Linear Gibbs Energy Relationship Research Articles

Perspective on theories for reversible potentials for reactions taking place on electrode surfaces

• Surface potential and activation energy from electron affinities: LRC. • Surface potential and activation energy from DFT with surface charging. • Surface potential from standard solution values and adsorption energies: LGER . • Surface potential standard hydrogen value and surface reaction energy: CHE. • A relationship between LGER and CHE explained: U LGER − U CHE = U CHE (aq) − U 0 . This article provides a brief overview of three models for calculating activation energies and reversible potentials for oxidation and reduction reactions involving protons at the electrochemical interface and advances the understanding of one of them. Two incorporate the electrode potential in the calculations, the local reaction center (LRC) model where an external electron source or sink is at the chosen potential, and slab-band density functional (DFT) codes which incorporate surface charging to set the potential. The simplest theory comes in two forms: the linear Gibbs energy relationship (LGER) and the computational hydrogen electrode (CHE) model. They have empirical components, inputting experimental data and predicting reversible potentials for surface reactions from calculations of energies for adsorbates at the vacuum interface. LGER uses experimentally measured standard reversible potentials as parameters and CHE employs the work function of the standard hydrogen electrode and the standard value of 0 V for this electrode as parameters. A relationship between LGER and CHE is derived. While LGER predictions depend on two calculated adsorption energies, CHE is demonstrated by means of a Haber cycle to effectively depend on the energy calculated for the reaction in solution as well as the two adsorption energies.

Solubility of carbon dioxide in binary mixtures of dimethyl sulfoxide and ethylene glycol: LFER analysis

The solubility of carbon dioxide was determined in dimethyl sulfoxide, ethylene glycol, and their binary mixtures at the temperatures ranging from 298.15 Kto 328.15 K and the pressures ranging from (0 to 6) bar (0 to 0.6 MPa). It was shown that the solubility of CO2 increased with the increasing of pressure while decreased with the increasing of temperature. The Henry’s constants and thermodynamic properties of solution were calculated from the solubility data. The solubility and Henry’s constant of CO2 in the solvent mixtures increased with increasing the mole fraction of dimethyl sulfoxide. Finally, the dependence of CO2 solubility on solvent properties was investigated using the linear Gibbs energy relationship method. Results showed that solute-solvent interactions in the scale of polarity/polarizability and hydrogen bond acceptor ability of the solvent were the main parameters which control the solubility of CO2 in the solvents.

Nucleophilic reactivities of Schiff base derivatives of amino acids

Treatment of α-imino esters derived from glycine esters and benzophenone or benzaldehydes with potassium tert butoxide in DMSO gave persistent solutions of carbanions at 20 °C. The kinetics of their reactions with quinone methides and benzylidene malonates (reference electrophiles) have been followed photometrically under pseudo-first order conditions. The reactions followed second-order rate laws. Since addition of 18-crown-6 ether did not affect the reaction rates, the measured rate constants correspond to the reactions of the non-paired carbanions. Plots of the second-order rate constants against the electrophilicity parameters E of the electrophiles are linear, which allowed us to derive the nucleophile-specific parameters N and sN, according to the linear Gibbs energy relationship lg k2(20 °C) = sN(N + E). The Ph2C = N- and PhCH = N- groups act as very weak electron acceptors with the consequence that Ph2C = N-CH–-CO2R and PhCH = N-CH–-CO2R have a similar nucleophilicity as Ph-CH–-CO2Et, the anion of ethyl phenylacetate.

Theoretical evidence of the relationship established between the HO[rad] radicals and H2O adsorptions and the electroactivity of typical catalysts used to oxidize organic compounds

This study aims to compute the electronic structures of “non-active” (BDD, SnO2, PbO2 and TiO2) and “active” (IrO2 and RuO2) electrodes for H2O oxidation, to yield HO using periodic models, and connect this information with their experimental trends of reactivity. The generation of radicals is modelled from H2O oxidation using the more stable and labile crystal face and structure of each material, and the relationship between its adsorption and reactivity towards organic compounds is analyzed. The method of linear Gibbs energy relationship (LGER) is likewise used to compute the reversible potential to oxidize H2O to HO. The adsorption energies, calculated for 25, 50 and 100% surface coverages of HO, decrease in the following order: IrO2> RuO2> SnO2≈TiO2> PbO2> BDD; while the reaction energies involved in the degradation of a model organic species (catechol) by this radical present an opposite trend: IrO2< RuO2< SnO2≈TiO2< PbO2< BDD, similar to the experimental electroactivity reported to oxidize organics on these materials. This theoretical finding quantitatively indicates that the reactive trend depending on potential for these catalysts is a tradeoff between the adsorption energies for H2O and HO, whereby an ideal material to perform organic degradation will not only weakly adsorb HO species, but will also present an even weaker H2O adsorption. Accordingly, the theoretical results described in this study can enable the design of new electrocatalysts through the search of low cost, non-toxic and durable materials with modulated adsorptive properties via computational methods.

Activity coefficients at infinite dilution, physicochemical and thermodynamic properties for organic solutes and water in the ionic liquid ethyl-dimethyl-(2-methoxyethyl)ammonium trifluorotris-(perfluoroethyl)phosphate

New values of activity coefficients at infinite dilution, γ∞ for 65 different solutes including alkanes, alkenes, alkynes, cycloalkanes, aromatic hydrocarbons, alcohols, thiophene, ethers, ketones, aldehydes, esters and water in the ionic liquid ethyl-dimethyl-(2-methoxyethyl)ammonium trifluorotris(perfluoroethyl)phosphate, were determined using inverse gas chromatography within the temperature range from (318.15 to 368.15)K. This is a continuation our study of ionic liquids based on this anion and 2-hydroxyethyl cation substituent. The experimental γ∞ values were used to calculate thermodynamics functions such as partial molar excess Gibbs energy ΔG1E,∞, enthalpy ΔH1E,∞ and entropy ΔS1E,∞. Additionally the (gas+liquid) partition coefficients of the solutes, KL were calculated and were used to determine the linear Gibbs energy relationship (LFER) system constants as a function of temperature. Values of the selectivity and capacity at infinite dilution for alkanes/thiophene extraction problems were also calculated. Results were compared to ionic liquids investigated previously with the same anion.

Mechanisms for Ethanol Electrooxidation on Pt(111) and Adsorption Bond Strengths Defining an Ideal Catalyst

Ethanol electrooxidation on the Pt(111) electrode has been studied with computational theory. Using a solvation model and a modified Poison-Boltzmann theory for electrolyte polarization, standard reversible potentials for forming 17 reaction intermediates in solution were calculated with density functional theory. Reversible potentials for adsorbed intermediates were then determined by inputting calculated adsorption energies into a linear Gibbs energy relationship. A path to CO2 was found where surface potentials were low and close to the calculated 0.004 V reversible potential for the 12 electron oxidation of ethanol. An exception was the 0.49 V potential for forming the OH(ads) from H2O(l), this being required for oxidation of CO(ads) and RH(ads) intermediates. The surface potentials show that acetyl, OCCH3(ads) forms at small positive potentials and decomposes to CH(ads), CH3(ads), and CO(ads), which poison the surface at these potentials. Energy losses due to non-electron transfer reaction steps are small and cause a small shift in the reversible potential for the 12 electron oxidation. Values for adsorption bond strengths over a perfect catalyst were determined. It is concluded that on an ideal catalyst most intermediates will adsorb more weakly and OH more strongly than on Pt(111).

Structure and Reactivity of Sub-Monolayer Pt on CeO2 Surface from First Principles Thermodynamics

Transition metal catalysts supported on metal-oxide surfaces are promising materials for usage in heterogeneous catalysis due to strong metal-support interaction, which affects the intrinsic activity at the surface, and results in enhanced dispersion of metal atoms in some cases, thus promoting stability. One of the most widely investigated such systems are Pt/CeO2 systems, which have been found to be highly active toward the water gas shift reaction [1]. Experimental and theoretical studies point to electron and oxygen transfer between adsorbed Pt atoms and CeO2 support as the reason for the enhanced activity in such systems [2, 3]. The effect of this metal-support interaction, however, is far from clear in context of the redox reactions that occur in DMFCs and PEMFCs. Especially, the role of CeO2, well known for its oxygen storage capacity, remains yet to be investigated in co-catalysis. To this end, understanding and characterizing the dispersion of Pt on the CeO2 surface is of utmost importance. Stability and activity of a few Pt layers on rutile metal-oxides has been investigated computationally, yielding insights into the geometric and electronic influences of the support on the catalyst [4]. Sub-monolayer deposition of catalyst atoms opens up the support surface to direct engagement with the reactants and is well worth investigating. In this study, first principles DFT calculations are used in combination with rigorous statistical mechanics methods to find stable phases of Pt atoms dispersed on the CeO2 (111) surface as a function of their chemical potential. Employing the Cluster Expansion formalism in tandem with the Metropolis Monte Carlo Method to account for the configurational contribution to the system’s free energy [5], the important interactions dictating the surface morphology are identified. In agreement with experiments [2], a remarkable transfer of oxygen from CeO2 to the Pt atoms is observed, and a tendency of Pt atoms to aggregate at low surface coverage is also seen. Further, using a linear Gibbs energy relation, the energetics of various reaction steps in a 2 e- oxygen reduction (ORR) process of the Pt/CeO2 system are computed for several instances of oxygen co-adsorption and are compared to those of a model Pt (111) system as a function of the electrode potential. Additionally, the effect of support on the dissolution potential of Pt atoms is also evaluated to understand the stabilizing effect of the support, which has been observed experimentally [6]. Enhancement in ORR kinetics for Pt/CeO2 systems has been observed experimentally, but such studies are few [7]. Two mechanisms are proposed in this study to explain such a behavior: (1) the preferential adsorption of OH on only Pt in contrast to the co-adsorption of O on both Pt and CeO2, and (2) the activation of O-O bond breaking due to the oxygen starved CeO2 surface. In principle, such systems with the possibility for the support material to take part in the reaction along with the catalyst atoms can open up new channels that facilitate ORR.

Effect of the nature of binary water-organic solvents on the thermodynamic characteristics of adsorption of certain 1,3,4-oxadiazoles and 1,2,4,5-tetrazines on phenyl-bonded silica gel

The thermodynamics of adsorption in the Henry region for certain 1,3,4-oxadiazoles and 1,2,4,5-tetrazines from water-acetonitrile, water-methanol, and water-isopropyl alcohol solutions on silica gel with grafted phenyl groups is studied according to the dynamic method under conditions close to equilibrium. The effect of the nature of the organic component of a solvent on the values of standard differential molar changes in Gibbs energy, enthalpy, and entropy is shown upon adsorption of the investigated substances from solutions. The role of intermolecular interactions occurring in bulk solutions and at the interface during the adsorption of heterocycles from diluted water-organic solutions is discussed. The compensation effect and linear Gibbs energy relationship upon the adsorption of 1,3,4-oxadiazoles and 1,2,4,5-tetrazines from the investigated water-organic solutions on silica gel with grafted phenyl groups is determined.

Solvation and Zero-Point-Energy Effects on OH(ads) Reduction on Pt(111) Electrodes

The linear Gibbs energy relationship (LGER) is a theoretical model in which one adds to the known bulk solution-phase reversible potential for a reaction involving electron transfer the internal energy change, divided by nF, when the reactants and products are adsorbed, where n is the number of electrons transferred and F is the Faraday constant. This yields predictions of the reversible potentials for the same reactions but with the reactants and products in adsorbed states on the electrode surface. The LGER theory has been used in previous studies where De bond strengths, measured from the bottom of the Born−Oppenheimer potential at equilibrium, were used rather than the Do values, which include zero-point vibrational energies. Here, it is shown that, when zero-point energies are included, the result is to increase the reversible potential for OH(ads) reduction to H2O(ads) on Pt(111) electrodes, an important fuel-cell cathode reaction, by 0.05 V. The effects of solvation are also shown to be small, leading to decrease in the LGER prediction by 0.09 V. These results were calculated by using a self-consistent theory incorporating two-dimensional slab-band density functional calculations with the solvation handled by a modified Poisson−Boltzmann theory and a dielectric-continuum model. The net result is to decrease the LGER prediction of 0.86 V for the reaction with hydrogen bonding of the reactant and product to adsorbed water to 0.82 V, which is a close match with the experimental value of about 0.77 V. These findings explain the usefulness of the LGER theory for rapid screening of fuel-cell electrocatalysts.

Selenium: A Nonprecious Metal Cathode Catalyst for Oxygen Reduction

From voltammetric studies, trigonal phase selenium (t-Se) nanotubes, which are bundles of hexagonally packed helical chains of Se atoms, have been shown by others to be stable in acid and have a double-layer region extending from −0.2 (standard hydrogen electrode) to 0.75 V. This is broader than the to double layer for platinum and presents a potential range that might allow oxygen reduction activity. This paper presents theoretical predictions of oxygen reduction mechanisms on t-Se. Adsorption energies from Gaussian cluster hybrid density functional and Vienna ab initio simulation program density functional calculations are used in the linear Gibbs energy relationship to predict the reversible potentials for the one-electron reduction steps during the four-electron reduction of to water, which ideally occurs at 1.229 V. Adsorption energies for reduction intermediates are calculated using single-chain models. Calculated reversible potentials for the four reduction steps lead to the prediction that the step with the highest overpotential is the reductive elimination of OH(ads) to form water and occurs at about 0.8 V. The overall behavior predicted for t-Se is similar to that of platinum, and it is suggested that t-Se is worthy of trials as a potential oxygen cathode electrocatalyst.

Theoretical Study of Early Steps in Corrosion of Pt and Pt/Co Alloy Electrodes

Theoretical studies of Pt and PtCo alloy electrode dissolutions in PEMFCs were made using adsorption energies from VASP slab band calculations on the metal surfaces in a linear Gibbs energy relationship. The reversible potential for Co−OH formation from oxidation of H2O on the Pt3Co(111) surface was calculated to be 0.50 V, which is significantly lower than the calculated 0.70 V reversible potential for Pt−OH formation on the Pt(111) surface. Co(OH)2 formation from oxidation of H2O on the Pt3Co(111) surface was calculated to take place at a lower potential than Pt(OH)2 formation on the Pt(111) surface, with the respective reversible potentials 0.58 and 1.92 V. These results for what may be the initial steps of anodic dissolution indicate that Co will dissolve at lower potential than Pt in the alloy surface and leave behind a Pt surface skin when the potential is >∼0.50 V. In addition, the reversible potential for OH formation on a step of edge atom on Pt(111) surface from oxidation of H2O was calculated to be 0.60 V, which is 0.10 V lower than reversible potential on the terrace sites, which implies that edge atoms are removed first. The final step of dissolution is believed to be the hydrolysis of the Pt2+ hydroxide, which considering the small equilibrium constant reported by Pourbaix, should proceed slowly.

Effect of the reaction series of hydroxyazomethine and chloride anions of variable concentrations on the passivation currents of nickel

Nickel passivation in 1 M H2SO4 in the presence of hydroxyazomethine derivatives (C = const) and chloride anions in variable concentrations was studied. Plots of the Ni passivation current vs. \(C_{Cl^ - } \) showed symbatic and antibatic changes, depending on the chloride concentration range. The results obtained were interpreted in terms of the Linear Gibbs Energy Relation (LGER).

Cyclic voltammetry of ion transfer across a room temperature ionic liquid membrane supported by a microporous filter

Cyclic voltammetry is used to study the transfer of a series of cations and anions across a room-temperature ionic liquid (RTIL) membrane composed of tridodecylmethylammonium cation (TDMA +) and tetrakis(pentafluorophenyl)borate anion (TPFPB −), and supported by a thin (∼112 μm) microporous filter. Essential advantage of the thin membrane system is the substantial reduction of the ohmic potential drop, which is compensated in voltammetric measurements. Reversible partition of TPFPB − allows fixing the potential difference at one membrane interface and polarizing the other membrane interface in a defined way. It is shown that the polarized potential window for the interface between an aqueous electrolyte solution and RTIL attains the value of ca. 0.7 V at the ambient temperature of 25 ± 2 °C. Tetraphenylarsonium tetraphenylborate hypothesis is used for the first time to estimate the standard Gibbs energies of ion transfer from water to RTIL and to establish the scale of the absolute potential differences. A linear Gibbs energy relationship is found for the ion transfer from water to RTIL and o-dichlorobenzene.

Experimental and Theoretical Study of Cobalt Selenide as a Catalyst for O2Electroreduction

Cobalt sulfides have been known for more than 30 years to be active toward oxygen reduction, and cobalt selenides have shown less activity. In this paper, a theoretical analysis is made of the four-electron reduction reaction of oxygen to water over the mixed anion and cation (202) surface of the pentlandite structure Co9Se8, one of several selenide phases. Reversible potentials for forming adsorbed reaction intermediates in acid are predicted using adsorption energies calculated with the Vienna ab initio simulation program (VASP) and the known bulk solution values together in a linear Gibbs energy relationship. Comparison with an earlier theoretical analysis of pentlandite structure Co9S8 shows that the overpotential is predicted to be larger for the selenide by around 0.22 V. Cobalt selenide electrodes of unspecified stoichiometry were prepared chemically on glassy carbon discs, and polarization curves were measured using rotating discs. When heat-treated at 900 °C, the onset potential for O2 reduction was found to be 0.5 V (normal hydrogen electrode, NHE), whereas electrodes not subject to heat-treatment were inactive. For Co3S4, onset potentials in the literature are ∼0.8 V (NHE), consistent with a ∼0.3 V higher measured overpotential for the selenide. The theoretical predictions for the pentlandite sulfide and selenide surfaces are in qualitative agreement.

Acid corrosion of iron in the presence of mixtures of anionic additives and compounds of the reaction series of o-hydroxyazomethine derivatives with nucleophilic substituents

The effects of halide-and sulfur-containing additives on iron corrosion in 1 M H2SO4 in the presence of nucleophilic o-hydroxyazomethine derivatives are studied. Dependences of the inhibition factor (as well as its sensitivity to a change in the polarity of the substituents) and the effective activation energy on the nature and concentration of both the groups of additives are interpreted in terms of the Linear Gibbs Energy Relation (LGER) and the principle of Hard and Soft Acids and Bases (HSAB).

Effect of some compounds on the sensitivity of the inhibitive properties of o-hydroxyazomethine derivatives to variation in the polarity of their electrophilic substituents

The sensitivity of the protective effect of an inhibitor from a reaction series to the variation of the polarities of electrophilic substituents in its molecule depends on the nature and concentrations of salt additives. The correlations obtained for iron corrosion were interpreted in terms of the Linear Gibbs Energy Relation (LGER) and the Principle of Hard and Soft Acids and Bases (HSAB).

A correlation between the inhibition of acid corrosion of iron by a mixture of compounds of a reaction series and the polar properties of their substituents

The character of the adsorption isotherm of a mixture of o-hydroxyazomethine derivatives at an iron electrode is insensitive to the total polarity of the substituents in their molecules. The surface coverage of the electrode by adsorbed compounds of this reaction series (RS) does not depend on the number and concentrations of the components of the mixture, provided that their total concentration and the total polarity of the substituents in their molecules are constant. According to the Linear Gibbs Energy Relation, the overall and partial inhibition factors of the acid corrosion of iron in the presence of mixtures of compounds of this RS are determined by the total polarity of their substituents.

On inhibition of hydrogen-sulfide corrosion of steels with quaternary ammonium salts

The corrosion and electrochemical behavior of carbon steels in standard 0.5% chloride electrolytes acidified with CH3COOH and saturated with H2S was studied. The possibility of protecting steels with quaternary ammonium salts (QASs) obtained by reactions of secondary and tertiary amines with benzyl chloride was investigated. It was found that the protective properties of QASs depend on their chemical structures and can be expressed, to a first approximation, in terms of the Linear Gibbs Energy Relation with the use of the hydrophobic f constants and Taft σ*-constants of the substituents. The presence of hydrophobic and electron-accepting substituents was found to enhance the protective properties of the inhibitors.

Mechanism of Scandium Ion Catalyzed Diels−Alder Reaction of Anthracenes with Methyl Vinyl Ketone

Rates of Diels-Alder cycloadditions of anthracenes with methyl vinyl ketone (MVK) are accelerated significantly by the presence of scandium triflate [Sc(OTf)3]. Sc(OTf)3 also promotes photoinduced electron-transfer reactions from various electron donors to MVK significantly. Comparison of the promoting effect of Sc(OTf)3 in photoinduced electron-transfer reactions of MVK with the catalytic effect of Sc(OTf)3 in the Diels-Alder reaction of 9,10-dimethylanthracene with MVK has revealed that the MVK-Sc(OTf)3 complex is a reactive intermediate in both the Diels-Alder and photoinduced electron-transfer reactions. The observed second-order rate constants of the Sc(OTf)3-catalyzed Diels-Alder reactions of anthracenes with MVK are by far larger than those expected from the observed linear Gibbs energy relation for the Diels-Alder reactions of anthracenes with stronger electron acceptors than MVK, which are known to proceed via electron transfer. This indicates that the Sc(OTf)3-catalyzed Diels-Alder reactions of anthracenes with MVK does not proceed via an electron-transfer process from anthracences to the MVK-Sc(OTf)3 complex.

Electrodeposition of a Cu–Cd Alloy in the Presence of Surfactant Mixtures from Several Reaction Series

The effects of one- to four-component mixtures of organic compounds from four reaction series on the currents and potentials of the electrodeposition of a Cu–Cd alloy were studied. The revealed correlation between the deposition parameters of compositionally different alloys and their constituents, on one hand, and the total polarity of substituents in surfactant molecules, on the other hand, was interpreted in terms of the Linear Gibbs Energy Relation.