Model for micelle formation in copolymer/homopolymer blends

Polydisperse micelle formation in dilute solutions of A-B diblock copolymer in A homopolymer is studied. The standard free energy of micellization, the critical micelle concentration (c.m.c.), the average micelle sizes, and the micelle size distribution are determined. The effects of copolymer concentration, B block length n_B, and temperature (in terms of the Flory's interaction parameter χ) on micellar behavior are examined. The width of the micelle size distribution is shown to be inversely proportional to the square root of the curvature of the standard free energy of micellization. The polydispersity of the micelles decreases with increasing copolymer concentration, being high for concentration below and around the c.m.c. The polydispersity also depends on n_Bχ, with high polydispersity corresponding to small n_Bχ values. The average micelle size exhibits sudden growth at the c.m.c. and increases slightly beyond the c.m.c.