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

Abstract

ABSTRACT:An attempt was made (I) to establish a theory on particle growth during the membrane formation by the phase separation method with an aid of computer simulation technique, and (2) to compare results of the computer simulation with those of actual experiments. In the particle simulation, primary particles consisting of polymer-rich phase are generated at random position in a hypothetical space, and moving velocity v1 was given to them, assuming Brownian movement in a solutfon of polymer-lean phase. If a distance between the centers of gravity of two arbitrary chosen particles is less than the summation of their radii, they are considered to have collided, yielding a new larger particle. The simulation reveals that the growth rate of particles is theoretically expected to be larger when the phase separation occurs under the conditions of lower concentration (i.e., lower viscosity) of polymer-lean phase and of smaller two phase volume ratio R( = V 0 if V<2>; V< 1> and V<2> are the volumes of polymer-lean and -rich phases, respectively). The lower viscosity yields lager velocity and the smaller R gives larger collision frequency. Particle size distribution N(S) and the number-average radius of growing particles S were evaluated by dynamic light scattering measurement on systems of polymer solution/coagulating solution, i.e., cellulose cuprammonium solution/acetone-ammonia-water solution and cellulose cuprammonium solution/sodium hydroxide-water solution and it is experimentally confirmed that the primary particles grow by amalgamation and under some conditions, their radii approach an asymptotic value, which is the radius of the secondary particle S2 •

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

“…KI confirmed the growth of the primary particles to the secondary particles in the above system of cuprammonium cellulose solution/acetone/water. 4 In this article, we attempted to investigate in a systematic manner phenomenological effects of solvent-casting conditions (i.e., the weight fractions of acetone w Acetone and ammonia wNH, in the coagulation solution, and the weight fractions of cellulose Wce1i and ammonia wNH, in the cast solution) on the pore characteristics of the resultant membranes such as radius of the secondary particles S 2 existing on the membrane surfaces, 2rr, the membrane porosity by the apparent density method 148 Pr( d 3 ) and the membrane thickness Ld and to determine the most important factors among casting conditions governing the membrane structure.…”

“…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). …”

Thermodynamics of Formation of Porous Polymeric Membrane by Phase Separation Method V. Probabilities of Finding Through-, Semi-Open, and Isolated Pores in Three-Dimensional Membrane Structure Model Constructed by Computer Simulation Experiment

“…Pr*~Pr=---RA+l (2) Therefore, probability that a given site is occupied by a polymer particle is equal to (I-Pr*).…”

Thermodynamics of Formation of Porous Polymeric Membrane by Phase Separation Method VI. Supermolecular Structure and Virus Separability of Porous Regenerated Cellulose Membrane Prepared by Phase Separation Method

“…3 • 4 In the previous papers, 5 -9 Kamide, Iijima and their collaborators studied more quantitatively the mechanism of membrane structure formation by the phase separation method from view point of "particle growth concept": In case where initial polymer volume fraction v~ is less than polymer volume fraction at a critical solution point v~, they have proposed a theory on the nucleation and growth of nuclei to the primary particles, 5 and have carried out computer simulation experiments on the growth of the primary particles to the secondary particles. 6 Furthermore, using a hexagonal lattice plane as a two-dimensional model of thin layers consisting of the membrane, they derived a theory (referred to as "lattice theory") giving pore size distribution N(r) (r, pore radius) and pore density Np (i.e., number of pores in unit area of membrane) and carried out computer simulation experiments concerning N(r) together with actual experiments on steps of formation of porous structures by 808 contacting the secondary particles. 7 • 8 They compared three kinds of pore size distribution: 1) N(r) by an electron microscopic method N(r)EM of an actual porous cellulose membrane, 2) theoretical N(r) calculated by using average radius of polymer particles on a front surface, membrane porosity estimated by an apparent density method Pr(d 3 ) and degree of contraction k for the actual porous cellulose membrane, and 3) N(r) by computer simulation experiments.…”