Free volume effects

The importance of free volume effects in diffusional processes at a molecular level should be further emphasized. An empirical relationship between viscosity and free volume was proposed by Doolittle ... 

In most investigations in solvents of medium or high viscosity, or in polymers above the glass transition temperature, the fluorescence quantum yields were in fact found to be a power function of the bulk viscosity, with values of the exponent x less than 1 (e.g. for p-N,N-dimethylaminobenzylidenemalononitrile, x = 0.69 in glycerol and 0.43 in dimethylphthalate). This means that the effective viscosity probed by a molecular rotor appears to be less than the bulk viscosity >/ because of free volume effects. 

Plasticizers are compounds which increase the flexibility and process -bility of polymers. It has been postulated that the added plasticizer reduces the intermolecular forces in PVC and increases the free volume. Effective plasticizers, like effective solvents, have solubility parameters within 1.8 H (Hildebrand units) of that of the polymer. 

The calculation of the solubility of gases and other small molecules in various polymers showed that for each polymer the relative solubility of the compounds was well predicted, but one polymer-specific correction had to be fitted. The results of this study are shown in Fig. 10.8. The correction constant may have to do with the missing combinatorial term, or with free-volume effects in polymers, or with structural differences of polymers, or with a combination of several such effects. The lack of a temperature dependence suggests that it is mainly of entropic nature. Unfortunately, no clear relationship between the value of... 

This relation holds well for semicrystalline polymers for amorphous polymers, it holds for T > Tg + 100°C. Below this region free volume effects predominate necessitating the use of the Arrhenius-WLF equation... 

Postcuring at elevated temperatures after a room temperature cure is a common process in epoxy technology, and this can moderately increase the Tf in some systems.26 Such effects could be due to secondary reactions (irreversible) or to free volume effects (reversible). These effects could also be realized during the normal aging of the epoxy system in service. One should be careful, however, in assuming that a low-temperature cure followed by an elevated-temperature postcure (cure condition 1) will provide properties equivalent to only a high-temperature cure (cure condition 2). As explained in the previous section, the types... 

In describing the polymer-polymer interaction parameters for pairs which are normally incompatible as those discussed in this work, it therefore appears that the free volume (or the equation-of-state) contribution can usually be neglected except when the pair is on the verge of compatibility. This is in a marked contrast to polymer-solvent systems where the free volume effect is usually very large. From this follows that the dependence of A for polymer-polymer pairs on concentration or on temperature would also be fairly small. Table I shows only a modest variation of A with a change in Wi from 0.1 to 0.9. The relatively more pronounced variation of A for NR/PS as compared with other two pairs still arises mostly from the contact enthalpy term and reflects the larger Sx/s2 ratio for this system. 

The presence of a temporary network structure manifests itself through the first factor in the right hand side of Eq. 17. It comes from the h (t) component of the relaxation function. The second factor results from fast non-isotropic motions of monomeric imits which give rise to the (t r(t) function defined in equations (6) and (9). It must be noticed that the reference temperature Ti = Tg(,xi,2) +50 which appears in NMR properties, is close to the reference temperature Tj introduced from viscoelastic measiurements [11]. The second factor reflects a free volume effect it depends necessarily on an expansion coefficient which is about equal to 10-3K. 

Eisenbach C. D., Dimberger, K., and Ficht, K. (1998). Matrix relaxation and local free volume effects in mono- and bichromophoric azobenzene polymers. Polym. Prepr. 39, 279-280. 

The existence of UCST is typically attributed to the energy differences between polymer and solvent and of LCST to the so-called free-volume effects, which are dne to the differences in size and free-volume between polymer and solvent. Free-volume effects are small for nonpolymeric solutions and are discussed in conjunction with free-volume-based activity coefficient models in Section 16.4. The LCST was first discovered by Freeman and Rowlinson only about 40 years ago, but is now considered to be a universal phenomenon of polymer-solvent systems at high temperatures. In some cases, it is not observed if the polymer degrades before reaching the LCST. 

Vetere " proposed combining the FH equation (empirically modified to account for free-volume effects) with the NRTL expression for the energetic effects. The two NRTL parameters were correlated with the solubility parameters of the components. The relative importance of the combinatorial and residual contributions was analyzed and satisfactory results (for both VLB and LLE) are obtained for some binary systems, including aqueous polymer solutions. This recent approach is under development. 

The improvement of the energy term of the FH equation is important. Local-composition terms like those appearing in NRTL, UNIQUAC, and UNIFAC models provide such an improvement. In addition, however, free-volume effects should be incorporated into the combinatorial term. The free-volume concept is discussed in Section 16.4.1 and some models that incorporate both free-volume and local composition effects are discussed in Sections 16.4.2 through 16.4.4. 

Therefore, one can expect two types of plasticizing action the more conventional type known in the prior art where a viscosity reduction arises from free volume effects (backbone plasticizers) and a second that acts ideally by diminishing the interchain association of the ionic groups on the polymer chain (ionic domain plasticizers). One would... 

For the naphthalene-ethylene and biphenyl-carbon dioxide systems, the effect of the binary liquid-gas critical point is rapidly diminished as the pressure is increased above the UCEP pressure. For the naphthalene-ethylene system, where the UCEP is at a modest pressure, the solid-fluid equilibrium curve quickly attains a limiting solubility at pressures greater than the UCEP pressure. For the biphenyl-carbon dioxide system, where the UCEP pressure is more than twice that of the naphthalene-ethylene system, the solid-fluid equilibrium curve decreases sharply to lower concentrations of heavy component as the pressure is increased above the UCEP pressure. This solubility behavior is a consequence of a free volume effect that results from the large disparity in size between biphenyl and carbon dioxide (Ranee and Cussler, 1974 von Tapavicza and Prausnitz, 1976). At very high pressures, increasing the pressure further reduces the free volume between carbon dioxide molecules available to the biphenyl molecules and reduces the solubility of biphenyl. Carbon dioxide essentially squeezes out the biphenyl at these high pressures. 

Despite its higher polarizability and critical temperature, propane is a much poorer solvent than ethylene for this copolymer (see table 3.4). It is the polar interactions between ethylene, which has a quadrupole moment, and the methyl acrylate groups in the backbone of the copolymer, which have dipole moments, that dominate free volume effects. There is no significant difference between the molar densities of propane and ethylene at the temperatures and... 

The van der Waals Equation and Free Volume Effects More Formal Treatments of Solutions Practical Characterization of Polymers and Solvents Additional Reading... 

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