THE STRUCTURE AND PHASE-TRANSITIONS IN POLYMER BLENDS, DIBLOCK COPOLYMERS AND LIQUID-CRYSTALLINE POLYMERS - THE LANDAU-GINZBURG APPROACH

The polymer systems are discussed in the framework of the Landau-Ginzb urg model. The model is derived from the mesoscopic Edwards Hamiltonia n via the conditional partition function. We discuss flexible, semifle xible and rigid polymers. The following systems are studied: polymer b lends, flexible diblock and multi-block copolymer melts, random copoly mer melts, ring polymers, rigid-flexible diblock copolymer melts, mixt ures of copolymers and homopolymers and mixtures of liquid crystalline polymers. Three methods are used to study the systems: mean-field mod el, self consistent one-loop approximation and self consistent field t heory. The following problems are studied and discussed: the phase dia grams, scattering intensities and correlation functions, single chain statistics and behavior of single chains close to critical points, flu ctuations induced shift of phase boundaries. In particular we shall di scuss shrinking of the polymer chains close to the critical point in p olymer blends, size of the Ginzburg region in polymer blends and shift of the critical temperature. In the rigid-flexible diblock copolymers we shall discuss the density nematic order parameter correlation func tion. The correlation functions in this system are found to oscillate with the characteristic period equal to the length of the rigid part o f the diblock copolymer. The density and nematic order parameter measu red along the given direction are anticorrelated. In the flexible dibl ock copolymer system we shall discuss various phases including the dou ble diamond and gyroid structures. The single chain statistics in the disordered phase of a flexible diblock copolymer system is shown to de viate from the Gaussian statistics due to fluctuations. In the one loo p approximation one shows that the diblock copolymer chain is stretche d in the point where two incompatible blocks meet but also that each b lock shrinks close to the microphase separation transition. The stretc hing outweighs shrinking and the net result is the increase of the rad ius of gyration above the Gaussian value. Certain properties of homopo lymer/copolymer systems are discussed. Diblock copolymers solubilize t wo incompatible homopolymers by forming a monolayer interface between them. The interface has a positive saddle splay modulus which means th at the interfaces in the disordered phase should be characterized by a negative Gaussian curvature. We also show that in such a mixture the Lifshitz tricritical point is encountered. The properties of this unus ual point are presented. The Lifshitz, equimaxima and disorder lines a re shown to provide a useful tool for studying local ordering in polym er mixtures. In the liquid crystalline mixtures the isotropic nematic phase transition is discussed. We concentrate on static, equilibrium p roperties of the polymer systems.