Glassy polymers correlation with

When a polymer is initially in the dry state, solvent must penetrate into the network by diffusion. When the polymer is rubbery, this diffusion process is rate limiting. If the polymer is in the form of a thin slab, then solvent uptake will initially be correlated with the square root of time [30,31]. When the polymer is in an initially glassy state, swelling kinetics become more complicated [30, 32-34]. While solvent diffusion into the polymer still initiates the swelling... 

Microhardness (MH), has been shown to be a convenient additional technique to detect accurately the ferro to paraelectric phase changes in these copolymers. The increase of MH as a function of VF2 polar sequences observed at room temperature is correlated with the contraction of the p-all-trans unit cell On the other hand, the fast exponential decrease of MH with increasing temperature, observed above Tc, is similar to that obtained for glassy polymers above Tg and suggests the existence of a liquid crystalline state in the high temperature paraelectric phase. This phase is characterized by a disordered sequence of conformational isomers (tg-, tg+, tt) as discussed for Condis crystals [109]. 

Carbon-13 rotating-frame relaxation rate measurements are used to elucidate the mechanism of gas transport in glassy polymers. The nmr relaxation measurements show that antiplasticization-plasticization of a glassy polymer by a low molecular weight additive effects the cooperative main-chain motions of the polymer. The correlation of the diffusion coefficients of gases with the main-chain motions in the polymer-additive blends shows that the diffusion of gases in polymers is controlled by the cooperative motions, thus providing experimental verification of the molecular theory of diffusion. Carbon-13 nmr relaxation... 

Section IIA summarizes the physical assumptions and the resulting mathematical descriptions of the "concentration-dependent (5) and "dual-mode" ( 13) sorption and transport models which describe the behavior of "non-ideal" penetrant-polymer systems, systems which exhibit nonlinear, pressure-dependent sorption and transport. In Section IIB we elucidate the mechanism of the "non-ideal" diffusion in glassy polymers by correlating the phenomenological diffusion coefficient of CO2 in PVC with the cooperative main-chain motions of the polymer in the presence of the penetrant. We report carbon-13 relaxation measurements which demonstrate that CO2 alters the cooperative main-chain motions of PVC. These changes correlate with changes in the diffusion coefficient of CO2 in the polymer, thus providing experimental evidence that the diffusion coefficient is concentration dependent. 

Correlation of the permeation properties of a wide variety of polymers with their free volume is not possible [32], But, within a single class of materials, there is a correlation between the free volume of polymers and gas diffusion coefficients an example is shown in Figure 2.24 [33], The relationship between the free volume and the sorption and diffusion coefficients of gases in polymers, particularly glassy polymers, has been an area of a great deal of experimental and theoretical work. The subject has recently been reviewed in detail by Petropoulos [34] and by Paul and co-workers [35,36],... 

Figure 4.7 Correlation between O2, N2 and CH4 permeability reduction rates and their volumetric relaxation rates for thin films of various glassy polymers [49], Reproduced with permission of Elsevier.

Because of the assumed dual sorption mechanism present in glassy polymers, the explicit form of the time dependent diffusion equation in these polymers is much more complex than that for rubbery polymers (82-86). As a result exact analytical solutions for this equation can be found only in limiting cases (84,85,87). In all other cases numerical methods must be used to correlate the experimental results with theoretical estimates. Often the numerical procedures require a set of starting values for the parameters of the model. Usually these values are shroud guessed in a range where they are expected to lie for the particular penetrant polymer system. Starting from this set of arbitrary parameters, the numerical procedure adjusts the values until the best fit with the experimental data is obtained. The problem which may arise in such a procedure (88), is that the numerical procedures may lead to excellent fits with the experimental data for quite different starting sets of parameters. Of course the physical interpretation of such a result is difficult. 

From the point of view of earlier discussions, namely the true prediction of diffusion coefficients for volatile and nonvolatile organic penetrants in glassy polymers, the diffusion equations derived in the framework of the DST have only a limited usefulness. That means that, because the parameters of the DST models are not directly related to first principles , the equations can be used with success to correlate experimental results, but not to truly predict diffusion coefficients. 

Anew experimental method based on the polarization-selective photochromic reactions is proposed to monitor extremely slow reorientation dynamics of molecular tracers in glassy polymer matrix. The correlations between the local relaxation processes of polymers and the reorientation dynamics of the tracers with different sizes are found from the experimental results obtained by this method. 

In the absence of specific penetrant/polymer interactions, solubility of the penetrant is determined mainly by its chemical namre and depends on condensability, which is represented by boiling temperamre (Tb), critical temperature (Ter), or Lennard-Jones constant (s/fe) [7,8]. It is known that in the hydrocarbon series the increase in condensability is accompanied by a parallel increase in the size of molecules (Table 9.1 [9-17]). It is therefore not surprising that in both glassy and rubbery polymers correlations of hydrocarbon solubility in the polymers with condensability and sizes of hydrocarbon molecules are observed (Figures 9.1 through 9.3). 

Figure 5. Correlation of the apparent solubility at 20 atm and 35 °C with the critical temperatures of various penetrants in a number of glassy polymers polycarbonate,...

The diffusion coefficient of small penetrants in glassy polymers can also be correlated with the polymer free volume. In view of the fact that experimental techniques for the determination of the free volume are inherently difficult, Shah, Stern, and Ludovice (Shah, V.M. Stern, S.A. Ludovice, P.J., submitted for publication in Macromolecules) have utilized the detailed atomistic modeling of relaxed polymer glasses developed by Theodorou and Suter ( 2, 3) to estimate the free volume available in polymer glasses for the diffusion of small molecules. 

These observations on PVC/penetrant systems suggest a correlation of sorption kinetics with the generalized isotherm for swelling penetrants in glassy polymers, as shown schematically in Figure 9. For sorption into an initially penetrant-free glassy... 

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