R. Paul

Order parameter and the orientational distribution function for 4-cyanophenyl-4′-n-heptyl benzoate in the nematic phase

X-ray diffraction studies on oriented samples of 4-cyanophenyl-4′-n-heptylbenzoate in the nematic phase are reported at different temperatures. The orientational distribution function f(β) has been calculated from the angular distribution of the X-ray intensities. The orientational order parameters 2 and 4 have been determined from f(β). 2 is found to be slightly greater than the value predicted by the Maier-Saupe molecular field theory, whereas the 4 values are much smaller than those given by theory. An approximate expression for the potential of the molecular field is obtained from the temperature variation of the distribution function. The value of l and the intermolecular distance D have been determined from X-ray photograph. l, which is often close to the molecular length is found to be 28 A. The length as measured from a model in a completely extended form is found to be 21 A. If we assume antiparallel associations of molecules as in most cyano compounds this difference can be explained.

X-ray diffraction, optical birefringence, dielectric and phase transition properties of the long homologous series of nematogens 4-(trans -4′- n -alkylcyclohexyl) isothiocyanatobenzenes

The temperature dependence of density, refractive indices, apparent molecular length and intermolecular distance of 11CHBT, are reported, together with the static dielectric permittivities, ε∥, ε┴, ε iso of 11CHBT and 12CHBT; the effect of chain length on various physical properties of the CHBT series is also discussed. All the temperatures T m, T NI and T NCr show an odd-even (OE) effect, but transition enthalpies ΔH m and ΔH c show no such behaviour. T m, T NI and T NCr and ΔH m are found to increase with chain length, while ΔH c shows a maxima at n = 6. At the common reduced temperature T* = 0.98 TNI, the density of the compounds are found to decrease with increasing chain length while the polarizability parameters αe, αo and α increase. However, the volume expansion coefficient, polarizability anisotropy and normalized polarizability anisotropy show a distinct OE effect. Similarly, n e decreases smoothly with chain length but n o and Δn show an OE effect like ε┴ and Δε. The ratio ln ⟨P 2⟩ /ln ⟨ P 4⟩ remains closer to Faber theory than MS theory. Effective dipole moments are found to be approximately constant in the series; antiparallel association is observed in all the members. Kirkwood correlation factors g┴ and Δg are found to exhibit an OE effect like ε∥ and ε∥, but g∥ and ε∥ show no such effect. The effects of substitution in the core and end polar group on these properties are also discussed.

Refractive Indices and Orientational Order Parameter of Five Liquid Crystals in Nematic Phase

Abstract Refractive indices of bis-(4′-n-alkyloxy benzal)-2-chloro-1,4 phenylene diamine (alkyl = hexyl, octyl and decyl), RO-TN-101 and RO-CE-154 have been measured over the whole nematic ranges for different wave lengths. A prism method has been employed for these measurements. The samples were aligned by surface rubbing and by the application of magnetic field. For all the samples, the refractive index for the extra-ordinary ray (ne ) decreases and that for the ordinary ray (no) increases with increasing temperature. At the nematic isotropic transition there is a discontinuity in the refractive indices values. The principal molecular polarizabilities (αe and αo) for the samples have been calculated using Neugebauers relation. The necessary density measurements have been made by us. The anisotropy of the molecular polarizabilities was calculated using Hallers extrapolation method. The orientational order parameters were calculated at different temperatures for the samples using principal polarizabilit...

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

Abstract 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.

Order parameters of some homologue cybotactic nematics from X-ray diffraction measurements

Abstract The hexyl, octyl and decyl members of the homologous series bis-(4′-n-alkoxybenzal)-2-chloro-1,4-phenylinediamine have been studied by X-ray diffraction at different temperatures under various magnetic fields. The intermolecular distance the tilt angle, the orientational distribution function and the orientational order parameters have been calculated. The intermolecular distance, tilt angle and the ‘degree of ordering’ is found to depend on magnetic field strength. Order parameters 〈P 2〉 and 〈P 4〉 are found to be slightly lower for BHeCP, more or less equal for BOCP, and slightly higher for BDeCP than those predicted by mean field theory. 〈P 2〉 values for BHeCP snd BOCP agree well with the values obtained from refractive-index measurements, but for BDeCP our 〈P 2〉 values are higher.

Small Angle X-Ray Diffraction Studies of an Ester/Biphenyl Mixture (5CB/ME 50.5) Showing an Injected Smectic Phase

Abstract The molecular organisation in a binary mixture of a strongly polar mesogen (5CB) and a weakly-polar mesogen (ME50.5) is investigated using results of X-ray scattering and density studies. Analysis of the intensity distribution of X-ray scattering has yielded results for orientational order parameters in addition to smectic layer spacings and effective molecular lengths. The results are compared with a mean field theory of the smectic phase. Previously unexplained results for mixtures showing a minimum in the anisotropy of physical properties coincident with a maximum in the nematic/smectic A transition entropy are shown to be consistent with the theory. We conclude that favourable packing of molecules in the injected smectic A phase stabilises the layers but increases the orientational free volume, consistent with a lower orientational order parameter.

Study of the physical properties of an ester/biphenyl mixture, exhibiting an injected smectic phase, by small-angle x-ray diffraction

Abstract Small angle x-ray diffraction intensities from binary mixtures of 4-n-pentyl 4′cyanobiphenyl (5CB) and 4-n pentyl phenyl 4-n′ hexyloxy benzoate (ME60.5), which show an injected smectic phase, have been analysed to determine the orientational order parameters (P 2) and (P 4), the translational order parameter, the layer thickness in the smectic phase, and the apparent molecular length in the nematic phase. The order parameters have been fitted satisfactorily to those calculated from McMillans theory by varying the potential parameters α and [sgrave]. The experimental variation of the layer thickness with mole fraction of 5CB has been explained fairly well by assuming the presence of both homo dimers (5CB + 5CB) and hetero dimers (5CB + ME 60.5) in the mixture. Orientational order parameters, layer thickness, and packing fraction all exhibit minima at about 50% molar concentration of 5CB.

Optical birefringence and order parameter of three nematogens

Results of the measurement of refractive indices and densities of three nematic liquid crystals at different temperatures are reported. The molecular polarizabilities have been calculated from refractive indices using both the Vuks’ and the Neugebauer’s relations. The orientational order parameters are determined from the polarizability values. The variation of order parameter with temperature for these compounds shows a reasonably good agreement with Maier and Saupe theory except near the clearing points where the experimental values are less than those obtained from the theory. The possible reasons for this have been discussed.

Comparison of the orientational order parameters determined from X-ray diffraction and 13C NMR studies of a hockey stick-shaped compound

Orientational order parameters (OOPs) have been determined in the Smectic A, Smectic C1 and Smectic C2 phases of a hockey stick-shaped compound from X-ray diffraction measurements and compared with NMR measurements. While the OOP values from NMR measurements abruptly drop at the Smectic C1 to Smectic C2 transition, those determined from X-ray diffraction measurements decreases sharply at the Smectic A to Smectic C1 transition. This drop in the OOP values from X-ray measurements has been explained using a model where the molecular director is randomly oriented in a cone about the smectic layer normal. OOPs from X-ray diffraction and NMR measurements have been successfully fitted with McMillans theory, after necessary correction to the potential, incorporating tilt angles, for three homologues with n = 10, 11 and 12. The temperature dependences of the optical birefringence, dielectric anisotropy and OOP values determined from birefringence measurements of compound 11 are also reported.

X-ray diffraction and optical studies of three mesogens of a homologous series of alkyl cyclohexyl cyanophenyl pyrimidine

Abstract The crystal and molecular structures of the three compounds belonging to the homologous series of alkyl cyclohexyl cyanophenyl pyrimidine had been determined by us earlier. In this paper we analyse our X-ray and optical data of the same compounds over their entire mesomorphic range. We have measured the refractive indices and densities at different temperatures. The orientational order parameter values have been calculated from molecular polarizabilities. Orientational order parameters and have also been determined from small angle X-ray diffraction photographs of magnetically aligned samples. Molecular parameters have also been determined from this X-ray study. Experimental order parameters are compared with both Maier–Saupe and Humphries–James–Luckhurst theories. The experimental values for one of the compounds (heptyl) possessing Smectic A phase have been compared with McMillans model.