TY - JOUR

T1 - Polymer chains in semidilute solutions confined to a square channel

T2 - Mean-field Gaussian chain theory and comparison with simulation results

AU - Teraoka, Iwao

AU - Cifra, Peter

N1 - Funding Information:
Financial support from NSF under DMR-9876360 and Slovak Academy of Sciences (SAS) under 2/7076/21 is acknowledged. Usage of computational resources of Computer Center of SAS is acknowledged.

PY - 2002/3/18

Y1 - 2002/3/18

N2 - We extend the mean-field Gaussian chain theory, originally developed for non-dilute solutions of athermal polymer chains in a slit, to solutions in a channel with a square cross section. The formulation allows one to calculate the monomer density profile, the chemical potential of the confined polymer chain, and therefore the partition coefficient. For the mean-field potential, we used the first-order approximation that neglects local monomer density fluctuations and the second-order approximation that takes into account the fluctuations. The results of the density profile and the partition coefficient were compared with those obtained in the lattice Monte Carlo simulations. The theoretical results obtained with the first-order approximation agreed well with the simulation results for chains of 100 beads below the average monomer density of ca. 0.2. At higher concentrations, the second-order results gave a better agreement. This cross over indicates a change in the interactions between polymer chains from those in one-dimension to those in three-dimensions as the correlation length in the confined solution becomes sufficiently shorter than the channel width.

AB - We extend the mean-field Gaussian chain theory, originally developed for non-dilute solutions of athermal polymer chains in a slit, to solutions in a channel with a square cross section. The formulation allows one to calculate the monomer density profile, the chemical potential of the confined polymer chain, and therefore the partition coefficient. For the mean-field potential, we used the first-order approximation that neglects local monomer density fluctuations and the second-order approximation that takes into account the fluctuations. The results of the density profile and the partition coefficient were compared with those obtained in the lattice Monte Carlo simulations. The theoretical results obtained with the first-order approximation agreed well with the simulation results for chains of 100 beads below the average monomer density of ca. 0.2. At higher concentrations, the second-order results gave a better agreement. This cross over indicates a change in the interactions between polymer chains from those in one-dimension to those in three-dimensions as the correlation length in the confined solution becomes sufficiently shorter than the channel width.

KW - Confinement

KW - Partitioning

KW - Semidilute solutions

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U2 - 10.1016/S0032-3861(02)00098-8

DO - 10.1016/S0032-3861(02)00098-8

M3 - Article

AN - SCOPUS:0037128593

VL - 43

SP - 3025

EP - 3033

JO - Polymer

JF - Polymer

SN - 0032-3861

IS - 10

ER -