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

Abstract

Off-lattice Monte Carlo simulations of both the single chain structure factor h(q) and the inter-chain structure factor HD(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 〈Rg2〉, $h(q)\}$ 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 ξ∝c-ν/(3ν-1). However, the inter-chain structure factor HD(q) disagrees with the corresponding predictions, we find a behaviour HD(q)∝q-3 only in an intermediate range but this is accidental: rather it is found that HD(q) smoothly bends over from its saturation value at small q to a behavior close to q-4 at q≈1/l, l being the length of effective bonds. This failure is traced back to the condition that the law HD(q)∝q-3 should only be observed for ξ-1≪q ≪l-1, a condition reached neither in the simulation nor in experiments. We also compare our results for HD(q) with the random phase approximation and find strong deviations.