Optical Hydrogen Nanothermometry of Plasmonic Nanoparticles under Illumination

The temperature of nanoparticles is a critical parameter in applications that range from biology, to sensors, to photocatalysis. Yet, accurately determining the absolute temperature of nanoparticles is intrinsically difficult because traditional temperature probes likely deliver inaccurate results due to their large thermal mass compared to the nanoparticles. Here we present a hydrogen nanothermometry method that enables a noninvasive and direct measurement of absolute Pd nanoparticle temperature via the temperature dependence of the first-order phase transformation during Pd hydride formation. We apply it to accurately measure light-absorption-induced Pd nanoparticle heating at different irradiated powers with 1 °C resolution and to unravel the impact of nanoparticle density in an array on the obtained temperature. In a wider perspective, this work reports a noninvasive method for accurate temperature measurements at the nanoscale, which we predict will find application in, for example, nano-optics, nanolithography, and plasmon-mediated catalysis to distinguish thermal from electronic effects.

The ∆ and H 2 partial pressure data used to create a Van 't Hoff plot are described in Figure S4. 4 Figure S3: a, b) Self-referenced initial extinction spectrum in Ar taken at the beginning of the measurement (t 0 ) plotted together with a representative spectrum at high hydrogen partial pressure in the reactor at t 1 . We note the appearance of a maximum and minimum at long and short wavelengths, respectively, which appear as a consequence of hydrogen sorption and the corresponding shift and the change in extinction of the LSPR peak as can be seen in the substrate-referenced spectra (c, d). These data were measured using (a, c) the low-power halogen light source and (b, d) the high-power plasma-arc lamp. In (b, d), the spectrum at t 1 exhibits a region of apparent zero extinction as a consequence of high intensity emission peaks that saturate the CCD pixels of the fixed-grating spectrometer at these wavelengths.  Figure S5: To determine the phase transition pressure, linear fits are applied to the three distinct isotherm regions (i.e., α-, β-, and α+β phases). The phase transition pressure is then defined as the midpoint of the two intersections, as indicated by the red cross.  were done with COMSOL for a Pd particle surface coverage of 11% and 18 %, as described in the SI section S1. The experimentally measured particle temperatures are corrected for fluctuations of the ambient temperature in the room, as was described in Figure S13. The error in T dense and T standard is derived from the 95% confidence interval in the linear fit to the Van 't Hoff calibration curve plus an estimated error of 0.2 °C for the room temperature measurement. The error in the optical power is estimated to be ±0.2 W.

Section S1: Critical Optical Power for Specific Sample Temperature
Our approach cannot just be used to measure particle temperature by varying the hydrogen pressure but also to determine the optical power necessary to reach a specific sample temperature. To demonstrate this concept in a proof-of-principle fashion, we set out to determine the optical power of a halogen light source that is required to reach an absolute Pd nanoparticle temperature of 50 °C. In a first step, we determined the hydrogen pressure required at 50 °C to induce the α-β phase transition by comparing to the pre-recorded Van 't Hoff plot, which results in a critical pressure of 81.4 mbar (Figure S15a). In the next step, we measured optical extinction spectra from the sample at a constant H 2 pressure of 81.4 mbar, while varying the output from 6.5 W to 2.3 W in eight steps. After data processing with the self-referencing approach for each power step (cf. Figure S3), we then end up with an isotherm with the optical power on the x-axis (Figure S15b), from which the required optical power to reach 50 °C particle temperature can be deduced. Figure S15: a) A Van 't Hoff calibration plot used to find a critical optical power needed to reach a particular absolute particle temperature upon illumination. In this case, a Pd nanoparticle is 50 °C when it exhibits the α-β transformation plateau at 81.4 mbar H 2 partial pressure (gray arrows). b) Using this information, when exposed to constant H 2 pressure of 81.4 mbar and varying illumination power (from 6.5 W to 2.3 W), the self-reference spectra of the nanoparticles (cf. Figure S3) exhibits a typical optical isotherm. By determining the optical power at which the phase transition happens one obtains the critical power to reach the 50 °C particle temperature that is 4.68 W. Note that data of 6.5 W was obtained in a separate measurement, as the setup did not allow for power changes of the needed magnitude in one measurement and was therefore marked separately (♦).

Section S2: Heat Distribution Simulations
To simulate the heat distribution on our samples we first calculated the absorbed power by the sample, using an FDTD simulation of the absorption cross section of a single Pd disk with a diameter of 140 nm of and a height of 25 nm as key input. The power absorption was normalized to the source power (see Figure S16) and the absorption of the glass substrate was neglected. As the total absorbed power, we used the integrated absorption over the visible light range which is P abs ≈3.7% of the source power. This assumption is reasonable because the plasma-arc light source used in the experiment is equipped with an IR filter and because the light has to pass multiple glass surfaces which remove most of the UV light before reaching the sample.
To get an estimate for a general temperature increase of the pocket reactor holding the sample induced by illumination, we measured this temperature increase with a thermocouple by illuminating a blank glass substrate inside the reactor and compared it to the results of a substrate with nanoparticles ( Figure S17). This comparison shows that the temperature is only few degrees higher with particles on the substrate, and that the heating due to the particles only accounts for around 10% of the total temperature increase. Therefore, we introduced a parameter, f = 0.1, to in the calculation quantify how much power is absorbed by the sample and how much by the setup.
Furthermore, the amount of power absorbed by the sample also depends on the coverage of the nanoparticles. Therefore, we took SEM images of the different samples (Figure 6a) and determined the Pd particle surface coverage, , obtaining and for the θ θ = 0.11 θ = 0.18 standard and dense sample, respectively.
All the above-mentioned factors were summarized in a pre-factor to calculate the power absorbed by the samples depending on the lamp power output. The pre-factor, P f , is defined as (S1) = abs θ where P abs is the mean absorption by the particles, θ the particle surface coverage of the sample, and f the fraction of light that reaches the sample. For the case at hand, we calculated the prefactor, P f = using the following input values: P abs = 0.037 , θ = 0.11, f = 0.10. 4.07 ⋅ 10 -4

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To simulate the heat distribution, we used COMSOL Multiphysics 5.6 with a conjugated heat transfer setup. The 9×9×0.5 mm 3 glass substrate was modeled in a glass pocket of 25×12×1 mm 3 with 1 mm wall thickness to also include the reactor pocket in the simulation. The pocket reactor is filled with air and a thermocouple made of Inconel 600 with a diameter of 0.5 mm touching the side of the sample is introduced (Figure S18). The material constants were taken from the COMSOL Multiphysics database.
The heat sources were the sample itself with a heating rate of (S2) = lamp where P lamp is the optical power of the lamp that is varied between 1 to 4.8 W. The pocket reactor is as a second heat source representing the power absorbed by the reactor with a heating rate such that the power absorbed by the pocket is 10% of the total absorbed power.
The last parameter of the simulation, the gas flow rate through the reactor pocket, was set to 27 ml/min. This value was chosen to closely match the temperature increase we see during the measurement. Thereby, the flow rate in the simulation was around 8 times higher than the real one in the experiment. This choice is also further justified because in the real setup there are more pathways for cooling, with the biggest contribution stemming from the outside of the pocket by the gas streaming by on the outside of the pocket (inside the reactor tube -c.f. Fig   SI1). Therefore, it is natural that the only cooling path in the simulation needs to be increased to match the experimental results. More importantly, we show that the flow rate has only a minor influence on the temperature difference between the center of the sample and the thermocouple -see Figure S19 below.  is the temperature increase upon illumination, is the nanoparticle absorption Δ σ abs cross section, I the irradiance, and the thermal conductivity of the substrate (SiO 2 ) and κ s κ the medium (Ar), respectively, S the side length of the array, and p the interparticle distance.
The thermal conductivity for the medium was chosen to be the one for pure Ar as our work is mostly carried out in Ar carrier gas in which H 2 is diluted, i.e., we operate in the range between 0 -25 % H 2 only. In other words, even at the highest H 2 concentrations, it is still Ar that predominantly dictates thermal conductivity. 5 The nanoparticle absorption cross section was obtained by FDTD calculations of a Pd disk with a diameter of 140 nm and a height of 25 nm on a SiO 2 substrate ( Figure S16). The used source was a total-field/scattered field source with a linearly polarized plane wave and the dielectric functions for Pd and SiO 2 were obtained from Ansys-Lumericals database originating from Palik et al. 4 From the estimation detailed in SI section S2 Heat Distribution Simulations above, we know that only ca. 10% of the heating upon illumination is caused by the particles. The rest of the heating is contributed by the rest of the setup ( Figure S17). Therefore, here we only calculated the heating induced by the particles and we assumed that only 10% of the irradiated power reaches the sample. We used this value since it is reasonable and describes our system well.
In summary the following parameters were used: 331 nm RDF ( Figure S10) 250 nm RDF ( Figure S10)