The density crossover scaling of various thermodynamic properties of solutions and melts of self-avoiding and highly flexible polymer chains without chain intersections confined to strictly two dimensions is investigated by means of molecular dynamic
s and Monte Carlo simulations of a standard coarse-grained bead-spring model. In the semidilute regime we confirm over an order of magnitude of the monomer density rho the expected power-law scaling for the interaction energy between different chains e_intersimrho^(21/8), the total pressure Psimrho^3 and the dimensionless compressibility gT=lim(q->0)(S(q)sim1/rho^2). Various elastic contributions associated to the affine and non-affine response to an infinitesimal strain are analyzed as functions of density and sampling time. We show how the size xi(rho) of the semidilute blob may be determined experimentally from the total monomer structure factor S(q) characterizing the compressibility of the solution at a given wavevector q. We comment briefly on finite persistence length effects.
We present here computational work on the center-of-mass displacements in thin polymer films of finite width without topological constraints and without momentum conservation obtained using a well-known lattice Monte Carlo algorithm with chain length
s ranging up to N=8192. Computing directly the center-of-mass displacement correlation function C_N(t) allows to make manifest the existence of scale-free colored forces acting on a reference chain. As suggested by the scaling arguments put forward in a recent work on three-dimensional melts, we obtain a negative algebraic decay C_N(t) sim -1/(Nt) for times t << T_N with T_N being the chain relaxation time. This implies a logarithmic correction to the related center-of-mass mean square-displacement h_N(t) as has been checked directly.
