The nature of the polymer collapse transition

In a good solvent, a polymer chain assumes an extended configuration. As the solvent quality (or the temperature) is lowered, the configuration changes to globular, which is more compact. This collapse transition is also called coil-globule transition in the literature. Since the pioneering work by de Gennes, it is known that it corresponds to a tricritical point in a grand-canonical parameter space. In the most used lattice model to study it, the chain is represented by a self-avoiding walk on the lattice and the solvent is effectively taken into account by including attractive interactions between monomers on first neighbor sites which are not consecutive along a chain (SASAW's: self-attracting self-avoiding walks). We will review the model and show that small changes in it may lead to different phase diagrams, where the collapse transition is no longer a tricritial point. In particular, if the polymer is represented by a trail, which allows for multiple visits of sites but mantains the constraint of single visits of edges, we find two distinct polymerized phases besides the non-polymerized phase and the collapse transition becomes a bicritical point.

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