Thermodynamic aspects of capillarity and electrocapillarity of solid interfaces

In the previous paper (Gutman, JOSSEC 18:3217–3237, 2014), we have shown that the main problem in capillarity and electrocapillarity of solid surfaces is the lack of clarity in determining the surface stress and basic equations. Now, we continue the survey of efforts to solve this problem and show origins of erroneous results, accenting some important items: comparative analysis of Gibbs and Guggenheim approaches in surface thermodynamics (a geometrical dividing surface and finite-thickness surface layer, respectively), transformation of fundamental equations on per-unit-area basis to obtain Gibbs adsorption equation for finite-thickness surface layer, different attempts to derive the thermodynamic definition of “surface stress” in frames of Gibbs’ theory (including Shuttleworth’s approach), atomistic calculations of surface stress, surface stress in rational continuum mechanics, “modifications” of Gibbs–Duhem relations made for solid interface, and Maxwell relations in capillarity and electrocapillarity of solid interface. It is shown that the erroneous Shuttleworth’s approach is present in an explicit or implicit form in all efforts to introduce the surface stress in frames of Gibbsian theory (although Gibbs did not introduce surface stress). Therefore, “modernizations” or “generalizations” of the Gibbs–Duhem relation, the Gibbs adsorption equation, and the Lippmann equation to adopt them for a solid surface are unnatural and not necessary. Therefore, we recommend withdrawing the Shuttleworth equation and its consequences from circulation, including the IUPAC Recommendations.     

Historical development of theories of the electrochemical double layer

This review describes the evolution of important concepts related to potential drops at interfaces in electrochemical systems. The role of the thermodynamic theory of electrocapillarity of perfectly polarizable electrodes in the development of interfacial electrochemistry is emphasized. A critical analysis of the phenomenological models of the electrical double layer on ideally polarizable electrodes is given. Certain trends in studying solid electrodes with well-defined surfaces brought into contact with electrolyte solutions are summarized. Attention is drawn to several unsolved problems crucial for the future development of electrochemical surface science. Finally, some recent experimental data are analyzed for selected models.     

Electrocapillarity behavior of Au111 in SO4(2-) and F-

We present the first set of results measuring the change in interfacial free energy and surface stress for Au(111) electrodes in an electrolyte containing a nonspecifically adsorbing anion and compare this behavior to that in an electrolyte containing an anion known to undergo specific adsorption. Generally, we find that the surface stress is more sensitive to changes in electrode potential and adsorption then the interfacial free energy. The results obtained in fluoride electrolytes are compared to the predictions of a thermodynamic analysis.     

Comment on “On the ‘simple check’ of electrocapillarity” by AY Gokhshtein

It is shown that the so-called “equation of solid-state electrocapillarity” derived by Gokhshtein from the simplest thermodynamic model, earlier used by Lippmann, is an incorrect modification that is returned to the classic Lippmann equation if to take into account the usual definition of differential capacity of the electrical double layer. Consequently, Gokhshtein’s experiments can actually confirm only the validity of the Lippmann equation (with deviations caused by physicochemical processes in the double layer, which could not be taken into account in the thermodynamic equations). The thermodynamic model is insufficient for the interpretations of these experimental results, whose understanding requires physical models of the different phenomena occurring at the electrode surface.     

The equation of state for an interface during the adsorption of organic substances on an electrode

The state of the interface between a metal and a solution of an electrolyte containing a neutral surfactant was investigated using a method alternative to the traditional thermodynamic approach. The method was based on the concept that there was a stability limit of a surfactant on an electrode, and the corresponding state could be described in terms of the catastrophe theory. The surface pressure was approximated by the Whitney polynomial in powers of the de Donder parameter (completeness of adsorption) with the coefficients depending on the chemical potential and polarization of the interface. The equation of state and the equation for the stability limit were obtained from the condition of zero first and second derivatives. These equations correctly described the results of electrocapillary measurements in the spirit of the law of corresponding states. The correlation between surface pressure maxima and critical stability potentials predicted by the theory was substantiated by the electrocapillary measurements data provided that the inflexions of surface pressure curves calculated from the electrocapillary data were related to the limiting stability at which the competing forces are balanced during the adsorption of surfactants. A simple equation for surface pressure was suggested in the form of a function of the state of thermodynamic parameters and completeness of adsorption. This function described the state of a surfactant at the interface. Equilibrium equations were derived for the state of a surfactant and the spinodal.     

Voltammetric studies of the activity of an electrode made of a graphite-epoxy composite in redox reactions of ascorbic acid and hydroquinone

The potentials of the anodic peak of ascorbic acid oxidation and the potential differences of anodic and cathodic peaks (ΔE _p) of the hydroquinone/benzoquinone redox system at an electrode made of a graphite-epoxy composite are determined in weakly acidic and neutral supporting electrolytes by direct and cyclic voltammetry. The results obtained are compared with thermodynamic values and with the available values of these parameters at different solid electrodes for the above-mentioned redox systems. The effect of aging of the surface of electrodes made of graphite-epoxy composites on the potentials and peak currents of the anodic oxidation of ascorbic acid are studied. It is demonstrated that the regeneration of the electrode surface by mechanically cutting thin layers is important for reducing the δE _p value of the hydroquinone/benzoquinone redox system down to 28–30 mV in supporting electrolytes with pH 2.0 and 7.0. This value is typical of thermodynamically reversible electrode reactions involving two-electron transfer at 20–25°C.     

Electrochemical microgravimetric study on microcrystalline particles of phenazine attached to gold electrodes

Phenazine solid crystals have been attached to gold electrodes and investigated by cyclic and potential step electrochemical quartz crystal microbalance (ECQM) measurements in the presence of aqueous acidic media. The freshly deposited phenazine layers exhibit a break-in phenomenon. The number of potential cycles required for the layer to be fully electroactive depends on its thickness and also on the nature and concentration of the supporting electrolyte as well as on the scan rate. After the break-in, a considerable amount of solvent molecules remains embedded in the surface layer. The protonated and unprotonated forms of phenazine, whose relative amounts depend on the pH of the contacting solutions, are reduced at different potentials; however, the stable product of the first electron transfer is the respective phenazylium salt. During the second reduction step 5,10-dihydrophenazine and charge-transfer complexes of different compositions are formed. Both the current and microgravimetric responses supplied evidences for the structural rearrangements of the solid phases that accompany the redox reactions. The large separation of the reduction and oxidation peaks relates to the additional energy needed to create the solid/solid interface between the reduced and unreduced or partially reduced forms. The chronoamperometric response shows the characteristics of nucleation and growth kinetics. The phase transformation proceeds with the release of hydration water, and the EQCM response is affected by the strain that develops as a consequence of the phase transformation.Dedicated to Prof. Zbigniew Galus on the occasion of his 70th birthday in recognition of his outstanding contributions to electrochemistry     

Diamond/porous titanium three-dimensional hybrid electrodes

Hybrid three-dimensional electrodes produced from microcrystalline boron-doped diamond (BDD) and/or nanocrystalline diamond films were grown on porous titanium (Ti) substrate by hot filament chemical vapor deposition (HFCVD) technique. Powder metallurgy technique was used to obtain the Ti substrates provided by interconnected and open pores among its volume. Diamond growth parameters were optimized in order to provide the entire substrate surface covering including the deeper surfaces, pore bottoms, and walls. The morphology and structure of these electrodes were studied by scanning electron microscopy (SEM) and visible Raman spectroscopy techniques, respectively. Electrochemical response was characterized by cyclic voltammetry measurements. Results showed a wide working potential window and low background current characteristic of the diamond electrodes. The kinetic parameters also pointed out to a quasi-reversible behavior for these hybrid three-dimensional diamond/Ti electrodes.     

Electrochemical behavior of new electrode material: Compact of boron-doped synthetic diamond

Electrochemical properties of new electrode material—compact of boron-doped synthetic diamond—is studied for the first time. Cylindrical samples 3.5–4 mm in diameter and 2.5 mm in height were obtained by thermobaric processing of graphite–boron carbide mixtures in the diamond thermodynamic stability region (at the pressure of 8–9 GPa and temperature of ~2500 K). Their electrode behavior is studied using cyclic voltammetry and electrochemical impedance spectroscopy techniques. The cyclic voltammograms of the compact samples showed that their electrode characteristics are similar to those of traditional thin-film diamond electrodes obtained by the chemical vapor deposition (CVD) technique. In particular, they demonstrate rather wide potential window, low background current in indifferent electrolytes, and good reproducibility. It can be concluded that the diamond compacts practically are not inferior to the thin-film CVD-diamond electrodes and can serve as indicator electrodes, e.g., in electroanalysis. At the same time their compact form may be a convenience in the designing of electrolyzers and other electrochemical devices.     

AGNES at vibrated gold microwire electrode for the direct quantification of free copper concentrations

The free metal ion concentration and the dynamic features of the metal species are recognized as key to predict metal bioavailability and toxicity to aquatic organisms. Quantification of the former is, however, still challenging. In this paper, it is shown for the first time that the concentration of free copper (Cu²⁺) can be quantified by applying AGNES (Absence of Gradients and Nernstian equilibrium stripping) at a solid gold electrode. It was found that: i) the amount of deposited Cu follows a Nernstian relationship with the applied deposition potential, and ii) the stripping signal is linearly related with the free metal ion concentration. The performance of AGNES at the vibrating gold microwire electrode (VGME) was assessed for two labile systems: Cu-malonic acid and Cu-iminodiacetic acid at ionic strength 0.01 M and a range of pH values from 4.0 to 6.0. The free Cu concentrations and conditional stability constants obtained by AGNES were in good agreement with stripping scanned voltammetry and thermodynamic theoretical predictions obtained by Visual MinteQ. This work highlights the suitability of gold electrodes for the quantification of free metal ion concentrations by AGNES. It also strongly suggests that other solid electrodes may be well appropriate for such task. This new application of AGNES is a first step towards a range of applications for a number of metals in speciation, toxicological and environmental studies for the direct determination of the key parameter that is the free metal ion concentration.     

Balance of force at curved solid metal-liquid electrolyte interfaces

We analyze the simultaneous mechanical and chemical equilibrium at the interface between a fluid electrolyte and a solid conductor in terms of a continuum theory, with attention to surfaces of varying orientation and of arbitrary curvature. On top of the variable which is conjugate to the surface stress, the tangential strain, we introduce an additional degree of freedom for the surface deformation, the surface stretch, to account for the observation of a reversible normal relaxation of the top atomic layer as a function of the electrochemical potential. We derive relations between the materials constants of the surface, for instance, the pressure dependence of the electric potential at constant superficial charge density, and discuss experiments-using cantilevers or porous solids-by which they can be measured.     

Region of zero charging

Unknown phenomenon was observed on the oxidized surface of a number of metals in water solutions including nickel, palladium, and platinum. Elastic extension of the metal decreases the interface capacity in wide potential region which reaches 0.4 V in the case of palladium. Within such region, the oscillograms “estance vs. potential” disclose an unusually long and low flat section which may be considered as the expanded zero of the differential charge density. The decrease of the capacity points out strengthening the bond of the water molecules to the surface oxide under its elastic extension which thickens the hydrated envelops of the adsorbed ions. Along the flat section, the state of the interface is reversible without changing the structure of the surface oxide. The anodic boundary of the flat section can be used as a sign of reaching the oxide monolayer. In the equations of solid state electrocapillarity, the potential of zero charge is presented explicitly. Its derivative with respect to elastic deformation is independent of the electrode potential and shifts the reversible section of the estance curve along the ordinate.     

A comparison of electrochemical and Auger analysis of the surface composition of platinum-rhodium alloys

Values of the surface composition of platinum-rhodium alloys determined electrochemically, utilizing the potential of the oxygen desorption peak on cyclic voltammograms, have been compared with those obtained by Auger electron spectroscopy (a.e.s.). This comparison confirms that the electrochemical method is applicable to analysis of the surface of cycled as well as untreated homogeneous noble metal alloys. The composition profile in the surface region of cycled electrodes was determined by sputtering of the surface followed by a.e.s. measurements. The rhodium content was found to increase linearly with depth. The depth scale was established from analyses of the metal dissolved during potential cycling. Consideration of the differences between data obtained from the electrochemical and a.e.s. studies leads to the conclusion that the surface zone involved in chemisorption extends over a few atomic layers.     

über SelektivitÄtskonstanten von Halogenidelektroden zweiter Art

The selectivity constants of halide electrodes of the second kind, prepared by electrolytical coating of silver rods, were determined and compared with the selectivity constants of the Orion solid state halide electrodes. The values of both electrode types are in good agreement. Three different determination methods were considered, where the results proved to be independent of the method, provided the appropriate concentration range is chosen for the measurements. A criterion for assessing whether or not selectivity values are real constants is discussed.     

LiF-Ni纳米复合薄膜的电化学性能研究

采用脉冲激光沉积法在不锈钢基片上制备了LiF-Ni纳米复合薄膜, 用充放电和循环伏安实验测量了该薄膜的电化学性能. 首次充电容量为107 mAh•g−1, 它对应第一次释放锂的过程. 在充放电循环过程中, 锂的嵌入、脱出通过非原位高分辨电子显微和选区电子衍射得到证实. 这一结果为LiF可以由过渡金属Ni驱动分解提供了直接的实验证据.