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° kink requiring an energy εb. While for εb = 0 this is the ordinary SAW, varying the parameter qb = exp(−εb/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 = 105 steps can be studied. In previous work it has already been shown that for contour lengths L = Nb (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 ∝ p1/4L3/4, 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 p2/D, and R‖ ∝ 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 ∝ p(D/p)4/3, while for L ≫ Lcross the chain is a string of blobs of diameter D, i.e. R‖ ∝ L(p/D)1/3. In the regime D < p, the chain is a sequence of straight sequences with length of the order p2/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.