Entropy of chains placed on the square lattice

Abstract

We obtain the entropy of flexible linear chains composed of M monomers placed on the square lattice using a transfer matrix approach. An excluded volume interaction is included by considering the chains to be self-and mutually avoiding, and a fraction rho of the sites are occupied by monomers. We solve the problem exactly on stripes of increasing width m and then extrapolate our results to the two-dimensional limit to infinity using finite-size scaling. The extrapolated results for several finite values of M and in the polymer limit M to infinity for the cases where all lattice sites are occupied (rho=1) and for the partially filled case rho<1 are compared with earlier results. These results are exact for dimers (M=2) and full occupation (ρ=1) and derived from series expansions, mean-field like approximations, and transfer matrix calculations for some other cases. For small values of M, as well as for the polymer limit M to infinity, rather precise estimates of the entropy are obtained.

6 pages, 7 figures

Cited by in corpus (6)

• Entropy of polydisperse chains: solution on the Husimi lattice
• Entropy of rigid k-mers on a square lattice
• Entropy of polydisperse chains: solution on the Bethe lattice
• Polydisperse chains placed on a one-dimensional lattice
• Asymptotic behavior of the entropy of chains placed on stripes
• Semi-flexible trimers on the square lattice in the full lattice limit