Landau theory for isotropic,nematic, smectic-A,and smectic-C phases

ABSTRACT

We use the Landau theory of phase transitions to describe the phase diagram of a liquid crystal displaying the isotropic (i), nematic (N), smectic-A and smectic-C phases. The order parameter of the smectic-C phase is defined as the projection of the director on the plane of the smectic layers, vanishing in the smectic-A phase. We present a detailed phase diagram that shows transition between any two of these phases, containing a triple point INA, a Lifshitz point NAC, a tricritical at the NA line, and a critical end point IAC. As one approaches the NC line from the smectic-C phase, the tilt angle approaches a nonzero value, but if the AC line is approached, the tilt angle vanishes according to the distance to the AC line to the power 1/2.     

Landau theory-based estimates for viscosity coefficients of uniaxial and biaxial nematic liquid crystals

Using Landau theory, it is shown that eight phenomenological parameters are needed to describe and distinguish the twelve viscosity coefficients of a biaxial nematic phase, or the five viscosity coefficients of a uniaxial nematic phase. The dependence of the coefficients on the macroscopic uniaxial and biaxial order parameters is established. Since these order parameters are determined by the anisotropies of the dielectric constant, we show that it should be possible to determine values for all eight of the phenomenological parameters of the theory from measurements of the temperature dependence of the five viscosities of a uniaxial phase.     

X-ray diffraction from the uniaxial and biaxial nematic phases of bent-core mesogens

X-ray diffraction patterns for the uniaxial and biaxial nematic phases exhibited by rigid bent-core mesogens were calculated using a simple model for the molecular form factor and a modified Lorentzian structure factor. The X-ray diffraction patterns depend strongly on the extent of the alignment of the molecular axes as well as the orientation of molecular planes. The X-ray diffraction can be unequivocally used to identify the biaxial nematic phase, study the uniaxial-biaxial phase transition, and estimate the order parameters of the nematic phase.     

Effect of the presence of strong and weak electrolytes on the existence of uniaxial and biaxial nematic phases in lyotropic mixtures

The lyotropic mixture of potassium laurate/decanol/water presenting only the uniaxial nematic calamitic phase was doped with one strong (potassium chloride, KCl) and 11 weak electrolytes with phenyl-rings (DL-mandelic acid, benzoic acid, DL-phenyllactic acid, phenylacetic acid, phenol and phenylmethanol) and with cyclohexyl-ring (RS-hexahydromandelic acid, cyclohexanecarboxylic acid, cyclohexaneacetic acid, cyclohexanol and cyclohexylmethanol), separately. We also chose two nonpolar dopant molecules, benzene and cyclohexane, for the comparison of them with weak electrolytes, since they are located in the hydrocarbon core of the micelle. The nematic phase sequences, in particular the presence of the biaxial nematic phase, were investigated as a function of the dopant molar concentration and temperature. The laser conoscopy and small-angle X-ray scattering techniques were used to characterise the different nematic phases. Weak electrolytes having –COOH group as polar part were found to be very effective in stabilising the three nematic phases (two uniaxial and a biaxial). Guest molecules with only the –OH group did not show any effect on the stabilisation of other nematic phases. The experimental results are interpreted considering the screening effect of the hydrophilic parts of the dopants on the repulsion between the polar heads of the main amphiphilic molecules at micelle surfaces. This process favours the increase of the more flat micellar surfaces of micelles, which triggers the orientational fluctuations responsible for the biaxial and discotic nematic phases.     

Towards the biaxial nematic phase through molecular design

In this article, the search for the elusive biaxial nematic phase (NB) in liquid crystals is considered. The structure of the phase is described along with theoretical and computational work which suggests how it might be realised. An overview of the work of the Exeter group in this area is then given showing the different approaches adopted and illustrating how one of these has led to a new type of amphiphilicity based on shape.     

Thermotropic uniaxial and biaxial nematic and smectic phases in bent-core mesogens

Two azo substituted achiral bent-core mesogens have been synthesized. Optical polarizing microscopy and synchrotron X-ray scattering studies of both compounds reveal the existence of the thermotropic uniaxial and biaxial nematic and three smectic phases at different temperatures in these single component small molecule systems. The transition from the uniaxial to biaxial nematic phase is confirmed to be second order. The transitions from the biaxial nematic to the underlying smectic phase and between the smectic phases have barely discernible heat capacity signatures and thus are also second order.     

The elastic distortion and stability of biaxial nematic liquid crystal on the surface grooves

Fukuda et al. reexamined the Berreman's model which attributes the surface anchoring to the elastic distortion of the uniaxial nematic liquid crystal induced by the grooves of a surface. They showed that at the variance with the assumption made in the original approach of Berreman, the azimuthal distortion of the director cannot be considered as negligibly small. Now this method is generalized to the biaxial nematic liquid crystals, with some approximations for the elastic constants. We obtain an additional term in the elastic distortion energy per unit area which depends on the second power of the cosine of the angle made between the main director n at infinity and the direction of the surface grooves. This additional term describes the distortion energy of the minor director m induced by the surface grooves when the n director is anchored exactly along the grooves. We have studied the stability of the n director around the grooves, and in one-constant model for each director the stability condition is that the elastic constant of the n director is the maximum.     

Coexistence of nematic and chiral nematic phases of an achiral liquid crystal trimer possessing an octafluorobiphenyl unit

We prepared some achiral flexible liquid crystal oligomers possessing an octafluorobiphenyl unit and investigated their phase transition properties using polarising optical microscopy and differential scanning calorimetry. All the compounds showed nematic phases. The trimer with even-numbered spacers was found to exhibit coexistence of the nematic regions and the chiral nematic regions with opposite twist senses of a sample contained in a homogeneous aligned cell during a cooling process, whilst that with odd-numbered spacers did not. We discuss how the even-numbered trimer produces the helical state.     

Synthesis and characterization of a hydrogen-bonded nematic network based on 4-propoxybenzoic acid side groups grafted onto a polysiloxane

A polymethylsiloxane with 4-propoxybenzoic acid side groups was prepared by hydrosilylation of polymethylhydrosiloxane and methyl 4-allyloxybenzoate followed by hydrolysis. The existence of strong hydrogen bonding interactions in this polymer due to dimerization of the carboxylic acid groups was demonstrated by FTIR. The polymer exhibits a nematic mesophase at elevated temperatures due to the self-assembly of hydrogen-bonded mesogens (dimers). After cooling from its nematic melt, a stable hydrogen-bonded nematic network structure was formed, as demonstrated by differential scanning calorimetry, polarizing optical microscopy, and X-ray diffraction. Temperature-variable FTIR analysis presents a convincing interpretation for the DSC thermogram of the polymer, and furthermore assists in understanding the process of formation of the nematic network and the reversibility of such hydrogen-bonded networks.     

Symmetry‐Breaking Transitions in HoCuAs2–xPx and ErCuAs2–xPx (x = 0–2): Crystal Structure,Application of Landau Theory,Magnetic and Electrical Properties

Crystal structures of compounds undergoing symmetry‐breaking transitions have been investigated by the X‐ray single crystal and powder methods. While the phases HoCuAs₂ through HoCuAs_1.33P_0.67 and ErCuAs₂ through ErCuAsP retain the tetragonal HfCuSi₂ structure (P4/nmm space group), the compounds HoCuAsP through HoCuAs_0.33P_1.67 and ErCuAs_0.67P_1.33 through ErCuAs_0.33P_1.67 undergo orthorhombic distortions to the GdCuAs_1.15P_0.85 structure (Pmmn space group). Further distortions follow in the phosphides: HoCuP₂ adopts a larger orthorhombic cell (Cmma, a = 5.273(3), b = 5.305(3), c = 9.645(5) Å) and ErCuP₂ has a monoclinic cell with a doubled parameter, the b parameter in the monoclinic cell (P2₁/n, a = 3.737(3), b = 19.239(15), c = 3.728(3) Å, β = 90.09(1)°). Zigzag chains are formed in the phosphorus layer of ErCuP₂. According to Landau theory the transitions from HoCuAs_1.33P_0.67 to HoCuAsP and from ErCuAsP to ErCuAs_0.67P_1.33 can be continuous, and the transitions from HoCuAs_0.33P_1.67 to HoCuP₂ and from ErCuAs_0.33P_1.67 to ErCuP₂ are necessarily first‐order. The results of magnetic and electrical measurements for HoCuAs₂ and HoCuP₂ are reported. Due to the magnetic moments localized on Ho atoms both compounds order antiferromagnetically at low temperatures. They exhibit metallic conductivity.     

Determination of elastic constants of a binary system (7CPB+9.CN) showing nematic,induced smectic Ad and re-entrant nematic phases

The temperature variation of the splay and bend elastic constants of a binary system exhibiting nematic-induced smectic A_d and re-entrant nematic phases measured by electric field-induced Freedericksz transition method has been reported. As bend deformation is not permitted in the smectic A phase, bend elastic constant (K₃₃) could only be determined in the nematic and re-entrant nematic phases. In both the nematic phases, the splay elastic constant has the same order of magnitude and does not show any pretransitional effect. However, in the induced smectic A_d phase, the value of K₁₁ is about one to two orders higher than that in the nematic phases. The bend elastic constant shows a strong pretransitional effect near the nematic–smectic and smectic–re-entrant nematic phase transitions. The influence of the presence of the induced smectic phase is observed even in those mixtures which have no induced smectic phases. As the smectic phase is approached, the ratio K₃₃/K₁₁ increases rapidly and diverges to infinity.     

On the phenomena of deformation and neck formation in LLDPE films subjected to uniaxial and biaxial loading conditions

Heterogeneous deformation in the form of dilatational bands is observed under certain biaxial stress states that closely resembles uniaxial necking in LLDPE blown films. The formation and orientation of dilatational bands is a function of film morphology and stress state. The dilatational bands form, with their lengths aligned with the machine direction (MD) of the film, under equibiaxial stress states and nonequibiaxial stress states when the higher principle stress is coincident with the transverse direction (TD). However, homogeneous deformation is observed if the higher principle stress is coincident with the MD. Similarly, uniaxial specimens show necking when the stress is applied in the TD and affine deformation when the stress is applied in the MD. Neck boundary propagation under uniaxial loading is due primarily to the consumption of undrawn material, while dilatational band boundary propagation under an equibiaxial loading also includes simultaneous continued deformation of the drawn material. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2651–2663, 1999