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Strictly two-dimensional self-avoiding walks: Density crossover scaling

Abstract

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 set by the intrachain subchain size distribution. With RN ν being the size of chains of length N and ρ 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

with ν = 3/4 and θ2 = 19/12 for dilute solutions and ν = 1/d and θ2 = 3/4 for Ng(ρ) ≈ 1/ρ2. Irrespective of ρ, long chains thus become compact packings of blobs of contour length

with d p = d − θ2 = 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 \(F(q)q^d /\rho \approx 1/(qR)^{\theta _2 } \) in the intermediate regime of the wavevector q. 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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Schulmann, N., Meyer, H., Kreer, T. et al. Strictly two-dimensional self-avoiding walks: Density crossover scaling. Polym. Sci. Ser. C 55, 181–211 (2013). https://doi.org/10.1134/S1811238213070072

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Keywords

  • Monte Carlo
  • Polymer Science Series
  • Random Phase Approximation
  • Persistence Length
  • Chain Size