Computer simulation of semidilute polymer solutions in confined geometry: Pore as a microscopic probe

We present a lattice computer simulation study on the geometrical confinement effect of polymer solutions in a wide range of concentrations. Polymer chains were equilibrated for a system that consists of a bulk solution and a slit between two parallel walls. The partition coefficient of the polymer was determined and found to increase as the bulk concentration ø increased, confirming the theoretical predictions. We applied the blob picture to analyze the partition coefficient data in the semidilute regime where the partitioning is considered to be controlled by the ratio of the blob size to the slit width, rather than by the ratio of the chain dimension to the slit width. Our simulation data and earlier experimental data support the application of the blob theory. Furthermore, we found it is possible to estimate the blob size in the bulk solution directly from the partition coefficient data by assuming that the confinement entropy of the blob depends on the blob size in the same way as the confinement entropy of the individual chain depends on the chain dimension at infinite dilution. The blob size thus determined confirms the scaling prediction; namely, the blob size ∝ ø-3/4. Some deviations from this simple picture, however, exist when the slit is narrow and the solution is concentrated

Effective-medium Gaussian-chain theory for semidilute polymer solutions confined to a slit

The Gaussian chain theory especially of the second-order approximation was used to decribe the density profiles and the partition coefficients of the chain dimensions perpendicular to the slit walls for polymer chains confined to a slit space. The strength of the theory is its capability to treat a biomodal polymer solution that consists of homologous polymers differing in length

Computer simulation studies on overlapping polymer chains confined in narrow channels

Conformation of polymer chains strongly confined in a narrow channel space was studied over a broad range of polymer volume fractions φ using lattice Monte Carlo simulations. The longitudinal component of the chain dimension decreased in a power law of ∼φ-1 as φ exceeded the overlap volume fraction. The conformation changed from the one extended along the channel to a random coil. The change occurred without much overlap between adjacent chains. As the conformational transition was completed, the chains started to penetrate each other. Contraction of the chains became more gradual, and eventually the longitudinal component of the chain dimension approached that of the unconfined chains with the overall chain dimension being smaller than that of the unconfined chains. Predictions of the scaling theory were thus confirmed with additional detailed information on the state of confined chains in each regime of characteristic φ dependence of chain dimensions. © 2004 Elsevier Ltd. All rights reserved

Structures and thermodynamics of nondilute polymer solutions confined between parallel plates

Lattice Monte Carlo simulations were conducted to study the thermodynamics and structures of linear chain molecules in solutions confined between two parallel plates of various widths over a wide range of concentrations. The results for the chemical potentials, anisotropic chain dimensions, and scattering structure factors are shown and compared with the scaling-law predictions by Daoud and de Gennes. The transition from a 3D-like solution to a 2D-like solution is observed in both dilute and semidilute regions when the confinement strength increases. In the dilute solution limit, the transition is characterized by an expansion in the chain dimension along the slit walls. In the semidilute region, the transition from 2D dilute pancakes to 2D semidilute pancakes and finally to 3D semidilute spheres with increasing concentration is observed in the dependence of the chain dimension on the concentration. This transition, however, is not clearly seen in the chemical potentials. The single chain structure factors of the confined chains exhibit 2D characteristics in the dilute solution with strong confinement but approach the Debye function in the 2D semidilute and 3D semidilute solutions

Crossover from two- to three-dimensional contraction of polymer chains in semidilute solutions confined to a narrow slit

After studying the contraction of 2D chains, the contraction in chains of different lengths confined to slits of different widths were compared to uncover universal crossover characteristics. Simulations were performed by generating self-avoiding random walks of N-1 steps, where N = 100, 200, 400, and 800, in a simulation box that consists of a given number of layers extending in x and y directions in a cubic lattice. The two layers adjacent to the box represented the slit walls. The slit width d was given by d/a = 1+(the number of layers in the box). A periodic boundary condition was applied to the x and y directions. Chains were moved by the reptation mechanism until equilibrium was reached