Simulation of polymers in a curved box : Variable range bond - ing models

– We propose new polymer models for Monte Carlo simulation and apply them to a polymer chain confined in a relatively thin box which has both curved and flat sides, and show that either an ideal or an excluded-volume chain spends more time in the curved region than in the flat region. The ratio of the probability of finding a chain in the curved region and in flat region increases exponentially with increasing chain length. The results for ideal chains are quantitatively consistent with a previously published theory. We find that the same effect appears with excluded-volume chains and a similar scaling relation can be applied to them up to a certain length of the polymer. Introduction. – The structure [1], [2], [3], [4] and dynamics [5], [6], [7] of polymer chains confined within a narrow space such as in a slit (Fig. 1) are important for practical applications, e.g. filtration, gel permeation chromatography and oil recovery, and have attracted much interest. [8] The effect of confinement on polymer chains was calculated theoretically in welldefined geometries (a slit and a tube) and was simulated by a lattice model [9] and an off-lattice model. [10] Recently, polymer confinement in curved boxes (a cylindrical shell, an undulated slit, etc) was studied. [11], [12] Such studies can relate to not only the behaviour of polymers confined in complex rigid geometries but also the behaviour of deformable bilayer membranes confining the polymer chains. Yaman et al. [11] showed that an ideal (Gaussian) polymer chain confined between cylindrical shells (Fig. 2) has a lower free energy than one confined between two flat surfaces (Fig. 1), and predicted that polymer chains confined in bilayer membranes reduce the effective bending rigidity of the membranes and might induce spontaneous curvature in the system, e.g. leading to transitions from lamellar to bicontinuous phases. (∗) E-mail address: [email protected] Typeset using EURO-TEX 2 EUROPHYSICS LETTERS