Structural hyperphase diagram

In the most generic model to describe discrete semiflexible polymers with self-interaction the energy of a conformation with N monomers is written as 

For the identification of the structural phases, we investigate thermal fluctuations of energy and radius of gyration as functions of T and k by canonical statistical analysis. The quantities we consider here are defined by temperature derivatives of the mean energy, in the form of the specific heat 

Both quantities can be considered as thermodynamic landscapes in parameter space (T, k), where cooperative behavior (resulting in structural transitions) is signaled by regions of high thermal activity ( ridges ). It should be noted that this kind of comparative canonical analysis leaves a systematic uncertainty in the estimation of transition lines, yielding a complete but rather qualitative picture of the transition behavior. This is due to the finite size of the system, and for this reason, structural phases identified here should not be confused with phase transitions in the thermodynamic sense. 

The most intricate conformational macrostates belong to the compact solid, globular phase C. In this regime, the polymer maximizes the number of pairwise monomer-monomer contacts and is therefore highly energy-dominated. Since monomers in the center 

Top Surface plot of cf(/ g) (T, k)/dT, with peaks indicated by circies, and subsequent lines highlighting conformational phase boundaries. Dashed lines indicate transitions suggested by the Khalatur parameters and the specific heat. Bottom Square radius of gyration /, relative number of pairwise monomer-monomer contacts /Vpair/W, and the number of icosahedral cores Qos for the low-energy conformations in dependence of/c, providing insight into differences of structural properties in the low-T phases. From [184]. 

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