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 inter-monomer interactions. It has also been conjectured that key critical exponents $\varphi$, measuring the growth of the contacts with the surface at the adsorption point, and $1/\delta$, 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 be identical, thus pointing to a potential breakdown of these standard scaling arguments. This is 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 inter-monomer interaction for trails, allowing us to probe the universality of adsorption. For each 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 $\varphi$ and $1/\delta$ indicates that there is a systematic error that exceeds the statistical error usually reported. We further suggest a methodology for consistent estimation of the key adsorption exponents which gives $\varphi =1/\delta =0.484(4)$ in three dimensions. We conclude that in three dimensions these critical exponents indeed differ from the mean-field value of $1/2$, but cannot find evidence that they differ from each other. Importantly, we also find no substantive evidence of any non-universality in the polymer adsorption transition.

References in corpus (2)

• On the location of the surface-attached globule phase in collapsing polymers
• Solvent-Dependent Critical Properties of Polymer Adsorption

Cited by in corpus (10)

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• Critical Behaviour of Magnetic Polymers in Two and Three Dimensions
• Adsorption of neighbor-avoiding walks on the simple cubic lattice
• Phase transitions in solvent dependent polymer adsorption in three dimensions
• Adsorption of 2d polymers with two- and three-body self-interactions
• Critical behaviour of the extended-ballistic transition for pulled self-avoiding walks
• Adsorption of interacting self-avoiding trails in two dimensions
• Adsorption of melting deoxyribonucleic acid
• Lattice polymers near a permeable interface
• Self-avoiding walks pulled at an angle