Mukherjee, C D

Saha, Jayashree

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Indian J. Phys. 72A (5), 427-431 (1998)IJP A— an international journalPhase alternation in liquid crystals with terminal phenyl ringJayashree Saha1 and C D Mukherjee2**S. N. Bose National Center For Basic Sciences, Block JD,Sector 111, Salt Lake, Calcutta-700 091, India 2Saha Institute of Nuclear Physics, l/AF Bidhannagar,Calcutta-700 064, IndiaAbstract : A mean-field model for the phase alternation between homologues, as observed in the case of some liquid crystalline homologous series with a terminal phenyl ring, is presented considering the anisotropic interaction of the rigid part and bulky ring of a molecule in the field of other molecules. Bui the chain interaction is ignored though the chain conformations influence the relative configuration of the other parts Numerical calculations were done to reproduce the phase diagrams of the phase alternation for the first five members of the homologous series m-phenylalkyl-4-p-phenylbenzylidene which is in good agreement with the experimental resultsKeywords : Terminal phenyl ring, phase alternations, mean-field theory PACS Nos. 61.30.64 70.M1. IntroductionUnusually pronounced even-odd effect in nematic-isotropic transitions has been observed in liquid crystalline compounds with terminal phenyl ring or o-phenylalkyl cinamates [1], These types of series also show the very interesting behaviour of phase among the homologues. The member of the series with odd number of the methylene units (N) in the flexible alkyl chain has both smectic and nematic phases but the same series with even N has only smectic phase. As a result an alternation of phase occurs [1], because nematic properties are extinguished for odd number of methylene units in the flexible alkyl chain. In an earlier work [2], we formulated a mean-field model by incorporating the effects of the chain conformation explicitly which directly influence the relative configuration of both parts (viz., central rigid part and the terminal phenyl ring) and as a result the longitudinal polarizability of the molecules is changed. This model has made it possible for us toConespondence electronic address : chandi9hpl.saha.emet.in© 1998IACS428 Jayashree Saha and C D Mukherjeereproduce the unusually pronounced even-odd effect in N -  /  transition. In this communication we present an extension of the earlier model to the smectic phase by introducing a pure translational McMillan parameter [3]. Conformational and dispersive energies for the rigid part and the terminal ring of a molecule in the field of the other molecules are considered. Numerical calculations have been done on the homologous series fl>phenylalkyl-4-p-phenyl benzylidene for the first five member of the series. The calculation reproduces the phase alternation behaviour which is observed in the experimental phase diagram of that series.2. MethodFollowing reference 2, we consider the mean-field experienced by a molecule to consist of three parts—one for the rigid core (£u), the other for the end phenyl ring (Eh) and the conformation energy of the chain segment (Econf). For simplification, we ignored the contribution of chain part to the mean-field as it is small compared to the other contribution. Before writing the energy expression let us state the definitions of the order parameters to be used.Orientational order parameter for the rigid partswhere 9a is the angle between the rigid part and the mean-field direction. < ^ means a statistical average.The phenyl ring order can be defined aswhere 9h is the polar angle between the phenyl ring and the direction of the field. </> is the angle of rotation of the ring about the rigid part.The translational order parameterT )a  =  { P 2 ( c o s f l a ) ) . (1)Tlh = ( P 2 (COS0h m ) . (2)(3)where d is the layer spacing and z is chosen along the layer normal. Then the energies can therefore be written as,7?6 y 2 (C O S 0 „)(4)(5)N£conf =and (6)Phase alternation in liquid crystals with terminal phenyl ring 429In the above expressions the suffixes ’a' and 1b’ have been introduced to denote entities pertaining to rigid and phenyl parts of a molecule respectively. Ca(N) and Cb(N) are the respective volume fractions of the tf-th member of the homologous series and Va, Vh are the molecular volumes of the two basic components. The volumes of the different parts are estimated from the table values for molecular weight and density data of the sample. Vua, Vm and Vah are the coupling constants for the interaction mean field with the first suffix representing the component molecule that experiences the mean field and the latter suffix indicating the mean field producing agent. By analogy with the result for the binary- mixtures of nematogenic molecules [4], we haveTherefore, only two of the coupling constants remain as adjnstable parameters, which are fixed from the nematic-isotropic transition temperature of two homologues, as explained in reference 2. The parameter 6 is the relative coupling strength of the Kobayashi two-particle potential [S] which is constant for a homologous series and also temperature independent. The value of this parameter is obtained by using the value of the smectic to nematic/isotropic transition temperature of the homologue. Here we assume that the correlation between the orientation order and translation order is very weak. Hence the mixed parameter term in the model potential is neglected. U is the internal energy of i-th segment of a chain and £ represents any of the three rotation isomer states namely r(trans), ^(gauche). The value of these states are given in reference [6]. The values of the order parameters at a particular temperature T can be obtained by full self-consistent solutions of the following equations :where Z„ is the partition function of the system in ordered phase at a particular temperature T and it is given by,For each temperature, the self-consistent solution of the order parameters is found and the stable solution is picked up corresponding to the minimum of the Helmholtz free energy per particle. The expression for this free energy is given as,Vok = / v « v *T= Jr X J0 Jo Jo C0S(r P )exp l£,/*r]rf(c°sfl)‘ty<fc (9)u allconf-*rta[z./z<] (10)where Zj is the partition function in isotropic phase.430 Jayashree Saha and C D Mukherjee3. Result and discussionThe calculated transition temperatures of the homologous series <o-phenyl alkyl-4-p- phenyl- benzylidene are compared with the experimentally observed value in Figure 1. The estimated volumes are, Vtl = 433.91 A \ Vh = 108.48 A3, together with the volume for the each chain segment 27 A3. The values of the coupling constants Vaa, Vhh and Vah are 2059950.0, 22162.85 and 213668.82 respectively in C G S unit. The value of 5 is0.37. It is to be noted that the ratio of the strength parameters are constant throughout the nematic phase and independent of the number of the homologue whose value is 9.64.Figure 1. Plot of tiansmon tempcratuie ( T) against number of methylene groups (jV) in the chain.In conclusion, we would like to mention that this is possibly the first calculation where the generally observed feature of the cinnamale homologous series, namely the phase alteration is well reproduced. The calculated transition points are seem to be only about 10 -  15 K off the experimental values. This small deviation may be due to the steric effect which has not been considered directly into our model potential expression. As the molecules are packed in a layer in the smectic phase there is considerable lateral steric repulsion between the molecules f7]. It is quite likely that those conformations for which the chain segments deviate much from the molecular axis are suppressed d\)e to the lateral repulsion by the neighbouring molecules. Further efforts should be made for better agreement with experiments.AcknowledgmentsWe are grateful to Prof. M K Roy and Prof. M Saha for their valuable comments and suggestions. One of us (J Saha) wishes to thank the Council of Scientific and Industrial Research, India for the Research Associateship offered to her.Phase alternation in liquid crystals with terminal phenyl ring 431References[1] GW Gray and K J Hanson Mol. Cryst. Liq. Cryst. 13 37 (1971); D Coates and G W Gray J. Physique, Colloque Cl C365(1975)[2] C D Mukheijee, T R Bose, D Ghosh, M K Roy and M Saha Mol. Cryst. Liq. Cryst 140 205 (1986)[3] W L McMillan Phys. Rev. A6 936 (1972)[4] R L Humphries, P G James and G R Luckhurst Sympositum of the Faraday Soc. 5 107 (1971)[5] K Kobnyashi and Oyo Butsuri 40 532 (1971)[6] J Saha, B Nandi. C D Mukheijee and M Saha Mol. Cryst. Uq. Cryst. 214 23 (1992)[71 M Nakagawa and T Akahone J. Phys. Soc. Japan 53 1951 (1984)72A(5).|J

Phase Alternation in Liquid Crystals with Terminal Phenyl Ring

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Phase Alternation in Liquid Crystals with Terminal Phenyl Ring

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