Free volume strain dependence

Ferry, J. D., and R. A. Stratton The free volume interpretation of the dependence of viscosities and viscoelastic relaxation times on concentration, pressure, and tensile strain. Kolloid-Z. 171, 107 (1960). 

The resulting strain dependence of (w ) and the width of the hole-size distribution computed from F(vh) are both in good agreement with the experimental data, assuming a value p = 0.65, indicative that the above-described free-volume model provides a satisfactory description of the PALS data. Computation of the fractional free volume from the experimental g(vh). 

As discussed in Chapter 2, the moleeular structure of polymers, whether glassy or semi-crystalline, incorporates a signifieant component of disordered material containing a certain fraction of free volume or a liquid-like material environment, depending on the thermal history of the polymer. The subject of this chapter is the small-strain reversible response of sueh polymeric materials and structures under stress that we refer to as linear viscoelasticity. 

Strain-Induced Dilatation. An alternative view of yield in polymers comes from the fact that a tensile strain induces a hydrostatic tension in the material and a corresponding increase in the sample volume. This in turn translates to an increase in the free volume, which increases the polymer mobility and effectively lowers the glass-transition temperature (Tg) of the polymer (alternatively it can be looked upon as increasing the free volume to the value it would have at the normal measured Tg). The increased mobility results in a lowering of the yield stress. Rnauss and Emri (35) used an integral representation of nonlinear viscoelasticity with a state-dependent variable related to free volume to model the yield behavior, with the free volume a function of temperature, time, and stress history. This model uses the concept of reduced time (see VISCOELASTICITY), where application of a tensile stress causes a volume dilatation and consequently causes the material time scale to change by a shift factor related to the magnitude of the applied stress. Yield occurs because the free-volume shift factor causes the molecular mobility to increase in such a way that yield can occur. 

The general issue of stability of composition of a solid solution is pursued further in the next subsection. Two potentially important physical effects are not taken into account in the discussion of energy variations with composition above. One of these effects arises from the possibility of atomic misfit of one species in the solution with respect to the other. The average unit cell dimension of a solid solution may depend on the composition, so that there is a stress-free volume change (or a more complex stress-free strain, perhaps) with change in concentration. For a spatially nonuniform composition, the associated stress-free strain field will be incompatible, in general, giving rise to a residual stress distribution. 

An example of nonlinear stress relaxation is shown in Fig. 16-17, where the ratio of time-dependent tensile stress to tensile strain is plotted logarithmically against time for different strains for cellulose monofilaments. (In this case the structure is no doubt preoriented.) The differences can be interpreted as due to a decrease in relaxation times with increasing stress, and the curves can be combined approximately into a composite curve by plotting with reduced variables, with a shift factor Os which decreases very rapidly with increasing strain. It is doubtful, how-ever, 2 whether the latter can be entirely related to fractional free volume in crystalline polymers as it is for amorphous polymers (Section Cl of Chapter 15). 

In Ref. [25], the asymmetrical periodic function is adduced, showing the dependence of shear stress x on shear strain (Fig. 4.2). As it has been shown before [19], asymmetry of this function and corresponding decrease of the energetic barrier height overcome by macromolecules segments in the elementary yielding act are due to the formation of fluctuation free volume voids during deformation (that is the specific feature of polymers [26]). The data in Fig. 4.2 indicate that in the initial part of periodic curve from zero up to the maximum dependence of x on displacement x can be simulated by a... 

The fundamental concept of the material clock or reduced time is similar to the principle described above in the discussion of time-temperature superposition. In the mechanical constitutive models, however, the change in the stress or deformation induces a shift in the material relaxation time. The fact that the time depends on the state of stress (or strain) or on its history leads to additional non-linearities in behavior from what is expected with, eg, the K-BKZ model. Physical explanations for the shifting material time are often based on free-volume ideas that are often invoked to explain time-temperature superposition. In addition, entropy changes have been invoked as have stress-activated processes. 

Orientation of the polymer may also influence the permeation properties. However, the overall effect is highly dependent upon crystallinity. For example, deformation of elastomers-has little effect on permeability until crystallization effects occur. " Orientation of amorphous polymers can result in a reduction in permeability of around 10-15%, whereas in crystalline polymers, e.g, poly(ethylene terephthalate), reductions of over 50% have been observed. At high degrees of orientation, time-dependent effects on permeability occur in both glassy and semi-crystalline polymers. These effects have been related to the relaxation recovery of strain-induced areas of free volume generated during orientation. ... 

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