Diffusion of gases in polymers

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... 

J.H. Petropoulos, Mechanisms and Theories for Sorption and Diffusion of Gases in Polymers, in Polymeric Gas Separation Membranes, D.R. Paul and Y.P. Yampol skii (eds), CRC Press, Boca Raton, FL, pp. 17-82 (1994). 

Non-celluloslc Membranes. While the development of CA gas permeation membranes can be directly attributed to the development of water desalination membranes, the Invention of modified silicone membranes and polysulfone membranes was more Influenced by the extension of knowledge of transport, sorption and diffusion of gases In polymers (24-27). In principle, rubbery polymers exhibit the highest gas permeabilities at the lowest selectlvitles, and. 

Wilson [666, 667] and Bauman and Maron [47] show that it is possible to express the reaction rate as a function of film thickness, diffusion constant and solubility of oxygen in the film. When the thickness of the film is reduced to less than a certain value, the chemical reaction and not the diffusion becomes the controlling factor. The activation energy of the oxidation reaction amounts to 16—35 kcal mole-1, or even more, whereas the activation energy of the diffusion of gases in polymer films [39] is of the order of only 10 kcal mole-1. Control by diffusion is facilitated at higher temperatures by the decrease of oxygen solubility in the films. 

Diffusivities of gases in polymers [5] is a model of diffusion through a membrane, which separates two compartments of a continuous-flow permeation chamber. Essentially, at time / = 0, a penetrant is introduced into one compartment (the upstream compartment) and permeates through the membrane into a stream flowing through the other (downstream) compartment. 

This relationship shows that the diffusion coefficient is inversely proportional to the molecular size. Although not very accurate for the diffusion of gases in polymers, this relationship does illustrate the link between the diffusion coefficient and the size. Relative small differences in size may have a very large effect on the diffusion coefficient. For... 

The diffusivities of gases in polymers are related to a variety of parameters temperature, pressure, the nature of the gas, and the nature of the polymer. 

The flame retardant mechanism for phosphorus compounds varies with the phosphorus compound, the polymer and the combustion conditions (5). For example, some phosphorus compounds decompose to phosphoric acids and polyphosphates. A viscous surface glass forms and shields the polymer from the flame. If the phosphoric acid reacts with the polymer, e.g., to form a phosphate ester with subsequent decomposition, a dense surface char may form. These coatings serve as a physical barrier to heat transfer from the flame to the polymer and to diffusion of gases in other words, fuel (the polymer) is isolated from heat and oxygen. 

At temperatures above the Tt> the diffusion of gases in amorphous polymers may be estimated from the following expression ... 

Section IA summarizes the molecular model of diffusion of Pace and Datyner (1 2) which proposes that the diffusion of gases in a polymeric matrix is determined by the cooperative main-chain motions of the polymer. In Section IB we report carbon-13 nmr relaxation measurement which show that the diffusion of gases in poly(vinyl chloride) (PVC) - tricresyl phosphate (TCP) systems is controlled by the cooperative motions of the polymer chains. The correlation of the phenomenological diffusion coefficients with the cooperative main-chain motions of the polymer provides an experimental verification for the molecular diffusion model. 

Recently Pace and Datyner (12) advanced a molecular theory of diffusion that correlates the diffusion of gases in a polymeric matrix with the cooperative motions of the polymer chains. The theory proposes that the diffusant molecule can move... 

In conclusion, the average rotating-frame relaxation rate of the methylene- and methine-carbons correlate with the apparent diffusion coefficients for H2 and CO in PVC when the main-chain molecular motions of the polymer are altered by an additive. (Fig. 2). These results provide experimental evidence that main-chain cooperative motions control the diffusion of gases through polymers. In Section IIB we will show that perturbation of polymeric cooperative motions is not restricted to classical plasticizing additives. 

The gas-polymer-matrix model for sorption and transport of gases in polymers is consistent with the physical evidence that 1) there is only one population of sorbed gas molecules in polymers at any pressure, 2) the physical properties of polymers are perturbed by the presence of sorbed gas, and 3) the perturbation of the polymer matrix arises from gas-polymer interactions. Rather than treating the gas and polymer separately, as in previous theories, the present model treats sorption and transport as occurring through a gas-polymer matrix whose properties change with composition. Simple expressions for sorption, diffusion, permeation and time lag are developed and used to analyze carbon dioxide sorption and transport in polycarbonate. 

In Section I we introduce the gas-polymer-matrix model for gas sorption and transport in polymers (10, LI), which is based on the experimental evidence that even permanent gases interact with the polymeric chains, resulting in changes in the solubility and diffusion coefficients. Just as the dynamic properties of the matrix depend on gas-polymer-matrix composition, the matrix model predicts that the solubility and diffusion coefficients depend on gas concentration in the polymer. We present a mathematical description of the sorption and transport of gases in polymers (10, 11) that is based on the thermodynamic analysis of solubility (12), on the statistical mechanical model of diffusion (13), and on the theory of corresponding states (14). In Section II we use the matrix model to analyze the sorption, permeability and time-lag data for carbon dioxide in polycarbonate, and compare this analysis with the dual-mode model analysis (15). In Section III we comment on the physical implication of the gas-polymer-matrix model. 

Figure 2.4 Simulated trajectories of helium, oxygen and methane molecules during a 200-ps time period in a poly(dimethylsiloxane) matrix [9]. Reprinted with permission from S.G. Charati and S.A. Stern, Diffusion of Gases in Silicone Polymers Molecular Dynamic Simulations, Macromolecules 31, 5529. Copyright 1998, American Chemical Society...

The sorption coefficient (K) in Equation (2.84) is the term linking the concentration of a component in the fluid phase with its concentration in the membrane polymer phase. Because sorption is an equilibrium term, conventional thermodynamics can be used to calculate solubilities of gases in polymers to within a factor of two or three. However, diffusion coefficients (D) are kinetic terms that reflect the effect of the surrounding environment on the molecular motion of permeating components. Calculation of diffusion coefficients in liquids and gases is possible, but calculation of diffusion coefficients in polymers is much more difficult. In the long term, the best hope for accurate predictions of diffusion in polymers is the molecular dynamics calculations described in an earlier section. However, this technique is still under development and is currently limited to calculations of the diffusion of small gas molecules in amorphous polymers the... 

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],... 

The second key factor determining permeability in polymers is the sorption coefficient. The data in Figure 2.18 show that sorption coefficients for a particular gas are relatively constant within a single family of related materials. In fact, sorption coefficients of gases in polymers are relatively constant for a wide range of chemically different polymers. Figure 2.25 plots sorption and diffusion coefficients of methane in Tanaka s fluorinated polyimides [23], carboxylated polyvinyl trimethylsiloxane [37] and substituted polyacetylenes [38], all amorphous glassy polymers, and a variety of substituted siloxanes [39], all rubbers. The diffusion... 

S.G. Charati and S.A. Stern, Diffusion of Gases in Silicone Polymers Molecular Dynamic Simulations, Macromolecules 31, 5529 (1998). 

A correlation between surface and volume processes is described in Section 5. The atomic-molecular kinetic theory of surface processes is discussed, including processes that change the solid states at the expense of reactions with atoms and molecules of a gas or liquid phase. The approach reflects the multistage character of the surface and volume processes, each stage of which is described using the theory of chemical kinetics of non-ideal reactive systems. The constructed equations are also described on the atomic level description of diffusion of gases through polymers and topochemical processes. 

All the known data on the diffusivity of gases in various polymers were collected by Stannett (1968). 

Typical values for diffusion constants and activation energies for gases in natural rubber, polyethylene, and polystyrene are shown in Table 3. It can be seen that as the size of the penetrant increases, the diffusion constant decreases but the activation energy increases. As a result, at high temperatures, the rate of diffusion of gases in molten polymers will not be very different from that for conventional liquids. 

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