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A new approach to polymer solution theory

M A Moore and C A Wilson

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Shows that in the usual treatment of the O(n) symmetric Ginzburg-Landau-Wilson field theory Goldstone modes induce a negative susceptibility for n<1 as the co-existence curve is approached. This situation affects the whole of the semi-dilute regime of polymer solutions. To examine the role of Goldstone modes within this formalism, the authors consider the generalised Heisenberg model of H.E. Stanley (1969) with self-avoiding constraint on a d=2 square lattice in the limit n to 0. By taking highly anisotropic couplings, the authors take the continuum limit in one direction for the transfer matrix and obtain a quantum mechanical Hamiltonian on a d=1 lattice. This is used to obtain perturbation series in the coupling between lattice sites for the inverse correlation length and susceptibility. The authors obtain the equation of state to second order, and show the existence of spontaneous magnetisation even though it is absent in d=1. The susceptibility is well behaved and positive. The calculations can be readily extended to systems of higher dimensionality.


PACS

61.25.H- Macromolecular and polymers solutions; polymer melts

75.30.Kz Magnetic phase boundaries (including magnetic transitions, metamagnetism, etc.)

75.10.Jm Quantized spin models

75.30.Ds Spin waves

75.30.Cr Saturation moments and magnetic susceptibilities

MSC

41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)

82C26 Dynamic and nonequilibrium phase transitions (general)

82D60 Polymers

82D15 Liquids

Subjects

Soft matter, liquids and polymers

Condensed matter: electrical, magnetic and optical

Dates

Issue 11 (1 November 1980)



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