Free volume increase with stress

The cause for the occurrence of the steps in the heat capacity and the expansion coefficient is easily seen. Cooling a sample below Tg results in a freezing of the o-modes. The observations tell us that the a-modes affect not only the shape of a sample, but also its volume and its enthalpy. This is not at all surprising. If segments move, they produce an additional volmne in their neighborhoods. In the literature, this is often called a free volume in order to stress that it is not occupied by the hard cores of the monomers. The free volume increases with temperature because motions intensify, that... 

If an increase in free volume arising from stress-induced dilatation contributes to the relaxation process in the same manner as dilatation by raising the temperature, we can estimate the shift in relaxation time with Equation 2 by substituting for the fractional free volume, f,... 

It is postulated that the reduction in A is related to an increase in molecular free volume associated with the higher mean stress level this increase in free volume, in turn, is believed to enhance chain segmental movements responsible for fracture energy absorption and overall toughening. 

Analogous results have been found for stress relaxation. In fibers, orientation increases the stress relaxation modulus compared to the unoriented polymer (69,247,248,250). Orientation also appears in some cases to decrease the rate, as well as the absolute value, at which the stress relaxes, especially at long times. However, in other cases, the stress relaxes more rapidly in the direction parallel to the chain orientation despite the increase in modulus (247.248,250). It appears that orientation can in some cases increase the ease with which one chain can slip by another. This could result from elimination of some chain entanglements or from more than normal free volume due to the quench-cooling of oriented polymers. 

Pons et al. have studied the effects of temperature, volume fraction, oil-to-surfactant ratio and salt concentration of the aqueous phase of w/o HIPEs on a number of rheological properties. The yield stress [10] was found to increase with increasing NaCl concentration, at room temperature. This was attributed to an increase in rigidity of films between adjacent droplets. For salt-free emulsions, the yield stress increases with increasing temperature, due to the increase in interfacial tension. However, for emulsions containing salt, the yield stress more or less reaches a plateau at higher temperatures, after addition of only 1.5% NaCl. 

DSC measurements showed that the crystallization ability of this interphase region was reduced by the silane modification of the glass beads. Despite an increase in the amount of amorphous material with increasing number of silane layers, a decrease in the intensity of the fourth lifetime was observed. This decrease in the free volume is in accordance with the earlier observed reduced mobility in the interphase region measured by dynamic-mechanical spectroscopy in the melt state [9,10] and creep and stress relaxation measurements in the solid state [12]. 

A linear decrease of KIc with an increase in crosslink density was reported for model PU based on triisocyanate and diols of various molar masses (Bos and Nusselder, 1994), and for epoxy networks (Lemay et al., 1984). It was suggested that the dilational stress field at the crack tip may induce an increase in free volume and a devitrification of the material. A linear relationship between GIc and M XJ2 was verified for these systems, although other empiric equations were found in other cases (Urbaczewski-Espuche et al., 1991). 

The same behavior is observed if the pressure is varied. As the pressure is increased, the free volume between the molecules is reduced, slowing down molecular movement. Here, an increase in pressure is equivalent to a decrease in temperature. In the melt state, the viscosity of a polymer increases with pressure. Figure 1.31 [7] is presented to illustrate the effect of pressure on stress relaxation. 

Even with the gaps in the theory, the fundamental concepts developed for continuum systems are substantially the same for systems of pharmaceutical powders. Powders confined and subjected to a compressive stress will rearrange until there is insufficient free volume to allow translation of particles. As the stress increases, particles make contacts which increase in area with stress, they will deform elastically (i.e.. reversibly) with Young s modulus (E) as the linear proportionality constant. The normal strain (eO in the loading direction for a material undergoing elastic deformation under uniaxial tension (cr) may be expressed as (2) ... 

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