Thermodynamics of the Interface

The exact position of the geometrical surface can be changed. When the location of the geometrical surface X is changed while the form or topography is left unaltered, the internal energy, entropy and excess moles of the interface vary. The thermodynamics of the interface thus depend on the location of the geometrical surface X. Still, eq. (6.13) will always be fulfilled. 

According to the thermodynamics of the interface, the adsorption induces the variation in the interfacial tension, y, a decrease (increase) in the case of the positive (negative) adsorption. In the case of the Frumkin isotherm, the decrease in y is given by [19]... 

Under these circumstances the distribution coefficient for MiXi is zero, and that for M2X2, infinity. It follows that the Galvani potential difference is not defined for this interface. However, the thermodynamics of the interface can be derived on the basis of the Gibbs adsorption isotherm. 

Note that the simple arguments of section 2.1, being essentially static and mechanical in character, fail to make any prediction about the dependence of the interfacial tension on temperature. We shall see that the determination of surface or interfacial tensions as a function of temperature can give considerable insight into the equilibrium thermodynamics of the interface, therefore the accurate measurement of surface and interfacial tension becomes of some significance. 

We have so far been concerned mainly with the structure and thermodynamics of the interface between two phases, and we have seen in outline, and sometimes in detail, the elements of the molecular theories that account for or predict that structure and thermodynamics. Macro-scopically, the interface between two bulk phases is two-dimensional and locally planar—although at the molecular level it has a discernible three-dimensional structure, which we have studied and related to the thermodynamics. 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

It was made clear in Chapter II that the surface tension is a definite and accurately measurable property of the interface between two liquid phases. Moreover, its value is very rapidly established in pure substances of ordinary viscosity dynamic methods indicate that a normal surface tension is established within a millisecond and probably sooner [1], In this chapter it is thus appropriate to discuss the thermodynamic basis for surface tension and to develop equations for the surface tension of single- and multiple-component systems. We begin with thermodynamics and structure of single-component interfaces and expand our discussion to solutions in Sections III-4 and III-5. 

The equations of electrocapillarity become complicated in the case of the solid metal-electrolyte interface. The problem is that the work spent in a differential stretching of the interface is not equal to that in forming an infinitesimal amount of new surface, if the surface is under elastic strain. Couchman and co-workers [142, 143] and Mobliner and Beck [144] have, among others, discussed the thermodynamics of the situation, including some of the problems of terminology. 

The interface region in a composite is important in determining the ultimate properties of the composite. At the interface a discontinuity occurs in one or more material parameters such as elastic moduli, thermodynamic parameters such as chemical potential, and the coefficient of thermal expansion. The importance of the interface region in composites stems from two main reasons the interface occupies a large area in composites, and in general, the reinforcement and the matrix form a system that is not in thermodynamic equiUbhum. 

In addition, the potential of the electrode can be varied, resulting in a change in the stmcture of the interface. If no current is passed when the potential of the electrode changes, the electrode is called an ideally polarizable electrode, and can be described using thermodynamics. 

An ordering phase transition is characterized by a loss of symmetry the ordered phase has less symmetry than the disordered one. Hence, an ordering process leads to the coexistence of different domains of the same ordered phase. An interface forms whenever two such domains contact. The thermodynamic behavior of this interface is governed by different forces. The presence of the underlying lattice and the stability of the ordered domains tend to localize the interface and to reduce its width. On the other hand, thermal fluctuations favor an interfacial wandering and an increase of the interface width. The result of this competition depends strongly on the order of the bulk phase transition. 

An evaluation of the retardation effects of surfactants on the steady velocity of a single drop (or bubble) under the influence of gravity has been made by Levich (L3) and extended recently by Newman (Nl). A further generalization to the domain of flow around an ensemble of many drops or bubbles in the presence of surfactants has been completed most recently by Waslo and Gal-Or (Wl). The terminal velocity of the ensemble is expressed in terms of the dispersed-phase holdup fraction and reduces to Levich s solution for a single particle when approaches zero. The basic theoretical principles governing these retardation effects will be demonstrated here for the case of a single drop or bubble. Thermodynamically, this is a case where coupling effects between the diffusion of surfactants (first-order tensorial transfer) and viscous flow (second-order tensorial transfer) takes place. Subject to the Curie principle, it demonstrates that this retardation effect occurs on a nonisotropic interface. Therefore, it is necessary to express the concentration of surfactants T, as it varies from point to point on the interface, in terms of the coordinates of the interface, i.e.,... 

A capillary system is said to be in a steady-state equilibrium position when the capillary forces are equal to the hydrostatic pressure force (Levich 1962). The heating of the capillary walls leads to a disturbance of the equilibrium and to a displacement of the meniscus, causing the liquid-vapor interface location to change as compared to an unheated wall. This process causes pressure differences due to capillarity and the hydrostatic pressures exiting the flow, which in turn causes the meniscus to return to the initial position. In order to realize the above-mentioned process in a continuous manner it is necessary to carry out continual heat transfer from the capillary walls to the liquid. In this case the position of the interface surface is invariable and the fluid flow is stationary. From the thermodynamical point of view the process in a heated capillary is similar to a process in a heat engine, which transforms heat into mechanical energy. 

Regarding the electrode/electrolyte interface, it is important to distinguish between two types of electrochemical systems thermodynamically closed (and in equilibrium) and open systems. While the former can be understood by knowing the equilibrium atomic structure of the interface and the electrochemical potentials of all components, open systems require more information, since the electrochemical potentials within the interface are not necessarily constant. Variations could be caused by electrocatalytic reactions locally changing the concentration of the various species. In this chapter, we will focus on the former situation, i.e., interfaces in equilibrium with a bulk electrode and a multicomponent bulk electrolyte, which are both influenced by temperature and pressures/activities, and constrained by a finite voltage between electrode and electrolyte. 

Now having specified the bulk electrode, the bulk electrolyte, and the interface between them, our aim in this section is to quantify the atomistic structure of the interface and derive an expression that allows us to evaluate its stabUity. Based on (5.5), we wUl extend the ab initio atomistic thermodynamics approach to electrochemical systems. 

The situation that no charge transfer across the interface occurs is named the ideal polarized or blocked interface. Such interfaces do not permit, due to thermodynamic or kinetic reasons, either electron or ion transfer. They possess Galvani potentials fixed by the electrolyte and charge. Of course, the ideal polarizable interface is practically a limiting case of the interfaces with charge transfer, because any interface is always permeable to ions to some extent. Therefore, only an approximation of the ideal polarizable interface can be realized experimentally (Section III.D). 

Thermodynamics of adsorption at liquid interfaces has been well established [22-24]. Of particular interest in view of biochemical and pharmaceutical applications is the adsorption of ionic substances, as many of biologically active compounds are ionic under the physiological conditions. For studying the adsorption of ionic components at the liquid-liquid interface, the polarized liquid-liquid interface is advantageous in that the adsorption of ionic components can be examined by strictly controlling the electrical state of the interface, which is in contrast to the adsorption studies at the air-water or nonpolar oil-water interfaces [25]. 

The interaction between the adsorbed molecules and a chemical species present in the opposite side of the interface is clearly seen in the effect of the counterion species on the HTMA adsorption. Electrocapillary curves in Fig. 6 show that the interfacial tension at a given potential in the presence of the HTMA ion adsorption depends on the anionic species in the aqueous side of the interface and decreases in the order, F, CP, and Br [40]. By changing the counterions from F to CP or Br, the adsorption free energy of HTMA increase by 1.2 or 4.6 kJmoP. This greater effect of Br ions is in harmony with the results obtained at the air-water interface [43]. We note that this effect of the counterion species from the opposite side of the interface does not necessarily mean the interfacial ion-pair formation, which seems to suppose the presence of salt formation at the boundary layer [44-46]. A thermodynamic criterion of the interfacial ion-pair formation has been discussed in detail [40]. 

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