Adsorption Gibbs

These surface active agents have weaker intermoiecular attractive forces than the solvent, and therefore tend to concentrate in the surface at the expense of the water molecules. The accumulation of adsorbed surface active agent is related to the change in surface tension according to the Gibbs adsorption equation... 

Donohue M D and Aranovloh G L 1998 Classifioatlon of Gibbs adsorption Isotherms Adv. Colloid Interface Sci. 76/77 137-52... 

In writing the present book our aim has been to give a critical exposition of the use of adsorption data for the evaluation of the surface area and the pore size distribution of finely divided and porous solids. The major part of the book is devoted to the Brunauer-Emmett-Teller (BET) method for the determination of specific surface, and the use of the Kelvin equation for the calculation of pore size distribution but due attention has also been given to other well known methods for the estimation of surface area from adsorption measurements, viz. those based on adsorption from solution, on heat of immersion, on chemisorption, and on the application of the Gibbs adsorption equation to gaseous adsorption. 

Thermodynamically Consistent Isotherm Models. These models include both the statistical thermodynamic models and the models that can be derived from an assumed equation of state for the adsorbed phase plus the thermodynamics of the adsorbed phase, ie, the Gibbs adsorption isotherm,... 

The quantitative relationship between the degree of adsorption at a solution iaterface (7), G—L or L—L, and the lowering of the free-surface energy can be deduced by usiag an approximate form of the Gibbs adsorption isotherm (eq. 9), which is appHcable to dilute biaary solutions where the activity coefficient is unity and the radius of curvature of the surface is not too great ... 

The value of 9 can be estimated on purely theoretical grounds from estimates of the adsorption of surfactant which, in turn, can be estimated from the Gibbs adsorption equation relating adsorption to surface-tension lowering. 

Adsorption onto Particles. The Gibbs Adsorption Law relates how adsorption (qv) onto surfaces affects interfacial tension,... 

Adsorbed-Solution Theoiy The common thennodynamic approach to multicomponent adsorption treats adsorption equilibrium in a way analogous to fluid-fluid equilibrium. The theory has as its basis the Gibbs adsorption isotherm [Young and Crowell, gen. refs.], which is... 

This equation has been criticized on thermodynamic grounds because it does not satisfy the Gibbs adsorption isotherm unless all monolayer capacities n] are equal. 

To satisfy the Gibbs adsorption isotherm for unequal monolayer capacities, exphcit isotherms can be obtained in the form of a series expansion [LeVan and Vermeulen,/. Phy.s. Chem., 85, 3247 (1981)]. A two-term form is... 

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 Gibbs adsorption equation for the adsorption of an ion / from solution can be written in the form of the thermodynamic equation... 

At constant p and T, the Gibbs adsorption equation for an electrode interface leads to the well-known Lippmann equation12 ... 

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

The amount of species of the adsorbed substance j (adsorbate) per unit area of the trae surface area of the electrode or of any other adsorbent will be labeled Aj and will be called real adsorption (in contrast to the notion of Gibbs adsorption T see Section 10.4.1). In the limiting case, all adsorbed particles are packed right again the adsorbent s surface. This limiting case is called monolayer adsorption. In other cases, several layers of the adsorbate can form on the adsorbent s surface multilayer adsorption). 

The parameter nf always has positive values, whereas the parameters and Fj can have positive or negative values. Parameter Fj is called the Gibbs adsorption or Gibbs surface excess. 

The appreciation of the importance of adsorption phenomena at liquid interfaces is probably as old as human history, since it is easily recognized in many facets of everyday life. It is not surprising that liquid interfaces have been a favorite subject of scientific interest since as early as the eighteenth century [3,4], From an experimental point of view, one obvious virtue of the liquid interfaces for studying adsorption phenomena is that we can use surface tension or interfacial tension for thermodynamic analysis of the surface properties. The interfacial tension is related to the adsorbed amount of surface active substances through the Gibbs adsorption equation. 

For this system the Gibbs adsorption equation, Eq. (1), takes the form [2]... 

Ag(p%+ are fulfilled. When in the system (13) the reference electrodes reversible to anion X and cation are connected to the phase w and o respectively, the Gibbs adsorption... 

This relationship is termed the Gibbs adsorption equation. 

When the adsorbed components are electrically charged, then the partial molar Gibbs energy of the charged component depends on the charge of the given phase, and thus the chemical potentials in the above relationships must be replaced by the electrochemical potentials. The Gibbs adsorption isotherm then has the form... 

Equation (4.3.37) can be used to determine the function = T1(c1), which is the adsorption isotherm for the given surface-active substance. Substitution for c1 in the Gibbs adsorption isotherm and integration of the differential equation obtained yields the equation of state for a monomole-cular film = T jt). 

The adsorption coefficient or / is a function of the standard Gibbs adsorption energy alone when the molecules do not interact and the adsorption occurs without limitation, i.e. at very low electrode coverage. This dependence is expressed by the relationship... 

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...

These excess quantities are independent of the thickness chosen for the interface as long as it incorporates the region where the concentrations are different from those in the bulk that is, it does not matter if one chooses too thick a region (see Problem 1). We cannot refer the surface concentrations of the metal particles M, Mz+, and e to the solution. Nevertheless we will drop the asterisk in their surface concentrations to simplify the writing we will eliminate these quantities later. We can now rewrite the Gibbs adsorption equation in the form ... 

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