Volumetric relaxation

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.

In general, the prediction of the asymmetric volumetric relaxation processes in glassy materials requires that expressions such as (4-6) and (4-10) that describe the dependence of the characteristic relaxation time on free volume or entropy be extended so that they can describe the nonequilibrium state. Several different expressions for in the nonequilibrium glassy state have been proposed (Scherer 1992). One simple expression is obtained by applying the free volume expression (4-6) to the nonequilibrium state. Then... 

The Narayanaswamy expression fits volumetric relaxation data well over a range of temperatures for some glass formers (Rekhson et al. 1971 Mazurin 1977 Scherer 1992). But the equation has been criticized for its lack of a physical basis, as well as for its prediction of an Arrhenius temperature-dependence of the relaxation time at equilibrium. Furthermore, near the glass transition, the best-fit value of A // is much larger than the activation energy of the relevant molecular conformational transitions. 

Figure 3.1. Schematic illustration of temperature dependences of the specific volumes of amorphous materials. This figure also illustrates the effects of the nonequilibrium nature of glass structure, which results from kinetic factors. Glass 1 and Glass 2 are specimens of the same polymer, but subjected to different thermal histories. For example, Glass 1 may have been quenched from the melt very rapidly, while Glass 2 may either have been cooled slowly or subjected to volumetric relaxation via annealing ( physical aging ) in the glassy state.

Next we note that there are two physieally different sources of temperature and pressure dependence of the elastic constants of polymers. One, in common with that exhibited by all inorganic crystals, arises from anharmonic effects in the interatomic or intermolecular interactions. The second is due to the temperature-assisted reversible shear and volumetric relaxations under stress that are particularly prominent in glassy polymers or in the amorphous components of semi-crystalline polymers. The latter are characterized by dynamic relaxation spectra incorporating specific features for different polymers that play a central role in their linear viscoelastic response, which we discuss in more detail in Chapter 5. 

Both ESR and fluorescence spectroscopy give an indirect measure of motion in polymers as they make use of either spin label or probe methods. In the case of ESR, nitroxyl radicals dispersed (spin probe) in a polymer matrix or covalently bonded to the polymer chains (spin label) are employed to probe the local environment. Therefore, ESR spectra provide information on molecular motion and microstructure of polymer matrices. Similarly, fluorescent probes are sensitive to the glass structure. This is because photon emission increases when non-radiative processes are hindered by lack of mobUity of the probe. Interestingly, studies on poly (vinyl acetate) (PVAc) have shown that changes in the fluorescence intensities with aging time and temperature follow closely those observed by volumetric relaxation [85]. 

Various theoretical and empirical models have been derived expressing either charge density or charging current in terms of flow characteristics such as pipe diameter d (m) and flow velocity v (m/s). Liquid dielectric and physical properties appear in more complex models. The application of theoretical models is often limited by the nonavailability or inaccuracy of parameters needed to solve the equations. Empirical models are adequate in most cases. For turbulent flow of nonconductive liquid through a given pipe under conditions where the residence time is long compared with the relaxation time, it is found that the volumetric charge density Qy attains a steady-state value which is directly proportional to flow velocity... 

The volumetric power deposition calculated for bound water was appreciably greater—up to about five times—than that for free water the maximum difference occurs near the bound water relaxation frequency. This enhanced energy deposition is localized in the bound water shell and therefore may cause more damage than if it were distributed uniformly throughout the medium. But Dawkins et al. consider the enhancement of biological damage by localiza-... 

Equation (6.1.4) asserts that the volumetric flow rate is a superposition of two components. They are the electro-osmotic component proportional to the electric field intensity (voltage) with the proportionality factor u> and the filtrational Darcy s component proportional to —P with the hydraulic permeability factor i>. Teorell assumed both w and t> constant. Finally another equation, crucial for Teorell s model, was postulated for the dynamics of instantaneous electric resistance of the filter R(t). Teorell assumed a relaxation law of the type... 

Fluids that show elasticity to some extent are termed viscoelastic fluids, and some polymer solutions demonstrate such behavior. Elasticity is the tendency of a substance or body to return to its original form, after the applied stress that caused strain (i.e., a relative volumetric change in the case of a polymer solution) has been removed. The elastic modulus (Pa) is the ratio of the applied stress (Pa) to strain (-). The relaxation time (s) of a viscoelastic fluid is defined as the ratio of its viscosity (Pa s) to its elastic modulus. 

Hope et al. (116) presented a combined volumetric sorption and theoretical study of the sorption of Kr in silicalite. The theoretical calculation was based on a potential model related to that of Sanders et al. (117), which includes electrostatic terms and a simple bond-bending formalism for the portion of the framework (120 atoms) that is allowed to relax during the simulations. In contrast to the potential developed by Sanders et al., these calculations employed hard, unpolarizable oxygen ions. Polarizability was, however, included in the description of the Kr atoms. Intermolecular potential terms accounting for the interaction of Kr atoms with the zeolite oxygen atoms were derived from fitting experimental results characterizing the interatomic potentials of rare gas mixtures. In contrast to the situation for hydrocarbons, there are few direct empirical data to aid parameterization, but the use of Ne-Kr potentials is reasonable, because Ne is isoelectronic with O2-. 

Figure 6. Pressure dependencies of the bulk modulus obtained by the direct numerical differentiation of the in situ volumetric measurements of the glassy B203 under pressure ( relaxed modulus) in the two different runs of compression (solid symbols) and decompression (open symbols). The significant jumps of the effective bulk modulus between the final of compression and onset of decompression for both runs correspond to the jumps between relaxed and almost unrelaxed values. The inset shows pressure dependences of the first coordination number for B from the recent X-ray diffraction data. Both data are from Ref. [129].

Measurements. The morphology of the blends was studied by optical microscopy (Leitz Dialux Pol), transmission electron microscopy (Jeol 100 U), and scanning electron microscopy (Cambridge MK II). Ultramicrotome sections were made with an LKB Ultratome III. Samples for scanning electron microscopy were obtained by fracturing sheets at low temperature. The fracture surfaces were etched with a 30% potassium hydroxide solution to hydrolyse the polycarbonate phase. Stress-relaxation and tensile stress-strain experiments were performed with an Instron testing machine equipped with a thermostatic chamber. Relaxation measurements were carried out in flexion (E > 108 dyn/cm2) or in traction (E < 108 dyn/cm2). Prior to each experiment, the samples were annealed to obtain volumetric equilibrium. 

FIGURE 41 (a) Higuchi slope (b) normalized Higuchi slope (c) relaxational constant of Peppas and Sahlin versus percentage of excipient volumetric fraction for batch A (50-100(tm KC1 and 150-200 pm HPMC K4M). 

In hydrophilic matrices the drug threshold is less evident than the excipient threshold, which is responsible for the release control [73], In order to estimate the percolation threshold of HPMC K4M, different kinetic parameters were studied Higuchi rate constant, normalized Higuchi rate constant, and relaxation rate constant. The evolution of these release parameters has been studied as a function of the sum of the excipient volumetric percentage plus initial porosity. Recent studies of our research group have found the existence of a sample-spanning cluster of excipient plus pores in the hydrophilic matrix before the matrix is placed in contact with the liquid, clearly influences the release kinetics of the drug [73]. 

Figures 42-45 show changes in the different kinetic parameters the Higuchi rate constant, normalized Higuchi rate constant, and relaxation rate constant. To estimate the excipient percolation threshold, these parameters were plotted versus the excipient volumetric fraction plus initial porosity.

FIGURE 45 Relaxational constant of Peppas-Sahlin (mean + SD, n = 3) versus percentage of excipient volumetric fraction plus initial porosity for all batches studied. 

The latter result indicates that the volumetric strains can be relaxed to some extent by matrix creep. This contrasts with the 3-D case where complete compatibility of strains precludes such relaxation. The extent to which the relaxation occurs has not yet been calculated. However, if it is assumed that the relaxation can be complete so that the matrix volumetric strain is zero, then the fiber stress tends towards aal3lf and, therefore, the composite strain approaches... 

The volumetric, elastic and dynamic properties of internally and externally plasticised PVC were studied and compared with those of unplasticised PVC. The glass transition temperature for the plasticised samples was markedly lowered and this decrease was more important for the externally plasticised ones. The positions of the loss peaks from dielectric alpha-relaxation measurements confirmed the higher efficiency of the external plasticisation. However, the shape of the dielectric alpha-relaxation function was altered only for the internally plasticised samples. The plasticisation effect was linked with a decrease in the intensity of the beta-relaxation process but no important changes in the activation energy of this process were observed. The results were discussed. 47 refs. 

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