Universality of crossover scaling for the adsorption transition of lattice polymers.

Abstract

Recently, it has been proposed that the adsorption transition for a single polymer in dilute solution, modeled by lattice walks in three dimensions, is not universal with respect to intermonomer interactions. Moreover, it has been conjectured that key critical exponents ϕ, measuring the growth of the contacts with the surface at the adsorption point, and 1/δ, which measures the finite-size shift of the critical temperature, are not the same. However, applying standard scaling arguments the two key critical exponents should rather be identical, hence pointing to a potential breakdown of these standard scaling arguments. Both of these conjectures are in contrast to the well-studied situation in two dimensions, where there are exact results from conformal field theory: these exponents are both accepted to be 1/2 and universal. We use the flatPERM algorithm to simulate self-avoiding walks and trails on the hexagonal, square, and simple cubic lattices up to length 1024 to investigate these claims. Walks can be seen as a repulsive limit of intermonomer interaction for trails, allowing us to probe the universality of adsorption. For each lattice model we analyze several thermodynamic properties to produce different methods of estimating the critical temperature and the key exponents. We test our methodology on the two-dimensional cases, and the resulting spread in values for ϕ and 1/δ indicates that there is a systematic error which can far exceed the statistical error usually reported. We further suggest a methodology for consistent estimation of the key adsorption exponents which gives ϕ=1/δ=0.484(4) in three dimensions. Hence, we conclude that in three dimensions these critical exponents indeed differ from the mean-field value of 1/2, as had previously been calculated, but cannot find evidence that they differ from each other. Importantly, we also find no substantive evidence of any nonuniversality in the polymer adsorption transition.