As their name indicates, liquid crystals simultaneously exhibit some characteristics common to both ordinary isotropic liquids and solid crystals. This ambivalence is also found in the effects of surfaces on these systems which lead to a great diversity of phenomena. These phenomena are reviewed focusing on nematic liquid crystals which have the simplest structure among the many existing types and which have been the most extensively studied. Three main kinds of effects can be distinguished. The first concerns the perturbation of the liquid crystalline structure close to the surface. Beyond this transition region, the bulk liquid crystalline structure is recovered with an orientation which is fixed by the surface: this phenomenon of orientation of liquid crystals by surfaces is the so-called anchoring. Finally, close to bulk phase transitions, critical adsorption or wetting can occur at surfaces as is also seen in isotropic systems.

https://iopscience.iop.org/article/10.1088/0034-4885/54/3/002/pdf

Surface effects and anchoring in liquid crystals

If the potential for a boom in the global hydrogen economy is realized, there will be an increase in the need for accurate hydrogen thermodynamic property standards. Based on current and anticipated needs, new fundamental equations of state for parahydrogen, normal hydrogen, and orthohydrogen were developed to replace the existing property models. To accurately predict thermophysical properties near the critical region and in liquid states, the quantum law of corresponding states was applied to improve the normal hydrogen and orthohydrogen formulations in the absence of available experimental data. All three equations of state have the same maximum pressure of 2000MPa and upper temperature limit of 1000K. Uncertainty estimates in this paper can be considered to be estimates of a combined expanded uncertainty with a coverage factor of 2 for primary data sets. The uncertainty in density is 0.04% in the region between 250 and 450K and at pressures up to 300MPa. The uncertainties of vapor pressures and saturated liquid densities vary from 0.1% to 0.2%. Heat capacities are generally estimated to be accurate to within 1%, while speed-of-sound values are accurate to within 0.5% below 100MPa.

/pdf/fundamental-equations-of-state-for-parahydrogen-normal-jfrnkfiwco.pdf

Fundamental Equations of State for Parahydrogen, Normal Hydrogen, and Orthohydrogen

Developments in the foundations of statistical mechanics during the past ten years or so. The author discusses how statistical concepts enter the treatment of deterministic mechanical systems, with particular reference to trajectory instabilities and to the KAM theorem. Then he deals with large systems: the thermodynamic limit and the theory of infinite systems. Non-equilibrium statistical mechanics is covered but LC relativistic statistical mechanics is not.

https://iopscience.iop.org/article/10.1088/0034-4885/42/12/002/pdf

Foundations of statistical mechanics

Phase transitions in liquid crystals

Landau theory of the nematic-isotropic phase transition

An adiabatic scanning calorimeter has been used to study the thermal behavior of the liquid-crystal octylcyanobiphenyl (8CB) in the temperature range between 10 and 50\ifmmode^\circ\else\textdegree\fi{}C. The solid---to---smectic-$A$ ($\mathrm{KA}$), the smectic-$A$---to---nematic ($\mathrm{AN}$), as well as the nematic-to-isotropic (NI) phase transitions, which fall in this temperature range, have been investigated in great detail. From our measuring procedure the enthalpy behavior (including latent heats) as well as the heat capacity have been obtained. For the KA transition the latent heat was 25.7\ifmmode\pm\else\textpm\fi{}1.0 kJ/mol and for the NI transition it was 612\ifmmode\pm\else\textpm\fi{}5 J/mol. Within the resolution of our experiment we find that the $\mathrm{AN}$ transition is a continuous one. For the latent heat, if any, we arrive at an upper limit of 0.4 J/mol (or 1.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ J/g). The observed anomaly in the heat capacity for the $\mathrm{AN}$ transition is not consistent with a nearly logarithmic singularity as predicted by the $\mathrm{XY}$ model, instead we obtain a critical exponent $\ensuremath{\alpha}={\ensuremath{\alpha}}^{\ensuremath{'}}=0.31\ifmmode\pm\else\textpm\fi{}0.03$. This result is consistent with the anisotropic scaling relation ${\ensuremath{\nu}}_{\ensuremath{\parallel}}+2{\ensuremath{\nu}}_{\ensuremath{\perp}}=2\ensuremath{-}\ensuremath{\alpha}$. The pretransitional effects near the NI transition are in qualitative agreement with the hypothesis of quasitricritical behavior.

Temperature dependence of the enthalpy and the heat capacity of the liquid-crystal octylcyanobiphenyl (8CB)

From adiabatic-scanning calorimetric results it is demonstrated that in mixtures of 9CB and 10CB, two compounds of the alkylcyanobiphenyl ($n\mathrm{CB}$) series, the nematic ($N$) to smectic-$A$ ($A$) transition becomes first order for narrow $N$ ranges. From the latent heats a tricritical point is located in the phase diagram. Measurements for 7CB+ 8CB mixtures show that the specific-heat exponent $\ensuremath{\alpha}$ depends on the width of the $N$ range for continuous $\mathrm{AN}$ transitions.

Nematic-Smectic- A Tricritical Point in Alkylcyanobiphenyl Liquid Crystals

An adiabatic scanning calorimeter has been used to investigate the temperature dependence of the enthalpy and the heat capacity near the smectic A (A) to nematic (N) phase transition in mixtures of alkylcyanobiphenyl (nCB) liquid crystals. Mixtures of 8CB + 10 CB with small N-ranges undergo first-order transitions, but mixtures with large N-ranges exhibit continuous ones. A tricritical point could be located for the 10CB mole fraction of 0.3135. For a nearly tricritical mixture, a critical exponent α = 0.50 ± 0.02 has been observed. For mixtures with continuous AN transitions it is seen that this specific heat exponent α decreases with the width of the nematic range.

Experimental Evidence for a Nematic to Smectic A Tricritical Point in Alkylcyanobiphenyl Mixtures

An adiabatic scanning calorimeter has been used in a calorimetric investigation of alkyl-cyanobiphenyl (nCB) liquid crystals. Measurements near solid to smectic (KA), smectic A to nematic (AN) and nematic to isotropic (NI) or smectic A to isotropic (AI) phase transitions have been carried out for scanning rates as low as a few μKs−1. Results for the temperature dependence of the heat capacity as well as for the enthalpy (including latent heats) have been obtained for 8CB, 9CB, 10CB and 11CB. Latent heat values are reported for the different KA, NI and AI transitions. For the two compounds 8CB and 9CB, which show a AN transition, it was found that, within the resolution of the experiments, these transitions are second-order. The anomalous heat capacity observed near the AN transition is much larger for 9CB than for 8CB. The critical exponent α obtained from power law fits to the heat capacity data is 0.31 ± 0.03 for 8CB and 0.50 ± 0.05 for 9CB. It is suggested that the AN transition in 9CB must be...

Heat Capacity and Enthalpy Behavior Near Phase Transitions in Some Alkylcyanobiphenyls

The specific heat Cpx has been measured for the binary system triethylamine–water as a function of temperature near the critical solution temperature at the critical concentration. Simple power law fits of the data resulted in rather large values (around 0.25) for the critical exponent α. For a fixed value of α equal to the Ising value αI=0.125 good fits could only be obtained if more complex expressions were used in fitting the data. For this case the best result was obtained by including a correction‐to‐scaling term. Combining our result for the amplitude of the specific heat singularity with the correlation length amplitude allowed us to test two‐scale‐factor universality. Our result strongly indicates that, in contrast to earlier findings, two‐scale‐factor universality is also valid for binary systems.

W. Van Dael

Papers

Temperature dependence of the enthalpy and the heat capacity of the liquid-crystal octylcyanobiphenyl (8CB)

Nematic-Smectic- A Tricritical Point in Alkylcyanobiphenyl Liquid Crystals

Experimental Evidence for a Nematic to Smectic A Tricritical Point in Alkylcyanobiphenyl Mixtures

Heat Capacity and Enthalpy Behavior Near Phase Transitions in Some Alkylcyanobiphenyls

Heat capacity of the binary liquid system triethylamine–water near the critical solution point