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. 2025 Jun 5;5(4):529–535. doi: 10.1021/acsmeasuresciau.5c00039

Measuring Temperature-Dependent Thermodynamics of Electrochemical Reactions

Xiaoli Ge †, Shwetha Prakash †, Ying Wang ‡, Ziyun Wang §, Yuguang C Li †,*
PMCID: PMC12371594  PMID: 40861905

Abstract

Temperature is a critical parameter that can significantly influence the outcome of the redox reactions. However, determining the temperature-dependent properties of redox couples is often time-consuming and susceptible to inconsistencies. In this work, we present a temperature-controlled electrochemical station capable of acquiring electrochemical measurements under preprogrammed conditions to extract key thermodynamic parameters. We demonstrate the functionality of this system using electrochemical impedance spectroscopy to determine the activation energies of the [Fe­(CN)6]3–/4– redox couple and the hydrogen evolution reaction on platinum and gold electrodes. Additionally, we illustrate automated cyclic voltammetry data acquisition for [Fe­(CN)6]3–/4–, [Ru­(NH3)6]2+/3+, benzoquinone, and anthraquinone. By analyzing the temperature-dependent shifts in E 1/2, we calculated the entropy changes and thermogalvanic coefficients of these systems. Furthermore, we examined the entropy variations of ferricyanide in mixed aqueous–organic electrolytes, highlighting the role of solvation reconfiguration. The versatility of this setup offers a robust and efficient platform for the rapid characterization of temperature-dependent redox properties, with implications for energy conversion and sensing applications.

Keywords: activation energy, thermogalvanic coefficient, instrumentation, physical electrochemistry, temperature

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Introduction

As electrochemical reactions play an increasingly important role in advancing renewable energy technologies, significant research efforts have focused on the development of new catalysts and systems to enhance reaction yields. However, several other factors also critically influence the performance of these reactions, one of which is the temperature. All electrochemical reactions are inherently sensitive to temperature changes, which affect both the enthalpy and the entropy of the reaction. Additionally, the temperature influences the vibrational energy and solvation barriers of reaction intermediates, thereby altering the activation energy. In essence, both the thermodynamics and kinetics of redox reactions are governed by the temperature. A deeper understanding of the temperature dependence of redox reactions could yield valuable insights for improving electrochemical processes.

A wide range of thermodynamic parameters exhibit temperature dependence, many of which are well described in standard textbooks. Among them, the Arrhenius law is a fundamental principle for describing the temperature dependence of reaction kinetics, from which the activation energy (E a), a key parameter for any chemical reaction, can be derived. Other important temperature-dependent factors include ion mobility, surface adsorption processes, and double-layer structure. Even the electrode potential itself is influenced by temperature, as described by the Nernst equation. The change in electrode potential with respect to temperature, known as the thermogalvanic temperature coefficient (α = ΔE/ΔT), has recently attracted considerable attention in the research community due to its relevance as a figure of merit in the design of waste heat recovery systems. − Given the broad range of fundamental parameters in electrochemical reactions that are temperature-dependent, it is essential to develop tools that can accurately and reproducibly measure these properties.

The experimental approach to investigating the temperature dependence of electrochemical reactions, such as measuring E a or α, would be to manually measure redox properties at a specific temperature one at a time. However, this method is often time-consuming, labor-intensive, and susceptible to human errors, rendering manual temperature control suboptimal. Recent literature has increasingly emphasized automation in electrochemical processes, offering new insights into redox mechanisms. For example, Baker et al. reported an electrochemical setup operating in a 96-well plate format, enabling the parallel acquisition of substantial data in a single run. Similarly, Rodríguez-López et al. recently introduced automated pH measurement tools for electrochemical applications. , These high-throughput strategies, whether applied in series or in parallel, provide standardized workflows that ensure data reproducibility while saving time. Beyond electrochemistry, automation has become a critical tool in chemical laboratories for developing new materials and performing physical characterizations. − These advances serve as the inspiration for this work, which aims to automate temperature control to investigate thermodynamic parameters of redox reactions more precisely.

In this study, we designed and implemented an automated electrochemical setup with a precise temperature control. Given the sensitivity of thermodynamic parameters to temperature fluctuations, maintaining fine control over the temperature profile of electrochemical reactions enables the extraction of valuable mechanistic information. Using temperature-dependent electrochemical impedance spectroscopy, we determined the activation energy for the ferri/ferrocyanide redox couple and the hydrogen evolution reaction (HER) using different electrodes. Furthermore, we calculated the reaction entropy and thermogalvanic coefficients (α) for the [Fe­(CN)6]3–/4–, [Ru­(NH3)6]2+/3+, benzoquinone, and anthraquinone redox couples. Detailed instructions for reproducing our setup are provided throughout the paper and in the Supporting Information. We believe that this system will benefit the broader electrochemical community by enabling accurate investigation of temperature-dependent redox processes and encouraging the integration of automation into renewable energy research.

Experimental Methods

Automation Setup

The overall system design is illustrated in Figures and S1. The electrochemical cell comprises a water-jacketed 100 mL beaker with a larger water container (ca. 5 L) serving as the temperature reservoir. A water heater regulates the reservoir temperature, and temperature probes are placed in both the water reservoir and the electrochemical cell to monitor the thermal conditions. The water heater is controlled via a solid-state relay switch, which toggled on or off in response to signals from the temperature probes. Electrochemical measurements were conducted by using a Metrohm Autolab PGSTAT204 potentiostat. To enable communication between the potentiostat and external devices, we employed the Autolab software development kit provided by the manufacturer, which allows the external hardware to initiate and control the potentiostat.

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Illustration of the automated temperature electrochemical setup. Electrochemical experiments are conducted in a temperature-controlled three-electrode configuration. Water heater, temperature sensor, and potentiostat are all connected to a data acquisition module and controlled via LabVIEW software. Photograph images of the actual setup are available in Figure S1.

LabVIEW software was used to coordinate the water heater, temperature sensors, and potentiostat, enabling full automation of the temperature control across various electroanalytical techniques. A comprehensive list of hardware components and detailed assembly instructions are provided in the Supporting Information.

In a typical temperature-dependent experiment, the water reservoir is initially set to approximately 0 °C using an ice–water bath. LabVIEW is programmed to initiate electrochemical measurements starting at a predefined temperature, typically 5 °C in this study. The temperature is then incrementally increased by 1 °C, and at each step, a predefined electroanalytical technique (e.g., cyclic voltammetry (CV), electrochemical impedance spectroscopy (EIS), and so forth) is executed. The experimental parameters for each technique are stored in the native Autolab file format and accessed by the LabVIEW program. As a result, most standard electroanalytical techniques are compatible with this setup. After measurements at each temperature are completed, the system automatically proceeds to the next temperature setting, continuing this sequence until all experiments are finalized. The resulting data are automatically exported as.csv files and batch-processed by using custom Mathematica scripts for analysis. Error bars reported in this study are standard deviations based on triplicate repeats of each experiment.

Electrochemical Experiments

EIS data for the [Fe­(CN)6]3–/4– redox couple (Figure ) were collected at the half-wave potential (E 1/2) using an AC amplitude of 20 mV, over a frequency range of 100 kHz to 10 Hz. The measurements were performed in a 50 mM [Fe­(CN)6]3– solution, with 1 M phosphate buffer (pH 7) as the supporting electrolyte. For the hydrogen evolution reaction, EIS experiments were conducted over the same frequency range with a DC bias of −0.05 V vs Ag/AgCl for the Pt electrode and −0.4 V vs Ag/AgCl for Au electrodes. The bias voltages were selected to be near the HER onset potentials for each electrode material, which differ between those of Pt and Au. All HER experiments were performed in 1 M H2SO4 solution.

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(a) EIS spectrum of [Fe­(CN)6]3–/[Fe­(CN)6]4– at E 1/2, from 5 to 60 °C. (b) Fitted line of i 0 vs 1/T to extract E a. (c) EIS spectrum of HER with the Pt electrode in 1 M H2SO4 solution, from 5 to 50 °C. (d) Fitted line of i 0 vs 1/T to extract E a.

Cyclic voltammetry data were collected at a scan rate of 50 mV/s in 1 M pH 7 phosphate buffer, unless otherwise specified. The thermogalvanic coefficient was extracted from the slope of the E 1/2 vs temperature graph, α=ΔEΔT . All electrochemical experiments were carried out under nitrogen-purged conditions to eliminate the influence of dissolved oxygen.

Results and Discussion

Determination of Reaction Activation Energy

As described by the Nernst equation, the temperature directly influences the formal potential of any redox couple. Therefore, it is essential to account for the temperature-induced shift in the Ag/AgCl reference electrode, which was used throughout the experiments. To quantify this temperature drift, we placed two identical Ag/AgCl reference electrodes in solutions at different temperatures, one in a heated solution and the other in room temperature, and measured the resulting potential difference (ΔV) as a function of the temperature difference. The data are presented in Figure S2. The measured drift for the Ag/AgCl reference electrode was ca. −0.5 mV/°C, which is close to the values reported in the literature. It is worth noting that this drift may vary depending on a number of physical parameters of the experiment, such as redox couple solubility, liquid junction potential, solvent thermal expansion, electrolyte composition, and so forth. As such, periodic temperature calibration of the reference electrode is recommended to ensure accurate measurements. For all subsequent voltage data presented in this study, we corrected the measured potentials to account for the temperature-dependent drift of the reference electrode.

Thermodiffusion effects, unequal ion concentration at hot vs cold electrode, could also impact the voltage measurement of an electrochemical device. However, in a low-viscosity solvent, such as water, the contribution of thermodiffusion is in the order of 10s μV/°C, much smaller than the thermogalvanic effect. , Thus, the thermodiffusion effect is not considered in our experimental measurements.

As an initial demonstration, we investigated the EIS of the ferri-ferrocyanide redox couple. In this experiment, the automated electrochemical station was programmed to collect EIS spectra over a temperature range from 5 to 60 °C, with measurements taken at 1 °C increments. The results are presented in Figure . First, we observed that the solution resistance, represented by the x-intercept on the real axis at high frequency, decreased with increasing temperature. This trend is consistent with the expected exponential relationship between the ionic mobility and temperature, as further illustrated in Figure S3.

The semicircular feature in the EIS spectra, commonly associated with the charge transfer resistance (R ct) of the redox reaction, is inversely proportional to the exchange current density (i 0), as described in eq . Since the exchange current density is proportional to the rate constant, it exhibits an Arrhenius-type temperature dependence, as described by eq . From the EIS data shown in Figure a, R ct values were extracted to calculate i 0 and, subsequently, determine the activation energy (E a) of the ferri-ferrocyanide redox couple. The fitted R ct values are provided in Table S1. Figure b displays the plot of ln­(i 0) vs 1/T. The activation energy, determined from the slope of the linear fit by using the Arrhenius equation, was found to be ca. 3.35 ± 0.51 kJ/mol. The linearity of the fitted plot highlights the capability of our setup to provide a rapid and reliable method for determining the activation energy of any redox systems.

Rct=RTnFi0 1
i0=A*exp(−EaRT) 2

It is important to note that the activation energy of redox reactions is potential-dependent, due to several factors, including the influence of overpotential on the Fermi levels of the oxidized and reduced species, variations in surface coverage of electroactive species at different applied potentials, and changes in the configuration of active sites on the electrode surface. − In Figure a, the EIS data were recorded at E 1/2; thus, the reported activation energy corresponds to the equilibrium electron transfer process of the [Fe­(CN)6]3–/[Fe­(CN)6]4– redox couple. If desired, the temperature-controlled setup described here offers a fast and efficient platform to determine E a at different potentials simply by modifying the DC bias in the EIS protocol.

Furthermore, we demonstrated that the extraction of the E a for the HER is a key electrocatalytic process. Pt, a well-established catalyst for the HER, exhibits a small semicircular arc in the EIS spectra, indicative of a low R ct. In contrast, when an Au electrode was used, a significantly larger R ct was observed (Figure S4). The fitted R ct values for Pt and Au electrodes are provided in Tables S2 and S3. These findings are consistent with the expectation that different materials possess distinct catalytic properties (i.e., different E a). The extracted activation energies for the HER on Pt and Au electrodes were found to be 18.9 ± 4.1 and 52.9 ± 4.2 kJ/mol, respectively. This demonstrates that our setup is well-suited for screening the activation energies of a wide range of catalytic reactions, providing fast and accurate temperature-dependent data.

Determination of Thermogalvanic Coefficient

The thermogalvanic temperature coefficient is a critical parameter that determines the operational efficiency of thermogalvanic cells. It is typically measured as the open-circuit voltage (V oc) between a hot and a cold electrode connected via an electrolyte. However, this traditional approach requires two separate temperature control and measurement systems, making the experimental setup complex and time-consuming. − An alternative method involves determining α using cyclic voltammetry under temperature-controlled conditions. However, the reproducibility of such measurements can be affected by numerous factors, including subtle variations in the electrode placement within the electrolyte. Moreover, in both methods, only a limited number of temperature data points are usually collected due to the labor-intensive nature of performing experiments at multiple discrete temperatures.

Our automated temperature control system provides a significant advantage by enabling continuous temperature sweeps within a single experimental run, typically completed in under 2 h. As shown in Figure , we demonstrate the extraction of α from CV measurements for [Fe­(CN)6]3–/[Fe­(CN)6]4–, hydrobenzoquinone, [Ru­(NH3)6]2+/3+, and anthraquinone redox couples. The resulting cyclic voltammograms exhibit excellent consistency across the temperature range. Each experiment requires ca. 1 to 2 h only, depending on the scan parameters, and operates entirely without human intervention.

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Cyclic voltammograms of (a) [Fe­(CN)6]3 –/4 –, (b) hydrobenzoquinone, (c) [Ru­(NH3)6]2+/3+ and (d) anthraquinone. (a–c) were conducted in 1 M pH 7 phosphate buffer, while (d) was conducted in 0.5 M TBAPF6 in DMF. Temperature was varied from 5 to 60 °C in all the experiments.

To determine α, the E 1/2 values from each cyclic voltammogram were extracted using a Mathematica code and plotted against temperature, as shown in Figure . The α value for the [Fe­(CN)6]3–/[Fe­(CN)6]4– redox couple was found to be–1.5 ± 0.12 mV/°C, which is in very good agreement with reported literature values of −1.4 mV/°C. ,, The temperature coefficients for hydrobenzoquinone and ruthenium hexamine were determined to be −0.59 and 0.65 mV/°C, respectively. In the case of anthraquinone in a nonaqueous solvent, two distinct redox peaks were observed, corresponding to two sequential reduction processes. The extracted α values were–0.05 and–0.9 mV/°C for the first and second reduction waves, respectively. The temperature coefficient is directly related to the entropy change of the redox reaction, according to the relationship α=ΔEΔT=ΔSnF . The entropy change may arise from intrinsic changes in the redox species or from modifications to their solvation environments. Under N2-purged, nonaqueous conditions, anthraquinone is reduced to its dianionic form. In such systems, the entropy change is predominantly influenced by the reorganization of the solvation shell. The second reduction introduces a higher negative charge, which necessitates a greater rearrangement of the solvation sphere, leading to a larger entropy change. These results demonstrate the capability of our automated temperature-control setup to accurately measure α, even for complex, multielectron redox systems.

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Linear fitted lines for (a) [Fe­(CN)6]3–/[Fe­(CN)6]4–, (b) hydrobenzoquinone, (c) [Ru­(NH3)6]2+/3+, and (d) anthraquinone. (a–c) were conducted in 1 M pH 7 phosphate buffer, while (d) was conducted in 0.5 M TBAPF6 in DMF.

In the pursuit of improving the efficiency of thermogalvanic cells for waste heat recovery, achieving a larger α is desirable as it enhances the voltage output per unit of temperature difference. One common strategy to tune α involves modifying the electrolyte composition by introducing organic solvents, thereby influencing the entropic change associated with the redox reaction. ,− This effect is generally attributed to changes in the solvation structures of solvent molecules surrounding the redox-active ions. However, the thermosensitive solubility of various electrolyte compositions can also influence α, as recently highlighted. Both increase and decrease in α for the [Fe­(CN)6]3–/[Fe­(CN)6]4– redox couple have been reported upon the addition of organic electrolytes. , Therefore, the ability to accurately and reproducibly determine α across diverse electrolyte systems is crucial for the rational design of high-performance thermogalvanic systems.

Here, we demonstrate the variation in the thermogalvanic coefficient for the [Fe­(CN)6]3–/[Fe­(CN)6]4– redox couple in electrolytes with varying ratios of water and acetonitrile. As shown in Figure a, the temperature coefficient becomes increasingly positive with a higher acetonitrile content. A concentration of 50 mM [Fe­(CN)6]3– was selected to ensure that the solubility limit of the redox couple was not exceeded during the experiment. Previous studies have reported that the α value for the [Fe­(CN)6]3–/[Fe­(CN)6]4– system becomes more negative upon the addition of organic solvents, which was attributed to the thermosensitivity of solubility. , However, when the solubility limit is not reached, the presence of organic solvents such as acetonitrile disrupts the hydrogen-bonding network in water, thereby reducing the entropy change of the redox reaction. , This effect is illustrated in Figure b, and it results in a more positive α. Our automated temperature control system offers a convenient and reliable method to investigate such solvent effects on thermogalvanic behavior with high precision.

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(a) Thermogalvanic coefficient, measured in different percentages of acetonitrile mixed with water. (b) Illustration of solvation effects on the thermogalvanic coefficient.

A current limitation of our automated temperature platform is its inability to decrease temperature, as the system presently includes only a heating element. Consequently, temperature profiling is restricted to a unidirectional, increasing sequence. However, incorporating a cooling system would be straightforward and would enable bidirectional temperature cycling between high and low set points. Another limitation is that the current water reservoir is not thermally insulated. At elevated temperatures (e.g., above 70 °C), significant heat loss to the environment occurs, which slows the heating process and limits the upper range of achievable temperatures. Insulating the water reservoir would improve thermal efficiency and extend the system’s operational temperature range. Furthermore, integrating a liquid-handling pump could facilitate automated electrolyte flushing and refilling, enabling a fully autonomous operation. These enhancements are part of ongoing efforts in our group to refine the platform for high-throughput, autonomous electrochemical data collection across a range of temperatures, pH values, and electrolyte compositions.

Conclusions

In conclusion, we present a programmable, temperature-controlled electrochemical station capable of measuring the thermodynamic parameters of redox reactions with high precision. The system was validated using electrochemical impedance spectroscopy and cyclic voltammetry with a variety of redox-active compounds, including [Fe­(CN)6]3–/[Fe­(CN)6]4–, hydrobenzoquinone, ruthenium hexamine, and anthraquinone. Activation energies for the [Fe­(CN)6]3–/[Fe­(CN)6]4– and the HER on Pt were determined to be 3.35 ± 0.51 and 18.9 ± 4.1 kJ/mol, respectively. Temperature coefficients for each redox species were extracted from temperature-dependent cyclic voltammograms, and the influence of the solvation environment on the entropy change of redox reactions was also demonstrated. This setup offers a robust and self-consistent platform for efficiently acquiring electrochemical data. Moreover, its compatibility with machine learning tools positions it for future integration into autonomous experimental systems. We are currently expanding the setup’s functionalities, such as integrating gas regulation and liquid handling to determine adsorption energy and pressure-dependent kinetics in electrocatalysis applications. We anticipate that this platform will facilitate fundamental electrochemical studies, accelerate catalyst screening, and advance electroanalytical testing for a range of practical applications.

Supplementary Material

tg5c00039_si_001.pdf (511.6KB, pdf)

Acknowledgments

Y.C.L. would like to thank the University at Buffalo for financial support to enable this work.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsmeasuresciau.5c00039.

  • Additional data on Ag/AgCl reference electrode temperature calibration, EIS solution resistance data, HER EIS data for Au electrode, CV data for mix solvents, and data table for fitted EIS parameters (PDF)

All authors have contributed to the discussion and writing of the manuscript. Y.C.L., Y.W. and Z.W. conceptualize the idea. X.G., S.P. and Y.C.L. designed the system and collected data.

The authors declare no competing financial interest.

Published as part of ACS Measurement Science Au special issue “2025 Rising Stars in Measurement Science”.

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Supplementary Materials

tg5c00039_si_001.pdf (511.6KB, pdf)

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