Unlike-molecule size parameter

Excess volume predictions are extremely sensitive to the value used for the unlike-molecule size parameter. Small deviations must be allowed from the commonly used arithmetic mean mixing rule for size parameters if quantitative results are to be obtained for VE simultaneously with other measurable excess thermodynamic functions (GE and HE). It should be noted that similar conclusions have been drawn for mixtures of globular molecules (8). 

Equations 13 and 14 follow from the Lorentz-Berthelot rules, an arithmetic mean for unlike-molecule size parameters and a geometric mean for unlike-molecule energy parameters, with deviations allowed for either rule. 

Deviations of from K can be of three sorts. Deviations at low and moderate concentrations from the zero-concentration limiting value are most important where ionic solutes are dissolved in nonionic solvents. Where all the solutes are molecular, even at extreme dilution, departures from Raoult s law on the part of each solute can arise in two distinct ways, with opposite effects. Deviations that are due to specific chemical or quasi-chemical attractive interactions between unlike molecules and that lead to enhanced mutual solubilities, lower partial vapor pressures, and activity coefficients less than unity are called negative deviations. Those that arise from mere differences between the molecules of the two kinds, such as differences of size or shape or of the intensity of intermolecular forces (reflected in differences in the solubility parameter, defined later), and that lead to diminished solubility, higher partial vapor pressures, and activity coefficients greater than unity are called positive deviations (see Fig. 1.2). 

Although certain of the above-mentioned theories are moderately successful in representing the experimental data of CF4 -t- CH and other fluorocarbon + hydrocarbon mixtures, experimental values of and x are required. At present there is no satisfactory method of obtaining these parameters a priori. Scott, in his 1958 review, considered the various possible factors that could lead to a weakening of the unlike interactions in such mixtures. He concluded that the three most significant were the presence of non-central forces, differences in ionization potential, and differences in size of the two component molecules. The use of the Kihara potential together with the Hudson and McCoubrey rule takes account of all these effects and thus the undoubted success of the Knobler treatment is not surprising. Criticisms could be levelled at his use of a spherically symmetric potential for substances such as n-hexane but the use of a more realistic potential such as the Kihara line-core potential is hardly justified until reliable experimental values for the ionization potentials of the fluorocarbons become available. 

Unlike simple molecules, polymer molecules are large in size. The physical parameter typically used to describe polymer size is molecular weight. With the exception of a few naturally available polymers such as proteins and DNA, a polymer sample consists of chains of varying length. That is why we talk about average molecular weight and not absolute molecular weight for polymers. 

Variational methods are at present used extensively in the study of inelastic and reactive scattering involving atoms and diatomic molecules[l-5]. Three of the most commonly used variational methods are due to Kohn (the KVP)[6], Schwinger (the SVP)[7] and Newton (the NVP)[8]. In the applications of these methods, the wavefunction is typically expanded in a set of basis functions, parametrized by the expansion coefficients. These linear variational parameters are then determined so as to render the variational functional stationary. Unlike the variational methods in bound state calculations, the variational principles of scattering theory do not provide an upper or lower bound to the quantity of interest, except in certain special cases.[9] Neverthless, variational methods are useful because, the minimum basis size with which an acceptable level of accuracy can be achieved using a variational method is often much smaller than those required if nonvariational methods are used. The reason for this is generally explained by showing (as... 

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