Pressure Gibbs adsorption isotherm

Gibbs adsorption isotherm can be written at constant pressure and temperature, dv=-9md7 -t 7 jdmj. 

The simplest way to predict the lipid/ water partition coefficient, Kiw, of a drug is based on measurements of the surface pressure, ttd, of the drug as a function of its concentration in the aqueous subphase (Gibbs adsorption isotherm). The Gibbs adsorption isotherm provides the air/water partition coefficient, Kaw, and the cross-sectional area, Ad of the drug and allows calculation of the lipid/water partition coefficient, K]w, according to Eq. (6) [59] ... 

Fig. 20.1. Correlation between the air/water partition coefficient, Kaw, determined from measurements of the surface pressure as a function of drug concentration (Gibbs adsorption isotherm) in buffer solution (50 mM Tris/HCI, containing 114 mM NaCI) at pH 8.0 and the inverse of the Michaelis Menten constant, Km obtained from phosphate release...

Equation 17.23 has the form of an adsorption isotherm since it relates the amount adsorbed to the corresponding pressure. This is known as the Gibbs Adsorption Isotherm. For it to be useful, an expression is required for T. Assuming an analogy between adsorbed and liquid films, Harkins and Jura(15) have proposed that ... 

Gibbs adsorption equation phys chem A formula for a system involving a solvent and a solute, according to which there Is an excess surface concentration of solute if the solute decreases the surface tension, and a deficient surface concentration of solute if the solute increases the surface tension. gibz ad sorp shan i.kwa-zhon Gibbs adsorption isotherm physchem An equation for the surface pressure of surface [< ... 

Equations (3.45) and (3.46) are called Gibbs adsorption isotherms. In general, isotherms are state functions plotted versus pressure, concentration, etc. at constant temperature. 

If we compress a surfactant film on water we observe that the surface tension decreases and the surface pressure increases. What is the reason for this decrease in surface tension We can explain it by use of the Gibbs adsorption isotherm (Eq. (3.52)). On compression, the surface excess increases and hence the surface tension has to decrease. This, however, is relatively abstract. A more illustrative explanation is that the surface tension decreases because the highly polar water surface (high surface tension) is more and more converted into a nonpolar hydrocarbon surface (low surface tension). 

On a liquid-gas interface, the partial pressure of the adsorbed gas is substituted in Equation 1.59. On the solid-gas and solid-liquid interfaces, only the excess surface concentration can be measured directly, and not the surface tension. The Gibbs adsorption isotherm is suitable for the calculation of the change of surface tension. 

In Fig. 8.2, the points are the results obtained by evaluating the transverse component of the pressure tensor obtained from Monte Carlo simulation and the line is the result of an integration of the Gibbs adsorption isotherm using the simulation data. The vertical dashed line shows the saturation vapor pressure. 

This result is known as the Gibbs adsorption isotherm and is the starting point for analyzing the properties of the surface phase at constant temperature and pressure. It is more commonly written as... 

At the end of this section, let us consider a general expression, which allows us to obtain the surface activity coefficient Yij directly from the surface pressure isotherm tt/fi). From the Gibbs adsorption isotherm, dn = T djUi, it follows that... 

Tn his classic book (I) N. K. Adam discussed the behavior of very dilute - monolayers at the air/water (A/W) interface and using measurements published ear her by Jessop and himself (2, 3, 4), he showed that surface pressure (n)-area (A) isotherms for insoluble uncharged species, when plotted on a nA vs. n basis, suggested a limit of IkT at zero II. The same limit was also suggested by Schofield and Rideal s plot (5) of Frumkin s surface tension data (6) using the Gibbs adsorption isotherm to calculate A. Adam (I) stressed that n should be measured to the second decimal place to establish this limit unequivocally Adam and Jessop (4) provide one of the few sound extrapolations to this limit with their data on the esters of some dicarboxylic acids. 

The Gibbs adsorption isotherm shows the dependence of the extent of adsorption of an adsorbent on its bulk concentration or pressure. However, we also need to know the state of the adsorbate at the surface. These are interrelated because the extent of material adsorb-tion on a surface depends on the state of the surface. The behavior of the molecules in the surface film is expressed by a surface equation of state which relates the spreading pressure, n, which is the difference between the solvent and solution surface tensions, %= % - y to the surface concentration of the adsorbent. This equation is concerned with the lateral motions and interactions of the molecules present in an adsorbed film. In general, the surface equation of state is a two-dimensional analogue of the three-dimensional equation of state of fluids, and since this is related to monomolecular films, it will be described in Sections 5.5 and 5.6. It should be remembered that on liquid surfaces, usually monolayers form, but with adsorption on solid surfaces, usually multilayers form (see Section 8.3). 

The tv o-dimensional spreading pressure jr is an intensive property of the adsorbed phase. Considering the adsorption of just a single (superscript 0) component i and respecting the Gibbs-Duhem equation provides for constant temperature and pressure and equilibrium conditions the vell-kno vn Gibbs adsorption isotherm (Myers and Prausnitz, 1965) ... 

The quantity characterizing the reversible adsorption of the i th component is its surface excess F defined by the Gibbs adsorption isotherm [1] at constant temperature (T = const) and pressure (p = const) ... 

The reduced spreading pressure xp can be derived from the Gibbs adsorption isotherm. With the condition... 

For a single-component system the relationship between spreading pressure and adsorbed phase concentration may be obtained directly by integration of the Gibbs adsorption isotherm [Eq. (3.32)] ... 

The adsorption isotherm (F vs c) describes the relationship at constant temperature, pressure, and electrical variable between the surface concentration, F, and bulk concentration of an adsorbed species. Two closely related concepts are the equation of state (n vs F) which describes how the surface pressure of the adsorbed layer varies with surface concentration, and the pressure equation (tt vs c) describing the relationship between surface pressure and bulk adsorbate concentration. These three relationships are often confused in the literature as they represent equivalent expressions for a particular physical model. The adsorption isotherm and the pressure equation can be obtained from a particular equation of state by substituting the latter into the Gibbs adsorption isotherm and integrating. The results for a number of well known isotherms are given in Table.5.1. 

In the final part of considerations about early adsorption science it should be stated that only the most important conceptions and equations of adsorption isotherms have been discussed. However, the isotherms including the lateral interactions between molecules in the surface monolayer as well as the equations concerning mobile and mobile-localized adsorption have been omitted. These equations can be derived in a simple way by assuming that molecules in the surface phase produce the surface film whose behaviour is described by the so-called surface equation of state. This equation is a two-dimensional analogue of the three-dimensional equation of state and relates the surface pressure (spreading pressure) of the film to the adsorption. This adsorption can be expressed by the Gibbs adsorption isotherm [26]. Consequently, it is possible to... 

The Gibbs adsorption isotherm is vaUd generally for each phase boundary, but is used mainly for mobile phase interfaces (gas Uquid and liquid-hquid systems). Solid phase-gas phase systems do not use the variable F (as surface energy is not constant), but the amount of gas adsorbed (a), which depends on temperature and pressure. It represents the amount of adsorbate to the amount of solid adsorbent and is expressed mostly in moles or mass units. Adsorption can then be characterised, for example, by an empirical Freundlich isotherm a = (or in linearised form In [Pg.488]

The quantity of the components adsorbed at the interphase is a significant parameter, whereas the relationship between the extent of adsorption and the interfacial tension is particularly of interest this is studied in terms of the Gibbs adsorption isotherm. At constant temperature and pressure, the Gibbs-Duhem relationship for an interphase is ... 

Employing the Gibbs adsorption isotherm for gas adsorption on the surface of a solid adsorbent and the equivalent of the ideal gas equation of state for the surface adsorbed phase, obtain Henry s law for pure gas adsorption in the form of (<7( /S ) = H, P, where H is the Henry s law constant for species i. Henry s law is valid for dilute/low-pressure adsorption systems. 

This is the Gibbs adsorption isotherm. The spreading pressure cannot be directly measured but can be calculated owing to this equation. The integration of Eq.7.73... 

Determination of the equilibrium spreading pressure generally requires measurement and integration of the adsorption isotherm for the adhesive vapors on the adherend from zero coverage to saturation, in accord with the Gibbs adsorption equation [20] ... 

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... 

An adsorption isotherm is a graph of the amount adsorbed versus the pressure of the vapor phase (or concentration in the case of adsorption from solution). The amounts adsorbed can be described by different variables. The first one is the surface excess I in mol/m2. We use the Gibbs convention (interfacial excess volume Va = 0). For a solid surface the Gibbs dividing plane is localized directly at the solid surface. Then we can convert the number of moles adsorbed Na to the surface excess by... 

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