A diagrammatic technique in the Landau theory with a two-component order parameterdescribing the phase transitions in heteropolymer liquids

Abstract

An original diagrammatic technique is advanced for calculating, in the first-harmonicapproximation of the Weak Segregation Limit theory, the coefficients of the amplitudeexpansion of the Landau free energy for a melt of a binary incompressible heteropolymercomprising linear macromolecules with arbitrary chemical structure. A universal approachto the calculation of these coefficients for heteropolymer liquids describable using theLandau theory of phase transitions with a two-component order parameter is put forwardfor the first time. This approach proves to be particularly efficient in a theoreticalconsideration of the thermodynamic behaviour of multiblock copolymers whosemacromolecules contain blocks of two types substantially differing in length. A generalalgorithm for finding the coefficients of the amplitude expansion of the Landau freeenergy in such systems is formulated for a number of mesophases showing twocharacteristic scales of spatial periodicity. The application of this algorithm isexemplified by considering a deformed hexagonally perforated lamellar mesophase.