Bifurcation analysis for the construction of a phase diagram of heteropolymer liquids

• DOI: 10.1063/1.1827323
• Publication Date: 2004-12-24T02:08:55Z
• Authors: A. N. Ivanova; S. I. Kuchanov; L. I. Manevitch
• Keywords: 0103 physical sciences; 01 natural sciences

Rather general mean field theory of heteropolymer liquids developed earlier reduces the problem of the phase diagram construction to the determination of extremals of the free energy functional. These should be subsequently analyzed for their local and global stability. Tackling of this problem traditionally involves the examination of the behavior of the solutions of a set of nonlinear algebraic and partial differential equations at various values of the control parameters. Besides, the necessity arises here to construct in space of these parameters the lines where a polymer system loses the thermodynamic stability. To overcome mathematical difficulties encountered we employed a complex approach that combines analytical and numerical methods. A two-step procedure constitutes the essence of such an approach. First, the bifurcation analysis is invoked to find the asymptotics of the extremals in the vicinity of bifurcation points. Then these asymptotics are used as an initial approximation for the numerical continuation of specific lines, where the stability loss occurs, into regions of the parametric space far removed from bifurcation values. We realized this approach for the melt of linear binary copolymers of various chemical structure with macromolecules having a pattern of arrangement of monomeric units describable by a Markov chain. Bifurcation and phase diagrams for some of these copolymers have been constructed within a wide range of temperatures and volume fractions of a polymer.