Refractive Indices,calculated orientational order Parameters,and Polarizability Anisotropies of Liquid Crystalline 3-(4-Alkyl-phenyloxy)-propane-1,2-diols

For a novel variant of smectic structures the S_A⁺ phase of the homologous 3-(4-alkyl-phenyloxy)-propane-1,2-diols the refractive indices n_e and n_o were measured in dependence on the temperatue. The polarizability anisotropy, the orientational order parameter, and the packing fraction were calculated using a mean field fitting method. The components of the internal field tensor were included in the fitting procedure. The increasing mobility of the alkyl chain for higher homologues reduces the orientational order in the smectic layers and also the birefringence which is very small. The molecular polarizabilities are increasing nearly linearly with the elongation of the alkyl chain. The small alternation of the polarizabilities corresponds to the alternating change of the length-to-breadth ratio. The calculated packing fractions are enhanced for higher homologues.     

Phase transitions from density and order parameter from polarisabilities in symmetric dimeric liquid crystals

As a part of our systematic studies on liquid crystal dimers, we present in this article the nature of phase transitions across isotropic–nematic and nematic–smectic-A exhibited by DLCs, α,ω-bis-(4-n-alkylaniline benzylidene-4?-oxy) alkanes. Further, the orientational order parameter in the nematic phase of these DLCs are estimated from the molecular polarisabilities calculated using the experimental refractive indices and density results. The molecular polarisabilities α_e and α_o are obtained for the compounds using the above results for both Vuks and Neugebauer local field models applicable to nematic liquid crystal. α_e and α_o calculated in this way are used to obtain Δα. The polarisability anisotropy in the perfect order (absolute K) is calculated semi-empirically using the δ-function model developed by Lippincott et al. and molecular vibration method. The values of polarisability anisotropy for both local electric field models differ significantly. No criterion is known to decide which value is correct. To avoid the determination of uncertain α and Δα values considering different local field models, a simple procedure developed by Kuczynski et al. was used for evaluation of S, based solely on birefringence δn = (n_e-n_o) and this value of S is compared with those obtained from field models.     

Determination of the Molecular Arrangement in Liquid Crystals by Polarization of Fluorescence

Polarized luminescence intensity reading and the polarized absorbance spectra of 4-diethyl-amino-4′-nitrostilbene “impurity” in the n-butyl-p/p-hexyloxyphenyloxycarbonyl/-phenyl-carbonate liquid crystal were measured. Degrees of orientational order, S₁ and S₂, of the nematic liquid were calculated from relative values of the absorbance and luminescence intensity components. A function, which describes the angular molecular distribution with respect to a preferred direction in the liquid crystal, is plotted.     

Influence of TiO2 and ZnO nanoparticles on orientational order parameter of LC compounds – An optical study

In the present paper ZnO and TiO₂ nano particles are dispersed in Cyano-biphenyl liquid crystalline compounds (n?=?7, 12). The thermal polarizing microscopy and differential scanning calorimetry techniques are employed to measure the transition temperatures. The Nematic transition temperatures are decreased by 2.34?°C and 1.53?°C in Heptylbiphenyl, 1.07?°C and 1.12?°C in dodecylbiphenyl compounds due to the dispersion of nanoparticles. The refractive indices and Newton’s rings methods are exploited to measure birefringence at different temperature in nematic phase. The orientational order parameters are estimated by finding the birefringence in perfect order. The orientational order parameter is increased in nanoparticles dispersed liquid crystals when compare to pure liquid crystalline compounds.     

Influence of a.c. Electric Field on Infrared Absorption Spectra of Liquid Crystals and Determination of Orientational Order Parameter by Infrared Dichroism. II. Molecules with Weak Negative Dielectric Anisotropy

The influence of a.c. electric field (10 kHz) on the IR spectra of the nematic phase of six p-alkoxybenzylidene-p,n-butylanilines with weak negative dielectric anisotropy was studied and the temperature dependence of the orientational order parameter and threshold voltage have been investigated. The values of band elastic constants K₃₃ were calculated for MBBA and EBBA.     

Thermal conductivity and refractive indices of Nd:GdVO4 crystals

The thermal conductivities of Nd:YAG, M(Y,Gd)VO₄ crystals were measured at 298 K. The value of Nd:GdVO₄ crystal along <001> direction was 11.4 W/mK, which was higher than that of YAG crystal measured to be 10.7 W/mK. The principal refractive indices of Nd:GdVO₄ crystal in the temperature range from 20 °C to 170 °C were determined by auto‐collimation method. Based on the measured values of refractive indices, the Sellmeier equation and expression of temperature dependence of refractive indices have been obtained. The measured results show that the birefringence Δn is 0.22007 at 20 °C and temperature coefficient of birefringence is 4.33 × 10⁻⁶/°C for 1.064 μm. These results prove that the GdVO₄ crystal is a laser crystal with excellent thermal and birefringence properties. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Measurement of the An isotropic Refractive Indices of Polybenzylglutamate Liquid Crystals. Molecular Factors and Dispersion

The ordinary and extraordinary refractive indices have been measured for lyotropic liquid crystal solutions of poly-γ-benzyl-L-glutamate. The onset of the liquid crystal formation is noted as an abrupt jump in the sample birefringence in the biphasic region. The concentration dependence is otherwise unremarkable. The polymer is found to add a small, anisotropic increment to the refractivity of the supporting solvent. Both n _o and n _e can thus be measured in an ordinary Abbé refractometer for the low refractive solvents common to these liquid crystal solutions. The optical birefringence does not depend significantly on polymer molecular weight. Data is also included for the wavelength dependence (dispersion) of n _o, n _e, and Δn.     

The Dielectric and Optical Properties of the Homologous Series of Cyano-Alkyl-Biphenyl Liquid Crystals

The electric permittivities, refractive indices and densities of the homologous series of alkyl-cyano-biphenyls (C_nH_2n+1.φ.φ.CN) have been measured as a function of temperature in the nematic phases for n = 5 to 9, and in the smectic phases for n = 8 and 9. The results have been analysed in terms of the Maier and Meier theory to yield values for the molecular dipole moments and polarizabilities. Kerr effect measurements on dilute solutions of 44′-n-pentyl-cyano-biphenyl at different temperatures are reported, and in conjunction with similar dielectric and optical measurements have provided results for the free molecule dipole moment and polarizabilites; values for the higher homologues are predicted using a bond additivity model. Bordewijk's theory is applied to the permittivity measurements, and using appropriate molecular parameters, dipole-dipole correlation factors are calculated.     

Orientational Distribution Function and Order Parameters of Two 4′-Alkoxy-4-Cyanobiphenyls in Mesomorphic Phase

X-ray diffraction studies on samples of 4′-Pentyloxy-4-Cyanobiphenyl and 4′-Octyloxy-4-Cyanobiphenyl over the entire mesomorphic range are reported in this paper. A magnetic field was used to align samples. The orientational distribution functions f(β) have been calculated from the angular distribution of X-ray intensities. Orientational order parameters ( P ₂) and ( P ₄) have been calculated and compared with Maier-Saupe theoretical values. Expressions for the angular part of the pseudopotentials have been obtained from the temperature variation of f(β). The intermolecular distances D have been calculated from the experimental data and it is found that D is significantly smaller for well aligned samples. The apparent molecular length in the nematic phase and the layer thickness in the smectic phase have also been determined and are found to be about 1.4 times larger than the true molecular length in the fully extended form. This is in accordance with the findings from other cyano compounds.     

Molecular Properties and Order Parameters of Schiff's Base Compounds

The refractive indices n_o, n_c and the order parameters are measured as a function of temperature for the Schiffs base compound PBBA. From the experimental data the molecular polarisabilities and its anisotropies at different wavelengths are calculated using different internal field models. The merits of each model are discussed. Order parameters (P ₂), (P ₄) and other molecular parameters of PBBA and EBBA are also calculated using X-ray diffraction techniques at different temperatures. Comparison with theoretical values shows the relative merits of different experimental techniques. The (P ₂) and (P ₄) values of other members of the Schiff's base compounds, already reported from our laboratory, have been given herewith to show the disagreement with the simple mean field theory. Possible causes for such disagreement have been discussed.     

Refractive Indices and Dielectric Studies of Three Phenylcyclohexane Liquid Crystals in the Nematic Phase

The refractive indices n_e, n_o and densities and the dielectric primittivities ε_∥ and ε_⊥ of three P-cyano-P-alkylcyclohexanes (PHC-3, PCH-5, PCH-7) have been measured at different temperatures. The order parameters calculated by using Neugebauer and Vuks' methods were comparable. A comparison of order parameters of the PCH with the corresponding alkylcyanobiphenyls at reduced temperatures τ (= T-T_NI/T_NI) shows that the replacement of a phenyl ring with a cyclohexyl ring decreases the order parameter appreciably. The experimental values of dielectric permittivities ε_⊥ in each of the PCHs are found to be less than half of the ε_⊥-value calculated from Maier and Meier equations using the polarizability and the order parameter obtained from refactive index measurements. This was explained as due to short range antiparallel ordering of strongly polar molecules in the nematic phase, as proposed by Chandrasekhar and Madhusudan, which was not taken into consideration in Maier and Meiers' theory     

Physical Studies of Homologous 4-Cyanophenyl Esters of 4′- n-Alkylcinnamic Acids

The mean polarizabilities of homologous series of nematic liquid crystals of 4-cyanophenyl esters of 4′- n-alkylcinnamic acids are evaluated by using the MLδP method. From these polarizabilities the mean diamagnetic susceptibilities of the liquid crystals are also calculated. The orientational order parameters of these compounds are also estimated using the Vuks and Neugebauer methods. The variation of the order parameter with temperature is discussed.     

A simple optical method of measuring the tilt bias angle of liquid crystals

A simple optical method based on refractive indices measurement for determining the tilt bias angle of liquid crystals is described. The required refractive indices n_o, n_e and n_θ are measured by (i) Abbe's refractometer and by (ii) optical wedge method. The tilt bias angle by this technique can be determined to accuracy of ± 0.2° in the high tilt angle range (20° to 40°). This method is rather simple and quick and does not require any external magnetic field and/or knowledge of other physical constant of liquid crystals, as are necessary in some of the earlier reported methods.     

Optical and static dielectric study of a terminally fluorinated liquid crystalline compound

Optical and static dielectric studies on a terminally fluorinated liquid crystalline compound have been carried out. Measurements of temperature variation of refractive indices of the compound are done by using thin prism method. A four-parameter model is validated by fitting the experimentally measured values of refractive indices, birefringence and average refractive indices of the compound with the theoretical ones. Refractive index and density data are utilized for determination of orientational order parameter. The temperature variation of dielectric permittivities of the compound are measured by a LCR meter.     

Local Refractive Index Measurement on a Cholesteric Liquid Crystal Using the Surface Plasmon Technique

Abstract

The surface plasmon technique is used to measure the local refractive indices in the quasi-nematic layers of a cholesteric liquid crystal with an accuracy of about 10^?4. The local linear birefringence reflecting the orientational order of molecules in the quasi-nematic layers shows a temperature dependence characteristic of a nematic and in good agreement with the theory of nematic ordering.     

Cotton-Mouton Effect in Monodisperse Suspensions of Liquid Crystals

Abstract

The collective Cotton-Mouton (C-M) effect in the system of micron-size liquid-crystal droplets freely suspended in the isotropic liquid is studied experimentally and theoretically. The collective C-M constant in liquid-crystal suspensions is found to be from 10⁴ to 10⁸ times higher than the respective “molecular” C-M constant in the isotropic phase of the same substance. These large values cause the saturation in the C-M effect at relatively low magnetic fields. Using the generalized nth order Langevin's functions L, _n the statistical therory is presented for the collective C-M effect in the monodisperse liquid-crystal suspensions. As a result, the induced birefringence is obtained in the form Δn = 1/2(Δn)∞ (3L ₂ – 1), where (Δn)∞ is the induced birefringence at saturation. The collective C-M constant is C _c = CN _s S _g where N ₈ is the number of molecules in the droplet, S ₈ is the orientational order parameter of the long molecular axes in the droplet, and C is the “molecular” C-M constant. The resultant (measured) C-M constant is C ₈ = C(1 + N ₈ S ₈). The relaxation time τ depends on the rotational (Brownian) diffusion constant D and after removing the field B the orientational order parameter of the optical axes of droplets in the suspension S _s = 1/2(3L ₂ – 1) vanishes exponentially as S _s = exp(?6Dt). Hence, the relaxation time τ = (6D)^?1.

The collective C-M effect and its saturation can be used as methods for the analysis of the presence and change of the orientational order within colloidal grains and the derivation of several parameters characterizing the aggregation, self-organization, and morphogenesis processes in multicomponent complex systems.     

Determination of refractive index and electronic polarisability of oxygen for lithium-silicate melts using ellipsometry

The refractive index of Li₂O–SiO₂ melts has been measured using the ellipsometer constructed for high-temperature use. Measurements were carried out on four samples having different compositions over a wide temperature range (1300–1800 K). The standard deviation for the values measured was within ±0.0005. Additions of Li₂O were found to cause increases of refractive index in the temperature range investigated. At Li₂O concentrations <25 mol% the refractive indices of the melts increased with increasing temperature, similar to SiO₂. However, this temperature dependence became smaller with additions of Li₂O and at Li₂O concentrations more than 30 mol% the refractive indices of the melts decreased with increasing temperature. The temperature dependence of the refractive indices has been discussed from those of the density and the molar electronic polarisability on the basis of the Lorentz–Lorenz equation. In addition, the electronic polarisability of oxygen derived from the molar electronic polarisability increased with increasing temperature in each melt, suggesting that the ionicity of oxygen increases as temperature increases. Furthermore, additions of Li₂O were found to cause increases in the electronic polarisability of oxygen, due to the formation of non-bridging oxygen ions.     

Change of the Prenematic Order in the Isotropic Phase Close to the Isotropic–Nematic Phase Transition with Increasing Aerosil Nanoparticles Density

The influence of the hydrophilic and hydrophobic aerosil nanoparticles density on the formation of the prenematic order close to the isotropic – nematic (I–N) phase transition is presented. The lowering of the activation energy, with the increase of aerosil nanoparticles density, suggests a change of the prenematic order in the isotropic phase. The temperature dependence of the static dielectric permittivity for 4–n–pentyl–4′–cyanobiphenyl (5CB) exhibits an anomaly near the I–N phase transition. With the increase of aerosil density, a substantial modification in the anomaly of the static permittivity was observed in the isotropic phase. Indicated changes are different for hydrophilic and hydrophobic aerosil as a result of different surface interaction between nematic molecules and aerosil nanoparticles.     

Computer Simulation Studies of Anisotropic Systems,III. Two-Dimensional Nematic Liquid Crystals

We have studied a two-dimensional ensemble of cylindrically symmetric particles interacting via a weak anisotropic potential using the Monte Carlo technique of computer simulation. The calculation is simplified by confining the particles to the sites of a triangular lattice. The internal energy, specific heat, second rank orientational order parameter and second rank orientational pair correlation function were calculated at various temperatures. The variation of the order parameter and pair correlation function shows that the system exhibits a transition from an orientationally disordered to a partially ordered phase. The temperature dependence of the specific heat suggests that the transition is second order or higher.

The possibility of the existence of order-disorder transitions in two dimensions is discussed. The results of the simulation are then compared with the predictions of a molecular field theory of orientational phase transitions. As expected the theory is found to be in poor agreement with the calculations.     

Dielectric Anisotropy and the Order Parameter of HXBBA

Abstract

Measurements of dielectric anisotropy (Δ?), refractive indices (n _e , n _o), birefringence (Δn) and density (ρ) have been made in the nematic and smectic phases of N(-p-hexyloxybenzylidene)-p-butylaniline (HXBBA). The results indicate that the various transitions are of the first order type except smectic B-smectic G, which may be a second order transition. The order parameter S has been determined using the isotropic internal field model (Vuks approach) and the anisotropic internal field model (Neugebauer's approach) and both the values agree fairly well. The dielectric anisotropy (Δ?) increases strongly in the smectic phases whle S increases only slowly. It is interpreted by an increase of dipole-dipole correlations.