Stochastic pore size distributions

Conventional filters, such as a coffee filter, termed depth filters , consist of a network of fibers and retain solute molecules through a stochastic adsorption mechanism. In contrast, most membranes for the retention of biocatalysts feature holes or pores with a comparatively narrow pore size distribution and separate exclusively on the basis of size or shape of the solute such membranes are termed membrane filters . Only membrane filters are approved by the FDA for sterilization in connection with processes applied to pharmaceuticals. Table 5.3 lists advantages and disadvantages of depth and membrane filters. 

If a large number of open-ended cylindrical pore segments (like the one in Fig. 2) are interconnected such that the diameter of any pore is independent of the size of neighbor pores, a so-called randomized, or stochastic, pore network is formed. Such a set can be assembled from a cohort obeying any stipulated pore diameter distribution function. If all the pore segments are of equal length with a connectivity of 4, a square network... 

Quantitative, nonempirical models of transport in porous materials require a more sophisticated description of the porous microstructure. For many materials the pore structure is stochastic, consisting of an ensemble of individual pores of random size distributed randomly throughout the material. Useful models of transport in these polymers can be based on percolation descriptions of porous media. Percolation descriptions have been used to describe fluid flow, electrical conduction, and phase transitions in random systems [26, 38]. 

Parallel bundles of pores (in which all pores of a given size or radius are bound to be equally accessible) are a highly unrealistic structural configuration. Stochastic networks are arrangements of pores into fiilly accessible inter-connected frameworks within which pores are assumed to be distributed randomly. In this way, the size of any pore is taken to be independent of its neighbours. A network may then be constructed to obey any stipulated distribution function by assigning pores from the distribution randomly to positions in the network. Stochastic networks are an attempt to incorporate the elements of randomness and chaos which are implicit to many porous media, in such a way as to retain a feasible computability. Modem computers (and now micro-computers) can readily compute mercury porosimetry into networks comprised of up to millions of pores 11.15). 

The above simple model of a steric exclusion mechanism was considered by several authors attempting to describe quantitatively the gel chromatographic separation process. Distribution coefficients were expressed on the basis of the model considerations of the dimensions of both the separated molecules and the pores of gel, as well as of the stochastic model approaches (for reviews see e.g.. Refs. 1, 3-6), and also of the thermodynamic reasoning on the changes of conformational entropy of macromolecules due to their transfer from the interstitial volume into the pores in the course of separation [7]. However, besides the steric exclusion from the pores, at least two other size-based mechanisms are operative in the ideal gel chromatography ... 

---