Penetrant transport through polymers

The study of the transport of penetrant molecules through polymers [1,2] is important in many areas of technology. There are two types of industrially important polymeric systems for which such transport phenomena are crucial ... 

For a polymer blend, the study of sorption, diffusion, and permeation of penetrant molecules provides additional means for its characterization. The diffusion and transport through polymer blends depend upon the blend composition, miscibility, and phase morphology. Most polymer blends, however, are heterogeneous, and consists of a polymeric matrix in which the second phase is embedded. 

Equation 2 is an analytical statement of the solution-diffusion mqdel of penetrant transport in polymers, which is the most widely accepted explanation of the mechanism of gas permeation in nonporous polymers (75). According to this model, penetrants first dissolve into the upstream (i.e, high pressure) face of Ae film, diffuse through the film, and desorb at the downstream (Le. low pressure) face of the film. Diffusion, the second step, is the rate limiting process in penetrant permeation. As a result, much of the fundamental research related to the development of polymers with improved gas separation properties focuses on manipulation of penetrant diffusion coefficients via systematic modification of polymer chemical structure or superstructure and either chemical or thermal post-treatment of polymer membranes. Many of the fundamental studies recorded in this book describe the results of research projects to explore the linkage between polymer structure, processing history, and small molecule transport properties. 

As far as the rate of penetrant transport through glassy polymers is coneemed, it is assumed that material contained in the microvoids or holes is completely immobilized and does not contribute to the diffusive flux. It is further assumed that diffusion of the mobile species follows Pick s first law in terms of the concentration gradient of and a constant diffusivity. Thus, the flux in the x direction is... 

When a polymer film is exposed to a gas or vapour at one side and to vacuum or low pressure at the other, the mechanism generally accepted for the penetrant transport is an activated solution-diffusion model. The gas dissolved in the film surface diffuses through the film by a series of activated steps and evaporates at the lower pressure side. It is clear that both solubility and diffusivity are involved and that the polymer molecular and morphological features will affect the penetrant transport behaviour. Some of the chemical and morphological modification that have been observed for some epoxy-water systems to induce changes of the solubility and diffusivity will be briefly reviewed. 

Other areas of technology where the transport of small molecules through polymers plays a key role include foams (where small molecules are used as blowing agents for foam expansion [9-11] and any gas trapped in the cells of a closed-cell foam affects key properties such as the thermal conductivity [12]), plasticization [13,14], removal of process solvents, residual monomers or other impurities by techniques such as supercritical fluid extraction [15,16], biosensors, drug implants, and polymer electrolytes (where the penetrants are ionic). 

Integration of Eq. (61.1) for the desired geometry and boundary conditions yields the total rate of permeation of the penetrant gas through the polymer membrane. Integration of Eq. (61.2) yields information on the temporal evolution of the penetrant concentration profile in the polymer. Equation (61.2) requires the specification of the initial and boundary conditions of interest. The above relations apply to homogeneous and isotropic polymers. Crank [3] has described various techniques of solving Pick s equations for different membrane geometries and botmdary conditions, for constant and variable diffusion coefficients, and for both transient and steady-state transport. 

Small molecule transport through nonporous polymers proceeds by the solution-diffusion mechanism. This a three-step mechanism where penetrant molecules... 

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