Weak violation of universality for polyelectrolyte chains: Variational theory and simulations |
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Authors: | G Migliorini VG Rostiashvili TA Vilgis |
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Institution: | (1) Max Planck Institute for Polymer Research, 10 Ackermannweg, 55128 Mainz, Germany, DE;(2) Laboratoire Européen Associé, Institute Charles Sadron, 6 rue Boussingault, 67083 Strasbourg Cedex, France, FR |
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Abstract: | A variational approach is considered to calculate the free energy and the conformational properties of a polyelectrolyte chain
in d dimensions. We consider in detail the case of pure Coulombic interactions between the monomers, when screening is not present,
in order to compute the end-to-end distance and the asymptotic properties of the chain as a function of the polymer chain
length N. We find R≃N
ν(log N)γ, where ν = and λ is the exponent which characterizes the long-range interaction U∝ 1/r
λ. The exponent γ is shown to be non-universal, depending on the strength of the Coulomb interaction. We check our findings
by a direct numerical minimization of the variational energy for chains of increasing size 24 < N < 215. The electrostatic blob picture, expected for small enough values of the interaction strength, is quantitatively described
by the variational approach. We perform a Monte Carlo simulation for chains of length 24 < N < 210. The non-universal behavior of the exponent γ previously derived within the variational method is also confirmed by the simulation
results. Non-universal behavior is found for a polyelectrolyte chain in d = 3 dimension. Particular attention is devoted to the homopolymer chain problem, when short-range contact interactions are
present.
Received 8 August 2000 and Received in final form 19 December 2000 |
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Keywords: | PACS 02 50 -r Probability theory stochastic processes and statistics – 36 20 Ey Conformation (statistics and dynamics) – 61 25 Hq Macromolecular and polymer solutions polymer melts swelling |
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