Thermodynamics of Formation of Porous Polymeric Membrane by Phase Separation Method I. Nucleation and Growth of Nuclei

Abstract

ABSTRACT: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 tJ.c/JCN and radius of the critical nucleus SCN were calculated by using the free energy change due to coagulation per unit volume tJ.fv and interfacial free energy between polymer-rich and -lean phases (J on various phase separation points located within the metastable region of phase diagrams. SCN of critical nucleus generated near a cloud point curve was larger than those near a spinodal curve, but tJ.c/JCN 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 So 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 tp, all the nuclei are conventionally defined as the primary particles. By combining the rate of production of critical nuclei and the total volume of So spheres including growing particles, tp was determined and distribution of those primary particles was calculated.

Phenomenological Effects of Solvent-Casting Conditions on Pore Characteristics of Regenerated Cellulose Membranes

“…Results of the previous paper 5 gave the same relation between Wee1i and d~ (see , Table IV Polym. Figure 6b shows that Pr(d 3 ) is almost constant over a whole range of wNH, (0-0.01) of coagulation solution. Ld also does not change in a range of wNH, of coagulation solution from 0 to 0.01 (Figure 6c).…”

“…fraction v~ is less than the polymer volume fraction at a critical solution point v~, the polymer-rich phase separates first as nuclei (steps a and bin Figure 1), which grow to the primary particles ( steps b-d in Figure l ), 3 and the primary particles amalgamate into the secondary particles (steps d-f in Figure 1). 4 In the subsequent steps, the secondary particles contact with each other to form gel membranes, which become dried membrane through desolvation and drying (steps g-j in Figure 1).…”

Formation of polymeric membranes by immersion precipitation: an improved algorithm for mass transfer calculations

“…(1)-(7) are no longer valid since the polymer film does not remain a continuum [12]. Therefore, in the present work, once the spinodal was crossed, the interface compositions were calculated, the diffusion profiles updated and the simulation stopped.…”

Thermodynamics of Formation of Porous Polymeric Membrane by Phase Separation Method II. Particle Simulation Approach by Monte Carlo Method and Experimental Observations for the Process of Growth of Primary Particles to Secondary Particles

“…Comparison of Figures 7a-7c shows that even at the same R the particles grow much faster from the solutions of lower initial concentration due to lower vp(ll (i.e., lower 17). Summarizing, the growth rate of the particles is theoretically expected to be larger when the phase separation occurs under the conditions of (1) lower polymer volume fraction of polymer-lean phase vp(tl and (2) smaller two-phase volume ratio R. Lower vp(ll yields the larger velocity and smaller R makes for a larger collision frequency. These conditions will be satisfied practically, at least, when a dilute solution is quickly cooled down ( or quenched) to a point in the metastable region near to the spinodal curve and kept there for a longer period.…”

“…In the previous paper, 1 we proposed a theory on the nucleation and growth of nuclei to the primary particles in the process of formation of the porous polymeric membranes by the phase separation method, i.e., the solventcasting method in the case when initial polymer volume fraction vg is less than polymer volume fraction at a critical solution point v~ (steps a-d in Figure 1). The subsequent steps are those, in which the primary particles grow to the secondary particles (steps d-f in Figure 1).…”