Strictly Two-Dimensional Self-Avoiding Walks: Density Crossover Scaling
N Schulmann and H Meyer and T Kreer and A Cavallo and A Johner and J Baschnagel and JP Wittmer, POLYMER SCIENCE SERIES C, 55, 181-211 (2013).
The density crossover scaling of thermodynamic and conformational properties of solutions and melts of self-avoiding and highly flexible polymer chains without chain intersections confined to strictly two dimensions (d = 2) is investigated by means of molecular dynamics and Monte Carlo simulations of a standard coarse grained bead-spring model. We focus on properties related to the contact exponent theta(2) set by the intrachain subchain size distribution. With R - N-nu being the size of chains of length N and rho the monomer density, the interaction energy e(int) between monomers from different chains and the corresponding number n(int) of interchain contacts per monomer are found to scale as e(int) similar to n(int) similar to 1/N-nu theta 2 with nu = 3/4 and theta(2) = 19/12 for dilute solutions and nu = 1/d and theta(2) = 3/4 for N >> g(rho) approximate to 1/rho(2). Irrespective of rho, long chains thus become compact packings of blobs of contour length L similar to Nn(int) similar to R-dp with d(p) = d - theta(2) = 5/4 being the fractal line dimension. Due to the generalized Porod scattering of the compact chains, the Kratky representation of the intramolecular form factor F(q) reveals a non-monotonous behavior approaching with increasing chain length and density a power-law slope F(q)q(d)/rho approximate to 1/(qR)(theta 2) in the intermediate regime of the wavevector. The specific intermolecular contact probability is argued to imply an enhanced compatibility for polymer blends confined to ultrathin films. We comment briefly on finite persistence length effects.
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