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Adsorption statistical mechanical theory

Suspension Model of Interaction of Asphaltene and Oil This model is based upon the concept that asphaltenes exist as particles suspended in oil. Their suspension is assisted by resins (heavy and mostly aromatic molecules) adsorbed to the surface of asphaltenes and keeping them afloat because of the repulsive forces between resin molecules in the solution and the adsorbed resins on the asphaltene surface (see Figure 4). Stability of such a suspension is considered to be a function of the concentration of resins in solution, the fraction of asphaltene surface sites occupied by resin molecules, and the equilibrium conditions between the resins in solution and on the asphaltene surface. Utilization of this model requires the following (12) 1. Resin chemical potential calculation based on the statistical mechanical theory of polymer solutions. 2. Studies regarding resin adsorption on asphaltene particle surface and... [Pg.452]

A deeper perception of the mechanistic implications of equation (9.2) can be had if the rational activity coefficients are described on the molecular level using the methods of statistical mechanics. This approach is the analogue of the statistical mechanical theory of activity coefficients for species in aqueous solution (Sposito, 1983). Fundamental to it is the prescription of surface speciation and the dependence of the rational activity coefficient on surface characteristics. Three representative molecular models of adsorption following this paradigm are summarised in Table 9.8. Each has been applied with success to describe the surface reactions of soil colloids (Goldberg, 1992). [Pg.250]

A() and m are experimental constants, Ao being the retention factor in pure strong solvent. Eq. (1.15) can be derived also on the basis of molecular statistical-mechanical theory of adsorption chromatography [,131. Eq. (1.15) applies in systems where the solute retention is very high in the pure non-polar solvent. If this is not the case, another retention equation was derived from the original Snyder model [34,351 ... [Pg.33]

The second model assumes an interfacial layer of finite and constant thickness T, so that K = T/lj is the volume of the interfacial layer, which has to be defined on the basis of some appropriate model of gas adsorption. For most practical purposes the two models are equivalent. The first model is easier to apply, but most of the authors in the early development of statistical mechanical theories of adsorption have expressed the problem in terms of an interfacial layer. For completeness, the appropriate definitions are given in relation to both formulations. [Pg.153]

The other model of the adsorption system, the so-caUed three-dimensional model, seems to be more realistic and promising. In this model, we do not assume the existence of a distinct surface phase but consider the problem of a fluid in an external force field. From a theoretical point of view a solution of this task requires only knowledge of the adsorbate-adsorbate and adsorbate-adsorbent interactions. However, in practice, we encounter difficulties connected with the mathematical complexity of the derived equations. The majority of the statistical-mechanical theories of nonuniform fluids have been formulated for adsorption on homogeneous siufaces. Nevertheless, the recent results obtained for heterogeneous sohds are really interesting and valuable [16]. [Pg.108]

To introduce statistical mechanics in the correct way through a suitable and complete theory of physical adsorption. In particular, the statistical mechanics theory developed by Steele [16-19] is known to be the most appropriate for rare gases onto well-defined surfaces. [Pg.434]

As was indicated in Section I, the study of physisorption of rare gases onto simple siufaces has been the main basis for the development of theories to describe adsorption. This is especially important in the case of statistical mechanics theories, where the behavior of rare gases as simple fluids permits a large number of simplifications. It is well known that migration barriers are very small in this case [150,151], which means that the films are highly mobile, and can thus be adequately represented by statistical mechanics models describing 2D fluids. In addition, theoretical calculations [33] are facilitated by the fact that the solid is composed of one kind of atom. Finally, there is added interest in the great variety of adsorbed phases that may be present. [Pg.450]

Application of the Significant Structure theory [60,184]. One of the first attempts to describe physisorption through statistical-mechanics theories was performed by McAlpin and Pierotti [60], who applied the Significant Structure theory to describe the physical adsorption of rare gases onto homogeneous solids. [Pg.454]

Steele s theory for monolayer physical adsorption [8,16-19,33]. This statistical mechanics theory is based on considering a classical gas interacting with an inert sohd and then to simphfy by imposing the so-called two-dimensional approxima-... [Pg.454]

Others. A number of different statistical mechanics approaches are available, although they have been less used. For example, Heer [80] developed a statistical mechanics theory, based on a localized-site model, which can reproduce adsorption isotherms for rare gases on heterogeneous surfaces at low pressures. [Pg.455]

Knowledge of the adsorbate-adsorbent interaction is fundamental in any statistical mechanics theory of adsorption. As indicated earlier, the comparison between experimental Henry s constants or gas-solid virial coefficients and theory [8,33] permits one to test the validity of a given model for the gas-solid potential. As a first approximation, the potential f/sf( ,) is considered to be a function only of the perpendicular distance z for monolayer mobile adsorption on homogeneous surfaces [29,33,43,219]. The analytical forms used are similar to the Lennard-Jones potential, but replacing r by z and considering different (10-4 or 9-3, for example) powers than the 12-6 case expressed in Eq. (12). In each case, the gas-surface molecular parameters, Sjf and cTsf, can be determined by comparison with experimental results. This procedure must be considered as semiempirical and thus not fidly theoretical. [Pg.459]

At 315°C. the rate constant ki has a value of 7.0 X 1016 molecules/sec.-cm.2-atm. From the definition of kh this represents the rate of adsorption of methylcyclohexane per cm.2 of bare platinum surface at a methylcyclohexane partial pressure of 1 atm. From kinetic theory and statistical mechanics, one can calculate the number of molecules striking a unit area of surface per unit time with activation energy Ea. This is given by... [Pg.52]

In this review, we introduce another approach to study the multiscale structures of polymer materials based on a lattice model. We first show the development of a Helmholtz energy model of mixing for polymers based on close-packed lattice model by combining molecular simulation with statistical mechanics. Then, holes are introduced to account for the effect of pressure. Combined with WDA, this model of Helmholtz energy is further applied to develop a new lattice DFT to calculate the adsorption of polymers at solid-liquid interface. Finally, we develop a framework based on the strong segregation limit (SSL) theory to predict the morphologies of micro-phase separation of diblock copolymers confined in curved surfaces. [Pg.156]

Up to this point, the theory has been presented in a form suitable only for adsorption systems which can be treated by classical statistical mechanics. When the quantization of the motion of the atoms is important, one must replace the Boltzmann factors in the integrals for ZN by the appropriate Slater sums. After integrating over the coordinates, one obtains... [Pg.275]

G. D. Halsey, Advances in Catalysisy 4 (1952), presents an excellent critique of the various theories of adsorption in the light of surface heterogeneity. T. L. Hill in the preceding chapter outlines the statistical mechanical and thermodynamics of the different sorption theories. [Pg.623]

For further reading on liquids in capillaries, see the reviews by R. Evans. J. Phys. Condens. Matter 2 (1990) 8989 and Microscopic Theories of Simple Fluids and Their Interfaces, in Liquids at Interfaces. J. Charvolin. J.F. Joanny and J. Zinn-Jusiin. Eds., Elsevier (1989). and D. Nicholson, N.G. Parsonage. Computer Simulation and the Statistical Mechanics of Adsorption. Academic Press (1982). [Pg.134]

A novel approach is reported for the accurate evaluation of pore size distributions for mesoporous and microporous silicas from nitrogen adsorption data. The model used is a hybrid combination of statistical mechanical calculations and experimental observations for macroporous silicas and for MCM-41 ordered mesoporous silicas, which are regarded as the best model mesoporous solids currently available. Thus, an accurate reference isotherm has been developed from extensive experimental observations and surface heterogeneity analysis by density functional theory the critical pore filling pressures have been determined as a function of the pore size from adsorption isotherms on MCM-41 materials well characterized by independent X-ray techniques and finally, the important variation of the pore fluid density with pressure and pore size has been accounted for by density functional theory calculations. The pore size distribution for an unknown sample is extracted from its experimental nitrogen isotherm by inversion of the integral equation of adsorption using the hybrid models as the kernel matrix. The approach reported in the current study opens new opportunities in characterization of mesoporous and microporous-mesoporous materials. [Pg.71]

Simple Models. Simulations are usually used for the direct calculation of properties or as an aid in the understanding of physical or chemical phenomena. However, they are also often carried as an aid in the development of simple models for future studies. This is particularly evident in the study of adsorption and flow in microporous systems, where standard hydrodynamic theories are inadequate but can in some cases be extended to treat the effects due to the confinement. Typically simulations of nanosystems need to be on longer timescales than those in the bulk due to the inhomogeneity of the system. Thus development of efficient models is important, and there has therefore been much activity in this field in recent years. Theories such as density functional theories have been extended and verified using simulation methods and simple statistical mechanical models have also been developed. [Pg.389]


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