Strictly two-dimensional self-avoiding walks: Thermodynamic properties revisited

Abstract

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 dynamics 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 ρ the expected power law scaling for the interaction energy between different chains e(int) ~ ρ(21/8), the total pressure P ~ ρ(3) and the dimensionless compressibility g(T) = lim(q→0)S(q) ~ 1/ρ(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 ξ(ρ) 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 wave vector q. We comment briefly on finite persistence length effects.

Shear modulus of simulated glass-forming model systems: Effects of boundary condition, temperature, and sampling time

“…( 4). We note that for isotropic d-dimensional systems it can be shown [21,39] that the Born-Lamé coefficient can be simplified as…”

“…[4] assumed explicitly a well-defined reference position and a displacement field for the particles, it has not been appreciated that this approach is consistent (at least if the initial pressure is properly taken into account) with the well-known pressure fluctuation formula for the compression modulus K of isotropic fluids [6][7][8][9] which has been derived several * Electronic address: joachim.wittmer@ics-cnrs.unistra.fr decades earlier, presumably for the first time in the late 1940s by Rowlinson [8]. In any case, the stress fluctuation formalism provides a convenient route to calculating the elastic properties in computer simulations which has been widely used in the past [7,[10][11][12][13][14][15][16][17][18][19][20][21]. It has been generalized to systems with nonzero initial stress [10], hard-sphere interactions [12] and arbitrary continuous potentials [5], or to the calculation of local mechanical properties [20].…”

“…While the elastic properties of crystals with one atom per unit cell are given by the Born term only, stress fluctuations are significant for crystals with more complex unit cells [5]. They become particularly pronounced for polymer like soft materials [21] and amorphous solids [7, 11, 13-18, 20, 22]. This is revealed by recent simulation studies of various glass formers [11], like Lennard-Jones (LJ) mixtures [13][14][15][16], polymer glasses [7,20] or silica melts [22].…”

“…This begs the delicate question of whether the general stress fluctuation formalism and especially Eq. ( 3) for the shear modulus only holds for elastic solids with a well-defined displacement field, as suggested in the early literature [4][5][6], or if the approach may actually be also applied through a solid-liquid transition up to the liquid state [8,21] with µ F → µ A and thus G = G τ τ → 0 as it should for a liquid. By reworking the theoretical arguments leading to Eq.…”

Semiflexible Chains at Surfaces: Worm-Like Chains and beyond

“…Only small subvolumes of much larger boxes are represented. The configurations have been sampled by increasing ϵ starting with flexible and compact chain systems (ϵ=0) [68,76,80]. While the chains remain compact and segregated at low densities and stiffnesses below the dashed line, they are seen in the opposite limit to align (at least) locally, forming bundles of chains with hairpins, which are extremely difficult to equilibrate.…”