Pseudo second phase transition

Equation 2.110, we obtain the analytical expression for the pseudo-second-phase-transition temperature (Wang, 1995a)... 

For simplicity, assume that vab is the geometrical mean of va and vb, i.e., the Berthelot law, and extend the free energy derived from Equation 2.f22 in the power series of Sa and, S),. The zero determinant of the quadratic coefficients gives the pseudo-second-phase-transition temperature as follows... 

In the second-order approximation of the free energy, above T, Sa and Sb are both zero. Below T, the order parameters are non-zero. At T, the quadratic terms vanish. This formula illustrates the pseudo-second-phase-transition temperature vs. the molecular parameters that shows the same shapes as those of the numerical calculations of the N-I transition temperature Tc, mentioned above. 

McCrone (1965) also noted that second-order phase transitions have been termed as pseudopolymorphic. Such transitions are difficult to detect by optical methods, because of the small structural changes that occur hence, the origin of the prefix pseudo sometimes used to describe them. However, the birefringence of the crystals changes during such phase changes (see Section 4.2), so the use of crossed polarizers makes the phase change readily detectable. 

The first term in the formula is the pseudo second order phase transition temperature T. The coefficient B is not great, therefore the second term is not significant. The difference of Tc and T is small, experimentally only a few degrees difference. 

Pseudo-second-order-phase-transition temperature... 

Fig. 5.2(a)] result in a pseudo-transition which is represented by the first specific-heat peak in Fig. 5.1. The second less-pronounced peak in Fig. 5.1 around T 0.6 — 0.7 signals the melting into globular structures, whereas at still higher temperatures T 1.5 the well-known collapse peak indicates the dissolution into the random-coil phase. The distribution of the maximum values of the specific heat with respect to the maximum temperatures is shown in Fig. 5.3. Not surprisingly, the peaks belonging to the... 

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