The low value of , where is the nematic-isotropic phase transition temperature and denotes the virtual transition temperature, is a long-standing puzzle in the physics of liquid crystals. The present review presents experimental and theoretical results on this long-standing problem. New experimental and theoretical results for the critical behaviour in the isotropic phase of nematogens are reviewed. We calculate in a unified approach the low value of , at both critical and tricritical points. The possibility of tricritical behaviour at the nematic-isotropic transition is also discussed by means of Landau theory. The various predictions are compared with the available experimental results.

http://iopscience.iop.org/article/10.1088/0953-8984/10/41/003/pdf

The puzzle of the nematic-isotropic phase transition

Results of studies of static dielectric permittivity (epsilon) and nonlinear dielectric effect (NDE) in the isotropic phase of 4-n-4'-isothiocyanatobiphenyl (nBT) homologous series from n = 2 to n = 10 exhibiting the isotropic-smectic E (I-SmE) transition, are presented. They are compared with results of similar studies in 4-cyano-4-n-alkylbiphenyls (nCB) from n = 4 to n = 12. In this homologous series isotropic-nematic (I-N) and isotropic-smectic-A (I-Sm-A) transitions take place. Despite significant differences between N, Sm-A, and Sm-E phases the same pretransitional behavior of epsilon and NDE in the isotropic phase, described by critical exponents gamma = 1 and alpha = 0.5, was found. It has been shown that when the length of the alkyl chain of a compound increases the discontinuity of the transition drops in nBT and rises in nCB. The influence of pressure on the discontinuity is also discussed.

Phase transitions from the isotropic liquid to liquid crystalline mesophases studied by linear and nonlinear static dielectric permittivity

The longitudinal relaxation time τ of a series of alkyl-isothiocyanato-biphenyls (nBT) liquid crystals in the smectic E phase was measured as a function of temperature T and pressure P using dielectric spectroscopy. This relaxation time was found to become essentially constant, independent of T and P, at both the clearing point and the lower temperature crystalline transition. τ(T,P) could also be superposed as a function of the product TVγ, where V is the specific volume and γ is a material constant. It then follows from the invariance of the relaxation time at the transition that the exponent γ superposing τ(T,V) can be identified with the thermodynamic ratio Γ=−∂log(Tc)∕∂log(Vc), where the subscript c denotes the value at the phase transition. Analysis of literature data on other liquid crystals shows that they likewise exhibit a constant τ at their phase transitions. Thus, there is a surprising relationship between the thermodynamic conditions defining the stability limits of a liquid crystalline phas...

Thermodynamic scaling and the characteristic relaxation time at the phase transition of liquid crystals.

Results are presented of studies on the low frequency (f' 250 kHz) non-linear dielectric effect on approaching the nematic and smectic A phases in 4′-cyano-4-n-alkylbiphenyls (nCB, for n = 6, 7, 8, 10, 11, 12). In all cases, the mean-field behaviour was valid up to the clearing temperature. In the case of the isotropic-nematic transition (6CB, 7CB, 8CB), a quantitative agreement with the relation based on the Landau-de Gennes model was also ascertained. The specific feature of the research method applied was that the characteristic time introduced by the measurement field (T′ ≊ 1/f) was always greater than the relaxation time τ, i.e. the condition: (T′/τ)>1 was satisfied up to T c.

Mean-field behaviour of the low frequency non-linear dielectric effect in the isotropic phase of nematic and smectic n-alkylcyanobiphenyls

Results of studies of the dielectric permittivity and nonlinear dielectric effect (NDE) in the isotropic phase of n-hexyl-cyanobiphenyl are presented. The data reported cover both pressure and temperature dependence. Measurements under atmospheric pressure were carried out in a wide range, up to 100 K from the clearing temperature. The application of a weak measurement frequency (f=67 kHz) resulted in a negligible influence of relaxation processes on NDE results. For both temperature and pressure paths, the dielectric permittivity and the NDE exhibited strong pretransitional effects, described by "critical" exponents phi =1-alpha approximately 0.5 and gamma=1, respectively. Scaling expressions for the pretransitional behavior of the NDE and of the dielectric permittivity have been proposed. The relationship between pretransitional effects in the isotropic phase of nematogens and in critical solutions has also been discussed.

T. R. Bose

Papers

Inclusion of density variation in the Landau-de Gennes theory of the nematic-isotropic phase transition.