Supersymmetry theory of microphase separation in homopolymer--oligomer mixtures

Abstract

Mesoscopic structure of the periodically alternating layers of stretched homopolymer chains surrounded by perpendicularly oriented oligomeric tails is studied for the 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. 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 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 strength of bonding. A whole set of parameters of the model used is found for strong, intermediate and weak coupled systems being P4VP--(DBSA)$_x$, P4VP-(Zn(DBS)$_2$)$_x$ and P4VP--(PDP)$_x$, respectively. A passage from the formers to the latters shows to cause crucial decrease of the magnitude of both parameters of hydrogen bonding and self--action, as well as the order--disorder transition temperature.