Supersymmetry theory of microphase separation in homopolymer-oligomer mixtures

The mesoscopic structure of periodically alternating layers of stretched homopolymer chains surrounded by perpendicularly oriented oligomeric tails is studied for systems with both strong (ionic) and weak (hydrogen) interactions. We focus on the consideration of the distribution of oligomers along the homopolymer chains that is described by the effective equation of motion with the segment number playing the role of imaginary time. The supersymmetry technique is developed to consider associative hydrogen bonding, self-action effects, inhomogeneity, and temperature fluctuations in the oligomer distribution. Making use of the self-consistent approach allows one to explain experimentally observed temperature dependence of the structure period and the order-disorder transition temperature and period as functions of the oligomeric fraction for systems with different bonding strengths. A whole set of parameters of the model used is found for strong, intermediate, and weak coupled systems being Poly (4-vinyl pyridine)-dodecyl benzene sulfonic acid [P4VP-(DBSA)(x)], P4VP-[Zn(DBS)(2)](x), and P4VP- 3-pentadecyl Phenol(x), respectively. A passage from the former two to the latter is shown to cause a crucial decrease in the magnitude of both parameters of hydrogen bonding and self-action, as well as the order-disorder transition temperature.