Solid-liquid interface model

A more recent model for the preexponential factor including viscous flow across the solid-liquid interface is [14]... 

The importance of the solid-liquid interface in a host of applications has led to extensive study over the past 50 years. Certainly, the study of the solid-liquid interface is no easier than that of the solid-gas interface, and all the complexities noted in Section VIM are present. The surface structural and spectroscopic techniques presented in Chapter VIII are not generally applicable to liquids (note, however. Ref. 1). There is, perforce, some retreat to phenomenology, empirical rules, and semiempirical models. The central importance of the Young equation is evident even in its modification to treat surface heterogeneity or roughness. ... 

Of particular interest has been the study of the polymer configurations at the solid-liquid interface. Beginning with lattice theories, early models of polymer adsorption captured most of the features of adsorption such as the loop, train, and tail structures and the influence of the surface interaction parameter (see Refs. 57, 58, 62 for reviews of older theories). These lattice models have been expanded on in recent years using modem computational methods [63,64] and have allowed the calculation of equilibrium partitioning between a poly-... 

J. P. Badiali, L. Blum, M. L. Rosinberg. Localized adsorption at solid-liquid interface the sticky site hard wall model. Chem Phys Lett 729 149-154, 1986. 

Chandra and his coworkers have developed analytical theories to predict and explain the interfacial solvation dynamics. For example, Chandra et al. [61] have developed a time-dependent density functional theory to predict polarization relaxation at the solid-liquid interface. They find that the interfacial molecules relax more slowly than does the bulk and that the rate of relaxation changes nonmonotonically with distance from the interface They attribute the changing relaxation rate to the presence of distinct solvent layers at the interface. Senapati and Chandra have applied theories of solvents at interfaces to a range of model systems [62-64]. 

Taking Simultaneous Micellizadon and Adsorption Phenomena into Consideration In the presence of an adsorbent in contact with the surfactant solution, monomers of each species will be adsorbed at the solid/ liquid interface until the dual monomer/micelle, monomer/adsorbed-phase equilibrium is reached. A simplified model for calculating these equilibria has been built for the pseudo-binary systems investigated, based on the RST theory and the following assumptions ... 

Halperin A (1999) Polymer brushes that resist adsorption of model proteins design parameters. Langmuir 15 2525-2533 Haynes CA, Norde W (1994) Globular proteins at solid-liquid interfaces. Colloid Surf B 2 517-566... 

The adsorption of soluble polymers at solid-liquid interfaces is a highly complex phenomenon with vast numbers of possible configurations of the molecules at the surface. Previous analyses of polymer adsorption have ranged in sophistication from very simple applications of "standard" models derived for small molecules, to detailed statistical mechanical treatments of the process. 

The equilibrium model for the adsorption of polymers at solid-liquid interfaces recently presented by Hogg and Mirville (1) has been evaluated at some length. It has been shown that, for polymers consisting of a reasonably large number of segments, the adsorption isotherms can be closely approximated by an expression of the form ... 

Fig. 15 Two of the simplest theories for the dissolution of solids (A) the interfacial barrier model, and (B) the diffusion layer model, in the simple form of Nemst [105] and Brunner [106] (dashed trace) and in the more exact form of Levich [104] (solid trace). c is the concentration of the dissolving solid, cs is the solubility, cb is the concentration in the bulk solution, and x is the distance from the solid-liquid interface of thickness h or 8, depending on how it is defined. (Reproduced with permission of the copyright owner, John Wiley and Sons, Inc., from Ref. 1, p. 478.)...

The interfacial barrier theory is illustrated in Fig. 15A. Since transport does not control the dissolution rate, the solute concentration falls precipitously from the surface value, cs, to the bulk value, cb, over an infinitesimal distance. The interfacial barrier model is probably applicable when the dissolution rate is limited by a condensed film absorbed at the solid-liquid interface this gives rise to a high activation energy barrier to the surface reaction, so that kR kj. Reaction-controlled dissolution is somewhat rare for organic compounds. Examples include the dissolution of gallstones, which consist mostly of cholesterol,... 

Electroosmosis or electroendosmosis is the bulk movement of the solvent (electrolyte solution) in the capillary caused by the zeta (0 potential at the wall/water interface of the capillary. Any solid-liquid interface is surrounded by solvent and solute constituents that are oriented differently compared to the bulk solution. Figure 17.2 illustrates a model of the wall-solution interface of the widely applied capillaries. Owing to the nature of the surface functional groups, in silica capillaries the silanol groups, the solid surface has an excess of negative... 

Slip is not always a purely dissipative process, and some energy can be stored at the solid-liquid interface. In the case that storage and dissipation at the interface are independent processes, a two-parameter slip model can be used. This can occur for a surface oscillating in the shear direction. Such a situation involves bulk-mode acoustic wave devices operating in liquid, which is where our interest in hydrodynamic couphng effects stems from. This type of sensor, an example of which is the transverse-shear mode acoustic wave device, the oft-quoted quartz crystal microbalance (QCM), measures changes in acoustic properties, such as resonant frequency and dissipation, in response to perturbations at the surface-liquid interface of the device. 

Molecular dynamics has been used extensively to explore the solid-liquid interface. In one such study, a modified Lennard-Jones potential has been used to model this interaction in the spreading of a droplet [4], of the form... 

The authors applied this model to the situation of dissolving and deposited interfaces, involving chemically interacting species, and included rate kinetics to model mass transfer as a result of chemical reactions [60]. The use of a stochastic weighting function, based on solutions of differential equations for particle motion, may be a useful method to model stochastic processes at solid-liquid interfaces, especially where chemical interactions between the surface and the liquid are involved. 

Although this treatment does not explicitly involve interactions at a solid-liquid interface, the application of Green s function to find the stochastic friction force may be an excellent opportunity for modeling interfacial friction and coupling, in the presence of liquid. An interesting note made by the authors is that the stochastic friction mechanism is proportional to the square of the frequency. This will likely be the case for interfacial friction as well. 

We have examined the many of the various factors that determine the proper boundary condition to use at the solid-liquid interface and considered many of the models associated with theses factors. The single-valued slip length model is the simplest and most convenient boundary condition, and it has been used successfully in many studies. However, it cannot describe coupling changes where there are changes in both the storage and dissipation properties. In this situation, a two-parameter complex value may be necessary. 

Equation 10.93 clearly shows that, if apparent partition coefficient is adopted instead of conventional partition coefficient K actually valid at the solid/liquid interface to model Rayleigh s crystallization, errors arise whose magnitudes increase the more K differs from 1 and the longer the process advances. This is clearly shown in figure 10.15, in which fractional differences — K )IK are plotted as functions of T for various values of K . 

Complementing the equilibrium measurements will be a series of time resolved studies. Dynamics experiments will measure solvent relaxation rates around chromophores adsorbed to different solid-liquid interfaces. Interfacial solvation dynamics will be compared to their bulk solution limits, and efforts to correlate the polar order found at liquid surfaces with interfacial mobility will be made. Experiments will test existing theories about surface solvation at hydrophobic and hydrophilic boundaries as well as recent models of dielectric friction at interfaces. Of particular interest is whether or not strong dipole-dipole forces at surfaces induce solid-like structure in an adjacent solvent. If so, then these interactions will have profound effects on interpretations of interfacial surface chemistry and relaxation. 

The above definition of the symmetric surface excess and the classical Guoy-Chapman model of the diffuse double layer are combined to show that the surface excess cannot be considered a surface concentration in the presence of an ionized monolayer on an impenetrable solid/liquid interface. 

We extend our description to adsorption at the solid-liquid interface. For many systems we can use the same models as for gas adsorption on a solid surface, we only have to replace the pressure P by the concentration c. The adsorption of macromolecules to surfaces is briefly discussed in Section 10.3.2. For macromolecules desorption is often negligible and thermodynamic equilibrium is only reached after a very long time, if at all. 

The two-film model representation can serve as a basis for more complicated models used to describe heterogeneously catalyzed RSPs or systems containing suspended solids. In these processes a third solid phase is present, and thus the two-film model is combined with the description of this third phase. This can be done using different levels of model complexity, from quasi-homogeneous description up to the four-film presentations that provide a very detailed description of both vapor/gas/liquid-liquid and solid/liquid interfaces (see, e.g., Refs. 62, 68 and 91). A comparative study of the modeling complexity is given in Ref. 64 for fuel ether synthesis of MTBE and TAME by CD. 

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. 

Assemblies formed by the coadsorption of surfactants at the solid-liquid interface represent attractive model systems for probing the nature and strength of lateral interactions among surfactants. These studies reveal strong synergistic effects in... 

Ari, T., and Norde, W. (1990) The behaviour of some model proteins at solid-liquid interfaces adsorption from single protein solutions. Colloids Surfaces 51, 1-15. 

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