Fluctuation effects in the theory of microphase separation in block copolymers

The effect of composition fluctuations on the microphase separation transition in diblock copolymers is investigated. Such fluctuation corrections, which were neglected in the mean field treatment of Leibler, are found to be significant for the molecular weights usually encountered. The analysis is facilitated by reducing the block copolymer Hamiltonian to a form previously studied by Brazovskii. Our principal results are the following: (i) A symmetric diblock copolymer is predicted to undergo a first order phase transition at a larger value of χN than the second order transition found by Leibler. The Flory interaction parameter is denoted χ and N is the number of statistical segments per chain. The location of the transition is predicted to be at (χN)t=10.495+41.022 N−1/3, where the peak in the scattering function attains its maximum value of 0.12328 N1/3. (ii) We find windows in composition, with finite width, through which it is possible to pass from the disordered phase to each of the ordered micropha...

[1]  R. Larson,et al.  Viscoelasticity of homogeneous polymer melts near a critical point , 1987 .

[2]  G. Fredrickson.  Nonequilibrium structure of the homogeneous phase of block copolymers under steady flow , 1986 .

[3]  K. Kawasaki,et al.  Equilibrium morphology of block copolymer melts , 1986 .

[4]  I. Sanchez,et al.  Theory of Microphase Separation in Graft and Star Copolymers , 1986 .

[5]  T. Hashimoto,et al.  Small-Angle X-Ray Scattering from Bulk Block Polymers in Disordered State. Estimation of χ-Values from Accidental Thermal Fluctuations , 1985 .

[6]  M. Folkes.  Processing, Structure and Properties of Block Copolymers , 1985 .

[7]  Victor Martin-Mayor,et al.  Field Theory, the Renormalization Group and Critical Phenomena , 1984 .

[8]  L. Leibler,et al.  Theory of correlations in partly labelled homopolymer melts , 1981 .

[9]  L. Leibler.  Theory of Microphase Separation in Block Copolymers , 1980 .

[10]  P. Gennes.  Scaling Concepts in Polymer Physics , 1979 .

[11]  J. Swift,et al.  Models for phase transitions with continuous constant energy surfaces , 1977 .

[12]  E. Helfand,et al.  Theory of unsymmetric polymer–polymer interfaces , 1975 .

[13]  A. Fetter,et al.  Quantum Theory of Many-Particle Systems , 1971 .

[14]  F. Bates,et al.  Block copolymers near the microphase separation transition. 3. Small-angle neutron scattering study of the homogeneous melt state , 1985 .

[15]  F. Bates.  Measurement of the correlation hole in homogeneous block copolymer melts , 1985 .

[16]  John Lewis.  Developments in block copolymers—1: Edited by I. Goodman. Applied Science Publishers, London, 1982. 358 pp. ISBN 0-85334-145-1. Price: £40·00 , 1983 .

[17]  J. Swift,et al.  Hydrodynamic fluctuations at the convective instability , 1977 .

[18]  Shang‐keng Ma.  Modern Theory of Critical Phenomena , 1976 .