Gibbs, adsorption equation potential

Information on the chemical potentials of components in a solution of biopolymers can serve as a guide to trends in surface activity of the biopolymers at fluid interfaces (air-water, oil-water). In the thermodynamic context we need look no further than the Gibbs adsorption equation,... 

This is the Gibbs adsorption equation that relates y to the number of moles and the chemical potentials of the components in the interface. 

The surface tension depends on the potential (the excess charge on the surface) and the composition (chemical potentials of the species) of the contacting phases. For the relation between y and the potential see - Lipp-mann equation. For the composition dependence see -> Gibbs adsorption equation. Since in these equations y is considered being independent of A, they can be used only for fluids, e.g., liquid liquid such as liquid mercury electrolyte, interfaces. By measuring the surface tension of a mercury drop in contact with an electrolyte solution as a function of potential important quantities, such as surface charge density, surface excess of ions, differential capacitance (subentry of... 

Here, Ms and Ms,ads are the electrochemical potentials of S in the bulk solution and in the adsorbed state. Let us apply the Gibbs adsorption equation to the interphase between a pure metal M and an aqueous solution containing molecular and ionic species denoted by the subscript j, in addition to water w and the species S. Choosing the neutral metal atoms M and the electrons e in excess with respect to metal atoms as the constituents of the metal phase, we may formally write ... 

Since l is a thermodynamic quantity, the most reliable procedures for its determination are based on a thermodynamic analysis of adsorption data, possibly at low coverages. Adsorption data to be analyzed by the Gibbs adsorption equation can be obtained by measuring the interfacial tension y, the charge density crM or the differential capacity C. Direct y measurements are equilibrium measurements that can only be carried out on mercury. Direct charge measurements are conveniently carried out by the potential-step chronocoulometric technique, which can be... 

As there is no analogue of Butler s equation for ionised surface layers, the procedure used to derive the equation of state has to be based on the Gibbs adsorption equation and a model adsorption isotherm. The isotherm equation can also be derived from the theoretical analysis of the expressions for electrochemical potentials of ions. For the solution of a single ionic surfactant RX, with the addition of inorganic electrolyte XY, starting from Eqs. (2.2) and (2.21) for the electrochemical potentials, one obtains the adsorption isotherm... 

Primarily, this approach was based on the formal analogy between a first order phase transition and the micellisation. When a new phase of a pure substance is formed the chemical potential of this substance and its concentration in the initial phase do not change with the total content of this substance in the system. A similar situation is observed above the CMC, where the adsorption and the surface tension become approximately constant. In reality variations of these properties are relatively small to be observed by conventional experimental methods. The application of the Gibbs adsorption equation shows that the constancy of the surfactant activity above the CMC follows from the constancy of the surfactant adsorption T2 [13]... 

The macroscopic description of the adsorption on electrodes is characterised by the development of models based on classical thermodynamics and the electrostatic theory. Within the frames of these theories we can distinguish two approaches. The first approach, originated from Frumkin s work on the parallel condensers (PC) model,attempts to determine the dependence of upon the applied potential E based on the Gibbs adsorption equation. From the relationship = g( ), the surface tension y and the differential capacity C can be obtained as a function of E by simple mathematical transformations and they can be further compared with experimental data. The second approach denoted as STE (simple thermodynamic-electrostatic approach) has been developed in our laboratory, and it is based on the determination of analytical expressions for the chemical potentials of the constituents of the adsorbed layer. If these expressions are known, the equilibrium properties of the adsorbed layer are derived from the equilibrium equations among the chemical potentials. Note that the relationship = g( ), between and , is also needed for this approach to express the equilibrium properties in terms of either or E. Flere, this relationship is determined by means of the Gauss theorem of electrostatics. 

A curious example is that of the distribution of benzene in water benzene will initially spread on water, then as the water becomes saturated with benzene, it will round up into lenses. Virtually all of the thermodynamics of a system will be affected by the presence of the surface. A system containing a surface may be considered as being made up of three parts two bulk phases and the interface separating them. Any extensive thermodynamic property will be apportioned among these parts. For example, in a two-phase multicomponent system, the extra amount of an i component that can be accom-mondated in the system due to the presence of the interface ( ) may be expressed as Qi Qii where is the total number of molecules of i in the whole system, Vj and Vjj are the volumes of phases I and II, respectively, and Q and Qn are the concentrations of i in phases I and II, respectively. The surface (excess) concentration of i is defined as Fj = A, where A is the surface area. At equilibrium, the chemical potential of any component is the same in each bulk phase and at the surface. The Gibbs adsorption equation, which is one of the most widely used expression in surface and colloid science is shown in Eq. (2) ... 

Ta types of anions with chemical potentials /ii- Using Hansen s reference system and choosing the solvents a and P as reference substances, one can write down Hansen s rendition of Gibbs adsorption equation ... 

Interaction Potential Between Two Flat Plates Using the Extended Gibbs Adsorption Equation... 

An alternative and insightful way to obtain the interaction potential is from the extended Gibbs adsorption equation [6-8]. The natural thermodynamic potential to describe the system depicted in Fig. 2.2 is the grand potential Q(r, V, p, h)... 

The limitation of the Deijaguin approximation is that it only provides reliable results for R > Rg. To obtain results for the interaction potential between spheres for arbitrary q = Rg/R we use the extended Gibbs adsorption equation. Taniguchi et al. [33] and, independently, Eisenriegler et al. [34] found the concentration profile of Gaussian ideal polymer chains around a single hard sphere with radius R which reads... 

FeP is adsorbed at the octane/water interface and produces a positive potential shift with respect to water as large as 0.46 V (Fig. 7). The adsorption of surface-active catalysts, such as coproporphyrin (CP) [51,52], at the octane/water interface has been studied. From the interfacial tension data, with the use of the Gibbs adsorption equation ... 

The interface in extraction systems is usually studied by measuring the interfacial tension, viscosity and potential. To study the adsorption kinetics, one usually plots the isotherms of the interfacial tension and uses the Gibbs adsorption equation to calculate the surface concentration of the extractant [15-22]. In practice, the concentration of the extractant is selected so as to saturate the monolayer at the interface. In such systems a rise in extractant concentration does not affect the extraction rate if the limiting stage is the surface reaction or a reaction in the adjoining layers [17-20,23]. 

Even in the primitive versions of the van dcr Waals theory with m independent of p, that coefficient may still depend on the temperature T (or, equivalently, on the chemical potential fi) at which the phases are in equilibrium. While in Chapter 5 we shall see some examples, or limiting idealized cases, in which m is a fixed constant, independent of T, and is determined by the intermolecular forces alone, as in (1.38), it will, more generally, depend on T and in that event, as we shall see in 3.4, the connection between this theory and the Gibbs adsorption equation (2.31) is not entirely straightforward and requires discussion. 

In this expression for the chemical potential, the first addendum, U(,(T), is a standard potential at a fixed pressure. The second addendum expresses the contribution from the fugacity of the pure component. The third addendum is due to mixing. The dependence/ (< >, T) may be found from the Gibbs adsorption equation (13b), where the integration is often carried out from zero pressure (and, correspondingly, the value of 0 is equal to zero). With such an expression for the chemical potentials of the adsorbed phase, equilibrium conditions (12), for the equilibrium with a nonideal gas phase, are reduced to the form... 

An alternative interpretation of the electrochemical double layer comes from a more thermodynamic approach. As an initial point, considering the Gibbs adsorption equation proved useful. This equation originally describes the dependence of the surface tension on the two-dimensional surface concentration (the surface excess F) of adsorbed particles as well as on their chemical potential p. The equation can be extended by introducing an electric term which considers the potential dependence of the surface tension. The Gibbs adsorption equation in its complete form is as follows ... 

They analyzed their results using a thermodynamic approach based on the Gibbs adsorption equation and the main conclusion of their work was that relative surface excesses of the ionic species were well described by the Gouy-Chapman theory. They adopted the MVN model of the ideally polarized interface stating that the compact layer is an ion-free layer consisting of laminated layers of water and nitrobenzene sandwiched between two diffuse layers. The potential difference across this inner layer was estimated to be about 20 mV at the PZC but was found to vary with the surface charge density. 

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