THERMODYNAMICS OF FORMATION OF POROUS POLYMERIC MEMBRANE BY PHASE-SEPARATION METHOD .5. PROBABILITIES OF FINDING THROUGH-PORES, SEMIOPEN, AND ISOLATED PORES IN 3-DIMENSIONAL MEMBRANE-STRUCTURE MODEL CONSTRUCTED BY COMPUTER-SIMULATION EXPERIMENT

On the basis of the particle growth concept proposed to explain polymeric membrane formation process by the phase separation method, an attempt was made (1) to establish a computer simulation method for constructing a three-dimensional multi-layered structure model of a membrane consisting of polymer particles, (2) to disclose a three-dimensional shape of through-pores, and (3) to establish relations between a probability of distributing a vacant particles in a site Pr* (i.e., porosity of a membrane) and existing probabilities of three kinds of pores such as through-, semi-open, and isolated pores, i.e., P-t, P-s, and P-i, respectively. In the simulation, number ratio of hypothetical vacant particles of polymer-lean phase to polymer particles of polymer-rich phase is predetermined by an apparent two-phase volume ratio R(A)(=V((1)A)/V((2)A), where V((1)A) and V((2)A) are apparent volumes of polymer-lean and -rich phases in the membrane, respectively), which is estimated from an overall porosity of a membrane Pr. Particles are assumed for convenience to have the same radius of S-2 and are arranged randomly on a hypothetical hexagonally close-packed lattice plane by Monte Carlo method. From study on the effects of number of layers of the model I and size of the layer s on relations between Pr* and P-t, P-s, and P-i, we concluded that it was enough for a three-dimensional model to have 20 layers, of which size is taken as 40 sites by 40 lines. Relations between Pr* and the existing probabilities P-t, P-s, and P-i constructed by the previous theory [S. Manabe, H. Iijima, and K. Kamide, Polym. J., 20, 307 (1988)] and those by the present simulation are compared and it is concluded that the previous approximate theory underestimates P-t (especially in the range of Pr* of 0.3 to 0.8) and P-i (especially at lower Pr*) significantly.