Free volume theory, description

It would be an advantage to have a detailed understanding of the glass transition in order to get an idea of the structural and dynamic features that are important for photophysical deactivation pathways or solid-state photochemical reactions in molecular glasses. Unfortunately, the formation of a glass is one of the least understood problems in solid-state science. At least three different theories have been developed for a description of the glass transition that we can sketch only briefly in this context the free volume theory, a thermodynamic approach, and the mode coupling theory. 

Detonation, Free Volume Theory of the Liquid State Developed by Eyring et al and by Lennard-Jones-Devonshire. The free volume theory of the liquid state developed by Eyring Hirshfelder (Ref 1) and by Lennard-Jones Devonshire (Ref 2) has provided a useful approximate description of the thermodynamic props of liquids in terms of intermolecular forces... 

The introduction forms Chapter 1 of this survey. Chapter 2 deals briefly with various approaches to the description of the concentration dependence of the viscosity of disperse systems, including the transition region from fluid to solid-like systems. Chapter 3 describes viscosity from the standpoint of the free volume theory and the specific features of the transition from mobile to glasslike systems. Chapter 4 presents the concept of the free volume of disperse systems developed by us as well as the results of experiments illustrating it Chapter 5 contains the pertinent generalizations and conclusions. 

The theories that describe diffusion in concentrated polymer solutions are approximate in nature. Among them, only one seems sufficiently developed to offer a good description of mass transfer in polymer-solvent systems the free-volume theory of diffusion. Though it affords good correlative success, it needs further testing. 

Several theoretical descriptions of the temperature dependence of the conductivity of these systems have been given. An example is the free-volume theory. The conductivity is proportional to a free volume , defined as the deviation of the real volume of the... 

In this chapter we discuss the basics of the phase behaviour of hard spheres plus depletants. Phase transitions are the result of physical properties of a collection of particles depending on many-body interactions. In Chap. 2 we focused on two-body interactions. As we shall see, depletion elfects are commonly not pair-wise additive. Therefore, the prediction of phase transitions of particles with depletion interaction is not straightforward. As a starting point a description is required for the thermodynamic properties of the pure colloidal dispersion. Here the colloid-atom analogy, recognized by Einstein and exploited by Perrin in his classical experiments, is very useful. Subsequently, we explain the basics of the free volume theory for the phase behaviour of colloids -I- depletants. In this chapter we treat only simplest type of depletant, the penetrable hard sphere. 

The first step in taking into account more appropriate polymer physics compared to the simple description of penetrable hard spheres is by considering the polymers as ideal chains. Then one needs to ineorporate the correct depletion thickness of non-adsorbing ideal chains near a eoUoidal hard sphere into free volume theory. 

The following paragraphs describe three main groups of theories of the glass transition (1, 72) free-volume theory, kinetic theory, and thermodynamic theory. Although these three theories may at first appear to be as different as the proverbial three blind men s description of an elephant, they really examine three aspects of the same phenomenon and can be successfully unified, if only in a qualitative way. 

Further modeling steps were made in Ref [34]. First, the ad hoc function (5.4) that gives only a qualitative description of the gel effect [34] was replaced by a function that was derived from the expression [43] for the termination rate given in terms of self-diffusion rates of polymer radicals, which in turn are found by applying the free volume theory [44,45]. Secondly, the effect of adding an inhibitor to the mixture was considered [34]. 

The model of free volume going back to the classical papers of Frenkel and Firing [48, 80, 144-147] has been widespread in the physics of liquid and solid states of matter. Some concepts allowing improvement in the nature of fluctuation free volume have been offered in the last 15 years [148-150]. Nevertheless, there is one more aspect of the problem, which has not been mentioned earlier. As a rule, the application of free volume theory for the description of the properties of amorphous bodies is based on a notion that the free volume characterises the structure of the indicated bodies. This postulate is due to a considerable extent to the absence of a quantitative model of the structure of the amorphous condensed state, including the structure of amorphous state polymers. Strictly speaking, one should understand that by structure we mean distribution of body elements in space [151]. It is evident that free volume microvoids cannot be structural elements and at best only mirror the structural state of the studied object. Taking the introduction of some structural elements (relaxators, see for example, [148]) into consideration has practically no influence on the structural representation of free volume. 

Pratt, L. R., Hummer, G., and Garde, S. (1999). Theories of hydrophobic effects and the description of free volume in complex liquids. In New Approaches to Problems in Liquid State Theory (C. Caccamo, J.-P., Hansen, and G. Stell, eds.), vol. 529, pp. 407-420. Kluwer, Netherlands. NATO Science Series. 

Endless discussion exists regarding whether a theory based on the configurational entropy or the excess free volume 8v provides the more correct description of glass formation. Thus, this section briefly analyzes the relation... 

The concept of free-volume appeared to be very useful and was applied for the theoretical description of many processes in liquids, including polymeric solutions and melts. Taking the free-volume concept as a basis, theories were developed for the diffusion of low-molecular-weight compounds into polymers14,1S, thermal conductivity16, solution and solubility of polymers17, etc. 

The term A is related to the solvent density and molecular weight and to the free volumes of the ions and the ion-pair [59]. Fjoi is the difference between the molar ion-pair solvation energy and the free ion solvation energy. The theory does not predict a simple linearity of In with lie. Actually solvent effects other than that due to the relative permittivity of the solvent are easily predicted, since the macroscopic e is only a rudimentary description of the real attenuation of the ionic interactions due... 

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