Figure 4: Scaling properties at the coil-globule transition.
From: First-order coil-globule transition driven by vibrational entropy
(a) Log–log plot of the maximum of the specific heat, CMAX as a function of the polymer length N for the ISAW model (black circles) and for the VISAW model in the two cases k=0 (blue circles) and k=2 (red circles). The VISAW-specific heat has been reduced by a factor to be plotted with the much lower one of the ISAW without compressing too much the latter. (b) Log–log plot of the ratio of the average radius of gyration, R, to the expected ideal scaling behaviour, N1/2, as a function of the polymer length. The data for the ISAW and VISAW (k=0) models have been taken at the transition point, identified as the temperature TC where the curves R(T)/N1/2 intersect, rather than as the temperature of the maximum of the specific heat, which is affected by considerable finite size effects. Importantly, in both cases, a temperature TC is well identified from the data (not shown). In the case of the VISAW (k=2), the data have been taken at the temperature of the maximum of the specific heat, as in this case no clear temperature can be found where the curves R(T)/N1/2 intersect, and because the data show, especially for longer polymers, that the transition temperature identified using the Maxwell construction (Fig. 1e) coincides with the one of the maximum of the specific heat. The inset shows the behaviour of R(N)0.587 as a function of polymer length to highlight that for longer lengths VISAW polymers behave as self-avoiding chains. Data keys in panel b are the same as in panel a.
