Modified free volume theory

Solute Diffusion in Biopolymers as a Function of Water Activity Using a Modified Free Volume Theory... 

H. L. Frisch, D. Klempner, and T. Kwei, Modified Free Volume Theory of Penetrant Diffusion... 

E 11 46 activation energy in modified free volume theory, or... 

Popelar, C. F. and Liechti, K. M., A Distortion-Modified Free Volume Theory for Nonlinear Viscoelastic Behavior , Mechanics of Time-Dependent Materials, 7 89-141, 2003. 

A modified version of the free-volume theory is used to calculate the viscoelastic scaling factor or the Newtonian viscosity reduction where the fractional free volumes of pure polymer and polymer-SCF mixtures are determined from thermodynamic data and equation-of-state models. The significance of the combined EOS and free-volume theory is that the viscoelastic scaling factor can be predicted accurately without requiring any mixture rheological data. 

In dense polymers, the self-diffusion of small plasticising solvent molecules has been measured PGSE methods [105]. For polymers above the glass-transition temperature, it is common to model the solvent diffusion using the free volume theory as modified for polymer systems by Fujita [122] and by Vrentas and Duda [123]. For solvent diffusion in dense polymers below Tg, an alternative model has been given by Frisch and Stern [124]. 

The free volume theory is modified so that the changes in free volume with temperature relate to a discontinuity that occurs at rather than Tg. 

Ertl and DuUien [ibid.] found that Hildebrand s equation could not fit their data with B as a constant. They modified it by applying an empirical exponent n (a constant greater than unity) to the volumetric ratio. The new equation is not generally useful, however, since there is no means for predicting /i. The theory does identify the free volume as an important physical variable, since n > for most hquids implies that diffusion is more stronglv dependent on free volume than is viscosity. 

Another microscopic approach to the viscosity problem was developed by Gierer and Wirtz (1953) and it is worthwhile describing the main aspects of this theory, which is of interest because it takes account of the finite thickness of the solvent layers and the existence of holes in the solvent (free volume). The Stokes-Einstein law can be modified using a microscopic friction coefficient ci micro... 

A very important aspect of kinetic theories now surfaces. Equation (5-23) is concerned with the time dependence of volume recovery after a temperature jump. For the volume to change, the molecules must move. However, as discussed in Chapters 3 and 4, the rate at which the molecules can move is a sensitive function of the free volume, and the free volume is varying with time in Figure 5-9. Thus, it is clear that the retardation time in equation (5-23) must itself depend upon 8 and vary with time. This situation can be treated in quite a straightforward way by modifying equation (4-16) as... 

We shall briefly summarize MD simulations of systems of PLC chains. First, the chains systems have to be constructed. There are various ways of generating them, and the mechanical behavior is little if at all influenced by the generation procedure. It is influenced, however, by the vacancies, or the amount of free volume as predicted by the chain relaxation capability (CRC) theory [125]. The problem is to create a realistic bulk polymer system. A procedure originally developed by Mom [126] has been modified to achieve a more realistic representation of polymeric chains [127-129]. 

The Flory-Huggins theory can be improved to incorporate new terms. For example, the Prigogine-Flory-Patterson theory introduces an entropic contribution due to free volume effects in order to obtain more realistic results [70]. This contribution does not modify the solubility criterion as stated above. When the Flory interaction parameter (/) is considered to have both an enthalpic component and... 

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