Free-disperse systems dispersion interactions

It has been shown that the free energy of adhesion can be positive, negative, or zero, implying that van der Waals interactions can be attractive as well as repulsive [130,133,134]. While Eq. (14) can, strictly speaking, be expected to hold only for systems that interact by means of dispersion forces only, there are no restrictions on Eq. (15). Since this equation describes very well the fundamental patterns of the behavior of particles, including macromolecules, independent of the type of molecular interactions present, it was found to be convenient to define an "effective Hamaker coefficient that reflects the free energy of adhesion [130],... 

The lattice fluid equation-of-state theory for polymers, polymer solutions, and polymer mixtures is a useful tool which can provide information on equa-tion-of-state properties, and also allows prediction of surface tension of polymers, phase stability of polymer blends, etc. [17-20]. The theory uses empty lattice sites to account for free volume, and therefore one may treat volume changes upon mixing, which are not possible in the Flory-Huggins theory. As a result, lower critical solution temperature (LCST) behaviors can, in principle, be described in polymer systems which interact chiefly through dispersion forces [17]. The equation-of-state theory involves characteristic parameters, p, v, and T, which have to be determined from experimental data. The least-squares fitting of density data as a function of temperature and pressure yields a set of parameters which best represent the data over the temperature and pressure ranges considered [21]. The method,however,requires tedious experiments to deter-... 

It has been already pointed out that the energy of interaction between dispersed particles depends on the particle size. As a result, for large particles, and especially for anisometric ones, oriented in a certain way with respect to each other, the presence of a secondary minimum may be of importance. For such particles this secondary minimum may be sufficiently deep in comparison with kT. In some cases these systems may experience a peculiar colloid phase transition from a free disperse system (at low concentrations of dispersed phase) to crystal-like periodic structures consisting of colloidal particles in equilibrium with the dilute sol consisting of single particles. Such periodic structures are observed in some biological systems, e.g. in tobacco mosaic virus, in V205 sols and in latexes. 

The origin of the critical point can be traced to the temperature effect on miscibility. Patterson [1982] observed that there are three principal contributions to the binary interaction parameter, the dispersive, free volume and specific interactions. As schematically illustrated in Figure 2.16, the temperature affects them differently. Thus, for low molecular weight systems where the dispersion and free volume interactions dominate, the sum of these two has a U-shape, intersecting the critical value of the binary interaction parameter in two places — hence two critical points, UCST and LCST. By contrast, most polymer blends derive their miscibility from the presence of specific interactions, characterized by a large negative value of the interaction parameter that increases with T. The system is also affected by the free volume contribution, as well as relatively unimportant in this case dispersion forces. The sum of the interactions reaches the critical value only at one temperature — LCST. 

SP is some free energy related solute property such as a distribution constant, retention factor, specific retention volume, relative adjusted retention time, or retention index value. Although when retention index values are used the system constants (lowercase letters in italics) will be different from models obtained with the other dependent variables. Retention index values, therefore, should not be used to determine system properties but can be used to estimate descriptor values. The remainder of the equations is made up of product terms called system constants (r, s, a, b, I, m) and solute descriptors (R2,7t2, Stt2, Sp2 log Vx). Each product term represents a contribution from a defined intermolecular interaction to the solute property. The contribution from cavity formation and dispersion interactions are strongly correlated with solute size and cannot be separated if a volume term, such as the characteristic volume [Vx in Eq. (1.6) or V in Eq. (1.6a)] is used as a descriptor. The transfer of a solute between two condensed phases will occur with little change in the contribution from dispersion interactions and the absence of a specific term in Eq. (1.6) to represent dispersion interactions is not a serious problem. For transfer of a solute from the gas phase to a condensed phase this... 

A number of molecular sieves ean be prepared as defect-free, neutral frameworks. Traditional, inorganic examples inelude pure silicas and aluminophosphates most of the organic-inorganie MOFs also fall into this eategory. In these cases the interactions of adsorbed moleeules are dominated by dispersive interactions of the adsorbed molecules with the atoms of the framework and so can be modelled by interatomic potential models that have been parametrised according to experimental data. Because these inorganic systems are so well defined and well characterised, they make exeellent model systems for ealculations. From an... 

In older studies adsorption of nucleobases on clay minerals was shown to be promoted by the presence of polyvalent cations [56,122], This finding corresponds well with our results [151]. Periodic plane wave calculations based on the PBE functional [146] revealed sizeable adsorption of thymine and uracil on the external surfaces of Na-montmorillonite in the case of surface free from Na+ (from —6 to —11 kcal/mol), due to the stabilizing effect of dispersion interactions. As one can see from the comparison of these interaction energies with the Ecorr values obtained for K(3t)Na and K(3t)NaW systems with thymine and uracil (—28, —25 kcal/mol for uracil and —27, —24 for thymine as given in Table 21.6) and for D(t), D(t)W without cation (from -1 to -9 kcal/mol) [147], the addition of Na+ leads to a significant stabilization of the tetrahedral systems. The same is true for K(3o)Na systems, for which interaction energies increase (in absolute value) from —30 to —36 for uracil... 

Strictly speaking, dispersion interaction is valid only for two highly rarefied systems, i.e., gages. Extension of the principal of additivity of forces to condensed systems that do not represent a simple sum of free molecules has not yet been justified by theory. The experimental value found by Bradley [25] for the force on interaction between two quartz and borate spheres, however, was close to the value calculated on the basis of his assumption of additivity of molecular interaction. Hence, we may a priori accept the additivity of London interaction and extend this principal to condensed systems since at the present time there are no other methods for evaluating molecular interaction of such bodies when they are separated by a small gap. 

A Contact Interactions and the Stability of Free-Disperse Systems... 

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