Thermal Investigations of Phase Transitions in Thermotropic Liquid Crystals

Abstract

Liquid Crystals in the Nineties and Beyond Downloaded from www.worldscientific.com by UNIVERSITY OF BIRMINGHAM LIBRARY -INFORMATION SERVICES on 03/19/15. For personal use only. 20 J. Tkoentransitions is discussed in Sec. 11. In order to avoid long chemical names, commonly used abbreviations listed in the Appendix are utilized in the text. Experimental Methods Purpose of thermal measurementsIn calorimetric experiments, one obtains information on the temperature dependence of the energy or enthalpy H(T) of a given sample. In many cases, one measures the heat capacity C p = (dH/dT) p and is satisfied with only the slope of the enthalpy curve (see Figs. 1 and 2) as a function of temperature. For second-order phase transitions, the information on the pre-transitional heat capacity is needed to analyze the relevant thermal aspects of critical fluctuations. For a first-order phase transition, the essential information on the latent heat A/ft, (see Figs. 1 and 2) cannot be obtained through heat capacity measurements and a direct measurement of the enthalpy is necessary. Fig, 1. (a) Schematic representation of the temperature dependence of the enthalpy H of a liquid crystal sample near a first-order (solid curve) or second-order (dashed curve) phase transition at 7V The dashed-dotted line gives the enthalpy of a (DSC) reference material with a nearly constant heat capacity and without a phase transition, (b) Corresponding DSC responses (from heating runs) for the first-order (solid curve) and second-order (dashed curve) cases of part (a)

The nematic-isotropic transition of the Lebwohl–Lasher model revisited

“…[41]. Above the NI transition, the form C(T * − T * C ) −α fits the temperature dependence of c * V across the temperature interval between T * = 1.1222 and 1.1500 (corresponding to ∼ 8 K) for C ∼ 0.5, T * C ∼ 1.1219 and α ∼ 0.4, while an exponent between 0.11 and 0.5 is expected here [41].…”

“…Since the latent heat at the weakly first-order NI transition is rather small, various physical observables might be expected to exhibit critical power-law behaviour similar to that observed in second-order transitions, at least very close to the transition [41]. We have thus attempted to estimate the corresponding critical exponents β, α and ν [42] by fitting the temperature dependencies of the order parameter, specific heat, and correlation length, respectively.…”

“…We have thus attempted to estimate the corresponding critical exponents β, α and ν [42] by fitting the temperature dependencies of the order parameter, specific heat, and correlation length, respectively. The fits turn out not to be very robust and are dependent on the fitting range as in real experiments [41]. On the one hand, the fitting temperature range should be narrow to remain in the vicinity of the NI transition and, at the same time, broad enough to exploit as many data points as possible for a representative fit.…”

“…Taking all the data points between T∗=1.1000 and 1.12255 (corresponding to ∼7 K for a room-temperature nematic, which is more than in a typical experiment) yields A ∼ 0.13, B ∼ 0.9, TC∗′∼1.1226 and β ∼ 0.3. (Experiments give here β ∼ 0.25 [41]. ) Similarly, the temperature dependence of the heat capacity cV∗, figure 3 a , b , can be fitted to the three-parameter form C′false(TC∗′−T∗false)−α′, yielding (in the same temperature interval as for 〈 P 2 〉), C ′ ∼ 1.3, TC∗′∼1.1226, and α ′ ∼ 0.4, the experimental values for α ′ usually falling between 0.3 and 0.4 [41].…”

“…(Experiments give here β ∼ 0.25 [41]. ) Similarly, the temperature dependence of the heat capacity cV∗, figure 3 a , b , can be fitted to the three-parameter form C′false(TC∗′−T∗false)−α′, yielding (in the same temperature interval as for 〈 P 2 〉), C ′ ∼ 1.3, TC∗′∼1.1226, and α ′ ∼ 0.4, the experimental values for α ′ usually falling between 0.3 and 0.4 [41]. Above the NI transition, the form Cfalse(T∗−TC∗false)−α fits the temperature dependence of cV∗ across the temperature interval between T∗=1.1222 and 1.1500 (corresponding to ∼8 K) for C ∼ 0.5, TC∗∼1.1219 and α ∼ 0.4, while an exponent between 0.11 and 0.5 is expected here [41].…”