Porous polymers, diffusive transport

Saltzman, W. M., Pasternak, S. H., and Langer, R., Micro-structural models for diffusive transport in porous polymers, in Controlled-Release Technology, ACS Symposium Series 348... 

The main emphasis in this chapter is on the use of membranes for separations in liquid systems. As discussed by Koros and Chern(30) and Kesting and Fritzsche(31), gas mixtures may also be separated by membranes and both porous and non-porous membranes may be used. In the former case, Knudsen flow can result in separation, though the effect is relatively small. Much better separation is achieved with non-porous polymer membranes where the transport mechanism is based on sorption and diffusion. As for reverse osmosis and pervaporation, the transport equations for gas permeation through dense polymer membranes are based on Fick s Law, material transport being a function of the partial pressure difference across the membrane. 

Microstructural Models for Diffusive Transport in Porous Polymers... 

The results from this analysis can now be used to construct geometrically accurate models of the diffusive transport in porous polymers. Previous models of diffusion in these polymers have used an empirically determined tortuosity factor as a lumped parameter to account for the retardation of release by all mechanisms (7-8). 

When the active centre is surrounded by a layer of solid polymer, further propagation will be controlled by the rate of monomer diffusion through the polymer layer. Usually it will be retarded. With a porous polymer layer surrounding the active centres, monomer transport will be easier. These effects must be considered when highly crystalline polymers are formed, especially when the chains grow from a non-transferring monomer as, for example, with coordination polymerizations [56],... 

Membrane Separations. Separation processes using polymeric membranes (30) have become important techniques because of their simplicity and low consumption of energy in comparison to alternatives such as distillation. Membranes for ultrafiltration are porous, and no diffusive transport actually occurs through the polymer itself. However, for separation at the molecular level, diffusion through the polymer provides a possible mechanism for selective passage of the desired small molecule. Reverse osmosis for desalination of water can occur by this mechanism, and large commercial processes using this technique are now in operation. 

The accumulation and distribution of licpiid water in the polymer electrolyte membrane fuel cell (PEMFC) is highly dependent on the porous gas diffusion layer (GDL). The accmnulation of liquid water is often simply reduced to a relationship between liquid water saturation and capillary pressure however, recent experimental studies have provided valuable insights in how the microstmcture of the GDL as well as the dynamic behavior of the liquid play important roles in how water will be distributed in a PEMFC. Due to the importance of the GDL microstmcture, there have been recent efforts to provide predictive modeling of two-phase transport in PEMFCs including pore network modehng and lattice Boltzmann modeling, which are both discussed in detail in this chapter. Furthermore, a discussion is provided on how pore-scale infonnation is used to coimect microstmcture, transport and performance for macroscale upscaling. 

Problems involving transport through porous media occur in many disciplines. Although the most frequently studied individual problem is the movement of fluid through porous soils or rocks, examples of transport in porous media occur in many distinct types of systems. For example, tissues In the body are composed of cells and extracellular regions, two phases which often differ dramatically in resistance to diffusion of solutes. In recent years -as researchers have learned more about the structure of heterogeneous materials like soils, porous polymers, and animal tissues--the application of techniques developed to understand transport in porous media increase. 

The problem of non-steady state flow-which is characteristic of absorbency in polymers-is analogous to the non-steady state diffusion of solutes in a porous material [2]. Therefore, much of this chapter focuses on the solution of the equations for non-steady state diffusion In a porous medium. The most challenging aspect of the general problem of transport in porous polymers is relating the microscopic characteristics of the pore space (porosity, tortuosity, connectivity) to the macroscopic property of interest (permeability or diffusion coefficient). This chapter describes some of the methods that can be used to relate microstructure to transport. While most of the models presented are based on the general problem of diffusion in porous polymers, they can be adapted to explore the mathematically equivalent problem of absorbency in polymers. 

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. 

Vol. 1 Polymer Engineering Vol. 2 Filtration Post-Treatment Processes Vol. 3 Multicomponent Diffusion Vol. 4 Transport in Porous Catalysts... 

A fundamental difference exists between the assumptions of the homogeneous and porous membrane models. For the homogeneous models, it is assumed that the membrane is nonporous, that is, transport takes place between the interstitial spaces of the polymer chains or polymer nodules, usually by diffusion. For the porous models, it is assumed that transport takes place through pores that mn the length of the membrane barrier layer. As a result, transport can occur by both diffusion and convection through the pores. Whereas both conceptual models have had some success in predicting RO separations, the question of whether an RO membrane is truly homogeneous, ie, has no pores, or is porous, is still a point of debate. No available technique can definitively answer this question. Two models, one nonporous and diffusion-based, the other pore-based, are discussed herein. 

Nonporous gel membranes - these membranes do not contain a porous structure and thus diffusion occurs through the space between the polymer chains (the mesh). Obviously in this case, molecular diffusion rather than convective transport is the dominant mechanism of diffusion in these membranes. 

As seen, diffusion in nonporous gel membranes differs from that in macro-porous or microporous membranes. Various theories based on solute diffusion through the macromolecula r free volume in the membrane have been proposed. It is clear from these theories that structural parameters of the polymer network such as degree of swelling, molecular weight between crosslinks, and crystallinity in addition to factors such as solute size and solvent free volume play important roles in this type of transport. 

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