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.

No abstract

No abstract

No abstract

ABSTRACT:An attempt was made to establish a theoretical method for calculating the cloud point curve (CPC) and critical point of solutions of polydisperse polymers in a single solvent (i.e., quasi-binary system) on the basis of the polydispersity of the polymer and concentration-and molecular weight-dependences of the polymer-solvent thermodynamic interaction parameter X· Expressions giving the cloud point curve were derived and a computer simulation technique, based on the theory, was developed. The effects of the average molecular weight, polydispersity of polymer and concentration dependence of x-parameter on CPC, threshold cloud point and critical point were clarified. In order to represent accurately the CPC for the entire concentration range from the molecular characteristics of the original polymer and operating conditions, such as polymer-volume fraction and x-parameter, the concentration dependence parameters p1 and p,, in the relation X= XoO + p1 v" + p2 v/) (x0 ; concentration-independent parameter, v", polymer volume fraction) should be adequately taken into account. Very delicate changes in p 1 and p2 cause significant variation in CPC and none of the literature data on p1 and p2 for polystyrene/ cyclohexane adequately represent the experimental CPC. From an actual CPC experiment, p 1 = 0.643 and p2 = 0.200 were evaluated. The effective role of the molecular weight dependence of x in CPC was shown in the lower v" region.