and measure.
This article is intended to help experimentalists discriminate between thermal and non-thermal effects in plasmon-driven chemical processes. To this aim, we propose seven simple experimental procedures that avoid the use of complex or expensive thermal microscopy techniques, which may sometimes be inaccurate29, 30. These procedures are described hereinafter and critically illustrated with some practical examples from the literature. In the last section, we also provide some practical guidance on how to avoid common pitfalls when using numerical simulations to estimate photothermal effects in plasmonic systems, highlighting the importance of collective photothermal effects in plasmonics.
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Instead of varying the illumination power, varying the light beam diameter can also provide valuable information. As shown further on, this procedure applies only for reactions occurring at the surface of a solid catalyst, such as a substrate covered with nanoparticles6, 38-40 or an optically thick pellet41. It does not apply for photochemical reactions occurring on nanoparticles suspended in a liquid42, where heat diffusion is more complex.
There are two common approaches to varying a light beam diameter on a sample plane: the constant-irradiance (power per unit area) approach and the constant-power approach. In the first case, the beam size is adjusted using a diaphragm on the beam path (Fig. 3a), and the number of photons is thus proportional to the area of the sample under illumination. In the second case, the beam is defocused to vary the beam size on the sample (Fig. 3b), and the number of photons impinging on the sample is therefore constant.
Fig. 3 Two setups for varying a laser beam diameter.
a Constant-irradiance setup: 4f optical configuration enabling the setting of an illumination diameter D1 at the sample location S by adjusting the diaphragm diameter D2, according to the relation . Note that for the 4f configuration to be appropriately used, the optical power density impinging on the diaphragm D has to be uniform, not Gaussian. b Constant-power setup: optical configuration, similar to a when removing lens L2, enabling the setting of an illumination diameter D1 at the sample location S, by adjusting the displacement δx of L1, according to the relation$ {{D}}_{\mathrm{1}}{{ = D}}_{\mathrm{2}}\cdot{{f}}_{{1}}{{/f}}_{{2}}$ . Note that L1 can be the objective lens of a microscope$ {{D}}_1 = \delta {{x}}\cdot{{D}}_2{{/f}}_1$ Let us first consider how these two modes of illumination affect a light-induced process when it is photochemically driven. For a photochemical process, the reaction rate is proportional to the rate of incident photons, as mentioned in procedure #1. In the constant-irradiance mode, the reaction rate is thus assumed to be proportional to the area of the light beam impinging on the sample surface, while in the constant-power mode, no beam-size dependence is expected since the rate of photons impinging onto the sample is constant. Thus, depending on how the illumination beam diameter is varied, the photochemical rate features radically different variations. Note that this reasoning makes no assumption on the sample thickness and, for this reason, applies not only for particles deposited on a flat substrate6, 38-40 but also for thick samples, e.g., made of compacted powders or pellets41.
Things are markedly different if the reaction is photothermally driven. With the constant-irradiance approach, the temperature increase is proportional to the beam diameter: $ \delta T \propto R_{{\mathrm{beam}}}$43. Thus, when opening the diaphragm, the reaction rate increases not only due to the enlarged irradiated area (as with a photochemical process) but also due to a higher temperature increase. With the constant-power approach, the temperature increase is inversely proportional to the beam radius: $ \delta T \propto 1{\mathrm{/}}R_{{\mathrm{beam}}}$43. The smaller the beam is, the higher the temperature. Thus, the rate of chemical reaction is no longer independent of the beam radius, such as with a photochemical process. In both cases (i.e., constant power and constant irradiance), the dependence of the chemical rate on the beam radius results from a subtle interplay between the variations of temperature and illuminated area. If one assumes moderate temperature variations leading to an Arrhenius law that resembles a linear law (as in Fig. 28), one obtains the dependencies summarized in Table 1. For both modes of operation, these relationships systematically differ for photochemical and photothermal processes. Investigating these dependences by varying the illumination diameter therefore appears to be an efficient means to elucidate the underlying mechanism, or at least to show that the underlying process is not purely photochemical. These dependences of δT on the beam radius assume that the heat produced by light absorption in the catalyst is efficiently dissipated via an infinite surrounding medium (as with Eq. (3), further on), as is typically the case with a solid photocatalytic substrate. These dependencies also assume a two-dimensional heat source43 and therefore a two-dimensional light-absorbing medium. If the absorbing medium is 3D or optically thick, such as with a pellet, these dependences are still valid, provided that the heat source remains effectively 2D. This happens when the light penetration depth into the sample is small compared to the beam size. In practice, this condition is generally valid with an optically thick substrate, such as pellets, since they are highly scattering and absorbing by nature.
Process Mode Photochemical Photothermal Constant power δη constant δη ∝ R Constant irradiance δη ∝ R2 δη ∝ R3 Table 1. Dependence of the reaction rate variation δη on the light beam radius R
We noted above that this procedure could be applied for solid samples, typically catalysts and nanoparticles dispersed on a planar substrate6, 38-40 or pellets41, in contact with a gas or a liquid phase, for which a heat source would remain two-dimensional. Indeed, the case of nanoparticles and reactants suspended in solution is more complex and cannot be faithfully investigated using this procedure. Similar dependences on the radius of an illuminated sphere can be derived for a three-dimensional heat source ($ \delta T \propto 1{\mathrm{/}}R_{{\mathrm{beam}}}$ for the constant-power approach and $ \delta T \propto R_{{\mathrm{beam}}}^2$ for a constant light power density approach (in this estimation, the 3D heat source consists of a sphere of radius Rbeam, surrounded by an infinite, conductive surrounding medium)), but these dependences still assume heat diffusion that efficiently occurs over an infinite surrounding medium, i.e., no accumulation of heat within a thermally insulated vessel. This assumption is rarely valid for plasmon-driven catalytic reactions in solution44, 45, where the surrounding medium (sample holder, surrounding air) may have a smaller thermal conductivity than that of the reaction medium itself (the liquid). This would lead to heat accumulation and uniformization within the whole liquid by heat conduction and convection, making any temperature estimation significantly more difficult than with a solid catalytic substrate, usually involving an efficient surrounding conductive medium, such as a stainless steel chamber.
Interestingly, such a technique was previously mentioned by the group of Moskovits in 1994 in the context of photoemission measurements46, although it was, in that case, rather used to discriminate between one-photon and two-photon processes. To our knowledge, this procedure has not yet been used to discriminate photothermal from photochemical effects in plasmon-assisted chemical reactions. For instance, it could have been relevant to studies such as ref. 9 by measuring the rate enhancement of H2 dissociation on gold nanoparticles as a function of the illumination area.
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An easy misconception in plasmon-driven chemistry that is often encountered in the literature is that wide-field illumination of a macroscopic sample can lead to highly localized thermal hotspots at the locations of metal nanoparticles. Against intuition, however, if one illuminates a macroscopic distribution of nanoparticles (say over 1 in ref. 2) in 2D or 3D samples, it is not possible to generate thermal hotspots around each nanoparticle. For instance, for a gold nanoparticle in a water-like medium under illumination, the temperature increase of the nanoparticle is given by83
$$ \delta T = \frac{{\sigma _{{\mathrm{abs}}}I}}{{4\pi \kappa \beta R}} $$ (2) where σabs is the nanoparticle absorption cross section, I the irradiance (power per unit area), κ the thermal conductivity of the surroundings, R the effective radius of the nanoparticle (radius of a sphere of identical volume), and β≥1 a correction factor taking into account the shape of the nanoparticle (β=1 for a sphere). For a 50-nm diameter nanosphere, to increase its temperature by 1K, the expression implies that one would need an irradiance I on the order of 0.1mW/µm2. This is possible by focusing a laser, but using wide-field illumination as performed in plasmon-assisted chemistry (for instance, 1 inch in diameter), a total light power of 10, 000W would be required. Despite this, Eq. (2) is very often used in plasmonics to calculate the magnitude of photothermal effects under wide-field illumination9, 28, 55, 80, 84, and naturally yields severe underestimations of the actual sample temperature increase, as it considers only the (negligible) local temperature increase while neglecting the (dominant) collective heating that we shall now explain.
When illuminating an ensemble of nanoparticles, in either a 2D layer65 or a 3D (liquid or solid) sample85, the most important parameter is no longer the absorption cross section of the individual nanoparticles but the absorbance of the sample, i.e., its color (white, dark gray, black, …). If the nanoparticle density is sufficiently high, a temperature increase will be observed. Notably, this temperature increase will be spread across the entire sample and will be continuous without any nanoscale features. This effect is commonly known as the photothermal collective heating or homogenization effect in plasmonics43, 47.
This result can be counterintuitive from an optics perspective. In most randomly dispersed plasmonic samples, if nanoparticles are separated by a few diameters, they can be considered optically decoupled, regardless of their quantity. This reasoning, however, does not apply in thermodynamics, where in addition to the average nearest-neighbor distance p and the particle size R, the number of nanoparticles N under illumination strongly matters. The temperature increase experienced by a nanoparticle results from two contributions: its own heat generation and the heat generated by the other N−1 nanoparticles under illumination in the sample. For a 2D distribution of nanoparticles, such as in heterogeneous chemistry where particles cover a flat substrate or in photovoltaics, the balance of these two contributions can be estimated using the dimensionless number $ \zeta _{{\mathrm{2D}}} = \delta T_{{\mathrm{NP}}}{\mathrm{/}}\delta T_{{\mathrm{all}}}$43, 47, indicating the ratio between the local and collective increases in temperature and defined as:
$$ \zeta _{2D}\sim p{\mathrm{/}}3R\sqrt N = p^2{\mathrm{/}}3RL = (3ARL)^{ - 1} $$ (3) where p is the average nanoparticle distance, R is the typical nanoparticle radius, N is the number of nanoparticles under illumination, L2=p2N is the heated area and A is the nanoparticle areal density. This expression assumes uniform and infinite media above and below the layer through which heat escapes.
As an example, from Fig. 7 taken from the literature, one can estimate $ {\zeta}_{{\mathrm{2D}}} = p^2{\mathrm{/}}3RL\sim 10^{ - 4} \ll 1$ (with R=7 nm, p=150 nm, and L=1 cm). Such a small ζ2D value indicates a dominant collective effect, characterized by a uniform sample temperature increase ~104 higher than what can be calculated with the expression (2) of δT for an isolated particle. In other words, the temperature increase of a given nanoparticle represented in Fig. 7 mostly comes from the heating of the other N−1 nanoparticles, although they may seem far away and are optically decoupled. Figure 7b–d presents numerical simulations related to the practical example given in Fig. 7a. Figure 7b plots the heat source density arising from the three particles in the field under illumination at 2.4W/cm2. Figure 7c plots the calculated temperature distribution if the three particles were the only ones under illumination. Localized temperature increases can be observed but with extremely small amplitudes. Conversely, Fig. 7d displays the temperature distribution considering the illumination of an area of 1 cm2, with the same nanoparticle density as in Fig. 7a, leading to two striking features: a uniform temperature without hotspots and a much higher temperature increase, ~4 orders of magnitude higher, as predicted by the estimation of ζ2D above.
Fig. 7 Illustration of collective photothermal effects in plasmonics.
a STEM bright field image of a 1% Au/SiO2 sample used in refs. 9, 28 for the plasmon-induced dissociation of H2 on Au. Reproduced from Supplementary information of ref. 28, with permission from the American Chemical Society, copyright 2014. b Calculated heat source density associated with a assuming an irradiance I=2.4 W/cm2, as in the original work. c Temperature distribution calculated using the Laplace matrix inversion (LMI) method104, assuming that only these three nanoparticles are illuminated with an irradiance I=2.4 W/cm2. d Temperature distribution using Eq. (19) of ref. 43, assuming macroscale illumination with an irradiance I=2.4 W/cm2 over a spot area of 1 cm2, featuring a perfectly uniform temperature, ~4 orders of magnitude higher than in cThe previous example considered a 2D distribution of nanoparticles. When nanoparticles are distributed in three dimensions, collective thermal effects are even stronger. Let us, for instance, consider the case of solar light illuminating a test tube (usually through a Fresnel lens to concentrate the light intensity55, 86) containing a solution of highly concentrated gold nanoparticles, so dense that it looks dark gray or even black. In this kind of study, using Eq. (2) can lead to an estimation of a temperature increase as small as 0.04℃, which contradicts the experimental observation of water boiling55. Indeed, using Eq. (2) amounts to considering that the system is composed of a test tube containing a transparent liquid in which a single nanoparticle is dissolved, while in reality, the system consists of a test tube that contains a very absorbent (black) solution. Illuminating the latter system naturally leads to much higher temperatures. In such studies involving a 3-dimensional system, simulations are more complicated than in 2 dimensions (as in Fig. 7). Appropriate numerical simulations, for instance, using the finite element method, should include the full geometry of the system (the absorbing solution and the ice bath86) as well as an estimate of the conductive and convective heat and mass transfer in the fluid42, 87. For systems in which collective thermal effects lead to a temperature profile that is smooth on the macroscopic scale, using a simple thermocouple (procedure #3) is the easiest way to accurately and faithfully monitor the temperature of the solution. For systems in which large temperature gradients arise due to the inhomogeneous distribution of absorbed optical power, however, multiple thermocouple readings paired with appropriate modeling of light propagation and heat dissipation can be used to suitably account for photothermal plasmonic effects42, 87.
Finally, let us discuss the case of pulsed laser illumination. Femto- to picosecond illumination can be used as a means to further confine the temperature increase around plasmonic nanoparticles under illumination88, but it does not prevent the occurrence of thermal collective effects. Even if the sample is illuminated by fs pulses of light characterized by a fluence F (energy per unit area) and a repetition rate f, there still exists an average irradiance 〈I〉=Ff (power per unit area) that contributes to an overall warming of the sample. The expected temperature increase $ \delta T_{{\mathrm{NP}}}^{{\mathrm{pulsed}}}$ experienced by a nanoparticle, following pulse absorption, can be much weaker than the overall temperature increase δTall experienced by the whole sample due to heat accumulation on the macroscale, especially if many nanoparticles are illuminated at once. To quantify one regime or another, there exists a simple dimensionless number quantifying the ratio $ \zeta _{{\mathrm{2D}}}^{{\mathrm{pulsed}}} = \delta T_{{\mathrm{NP}}}^{{\mathrm{pulsed}}}{\mathrm{/}}\delta T_{{\mathrm{all}}}$ defined as43:
$$ \zeta _{{\mathrm{2D}}}^{{\mathrm{pulsed}}} = \frac{{\kappa p^2}}{{\rho c_pfR^3L}} $$ (4) where κ is the thermal conductivity of the surrounding medium (or an average of the different media), p is the typical nanoparticle nearest-neighbor distance, ρ and cp are respectively the mass density and specific heat capacity of the nanoparticle, R is the typical size of the particle and L is the typical size of the nanoparticle assembly under illumination, usually corresponding to the size of the laser beam.
As an example, in recent reports on heterogeneous catalysis of H2 dissociation on Al–Pd heterodimers under fs-pulsed illumination40, 89, the temperature increase $ \delta T_{{\mathrm{NP}}}^{{\mathrm{pulsed}}}$ was computed using a valid expression, but thermal collective effects were not considered. Based on the experimental details, however, one can calculate $ \zeta _{{\mathrm{2D}}}^{{\mathrm{pulsed}}}\sim 10^{ - 4} \ll 1, $ meaning that the temperature increase is rather mainly dominated by collective thermal effects.