Coalescence in quiescent polymer blends with a high content of the dispersed phase

Coalescence in molten quiescent polymer blends induced by van der Waals forces is studied theoretically. Interaction between a droplet and its nearest neighbor keeping spherical shape during drainage of the matrix trapped between them is considered. It is assumed that droplets with time dependent radius R or effective droplets with radius R + h_c/2, where h_c is the critical inter-droplet distance for breakup of the matrix trapped between them, are randomly distributed in the blend through the whole course of the coalescence. Various approaches to calculation of the average time of coalescence, t_c (calculation with preaveraged distance between a droplet and its nearest neighbor at the start of coalescence, h₀, direct averaging of t_c and averaging coalescence frequency, 1/t_c) are compared. Calculated dependence of R on the time of coalescence, t, is compared with experimental results for polypropylene/ethylene–propylene rubber (PP/EPR) blends with EPR content from 15 to 30 wt.%. Calculations using average h₀ and direct averaging of t_c lead to more-less linear dependence of R³ on t. Bare averaging of 1/t_c leads to a steeper than linear dependence of R³ on t and to unreasonably high rate of the coalescence; averaging of 1/t_c with exclusion of pairs with elapsed coalescence time leads to decreasing rate of R³ growth but unreasonably low rate of coalescence. Theories based on the concept of effective droplet radius give smaller differences among various methods of calculations of t_c than the theories assuming random distribution of the droplets. Experimental results show decreasing slope of R³ vs. t dependence, especially for a higher content of dispersed EPR. Theories using average h₀ or direct averaging of t_c predict somewhat smaller rate of coalescence than that experimentally determined for PP/EPR blends. Reasons of these differences are discussed.