On the location of the surface-attached globule phase in collapsing polymers

We investigate the existence and location of the surface phase known as the “Surface-Attached Globule” (SAG) conjectured previously to exist in lattice models of three-dimensional polymers when they are attached to a wall that has a short range potential. The bulk phase, where the attractive intra-polymer interactions are strong enough to cause a collapse of the polymer into a liquid-like globule and the wall either has weak attractive or repulsive interactions, is usually denoted Desorbed-Collapsed or DC. Recently this DC phase was conjectured to harbour two surface phases separated by a boundary where the bulk free energy is analytic while the surface free energy is singular. The surface phase for more attractive values of the wall interaction is the SAG phase. We discuss more fully the properties of this proposed surface phase and provide Monte Carlo evidence for self-avoiding walks up to length 256 that this surface phase most likely does exist. Importantly, we discuss alternatives for the surface phase boundary. In particular, we conclude that this boundary may lie along the zero wall interaction line and the bulk phase boundaries rather than any new phase boundary curve. The phase transitions of a single isolated polymer in solution continue to attract attention as single polymers are fundamental components in more complicated modelling scenarios and these transitions are not yet fully understood. The collapse transition [1] mediated by the intra-polymer attractive interactions and the adsorption transition [2] when a polymer is attached to a sticky wall, are two of the key transitions that have been well studied. The situation when both transitions can occur in the same system has been studied less intensely due to the difficulty of numerical work such as Monte Carlo simulations when two independent parameters compete. However, with the advent of more powerful computers and sophisticated algorithms this situation has received some attention. The standard lattice model for polymers is the self-avoiding walk (SAW) with the sites of the walk called monomers. The intra-polymer attraction is modelled by a potential energy εp associated with monomers that are nearest-neighbours on the lattice. These instances will be referred to as (nearest-neighbour) contacts. To consider adsorption a wall is introduced, so that the polymer is restricted to one side of the wall, or may visit the wall, with one end of the polymer (SAW) attached to the wall. Any monomer which visits the wall, other that the one fixed on the wall, is given a potential energy εw. These monomers will be referred to as visits. Various different phases