Inter-Chain Structure Factors of Flexible Polymers in Solutions: A Monte Carlo Investigation

V. Yamakov; A. Milchev; K. Binder

doi:doi:10.1051/jp2:1997176

Numéro		J. Phys. II France Volume 7, Numéro 8, August 1997


Page(s)		1123 - 1139
DOI		https://doi.org/10.1051/jp2:1997176

DOI: 10.1051/jp2:1997176
J. Phys. II France 7 (1997) 1123-1139

Inter-Chain Structure Factors of Flexible Polymers in Solutions: A Monte Carlo Investigation

V. Yamakov¹, A. Milchev^{1, 2} and K. Binder²

¹ Institute for Physical Chemistry, Bulgarian Academy of Sciences 1113 Sofia, Bulgaria
² Institut für Physik, Johannes-Gutenberg-Universität-Mainz, Staudinger Weg 7, 55099 Mainz, Germany

(Received 22 November 1996, revised 21 March 1997, accepted 22 April 1997)

Abstract
Off-lattice Monte Carlo simulations of both the single chain structure factor h(q) and the inter-chain structure factor $H_{\rm D}(q)$ of flexible polymers in solutions are presented over a wide range of both wavenumber q and concentration c from the dilute to the concentrated regime, for chain lengths up to N = 256. The single chain properties $\{$ gyration radius $\langle R_{\rm g}^2\rangle$ , $h(q)\}$ are in reasonable agreement with the expected theoretical behavior, showing a crossover from swollen chains $\{\langle R_{\rm g}^2\rangle \propto N^{2\nu} ,~ h(q) \propto q^{-1/\nu}\}$ to Gaussian chains, and the data comply with a scaling description, with a correlation length $\xi\propto c^{-\nu/(3\nu-1)}$ . However, the inter-chain structure factor $H_{\rm D}(q)$ disagrees with the corresponding predictions, we find a behaviour $H_{\rm D}(q)\propto q^{-3}$ only in an intermediate range but this is accidental: rather it is found that $H_{\rm D}(q)$ smoothly bends over from its saturation value at small q to a behavior close to q^-4 at $q\approx1/\ell$ , $\ell$ being the length of effective bonds. This failure is traced back to the condition that the law $H_{\rm D}(q)\propto q^{-3}$ should only be observed for $\xi^{-1}\ll q \ll \ell^{-1}$ , a condition reached neither in the simulation nor in experiments. We also compare our results for $H_{\rm D}(q)$ with the random phase approximation and find strong deviations.