Pore-boundary interactions

Figure 11.2. Dependence of the type of pore/boundary interaction on microstructural parameters (pore size and grain size) when pores move by surface diffusion. ...

Svoboda, J. and Riedel, H., Pore-boundary interactions and evolution equations for the porosity and the grain size during sintering, Acta MetalL Mater., 40, 2829-40, 1992. 

To discuss even a fraction of these possibilities in any detail is clearly not within the scope of this book. What is attempted instead is to consider in some detail one of the more important grain boundary interactions namely, that between the grain boundary and pore. 

Brook RJ (1969) Pore-grain boundary interactions and grain growth. J Am Ceram Soc... 

The above specific examples are only for illustrative purposes. These examples show how to implement the technology of Fokker-Planck formalism and how to apply the derived equations for a given situation. Variations in the shape of the pore, entropic barrier, pore-polymer interaction, electrical forces inside and outside the pore, hydrodynamic flows, electroosmotic flows, pressure gradients, polymer sequence, boundary conditions, etc., can be readily addressed by performing calculations analogous to those presented above. 

In the last section of this chapter, we summarize diffusion affected by solute-boundary interactions, which is the third important group of interactions. Solute-boundary interactions occur in porous solids with fluid-filled pores. They include such diverse phenomena as Knudsen diffusion, capillary condensation, and molecular sieving. Because these phenomena promise high selectivity for separations, they are an active area for research. They and the other interactions illustrate the chemical factors that can be hidden in the diffusion coefficients which are determined by experiment. 

I have tried to force an organization on these examples as follows. In Section 6.4.1, I have discussed the simplest empirical methods of organizing experimental results. In Section 6.4.2, I have reviewed theories for solute diffusion in a solvent trapped within cylindrical pores in an impermeable solid. In this case, solute-solvent interactions still control diffusion and the solid only imposes boundary conditions. Cases where the interactions are between the diffusion solute and the pores boundaries are covered in Section 6.4.3. Finally, cases not of cylindrical pores but of other composite structures are described in Section 6.4.4. 

Kingery WD and Francois B 1965 The sintering of crystaiiine oxides, i. interactions between grains boundaries and pores Sintering and Related Phenomena ed G C Kuczynski, N A Hooton and C F Gibbon (New York Gordon and Breach) pp 471-98... 

Two macromolecular computational problems are considered (i) the atomistic modeling of bulk condensed polymer phases and their inherent non-vectorizability, and (ii) the determination of the partition coefficient of polymer chains between bulk solution and cylindrical pores. In connection with the atomistic modeling problem, an algorithm is introduced and discussed (Modified Superbox Algorithm) for the efficient determination of significantly interacting atom pairs in systems with spatially periodic boundaries of the shape of a general parallelepiped (triclinic systems). 

Strong preference to block copolymer. A cylindrical pore with a size of Rex x Lz was used in the simulation, where Rex is the exterior radius of pore and Lz = 50 is the length of pore. The periodic boundary condition was applied in the axial direction ab = 0.5/cgT is the interaction energy between A and B segments, while as = — bs =... 

We notice that stress tensors are not a priori symmetric for (16) and that c)J. symmetric tensors. Further, the 3rd order microstress tensor Ss is normally related to boundary micro tractions, even if, in some cases, it could express weakly non-local internal effects % is interpreted as an externally controlled pore pressure (s includes interactive forces between the gross and fine structures. 

The transport mechanisms through zeolite membranes depend on different variables such as operation conditions (especially temperature and pressure), membrane pore size distribution, characteristics of the pore surface of the zeohtic-channel network (hydrophilicity/hydrophobicity ratio), as well as the characteristics of the crystal boundaries and the characteristics of the permeating molecules (kinetic diameter, molecular weight, vapor pressure, heat of adsorption), and their interactions in the mixture. 

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