Gibbs equation, for

The Gibbs equation for metal-electrolyte interfaces is of the form... 

Combining the IAS theory with the Gibbs equation for isothermal adsorption gives the relationship necessary for equilibrium calculations ... 

This is the form of the Gibbs equation for an aqueous solution containing three different ionic species (e.g., R, Na, Cl). Thus, the more general form for solutions containing i number of ionic species would be... 

In principle, the penetration or adsorption of surfactant, Tg is given by the Gibbs equation. For a non-ionic monolayer and an ionised surfactant (as in the system examined), this equation is ... 

The material in this chapter is organized broadly in two segments. The topics on monolayers (e.g., basic definitions, experimental techniques for measurement of surface tension and sur-face-pressure-versus-area isotherms, phase equilibria and morphology of the monolayers, formulation of equation of state, interfacial viscosity, and some standard applications of mono-layers) are presented first in Sections 7.2-7.6. This is followed by the theories and experimental aspects of adsorption (adsorption from solution and Gibbs equation for the relation between... 

From adsorption studies with the help of inverse gas chromatography The interaction between a stationary phase and a well known gas or solvent is measured as in standard gas chromatography. The results are, however, used to characterize the stationary phase. Therefore, let us assume that n moles adsorb on a surface A. The interface excess concentration is T = n/A. With the Gibbs equation for a two-component system (Eq. 3.55) T = — l/RT dy/d wP) we get... 

A more comprehensive introduction is Ref. [399], We restrict ourselves to uncharged species and dilute solutions (not binary mixtures). The important subject of polymer adsorption is described in Ref. [400], Adsorption of surfactants is discussed in Ref. [401], Adsorption of ions and formation of surface charges was treated in Chapter 5. In dilute solutions there is no problem in positioning the Gibbs dividing plane, and the analytical surface access is equal to the thermodynamic one, as occurs in the Gibbs equation. For a thorough introduction into this important field of interface science see Ref. [8],... 

Assuming the validity of Adam-Gibbs equation for relaxation dynamics and the hyperbolic temperature dependence of heat capacity, the strength parameter is found to be inversely proportional to the change in heat capacity [see Eq. (2.10)] at the glass transition temperature [48,105]. 

Hua, X.Y. and Rosen, M.J. (1982) Calculation of the coefficient in the Gibbs equation for the adsorption of ionic surfactants from aqueous binary mixtures with nonionic surfactants. /. Colloid Interface Sci., 87, 469. 

The strict thermodynamic analysis of an interfacial region (also called an -> interphase) [ii] is based on data available from the bulk phases (concentration variables) and the total amount of material involved in the whole system yielding relations expressing the relative surface excess of suitably chosen (charged or not charged) components of the system. In addition, the - Gibbs equation for a polarizable interfacial region contains a factor related to the potential difference between one of the phases (metal) and a suitably chosen - reference electrode immersed in the other phase (solution) and attached to a piece of the same metal that forms one of the phases. 

The 1 IT and fi/T appear in the thermodynamic conjugates of the extensive variables in the Gibbs equation for the system entropy... 

In extended nonequilibrium thermodynamics of polymer solutions, the generalized extended Gibbs equation for a fluid characterized by internal energy U and viscous pressure Pv is... 

Using the Kelvin-Gibbs equation for the effect of radius of curvature on vapor pressure of a spherical droplet (T3, LI)... 

Gibbs Equation for an Open System For an open system, we can write the following equation (3) by combining equations (1) and (2) which is a form of Gibbs equation. 

If the solution studied is not too different from the ideal one, the activity coefficient, a 1, and the Gibbs equation for two-component system is... 

The fundamental Gibbs equation for surface tension can be written for the non-equilibrium state as... 

Adsorption kinetics and isotherms. According to the Gibbs equation for ideal systems, the adsorption of classical surface-active molecules at fluid interfaces decreases the surface tension ... 

Figure 2 (a) Wei (spherical) foam, (b) transition state and (c) dry (polyhedral) foam Foams are thermodynamically unstable l The Gibbs equation for a system is given by dG = VdP + SdT + ffdA ( +iMdn,+. ..)... 

The Adam-Gibbs equation for viscous liquid relaxation asserts that the time scale for re-equilibration after some perturbation is related to the excess entropy of liquid over crystal, according to... 

The general Gibbs equation for the inner energy in the presence of E is obtained by substitution of Eq. (4.7) into (3.26) ... 

The change of entropy, AS, is calculated from the Gibbs equation for mixing of ideal gases. The calculated values are always positive. 

Gibbs equation for more complex situations is used for calculating the rate of internal production of entropy in contrast with the case discussed in Section 2.2, with the objective of identifying fluxes and forces for typical phenomena (systems). 

Using second law of thermodynamics, Gibbs equation for discontinuous systems can be written as... 

On combining the balance equation for energy assuming the absence of velocity gradients, the first law of thermodynamics and assuming Gibbs equation for entropy production for the case of local equilibrium, a the entropy production per unit volume per unit time due to the occurrence of irreversible processes in the system is given by... 

Subtracting eq. (2.3-8) from eq. (2.3-6), we have the Gibbs equation for a planar surface ... 

The relationship between the adsorption of a molecule at an oil-water interface and the resulting interfacial tension is an important one and warrants a brief review here. The Gibbs equation for a system composed of one phase containing a nonionic solute adsorbing at the interface with a second phase is written... 

The entropy term TdS in Eqn (1.50) is the same for the irreversible process and the corresponding reversible process. Therefore, Eqn (1.50) represents the Gibbs equation for an irreversible process. With the first law of thermodynamics, dU — dW = 6q, Eqn (1.50) becomes... 

Based on the extended irreversible thermodynamics, the Gibbs equation for a simple single-component fluid in the presence of a viscous pressure tensor P (up to the second order in P ) is... 

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