Inversion symmetry, architecture and dispersity, and their effects on thermodynamics in bulk and confined regions: From randomly branched polymers to linear chains, stars and dendrimers

摘要

Theoretical evidence is presented in this review that architectural aspectsudcan play an important role, not only in the bulk but also in confined geometriesudby using our recursive lattice theory, which is equally applicable toudfixed architectures (regularly branched polymers, stars, dendrimers, brushes,udlinear chains, etc.) and variable architectures, i.e. randomly branchedudstructures. Linear chains possess an inversion symmetry (IS) of a magneticudsystem (see text), whose presence or absence determines the bulkudphase diagram. Fixed architectures possess the IS and yield a standardudbulk phase diagram in which there exists a theta point at which two criticaludlines C and C′ meet and the second virial coefficient A₂ vanishes.udThe critical line C appears only for infinitely large polymers, and an orderudparameter is identified for this criticality. The critical line C′ exists for polymersudof all sizes and represents phase separation criticality. Variable architectures,udwhich do not possess the IS, give rise to a topologically differentudphase diagram with no theta point in general. In confined regions next toudsurfaces, it is not the IS but branching and monodispersity, which becomesudimportant in the surface regions. We show that branching plays no importantudrole for polydisperse systems, but become important for monodisperseudsystems. Stars and linear chains behave differently near a surface.