J. Phys. II France
Volume 1, Number 11, November 1991
Page(s) 1387 - 1404
DOI: 10.1051/jp2:1991147
J. Phys. II France 1 (1991) 1387-1404

Fluctuation effects in the theory of weak supercrystallization in block copolymer systems of complicated chemical structure

A. V. Dobrynin and I. Ya. Erukhimovich

Institute of Mineralogy, Geochemistry and Crystal Chemistry of Rare Elements, Veresaev Street, 15, Moscow 121357, U.S.S.R.

(Received 3 June 1991, revised 1 July 1991, accepted 22 July 1991)

To investigate the influence of fluctuation effects on conditions of microphase separation in two-component incompressible molten block copolymers of complicated chemical structure an alternative and more general formulation of the weak crystallization theory is developed using a new variational principle for the calculation of the free energy. Unlike the Fredrickson-Helfand theory, ours accounts for a given angular dependence of vertex functions more rigorously and enables us to evaluate correlation functions in both disordered and supercrystal states. A comparison of phase diagrams constructed by means of both our and the FH theories is made for the case of star copolymers $({\rm A}_n)_k ({\rm B}_m)_k$. The numerical minimization of free energies corresponding to supercrystal and homogeneous states was carried out with account of exact expressions for higher correlators of these systems calculated by us early. It is shown that both theories are in good agreement within the limit of strong fluctuation effects whereas the FH theory underestimates moderate fluctuation effects in crossover region.

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