Isotherms Gibbs

In geological surfaces, the solid-gas and solid-liquid interfaces are important, so the correct thermodynamic adsorption equation (Gibbs isotherm) cannot be used. Instead, other adsorption equations are applied, some of them containing thermodynamic approaches, and others being empirical or semiempirical. One of the most widespread isotherms is the Langmuir equation, which was derived for the adsorption of gas molecules on planar surfaces (Langmuir 1918). It has four basic assumptions for adsorption (Fowler 1935) ... 

The capillary-rise method is used to study the change in surface tension as a function of concentration for aqueous solutions of />butanol and sodium chloride. The data are interpreted in terms of the surface concentration using the Gibbs isotherm. 

In [17] we have calculated (Ss(r)) and shown that the value of (,s(r)) on the wall verifies the contact theorem. The integral of (s(r)) gives the adsorption I. From the calculation of the free energy we have obtained the surface tension and shown that the Gibbs isotherm leads to the same F as the one calculated via the density profile. Thus, as in the case of the homogeneous Yukawa fluid we have a totally self consistent calculation. 

Gas-solid equilibria have been studied for over 200 years, since Fontana showed that activated charcoal adsorbs gases and vapors at room temperature [1]. A considerable amoxmt of theoretical and experimental literature is available. The Gibbs isotherm [2] and the multilayer adsorption theory of Brunauer, Emmett and Teller [3], provide serious theoretical guidelines and support in understanding the results of experimental studies. Although, gas-sohd isotherms are difficult to predict quantitatively [4], this branch of adsorption thermod3mamics is much easier than liquid-solid adsorption because of the relative simplicity of the gas-sohd interface as compared to the liquid-solid interface. The Gibbs equation relates the amoimt of a compoimd adsorbed per unit surface area of a hquid-gas or a hquid-hquid interface and the surface or interfacial tensions [2]. This relationship provides a useful theoretical framework. 

The procedure used to derive Eq. 3.5 is the same as for the derivation of the Gibbs-Duhem equation. Substituting the expression for the chemical potential of an ideal gas in Eq. 3.5 provides the classical Gibbs isotherm ... 

Combined with the Gibbs isotherm (Eq. 3.6) it gives the virial isotherm equation... 

Two serious difficulties are encountered with the Freimdlich isotherm. First, from a fundamental point of view, this isotherm violates the Gibbs isotherm equation and it is not thermodynamically consistent. From a more practical point of... 

The surface tension of aqueous organic solution is lower than that of water. " The Gibbs isotherm predicts surface excess of organic molecules at the gas/ liquid interface, leading to a nonlinear decrease of the surface tension with respect to the bulk mole fraction of organic molecules in the solution. The same effect is expected to occur in the condensed liquid layer of water and alcohol on the substrate surface. The saturated surface concentration of small alcohols reaches molecules/cm, resulting in an... 

Adsorption Isotherm The mathematical relationship between the equilibrium quantity of a material adsorbed and the composition of the bulk phase at constant temperature. See also Gibbs Isotherm, Langmuir Isotherm. 

Gibbs Adsorption See Gibbs Isotherm, Gibbs Surface. 

Gibbs Isotherm An equation that relates the Gibbs surface excess... 

Perhaps the most useful general approach is still the ideal adsorbed solution theory (lAST) developed many years ago by Myers and Prausnitz [26]. The spreading pressure for the pure components may be calculated as a function of equilibrium pressure (p,) by integration of the Gibbs isotherm ... 

Let s introduce the concept of surface concentration of surfactant (measured in g mole/m ) [2]. If the environment is a binary solution with the volume molar concentration C of surfactant dissolved in it, then the quantities F and C are related by the Gibbs equation (aka the Gibbs isotherm) ... 

In many practical applications, the wetting liquid in question is a solution, e.g. an aqueous solution containing surface-active components. Then, the possibility of adsorption at all interfaces surrounding the three-phase contact-line (tcl) must be considered. According to the Gibbs isotherm for adsorption at the ij interface ... 

Substituting eq.(2.3-12) into eq.(2.3-ll), the following Gibbs isotherm equation is derived ... 

It is now seen that the Gibbs isotherm equation (2.3-13) is very general, and with any proper choice of the equation of state describing the surface phase an... 

Using the equation of state (2.7-3) into the Gibbs isotherm equation (eq. 2.3-13), they obtained ... 

The approach of IAS of Myers and Prausnitz presented in Sections 5.3 and 5.4 is widely used to calculate the multicomponent adsorption isotherm for systems not deviated too far from ideality. For binary systems, the treatment of LeVan and Vermeulen presented below provides a useful solution for the adsorbed phase compositions when the pure component isotherms follow either Langmuir equation or Freundlich equation. These expressions are in the form of series, which converges rapidly. These arise as a result of the analytical expression of the spreading pressure in terms of the gaseous partial pressures and the application of the Gibbs isotherm equation. 

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