THERMODYNAMICS OF FORMATION OF POROUS POLYMERIC MEMBRANE BY PHASE-SEPARATION METHOD .1. NUCLEATION AND GROWTH OF NUCLEI

An attempt was made to clarify a general principal describing the steps of nucleation to the growth of the primary particles, based on the thermodynamics of phase equilibrium of mono-dispersed polymer/single solvent systems. Activation energy of formation of critical nucleus DELTAphi(CN) and radius of the critical nucleus S(CN) were calculated by using the free energy change due to coagulation per unit volume DELTAf(v) and interfacial free energy between polymer-rich and -lean phases a on various phase separation points located within the metastable region of phase diagrams. S(CN) of critical nucleus generated near a cloud point curve was larger than those near a spinodal curve, but DELTAphi(CN) became smaller when the phase separation occurred near the spinodal curve, indicating that nucleation tends to occur much more easily near the spinodal curve. Nuclei thus formed and passed though a potential barrier are considered to be in equilibrium with the region surrounded by the local solution spheres of polymer-lean phase. The spheres having radii of S0 are surrounded by an outer original bulk solution. Growth rate of growing particles were obtained in the isothermal process by solving the general equation of diffusion of polymer molecules from the outer phase. When the phase separation of whole system is attained at time t(P), all the nuclei are conventionally defined as the primary particles. By combining the rate of production of critical nuclei and the total volume of S0 spheres including growing particles, t(P) was determined and distribution of those primary particles was calculated.