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Probabilities of Finding Isolated, Semi-Open, and Through Pores in Porous Polymeric Membrane Prepared by Micro-Phase Separation Method

The existing probabilities of isolated (Pi), semi-open (Ps), and through pores (Pt) in the micro-porous polymeric membrane were evaluated by analyzing the experimental porosity (Pre) data. Here, the following assumptions were employed: (1) the membrane consisted of the multi-thin layers, (2) the network-like structure in one layer was constituted by numerous secondary particles which grew from the primary particles generated as polymer-rich phase from the casting solution in the occurrence of the micro-phase separation, (3) the secondary particles were packed in the hexagonal closest packed model and the vacant space originating from the polymer-lean phase was composed of imaginary vacant particles having the same diameter as the secondary particle. The probability that the secondary particles surround the vacant particles perfectly corresponds to Pi, and the probability of connecting with each vacant particles continuously from the front surface to back surface equals Pt. The theoretical relations between Pi, Ps, Pt, and the structural parameters were derived. The numerical calculations were carried out for a given Pre using the equations derived. It was concluded that Pi>>Ps>Pt for Pre≤0.15, and Ps>>Pi>Pt for 0.15Ps and Pi=0 for Pre≥0.4.