In contrast, there has been much less interest in the possibility of a low temperature order-disorder transition between two dense phases both because of the greater difficulty of simulating dense polymers and because fewer theoretical expectations for such a transition are available. This situation contrasts with that for heteropolymers where, in the context of protein folding, there has been intense interest in the transition between the molten globule and the native state of the protein. The structure of the native state reflects the amino acid sequence and the specific interactions between these units, and so it might be thought that an ordered structure is less likely when all polymer units are identical. However, this is not the lesson from other finite systems. For example, homogeneous atomic clusters show a rich low temperature phase behaviour; there is the finite-size analogue of the first-order melting transition,[4,5] surface melting,[6] and even low temperature transitions between different ordered forms.[7]
Recently, the existence of an isolated homopolymer order-disorder transition has begun to be confirmed.[8,9,10] In their study of a lattice homopolymer model which involved three-body forces Kuznetsov et al. found phases with orientational order,[9] and in their simple off-lattice model Zhou et al. observed a order-disorder transition and also a solid-solid transition.[10] Moreover, in some earlier studies of the collapsed polymer glimpses of these transitions were seen.[11,12,13,14] Here, we add to this growing understanding of the low temperature phase behaviour of isolated homopolymers by studying a lattice model of a semi-flexible polymer, looking particularly at the effect of stiffness on the order-disorder transition. We compare our results with the phase diagram calculated in recent theoretical[15] and simulation[16] studies of the polymer model we use here.