Electric dipole interactions of chain molecules in nematics: The analysis ofsegmental ordering in α, ωdibromoalkanesD. J. Photinos and E. T. Samulski Citation: The Journal of Chemical Physics 98, 10009 (1993); doi: 10.1063/1.464433 View online: http://dx.doi.org/10.1063/1.464433 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/98/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in The nonlinear dielectric effect of α,ωdibromoalkanes J. Chem. Phys. 76, 3186 (1982); 10.1063/1.443362 A Kerr effect and dielectric study of α, ωdibromoalkanes J. Chem. Phys. 75, 5031 (1981); 10.1063/1.441893 Correlation and Distribution of Segments in a Chain Molecule J. Chem. Phys. 51, 1215 (1969); 10.1063/1.1672124 Dipole Moments in Relation to Configuration of nAlkane Chains Bearing α, ω Dipolar Substituents J. Chem. Phys. 43, 2256 (1965); 10.1063/1.1697119 Restricted Rotation Parameters from the Dipole Moments of α,ωDibromoparaffins J. Chem. Phys. 28, 890 (1958); 10.1063/1.1744289

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Electric dipole interactions of chain molecules in nematics: The analysis of segmental ordering in a, m-dibromoalkanes

D. J. Photinos Department of Chemistry, Venable and Kenan Laboratories, University of North Carolina, Chapel Hill, North Carolina 27599-3290 and Department of Physics, University of Patras, Patras 26110, Greece

E. T. Samulski Department of Chemistry, Venable and Kenan Laboratories, University of North Carolina, Chapel Hill, North Carolina 27599-3290

(Received 14 December 1992; accepted 27 January 1993)

The residual electric dipole interactions recently detected in the deuterium NMR spectra of a,cu-dibromoalkanes dissolved in nematic liquid crystalline solvents [J. Phys. Chern. 96, 8176 (1992)] are analyzed in the context of the modular formulation of flexible molecule ordering. The chord model realization of this formulation, previously applied to the study of n-alkanes, is minimally extended to include the additional coupling of the dipole carrying segments of the solute molecules to the dipolar bias produced by the solvent. The ensuing simple model successfully reproduces the observed segmental order parameter profiles of the solute over the entire nematic temperature range of the solvents. Three types of solvents are considered (Phase V, 5CB, 50CB) differing in their molecular dipole moment constitutions. It is found that in all solvent cases the orientational ordering is suppressed at the dipole moment carrying ends of the solute molecules whereas the ordering in the main body could either be reduced or elevated depending on the configuration of the dipole moments on the solvent molecules. Quantitative results for the effects of the dipolar bias on the potential of mean torque are presented and the mechanism of electric dipole driven ordering in these solvent-solute systems is discussed.

I. INTRODUCTION

The presence of permanent electric dipole moments in molecules having anisotropic shapes is known to affect their tendency to form liquid crystalline phases. I

-5 A vari­

ety of manifestations4-8 of the electric dipolar interactions between such molecules are expected since these interac­tions are sensitive to a number of factors. For example, the type of ordering (nematic, smectic, etc.) in the phase, the details of molecular shape, the size and positioning of the dipole moments within the molecules, etc., could influence the ultimate expression of such dipolar interactions.9

-12

Above and beyond such diverse influences there is a fun­damental difference between how these interactions are manifested in rigid vs flexible molecules: The intermolecu­lar interactions between isolated dipole moments-well­defined bond dipoles fixed in on the molecular structure­will of necessity have a global effe.ct on the ordering of a rigid molecule despite the isolated character of such direc­tional, site-specific interactions. On the contrary, the pos­sibility of internal motions within a flexible molecule al­lows for local manifestations of an isolated, intermolecular, dipolar interaction. Thus in a nematic, the interplay be­tween global molecular interactions (excluded volume13

)

and local interactions (site-specific electric dipoles) may produce a rich variety of ordering phenomena when the interactions are coupled in flexible molecules. Mesogens, the molecules comprising liquid crystalline phases, typi-

cally fall into this category. However, the direct study of such phenomena in the neat, ordered phase of common mesogenic molecules offers little insight due to the molec­ular disposition of the site-specific dipoles. A mesogen in­variably possesses a rigid (or practically rigid) "core"­usually comprised of para-linked aromatic rings-which contributes the molecular shape anisotropy. This global shape is ordered by intermolecular packing (excluded vol­ume "interactions"). The flexible part of meso gens consists of one or more pendant alkyl chains whose orientational ordering in the mesophase is dominated by the ordering of the mesogenic core. Site-specific permanent dipole mo­ments are, with few exceptions (e.g., chiral smectics I4

),

located on the core.4,7,8 Accordingly, orientational order­ing phenomena resulting from dipolar interactions produce an essentially global effect on the mesogen and therefore, at most an indirect influence on the ordering of the flexible alkyl chain(s).

The possibility of separating orientational ordering driven by dipolar interactions from that originating from excluded volume effects becomes considerably more trac­table in the case of a sufficiently flexible solute molecule in a liquid crystal solvent. By chemically altering the dipole moment constitution of the solvent and solute molecules, one may expect to observe the extent to which the dipole interaction affects the different parts of the flexible solute molecule. Weare able to pursue this by monitoring incom­pletelyaveraged, anisotropic NMR (nuclear magnetic res-

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10010 D. J. Photinos and E. T. Samulski: Dipole interactions in nematics

onance) interactions (nuclear dipolar coupling and qua­drupolar coupling) in partially oriented, flexible, aliphatic (probe) solutes in nematics. 15 The partitioning of the ori­entational potential experienced by a solute molecule (po­tential of mean torque) into electric dipolar and excluded volume contributions requires a reliable model of solute shape-driven orientation in a nematic solvent. Until re­cently, this posed a major difficulty because the ordering of even the simplest types of flexible molecules (e.g., chain molecules with no dipole moments), was poorly under­stoOd. 16 New advances in modelingl6-18 using a modular formulation of molecular interactions, have improved the understanding of the role of excluded volume in flexible solute ordering and now make it possible to address quan­titatively questions concerning the modification caused by site-specific, directionally interacting elements (dipoles).

The first experimental study of electric dipole ordering effects on flexible molecules was carried out recently15 us­ing deuterium NMR to measure the segmental orienta­tional ordering of a,ill-dibromoaIkane solutes (hereafter abbreviated DBr-CN, where N is the number of carbon atoms in the alkyl chain) in three nematic solvents (Phase V, SCB, and SOCB) that differ in the dipole moment dis­position on their respective mesogenic cores:

fl<O/N~N~O~(CH')-CH, CHs ~ N

Phase V

N=C~(CH')fH, SOCB

N=C<OXO/(CH,)fH, SCB

The earlier study15 of DBr-CN solutes produced clear evidence of (i) the existence of significant ordering effects originating from dipole interactions in the (apolar) nem­atic phases and, (ii) the different ways in which these in­teractions affect the various parts of the flexible dibromoal­kanes (the chain ends versus the central methylene units). Interestingly, this study showed that relative to an n-aIkane, the ordering of the dipole-carrying end segments of the a,ill-dibromoalkane (the C-Br bonds) is suppressed whereas the ordering of the inner C-C segments is en­hanced, i.e., the electric dipole contribution to segmental ordering changes sign on moving from the end of the solute chain to its center.

The purpose of the present study is twofold: First, we want to obtain a quantitative measure of the ordering ef­fects due to electric dipole-dipole interactions (the dipolar bias, for brevity) in a manner that enables us to unambig­uously separate such effects from the ordering contribu~

b) dibromoalkane

FIG. 1. Molecular diagrams showing chord structure and site numbering used in the text for n-alkanes and a, w-dibromoalkanes.

tions associated with excluded volume considerations, dis­persion interactions, etc. Second, we want to exploit a simple inclusion of the dipolar bias in an orientational po­tential V(ill,n) so that it might be of significant predictive utility in the search for mesomorphism in new classes of molecules. We attempt the quantification of the dipolar bias in terms of the coupling constants used to construct V(ill,n) which in tum, describes the alignment of the flex­ible solute's modules (submolecular segments) in the nem­atic environment. Given the successful description of non­polar n-alkane solutes in the nematic phase using the chord mode116,18 [a particularly simple yet sufficiently accurate realization of the modular approach to the construction of V( ill,n)], the idea of extending the modular formulation to include localized interactions becomes increasingly attrac­tive: It offers a relatively simple and reasonably accurate method for predicting the ordering tendency of complex molecules (multimodule, rigid, or flexible structures, with or without site-specific interactions) in terms of a small number of coupling constants pertaining to the kinds of submolecular segments typically encountered in mesogenic materials.

II. THE CHORD MODEL OF ORIENTATIONAL ORDERING FOR SUBSTITUTED ALKANES

We begin by briefly reviewing the chord model for n-alkanes (see Refs. 16-18 for extensive presentations of theory and applications) in order to introduce the modifi­cations required to extend the model to the description of a,ill-dibromoaIkanes. The orientational potential V(ill,n) for a linear alkane solute molecule (with N carbons) in a nematic medium is obtained in the context of the chord model as a sum of orientational contributions from the N-2 chords [linear segments joining the midpoints of adjacent C-C bonds, see Fig. lea)] and from the two terminal end segments as follows:

N-l

V(ill,n)=-g L P2(ec)-&[P2(tl)+P2(tN)]· (1) c=2

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D. J. Photinos and E. T. Samulski: Dipole interactions in nematics 10011

In Eq. (I) w denotes the orientation of the solute molec­ular frame relative to the director of the nematic solvent, n labels the solute conformation, the index c labels the chords into which the chain is subdivided, Be denote the angles of the chords relative to the director, tl and tN de­note the angles of the terminal segments (directed along the terminal C-CH3 bonds) relative to the director, and P2(O) = (3 cos2 0- 1)/2. The quantity g parameterizes the strength of the orientational potential of a single chord in the nematic medium. In the mean field approximation g is proportional to the principal order parameter S of the sol­vent (for simplicity we ignore the order parameters per­taining to the molecular biaxiality of the solvent),

g=(3/2)gS. (2)

The coupling constant g is obtained by the positional av­eraging of the solvent-solute interaction. It may be ex­pressed as g=ff fI' where ff is the solvent density and fI is a temperature independent, reduced coupling constant whose value is dictated by the form, and in particular, the short-range behavior of this interaction. Accordingly the temperature dependence of g is determined by the factor ./I/'S which is, in tum, dominated by the variation of S with temperature. The quantity it measures the strength of the orientational potential's influence on the terminal seg­ments. This quantity is not independent of g: The assumed equivalence (of the ordering properties) of all the C-C bonds of the chain imposes the geometrical relation

it=g[Lee/2Leec1 2, (3)

where Lecc is the length of the chord segment and Lee that of the C-C bond (the length of the terminal segment is Lee/2).

An equivalent representation for V(w,n) can be ob­tained using the C-C bond segments as the basic interact­ing modules instead of the chords. In this equivalent rep­resentation, however, terms referring to correlated ordering of adjacent C-C bond pairs appear, in addition to the single bond orientational contributions, in an expres­sion of the form

N N-'

V(w,n)=-wo 2: P2(OJ-w, 2: P2 (O,.()i+')' (4) i=' i='

In this representation Wo and WI parameterize the strength of the coupling of individual C-C bonds and bond pairs, respectively, to the nematic field; Bi denote the angles of the bonds relative to the director and P2 (Bb Bi+ l )

= (3 cos 0i cos Oi+ I +cos a v)/2, where a v denotes the car­bon bond valence angle. Imposing the conditions

(5)

the left-hand sides of Eqs. (1) and (4) become exactly equivalent. Thus the chord model is obtained as the limit­ing case of a formulation that includes intramolecular ori­entational correlations. In fact, Eq. (4) with WO=FWI is

itself a truncated (at the nearest neighbor range) version of a general expansion that includes correlations among sec­ond, third, etc., neighbor bond pairs. Although such addi­tional contributions are in general non-negligiblel6 and im­prove the resolution of the modular representation of excluded volume interactions, the simple chord model ver­sion of V( UJ,n) in Eq. (1) will be used for the description of the (dipole-free) interactions in the present analysis of normal alkanes in order to illustrate the underlying phys­ics. 'It will become evident that a minimal extension of this model to encompass the dipole interactions in the case of terminally substituted alkanes is quite adequate to eluci­date the effects of the dipolar bias on the ordering of such polar chain solutes.

As far as their orientational properties are concerned, the a,w-dibromoalkanes may be regarded to differ from the n-alkanes only in that a terminal CH2-CH3 bond is re­placed by a CH2-Br bond. This replacement affects the chord picture of the chain molecules in two respects:

( I) The chords associated with the terminal C atoms (i.e., the segments joining the midpoint of a C-Br bond with that of the adjacent C-C bond) in the a,w­dibromoalkanes are not equivalent to the other chords [due to the difference between the lengths of the C-C and C-Br bonds; see Fig. 1 (b)]. Accordingly the coupling strength to the nematic medium is different for these two types of chords. For the a,UJ-dibromoalkane solutes we shall use g' to represent the coupling of the [C-C,C-C] chords and gil for the [C-C,C-Br] chords. Within the chord model ap­proximation, the difference between the couplings of these two segments is simply related to their geometrical differ­ences. In particular, it is straightforward to show that in order to establish the equivalence between the representa­tions of Eqs. (1) and (4) in the case of bonds with unequal lengths,'7 the Wo couplings should scale according to the square of the length of the respective bond and the WI couplings should scale according to the product of the lengths of the respective pair of adjacent bonds. Thus for the a,w-<iibromoalkanes we have the relations

(6)

where the double prime refers to the couplings involving the C-Br bond and the primed couplings correspond to segments involving only C-C bonds. The chord represen­tation is obtained in this case by imposing on wo, wI, and g' the analogs of the conditions of Eq. (5) and thereby leads to the following expression for the potential V~Br.eN of the DBr-CN molecule in the absence of any dipole interactions with the solvent

N-I

J1>Br-eN(w,n) = -g' 2: P2( Be) _gil [P2(B,) e=2

+P2(ON)]-g; [P2(to) +P2(tN+')]' (7)

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10012 D. J. Photinos and E. T. Samulski: Dipole interactions in nematics

Here as a result of the relations in Eq. (6), the couplings gil and g; are related geometrically to g' as follows:

(8)

with L CCBr denoting the length of the [C-C,C-Br] chord segment. Thus in the case where the nematic solvent mol­ecules do not possess permanent electric dipoles, the chord model potential ro'Br-CN (w,n) for the a,w-dibromoalkanes is parameterized by a single quantity g', just as in the analogous potential V(w,n) of the n-alkane molecule, the difference between the two potentials being merely "geo­metrical" in the sense described above.

(2) The terminal substituent has an additional (non­geometrical) implication for the chord representation of

. the DBr-CN solutes; the C-Br bond differs from the C-C bond in that it carries a site-specific permanent dipole mo­ment fJLCC-Br) = 1.8 D, assumed to be collinear with the bond]. Thus in addition to the excluded volume contribu­tions of the C-Br bond to the ordering, there will be con­tributions from the local solute-solvent dipole-dipole in­teractions if the nematic solvent molecules possess permanent electric dipoles. When these interactions are av­eraged over the solvent molecules in the apolar nematic phase, their leading anisotropic contribution to the seg­mental ordering of the solute dipoles will have its principal axis along the C-Br bonds [i.e., the directions of the ter­minal segments to and tN + 1 in Fig. l(b)] and may be writ­ten in the form gd[P2(tO) +P2(tN+1)]. Here by analogy with g; the coupling strength gd may be expressed as gd = (3/2)gtP, where gd is independent of the degree of or­dering in the nematic solvent but depends on the size, shape, and electric dipole constitution of the solvent mol­ecules.

When this contribution is combined with the "dipole free" potential ofEq. (7), the result is equivalent to simply replacing the coupling g; of the end segments by (g; + gd). Accordingly we use Eqs. (6) and (7) to write the complete chord model potential of the a,w-dibromoalkane molecule in the form

VOBr.CN(w,n) = -g'{ 1: P2(Oc) +y[P2 (OI) +P2(ON)]

+(Yt+Ad)[P2(tO)+P2(tN+1)]} . (9)

Note that this extended parameterization now involves two independent quantities, namely, g' and the ratio Ad=gd/g'. Of these, only g' depends on the degree of orientational ordering (and consequently the temperature) of the nem­atic solvent. The ratio Ad=gdlg', is expected within the mean field factorizations of the type in Eq. (2) to be equal to the ratio of the reduced couplings Ad=rrdl rr'. Therefore, to the extent that all but the principal order parameter S are negligible, Ad should be constant for a given nematic solvent.

The values of g' and Ad can be determined from the NMR segmental order parameter measurements. Such measurements provide a sensitive test for the accuracy of the chord model parameterization of the potential of mean torque in Eq. (9) through comparisons with the theoreti­cally predicted segmental order parameter profiles. Fur­thermore, by studying the temperature dependence of the NMR spectra one can test the degree of validity of the mean field assumption used to relate the coupling strengths g; g', and gd to the solvent order parameter S. In particular for the internal consistency of the mean field aspect of the modeling it is required that the (intramolecular) ratio Ad =gdlg' be temperature independent as discussed above, and similarly for the ratio g'lg of couplings for different molecules, i.e., the a,w-dibromoalkane and the n-alkane, in the same solvent.

III. CALCULATION OF SEGMENTAL ORDER PARAMETERS OF ALKYL CHAIN SOLUTES

The predictions of the ordering mechanism described in the preceding section are tested against the flexible sol­utes' segmental orientational order profiles obtained with deuterium NMR measurements from Ref. 15. These mea­surements cover all of the solvent-solute combinations for the perdeuteriated, flexible, solute molecules (n-decane (ClO-d22 ), DBr-ClO-d2o, and DBr-C9-dI8 ) in the nematic solvents (Phase V, 5CB and 50CB). The measured quan­tities, quadrupolar splittings A~ of each distinguishable deuterated site j in the solute, result from the incomplete averaging of the respective NMR quadrupolar interactions and therefore give direct information on the orientational ordering of these sites.

In order to evaluate thermal averages of molecular properties of nonrigid solutes in anisotropic solvents it is necessary to specify, in addition to the orientational poten­tial, the geometry and probabilities in the different molec­ular conformations. Here the flexibility of the chain solutes is modeled within the usual three-state rotational isomeric state (RIS) approximation. 19 Except for the terminal C-C bonds of the DBr-CN, we use the standard RIS parameters CPg= 113° for the gauche dihedral angle, Etg=0.5 kcallmol for the gauche-trans energy difference and Eg'F g± = 3 kcall mol for the energy of consecutive g+g- states. The pres­ence of the bromine atom changes the dihedral rotational energetics at the terminal C-C bonds. Although there are no narrowly defined ranges for the values of Eg' or cPg' for these bonds in the literature,19-21 there appears to be an upper bound of 0.3 kcallmol for Eg , and a range of 80°_ l20° for CPg'. In the present calculations we use CPg'= 113° (i.e., the same value as for the internal C-C bonds) and Eg ,=O.l kcallmol. These values are suggested by calcula­tions of the magnitUde of the total dipole moment of di­bromoalkanes in isotropic solvents21-23 and are further sup­ported by the present calculations as will be discussed below. In any case the essential results of the calculations in the present work were found not to depend critically on reasonable variations of these structural parameters.

A further perturbation on the conformer statistics is introduced by the intramolecular interaction between the

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D. J. Photinos and E. T. Sarnulski: Dipole interactions in nernatics 10013

C-Br dipole moments at the two ends of the chain. This is taken into account by adding the intramolecular electro­static dipole-dipole energy to the RIS energy of each con­former. However, this additional energy does not affect appreciably the final results due to the large number of conformations and the relatively large separations of the site-specific dipoles (the C-Br bonds) in the statistically significant conformations of the DBr-C9 and DBr-ClO sol­utes considered here. Finally, some of the conformations generated with the RIS method were found to lead to self­intersections of the chain molecule; these were rejected.

The geometrical data used in the calculations are Lcc =1.53 A for the C-C bond lengths, LcBr=2.14 A for the C-Br bonds, av= 1120 for the C-C-C and C-C-Br valence angle and aoco= 1090 for the D-C-D angles. Accordingly the geometrical parameters of Eq. (8) are fixed to the val­ues Y= 1.46 and Yt=0.712.

The determination of the coupling parameters in the orientational potentials of Eqs. (1) and (9) is carried out for the cases of ClO and the two DBr-CN solutes by cal­culating the theoretical quadrupolar splittings A~alc and varying the parameters, g and gf, Ad' respectively, to opti­mize the agreement with the experimentally observed val­ues Av.{xpt for the solute-solvent pairs. The splittings are calculated from the order parameters of the C-D bonds of the deuteriated chain according to

. 3 . Av'ca1c=2I'q(P2(COS e'», (10)

where vq= 163 kHz, and e" is the angle betw.een the C-D bond at the jth carbon and the nematic director. The av­eraging in Eq. (10) is performed over the orientations m and conformations n using the distribution function 16

I(m,n) =S--IG(n)exp[ -{Econf(n) + Vor(m,n)}/kT] , (11 )

where G(n) is the rotational kinetic energy factor, Econf(n) is the conformer energy (RIS energy and intramolecular dipole-dipole energy), Vor(m,n) is the chord model orien­tational potential [given by Eq. (1) or (9) depending on whether the solute is decane or DBr-CN], and S- is the normalization factor.

IV. RESULTS

The quadrupolar splittings of the DBr-C9 and DBr­CI0 solutes in Phase V were fitted according to the proce­dure outlined above within the temperature range 300 to 335 K (Fig. 2). It was observed that the ratio of the opti­mum values of the parameters gf and gd obtained from these fits remained practically constant at Ad=-0.82 ±0.01 (for DBr-C9) and Ad= -0.90±0.01 (for DBr­ClO) throughout the entire temperature range. The fitting was then repeated by optimizing with respect to gf at the respective constant Aavalues yielding the comparison of experimental and calculated DBr-CN splittings shown in Fig. 2, where it is evident that the accuracy of these single parameter fits is quite good. The optimal values of gf for the DBr-CN solutes in Phase V are plotted in Fig. 3 against the reduced temperature T red = TIT NI of the solvent. The same fitting procedure was repeated for the case of the

60

50

40

'N ::r: -'" ';: 30 <I

20

10

0 2 3

300 .105

310

.115

320

325

DBr-C9

4 5

60

50

40

30

20

10

0

DBr-CIO

2 4 5

300

.105

.1I0

.115

320

FIG. 2. Temperature dependence of deuterium NMR splittings of 1,10-dibromodecane-d2o (DBr-CIO), and 1,9-dibromononone-d18 (DBr-C9) in the nematic solvent Phase V. Circles represent the measured splittings. Dots represent the results of fits using the potential of Eq. (9) with Ad= -0.82 for DBr-C9 and Ad= -0.90 for DBr-CIO. The optimal values of g' for DBr-CIO are plotted in Fig. 3 and are practically identical to the respective values for DBr-C9.

nematic solvents 5CB and 50CB. The results at a single reduced temperature Tred~0.95 (291 K for 5CB and 325 K for 5 OCB) are shown in Fig. 4 together with the opti­mal values of gf and Ad'

Fits of the decane splittings in Phase V over the tem­perature range 300 to 335 K were performed using V(m,n) of Eq. (1) and optimizing with respect to g; the optimized coupling parameter is also shown in Fig. 3. The ratio of gf Ig in Phase V remains essentially constant at 1.14 ± 0.02 (for both DBr-C9 and DBr-lO) throughout the nematic temperature range. A plot of g vs gf for this temperature range is shown in Fig. 5. Small deviations from a strictly constant ratio are primarily attributed to the neglect of

FIG. 3. Temperature dependence of the optimal values ofg' (circles) for the fits of deuterium NMR spectra of DBr-CIO in Fig. 2. Also shown are the optimal values of g (squares) for the respective fits of n-decane-d22 (CIO) using the chord model potential of Eq. (1).

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10014 D. J. Photinos and E. T. Sarnulski: Dipole interactions in nernatics

40.------------------------.

5CB

~30 50CB '-'

>­<l

>-<l

20

DBr-C9

2 3 4 5

j

40.-----------------~------,

5CB

20

DBr-CIO

2 3 4 5

j

FIG. 4. Plots of measured (open circles) and calculated (dots) deute­rium NMR splittings for DBr-C9 and DBr-CIO in the nematic solvents 5CB and 50CB at the reduced temperature T red zO.95. Optimal values used in the fits are g' =0.213 kcallmol and A.d=--0.48 for DBr-C9 in 5CB, g'=0.222 kcallmol and A.d=-0.50 forDBr-CIO in 5CB, g'=0.191 kcallmol and A.d=O.44 for DBr-C9 in 50CB, g'=0.195 kcallmol and A.d=0.47 for DBr-CIO in 50CB.

biaxial order parameters of the solvent molecules when deriving Eq. (2). In Fig. 5 we also show the results ex­tracted from fittings of the CIO spectra in the other two solvents, i.e., fittings yielded i'li values of 0.91 (for DBr­C9; open squares) and 0.93 (for DBr-ClO; solid squares) in 5CB, and 1.05 (for DBr-C9; open triangle) and 1.07 (for DBr-ClO; solid triangle) in the 5 OCB.

Efforts to fit the NMR data using different values of <P~ (in the range 80° to 120°) and E;g (0 to 0.2 kcallmol) give essentially the same optimal values of i'. The absolute val­ues of Ad showed a moderate increase with increasing E;g or decreasing <p~. The fittings were most accurate in the cen­tral region of the range studied and tended to become ap­preciably less accurate towards the low extreme of the <p~ range.

V. DISCUSSION AND CONCLUSIONS

As can be seen from Figs. 2 and 4, the theoretical reproduction of the experimental order parameter profiles is, in all solvent-solute pairs, rather accurate (essentially

.0.35

0.15 0.15 0.25 0.35

g (kcal/mol)

FIG. 5. Plots of the optimal values of g' from fittings of NMR spectra of DBr-C9 (open symbols) and DBr-CIO (filled symbols) solutes in differ­ent solvents, vs the optimal values of g from respective fits of n-decane spectra in the same solvent and temperature. The plotted g' and g values for Phase V (circles) are taken from Fig. 3, those for 5CB (squares) correspond to solvent temperatures of T=29l and T=297 K, and those for 50CB (triangles) correspond to 325 K.

exact to within experimental error) indicating that the form of the orientational potential in Eq. (9) is quite ad­equate for the description of ordering of the DBr-CN sol­utes in the nematic environment. The specific values ob­tained for the model parameters of this potential in the different solvents raise the following issues that we discuss individually:

In all three solvents the values of Ad are substantial and negative, clearly indicating that the solvent-solute inter­molecular dipole interactions oppose the alignment of the terminal C-Br chain segments parallel to the director. The opposition is largest in the Phase V solvent where, in fact, it overcomes the excluded volume tendency for alignment of the terminal segments. This substantial opposition to C-Br alignment along the director is indicated by the fact that the overall relative coupling strength [Yt+Ad of Eq. (9)] for these segments is negative. In the two CB solvents Ad is also negative but not large enough to reverse the alignment tendency imposed by excluded volume on the terminal segments (along the director); however, it re­duces this tendency considerably as indicated by the fact that the overall coupling (Yt+Ad) is less than 40% of Yt"

The suppression of terminal-segment alignment by the dipolar bias can be qualitatively understood in the case of the Phase V solvent by simply noting that the major elec­tric dipole [approximately along the N-O direction, p,(N-0) ~ 3D] in this solvent is positioned in the central part of the meso genic core and is directed transverse to the long molecular axis of the mesogen. Therefore, an energetically favorable configuration of the solvent-solute dipole mo­ments would tend to orient the terminal segments (C-Br bonds) of the latter essentially perpendicular to the direc­tor.

The situation in the cyanobiphenyl (CB) solvents is not as straightforward. Here the major dipoles are longi-

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D. J. Photinos and E. T. Samulski: Dipole interactions in nematics 10015

tudinal and positioned at the C=N extreme of the CB mesogenic core r.u(CN) ~4D]. Therefore, association of the solvent-solute dipoles should enhance the solute's terminal-segment ordering. This explains why suppression of terminal-segment ordering in the CB solvents is moder­ate relative to Phase V. However, to address the question of why in these CB solvents suppression is exhibited at all, the following considerations are proposed. Since the C-Br dipole moment is at an angle of ~35° relative to the local chain contour (see sketch I),

I'·I"·'\~ .L"!I~ ':

(I) the preferred accommodation of the chain contour parallel to the director does not favor the association of CB solvent-solute dipoles. The probability of such solvent­solute associations is further reduced by dipole associations among the solvent molecules themselves; this is expected to be substantial for CB liquid crystals.4,6,7 Thus when aver­aging over the solute molecules in order to obtain the ef­fective coupling strength id in the CB solvents, the distri­bution will be weighted more towards configurations with favorable excluded volume (solute chain contour parallel to the CB long molecular axis and hence the C-Br dipole at sizable angles with respect to the CB axis) than configu­rations satisfying parallel and antiparallel solvent-solute di­poles.

(2) The ratio i'li for the couplings of the interior chords of the solute (where there are no direct dipole in­teractions) is in general different from unity. Moreover, the ratio shows a solvent dependence (Le., the chord cou­pling strength depends on the dipole moment composition of both the solvent and the solute molecules). The finding that 'i' =l=i is the quantification of the global influence of the dipolar bias on the solute molecule. Indeed, the fact that the coupling strength of segments in the middle of the chain depends on whether or not the ends of the chain are capable of having site-specific interactions with the solvent molecules, is a direct indication of the extension of the effects of such interactions beyond the respective sites. From this point of view, the dependence of i'li on the solvent is hardly unexpected if one takes into account that the chord coupling strengths are obtained by averaging the solute-solvent interactions over the molecules of the latter. The presence of dipole interactions would certainly modify both the positional and orientational aspects of this aver­aging and would therefore influence the effective coupling strength of all of the molecular segments, not just the ones that carry dipoles.

In the Phase V solvent the dipole interactions enhance the ordering of the inner chords (i' = 1.14g) and similarly, but to a smaller extent, in the 50CB solvent (i' = 1.06i). On the contrary, the dipole interactions in 5CB reduce the

coupling of the chords to the nematic mean field ('i' =O.93g). The factor differentiating this behavior ap­pears to be the presence of dipoles in the central portion of the solvent molecule. Indeed, the major dipole in Phase V and the secondary dipole in 50CB r.u(COC) ~2D] are situated centrally on the molecule and thus interactions with the C-Br dipoles of the solute bring the contour of the solute chain closer to the (excluded volume) orienting influence of the mesogenic core. By contrast the extreme positioning of the dipole moment in 5CB enables a direct interaction with the dipoles at the ends of the DBr-CN chains while holding the bulk of the DBr-CN molecule away from the core of the 5 CB mesogen, and thereby effectively attenuating the otherwise dominant excluded volume ordering mechanism.

(3) There is a slight but clearly detectable solute chain-length dependence (DBr-ClO vs DBr-C9) in the val­ues of Ad in all three solvents. In particular, the absolute value of Ad is always larger for DBr-ClO than for DBr-C9. To a smaller extent, i'li appears length dependent in the CB solvents (see Fig. 5). The origin of these solute chain­length dependences is of a different nature from the small variations of the coupling constants with chain length (dis­cussed for alkanes in Ref. 24) since here they refer to the ratio of two coupling constants at a given solute chain length. A plausible explanation of this variation involves the chain-length parity effect: Whereas the DBr-ClO chain has a significant number of conformers for which the ter­minal dipoles are mutually antiparallel, the DBr-C9 has practically none.25 Thus the total dipole moment probabil­ity distribution will be different for an even- and an odd­carbon number solute and, in addition to the factors stated in (1) and (2) above, this chain parity property will in principle affect the averaging of the solute interaction over the solvent molecules.

Finally, it is perhaps instructive to isolate the ordering effects of the dipolar interaction by evaluating the segmen­tal order parameters (equivalently, the theoretical quadru­polar splittings) along the DBr-CN chain in the absence of any dipole-dipole interactions. The precise predictions of the chord molecule allow us to quantitatively study this excluded volume aspect of the solute ordering by "turning off" the dipole-dipole interaction. This may be simply re­alized by using for the orientational potential the expres­sion in Eq. (7) [equivalently, Eq. (9) with Ad=O] wherein we set the value of i' to be numerically equal to the value of i for decane in the same solvent and at the same tem­perature. The results (.6.vj -values vs position j) are shown in Fig. 6 for DBr-lO in Phase V and SCB. For comparison we plot on the same graph the actual (Le., with the dipole interaction operative) quadrupolar splittings. Itis evident from these plots that in the case of Phase V [Fig. 6 (a)] the effects of dipole interactions on segmental ordering are dra­matic and affect both the outer and the central parts of the chain albeit in opposite directions. These predictions could be verified experimentally if one could synthesize a dipole­free nematic solvent that would order n-alkanes in the same way that Phase V does (in other words, the solvent would be identical to Phase V as far as the excluded vol-

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10016 D. J. Photinos and E. T. Samulski: Dipole interactions in nematics

45 b) CBr-ClO in 5CB

-----tive, parameterization of the contributions of both ex­cluded volume and dipole interactions. It also offers insight into the diversity in which the latter interactions are man­ifested on segmental ordering in flexible molecules. Lastly, this transferrable extension of the chord model would be a valuable component of molecular structural screening par­adigms that could be designed for the purpose of discov­ering new types of mesogens.

25

20L---~---L---L--~----L-~

2 3 4 5 j

50.------------------------.

a) CBr-C lOin Phase V 45

40

25

FlO. 6. Squares: Quadrupolar splittings exhibited by the solutes DBr-ClO vs carbon atom position j in the nematic solvents; (a) Phase V (at T=320 K); (b) 5CB (at T=297 K). Triangles: Respective profiles of splittings calculated with the solvent-solute electric dipole interactions "turned off."

ume and other nondipole interactions are concerned). Al­ternatively, the opposing results in Figs. 6(a) aJld 6(b) suggest that a judicious mixture of these solvents would appear to have no global dipolar bias on the interior seg­ments of the DBr-ClO.

In conclusion, the extension of the chord model to encompass electric dipole interactions in the nematic phase can provide a consistent and accurate description of seg­mental ordering of flexible solutes using simple, yet sensi-

ACKNOWLEDGMENTS

Hirokazu Toriumi stimulated the initial experimental foundations of this work and Chi-Duen Poon helped us widi the-graphics. E:T.S. is supported in part by Wright Patterson Materials Lab under Air Force Prime Contract No. F3361-90-C-5813.

. ~ . -,.-- -." ....

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