In Situ Calorimetry at Metal−Electrode Liquid Electrolyte Interfaces As

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In Situ Calorimetry at Metal-Electrode Liquid Electrolyte Interfaces As Monitored by Probe Beam Deflection Techniques Bin Hai and Daniel Scherson* Department of Chemistry, Case Western ReserVe UniVersity, CleVeland, Ohio 44106-7078 ReceiVed: June 13, 2009; ReVised Manuscript ReceiVed: August 21, 2009

A probe beam deflection method that allows for the heat generated or absorbed during an interfacial process to be determined in situ is herein described. These optical measurements are performed using a collimated laser beam propagating parallel to the interface through the back of a flat, optically transparent ZnSe crystal that supports a very thin film of a metal electrode in contact with the electrolyte solution. Analysis of experimental data collected for a Au electrode in sulfuric acid aqueous solutions using numerical simulations were found to be consistent with the release of ∼375 kJ/mol upon formation of a monolayer of Au oxide. This value is very similar to the value observed using the same methodology for the reduction of the Au oxide layer under otherwise the same experimental conditions. Introduction Reports from several laboratories,1-3 including ours,4,5 have shown that conventional, solution-phase, in situ probe beam deflection (PBD) is sensitive enough to monitor interfacial processes involving adsorption and desorption of species at submonolayer coverages; however, the precise origin of the signals observed has not as yet been fully elucidated. As has been amply discussed in the literature, PBD originates from spatial variations in the index of refraction, n, of a media along an axis normal to the direction of light propagation. For the type of systems of relevance to this work, such changes are most commonly induced by the consumption of reactants and generation of products at the surface, and also by the dissipation of heat produced or absorbed by the interfacial reaction. Unfortunately, some of the parameters associated with these processes are not known with certainty, making it very difficult to separate contributions due to concentration and temperature gradients via the analysis of conventional solution-phase PBD. The tactic herein described, to be referred to hereafter as optical interfacial microcalorimetry (OIM), affords means of isolating effects due solely to changes in the temperature at the interface, opening prospects for a more quantitative interpretation of in situ PBD measurements. More specifically, OIM relies on the use of a thin metal film electrode supported on the surface of an optically transparent flat plate made of a material endowed with suitable thermal and thermooptical characteristics. Unlike conventional in situ PBD, the laser probe beam is aimed along an axis parallel to the metal film|solution interface, (see Figure 1) through the optical plate, as opposed to through the electrolyte. Under such conditions, heat generated or absorbed at the metal film|electrolyte interface associated with, for example, a potential-driven process, will propagate normal to the interface through the two phasessthat is, the solution and transparent platesand thereby create a temperature gradient along that direction. Since n is a function of temperature, the beam will be expected to deflect, the extent of which can be determined with a position sensitive detector (PSD). Zinc selenide (ZnSe) displays a temperature-dependent index of * Corresponding author. E-mail: [email protected].

Figure 1. System consisting of two planar dissimilar phases, 1 and 2, in contact. Heat is generated or absorbed at the interface between the two phases at a rate specified by the function S(t) (see text) and dissipates into each of the two phases. The thick line represents the laser beam propagating through phase 2, which is being deflected due to a temperature gradient induced by the heat generated at the interface. The short, light, thick line (not considered in the heat transfer theoretical model) represents an electrode, and the four quadrant circle, a positionsensitive detector.

refraction, dn/dT ) 1.06 × 10-4 K-1,6 and a thermal conductivity, κ (∼20 °C) ) 13 W m1- K-1,7 that are much larger than those of water (see Table 1), dn/dT ) -9.1 × 10-6 K-1,7 and κ (∼20 °C) ) 0.598 W m1- K-1,7 and, as such, appears particularly suited for this type of application. This work describes various experimental and theoretical aspects of OIM and presents preliminary results for the formation and reduction of Au oxide(s) in sulfuric acid aqueous solutions. It should be mentioned that a different approach toward measuring in situ heats of reactions at metal|solution interfaces has been implemented by Schuster et al.,8 who adapted a method based on the pyroelectric properties of poly(vinylidene)fluoride, originally introduced by Campbell et al.,9 to examine microcalorimetric aspects of underpotential deposition and stripping of Cu on Au electrodes in aqueous electrolytes. Experimental Section The electrochemical cell employed in these OIM studies consists of a Teflon body attached to the surface of a ZnSe crystal of the type used for attenuated total reflection (ATR) in the infrared spectral region (Harrick, Corp.: 50 × 20 × 3 mm). As indicated in Figure 2, one of the rectangular large sides of the ATR element was coated with a thin Ti layer (20 nm) to improve adherence, followed by a Au layer (∼200 nm thick;

10.1021/jp905551b CCC: $40.75  2009 American Chemical Society Published on Web 09/29/2009

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TABLE 1: Physical Properties of Steel and Copper of Relevance to This Work physical properties

material

thermal diffusivity; R, m2 s-1 × 107

thermal conductivity; κ, W m-1 K-1

density; F, kg m-3

heat capacity; -1 K-1 pI kg

β ) √R/κ√π; m2 s-1/2 K W-1

steela (AISI 4340) coppera airb water (20 °C)b Auc ZnSeb

119.34 1194.2 221 1.43 1277.3 72.8

44.5 400 0.0261 0.598 318 (300 K) 13

7850 8700 1.17 1000 19300 5270

475 385 1010 4180 129 339

1.831 0.644

refractive index; n

dn/dT; K-1 × 105

-0.088 -0.91

1.0008 1.333

10.6d (0.632 µm)

2.43

a http://www.comsol.com. b Bialkowski, S. Photothermal Spectroscopy Methods for Chemical Analysis; John Wiley: New York, 1996. c Lide, D. CRC Handbook of Chemistry and Physics, 89th ed.; CRC Press: Boca Raton, FL, 2008. d Feldman, A. National Bureau of Standards Technical Note 933; 1978, 53.

the two phases at a rate prescribed by an arbitrary function, S(t) in Jm-2 s-1.12 The governing differential equations and initial and boundary conditions for this problem may be summarized as follows:

∂2Ti 2

)

∂x

1 ∂Ti Ri ∂t

(i ) 1, 2), x > 0, t > 0

(1)

Ti ) 0, t ) 0, x > 0

[

T1 - T2 ) R C1 S(t) + κ1

[

]

∂T1 ) ∂x

-R C2 S(t) + κ2

∂T2 ∂x

(2)

]

for x ) 0 (3)

Ti ) 0, t > 0, C1 + C2 ) 1 Figure 2. Diagram of the cell employed for in situ interfacial optical calorimetry measurements at electrode|electrolyte interfaces.

see Figure 2). A compressible Teflon sheet gasket in the form of a flat, ring-like frame was laid down onto the Au electrode exposing to the electrolyte solution a disk 0.9 cm in diameter. Since the physical properties of ZnSe of relevance to PBD are accurately known (see Table 1), the deflection signal becomes a function of the time-dependent generation/absorption of heat at the interface. Some aspects of the overall geometric arrangement as well as the principles of OIM bear close similarity to those associated with photoacoustic spectroscopy.10,11 In this latter case, the media is normally air, and the thermal excitation of the media whose spectral properties are being sought is provided by a second (commonly pulsed) laser beam aimed normal to the interface between the two phases. Interfacial optical calorimetry measurements were performed in 0.1 M H2SO4 using a Au foil as a counter and a SCE as a reference electrode. PBD signals were averaged while cycling the Au electrode at a scan rate of 1 V/s over a potential range wide enough to embrace the oxide formation and reduction regions. As will be shown, several hundred acquisitions were required to obtain well-defined PBD transient profiles. Theoretical Consider a system consisting of two flat plates of different materials, 1 and 2, in contact, as shown in Figure 1, and assume that heat is generated or absorbed at the planar interface between

(4)

where Ri and κi represent the thermal diffusivity and thermal conductivity of phase i, respectively. The initial condition in eq 2 stipulates that the temperature, T, is constant and, without loss of generality, equal to zero, whereas the interfacial boundary condition is given in eq 3, where R represents an interfacial resistance to the flow of heat. For R * 0, the temperature difference between the two phases at the interface (x ) 0), T1 - T2, will, in general, be different from zero and equal to the two terms on the right-hand side of this expression. As shown by Schaaf,12 the problem thus stated requires that C1 + C2 ) 1 (see eq 4). The solution to eq 1 for the temperature in phase 1, T1, subject to the initial and boundary conditions in eqs 2-4 may be shown to be given in Laplace space by

[

T1* ) β1S*

β2√π + C1R√s

√π exp(-y1√s)

(β1 + β2)√π + R√s

√s

]

(5)

where βi ) Ri/κiπ and S* is the Laplace transform of S(t). Upon inversion, eq 5 yields an explicit expression for T1(y1, t), the transient temperature profile within that phase; namely,

T1 ) β1

[

{

∫ S(t - u) t

0

2

C1 exp(- y1 /4u)

√u

+

π(β2C2 - β1C1) × R

] [

y1 β1 + β2 β1 + β2 (β1 + β2)2 √πu + exp πu erfc y1√π + 2 R R R 2√u

]}

du

(6)

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Figure 3. Temperature (see center axis) vs distance for the system shown in Figure 1, for phase 1 ) steel (left panel) and phase 2 ) Cu (right panel) obtained at a time of 5 s, for S(t) ) t (see text) and R ) 4.2. The left and right axes are the ratios of the solutions obtained by Comsol and by a numerical inversion of the Laplace transform of eq 5 for the specified S(t) using the Talbot option in Mathematica, denoted as Comsol/Talbot. The results obtained with the two methods are very close, and the two curves virtually overlap.

TABLE 2: Temperature Discontinuity at the Boundary between Steel and Copper, ∆ ) T1 - T2, F1 and F2, and their Differences as Determined by a Numerical Inverse Laplace Transform and by Comsol quantity

method of evaluation

∆ ) T 1 - T2

F1 ) R(C1S + K1∂T1/∂x) |x)0

F2 ) - R(C2S + K2∂T2/∂T2) |x)0

% difference (F1 - ∆T)/∆T (F2 - ∆T)/∆T

numerical inverse Laplace transform (Talbot) Comsol

9.55997 - 6.23933 ) 3.32064

3.315

3.31343

-0.1698, -0. 217

9.60516 - 6.27079 ) 3.33473

3.285

3.3849

-1.49, 1.504

where yi ) xi/Ri (i ) 1, 2). For our experiments, however, R is negligible; hence,

[

]

β1β2 T1 ) (β1 + β2)

y12 1 S(t - u) exp 0 4u √u

T1*

β1β2 √π exp(-y1√s) ) S* (β1 + β2) √s

∫

t

{ ( )}

(7)

du

(8)

The corresponding solution for T2 can be obtained by exchanging the indices 1 and 2 in eqs 5-8.12 Two different commercial routines were employed to determine transient temperature profiles T(x, t), using S(t) ) t as a test heat input function. The first relies on a numerical inversion of the Laplace transform (Mathematica),13 whereas the second integrates the governing differential equations subject to the appropriate boundary and initial conditions in real space (COMSOL).14 The results obtained were compared with those provided in the original work of Schaaf.12 The extent of beam deflection, φ(x′, t), where x′ emphasizes the fact that the deflection depends on the distance between the probe beam and the interface, is given by φ(x′, t) ) l/n × dn/ dT × dT/dx, where l is the length of the electrode along the propagation axis of the probe beam; n is the index of refraction; dn/dT, the temperature coefficient of n; and dT/dx is the temperature gradient along an axis normal to the interface. Of particular interest is determining S(t) from the experimentally

measured φ(x′, t). A procedure for solving this inverse problem is described in the next sections. Results and Discussion A. Theoretical. Shown in Figure 3 are plots of T versus x, the distance normal to the interface for steel (left panel) and copper (right panel) at a time of 5 s, assuming parameters for the two metals reported in the literature (see Table 1), and a value of 1.003 × 10-4 m2 K W-1. As evidenced from these data, hardly any differences could be found between a numerical inversion of the Laplace transform using the Talbot (and also the Durbin and Stehfest) approach and the results obtained from Comsol (see thin lines, right and left ordinates for their ratios, labeled as Comsol/ Talbot). In fact, both sets of data (except for an arbitrary factor) were very close to those reported by Schaaf. It may be noted that other inverse Laplace tactics available in Mathematica were not found to yield as precise results. Despite the good agreement between these two very different approaches, it is important to check whether the solutions obtained do, in fact, obey the differential equations and boundary conditions. To this end, the profiles at a few selected times were fitted with fourth-degree polynomials, and the derivatives were then calculated analytically for both steel and copper. Values of ∆T ) T1 - T2, that is, at the boundary between the two phases, x ) 0, R(C1S + K1(∂T1)/∂x)|x)0 and -R(C2S + K2(∂T2)/ ∂x)|x)0 for t ) 5 s determined from the two methods of calculation are compiled in Table 2. The good agreement between the solutions obtained from the two numerical approaches lends support to the reliability of each of the two methods of analysis.

Metal-Electrode Interface Calorimetry

Figure 4. Plots of dn/dT (left ordinate) {based on the empirical, bestfit formula reported by Abbate, G.; Bernini U.; Ragozzino, E.; Somma, F. J. Phys. D: Appl. Phys. 1978, 11, 1167; -∂nwater/∂T ) B[1 - exp(-(T - T0)/Tk)], where B ) 26.2 × 10-5 K-1, T0 ) 2 °C, and Tk ) 48.5 °C (see original reference for additional details, for λ ) 632 nm)} and thermal diffusivity, R (right ordinate), R (water) ) (1.35 + 0.002T) × 10-3 cm2/s as a function of temperature for both ZnSe and water.

Figure 5. Plot of the temperature, T, as a function of distance from the boundary of ZnSe|water and steel|Cu interfaces at a time of 5 s for comparison. S(t) ) t, for R ) 0.

It is of interest to compare the behavior of the same twophase geometry for two materials that possess very different thermal properties. Since probe beam deflection requires the media to be transparent to light, we selected ZnSe as phase 1 and water as phase 2, for which the physical properties of relevance to the problem at hand are given in Table 1 and also in Figure 4. Calculations were performed using the same conditions as those employed to obtain the data in Figure 3 (i.e., S(t) ) t), except that the interfacial resistance R was assumed to be zero. Shown in Figure 5 are plots of the temperature, T as a function of distance from the boundary of the ZnSe|water interface at a time of 5 s. As before, the agreement between the two methods was very good (no ratio provided). Also given in this figure are the same data for steel|Cu under the same conditions to contrast the behavior between the two interphase systems. Insight into the temperature profile evolution of each of the phases of the ZnSe|water system was gained using a heat input function, S(t) (see below), that closely mimics the cyclic voltammetry of Au, including oxide formation and reduction,

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Figure 6. Plot of the S(t) function used for the simulations bearing characteristic features for oxide formation and reduction on Au, assuming for simplicity no contributions due to double layer charging. Note that the waveform is not symmetric.

assuming, arbitrarily, a heat associated with the formation (release) and reduction (absorption) of surface oxide of 418 kJ/ mol shown in Figure 6 and neglecting any contributions due to double layer charging. It must be strongly emphasized that these theoretical simulations were performed purely for illustrative purposes and do not necessarily reflect the heat released or absorbed during the actual interfacial reactions. In fact, the actual heat contribution will be determined directly from the experimental PBD data, as will be discussed below. In view of the complex character of the function S(t), no solutions could be obtained using Laplace transform methods; hence, all the results presented in this section were obtained with Comsol using a 2-dimensional domain, 2 mm high (insulating boundaries) and 10 cm wide, for each of the adjoining phases, along the axis of heat propagation, which is long enough for the temperature profiles not to approach the (insulating) back boundaries. A series of temperature profiles within the ZnSe phase of the ZnSe/water system determined at various times during the application of the ninth cycle of the S(t) function are given in Figure 7, where the scans in the positive and negative directions are given in panels A and B, respectively. Each of the profiles displayed in panel A were calculated in increments of 0.1 s starting from 0.1 s up to 1.1 s (thin lines from bottom, uppointing arrow), followed by 1.2-1.5 s (thick lines from top, down-pointing arrow) for the scan in positive direction (panel A). For the subsequent scan in the negative direction (see panel B), the profiles start from a time of 1.6 s (thick line from top, downpointing arrow) and continue with the bottom thin line upward, as indicated by the thin arrow to the end of the cycle at 2.5 s. It becomes then possible to calculate φ(x′, t) (i.e. the transient response of the PBD during application of the heat function S(t)) from the values of derivatives of the profiles in Figure 7 at specific distances, x′ (see Figure 1) from the interface along the axis of light propagation, dT/dx, using the known values of n as a function of T for the two phases (see Figure 4 for ZnSe and water). Shown in Figures 8 and 9, respectively, are plots of ∂T/∂x|x)x′ vs t for specific values of x′ (within the ZnSe phase) and of ∂T/∂x|x)x′ vs t, for x′ ) 200 µm for the 10th cycle (left ordinate, Figure 9). As evident from the results obtained, the differences between the PBD responses between cycles 9 (not shown) and 10 (right ordinate, Figure 9) were very small. On this basis, it is reasonable to surmise that the response is

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Figure 7. Series of temperature profiles within the ZnSe phase of the ZnSe/water system for various times during the application of the ninth cycle of the S(t) function for the scans in the positive (panel A) and negative (panel B) directions, respectively. Each of the profiles was calculated in increments of 0.1 s starting at 0.1 s up to 1.5 s in the left panel and in the range 1.6-2.5 in the right panel. The arrows are associated with the set of profiles, thin for upgoing and thick for downgoing (see text for a detailed explanation).

Figure 8. Plots of ∂T/∂x|x)x′ vs t (left ordinate) for specific distances x ) x′ from the interface (within the ZnSe phase) for x′ ) 100, 200, 300, 401, 500, 800, 1000, 1500, and 2000 µm in the order shown by the arrow. Also shown, the right ordinate represents the heat flux function at the interface as a function of time to underscore its similarity to ∂T/∂x|x)x′ vs t in the limit as the interface is approached; that is, x′ f 0.

representative of a stable periodic state. This is an important consideration, because several hundred cycles were often found to be required to obtain a well-defined PBD signal. Several interesting aspects can be gleaned from these data: i. The predicted PBD signals bear close resemblance to S(t) shown in dotted lines in Figure 8. In fact, in the limit as x′ f 0, S(t) becomes proportional to the PBD signal. ii. As x′ increases, the overall intensity of the signal decreases, and the separation between the positive and negative peaks increases. Shown in Figures 10 and 11, respectively, are plots of the peak heights and peak positions for both the positive and negative cycles in S(t), where the solid lines are best fits to the data in terms of fourth-degree polynomials. On this basis, measurements performed at different distances from the interface would allow extrapolations to be made to the interface itself, which is not amenable to experimental determination, yielding, as desired, a function proportional to S(t).

Figure 9. Plots of ∂T/∂x|x)200µm for scans 9 and 10 (see left ordinate) 10 9 - (∂T/∂x)|x)200µm } (right ordinate). and their difference {(∂T/∂x)|x)200µm

B. Experimental. Shown in Figure 12 are plots of the averaged (5 adjacent points; left ordinate; number of acquisitions, 384) PBD signals (φ, in µrad) and current (I, right ordinate) as a function of time recorded simultaneously, while scanning the potential linearly between 0.25 and 1.5 V vs SCE at a rate of 1 V s-1. For these measurements, the center of the collimated laser beam (∼0.5 mm in average cross section) was placed within the ZnSe phase, ∼200 µm away from and parallel to the interface. To calculate the deflection φ(t), the transient values of the shift in the position of the laser beam at the PSD were divided by the distance between the close edge of the electrode and the surface of the PSD (see ∆ in Figure 1); that is, 45 cm. As indicated, the maximum deflection amounts to ∼1 µrad. Most interesting, however, is the fact that the sign of the deflection is the same both for the formation and for the reduction of the oxide on the gold surface. On the basis of the settings of the instrument, a positive deflection is consistent with heat being released at the interface. A quantitative analysis of these data was pursued by first fitting the transient PBD response, φ(t), to an

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{

( x -0.351.18 ) ] + x - 2.03 Jm 0.82 × exp[-2 × ( 0.206 ) ]}

[

S(t) ) 48.76 × 0.58 × exp -2 ×

Figure 10. Peak heights of the derivatives of the temperature profiles 9 in cycle 9 (i.e. (∂T/∂x)|x)x′ ) as a function of x′ based on the data shown in Figure 8 recorded during the scan in the positive (left ordinate) and negative directions (right ordinate).

Figure 11. Peak position of the derivatives of the temperature profiles 9 in cycle 9 (i.e. (∂T/∂x)|x)x′ ) as a function of x′ based on the data shown in Figure 8, recorded during the scan in the positive (+) and negative (-) directions.

2

2

-2 -1

s

On the basis of the data reported by Conway and coworkers,15 the atom density (1.25 × 1015) cm-2 of a nominally polycrystalline Au electrode surface, that is, 1.25 × 1015 cm-2, is very similar to that found for Au(100), for which the reduction of a full monolayer of oxide in 0.01 M HClO4 involves 520 µC/cm2,15 assuming that the peak observed in Figure 12 during the potential scan in the negative direction corresponds to the reduction of a full monolayer of Au oxide yielded a value of 440 µC/cm2, which corresponds to an area of 0.85 cm2. Since the cross-sectional area of the electrode is ∼0.64 cm2, the roughness factor is on the order of 1.3. Integration of the heat generation function peak associated with the reduction of the oxide based on the transient PBD data gave a value of 1.04 × 10-3 J/cm2. On the basis of the mol atom density of smooth Au (i.e., 2.08 nmol cm-2) and the roughness factor, the heat associated with the interfacial reduction process yielded a value of ∼375 kJ mol-1 or 90 kcal mol-1, a value that is, indeed, very reasonable. Analog calculations involving the oxidation peak yielded very similar values, including the sign. This implies that heat is being released during the formation and also during the reduction of the Au oxide film. It may be argued that, since the sign of the heat is the same, regardless of the sign of the current, the signal could be derived from simple Joulean heating of the film or the solution (or both); that is, QJ ) I2Rt, where R is the resistance of the medium, I is the current, and t is the time during which the current flows. On the basis of our experimental results, I will be assumed to be 1 mA and t equal to the time associated with a single full linear scan in a specific direction; that is, 1.25 s. On this basis, QJ (J ) film, f, or solution, sol) will be calculated next. Metal Film. It will be assumed in what follows that I flows through a Au film ∼2 cm long (l), 1 cm wide (w), and 2 × 10-5 cm thick (τ). These dimensions would place an upper limit for the resistance, Rf, and thus for the Joulean heat that would be generated, Qf. Specifically, Rf ) FAul/Af, where FAu ) 2.214

analytic function using features available in Origin (see solid line through the scattered points in Figure 12), yielding

[

φ(t) ) 0.58 × exp -2 ×

( x -0.351.20 ) ] + 0.82 × x - 2.05 exp[-2 × ( 0.206 ) ] 2

2

The next step in the analysis involves the search of a function S(t), the heat input at the interface, that is, x′ ) 0, consistent with the experimentally observed φ(t) recorded at x′ ) 200 µm. On the basis of the values of l, n and dn/dT being known, it follows that φ ) 0.4 × dT/dx (µrad). It only remains to determine if the values of dT/dx can be calculated using Comsol. This represents a type of inverse problem, which in our case was approached by a trial and error, yielding for S(t) the following expression:

Figure 12. Plots of the averaged (384 acquisitions, 5 adjacent points, left ordinate) PBD signals, φ (scatter points, left ordinate), and current (I, right ordinate) as a function of time recorded simultaneously while scanning the potential linearly between 0.24 and 1.5 V vs SCE, at a scan rate of 1 V/s. The area of the electrode exposed to the electrolyte was 9 mm in diameter. The solid line through the scattered points represents the best fit to the data (see text).

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× 10-6 Ω cm is the resistivity of Au, and Af ) w × τ is the cross-sectional area of the film; that is, 2 × 10-5 cm2, yielding Rf ∼ 0.22 Ω. This calculation neglects the contribution due to the Ti film, for which the resistance is ∼200 higher than that of the Au film. On this basis, Qf ) 2.8 × 10-7 J, and hence, the temperature increase of the film, ∆T, due to the heat released would be given by Qf ) mAuCp∆T, where mAu is the mass of the film (77.2 × 10-5 g) and Cp is the heat capacity of Au, yielding a value of ∼3 mK. Electrolyte Solution. According to the literature, the electrical conductivity, κ, of a solution of 0.1 M H2SO4 is 47.8 mS cm-1,16 assuming the distance between the film and the counter electrode (placed parallel to the working electrode), L, to be 1 cm; hence, the resistance due to the electrolyte solution, Rsol ) FsolL/Asol, where Fsol is the resistivity of the solution (1/κ) and Asol is the cross-sectional area of the solution, would be ∼32.7Ω. On this basis, Qsol is ∼4.1 × 10-5 J. Hence, the temperature increase in the solution, ∆Tsol ) Qsol/msolCsol, where msol is the mass of the solution (0.64 g) would amount to 1.53 × 10-5 K. In stark contrast, ∆T induced by the interfacial process based on a value of 418 kJ/mol and 1 nmol/cm2 of reaction can be calculated by assuming an instantaneous thermal equilibration of the Ti/Au film so that ∆T will be common to both materials; namely, ∆T ) QAu/mAuCAu ) QTi/mTiCTi where mi and C represent the mass and heat capacity, respectively, for i ) Au or Ti of the materials in question. In addition, the total heat released by the reaction will partition between the two metals, that is, QAu + QTi ) 2.68 × 10-4 J, which is very close to the value we found experimentally. Solving these two equations yields a value of ∆T ) 6.5 K, which is much larger than the Joulean heats associated with both phases. Further evidence for the proper operation of our system was afforded by experiments involving Ni oxyhydroxide films electrodeposited on the same Au substrate for which the forward and reverse processes had opposite signs. On this basis, it can be concluded that the common sign of the heat associated with the forward and reverse processes must originate from the intrinsic characteristic of the interfacial processes themselves. In summary, optical interfacial microcalorimetry, a technique based on beam probe deflection introduced in this work, affords

Hai and Scherson expedient means of monitoring in situ heat absorbed and released at electrode surfaces due to redox reactions involving species at monolayer coverages. Analysis of OIM data using commercial differential equation solvers, such as Comsol, allows for a quantitative determination of heats of interfacial reactions. An illustration of the power of this method was provided for the case of oxide formation and reduction on Au in sulfuric acid solutions, which yielded for both processes values for the heat released of ∼375 kJ/mol. Acknowledgment. This work was supported by NSF. The authors express their deep appreciation to Prof. Yuriy Tolmachev from Kent State University, Kent, OH, for enlightening discussions. References and Notes (1) Bidoia, E. D.; McLarnon, F.; Cairns, E. J. J. Electroanal. Chem. 2000, 482, 75. (2) Henderson, M. J.; Bitziou, E.; Hillman, A. R.; Vieil, E. J. Electrochem. Soc. 2001, 148, E105. (3) Kotz, R.; Barbero, C.; Haas, O. Ber. Buns.-Gesell.-Phys. Chem. Chem. Phys. 1993, 97, 427. (4) Shi, P.; Fromondi, I.; Shi, Q. F.; Wang, Z. G.; Scherson, D. A. Anal. Chem. 2007, 79, 202. (5) Wang, J.; Wang, Z.; Scherson, D. J. Electrochem. Soc. 2007, 154, F165. (6) Feldman, A. National Bureau of Standards Technical Note 933 1978, 53. (7) Bialkowski, S. Photothermal Spectroscopy Methods for Chemical Analysis; John Wiley: New York, 1996. (8) Schuster, R.; Rosch, R.; Timm, A. E. Z. Phys. Chem. 2007, 221, 1479. (9) Stuckless, J. T.; Frei, N. A.; Campbell, C. T. ReV. Sci. Instrum. 1998, 69, 2427. (10) Boccara, A. C.; Fournier, D.; Badoz, J. Appl. Phys. Lett. 1980, 36, 130. (11) Jackson, W. B.; Amer, N. M.; Boccara, A. C.; Fournier, D. Appl. Opt. 1981, 20, 1333. (12) Schaaf, S. A. Q. Appl. Math. 1947, 5, 107. (13) Valko´, P. http://library.wolfram.com/infocenter/MathSource/5026/, 2003 (accessed Sept 10, 2009). (14) http://www.comsol.com (accessed Sept 19, 2009). (15) Angersteinkozlowska, H.; Conway, B. E.; Hamelin, A.; Stoicoviciu, L. Electrochim. Acta 1986, 31, 1051. (16) Weast, R. C.; Astle, M. J. CRC Handbook of Chemistry and Physics, 63rd ed.; CRC Press: Boca Raton, FL, 1982; p D271.

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