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Physical properties of nematic Schiff’s bases

F. Leenhouts, W. H. de Jeu and A. J. Dekker

Solid State Physics Laboratory, Materials Science Centre, University of Groningen, Groningen, The Netherlands

(Reçu le 12 avril 1979, accepté le 12 juin 1979)

Résumé. 2014 Dans cet article nous présentons des mesures de l’anisotropie de la susceptibilité diamagnétique,de la densité et du changement d’entropie à la transition nématique-isotrope d’un nombre de bases de Schiff struc-turellement corrélées. Les paramètres d’ordre ont été déduits des anisotropies diamagnétiques. Les résultatsmontrent l’existence d’une correspondance étroite entre le paramètre d’ordre et le changement de densité à latransition nématique-isotrope. Les données suggèrent que les chaînes alkyls sont très flexibles, aussi bien dansla phase nématique que dans la phase isotrope. Les résultats expérimentaux peuvent être expliqués dans le cadredes théories, qui tiennent compte de la flexibilité moléculaire.

Abstract. 2014 The anisotropy of the diamagnetic susceptibility, the density and the entropy change at the nematic-isotropic transition of a number of structurally related Schiff’s bases are reported. Order parameters have beencalculated from the anisotropies of the susceptibility. The results indicate that there is a close correspondencebetween the order parameter and the relative volume change at the nematic-isotropic transition. The experimentaldata suggest that there exists considerable flexibility of the alkylene chains both in the nematic and isotropicphases. The experimentally observed trends can be understood within the framework of theoretical models,which take account of molecular flexibility.

LE JOURNAL DE PHYSIQUE TOME 40, OCTOBRE 1979,

Classification

Physics Abstracts61. 30

1. Introduction. - In the nematic liquid crystallinephase the long axes of the elongated molecules tendto align along a preferred direction, represented bya unit vector n, the director. The molecular centresof mass on the other hand are distributed at random.The nematic phase is uniaxial, which implies thatvarious macroscopic physical quantities are aniso-

tropic in nature. In this paper the anisotropy of thediamagnetic susceptibility of a number of structurallyrelated Schiff’s bases is considered. The diamagneticsusceptibility relates the magnetic moment M, inducedby an applied field H, to the field according to

where X,,,, denotes an element of the susceptibilitytensor x. Choosing the z-axis along the director, thetensor in the nematic phase is given by

where vl, and xi denote the volume susceptibilitiesparallel and perpendicular to the director, respectively.Since magnetic interactions between the molecules are

small, the anisotropy Av = x Il - x~ is related in a

simple way to the degree of orientational order ofthe molecules (see section 4). In order to obtainadditional information with regard to the nematic-isotropic transition, we have also measured the

entropy change at this transition. Moreover thedensities have been determined as a function of

temperature, from which the relative volume changesat the transition and the packing fractions have beencalculated. The observed trends will be related to

differences between the molecular structures and

properties of the various compounds.The compounds studied are o-hydroxy-p-methoxy-

benzylidene-p’-butylaniline (OHMBBA), p-methoxy-benzylidene-p’-cyanoaniline (MBCA), anisylidene-p-aminophenylacetate (APAPA) and a number of

homologues of APAPA. The molecular structure ofthese materials can be represented by the formula

- -i

where R1 and R2 are side and end groups, respecti-vely. A list of abbreviations and nematic ranges ofthese materials is given in table 1. The side group R1

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019790040010098900

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Table 1. - List of liquid crystals studied. Tm and T,are the transition temperatures crystal-nematic andnematic-isotropic. The anisotropy of the mass suscep-tibility can be calculated according to eq. (5) withthe parameters dxg(0), fi and y.

is a hydrogen for all compounds except OHMBBA,where R1 represents a hydroxy group (OH). Theend group R2 is a butyl (C4H9), cyanide (CN) andacetate (OCOCH3) group for OHMBBA, MBCAand APAPA respectively. The homologues of APAPAhave been denoted for simplicity as APAPAn. Forthese materials R2 stands for the ester group

The compounds studied have no smectic phases.Consequently we can exclude smectic-like shortrange order, which could influence the trends invarious physical properties observed in the nematicphase.

2. Expérimental. - The compounds studied werepurchased from various factories and purified beforeuse by. several recrystallizations from methanol. Thetransition temperatures were determined using a

Mettler FP5 hot stage. After several recrystallizationsthe nematic-isotropic melting ranges appeared to beof the order of 0.1 °C.The magnetic susceptibilities have been measured

at the Philips’ Research Laboratories (Eindhoven)using the Faraday-Curie method. We have used thesame equipment as employed by de Jeu and Claas-sen [1], who have investigated the diamagneticsusceptibility of two homologous series of azoxy-benzenes. For a description of the experimentalset-up and possible sources of errors connected withthis method we therefore refer to these authors. The

Faraday-Curie method allows a determination ofthe mass susceptibility xg = X/p, where p is the density.Since for the compounds studied, xfi is less negativethan x1, the director n is aligned parallel to the

magnetic field direction. As a consequence one canmeasure in the nematic phase only xTI. However,since Xrso, the susceptibility in the isotropic phase, is

independent of temperature, AXg = X’I - xl can beobtained from the expression

We have measured the densities, using an apparatusbuilt in this laboratory. The central part is a hollowV-shaped glass tube, which can be filled with a

liquid. The tube is cemented tightly at the ends in acopper block. The principle of operation is basedon the variation of the natural oscillation frequencyof the tube, due to changes in its mass [2]. If the tubecontains a liquid with density p, the oscillation

period is given by

where A and B are constants, depending on the

properties of the tube. We have calibrated the tubeusing two organic fluids with known densities, viz.

acetophenone and meta-xylene. The accuracy of thecalibration has been checked by measuring the den-sity of double distilled water. The measured densityof this liquid appeared to deviate less than 0.1 %from tabulated values. The oscillator was mountedin a massive copper block, which was heated elec-trically. The estimated accuracy of the measurementsis about 0.1 %.The entropy change AI, associated with the

nematic-isotropic transition, has been determined forthe series APAPAn by means of differential scanningcalorimetry, using a Perkin Elmer DSC meter

(type 1 B). The values of AI were derived from thetransition heats, using pure In as a standard.

3. Results. - As an example of the susceptibilitymeasurements figure 1 shows the anisotropy of themass susceptibility as a function of temperature forthe compound OHMBBA. The solid curve throughthe points is a least squares fit according to the formula

where AX9(0), fi and y are fitting parameters, T isthe temperature and Tc the nematic-isotropic transi-

Fig. 1. - Anisotropy of the mass susceptibility as a function ofreduced temperature for OHMBBA. The open and filled circlesrepresent two independent measurements.

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tion temperature. In table 1 we have collected the

values of 0394xg(O), 03B2 and y for the various compounds,which have been obtained from least squares fits

using eq. (5). The parameters for the structurallyrelated material MBBA, as measured by de Jeuet al. [3] have been included in the table.

In figure 2 the results of a density measurementhave been displayed. The density could be fitted

quite well to the formula

in the nematic phase and the formula

Fig. 2. - Density as a function of reduced temperature for

APAPA.

in the isotropic phase. In table II we have listed thecoefficients ai and bi, obtained from least squaresfits using eqs. (6) and (7). The coefficients bo and blcan be used only in a temperature interval of some5 degrees above Tc, since we did not measure thedensities up to higher temperatures. As far as weknow densities of the materials listed in table 1 havenot yet been reported with the exception of APAPAand APAPA3, which have been measured by Soma-shekar et al. [4]. The agreement with our measurementsis reasonable for APAPA3. However, our data forAPAPA are substantially lower.

Table II. - Coefficients to calculate the densities

(g/cm3) according to eqs. (6) and (7).

The entropy change DE has been determined forthe homologous series APAPAn. We emphasizethat we did not take into account the pretransitionaleffects in calculating DE. As far as we know, APAPAis the only compound of the series for which AIhas been measured [5]. For this material the reportedvalue is considerably higher than the value found byus (0.34 cal. K - 1 mole-1). The results of the entropymeasurements will be given in section 4.3.

4. Discussion. - 4.1 MOLECULAR FLEXIBILITY. -

The trends in various physical properties, observedin homologous series, are closely related to the

properties of the alkyl chains. An important questionin this respect is how flexible the chains of nemato-genic molecules are, as compared with, for example,n-alkanes in the liquid state. Raman [6] and DMR [7]measurements indicate that the chains indeed are

rather flexible. X-ray measurements [8] on the otherhand yield a somewhat more rigid picture. In the

liquid state n-alkanes are not rigid, i.e. are not exclu-sively in the extended trans configuration, but canadopt a great number of conformations. The bondsoccur in three possible states, i.e. the energeticallyfavourable trans state (t) and the two symmetricalgauche states (g+, g-), obtained by rotations aroundthe carbon-carbon bonds of about + 1200. The

gauche/trans energy différence per mole, Egt, is ameasure of the flexibility ; the statistical weight of agauche state is equal to exp(- Egt/RT), where R is

the gas constant. For n-alkanes Egt = 500 cal/mole [9].It is conceivable that in the nematic phase the formingof gauche conformers will be suppressed to some

extent as a result of the presence of the ordering fieldoriginating from the neighbouring molecules. Theseexternal conformational constraints can equivalentlybe interpreted in terms of an effective gauche/transenergy difference Egt, which is higher compared withthe n-alkane value. At the clearing point Tc, the

.

conformational constraints disappear and it may beexpected that the chains have conformational free-dom comparable to that of the n-alkanes. Possibly Egtis somewhat higher than 500 cal/mole as a result ofshort range correlations in the isotropic phase. Thedifférence in population of chain conformationsbetween the nematic and isotropic phase, due to adifferent value of Egt, will be reflected in the entropychange at the nematic-isotropic transition. This ideahas led Martire [10] to calculate Egt in the variousmesophases of the dialkoxyazoxybenzenes from theincrements in AE per methylene group, by analogyto the melting of n-alkanes. Assuming that

Egt = 500 cal/mole

in the isotropic phase, he obtained a value of1 050 cal/mole in the nematic state. However,assuming that in the smectic phase the chains arein the extended trans configuration, as suggestedby X-ray work, the result was 3 150 cal/mole for Egt

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in the nematic and 2 600 cal/mole for Egt in the

isotropic phase. The majority of experimental studiessuggest a value of Eg, in the isotropic phase close to500 cal/mole.

Although the nematic-isotropic transition has beenstudied in a variety of papers, only a few of them dealwith molecular flexibility. In this respect we shouldmention the models developed by Dowell and Mar-tire [11] and Marëelja [12]. Dowell and Martire havestudied the effect of chain flexibility and chain lengthon the transition properties, using a steric meanfield cubic lattice model. The molecules are thoughtto be composed of a number of flexible and rigidsegments, which can occupy only a finite number oforientations. Both attractive and repulsive forces aretaken into account. In Marcelja’s theory on theother hand, steric repulsions have been neglected.Starting point is the mean field theory of Maierand Saupe [13]. The van der Waals forces betweenthe anisotropically polarizable molecules are des-cribed in terms of a number of coupling constants,which take account of the interaction between the

rigid cores and flexible chains. Our results can beinterpreted reasonably well within the framework ofthese models, as will be shown in the next sections.

4.2 ORDER PARAMETERS AND DENSITY. - If 03BE,il and ( are the axes of a coordinate system, fixed tothe molecules, the degree of orientational order canbe described by the tensor S with elements [14]

Here z denotes the preferred direction. By a properchoice of 03BE, fi, and 03BE the tensor S can be diagonalized.Since S has zero trace, there are two independentorder parameters. Taking the 03BE-axis as the longmolecular axis, we choose S = S03BE03BE and D = Sçç - S~~.The relation between dx, the components of S andthe diagonal components of the molecular diama-gnetic polarizability tensor K can be expressed as [15]

Here the number density N = NA p/M, where NA,p and M are Avogadro’s number, the density andthe mass number, respectively. The order parameter Ddescribes the difference between the tendencies ofthe two transverse molecular axes to align along thepreferred direction. D is related to the deviationfrom axial symmetry around the long molecularaxis. For cylindrically symmetric molecules D = 0and eq. (9) reduces to

In order to calculate S, we shall use eq. (10), whichis only justified if the term (Kçç - K~~) D/2 in eq. (9)is small. Information about D is scarce. Nuclear

magnetic resonance on deuterated p-cyano p’-pentyl-biphenyl [16] indicates that D is about 0.05 whilefor PAA a value of about 0.04 has been reported [17].However these results depend strongly on the choiceof various molecular parameters, as has been demons-trated by Hôhener et al. [18] for MBBA. Theseauthors were able to fit their spectra assuming D = 0,indicating that the value found for D strongly dependson the experimental technique used, as de Jeu suggest-ed previously [1]. Assuming nevertheless D = 0.05and a twist angle of 450 between the aniline and

benzylidene ring [19] and using the benzene valuesfor K44 and K"" [10], the term NA(K03BE03BE - iç,,,) D/2is calculated to be

which is about 7 % of the measured anisotropy ofthe molar susceptibility of MBBA [3]. We concludetherefore that, irrespective of the uncertainty about D,disregarding the D-term will not lead to substantialerrors.

Eq. (10) shows that S can be calculated providedthe factor 0394xm = N A[K03BE03BE - (K44 + K~~)/2] is known.In order to obtain AXM, Haller [21] applied an extra-polation of ln AX vs. ln (1 - T/Tc) to zero tempe-rature, where S was assumed to be unity. Howeverthis procedure can only give a rough estimate, sincethe extrapolation covers a very broad temperatureinterval. A better approach is to derive AXM fromsusceptibility measurements on solid single crystals.Unfortunately, no data of Kii have been reported forthe materials considered. Sherrel and Crellin [22]have calculated AXM for MBBA, applying Pascal’sadditivity rules [23] and using tabulated bond sus-ceptibilities [20] and obtained the value

Using this value and de Jeu’s [3] susceptibility datafor MBBA, the values of S calculated from eq. (10)appeared to agree excellently with S-values obtainedfrom various different techniques [24]. With thisvalue of 0394xM for MBBA as a starting point, we havecalculated this quantity for the other compounds,using tabulated magnetic bond polarizabilities [20].The magnetic anisotropy of the chains has beencalculated assuming that only the trans configurationgives a contribution. We have used the molecularmodel, drawn in figure 3, taking for fl the value 6.50,

Fig. 3. - The molecular structure of the homologues of APAPA.

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Table III. - Order parameters Sc, densities Pc, relative density changes àplp,, and packing fractions ~, af the

nematic-isotropic transition. V is the molecular volume and AX’ the calculated anisotropy of the molar susceptibilityfor S = 1.

found for APAPA [25]. The probability that thechain is in the trans configuration has been calculatedusing Egt = 1 050 cal/mole (see section 4 1). Thevalues of AX’ calculated in this way have been col-lected in table III.

Within the homologous series, the well knownodd-even effect is observable, which levels off withincreasing chain length.Knowing the factors DxM, the parameters S can

be calculated. These parameters represent in factsome average, since the ordering of the rigid coresdiffers from the ordering of the flexible tail segments,as has been shown experimentally [7]. However,since the magnetic anisotropy of the chains is smallcompared with the anisotropy of the cores, thecalculated order parameters reflect to a high approxi-mation the ordering of the cores. In figures 4 and 5we have displayed S as a function of temperature fora number of compounds. A remarkable feature isthat within the series APAPAn the temperaturedependence of S seems to become stronger withincreasing chain length. This behaviour could beattributed to the assumption of zero D, which is

increasingly less justified if D increases within theseries. An increase of D is plausible, since with

increasing chain length the molecular shape is deter-

Fig. 4. - Order parameter versus reduced temperature for

OHMBBA, APAPA and MBCA.

Fig. 5. - Order parameter versus reduced temperature for a

number of homologues APAPAn. The numbers accompanyingthe curves denote the number of carbons of the alkylene chain.

mined more and more by the shape of the chain,which is somewhat flat because the planar trans

state is energetically favourable.In molecular statistical theories dealing with the

nematic-isotropic transition, the values of various

physical properties at Tc are important parameters.We have listed in table III the order parameters Sc,the nematic densities Pc and the relative densitychanges 0394p/pc at Tc. Besides, we have included inthe table the molecular volumes V (calculated fromtabulated bond lengths and intermolecular radii [27]and the packing fractions l1c = NA Pc V/M. Theerrors in Sc and Ap/pc are estimated to be approxi-mately 7 and 10 percent, respectively, since these

parameters are obtained from an extrapolation pro-cedure. The table shows clearly that there is a closecorrespondence between Sc and Ap/pc’ As we wouldexpect intuitively a high value of 5c is observed for

compounds with a high relative volume change. Inaddition a gradual decrease of 0394p/pc and, conse-quently, of 5c, with increasing chain length is noti-ceable in the series APAPAn. The trends in 5c and0394p/pc observed within the homologous series are

qualitatively in agreement with the predictions ofthe Dowell-Martire model [11]. The decrease of the

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packing fractions can only be explained within theframework of this model if the chains are assumedto be somewhat less flexible (e.g. Egt ~ 800 caljmo le)than the n-alkanes (Egt = 500 cal/mole). Acceptinga value of 800 cal/mole for Egt, a decrease of Tc is

predicted in the lattice model if the attractive forcesare assumed to be somewhat anisotropic, which

certainly holds for the compounds studied. A decreaseof Tc can also be understood within the frameworkof the theory of Marëel a [12].One might wonder whether the experimentally

observed trends can also be explained in terms oftheories which do not take account of molecular

flexibility. For this purpose the molecular statisticaltheory of Ypma and Vertogen [28] provides a suitablestarting point. In this theory an equation of statewas derived for the nematic phase, based on bothanisotropic attractive forces and the anisotropicshape dependent steric repulsions. The theory predictsan increase of Sc and ~p/pc with increasing molecularlength to width ratio. The experimentally observedtrends in Sc and ~p/pc within the series APAPAncan only be reconciled with the predictions of thismodel, if the length to width ratio is assumed todecrease with increasing chain length. This possibilityhas been suggested in a previous paper [26], in whichwe presented calculations of the length to widthratio of the chains, statistically averaged over all

conformations, using the n-alkane value for Egt.Although we found that the chains tend towards amore spherical shape with increasing length, a

decreases of the overall molecular length to widthratio could only be found, if unrealistically lowvalues of Egt were used (less than 400 cal/mole). Weconclude that the effect of molecular flexibility mustbe incorporated in theories of the nematic-isotropicphase in order to understand the trends observed inhomologous series.

4. 3 ENTROPY CHANGE. - A simple Landau theo-ry [29] predicts that the entropy change at the nematic-isotropic transition is proportional to Sc2. The observedalternation in AZ (see Fig. 6) can be attributed indeedlargely to the alternation in Sc. However it is clearthat this simple relationship fails to explain theincrease in AL with increasing chain length, since Scdecreases somewhat. An increase of Ar with increasing chain length is

usually observed within homologous series [30].However, in the majority of cases these series exhibitboth nematic and smectic phases. In these series,therefore, part of the increase of AI is possibly dueto an increase of smectic short range order, as hasbeen suggested by Arnold [31]. This possibility canbe ruled out in our case, since the compounds studiedin this paper only show nematic liquid crystallinebehaviour.

An increase of ~03A3 is predicted both by the latticemodel of Dowell and Martire [11] and the mean

Fig. 6. - Entropy change AI and order parameter Sc at the

nematic-isotropic transition versus n, the number of carbons ofthe alkylene chain, for the series APAPAn ; circles : entropychange ; triangles : order parameter.

field theory of Marcelja [12]. In Marëelja’s theorypacking effects, associated with hard core repulsions,have not been taken into account. Part of the entropychange in this model results from the difference inconformational freedom of the chains between thenematic and isotropic phase. Evidently this effectplays a role in the present series. This is supported bythe observation that if the length of APAPA isincreased using relatively rigid substituents, no

increase of 039403A3 is observed. The increase of AE forAPAPAn, attributed to an increasing populationdifference of gauche conformers, allows an estimate ofthe effective gauche/trans energy différence Eg, in thenematic phase, as has been discussed in section 4. 1.Again taking the liquid n-alkane value of 500 cal/molefor the isotropic phase, this means for the presentseries a value Egt ~ 1 000 cal/mole. This indicatesthat the flexibility of the chains is still considerable.

5. t nnclusions. - In this paper, we have investi-

gated a number of structurally related Schiff’s bases.Since the materials only show nematic liquid crys-talline behaviour, the experimentally observed trendsare probably not obscured by possible influences ofshort range smectic order. The present study hasshown that,

1) there is a close correspondence between theorder parameters Sc and the relative volume changeat the nematic-isotropic transition ;

2) the trends observed in the homologous seriescan only be understood in terms of theories whichtake account of molecular flexibility ;

3) the increase of the entropy change AI at Tcwith increasing chain length cannot be explained interms of a simple Landau theory. Part of M resultsfrom a difference in conformational freedom of the

alkylene chains between the nematic and isotropicphase. Nevertheless there is considerable chain flexi-bility in both phases.

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Acknowledgments. - The authors wish to thankH. J. Roebers for technical assistance and Dr. G. Ver-

togen and B. W. van der Meer for valuable discus-sions. This work was performed as part of the research

program of the « Stichting voor Fundamenteel Onder-zoek der Materie » (FOM) with financial supportfrom the o Nederlandse Organisatie voor Zuiver

Wetenschappelijk Onderzoek » (ZWO).

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