Dispersion-force model

Wilson, K. C. and Puoh, F. ]. Can. Ji. Chem. Eng. 66 (1988) 721. Dispersive-force modelling of turbulent suspensions in heterogeneous slurry flow. 

The partitioning chemical potentials, Ui, and the dispersion force coefficients, Bi, are treated as adjustable parameters, although the latter can in principle be estimated from spectroscopic data. These two models are quite different in terms of their details, but also in terms of principle. The dispersion-force model treats the ion-lipid interface as a mathematical discontinuity and modifies the ion-lipid wall PMF, while the partitioning model promotes an alternative, Swiss-cheese-like picture of the ion-lipid interface. It is worthwhile to mention here that this penetration of anions within the lipid interface was observed in recent computer simulation work." ... 

In Fig. 8 it can be seen that the same data (DPPC monolayer surface pressure increments in the presence of various salt concentrations at 85 A per molecule) can be fitted equally well by the partitioning and the dispersion-force model, but not by the simple local binding model. 

Fig. 8. Best fits of surface pressure increments for DPPC monolayers over electrolyte solutions at 85 per molecule calculated using (a) the binding model, (b) the ion penetration model, and (c) the dispersion-force model. Results for NaBr, Nal and NaSCN are shown.

In this section we consider electromagnetic dispersion forces between macroscopic objects. There are two approaches to this problem in the first, microscopic model, one assumes pairwise additivity of the dispersion attraction between molecules from Eq. VI-15. This is best for surfaces that are near one another. The macroscopic approach considers the objects as continuous media having a dielectric response to electromagnetic radiation that can be measured through spectroscopic evaluation of the material. In this analysis, the retardation of the electromagnetic response from surfaces that are not in close proximity can be addressed. A more detailed derivation of these expressions is given in references such as the treatise by Russel et al. [3] here we limit ourselves to a brief physical description of the phenomenon. 

When viscometric measurements of ECH homopolymer fractions were obtained in benzene, the nonperturbed dimensions and the steric hindrance parameter were calculated (24). Erom experimental data collected on polymer solubiUty in 39 solvents and intrinsic viscosity measurements in 19 solvents, Hansen (30) model parameters, 5 and 5 could be deterrnined (24). The notation 5 symbolizes the dispersion forces or nonpolar interactions 5 a representation of the sum of 8 (polar interactions) and 8 (hydrogen bonding interactions). The homopolymer is soluble in solvents that have solubility parameters 6 > 7.9, 6 > 5.5, and 0.2 < <5.0 (31). SolubiUty was also determined using a method (32) in which 8 represents the solubiUty parameter... 

This model was later expanded upon by Lifshitz [33], who cast the problem of dispersive forces in terms of the generation of an electromagnetic wave by an instantaneous dipole in one material being absorbed by a neighboring material. In effect, Lifshitz gave the theory of van der Waals interactions an atomic basis. A detailed description of the Lifshitz model is given by Krupp [34]. 

The Air Force Dispersion Assessment Model (ADAM -1980s) calculates the source term and dispersion of accidental releases of eight specific chemicals chlorine, fluorine, nitrogen tetroji ogen sulfide, hydrogen fluoride, sulfur dioxide, phosgene, and ammonia. It Ut a ... 

This type of liquid is characterized by direction independent, relatively weak dispersion forces decreasing with r-6, when r is the distance between neighbouring molecules. A simple model for this type of liquid, which accounts for many properties, was given by Luck 1 2> it is represented by a slightly blurred lattice-like structure, containing hole defects which increase with temperature and a concentration equal to the vapor concentration. Solute molecules are trapped within the holes of the liquid thus reducing their vapor pressure when the latter is negligible. 

Figure 2.8 Attractive dispersion forces in nonpolar molecules are caused by temporary dipoles, as shown in these models of pentane, C5H12-...

Instead of the hard-sphere model, the Lennard-Jones (LJ) interaction pair potential can be used to describe soft-core repulsion and dispersion forces. The LJ interaction potential is... 

H-bonding is an important, but not the sole, interatomic interaction. Thus, total energy is usually calculated as the sum of steric, electrostatic, H-bonding and other components of interatomic interactions. A similar situation holds with QSAR studies of any property (activity) where H-bond parameters are used in combination with other descriptors. For example, five molecular descriptors are applied in the solvation equation of Kamlet-Taft-Abraham excess of molecular refraction (Rj), which models dispersion force interactions arising from the polarizability of n- and n-electrons the solute polarity/polarizability (ir ) due to solute-solvent interactions between bond dipoles and induced dipoles overall or summation H-bond acidity (2a ) overall or summation H-bond basicity (2(3 ) and McGowan volume (VJ [53] ... 

Bade WL (1957) Drude-model calculation of dispersion forces. I. General theory. J Chem Phys 27(6) 1280-1284... 

Prausnitz and coworkers [91,92] developed a model which accounts for nonideal entropic effects by deriving a partition function based on a lattice model with three categories of interaction sites hydrogen bond donors, hydrogen bond acceptors, and dispersion force contact sites. A different approach was taken by Marchetti et al. [93,94] and others [95-98], who developed a mean field theory... 

This simple three-state model of protein folding, shown schematically in Figure 7, ascribes a separate force to shaping the structure of each state. Local steric interactions trap the protein chain in a large ensemble of conformations with the correct topology hydrophobic interactions drive the chain to a smaller, more compact subset of conformations then dispersion forces supply the enthalpy loss required to achieve a relatively fixed and rigid ensemble of native conformations. 

The Smoluchowski-Levich approach discounts the effect of the hydrodynamic interactions and the London-van der Waals forces. This was done under the pretense that the increase in hydrodynamic drag when a particle approaches a surface, is exactly balanced by the attractive dispersion forces. Smoluchowski also assumed that particles are irreversibly captured when they approach the collector sufficiently close (the primary minimum distance 5m). This assumption leads to the perfect sink boundary condition at the collector surface i.e. cp 0 at h Sm. In the perfect sink model, the surface immobilizing reaction is assumed infinitely fast, and the primary minimum potential well is infinitely deep. 

The model presented here develops these ideas and introduces features which make the calculation of mixture properties simple. For a polar fluid with approximately central dispersion forces together with a strong angle dependent electrostatic force we may separate the intermolecular potential into two parts so that the virial coefficients, B, C, D, etc. of the fluid can be written as the sum of two terms. The first terms B°, C°, D°, etc, arise from dispersion forces and may include a contribution arising from the permanent dipole of the molecule. The second terms contain equilibrium constants K2, K, K, etc. which describe the formation... 

Rather, correlations are presented with the dielectric constant or with solvent polarity . It is true that the magnitude of the effects observed is frequently in the range of 0.2 -0.5 Hz as predicted by Raynes. Some evidence for specific interaction is suggested by the collision complex model 50> and by the deviations observed in chloroform solutions, acids and gases. A few investigators have noted that no correlation was found with the refractive index of the solvents suggesting that dispersion forces are not important for 2/H H, at least in those compounds studied. 

The distinction here is that the kK calculated from Eq. (9.19) would be used in a linear driving force model for the actual uptake rate expression and an axial dispersion coefficient would be substituted into the pde. If however one simply desires to match the adsorption response or breakthrough curves then the kK calculated according to Eq. (9.20) would provide very satisfactory results for estimation of the length of the mass transfer zone. 

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