Van der Waals theory of adsorption

From the discussion up to this point the reader will surely appreciate that a rigorous, first-principles calculation of the partition function for a macroscopic system is generally precluded even in the classical hmit with the exception of rather simple models of limited usefulness (see Chapter 3). However, the problem of calculating the partition function (or the configuration integral) in closed form becomes tractable if we introduce as a key assiunptiou that correlations between molecules arc entirely negligible. 

One may, for example, regfnd the (planar) substrate(s) of a slit-pore as the surface of a spherical particle of infinite radius. The confiniKl fluid plus the substrates may then be perceived as a binary mixture in which macro-scopically large (i.e., colloidal) particles (i.e., the substrates) are immersed in a sea of small solvent molecules. The local density of the confined fluid may then be interpreted as the mixture (A-B) pair correlation function representing correlations of solvent molecules (A) caused by the presence of the solute (B). 

As we shall demonstrate in this section, a simple mean-field theory of 

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One important direetion of study has been to use empirieal adsorption data, together with the preassumed model for loeal adsorption, and attempt to extraet information about the form of x(e) [13,14]. The ehoiee of the model for loeal adsorption, whieh is an important input here, has been eustomarily treated quite easually, assuming that it has rather limited influenee on the form and properties of the evaluated EADFs. Usually, one of so many existing equations developed for adsorption on uniform surfaees is used as the loeal adsorption isotherm. The most often used forms of 0 p, T,e) are the Langmuir [6] and the Fowler-Guggenheim [15] equations for loealized adsorption. Ross and Olivier [4] extensively used the equation for mobile adsorption, whieh results from the two-dimensional version of the van der Waals theory of fluids. The most radieal solution has been... 

Consider, for example, the physical adsorption of a gas by a solid. If the solid is regarded as a giant sphere, the adsorption of the gas can be regarded as the interaction of a gas with a single infinitely large molecule dissolved in that gas. If the simplest form of the van der Waals theory of mixtures is applied to that system, then the adsorption isotherm is just... 

When the functional form of the correlation is suggested by theory, there is a great deal more confidence that the correlation can be extrapolated into regions of P that have no experimental data, and can be used for other families of compounds other than the training set S. Examples of theory-suggested functional forms include the van der Waals equation of state for gases, the Langmuir isotherm for adsorption and catalysis, and the Clausius-Clapeyron equation for the vapor pressure of liquids. 

As expected, the total interaction energies depend strongly on the van der Waals radii (of both sorbate and sorbent atoms) and the surface densities. This is true for both HK type models (Saito and Foley, 1991 Cheng and Yang, 1994) and more detailed statistical thermodynamics (or molecular simulation) approaches (such as Monte Carlo and density functional theory). Knowing the interaction potential, molecular simulation techniques enable the calculation of adsorption isotherms (see, for example, Razmus and Hall, (1991) and Cracknell etal. (1995)). 

As explained under the adsorption theory of adhesion,3 an adhesive must first wet the substrate and come into intimate contact with it. (A brief description of the adsorption theory of adhesion is presented in the section below.) The result of good wetting is simply that there is greater contact area between adherend and adhesive over which the forces of adhesion (e.g., van der Waals type of forces) may act. For good wetting, the surface free energy (surface tension yLV) of the liquid adhesive must be less than that (critical surface tension yc) of the solid adherend, or... 

The DLVO theory explains these results quite readily. To demonstrate this, we will discuss predictions of the adsorption characteristics of poliovirus on Si02 as a function of pH. To make these predictions we have adopted free energy values and electrodynamic and electrostatic adsorption potential equations found in the earlier sections of this study to characterize virus adsorption. These equations are then used to predict the effect of altering pH on the basis of electrochemical theory. We selected the measured van der Waals potential of —52 kj mol" and added the double-layer potential as evaluated by Gregory s LSA expression to calculate an estimate of the fraction of virus adsorbed (Fads) with Equation 2. We selected a system containing 1 m of Si02 and 1 L of 0.02M NaCl for the demonstration. 

In the present theory of van der Waals adsorption, the multilayer starts below the pressure P and builds up with increasing pressure, and the capillaries are not filled up even for pressures greater than this condensation pressure P, which contradicts the capillary condensation. This means that the multilayer theory based on van der Waals adsorption has an upper limit in the pressure range. Despite this limitation, the van der Waals theory puts all five types of adsorption isotherm shape into one framework, that is it can deal with unimolecular adsorption (Langmuir), multilayer adsorption (BET) and enhanced adsorption in capillaries (BDDT). 

Islam, M. M. Alam, M. T. Okajima, T. Oshaka, T. (2009). Electrical double layer structure in ionic liquids an understanding of the xmusual capacitance-potential curve at a nonmetallic electrode. /. Phys. Chem. C, Vol. 113,3386-3389 Johnson, M. Nordholm, S. (1981). Generalized van der Waals theory. VI. Application to adsorption. /. Chem. Phys., Vbl. 75,1953-1957... 

Roth, CM Lenhoff, AM, Electrostatic and van der Waals Contributions to Protein Adsorption Comparison of Theory and Experiment, Langmuir 11, 3500, 1995. 

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