Free volume expansion ratio

Equation (54) represents the ratio of real volume of holes and expansion volume to the total free-volume, as distinct from its usual definition as the ratio of free-volume to total volume, the latter being determined by... 

Equations (65) and (66) of Simha and Weil provide the most general expression of the SB rule and free-volume ratios as a function of the thermal expansivities at and Og. The authors have shown that, since a < 8 10 4 deg-1 and Te < 5 102 K, for most polymers the exponentials may be expanded to yield ... 

As seen in Table 1, the decrease in permeability can be directly attributed to a dramatic reduction in the effective diffusion coefficient, while there is a much smaller effect on the apparent solubility. A similar dependence of the solubility and diffusion coefficients on the draw ratio has been observed in other uniaxially oriented polymers (35-37). Because the glass transition and density of the polystyrene samples were found independent of the draw ratio, they concluded that the reduction in diffusivity was due to anisotropic redistribution of the free volume during drawing. Using an expansion coefficient related to draw ratio, the polystyrene data were successfully correlated using the Cohen-Turnbull free volume theory. However, the situation was found to be more complex for PVC (i ) ... 

The expansion and free volume can then be characterized by the ratio of the thermal energy arising from the external degrees of freedom available to the component, and the intraaction rarergy between neighboring nonbonded seg-... 

Recently Kusy and Greenberg introduced a reduced variables technique which simplified the use of the rather unwieldy statistical mechanical equations. Subsequent expansion of this work in terms of the inter- intramolecular energy ratio (r) and the fractional free volume at Tg(VQ) explicitly characterized the functional dependence... 

As the stress-strain linearity limit of most thermoplastics and their blends is very low, nonlinear viscoelastic behavior of heterogeneous blends needs to be considered in most cases. The nonlinearity is at least partly ascribed to the fact that the strain-induced expansion of materials with Poisson s ratio smaller than 0.5 markedly enhances the fractional free volume (240). Consequently, the retardation times are perpetually shortened in the course of a tensile creep in proportion to the achieved strain. Thus, knowledge of creep behavior over appropriate intervals of time and stress is of great practical importance. The handling and storage of the compliance curves D (t,a) in a graphical form is impractical, so numerous empirical functions have been proposed (241), eg. 

A portion of this volume increase may be attributed to expansion of free volume, and since it is caused by the dilatational component of the applied stress, the proportion can be estimated to be the same as the ratio of the compressibilities 8/ and (Chapter 11, Section Dl) then bf/be = (jS// 8)(l/ )(diVdc). Substitution into equation 49 of Chapter 11, for small tensile strains where d//d can be approximated by (J2 —/i)/f, predicts that all relaxation times will be modified by a shift factor whose value is given by ... 

DMA Frequency response analysis (single or multiple frequencies) Mechanical strength and energy loss Storage modulus Loss modulus Loss factor Activation energies of relaxations Free-volume ratio (thermal expansion coefficient)... 

A prolate shape also appears to explain better the hydrodynamic properties of iron-free (142) and of iron-saturated (143) transferrin. Ferric transferrin (a/b = 3) would, however, be more elongated than the iron-free form (a/b =2) while the effective hydrodynamic volume (Ve) would be higher for the iron complex than for the apoprotein. These results not only differ from those given in Table 3 for conalbumin but are also in partial disagreement with dielectric dispersion and viscosity measurements (144) which have indicated that human transferrin assumes a more spherical shape with iron-saturation, the axial ratio decreasing from 2.5 (apo) to 2.0 (ferric). This latter investigation also indicates a slight expansion (15.4 16.9) of the hydrated volume... 

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