Multilayer adsorption surface tension

Use the Kelvin equation to calculate the pore radius which corresponds to capillary condensation of nitrogen at 77 K and a relative pressure of 0.5. Allow for multilayer adsorption on the pore wall by taking the thickness of the adsorbed layer on a non-porous solid as 0.65 nm at this relative pressure. List the assumptions upon which this calculation is based. For nitrogen at 77 K, the surface tension is 8.85 mN m-1 and the molar volume is 34.7 cm3 mol-1. 

Waals forces and the liquid/gas surface tension forces in the multilayer gas adsorption EDLC Electric double-layer capacitor... 

In mesopores a multilayer film will be adsorbed at the pore wall as the saturation pressure is approached. The stability of this film is determined by the interaction with the wall, e.g. long-range Van der Waals Interaction, and by the surface tension and curvature of the liquid-vapour interface. Saam and Cole -have advanced a theory, showing how the curved film becomes unstable at a certain critical thickness t = a-r. The adsorption process is shown schematically in fig. 1.32a (1) (3). During desorption (4) -> (6) an asymmetrical state... 

Here is expressed by eq.2. Ap, depends on the shape of the meniscus in the pore. For the transformation of multilayer adsorption to capillary condensation, Aju, is given by -yV /a, where y and F , denote the surface tension and molar volume of the condensate a = R - / Hence, the chemical potential change of the multilayer adsorbed state, is expressed by eq.4. 

The Saam-Cole approach has several approximations, among which are the neglect of the sohd-adsorbate interaction and curvature effects on the adsorbate chemical potential, and curvature effects on surface tension in symmetrical and asymmetrical states, while modeling the multilayer region. Here, a more accurate version of the above approach has been introduced and tested for explaining the reversibihty of adsorption in MCM-41. For fluid molecules inside a cyhndrical pore of radius R, the incremental potential function has been expressed as [4,6,7]... 

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 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). 

In a porous adsorbent there is a continuous progression from multilayer adsorption to capillary condensation in which the smaller pores become completely filled with liquid sorbate. This occurs because the saturation vapor pressure in a small pore is reduced, in accordance with the Kelvin equation, by the effect of surface tension. 

Gregg used the same solvent [53] but determined the amount adsorbed using a surface tension balance. Smith and Hurley [17] recommended the use of cyclohexane as solvent, and stated that with some solvents multilayer adsorption takes place. Hirst and Lancaster [54], instead of adding more fatty acid to the solvent, increased c/cj by lowering the temperature of Uie solution. 

Polysaccharides interfaced with water act as adsorbents on which surface accumulations of solute lower the interfacial tension. The polysaccharide-water interface is a dynamic site of competing forces. Water retains heat longer than most other solvents. The rate of accumulation of micromolecules and microions on the solid surface is directly proportional to their solution concentration and inversely proportional to temperature. As adsorbates, micromolecules and microions ordinarily adsorb to an equilibrium concentration in a monolayer (positive adsorption) process they desorb into the outer volume in a negative adsorption process. The adsorption-desorption response to temperature of macromolecules—including polysaccharides —is opposite that of micromolecules and microions. As adsorbate, polysaccharides undergo a nonequilibrium, multilayer accumulation of like macromolecules. 

---