A diagrammatic technique in the Landau theory with a two-component order parameter describing the phase transitions in heteropolymer liquids
Pichugin, V E; Kuchanov, S I; Pichugin, V E; Polymers and Crystals Chair, Physics Department, Lomonosov Moscow State University, Vorobjevi gory, 119992, Moscow, Russia; Kuchanov, S I; Polymers and Crystals Chair, Physics Department, Lomonosov Moscow State University, Vorobjevi gory, 119992, Moscow, Russia ; Keldysh Institute of Applied Mathematics, Miusskaya Square 4, 125047, Moscow, Russia
Журнал:
Journal of Statistical Mechanics: Theory and Experiment
Дата:
2005-07-01
Аннотация:
An original diagrammatic technique is advanced for calculating, in the first-harmonic approximation of the Weak Segregation Limit theory, the coefficients of the amplitude expansion of the Landau free energy for a melt of a binary incompressible heteropolymer comprising linear macromolecules with arbitrary chemical structure. A universal approach to the calculation of these coefficients for heteropolymer liquids describable using the Landau theory of phase transitions with a two-component order parameter is put forward for the first time. This approach proves to be particularly efficient in a theoretical consideration of the thermodynamic behaviour of multiblock copolymers whose macromolecules contain blocks of two types substantially differing in length. A general algorithm for finding the coefficients of the amplitude expansion of the Landau free energy in such systems is formulated for a number of mesophases showing two characteristic scales of spatial periodicity. The application of this algorithm is exemplified by considering a deformed hexagonally perforated lamellar mesophase.
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