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Weak violation of universality for polyelectrolyte chains: Variational theory and simulations

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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 RN 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.

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Received 8 August 2000 and Received in final form 19 December 2000

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Migliorini, G., Rostiashvili, V. & Vilgis, T. Weak violation of universality for polyelectrolyte chains: Variational theory and simulations. Eur. Phys. J. E 4, 475–487 (2001). https://doi.org/10.1007/s101890170103

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  • DOI: https://doi.org/10.1007/s101890170103

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