Entropy in the Coil-to-Globule Transition of Macromolecules : Insights from Simple Models

The coil to globule transition is a fundamental phenomenon in the physics of macro-molecules by reason of the multiplicity of arrangements of their conformation. Such conformational freedom is the main source of entropy in the molecule and is the main opponent to the transition towards the compact state, since a system tends to the state of maximum entropy. This phenomenon is captured by very simple models, such as the ensemble of Interacting Self avoiding Walks on the lattice. This model shows that the coil to globule transition belongs to the universality class of continuous transition called Θ point. Starting from a critical inspection of the definition of the interacting walks model, we introduce a refinement aiming to represent more precisely the entropy sourced from the local fluctuations of the molecule around its equilibrium conformations; this contribution is absent in the standard model which includes only the entropy generated by the multiplicity of the global conformations. Through the study of the vibrational properties of the model and an exhaustive numerical simulation of the phase transition we show that the new model presents a transition which is different in character and belongs to a distinct universality class. In particular, in 3 dimensions the model shows a discontinuous transition; thanks to this, the model presents a common framework underlying the physics of both homo-polymers and proteins. Considering the results obtained in 2 and 3 dimensions we identify the convexity of the vibrational entropy as the responsible of the new class of transitions. These results and a revision of experimental measures of viscosity bring into question the standard description of the homo-polymer transition.