Exact enumeration and Monte Carlo results for self-avoiding walks in a slab

We analyse exact enumeration data and Monte Carlo simulation results for a self-avoiding walk model of a polymer confined between two parallel attractive walls (plates). We use the exact enumeration data to establish the regions where the polymer exerts an effective attractive force between the plates and where the polymer exerts an effective repulsive force by estimating the boundary (zero-force) curve. While the phase boundaries of the phase diagram have previously been conjectured we delineate this further by establishing the order of the phase transitions for the so-called infinite slab (that is, when the plates are a macroscopic distance apart). We conclude that the adsorption transitions associated with either plate are similar in nature to the half-space situation even when a polymer is attached to the opposite wall. The transition between the two adsorbed phases is established as first order. Importantly, we conjecture a scaling theory valid in the desorbed and critically adsorbed regions of the phase diagram and demonstrate the consistency of the Monte Carlo data with these hypotheses by estimating the corresponding scaling functions. PACS numbers: 05.70.Fh, 05.50.+q, 61.25.Hq (Some figures in this article are in colour only in the electronic version) 1