What is the distance to the wall in lattice simulations?

Iwao Teraoka, Peter Cifra, Yongmei Wang

Research output: Contribution to journalArticlepeer-review


Lattice Monte Carlo simulations are widely used to study the effect of walls on the concentration profile in polymer solutions. The scaling theory predicts that the monomer density at a distance x from the wall, reduced by the bulk density, is proportional to (x/Rg0)1/v at low concentrations, and the correlation length replaces Rg0 in the semidilute solution, where Rg0 is the radius of gyration and v is the Flow exponent for the chain dimension. We conducted simulations for long chains on a cubic lattice to find that a positive penetration depth γ is needed to see an agreement with the theory. The monomers perceive a theoretical wall at an off-lattice position of γ behind the presumed wall on the lattice points. We found γ ∼ 0.13 of the lattice unit at low concentrations but ∼0.36 in the semidilute solution for athermal chains. For Θ solutions, γ was 0.31-0.36 at all concentrations. We ascribe the positive γ to uneven chain segment propagation in the chain update in a nonuniform density profile.

Original languageEnglish (US)
Pages (from-to)7121-7126
Number of pages6
Issue number20
StatePublished - Sep 25 2001

ASJC Scopus subject areas

  • Organic Chemistry
  • Polymers and Plastics
  • Inorganic Chemistry
  • Materials Chemistry


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