Semi-flexible polymer chains in quasi-one-dimensional confinement: a Monte Carlo study on the square lattice

Single semi-flexible polymer chains are modeled as self-avoiding walks (SAWs) on the square lattice with every 90 degrees kink requiring an energy 3b. While for 3b 0 this is the ordinary SAW, varying the parameter qb exp(-3b/kBT) allows the variation of the effective persistence length ` p over about two decades. Using the pruned-enriched Rosenbluth method (PERM), chain lengths up to about N=10(5) steps can be studied. In previous work it has already been shown that for contour lengths L N` b (the bond length ` b is the lattice spacing) of order ` p a smooth crossover from rods to two-dimensional self-avoiding walks occurs, with radii R f ` p 1/4L3/4, the Gaussian regime predicted by the Kratky-Porod model for worm-like chains being completely absent. In the present study, confinement of such chains in strips of width D is considered, varying D from 4 to 320 lattice spacings. It is shown that for narrow strips (D < ` p) the effective persistence length of the chains (in the direction parallel to the confining boundaries) scales like ` p 2/D, and R k f L (with a pre-factor of order unity). For very wide strips, D [ ` p, the two-dimensional SAW behavior prevails for chain lengths up to Lcross f ` p(D/` p) 4/3, while for L[ Lcross the chain is a string of blobs of diameter D, i. e. R k f L(` p/D) 1/3. In the regime D < ` p, the chain is a sequence of straight sequences with length of the order ` p 2/D parallel to the boundary, separated by sequences with length < D perpendicular to the boundary; thus Odijk's deflection length plays no role for discrete bond angles.