THERMODYNAMICS OF FORMATION OF POROUS POLYMERIC MEMBRANE BY PHASE-SEPARATION METHOD .3. PORE FORMATION BY CONTACTING SECONDARY PARTICLES - THEORY AND ITS COMPARISON WITH EXPERIMENTS

An attempt was made (1) to establish a theory of pore characteristics, including pore size distribution N(r) (r, radius of pore) for porous polymeric membranes, prepared by the phase separation method, using two-phase volume ratio R (=- V(1)/V(2); V(1) and V(2) are volumes of polymer-lean and -rich phases, respectively) and radius of secondary particle S2 and (2) to compare the N(r) calculated from R and S2 with that by an electron micrographic (EM) method. For this purpose, we assume that secondary particles (i.e., polymer-rich phase) and hypothetical vacant particles (i.e., polymer-lean phase) are placed randomly on a hexagonal closest packing lattice and that x vacant particles contact with each other to form a pore (referred to as vacant-particle pore). An expression of the probability P(x) that a given pore contains x vacant particles was derived. With consideration of an increase in pore size after drying, N(r) for vacant-particle pores, N(v)(r) was derived, using R, S2 and pore density of vacant-particle pores N(p) (number/m2), and by translating x to pore radius r. The condition of determining N(p) from R and S2 was established. N(r) for inter-polymer-particle pores, N(i)(r) (i.e., crevasses of closest-packed secondary particles) was also calculated by using R and S2. The theory predicts that smaller pore size can be attained with smaller R and S2. Phase volume ratio R was found to be determined through use of a theoretical equation on porosity, using experimental porosity Pr(d4) determined from electron micrographs and approximate of degree of collapse of a membrane k'(= L0/L(d); L0, thickness of cast solution, L(d), that of dried membrane). Collapse of a hypothetical gel membrane during coagulation process explains well the findings that theoretical N(r) coincides fairly well with that by EM method only when apparent phase volume ratio R(A) is employed instead of R.