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. 2023 Feb 21;3(3):241–251. doi: 10.1021/acsphyschemau.2c00063

On the Temperature Sensitivity of Electrochemical Reaction Thermodynamics

Haley A Petersen †, Emmet N Miller †, Phuc H Pham †, Kajal †, Jaclyn L Katsirubas †, Hunter J Koltunski †, Oana R Luca †,§,‡,*
PMCID: PMC10214520  PMID: 37249933

Abstract

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Herein, we report a method to estimate the thermodynamic potentials of electrochemical reactions at different temperatures. We use a two-term Taylor series approximation of thermodynamic potential as a function of temperature, and we calculate the temperature sensitivity for a family of twenty seven known half reactions. We further analyze pairs of cathode and anode half-cells to pinpoint optimal voltage matches and discuss implications of changes in temperature on overall cell voltages. Using these observations, we look forward to increased interest in temperature and idealized half-reaction pairing as experimental choices for the optimization of electrochemical processes.

Keywords: thermodynamics, electrochemistry, temperature, electrocatalysis, electroanalytical chemistry, electrosynthesis, physical electrochemistry

Introduction

In the realm of chemical synthesis, several parameters can be used to optimize reactions. In a standard isothermal process, reaction solvents, pressure, and reagent concentrations can be changed to control the mechanism, improve reaction yields, and minimize side reactions.1 The landscape of parameters that can influence the outcome of an electrochemical reaction is often more complex than that of a standard nonelectrochemical process; the presence of electrodes leads to additional elements that control the flux of electricity passed through the system. Temperature is a relatively underexplored parameter in electrochemical reaction development. To address this gap, the goal of the present work is to provide a useful tool that allows for (1) the estimation of thermodynamic voltages for electrochemical half reactions at varying temperatures and (2) the identification of optimal counter electrode reactions through the analysis of matches between anode and cathode reaction potentials. While this type of analysis is common in electrochemical engineering analyses, we believe that renewed consideration of these points can benefit chemists who develop catalytic reactions driven by electricity.

In an electrochemical reaction, two electrodes allow for the passage of charge. The reduction electrode (the cathode) enables the passage of negative charge through the solution, whereas the oxidation electrode (the anode) enables the removal of electrons from the system. An electrolysis is an electrochemical reaction that produces a macroscopic amount of isolable product. Such a reaction involves simultaneous oxidation and reduction processes at the two electrodes, which in many cases are separated by either a membrane or a glass frit. Both electrodes operate simultaneously and can become limiting to one another. For example, if the counter electrode is unable to sustain the balance of charge in the system, the instrument will increase the applied parameters (e.g., applied voltage in a controlled potential experiment) until the instrument limit is reached. If this limit, the compliance voltage, is exceeded, the instrument will be unable to execute the desired parameters and will eventually cease the experiment.

In this Perspective, we estimate the thermodynamic potentials necessary to drive electrochemical half reactions at different temperatures and provide a blueprint for electrochemical reaction optimization in the temperature parameter space. Additionally, we match thermodynamic potentials for anodic and cathodic reactions and pinpoint the minimum electrolyzing voltage.

Two terms utilized in our analysis are defined below.

Cell voltage (or potential) can be estimated from the sum of the two half reactions’ equilibrium potentials, for reactions that are reversible, or from the sum of the electrode potentials if the chemistries are not reversible. In an experiment, the cell voltage will need to be sufficient to overcome all cell resistances and its minimum theoretical value is the open-circuit voltage (EOC).

Open circuit voltage (EOC) is the minimum electrolyzing voltage that can drive an electrolysis reaction. In this Perspective, we determine EOC values for electrochemical half reactions from free-energy data available from NIST and the literature. A high and positive value of open circuit voltage describes a spontaneous reaction from a thermodynamic point of view; however, in practice kinetic and device design limitations need to be overcome.

Derivation of Electrochemical Potentials at Temperature

The derivation is adapted from Goodrich and Scott.2

Consider a generic cathodic half reaction:

graphic file with name pg2c00063_m001.jpg a

The Gibbs free energy change for the half reaction at temperature (ΔG)T,P is the total sum of the electrochemical potentials of the species.

graphic file with name pg2c00063_m002.jpg b

n is the number of electrons, F is Faraday’s constant and E is the potential of the half-reaction.

Let us now consider the role of temperature in the estimation of EOC for an electrochemical reaction. From the Gibbs–Helmholtz equation:

graphic file with name pg2c00063_m003.jpg c

ΔS is the change in entropy for the process and

graphic file with name pg2c00063_m004.jpg d

ΔH is the enthalpy of the half reaction; substituting eq c into eq d, we obtain

graphic file with name pg2c00063_m005.jpg e

Further substituting eq b in eq e, we obtain

graphic file with name pg2c00063_m006.jpg f

Therefore,

graphic file with name pg2c00063_m007.jpg g

From eq g, the standard electrode potential can be estimated using a Taylor series expansion as follows:

graphic file with name pg2c00063_m008.jpg h

The first two terms of this Taylor series are sufficient to produce a good approximation of EOC thermodynamic values. A third term can also be obtained through differentiation for a more accurate value, but the magnitude of this term is negligible.

Further examination of eq h reveals that the slope of our two-term temperature approximation, representing the temperature sensitivity of the thermodynamic potential has an entropy dependence. From eqs b and c, we find a simplified expression for the Inline graphic term of eq h, which we define as the temperature sensitivity, α:

graphic file with name pg2c00063_m010.jpg i

As expected, this suggests that the sign of the entropy change of the electrochemical reaction in question is related to whether an increase in temperature increases or decreases E.

With this mathematical estimation of thermodynamic values for potentials at temperature, twenty seven different electrochemical half reactions from the solar fuels and synthetic literature were selected: conversions of carbon dioxide to fuels, fuel precursors and building materials (Entries 1–6 in Table 1), water reduction (Entry 7), conversion of ammonia to fuels and fertilizer (Entries 8–12), oxygen reduction (Entries 14–17), alcohol oxidation (Entries 20–21), metal oxidation used in electrolyses with sacrificial anodes (Entries 22–23), chloride oxidation (Entry 25), alkene epoxidation (Entry 26), and dihydroxylation reactions (Entry 27). For each of these half reactions, thermodynamic potentials were calculated using data from the NIST database3 as well as the literature4−16 under standard conditions (1 atm pressure for gas species and 1 M concentration of species in solution) for a series of lab-relevant reaction temperatures. The data is summarized in Table 1.

Table 1. Summary of thermodynamic potentials for a series of electrochemical half reactions at temperature under standard conditions (1 atm pressure for gas species and 1 M concentration for dissolved species).

entry reaction potential V at 10 °C (283 K) potential V at 25 °C (298 K) potential V at 40 °C (313 K) potential V at 60 °C (333 K) potential V at 80 °C (353 K) temp sensitivity mV/10 °C
cathodic reactions
1
graphic file with name pg2c00063_m039.jpg
 –0.609 –0.641 –0.672 –0.715 –0.757 –21.3
2
graphic file with name pg2c00063_m040.jpg
 –0.098 –0.104 –0.109 –0.117 –0.125 –3.97
3
graphic file with name pg2c00063_m041.jpg
 –0.185 –0.199 –0.213 –0.232 –0.251 –9.54
4
graphic file with name pg2c00063_m042.jpg
 –0.060 –0.071 –0.083 –0.099 –0.115 –7.91
5
graphic file with name pg2c00063_m043.jpg
 0.026 0.016 0.005 –0.009 –0.023 –7.06
6
graphic file with name pg2c00063_m044.jpg
 0.177 0.169 0.161 0.151 0.140 –5.32
7
graphic file with name pg2c00063_m045.jpg
 –0.815 –0.828 –0.840 –0.857 –0.873 –8.35
8
graphic file with name pg2c00063_m046.jpg
 0.046 0.042 0.039 0.034 0.028 –2.56
9
graphic file with name pg2c00063_m047.jpg
 –1.239 –1.249 –1.259 –1.273 –1.287 –6.91
10
graphic file with name pg2c00063_m048.jpg
 0.062 0.057 0.052 0.045 0.038 –3.42
11
graphic file with name pg2c00063_m049.jpg
 –0.374 –0.387 –0.399 –0.417 –0.434 –8.57
12
graphic file with name pg2c00063_m050.jpg
 0.031 0.028 0.026 0.022 0.019 –1.71
13
graphic file with name pg2c00063_m051.jpg
 0.019 0.017 0.016 0.013 0.011 –1.03
14
graphic file with name pg2c00063_m052.jpg
 0.426 0.401 0.376 0.342 0.309 –16.8
15
graphic file with name pg2c00063_m053.jpg
 0.710 0.695 0.680 0.660 0.640 –9.92
16
graphic file with name pg2c00063_m054.jpg
 1.242 1.229 1.216 1.199 1.183 –8.46
17
graphic file with name pg2c00063_m055.jpg
 –0.301 –0.330 –0.359 –0.399 –0.438 –19.7
anodic reactions
18
graphic file with name pg2c00063_m056.jpg
 –1.242 –1.229 –1.216 –1.199 –1.183 8.46
19
graphic file with name pg2c00063_m057.jpg
 –1.774 –1.763 –1.753 –1.739 –1.725 7.00
20
graphic file with name pg2c00063_m058.jpg
 –0.238 –0.232 –0.226 –0.218 –0.210 3.98
21
graphic file with name pg2c00063_m059.jpg
 –0.026 –0.016 –0.005 0.009 0.023 7.06
22
graphic file with name pg2c00063_m060.jpg
 0.764 0.763 0.761 0.759 0.757 –0.99
23
graphic file with name pg2c00063_m061.jpg
 1.684 1.676 1.668 1.657 1.646 –5.33
24
graphic file with name pg2c00063_m062.jpg
 2.359 2.356 2.353 2.348 2.344 –2.09
25
graphic file with name pg2c00063_m063.jpg
 –1.377 –1.358 –1.339 –1.314 –1.289 12.5
26
graphic file with name pg2c00063_m064.jpg
 –0.727 –0.715 –0.704 –0.689 –0.674 7.46
27
graphic file with name pg2c00063_m065.jpg
 –0.315 –0.316 –0.316 –0.317 –0.317 –0.27
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To compare the thermodynamic potentials of the half reactions and their trends with respect to temperature changes, we report the temperature sensitivity as described in eq i in units of mV/10 °C. In the following sections, each of the individual reactions are described and the implications of the temperature variation of the half reactions shown is discussed. A positive temperature sensitivity indicates an increase in Eoc and therefore correlates to an increase in thermodynamic favorability with an increase of temperature.

Temperature Sensitivity of CO2 Reduction

The increase of atmospheric CO2 concentrations from preindustrial revolution levels of 280 ppm to 415 ppm and rising has prompted increased interest in carbon capture, utilization, and storage (CCUS) as a method of mitigating CO2 emissions and addressing climate change.17,18 One type of utilization of captured CO2 involves the conversion of CO2 to reduced products, as in eq 1 – 6.

graphic file with name pg2c00063_m011.jpg 1
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graphic file with name pg2c00063_m016.jpg 6

These reactions turn a gas with deleterious environmental impacts into useful or more environmentally benign reduced products. Different products can be obtained as a function of the electrocatalyst and conditions used for reduction. Equations 1 and 2 produce CO, a valuable fuel precursor that can be utilized in the Fischer–Tropsch process to produce alkanes. In the presence of an appropriate catalyst, eq 1 illustrates the production of CO through a proton-free 2 e– reduction of CO2 that also produces carbonate, CO32–.19 The carbonate byproduct additionally finds use as a building material in cement additives and as an emissions-negative product that can permanently store CO2.

Other reactions produce value-added commodity chemicals or fuels directly from CO2. Equation 3 depicts a 2 H+, 2 e– reduction of CO2 but produces formic acid rather than CO and water. Formic acid is an important commodity chemical, with major uses in textiles and the agricultural sector,20 and can also be used in fuel cells.21 Further reduced products are also observed with some electrocatalysts; eq 4 shows the 4 H+, 4 e– reduction of CO2 to produce water and formaldehyde, an important feedstock for industrial synthesis of more complex products and a valuable product in its own right for use in textiles, biocides, and tissue fixatives for chemical biology research.22

Equation 5 shows the reduction of CO2 by 6 H+ and 6 e– to produce water and methanol, a highly desirable product in the field of CO2 reduction. As a liquid at room temperature with relatively high energy density, methanol holds promise as a fuel that can be transported through existing liquid fuel infrastructure or even used in existing combustion engine technologies with minimal modification.23,24 Finally, eq 6 shows the 8 H+, 8 e– reduction of CO2 to produce water and methane, which also holds importance as a fuel due to its high gravimetric energy density.

While a great effort is focused on the development of the reactions from Entries 1–6 that electrochemically convert CO2 to fuels and useful chemicals, current research in the field of aqueous CO2 reduction is often focused on screening conditions close to ambient temperature and pressure. Although CO2 electrolysis has been demonstrated with success at nonstandard temperatures, these examples typically employ extremely elevated temperatures (>500 °C) with nonaqueous electrolytes that are solid at room temperature, such as molten carbonate or solid oxide fuel cells for conversion of CO2 to CO.25 Such reductions of CO2 to CO occur with simultaneous evolution of O2 gas, resulting in a positive change in entropy and, by eq i, a favorable effect from increasing temperature. However, each of the aqueous CO2 reduction reactions given in eqs 1–6 exhibits a negative temperature sensitivity value as shown in Table 1, indicating that these reactions become less favorable at higher temperatures. Decreasing reaction temperatures could thus be a strategy for improving the favorability of these reactions. For example, lowering the temperature of an electrochemical reactor in which CO2 is reduced to CO and CO32– at the cathode would drive the thermodynamic potential more positive by 21.3 mV per each 10 °C decrease in temperature.

However, the choice of solvent may limit the extent to which this temperature sensitivity factor can be leveraged in an experimental design. In an aqueous solution, the lower limit for operating temperature will be near 0 °C before the solution freezes or becomes excessively viscous, depending upon the electrolyte concentration. In such situations, there may be benefits to using polar organic solvents, whose freezing points are substantially lower than that of water. Although lower temperatures are associated with slower kinetics for relevant chemical steps, it is worth noting that in such cases, the increasing solubility of gaseous starting materials in the liquid phase at lower temperature may help to offset the kinetic penalties of low operating temperature.

It is also worth noting that with any modification to the reactions as written (e.g., use of a different solvent rather than water, variations in concentration, or variations in pressure), the thermodynamic potential at a given temperature will be impacted. The effects of such changes must also be considered when choosing optimized temperature conditions for a reaction.

Temperature Sensitivity of Water Reduction

Hydrogen gas (H2) has long been investigated for its potential as a clean energy carrier to address rising energy demands and greenhouse gas emissions. Hydrogen has an energy density over twice that of typical solid fuels at 140 MJ/kg and is especially attractive when paired with renewable energy like wind and solar power.63 In addition to its potential as an energy carrier, hydrogen is an important industrial chemical. The vast majority of industrial hydrogen is currently made from natural steam gas reforming, oil reforming, and coal gasification, which are all processes detrimental to the environment.26 Thus, the shift over to more sustainable means of hydrogen production is a pressing scientific endeavor.

The reaction for electrochemical water reduction is shown below.27

graphic file with name pg2c00063_m017.jpg 7

At the cathode, water is reduced to make H2 in a process known as the hydrogen evolution reaction (HER).28 The HER suffers from significant kinetic energy barriers from the high stability of water molecules at ambient conditions; high overpotentials are often necessary to reach functional current densities and satisfactory energy conversion efficiencies.29 Therefore, transition metal-based catalysts are typically employed to help overcome the energy barriers.

Although new catalysts continue to be developed, temperature is an underexplored parameter in HER catalysis. The temperature sensitivity of water reduction, eq 7, would suggest that a higher temperature would drive the overall thermodynamic cell voltage to more negative values with a change of −8.35 mV for each 10 °C increase in temperature. Lower temperatures may therefore benefit this reaction, although the necessity of operating in aqueous conditions for this reaction limits the extent to which temperature may be lowered.

Temperature Sensitivity of N2 Reduction

The reduction of nitrogen gas to ammonia is a useful reaction given the importance of ammonia in the use of fertilizer, as well as in biological systems.30 In general, this reaction is energy intensive as the nitrogen–nitrogen triple bond is very strong.

graphic file with name pg2c00063_m018.jpg 8
graphic file with name pg2c00063_m019.jpg 9
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graphic file with name pg2c00063_m021.jpg 11
graphic file with name pg2c00063_m022.jpg 12
graphic file with name pg2c00063_m023.jpg 13

Ammonia is produced on an industrial scale through the Haber–Bosch process which produces 2% of yearly greenhouse emissions globally, due to the high energy input and temperature required.30 Electrochemical reactions in which ammonia is produced close to ambient temperature are therefore sought. Using these types of methods, nitrogen can be reduced to ammonia (eqs 8, 10, 12, 13), but also hydrazine (eq 9) and diazene (eq 11).

Nitrogen reduction is also seen in biological systems through nitrogenase reactions in which ammonia and hydrogen are produced in varying stoichiometries by molybdenum- (eq 11), vanadium- (eq 12), and iron-based (eq 13) nitrogenases.31 In nature, these nitrogenase reactions occur with concomitant conversion of ATP to ADP to give the ammonia product, which can then be used in the rest of the body or biological system. In general, nitrogen reduction is a difficult and energy-intensive process, but these natural enzymes have shown great capability in the production of ammonia and may be the key to understanding ammonia production. Understanding the mechanism of these reductions may also help to elucidate what leads to the preferential formation of some products over others in synthetic systems.

Just as with the previously discussed reduction reactions (eqs 1–7), each of the nitrogen reduction reactions discussed herein is associated with a negative temperature sensitivity value, indicating that the thermodynamic potential becomes more negative and unfavorable with increasing temperature. Decreasing the operating temperature for an electrolysis cell carrying out nitrogen reduction would therefore improve the favorability of the nitrogen reduction half-reactions, though it is worth mentioning that each reaction for the reduction of N2 to NH3 is relatively temperature-insensitive, with small values of α. At lower temperature, pathways for the reduction of N2 to N2H2 or N2H4 increase in favorability more than those producing NH3. When paired with kinetic arguments, this observation may help to explain changes in observed product selectivity at different temperatures.

Temperature Sensitivity of Electrochemical Oxygen Reduction

The catalytic oxygen reduction reaction (ORR) and its counterpart, the oxygen evolution reaction (OER), are ubiquitously found in critical physiological processes and are key constituents in abiotic energy-converting platforms such as fuel cells and metal-air batteries.18−23 These reactions have been investigated in a wide selection of solvents and electrolytes on different electrode surfaces. In aqueous systems, ORR occurs mainly through a direct 4 e– reduction pathway whereby O2 is converted to H2O (or to OH– at alkaline pH) and, less commonly, to hydrogen peroxide (H2O2) by a 2 e– transfer pathway (eqs 14–16).23−26 Direct reduction to water is preferred in most fuel cell applications due to its higher energy conversion efficiency.27 The formation of H2O2 is often referred to as a side reaction of the 4 e– pathway, which could be destructive due to the formation of reactive oxygen species (ROS). Carbon-based electrodes have low efficiency for the 4 e– ORR, thus the accumulation of a useful concentration of the H2O2 intermediate could be valuable for cathodic H2O2 production.24,25,27,28

graphic file with name pg2c00063_m024.jpg 14
graphic file with name pg2c00063_m025.jpg 15
graphic file with name pg2c00063_m026.jpg 16

Additionally, one-electron reduction of O2 leads to the formation of superoxide ion (O2–•), as shown in eq 17 below. The superoxide and its protonated hydroperoxyl radical (HO2•, pKa = 4.88) are also involved in autoxidation and photolysis-induced oxidation of industrially relevant chemicals, waste polymers, and atmospheric chemicals.21,22,29,30 Solvent stability and the reactivity of electrogenerated superoxide have also been intensively studied in the context of reversible metal-air batteries.31,32 The commonly used standard reduction potential for the O2(g)/O2–•(aq) redox couple of −0.33 V vs SHE (eq 17) is derived from various studies in different chemical and biological systems including certain enzymes, alkaline solution under radiolytic and photolytic conditions, and various quinone/semiquinone redox systems.25,33 The reactivity of superoxide in aqueous media is often explained by its mild basicity and its degraded products from superoxide dismutation.22,29 Superoxide ion is known to react rapidly with H3O+ to form H2O2 and O2 or, at strong alkaline pH, to form hydroperoxide anion (HO2–), hydroxyl anion (OH–), and dioxygen.22,34 On the other hand, the electrogenerated superoxide ion in organic solvents can be involved in useful reactions with organic compounds as a nucleophile, mild reducing agent, or in some cases an overall oxidant by initializing proton/hydrogen abstraction from susceptible substrates.22,29,35

graphic file with name pg2c00063_m027.jpg 17

Much like the previously discussed reduction half-reactions, the oxygen reduction reactions have negative temperature sensitivities. The most temperature sensitive of these reactions is the energetically uphill 1 e– pathway to superoxide (eq 17), whose thermodynamic potential shifts negatively by 19.7 mV for every 10 °C temperature increase. In this regard, O2–• is not thermodynamically beneficial as a targeted cathodic discharge product in most fuel cell applications when compared to the other ORR reaction variants, especially in protic solvents or at higher temperatures.

Temperature Sensitivity of Electrochemical Water Oxidation

In conjunction with the oxygen reduction reactions, water oxidation reactions are globally important due to their involvement in the O2-evolving unit of Photosystem II.32 Abiotic versions of the water oxidation reactions using electricity and catalysts can occur through a 4e– transfer pathway to produce oxygen or through 2e– oxidation (eq 18) of water to hydrogen peroxide (eq 19).33−35 Although the oxygen evolution reaction (OER) is the canonical anodic half reaction in water splitting, researchers often seek value-adding alternatives to this anodic counterpart since this process generates unneeded O2 and contributes significantly to efficiency losses due to sluggish kinetics.36,37 However, the 2e– pathway of H2O2 electrosynthesis from water has recently gained attention as a green and cost-effective alternative to the multistep anthraquinone autoxidation process, the current method to produce hydrogen peroxide industrially. Anthraquinone autoxidation is costly and imposes safety risks due to the generation of highly concentrated aqueous H2O2.34,38,39 In terms of thermodynamics, the electrochemical production of H2O2 from water is unfavorable due to complications with H2O2 overoxidation to O2 at low electrode potentials.34,38,40 Both forms of water oxidation described in eqs 18 and 19 have positive temperature sensitivities, becoming slightly more favorable at higher temperatures. Therefore, the development of electrode materials to enhance selectivity and/or current density for H2O2 production is an emerging field of research.34,37,39

graphic file with name pg2c00063_m028.jpg 18
graphic file with name pg2c00063_m029.jpg 19

Temperature Sensitivity of Electrochemical Methanol Oxidation

The electrochemical oxidation of aqueous methanol solutions is a key reaction in fuel cell chemistry. In this technology, methanol is used as the anodic feeding fuel coupled with an O2 or air gas diffusion cathode in direct methanol fuel cells (DMFCs).41,42 The desired anodic reaction in DMFCs is the complete oxidation of methanol to CO2, 6 H+, and 6e–.

The oxidation of methanol to formaldehyde (HCHO) is an example of incomplete oxidation of an alcohol to an aldehyde, likely an intermediate in the multipathway process to CO2 evolution.41 In addition to relevance to organic electrosynthesis, the uses of methanol and other organic molecules as anodic sacrificial reagents have been shown to increase electrochemical and photoelectrochemical hydrogen evolution efficiency, by avoiding the kinetic limitations of the water oxidation half reaction.37,43,44 Based on our estimations, the oxidation potential of methanol to formaldehyde (eq 20) is relatively temperature insensitive, becoming only slightly more favorable at a rate of 3.98 mV for every 10 °C increase.

graphic file with name pg2c00063_m030.jpg 20

For the complete oxidation of methanol to CO2 in the presence of water, which produces 6 H+ and 6 e– (eq 21) a slightly larger temperature sensitivity is observed. With an increase in temperature, methanol oxidation to CO2 becomes slightly more favorable at a rate of 7.06 mV/10 °C.

graphic file with name pg2c00063_m031.jpg 21

Oxidation of Metal Anodes

The use of metals and metal alloy electrodes as sacrificial anodes is a principal method of galvanic cathodic protection in corrosion chemistry.45 During the charge transfer process, metal dissolution occurs as oxidized metal ions being transferred into solutions. Mg- and Al-based alloys are the most commonly used galvanic anodes and, to a lesser extent, Zn and its alloys are employed in applications where hydrogen embrittlement is problematic.45,46 Aside from this issue, these three metals are important components in aqueous metal-air batteries.47 During discharge, these anodic materials are oxidized alongside the catalytic O2 reduction occurring at the gas diffusion cathode. The use of Mg, Zn, and Al as stoichiometrically consumed anode materials are additionally important for electroreduction in the realm of organic synthesis.48,49 The liberated metal ions are often considered inert species that interact minimally with electrogenerated organic radical species.48 The anodically dissolved Mg2+ and Al3+ ions were however found to promote the reduction of aliphatic esters and the Birch reduction of aromatic compounds.48,50,51 The solvated metal ions are suspected to play a key role in coordinating anionic intermediates that facilitate their reduction or act as electron transfer catalysts.52−54

graphic file with name pg2c00063_m032.jpg 22
graphic file with name pg2c00063_m033.jpg 23
graphic file with name pg2c00063_m034.jpg 24

Unlike the previously described oxidation half-reactions, the metal anode oxidations become slightly less favorable at higher temperature. Although eqs 22–24 have negative temperature sensitivity values, their highly positive standard reduction potentials still render the EOC of electrochemical cells utilizing these half reactions positive at elevated temperatures. However, the use of Mg- and Al-based electrodes in aqueous metal-air batteries is still limited despite their considerable theoretical energy density, most likely due to the parasitic corrosion of these anode materials in contact with the aqueous electrolyte or sensitivity to air or moisture in case of metallic Mg.55,56

Chloride Oxidation

graphic file with name pg2c00063_m035.jpg 25

Chloride oxidation (eq 25) is utilized to produce chlorine gas and sodium hydroxide on industrial scale.57 Known as the chlor-alkali process, the electrolytic decomposition of chloride brines operates with the production of hydrogen as the cathode half reaction.

The chloride ion oxidation half reaction has been proposed as an alternative to water oxidation in solar-fuel producing devices.58 While the reactions are quite different, we note that the positive temperature sensitivity of reaction 25, 12.5 mV per temperature decade, is quite similar to the temperature sensitivity of the water oxidation reactions with 8.46 and 7.00 mV/10 °C of reactions 18 and 19, respectively. This suggests that chloride oxidation slightly could enhance favorability at higher temperatures.

Temperature Sensitivity of Alkene Oxidation Reactions

graphic file with name pg2c00063_m036.jpg 26

Equations 26 and 27 describe transformations of alkenes to epoxides and diols, important functional groups in the context of larger synthetic pathways. Equation 26 describes an electricity-driven organic epoxidation reaction on ethylene to produce ethylene oxide, an important industrial precursor for plastics synthesis. The calculated value for the thermodynamic potentials for this process can assist in selecting a suitable counter electrode reaction.59,60

Temperature sensitivity analysis of the electrochemical epoxidation of olefins suggests that an increase in temperature will increase the thermodynamic potentials for the oxidation by 7.46 mV per temperature decade.

graphic file with name pg2c00063_m037.jpg 27

Dihydroxylation of olefins has been demonstrated for the production of optically active glycols with high enantiomeric excess.19,61 This reaction’s temperature sensitivity of −0.265 mV/10 °C is low compared to other reactions, allowing for many different possible reaction couplings without concern for the effects of temperature on this half-reaction.

Effect of Temperature on Full Electrochemical Cells

Based on thermodynamic analyses of our matched half reactions, we can identify pairs of reactions in which the thermodynamics are uniquely favorable in Figure 1. In the heatmaps below, we calculate the Eoc for full electrochemical cells assembled from pairs of our anodic and cathodic reactions; the positive Eoc in red suggests that those reactions are thermodynamic matches. Reaction sets in blue, on the other hand, are thermodynamically mismatched and therefore will likely require a relatively large energy input. Several trends emerge upon visual assessment of the heatmaps. The reactions for the reduction of O2 generally have favorable thermodynamics across the landscape of anodic reactions except for chloride oxidation and oxidation of water. This is consistent with the use of the O2 reduction reactions in various device applications related to fuel cells. Coupling of the organic oxidations (eqs 25–27) with O2 reduction also leads to a more positive EOC and therefore points at an interesting match for future reaction optimizations. Additionally, Mg anodes have favorable thermodynamics when coupled with most cathodic processes. However, this reaction presents a variety of safety issues. Al and Zn anodes, in turn, have slightly less favorable thermodynamics but avoid the safety issues associated with the Mg oxidation reaction.

Figure 1.

Figure 1

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Open circuit voltage at (a) 10 °C, (b) 25 °C, and (c) 60 °C for electrochemical cells consisting of a series of reduction (x-axis) and oxidation (y-axis) half-cell pairs.

To visually summarize the findings in our paper, we proceeded to reduce the thermodynamic potentials from Figure 1 to a map of temperature sensitivities for pairs of oxidation and reduction half-reactions (Figure 2).

Figure 2.

Figure 2

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Temperature sensitivity (mV/10 °C) of EOC for matched electrochemical half cells; Reduction (x-axis) and oxidation (y-axis).

Most reactions with high favorability also have a significant temperature sensitivity. In the Figure 2 heatmap, we analyze the paired half reactions and map the temperature sensitivity. This reveals that a decrease in temperature in reactions with dissolving anodes would lead to more favorable thermodynamics. On the other hand, cells employing reduction half-reactions for solar fuel producing reactions vary in their temperature sensitivities. For most CO2 reduction reactions paired with most oxidation counter reactions, lower temperature is beneficial. However, cells employing nitrogen fixation reactions tend to benefit from higher temperatures, with the exception of those paired with the dissolving anodes whose strong negative temperature sensitivities influence the effect of temperature on the overall cell. Consideration of both half-cells employed is therefore important when determining the effect of temperature on the overall cell.

In principle, the temperature of the cathode and anode may also be controlled independently. This approach may be beneficial to maximize the favorability of both half-reactions when they have opposite trends for temperature sensitivity. However, implementation of this strategy may be rendered more difficult by the need for custom electrolysis setups allowing for separate temperature control.

Resistance Varies with Temperature

While the thermodynamic analysis herein does not include aspects related to changes in the environment at different temperatures, resistance is a key component of electrochemical reaction processes. For this reason, we want to make a few minor notes related to it. Resistance increases with temperature according to eq j, which linearly approximates the resistance at a new temperature. This approximation is considered valid at higher temperatures due to a logarithmic relationship between resistance and temperature.62

graphic file with name pg2c00063_m038.jpg j

In this equation, αR is the temperature coefficient (units of °C–1), which controls how the resistance changes with temperature. Ro is the initial resistance, which corresponds to the resistance at the initial temperature. Many temperature coefficients for single elements are known with values generally around 10–3 °C–1. For electrochemical reactions, the temperature coefficient of the reaction medium at the start, throughout, and at the end of the reaction will need to be considered.

It is also worth noting that the passage of current through any material of nonzero resistance releases heat, called resistive heating. Although resistance increases at higher temperature by eq j, a high temperature electrolysis may leverage this released energy to heat the cell, thereby increasing the overall energy efficiency of the electrolysis.

Conclusion

Our findings show that, by estimating the thermodynamic potentials of individual half-reactions and full electrochemical cells at varying temperatures, we can elucidate the effect of temperature on half-reactions of interest and identify a thermodynamically matched counter electrode reaction. Although temperature is a commonly controlled parameter in laboratory-scale synthetic experiments, it is often overlooked in electrochemical experiments focused on the development of chemistries for a specific half reaction. Our analyses show that changes in temperature can have significant impacts on the favorability of certain electrochemical reactions. Tailoring experimental conditions to suit the temperature sensitivity of a reaction of interest is a significant yet underused strategy for the optimization of electrochemical synthetic reactions.

Although we have mapped general temperature dependence trends for a variety of reactions, the choice of temperature conditions for an actual electrochemical experiment will depend upon several other factors. Changing solubility for the starting materials or products of a given reaction, for instance, may render certain temperature-changing strategies more or less favorable or hinder feasibility altogether. Low temperatures, for example, may cause solid starting materials to precipitate out of solution; on the other hand, lower temperature often increases the solubility of gas-phase species. Furthermore, electrolyses in aqueous media have a lower limit for usable temperature dictated by the freezing point of water, despite the observation that many reactions discussed herein become more thermodynamically favorable at lower temperature. Alternative solvents for the reactions discussed herein, such as polar organic media, may therefore be worthy of consideration for low-temperature applications. Moreover, electrochemical reactions are not often conducted at standard conditions (e.g., 1 M for all dissolved components such as H+) in practice; the effect of pH, for instance, will therefore be a critical consideration in aqueous media. The kinetics of a given reaction are of course another important consideration. A larger applied potential may be necessary to drive a given electrochemical reaction at a desired rate, and the kinetics of chemical processes are expected to vary in accordance with the Arrhenius equation as temperature is changed, impacting the overall rate of reaction. The design of appropriate catalysts to modify these kinetic barriers therefore remains a key aspect of electrochemical synthesis. Finally, the open-circuit voltages presented herein are limited in precision by the use of a two-term approximation method derived from eq h and are intended to provide rough estimations of the potentials under consideration for the identification of broad trends, rather than exact values.

With this analysis, we hope to draw attention to changes in thermodynamics as a function of temperature. These changes have significant implications in the development of paired electrochemical reactions, but could also be important considerations in mechanistic studies at different temperatures. Using the trends discussed herein, we look forward to increased interest in temperature and idealized half-reaction pairing as tunable parameters for the optimization of electrochemical reactions.

Acknowledgments

This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE 2040434 (H.A.P.). O.R.L., P.H.P., K., H.K., and E.J.M thank the University of Colorado for startup funds. J.L.K. would like to thank CU Boulder for funding through the UROP program. This work was supported in part (OL and PP) by the National Renewable Energy Laboratory (NREL), operated by Alliance for Sustainable Energy, LLC, for the U.S. Department of Energy (DOE) under Contract No. DE-AC36-08GO28308. This work was supported by the Laboratory Directed Research and Development (LDRD) Program at NREL. The views expressed in the article do not necessarily represent the views of the DOE or the U.S. Government. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for U.S. Government purposes. We also thank the reviewers for their time and expert feedback.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsphyschemau.2c00063.

  • Full tabulated thermodynamic values for each reaction examined (PDF)

Author Contributions

∥ H.A.P. and E.N.M. contributed equally to this paper.

The authors declare no competing financial interest.

Supplementary Material

pg2c00063_si_001.pdf (261.5KB, pdf)

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Supplementary Materials

pg2c00063_si_001.pdf (261.5KB, pdf)

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