Adsorption spreading pressure

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] ... 

Rowley H.H. and Innes W.B. Relationship between the spreading pressure, adsorption and wetting. 1942. 

Equation (23) holds only when If and T in the mixture are the same as those in the respective single-solute systems. Spreading pressure can be related to the characteristic adsorption equilibria of each single solute system according to the following relationship ... 

It should be noted that, in the above equations, the effects of adsorption of vapor or gas on the solid surfaces are completely neglected. The amount of adsorption can be quite large, and may approach or exceed the point of monolayer formation at saturation. The spreading pressure, n, which is the amount of the reduction in surface energy on the solid surface due to the adsorption of vapor in equilibrium, is given by (Adamson, 1982)... 

A fundamental equation derived by Gibbs is used to calculate the spreading pressure of films on solids where, unlike films on liquids, it cannot be experimentally determined. Guggenheim and Adam reduced Gibbs general adsorption equation to equation (7.3) for the special case of gas adsorption... 

The value of is very small for low energy surfaces, but it cannot be neglected for fillers, on the contrary can be used for the calculation of the thermodynamic characteristics of their surface. The spreading pressure can be determined from the adsorption isotherm in the following way [74] ... 

Spreading Pressure Values, v>,, for the Adsorption of Vapors on Analaae and Graphite ... 

Ideal Adsorbed Solution Theory. Perhaps the most successful general approach to the prediction of multicomponent equilibria from single-component isotherm data is ideal adsorbed solution theory. In essence, the theory is based on the assumption that the adsorbed phase is thermodynamically ideal in the sense that the equilibrium pressure for each component is simply the product of its mole fraction in the adsorbed phase and the equilibrium pressure for the pure component at Ike same spreading pressure. The theoretical basis for this assumption and the details of the calculations required to predict the mixture isotherm are given in standard texts on adsorption. Whereas the theory has been shown to work well for several systems, notably for mixtures of hydrocarbons on carbon adsorbents, there are a number of systems which do not obey this model. Azeotrope formation and selectivity reversal, which are observed quite commonly in real systems, are not consistent with an ideal adsorbed phase and there is no way of knowing a priori whether or not a given system will show ideal behavior. 

The equilibrium thermodynamic functions describing the retention process are essentially related to the net retention volume. For example, the intermolecular adsorption of Gibbs free energy, —AGa, for one mole of solute vapor from a reference gaseous state with the partial pressure, Po, to a reference adsorbed state with the equilibrium spread pressure (or two-dimensional pressure), no, is given as [115]... 

According to second and third observations, it is difficult to appreciate the maximum value of the surface free energy and surface enthalpy of a solid, especially in the case of microporous materials which are widely efficient adsorption properties of the surface (sample V). Therefore, for this material, more works may be needed on the adsorption isotherm, spreading pressure, isosteric heat of adsorption, and even heterogeneities of solid surfaces. They are concerned with the finite concentration technique with increasing amount adsorbed, which will be dealt to some extent in the next section. 

Equation (2.34) is often referred to as the Gibbs adsorption equation where the interdependence of r and p is given by the adsorption isotherm. TTie Gibbs adsorption equation is a surface equation of state which indicates that, for any equilibrium pressure and temperature, the spreading pressure II is dependent on the surface excess concentration r. The value of spreading pressure, for any surface excess concentration, may be calculated from the adsorption isotherm drawn with the coordinates n/p and p, by integration between the initial state (n = 0, p = 0) and an equilibrium state represented by one point on the isotherm. 

Comparison of Equations (2.61) and (2.67) shows that the second term of the right-hand side of Equation (2.67) is due to the spreading pressure, which is related to the interactions between adsorbed molecules, often referred to as the lateral interactions . It is only at very low coverages, where the spreading pressure is negligible, that the integral molar entropy of adsorption is simply dependent on the adsorbate-adsorbent interaction. 

Equation (2.72) is not easy to use in the general case in which the spreading pressure is unknown. But in the particular case of stepwise isotherms where there are two adsorbed phases in equilibrium with the gaseous adsorptive (i.e. in the case of a univariant adsorption system), Larher (1968, 1970) showed that the isosteric method may be used with the transition pressure p" to give integral molar energies un and entropies sn of the quasi-layer ... 

If one pictures the adsorbed monolayer as a two-dimensional imperfect gas, it seems reasonable to assume the applicability of a two-dimensional form of the van der Waals equation in which the gas pressure is replaced by the spreading pressure and the volume by the surface area. By combining this with the Gibbs adsorption equation - Equation (2.34) - de Boer (1968) obtained the equation... 

Assessment of wettability from the gas adsorption isotherm. If the solid is covered with a liquid film in equilibrium with saturated vapour p°, the spreading pressure of the film can be derived from Equation (2.22). Thus ... 

TABLE 4 Spreading Pressure (in I0 3 N/m) of Adsorbed Films on Solids Measured by Adsorption Experiments... 

Experimentally it is much simpler to consider changes in adsorption at constant surface coverage rather than at constant spreading pressure. Unfortunately, the mathematical analysis now is also more complicated. When r T, P) is held fixed P and T are no longer independent. We set dP = (dP/dT)r dT, and we rewrite Eq. (5.2.7) in the form... 

Multilayer adsorption isotherms are usually analyzed in terms of the Brunauer, Emmett, Teller equation C/Cm = cx/(l —x)(l —x-f cx), wherex s P/Pq. where Pq is the saturation vapor pressure of the liquid c is a parameter, and the other symbols have been defined earlier. Find the equation for the spreading pressure for X < 1. Sketch plots of C/Cm and of fvs. x. 

The prediction of mixed-gas adsorption equilibria by ideal-adsorbed-solution theorf is based onEqs. (14.124) and (14.128). The following is a brief outline of the procedure. Since there are N "r 1 degrees of freedom, both T and P, as well as the gas-phase composition, must be specified. Solution is for the adsorbate compositionand the specific amount adsorbed. Adsorption isotherms for eachpure species must be known over the pressure range from zero to the value that produces the spreading pressure of the mixed-gas adsorbate. For purposes of illustration we assume Eq. (14.107), the Langmuir isotherm, to apply for each pure species, writing it ... 

The Henry s law constants varied linearly with the temperature. Heats of adsorption (Table I) were calculated from Equation 3. Standard surface free energies of adsorption (Table I) were calculated from Equation 2 using de Boer s standard state for spreading pressure. 

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