For rubbery and glassy polymers

The following two anbsections provide physical interpretations of the forms of soiption isotherms and oonoentration-dependent diffusion coefficients observed for rubbery and glassy polymers, respectively. These sections are not requited for simulation of module operations if a complete set of empirical pressure, temperature, and composition-dependent permeation data are available. A simple polynomial fit of permeability data as a function of all operating variables would suffice for design and simulation. 

Figure 4.1 Schematic illustration of how the (a) diffusion coefficient of penetrants depend on their size in rubbery and glassy polymers and (b) solubility coefficients for penetrants depend on their condensability.

Table 4.2 illustrates the various selectivity factors for some typical rubbery polymers, that is, silicone rubber, poly(dimethyl siloxane), and natural rubber, polyiso-prene, and a glassy polymer, polysulfone. Here, we consider the important 02/N2 pair and several pairs involving C02 that will be our focus later. In all the cases, the solubility selectivity is greater than unity and there is not a large difference between rubbery and glassy polymers. For most of these pairs, the diffusion selectivity is greater than unity, but there are some exceptions for C02/02 and C02/N2 that reflect... 

The above-mentioned inverse selectivity/permeability relationship of polymers has been summarized by Robeson by means of log-log plots of the overall selectivity versus the permeability coefficient, where A is considered to be the more rapidly permeating gas. These plots were made for a variety of binary gas mixtures from the list He, H2, O2, N2, C02, and CH4, and for a large number of rubbery and glassy polymer membranes. Such representations, shown in Fig. 8 and Fig. 9 are often referred to as upper bound plots (Robeson, 1991). The upper bound lines clearly show the inverse selectivity/permeability relationship of polymer membranes. While these plots were prepared in 1991, only small advances have been made to push the upper bound higher since that time. 

This classification should in principle be valid for both rubbery and glassy polymers. However, as will be shown in this section, until now more detailed and true microscopic" treatments have mainly been models for diffusion in rubbery polymers. An explanation for this may be the much more complex nature of the diffusion process in glassy polymers (9,13,32-34). 

Considerable effort has been made during the last two decades to develop a "microscopic" description of gas diffusion in polymers, which is more detailed than the simplified continuum viewpoint of Fick s laws. It has been known for a long time that the mechanism of diffusion is very different in "rubbery" and "glassy" polymers, i.e., at temperatures above and below the glass-transition temperature, Tg, of the polymers, respectively. This is due to the fact that glassy polymers are not in a true state of thermodynamic equilibrium, cf. refs. (1,3,5,7-11). Some of the models and theories that have been proposed to describe gas diffusion in rubbery and glassy polymers are discussed below. The models selected for presentation in this review reflect only the authors present interests. 

The dependence of permeability, diffusion, and solubility coefficients on penetrant gas pressure (or concentration in polymers) is very different at temperatures above and below the glass transition temperature, Tg, of the polymers, i.e., for mbbery and glassy polymers, respectively. Thus, when the polymers are in the rubbery state the pressure dependence of these coefficients depends, in turn, on the gas solubility in polymers. For example, as mentioned in Section 61.2.4, if the penetrant gases are very sparsely soluble and do not significantly plasticize the polymers, the permeability coefficients as well as the diffusion and solubility coefficients are independent of penetrant pressure. This is the case for supercritical gases with very low critical temperatures (compared to ambient temperature), such as the helium-group gases, Ha, Oa, Na, CH4, etc., whose concentration in rubbery polymers is within the Heruy s law limit even at elevated pressures. 

It has been shown in a previous section that, in most cases of practical interest, the rate of gas permeation through nonporous polymer membranes is cOTitrolled by the diffusion of the penetrant gas in the polymer matrix. Many theoretical models have been proposed in the literature to describe the mechanisms of gas diffusion in polymers on a molecular level. Such models provide expressions for gas diffusion coefficients, and sometimes also for permeability coefficients, derived from free volume, statistical-mechanical, energetic, structural, or other considerations. The formulation of these coefficients is complicated by the fact that gas transport occurs by markedly different mechanisms in rubbery and glassy polymers. 

A very large body of data on the gas permeability of many rubbery and glassy polymers has been published in the literature. These data were obtained with homopolymers as well as with copolymers and polymer blends in the form of nonporous dense (homogeneous) membranes and, to a much lesser extent, with asymmetric or composite membranes. The results of gas permeability measurements are commonly reported for dense membranes as permeability coefficients, and for asymmetric or composite membranes as permeances (permeability coefficients not normalized for the effective membrane thickness). Most permeability data have been obtained with pure gases, but information on the permeability of polymer membranes to a variety of gas mixtures has also become available in recent years. Many of the earlier gas permeability measurements were made at ambient temperature and at atmospheric pressure. In recent years, however, permeability coefficients as well as solubility and diffusion coefficients for many gas/polymer systems have been determined also at different temperatures and at elevated pressures. Values of permeability coefficients for selected gases and polymers, usually at a single temperature and pressure, have been published in a number of compilations and review articles [27—35]. 

Fig. 40. Permeability as a function of molar volume for a rubbery and glassy polymer, illustrating the different balance between sorption and diffusion in these pol5rmer types. The rubbery membrane is highly permeable the permeability increases rapidly with increasing permeant size because sorption dominates. The glassy membrane is much less permeable the permeability decreases with increasing permeant size because diffusion dominates (85)., 0.335 X 10 i m mol / 10" cm (STP) cm ...

Therefore, most commercial solution-diffusion membranes contain polymer materials, which can be divided into rubbery and glassy polymers. Glassy polymers show very attractive separation characteristics. Rubbery polymers show comparably low selectivity with high permeability for common gas pairs such as O2/N2, H2/CH4, CO2/CH4, and so on. > Of the glassy polymers, polyimides have been found to be very promising as... 

This article focuses on transport that proceeds by the solution-diffusion mechanism. Transport by this mechanism requires that the penetrant sorb into the polymer at a high activity interface, diffuse through the polymer, and then desorb at a low activity interface. In contrast, the pore-flow mechanism transports penetrants by convective flow through porous polymers and will not be described in this article. Detailed models exist for the solution and diffusion processes of the solution-diffusion mechanism. The differences in the sorption and transport properties of rubbery and glassy polymers are reviewed and discussed in terms of the fundamental differences between the intrinsic characteristics of these two types of polymers. 

Log Do may be related to Ej for a wide range of rubbery and glassy polymers and for a variety of permeants by a pair of Arrhenius equations which are valid for values of Dq over a range of more than nine orders of magnitude. 

Blending of ABS with an acrylic material such as poly(methyl methacrylate) can in some cases allow a matching of the refractive indices of the rubbery and glassy phases and providing that there is a low level of contaminating material such as soap and an absence of insoluble additives a reasonable transparent ABS-type polymer may be obtained. More sophisticated are the complex terpolymers and blends of the MBS type considered below. Seldom used on their own, they are primarily of use as impact modifiers for unplasticised PVC. 

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