Nematic-isotropic transition heat capacity

Experimentally, the careful measurement of the heat capacity of low molar mass liquid crystals shows this "diverging" behavior at the nematic-isotropic transition, and also at the smectic-nematic transition For polymers, there is a limitation in the measurement of heat capacities, since the transition takes place in a relatively large temperature range, and thus, there is at each temperature a mixture of heat capacity and heat of transition. In order to solve this problem, we have built a tool for being able to make the difference between the first and the second order component of a DSC transition peak. The basic idea is that these two contributions of the total recorded heat power will behave in a different manner when the heating rate or the mass of sample are changed. 

Its N value is 1.4 (measured with l p=2.5, 5 and 10 C/min). The second peak at 135 C is the nematic-isotropic transition peak. Its N value is 1.3 (same heating rates). These two N values are typically the ones of first order phase transitions. The heat capacity of PAA is small compared to the height of the peak. Even if an anomalous second order phenomenon occurs, increasing the heat capacity jump under the nematic-isotropic peak by 100% or 200%, it cannot shift N towards two in a detectable way. 

In SMPs with a liquid crystalline transition the specific heat capacity increases significantly up to the transition point due to long range fluctuations of the order parameter near the transition [49]. At the transition temperature, a first-order phase transition occurs. The recorded DSC peak of the liquid crystalline transition will be the mixture of these two contributions. A schematic example for a liquid crystalline polymer is shown in Fig. 2 (diagram e), showing transitions in the form of sharp endothermic peaks, Tc-n for the crystal-nematic transition and for the nematic-isotropic transition. 

As a rule, the phase transition from the isotropic phase into the nematic phase is a weak first-order transition [6] with a small jump in the order parameter 5 (Fig. 1.3 [7]) and other thermodynamic properties. The so-called clearing point corresponds to this first-order transition temperature Tni. At the same time, in the pretransitional region of the isotropic phase we can observe the temperature divergence in some physical parameters, such as heat capacity, dielectric permittivity, etc., according to the power law (T — T i) where T j is the other, virtual, second-order phase transition point, (Tni — T 0.1 K) and t) is an exponent, depending on the physical property under consideration. 

In the isotropic phase Q = 0 and in the nematic phase Q O. In Eq. (34) one has A = a(T-T )/Tf i and B>0. The presence of the cubic term, which does not disappear at rN, leads to a first-order transition with a finite discontinuity in the order parameter (0N-i = 2fi/3C). T is the stability limit of the isotropic phase. For B = 0, a normal second-order transition at N- I is expected. The excess heat capacity in the nematic phase is given by [16] ... 

Figure 9. Temperature dependence of the reduced heat capacity per moie (R is the gas constant) near the nematic to isotropic (N-I) transition for hexylcyano-biphenyl (6CB). The width of the arrow on the temperature axis represents the two-phase region [5].

Different phase transitions involving blue phases are expected theoretically to be first-order [54] except the BPm to isotropic transition which could become second order [54] in an isolated critical point at the termination of a first-order line [6, 55], Figure 10 shows Cp results of cholesteryl non-nanoate (CN) with adiabatic scanning calorimetry [56]. From Fig. 10 it is clear that there are substantial pretransitional heat capacity effects associated with the BPm-I transition, which means that a large amount of energy is going into changing the local nematic order. The other transitions appear as small, narrow features on the BPm-I transition peak. From the inspection of the en-... 

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