Laser Induced Temperature Perturbation on Ultramicroelectrodes: Unsupported Solutions in Nonaqueous Methanol

The solvent for nonaqueous solutions was methanol, MeOH, (HPLC grade, Pharmco-AAPER) purified by incubating in activated alumina (Al₂O₃, Alumina N-Super 1, MP Biomedicals), for at least one week in an Ar glove box. After transferring the MeOH outside the glovebox into the cell with a septum seal, an Ar blanket is maintained at constant flow over the photoelectrochemical cell. For the temperature-controlled cell, we did not attempt to keep the solution under Ar, although we note that solution volume was much larger (ca. 30 ml). All aqueous solutions were prepared in 18 MΩ·cm (Barnstead Nanopure, Thermo Scientific) Tetrabutylammonium perchlorate, electrochemical grade (Alfa Aesar, Thermo Fischer Scientific) was purchased and recrystallized in absolute ethanol before use. Iodine, ≥ 99.99% trace metal basis (Sigma Aldrich).Tetrabutylammonium iodide (TBAI) ≥ 99% (Sigma Aldrich). Ferrocene (Fc) 99% (Alfa Aesar) was used as received.

We performed all experiments in a 3-electrode cell. The working electrodes (WE), were a 10-μm diameter gold disk electrode (Goodfellow wire, Devon, PA, 99.99%) sealed in a soda-lime glass with an inner diameter of 1.10 mm and outer diameter of 1.65 mm (Dagan Corporation) and a 10-μm diameter platinum disk electrode (Goodfellow wire, Devon, PA, 99.99%) sealed in a borosilicate capillary tube with 2.0 mm and 1.5 mm of outer and inner diameter (FHC Inc.). The counter electrode (CE) was a platinum spiral wire, 0.5 mm diameter, annealed, 99.95% metal basis (Alfa Aesar, Thermo Fischer Scientific). The reference electrode, RE, was a home-made ³⁸ I⁻/I₃ ⁻ reference electrode (RE: Pt/ I⁻ ([TBAI] = 20 mM)/I₂(10 mM), TBAP (100 mM), CH₃OH//CH₃OH//), the reference electrode has a double compartment. Electrochemical measurements were done in a CH Instruments potentiostat (Austin, TX), model 760D.

We calibrated the i_ss by measuring LSVs and currents at constant temperature in a jacketed cell (j-cell) with an inlet and outlet connected to a Fisher Scientific Isotemp 3016H circulating water bath. The Isotemp water bath recirculation (15 L min⁻¹) ensures a constant temperature in the water reservoir of the j-cell, allowing control of the temperature inside the cell to within 0.5 K. The temperature inside the cell was monitored with a PTFE coated stainless sheath of 1/8 × 6 in, type sensor K (Part No. 12182–20) connected to a VWR dual thermometer amplifier. An hour after the desired temperature was reached (by reading a constant temperature with the thermocouple) the electrochemical measurements were taken to allow thermal equilibration of the cell and electrodes. The i_ss was measured at room temperature, before heating the solution, at a higher temperature, and again, after cooling back to room temperature. We corrected the i_ss value after the more elevated temperature measurements to account for changes in concentration due to losses during solution heating. Briefly, the thermal bath is set to r.t. to measure the first set of electrochemical curves: CVs, and CAs. We warm up the cell and measure the second set of curves. Finally, we bring the temperature down of the cell with ice and set the thermal bath back to r.t. to obtain a new CV and i_ss to recalibrate for possible concentration losses due to heating.

Photoelectrochemical measurements with laser radiation experiments were performed by illuminating through a glass window in a three-branched electrochemical cell, each branch divided by fritted glass. Thus, the reference and counter electrode are far away from the laser path ca. 6 cm, see Fig. 2c schematics of the cell from the top. Figure 2a shows how the laser-illuminated "from the front" of the UME; the beam covered most of the glass around the electrode; this configuration ensures that the Pt UME is under the beam. The laser system is a continuous-wave laser of HeCd ($\lambda =325\,nm$) model IK3501R-G with Gaussian beam radius of 1.2 mm (${\omega }_{0}$), power of the incident beam 50 mW, transverse mode TEM₀₀, and linear polarization (Kimmon Koha Lasers). Moreover, the laser is a Class 3B laser, which radiation is considered to be an acute hazard to skin and eyes upon direct radiation. UV protective eyewear with OD, optical density, 2.3 has to be used at all times when operating the laser. UV protective gloves have to be used when working near the laser area. Moreover, UV protective gloves must be used when closing/opening the laser shutter. The sampling interval of the chronoamperograms was 5.12 ms and for the cyclic voltammetry 1 ms. Additionally, the experiments, used for the calculations of ratios, were smooth using a rectangle low pass filter with a cutoff frequency of 5 Hz; the reported figures are not filtered.

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Figure 2b shows a schematic of the cell where the laser beam illuminates the WE normal to the plane of the disk electrode. The radius of the laser beam is 120 times greater than the radius of the UME. The relation between the borosilicate capillary diameter on the UME and the laser beam is 1.67 (2 mm/1.2 mm). Furthermore, the laser beam is at a path length between the cell window and the working electrode of ˂ 1 mm. The laser was warmed up for 30 min before experiments. The laser is mounted on a Newport optical table, on the top of an anti-vibration table (made in-house). The illumination is controlled by an electronic shutter (custom-built, with a shutter speed of $\sim$ 6 ms). Note that the reference electrode and the counter electrode have different compartments, and they are away from the illumination path (Fig. 2c). The volume of the cell is relatively large: the WE compartment is 10 ml, while the CE and RE compartment contain approximately 2 ml each.

To estimate the error of T_y, σ_Ty, we apply the usual propagation of error to Eq. 15.

$$\begin{eqnarray}&&{\sigma }_{Ty}^{2}=\displaystyle \sum _{j}{\left(\displaystyle \frac{\partial {T}_{y}}{\partial {x}_{j}}\right)}^{2}{\sigma }_{xj}^{2}\end{eqnarray} \tag{ 16 }$$

Where x_j are the variables in Eq. 15. The operation yields Eq. 17:

$$\begin{eqnarray}&&{\sigma }_{{T}_{y}}^{2}={\left({T}_{r.t.}\displaystyle \frac{{i}_{y}{e}^{y}}{{i}_{x}{\eta }_{r.t.}}\right)}^{2}\left\{\displaystyle \frac{{\sigma }_{{T}_{r.t.}}^{2}}{{T}_{r.t.}^{2}}+\displaystyle \frac{{\sigma }_{{i}_{r.t.}}^{2}}{{i}_{r.t.}^{2}}+\displaystyle \frac{{\sigma }_{{\eta }_{r.t.}}^{2}}{{\eta }_{r.t.}^{2}}+\displaystyle \frac{{\sigma }_{{i}_{y}}^{2}}{{i}_{y}^{2}}+{\sigma }_{{\eta }_{y}}^{2}\right\}\end{eqnarray} \tag{ 17 }$$

Where y = (A + B/T_y) for convenience. The errors in Eq. 17 come from different sources. The error in measuring the initial temperature, σ_Tr.t., is due to the accuracy of the thermocouple (± 0.5 K). Again, we estimated the steady-state current errors, σ_ir.t. and σ_iy from the standard deviation of the i_ss measurement; for more detailed information, see SI, section S7. We estimate the uncertainty in the viscosity at room temperature σ_ηr.t., on the reported values, ³⁷ which are accurate to 1 × 10⁻⁵ mPa s. In contrast, the uncertainty in σ_ηy comes from the error of fitting Eq. 13 to experimental data. For the TBAI data, σ_Ty = ±1 K.

Finally, we performed chopping experiments to understand the heating process, and how long it takes to equilibrate the solution under laser heating, see Fig. 7. In Fig. 7a all curves are labeled sequentially. The black curve in Fig. 7a is a chronoamperogram with the laser shutter closed, thus r.t., or laser gate closed experiment. The transient i–t at room temperature and the LGO are sampled at a different frequency, higher frequency, since the period of the experiment is shorter. We did not attempt to filter these curves in order to point out that the red curve in Fig. 7a has a different sampling rate compared with all the i–t data shown in this work, and this is necessary to obtain the temporal resolution to observe the temperature change at short times after opening the laser gate. In addition, the filtering is only performed to report current ratios. For the chopping experiments, the red curve wasperformed using a shutter with an openning time of $\unicode{x00303}\,\,$60 ms see Fig. 7b; where after 300 s in the dark, we opened the shutter to illuminate the sample. Immediately after the laser illuminates the electrode, a relatively rapid change in D_app is observed for TBAI, which continues for ca. 8 s. Finally, a slower heating regime follows, and this achieves a quasi-steady state region after 300 s of illumination (600 s in Fig. 7a). Figure 7b is a zoom of the fast region that shows the rapid change in current in < 1 s that results from the shutter opening, approximately 60 ms. We convert the change in current to a temperature scale (Fig. 7c) within the first 14 s of photon irradiation; the slope of the first 5 s is in the order of 1 K s⁻¹. Taking the mass of a 10 μm Pt wire, 0.5 cm long, (m = 1.65 × 10⁻⁵ g of Pt) and the average heat capacity, C_p = 0.13 kJ kg⁻¹ K⁻¹, ΔT = 3 K, we can estimate the heat rate absorbed by the Pt, Q = mC_pΔT = 1 μJ, which corresponds to 1 μW. The heating rate of the Pt wire will be around 1.3 μW and this describes the faster heating regime slope: the first 8 s in Fig. 7b, considering a 48% reflectance of the Pt surface, ³⁹ and the absorbance of the solution and glass wall. The slower regime, after 8 s, could be due to heat dissipation, as the temperature increases the glass and methanol in the vicinity of the Pt electrode are more effective in dissipating heat, because of the higher ΔT; this higher driving force, in turn, slows the Pt heating rate, before the break in the x-axis in Fig. 7c. In the second heating regime, there is a nearly constant change on the temperature. This regime is likely the result of heat transfer from the medium, as it gradually heats up due to the laser, as discussed in more detail below. Although here we propose that convection is negligible, based on the discussion below, it is possible that this regime includes some convection. ¹¹ This would mean that the method overestimates our temperature for the data in Fig. 7. In addition, the change in current from 8 to 300 s is 5% which we assume is due to the change in mass transport by diffusion. However, if this 5% larger current has a convection contribution, this will mean the change in current, which in this case corresponds to an increase of < 0.2 K over the 8 to 300 s, is an error due to convection. Since this <0.2 K error is smaller than the method error (ca. 1 K), we assume the convection error, if present, is negligible in the current state of the method.

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We discussed above that the main source of heating the electrode surface is the laser beam power that reaches the electrode surface. We propose that heat transfer by convection could be neglected; i.e., the convective flux due to density and viscosity changing across a temperature gradient is negligible. We discuss two methanol dimensionless numbers relevant to natural convection: Prandtl (P_r), which is the ratio of momentum to thermal diffusitivites ⁴⁰ :

$$\begin{eqnarray}&&{P}_{r}=\frac{{c}_{p}\mu }{k}\end{eqnarray} \tag{ 18 }$$

Where c_p is the specific heat, µ dynamic viscosity, and k the thermal conductivity. For MeOH, P_r = 6.6 which is close to 1. In general, for P_r ≫ 1, e.g., for an oil (P_r > 300), ⁴⁰ convection dominates over conduction. Another parameter relevant to heat transfer by convection is the Grashof number,

$$\begin{eqnarray}&&{G}_{rL}=\displaystyle \frac{g\beta \left({T}_{s}-{T}_{\infty }\right){L}^{3}}{{\nu }^{2}}\end{eqnarray} \tag{ 19 }$$

Where g is the gravitational acceleration, β is the coefficient of thermal expansion, Ts is the surface temperature, T_∞ is the bulk temperature, L is the charateristic distance (electrode diameter) and ν is the kinematic viscosity. For MeOH under our conditions, G_rL = 6.3 × 10⁻⁵, which is significantly smaller than the value expected for natural convection. For example, for water next to a stagnant wall, Gr = 10⁴ to 10⁹ for effective dissipation through natural convection. ⁴⁰ In other words, the P_r and G_rL numbers have values consistent with negligible convection in comparison with heat dissipation by conductivity. These numbers are also consistent with our observation that the temperature gradient causes negligible mass transport convection (Fig. 5) in the steady-state current due to diffusion-limited mass transport to the UME.

Another possible source of heat is the laser power absorbed by the solution in the beam path. For a 1 mM TBAI (A = 0.0419, SI, Fig. S1 (available online at stacks.iop.org/JES/169/016509/mmedia)), the power absorbed by the solution under laser illumination is 3.8 mW for a Pyrex cell. Assuming that a cylinder of 1 mm with the diameter of the beam (1.2 mm), and V = 1.13 × 10⁻³ cm³, and that the solution converts all the absorbed energy to heat, over 300 s, this corresponds to 1.14 J. On the other hand, given the heat capacity of CH₃OH, C_p,MeOH = 3.62 J g⁻¹ K⁻¹, to increase the solution temperature in 4 K will take 13 mJ. Therefore, there would be excess power to heat the solution in the vicinity of the electrode to 4 K, and the same applies above, for the case of 1 mM TBAI. For Fc, with a larger absorption at 325 nm, there will be a larger laser power absorbed. Therefore, we propose that the heat absorbed by the solution volume in the beam path between the electrode and the cell is dissipated by conduction to the larger volume of solution in the WE cell compartment. We consider a cylinder of radius r₁ = laser beam radius = 0.6 mm and length L_cyl, that conducts heat to a larger cylinder of radius r₂. The thermal conduction rate in cylindrical coordinates is given by ⁴⁰ :

$$\begin{eqnarray}&&{Q}_{cond}=\,\frac{2\pi k{L}_{cyl}\left({T}_{2}-{T}_{1}\right)}{\mathrm{ln}\,\displaystyle \frac{{r}_{2}}{{r}_{1}}}\end{eqnarray} \tag{ 20 }$$

where k is the thermal conductivity of MeOH, k_MeOH, T₁ and T₂ are the temperatures at r₁ and r₂, respectively. For k_MeOH = 0.2 W m⁻¹ K⁻¹, and Q_cond = 3.8 mW, and ΔT = 5 K, we obtain r₂ = 4 mm. In other words, a stagnant volume of CH₃OH can dissipate the laser energy as heat over a radius of 4 mm, which is well within the dimensions of our cell compartment. Based on the heat conduction analysis and the data below, on the time dependence of the D and D_app and temperature change, it follows that the metal illumination is the main heating mechanism causing a change in mass flux.

Because the laser heating the electrode is the main illumination mechanism, we discuss the beam shape and its implications. The Gaussian beam radius of the laser is 1.2 mm, much larger than the 10 μm disk. The laser specifications are: Gaussian beam radius of 1.2 mm (${\omega }_{0}$), power of the incident beam 50 mW, transverse mode TEM₀₀, and linear polarization. The power intensity is described with a Gaussian function on a perpendicular plane from the laser beam, as given by Eq. 21.

$$\begin{eqnarray}&&P=P\left(\infty \right)\left[1-\exp \left(\displaystyle \frac{-2{r}^{2}}{{\omega }_{0}^{2}}\right)\right]\end{eqnarray} \tag{ 21 }$$

The beam radius, ${\omega }_{0},$ is used by the manufacturer to define the decay of the power from the center of the beam. From Eq. 21, the distance from the beam axis where the intensity drops to $\sim 13.5\, \%$ (1/e2) of the maximum value is at ${\omega }_{0}.$ Thus, this specific CdHe laser can transmit $\unicode{x00303}\,86.5 \%$ of the optical power at 0.6 mm from the center of the beam. Moreover, we aligned the laser by sweeping the mirrors on the micrometer range, thus, we set the laser beam irradiating the electrode at the global maximum photocurrent (ca. 90% of the maximum power of the laser) which aligns the electrode at the maximum power irradiation. Assuming our electrode is within a circle of 100 μm in diameter, within the center of the laser, the variation would be, based on Eq. 21, is 0.3% of the laser power. Moreover, local and non-uniform heating could result from surface defects. However, in order to address local/non-uniform heating, we would need to do a surface-sensitive characterization like SECM, ^28,30 which is beyond the scope of this work.

Our results indicate that we can measure changes in temperature using the difference in the diffusion-limited current within a 1 K accuracy. For the data in Table I, we can apply the method to the current-ratio measured under thermostatic conditions. We get an increment of 4.₅ K_, which is within the ± 1 K that we estimate for the error with Eq. 17 and we discuss the factors that limit the accuracy of the measurement. The method is analogous to a ratiometric fluorescence measurement because by taking the current ratios, the concentration, C*, and the electrode radius, a, in Eq. 6 cancel out in the derivation of Eq. 12. Therefore, using the current ratios removes uncertainties on the UME radius, which is difficult to standardize if the experiments do not modify the electrochemical surface area. We monitored changes in C* during heating by collecting i_ss values either by LSV or CA once the solution has cooled back to r.t.. We can address error contributions by looking at the relative weight of the terms between brackets in Eq. 17. Interestingly, we found that the more significant contributions come from the current measurement errors. For example, 46% of the overall error is due to σ_ix while ca. 35% to the current measured at a higher temperature, σ_iy, for the unfiltered photoelectrochemical ratios, see Table SVII in the SI. Figure 6 shows the current ratios as a function of time for Fig. 3, which shows the significant error obtained in these measurements. The current envelope has periodic components, which points to an instrumental source of error. For the measurements with the thermostatic conditions, the bath pump and heating element likely contribute to the noise. In summary, the relatively large noise level on the current measurements for UMEs decreases the method's accuracy, especially when the cell is heated. The third significant contribution is the error in the initial temperature, σ_Tx = ± 0.5 K, with 17% for the same case in Table SVII, simply because of the limitations of our thermocouple. Therefore, to increase the accuracy of the measurement, we need to calibrate the currents under constant temperature with lower noise levels. As described above, we also use a digital filter to minimize the instrumental error. This improved our results, making the error for our most precise measurements ± 0.6 K. However, the use of filtering or sampling at lower times has a relatively low effect, because we average the data over 300 s in the measurements reported here. Also, the data in Table SV shows that under conditions where adsorption occurs, the error of the measurements is larger (e.g., ±4 K for Fc/Au with a pyrex cell), which indicates that surface reactions can also introduce noise, which we are currently investigating. In addition, convection could be a source of error as described above, but based on our current results, we expect convection to be negligible in both mass transport and heat transfer.

Other known sources of uncertainty include the error of fitting viscosity data to Andrade's model has a lower contribution (< 0.5%) to the overall error of the temperature estimate. Therefore, even though more advanced viscosity models exist ³⁷ the fitting to Andrade's model, a time-honored equation, provides accurate results if the viscosity data brackets the temperature interval of interest. Another error source could arise because of deviations from the viscosity of pure solvents. The redox-active molecules or impurities that build up during the experiment can cause the viscosity to deviate from the value of the pure solvent. In this case, it should be possible to measure the viscosity for the specific solution under study.

Our results show that the change in temperature of (4 ± 1) K is relatively low considering that the CW laser illuminates the electrode surface constantly. We collected the data in Fig. 6 over 300 s, a typical time scale when collecting stochastic photoelectrochemistry data. Note that there is no upwards trend in Fig. 6, which indicates that the system has reached thermal equilibrium. It follows that the electrode materials and the cell, e.g., the glass around the UME, and the large solvent volume, which is not illuminated, act as effective heat sink opposing a temperature change. The region illuminated by the laser overall has a tendency to remain close to room temperature. This 4 K temperature increment is tolerable for many applications. For example, Smalley et al. ³ point out that a 4 K temperature jump does not significantly affect electron transfer measurements of fast outer sphere reactions. Also, when working with volatile solvents, such as many organic solvents, with higher vapor pressures than water, it is crucial to keep the light source from making the solution boil. Finally, we emphasize that we did not add any supporting electrolyte, which indicates that the temperature effect does not change the relative contribution of migration in the unsupported iodide solution.