Hole theory of liquids

On the basis of the hole theory of liquids, Wunderlich (1960) concluded that the difference Cp — Cp at the glass transition temperature should be constant per structural bead in the polymer. A structural bead in this sense is defined as the smallest section of the molecule that can move as unit in internal rotation. 

Smith (1970) derived an equation of state for liquid polymers based on the hole theory of liquids. For higher temperatures, this equation can be reduced to a form equivalent to that of Eq. (7.26). 

Auluck and Rai, from the hole theory of liquids, calculated that van der Waals s a constant is given hy a—k Vm oipQ fh ) where is a constant, theoretically 2 4 but experimentally 1-44, and h is Planck s constant,... 

According to the hole theory of liquids, first developed by Eyring [31], molecular motion in liquids depends on the presence of holes or voids, i.e., places where there are vacancies. When a molecule moves into a hole, a... 

Wunderlich suggested [35], on the basis of the hole theory of liquids, that the value of ACp(Tg) per mobile bead in the polymeric structure should be roughly constant. According to a... 

According to the hole theory of liquids (Eyring, 1936), molecular motion in liquids depends on the presence of holes or voids, i.e., places where there are vacancies, as illustrated in Fig. 2.22. For real materials, however. Fig. 2.22 has to be visualized in three dimensions. A similar model can also be constructed for the motion of polymer chains, the main difference being that more than one hole will now be required to be in the same locality for the movement of polymer chain segments. On this basis, the observed specific volume of a sample, v, can be described as a sum of the volume actually occupied by the polymer molecules, vq, and the free volume (empty spaces), uy, in the system [see Fig. 2.23(a)], i.e.,... 

Cohen and Turnbull s critical free-volume fluctuations picture of selfdiffusion in dense liquids is similar to the vacancy model of self-diffusion in crystals. However, in crystals individual vacancies exist and retain their identity over long periods of time, whereas in liquids the corresponding voids are ephemeral. The free volume is distributed statistically so that at any given instance there is a certain concentration of molecule-sized voids in the liquid. However, each such void is short-lived, being created and dying in continual free-volume fluctuations. The Frenkel hole theory of liquids ignores this ephemeral, statistical character of the free volume. 

Somcynsky, T., and Simha, R., Hole theory of liquids and glass transition, J. Appl. Phys., 42, 4545 548 (1971). 

The other and better known is the absolute rate approach, based on the hole theory of liquid state. Eyring, 1936 (29) assumed that during a chemical reaction there is one step which can be identified with an activated state and that the process is uni-molecular. The reaction rate constant k can be expressed as... 

The hole theory of liquids — based on the conception that within a liquid there are statistically distributed vacancies or holes, whose number and volumia decrease with decreasing temperature has been applied by Fox and Flory (127), Hirai and Eyring 128), Kanig (121), Kovacs (129), Someynsky and Simha (130), and others, to explain various aspects of the glass transition in polymers. In its simplest form the theory ddines the molar V and occupied volume F ( = N y ) as they are related to the number of holes (N) in the following way ... 

The hole theory of liquids may be considered as a special case of the cell theory including multiple cell occupations corresponding to the restriction... 

In fact the hole theory of liquids was developed before the multiple cell occupation model (Cernuschi and Eyeing [1939], Ono [1947], Peek and Hill [1950], Rowlinson and Curtiss [1951], Mayer and Careri [1952], De Boer [1952]). 

According to the hole theory of liquids (Sect. 3.3.1) the surface tension should be inversely proportional to the 2/3 power of the void volume. As applied by Laniba et al. to ionic liquids [229] ... 

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