Dynamic and static properties of a polymer chain without self-excluded volume, which performs Brownian motion between randomly distributed impenetrable fixed obstacles, have been investigated by Monte Carlo simulations and analyzed by scaling considerations. The mean square radius of gyration 〈S2〉, the center-of-mass diffusion coefficient D, and the longest relaxation time τ are functions of x=(1−p)(N)1/2 for all chain lengths N and porosities p above the percolation threshold. Simulations have been performed for x≲10. With increasing x the radius of gyration exhibits a crossover from Gaussian statistics 〈S2〉∼N to a collapsed state where 〈S2〉 is independent of N. This phenomenon is attributed to the effects of both the lack of self-excluded volume and the presence of an effective self-attractive potential arising from random repulsion between polymer and the solid particles of the medium. The strong dependency upon chain length of D∼N−2.9±0.3 and τ∼N4.0±0.4 is conjectured to result from randomly distributed bottlenecks and traps in the porous solid. If these local constraints are released by arranging the obstacles in a periodic array, familiar reptation dynamics and 〈S2〉∼N are observed.

We calculate the order parameter and anisotropy (elongation) of the configurations of a nematic polymer in the nematic phase. At low temperatures we find exponentially rapid growth of chain dimensions as a function of inverse temperature. In the nematic direction the chain eventually adopts a rod-like state. The thermal activation of hairpins (abrupt reversals in chain directions) causes this behaviour. However, at even lower temperatures the deviation from rod-like alignment is governed by gentle meandering away from the mean field direction. We construct a Maier-Saupe mean field theory of the nematic-isotropic transition, calculating for long chains the transition temperature as a function of chain properties and predicting a universal jump in the order parameter at the transition, ASnL = f .

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The nonspecific lipid-mediated attraction between two proteins embedded in a bilayer membrane have been investigated for a model system using Monte Carlo simulations. We found two types of attraction with different regimes. A depletion-induced attraction in the range r < sigmaL, where sigmaL is the diameter of a lipid and r is the distance between the surfaces of the two proteins, and a fluctuation-induced attraction in the range 1 < r/sigmaL < 6, which originates from the gradients of density and orientational fluctuations of the lipids around each protein. The effective potential of the latter type of attraction decays exponentially with U(r) approximately exp(r/vi) where the correlation length is vi/sigmaL approximately 3.2 in the present model system.

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PACS. 06.40 -Fluctuation phenomena, random processes, and Brownian motion. PACS. 36.20 -Macromolecules and polymer molecules. PACS. 68.10 -Fluid surfaces and interfaces with fluids (inc. surface tension, capillarity, wetting and related phenomena).

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Polymer chains adsorbed on rough impenetrable surfaces have been investigated analytically and by simulations. The cases of physical and chemical roughness of surfaces are identified and their distinctive effects on the adsorption characteristics are studied. For the chemically rough surface the adsorption temperature is depressed by an amount proportional to the concentration of the impurities. A polymer adsorbed on a physically rough surface can be interpreted using the analogy to a one-dimensional electron in a periodic potential. It is shown that at low temperatures the chain is ‘‘localized’’ in one of the wells. Between the localized regime and the unbinding transition point, there exists a ‘‘diffusive’’ regime, where the chain is diffusing by being shared by several potential wells. This regime is equivalent to the conduction band in the electron analogy. In contrast to the case of a flat surface, the unbinding transition of a chain from a periodically rough surface is markedly sharp due to an effective anchoring of the chain in the wells.