Phase transitions in liquid crystals

Recent experiments have reported that ferroelectric nanoparticles have drastic effects on nematic liquid crystals---increasing the isotropic-nematic transition temperature by about 5 K, and greatly increasing the sensitivity to applied electric fields. To understand these effects, we develop a theory for the statistical mechanics of ferroelectric nanoparticles in liquid crystals. This theory predicts the enhancements of liquid-crystal properties, in good agreement with experiments. These predictions apply even when electrostatic interactions are partially screened by moderate concentrations of ions.

http://absimage.aps.org/image/MAR09/MWS_MAR09-2008-002758.pdf

Theory of Ferroelectric Nanoparticles in Nematic Liquid Crystals

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

Several experiments have reported that ferroelectric nanoparticles have drastic effects on nematic liquid crystals-increasing the isotropic-nematic transition temperature by about 5 K, and greatly increasing the sensitivity to applied electric fields. In a recent paper [Lopatina and Selinger, Phys. Rev. Lett. 102, 197802 (2009)], we modeled these effects through a Landau theory, based on coupled orientational order parameters for the liquid crystal and the nanoparticles. This model has one important limitation: Like all Landau theories, it involves an expansion of the free energy in powers of the order parameters, and hence it overestimates the order parameters that occur in the low-temperature phase. For that reason, we now develop a new Maier-Saupe-type model, which explicitly shows the low-temperature saturation of the order parameters. This model reduces to the Landau theory in the limit of high temperature or weak coupling, but shows different behavior in the opposite limit. We compare these calculations with experimental results on ferroelectric nanoparticles in liquid crystals.

/pdf/maier-saupe-type-theory-of-ferroelectric-nanoparticles-in-1v04njs3wf.pdf

Maier-Saupe-type theory of ferroelectric nanoparticles in nematic liquid crystals

Non-mesomorphic solutes depress the normal nematic-isotropic transition temperature in liquid crystals. When non-mesomorphic solutes are added to a nematic liquid crystal, the nematic-isotropic transition temperature is depressed and a two phase region is formed due to the presence of impurities of the solutes. The present paper explains the formation of this two phase region by the Landau-de Gennes phenomenological theory, which agrees fairly well with the experimental observations. We also note that this two phase region indicates the tricritical behaviour of the nematic-isotropic phase transition and the phase diagram near the tricritical point is also obtained.

Influence of non-mesogenic impurities on a nematic to isotropic phase transition

A phenomenological theory is developed for uniaxial and biaxial nematic phases, based on a two component tensor order parameter. Phase diagrams are plotted and investigated in the plane of two thermodynamic parameters. Anomalies in thermal properties are studied in the vicinity of an isolated four-phase critical point. The temperature dependences of the order parameter and the thermodynamic quantities are also calculated theoretically for the first time.

Improved analysis of the Landau theory of the uniaxial-biaxial nematic phase transition

The influence of spontaneous polarization on the smectic C*-smectic A* phase transition was studied theoretically by means of Landau theory. calculations that the transition temperature from a non-chiral to chiral smectic C phase is shifted due to the effect of bilinear and biquadratic couplings. A qualitative relationship has also been derived between spontaneous polarization and cell thickness which supports the experimental observations of the increase of spontaneous polarization with the increase of cell thickness for surface-stabilized ferroelectric liquid crystals. It was observed from the theoretical

Effect of spontaneous polarization on smectic C*-smectic A* phase transition temperature and the thickness dependence of the spontaneous polarization of ferroelectric liquid crystal

Density effects at the nematic–isotropic phase transition is studied by means of Landau–de Gennes theory. The analysis shows that the density variation shifts the nematic–isotropic transition temperature TNI and changes the Landau–de gennes free energy expansion coefficients. The possibility of the tricritical behaviour of the nematic–isotropic phase transition is also discussed by the density variation. The low value of TNI-T* (T* is the absolute stability limit of the isotropic phase) and the various thermodynamic quantities are also calculated to compare with the experimental data.

Prabir K. Mukherjee

Papers

Influence of non-mesogenic impurities on a nematic to isotropic phase transition

Improved analysis of the Landau theory of the uniaxial-biaxial nematic phase transition

Effect of spontaneous polarization on smectic C-smectic A phase transition temperature and the thickness dependence of the spontaneous polarization of ferroelectric liquid crystal

Density Effects in the Landau-De Gennes Theory Near the Nematic-Isotropic Phase Transition

Effect of magnetic nanoparticles on the nematic-smectic-A phase transition