Nuclear magnetic resonance studies of liquid crystals under pressure

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Nuclear magnetic resonance studies of liquid crystals under pressure

G.P. Wallis, S.K. Roy

To cite this version:

G.P. Wallis, S.K. Roy. Nuclear magnetic resonance studies of liquid crystals under pressure. Journal

de Physique, 1980, 41 (10), pp.1165-1172. �10.1051/jphys:0198000410100116500�. �jpa-00208943�

Nuclear magnetic ^{resonance studies of} liquid crystals ^under pressure

G. P. Wallis (*) ^{and S. K.} Roy

Cavendish Laboratory, Cambridge, England (Reçu ^{le 24}

1980, accepté ^{le 23} juin 1980)

Résumé. 2014 La largeur ^{de raie} (0394H) de la résonance du proton ^a été mesurée (en fonction de la température ^{et de la} pression) pour quatre homologues de la série alkyl cyanobiphenyl (5, 6, ^{7 et 8} CB) ^et aussi pour le methoxy- cyanobiphenyl, p-azoxyanisole (PAA) ^{et le} quinquephenyl. ^On peut obtenir les valeurs du paramètre ^{de l’ordre} nématique (S2 = P2(cos 03B8) >) ^en divisant les résultats par ^un facteur d’échelle (0394H/S2), qu’on peut déduire soit

théoriquement, soit par référence à des ^mesures de susceptibilité magnétique ^{à la} pression atmosphérique. ^{On a}

observé dans la forme de la résonance, ^{et non} dans sa largeur, ^des changements ^faibles qui ^donnent l’impression

que la conformation moyenne de la molécule n’a tendance à changer ^{avec la} température ^{et la} pression que dans les cas où elle est souple ^en fin de chaîne. En principe, ^{dans de tels cas,} le facteur d’échelle (0394H/S2) peut ^aussi changer

avec la température ^{et la} pression, ^{mais en} pratique, la variation semble être faible.

Nos résultats pour 5 CB ^et PAA sont, ^en général, ^{en accord avec ceux de Horn et Faber, et McColl,} respectivement.

A la transition nématique-isotropique, la valeur de S2(S2c) ^diminue quand ^on comprime ^{5 CB, 7 CB et 8 CB,}

mais elle reste constante pour 6 CB ^et pour les ^autres substances que ^{nous avons} étudiées.

Abstract.

The line width (0394H) ^{of the} proton ^resonance has been measured as a function of temperature ^and pressure for four homologues ^{of the} alkyl cyanobiphenyl ^series (5, ^{6, 7 and 8} CB) and also for methoxy-cyano- biphenyl, p-azoxyanisole (PAA) ^and quinquephenyl. ^{Values of} the nematic order parameter (S2 = P2(cos 03B8)>)

may be obtained from the results by dividing ^them by ^a scaling ^factor (0394H/S2), ^{which can in some cases be deduced} theoretically and in other cases obtained by ^{reference to} magnetic susceptibility measurements at atmospheric

pressure. Slight changes ^{which we have} observed in the shape ^{of the resonance line as} opposed ^{to its width} suggest that the mean conformation of the molecule is liable to vary with temperature and pressure in ^cases where it has

a flexible end chain, though ^not otherwise. In principle ^the scaling ^factor (0394H/S2) may also vary with temperature and pressure in such ^cases, but the variation appears ^to be rather slight ⁱⁿ practice.

Our results for 5 CB and PAA are in general agreement with those reported by Horn and Faber and McColl

respectively, ^who also used elevated pressures. The magnitude ^of S2 at ^the nematic-isotropic transition (S2c)

decreases on compression ^{for 5 CB,} 7 CB and 8 CB, but for 6 CB and the other substances we have investigated

it appears ^to remain constant.

Classification

Physics ^Abstracts

61.30 - 76.60 - 64.70E

1. Introduction.

When the investigations

described in this _paper were begun, ^{it was} hoped ^that they ^would provide information concerning ^the

variation of the order parameter S2 (= ^{P2(cos 0)} »

with both temperature ^and pressure, for a parti- cularly simple ^nematic substance, namely p-quinque- phenyl. ^Horn [1] ^had obtained such information for 4-p-pentyl-4’-cyanobiphenyl (5 CB) by measuring

its optical birefringence ^{inside a} pressure vessel, but the 5 CB molecule includes a strongly polar-CN

group and a flexible end chain, and the failure of Horn’s results to conform to the predictions ^{of mean}

field theories [2] ^could perhaps ^{be blamed on these}

features. The p-quinquephenyl ^molecule, by ^contrast,

is non-polar ^{and more or less} rigid. ^{At the} high ^tem-

peratures ^{at which} p-quinquephenyl ^is nematic, ^how-

ever, the technique ^used by ^{Hom would be} difficult,

if not impossible, ^to apply. Of the other techniques

which have been used to measure nematic order parameters ^at atmospheric pressure, nuclear magnetic

resonance seemed to constitute the only ^feasible

alternative. It had been applied ^with apparent ^success

to nematic PAA under _pressure by Deloche et al. [3]

and McColl and Shih [4].

In the event, we were unable to prevent ^our speci-

mens of p-quinquephenyl ^from becoming ^conta- minated, ^{and our resultls} for this substance are

incomplete ⁱⁿ consequence. Much of this paper is, therefore, concemed with four members of the homo-

logous ^{series of} 4-n-alkyl-4’-cyanobiphenyls, namely 5 CB, 6 CB, 7 CB, ^and 8 CB, for which we have obtained results which confirm and extend those of Horn.

The _paper includes a brief report ^{on some} pre- (*) ^Present address : British Nuclear Fuels Limited, Chester,

England.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198000410100116500

1166

liminary results for PAA and also for p-methoxy- cyanobiphenyl (1 OCB). Gray [5] ^{has noted evidence}

that the temperature (T,) ^{at which} the nematic and

isotropic liquid phases could co-exist is 84°C for the latter substance at atmospheric pressure, whereas the melting point of the solid phase (Tm) is 104 °C.

Since (dTc/dp) generally ^exceeds (dTm/dp), ^{it was to}

be expected ^that Tc would become greater ^than Tm

at a pressure of a few kilobars. This expectation

was confirmed, ^{and in fact it} proved possible ^{to make}

nmr measurements on a monotropic (i.e. metastable)

nematic phase ^{of 1 OCB at} pressures ^as low as 0.5 kbar.

Since the 1 OCB molecule, although polar, ^is probably

the shortest and most rigid nematogenic ^molecule

yet known, this substance should _repay further

study. ^{Our first} specimen ^{of 1 OCB was} kindly supplied by ^Professor Gray, ^and he gave ^{us some} 1 CB also. The latter substance showed no sign ^of

nematic behaviour, however, ^{even at 6 kbar.}

2. Experimental ^détails.

^{The nmr lines studied}

in this work were those of the proton ^{resonance at}

a frequency ^{of 27 MHz. A home-made} spectrometer incorporating ^a Robinson oscillator was used. The rf coil was enclosed in a capsule ^{made of Be-Cu,} topped ^{with a} collapsible bellows made of brass or

phosphor-bronze, which could be evacuated and then filled in vacuo with the substance of interest, using ^a specially designed syringe. Apart ^{from the}

1 OCB mentioned above, ^our samples ^were pur- chased from commercial suppliers ^{and were used}

without further purification. ^After filling ^and sealing,

the capsules ^were inserted into a pressure vessel made from a nickel-chromium alloy (N imonic ⁸⁰ A),

which had an internal diameter of 9.5 mm, ^an external diameter of 3.8 cm, and a length ^{of 12.5 cm. The}

vessel was then filled with a suitable _pressure trans-

mitting fluid, normally ^a 50 : 50 mixture of kerosene and motor oil, and connected by ^{means of small}

bore tubing ^{to a} pressure intensifier and a manganin

pressure gauge. The entire vessel (but ^{not the inten-} sifier and the gauge) could be heated by ^{means of}

a coil on its outside, ^to which the power input ^was regulated by ^{a standard} temperature controller. The temperature ^{of the} specimen ^{itself was measured} by ^{means of a} thermocouple inside the _pressure vessel, with its junction embedded in the plug ^which capped ^{the bellows.} Temperatures up ^to 100 °C could be controlled and measured to within + 0.1 ^OC.

while at 400,OC the _accuracy was probably ^{± 1 OC.}

The manganin gauge, accurate to ± ^{5 bars had} been calibrated against ^a deadweight ^{tester at} Imperial College. ^{It was} compared ^{with the one used} by ^Horn [ 1 ] and the two gave entirely consistent readings ^{at room} temperature. ^Our clearing ^{curve for 5} CB, ^however.

is significantly different from Horn’s. We attributc the discrepancy ^to the fact that whereas our gauge

was in a separate ^{vessel remote from the} sample ^and

remained at room temperature throughout, ^Horn’s

gauge ^was close to his specimen and therefore varied in temperature. ^We suspect ^{that on this account his} pressure readings ^{were affected} by ^{a zero error}

which was a function of temperature only. ^{In com-} paring ^our results for 5 CB with Horn’s we have shifted his pressures downwards by ^{the amounts} required ^to bring ^our respective clearing ^{curves into}

coincidence.

At the high temperatures ^{needed to make} p-

quinquephenyl ^{nematic we} found it convenient to use a 30/70 eutectic mixture of biphenyl ^and o-terphenyl ^as the pressure transmitting fluid instead of the kerosene and motor oil mixture and we have

reason to believe that the contamination of our

p-quinquepehnyl samples ^{was due in} part ^to seepage of this mixture through pinholes ⁱⁿ the bellows that gave ^no trouble at lower temperatures. ^{It is} probable, however, ^{that the} p-quinquephenyl ^{was in} any ^case

decomposing [7].

For each substance we recorded nmr spectra ^at various pressures along ^a limited number of isothermal lines. The clearing pressure (Pc) could be identified with precision, ^as could the width of the nematic line at this _pressure, because small amounts of the

isotropic phase contribute a sharp ^and easily ^detec-

table peak ^{at the line centre. Further} details of the

experimental technique may be found elsewhere [8].

3. Transition curves.

The clearing ^{curves which}

we observed for the alkyl cyanobiphenyls ^{could be} accurately ^fitted by ^the polynomial expression

T,,:(p) = Tc(°) ⁺ A(pjkbar) - B(p/kbar)2 , (i) using ^the coefficients listed in table 1. The same

equation could be fitted to the smectic-nematic (Tsn)

transition curve which we were able to observe for 8 CB. Table 1 includes for comparison the coeffi- cients reported by Shashidhar and Venkatesh [9],

and there is fair agreement except ^{in the case of} 7 CB. Both sets of data for 8 CB are reasonably

consistent with the phase diagram for this substance

reported by Liebert and Daniels [10].

The results quoted ^{in table 1 for} p-methoxy- cyanobiphenyl (1 OCB) ^and p-quinquephenyl (5 Ph)

Table I. - Transition data.

Fig. ^1.

Derivative line shapes ^of (a) ^{5 Ph} (uncontaminated spécimen) ; (b) ^{PAA and} (c) ^{1 OCB.}

are of uncertain _accuracy because the specimens ^of

both these substances became contaminated during

use. We quote ^no results for PAA because our obser- vations on this substance were so limited (see below),

but transition data for it are available from the work of Spratte and Schneider [11].

4. Line shapes.

Of the substances investigated

in this work 5 Ph showed the simplest proton ^line

shape : ^a sharp ^central peak ^flanked by ^two wings

with little if _any structure. A typical ^{chart record of}

the derivative of the line shown by ^an uncontamined

specimen ^is reproduced ⁱⁿ figure ^{la. The area under}

the central peak ^{was found} by integration ^{of such}

traces to be about 1 /11 of the total area, so there is little doubt that the central peak is contributed almost entirely by ^{the 2} protons ^{which lie at the ends} of the 5 Ph molecule, ^{while the 20} _protons ^which

lie along its sides contribute the wings. ^{Because the}

vectors joining ^{each end} proton ^{to the} adjacent

side protons ^{make an} angle ^{of 600} with the axis of the molecule, ^the averaged dipolar coupling ^between

end and side protons ^is very weak.

It would require ^a lengthly calculation to explain

the line shape ^{of 5 Ph in} detail, because there are as many ^as 10 protons ^on each side of the molecule, forming ^{a chain} along ^{which the} nearest-neighbour coupling ^is relatively strong. ^{The case of PAA is} easier to handle theoretically, because the two C6 rings ^{in the PAA molecule are} separated by ^an azoxy

(-N20-) group, which greatly ^{reduces the} strength

of the coupling between the second and third members of each chain of side protons. ^{In PAA the end} protons of 5 Ph are of course replaced by methoxy (CH30-)

groups, but the _oxygen atoms in these help ^to keep

the three protons away from the protons ^{on the}

rings. ^{To a first} approximation ^the contributions to

the line shape ^made by ^the methoxy protons ^{and the}

ring protons may be treated separately [12]. ^An acceptable ^{fit to the line} shape ^{for PAA has been}

achieved in this _way by Rowell et al. [13]. We repro- duce a typical chart record for PAA in figure ^{lb to}

show that the line has appreciably ^{more structure}

in the wings than the 5 Ph line, ^and more, incidentally,

than McColi [6] appears ^to have detected.

The 1 OCB molecule resembles 5 Ph in that there is no azoxy group ^to separate ^{the two} C6 rings, ^but

it resembles PAA in having ^a methoxy group ^{at one}

end; ^{the -CN} group ^at the other end is irrelevant, except ^{in so far as it} may indirectly ^{affect the} angle f3 through ^{which one} ring ^is twisted with respect ^{to the} other, and thereby affect the strength ^{of the} coupling

between the second and third members of each chain of 4 side protons. ^{The line} shape ^{to be} expected

from each such chain has been discussed elsewhere

by ^Wallis [8]. ^{He was able to achieve an} acceptable

fit to the line shape ^{of the 1 OCB molecule as a whole}

by assuming fi ^{to be} 35( ± 3 y). As may be ^seen from

1168

the typical ^{chart record} reproduced ⁱⁿ figure ^{1 c}

there is more structure in the wings ^{for 1 OCB than}

for 5 Ph, but less than for PAA.

Progressive contamination during ^use caused the central peak ^to get bigger ^{for both 5 Ph and 1 OCB}

but did not appear ^to affect the wings. ^{Our obser-}

vations strongly suggest, ⁱⁿ fact, ^{that the line} shape (as opposed ^{to the line width)} for uncontaminated

specimens ^is independent ^of temperature ^and pressure

Fig. ^2.

^The change ^{in line} shape ^{in 6 CB with} change in pressure at 104.2 OC. (a) p

^2.25 kbar; (b) p

^{3.25 kbar.}

for all three of the substances so far discussed. That is not the _case, however, ^{for the} alkylcyano-biphenyls.

For all four of the alkylcyano-biphenyls ^{which we}

have studied the lines have enough ^{structure in the} wings ^{for two distinct maxima to be seen on the}

derivative trace on each side of its centre, and the outer of these becomes more prominent ^{when the}

temperature ^{is reduced} at constant t pressure, ^or the pressure increased at constant temperature. ^{The effect} is illustrated by typical ^{traces for 6 CB in} figure ² (only ^{half of each trace} being reproduced ^because they ^{were both} antisymmetric about the centre).

Since in these substances the alkyl protons ^and the ring protons ^{are liable to} couple strongly ^not only ^between themselves but with each other, ^we have little hope ^of being ^{able to} interpret ^{the line} shape in detail. But the fact that it changes, ^{when no}

such change ^is detectable for 5 Ph, PAA, ^{or 1} OCB, is probably ^a sign, ^{that the mean} conformation of the molecule changes ^with temperature and volume.

Presumably ^a higher temperature, ^{or a} larger ^volume,

enables the flexible end chains to explore ^a greater number of configurations. ^{As is now well-reco-} gnized [14] ^the conformation of the end chains can

be investigated by ^{nmr methods} using selectively

deuterated compounds, ^{but such} compounds ^are

still rather too precious ^{to be} used inside a pressure vessel, where the risk of loss or contamination is

always appreciable.

5. Line widths and the order parameter.

^The line width _{may be} conveniently characterized by ^the

distance AH (in gauss) between the two principal

maxima in the wings, ^{i.e. between zeros on the deri-}

vative trace as shown in figure ^{1. Provided that the}

line shape, ^{and hence the mean} conformation of the molecule is fixed, ^{dH should be} proportional ^to S2.

According ^{to McColl} [6], ^who based his analysis

on the second moment calculations of Weber [12], (AHIS2) is 6.2 gauss for PAA. According ^{to Wallis} [7]

it is 4.8 ( ± 0.3) gauss for 1 OCB. For the other materials of interest here we are obliged ^to rely ^on independent

measurements of S2 ^{to obtain the} estimates of this

scaling factor which are listed in table II. Of course,

for the alkyl cyano-biphenyls, where the mean

conformation of the molecules _may ^not be fixed, (AHjS2) ^{is not} necessarily ^{constant. a} point ^{to which}

we shall retum below.

Table II. - Scaling factors for line m-idths.

5.1 PAA. - Our line width measurements on

PAA were confined to various temperatures ^at

atmospheric pressure (where Tc ^{is about} 136 °C),

and to various _pressures at a temperature ^{of 146 °C}

(where p, is about 0.2 kbar). ^We present ^{both sets} of data on a single diagram by plotting S2 (= AH/6.2) against (7c-r)p ^{or (P-Pc)T as the case may be. If}

the abscissa scales are adjusted, ^{as in} figure ^{3, so that}

46 °C on one is equivalent ^{to 1 kbar on the other,}

then the ^{two sets} of points ^lie virtually ^{on the same}

curve. Previous authors [3, 4] ^have claimed that S2

is constant along ^the nematic-isotropic ^transition

curve for PAA, ^{and our results} are consistent with that claim over the small range we, ^{have- explored.}

Since 46 °C kbar-’ is close to the slope ^{of the transi-}

tion curve [11], ^{it follows that contours of constant} S2 (> S2,) ^{on the} T-p plane ^{must be almost} parallel

to the transition curve, and hence that the value of S2 ^{at the} solid-nematic transition must steadily

increase on compression. ^{Here too we are in} quali-

tative agreement ^with previous ^{authors. But the}

values of S2 which McColl [4, 6] ^has reported ^for atmospheric pressure, and for ^a variety ^of pressures at 146 °C, ^{are not} consistent with ours in détail ; they would lie near the broken curve in figure ^3.

We attribute the discrepancy ^to whatever limitation in McColl’s apparatus ^{such as} inhomogeneity ^or

overmodulation, ^caused his resolution to be less

good ^{than ours.}

Fig. ^3.

S2 plotted against (T,-T) ^and (p-p,,) ^{for PAA. 0 Present}

work at P

0; . Present work at T

146 OC. The broken

represents McColl’s data at 146 °C [4, 6]. The abscissa scales

adjusted that 46 "C is equivalent ^{to 1 kbar.}

5.2 1 OCB. - Our preliminary measurements for 1 OCB indicate a pattern of behaviour _very similar

to that for PAA. In particular, ^{the values of} S2, ⁽⁼ AH/4.8) ^{which we} have measured along ^the nematic-isotropic transition curve for pressures up to 5 kbars lie in the range 0.34 ± ^{0.01 and} show no

systematic ^{increase or decrease on} compression.

5.3 5 Ph.

The curve in figure ^{4 for the order} parameter ^versus (Tc-T) ^{in nematic 5 Ph at} atmosphe-

ric pressure represents ^an analytical expression ^which

Sherrell and Crellin [8] ^{have used to} represent ^their

measurements of the magnetic anisotropy A/,

Fig. ^4. - S2 plotted against (Tc-T) ^{for 5 Ph at} atmospheric pressure.

The points

taken from the present work and the curve repre- sents S2 obtained from àX measurements (curve pl. ^{of ref.} 9).

scaled by their estimate of 2.83 ^x 106 gm for S2jX(m);

an estimate based on calculated values for the princi- pal components ^{at the} polarization ^{tensor for the}

5 Ph molecule; ^it corresponds ^{to curve Pl rather}

than P2 in Sherrell and Crellin’s figure ^{4, i.e. to the}

first of their two runs. The points ⁱⁿ figure ⁴ represent the line widths which we have measured for 5 Ph at atmospheric pressure, scaled so as to lie close

to the curve at the lower end of the temperature

range. To achieve this fit we needed to use the plau-

sible value of 4.6 G for (AHIS2) in 5 Ph. The fact that our points ^lie slightly ^{above the curve for tem-}

peratures ^{close to} 7c ^{confirms the} suspicion ^enter-

tained by Sherrell and Crellin that even during ^their

first run their specimen ^was becoming contaminated and that S2 ^was probably being depressed ^{in conse-}

quence, especially ^{close to} T,. ^{For our} atmospheric

pressure work ^on 5 Ph the specimen ^was, excep-

tionally, ^{contained in a sealed} glass ampoule ^rather

than in a metal capsule. ^We believe it to have stayed relatively pure, ^as Tc ^fell by only 12 ^{OC after 3} days

at temperatures ^{close to 400 °C.}

Figure ⁴ implies ^that S2 ^at T, is less for 5 Ph than for either of the nematics discussed above, ^and less, indeed, than for _any other nematic for which results

are available : S2, appears ^to be 0.28 instead of _say 0.35 (1). ^{If one} attempts ^to dispose ^{of this} anomaly by arguing that Sherrell and Crellin’s value for

S2/A/ ^{is too} high, ^{and hence that our value for} (AHIS2) ^{is too} low, ^it merely reappears in another form elsewhere. For while working ^under pressure at points ^{in the} p- Tc plane ^{not far} from the solid- nematic transition we twice observed line widths of over 3 G. If (AHIS2) ^{is 4.6 G,} such line widths would correspond ^{to values} of over 0.65 for S2, ^which

would be normal enough. ^{But if} (AH/S2) ^{is assumed to}

be 4.6 x 0.28/0.35

^{3.7 G} say, they ^{would corres-} pond ^{to values of over} 0.81, which would be _excep-

tionally high.

(’) ^{The value} predicted ^for S2c by the well-known

field

theory of Maier and Saupe ^{is, of} course, 0.43.

1170

The results we obtained for 5 Ph under pressure suggest ^{that it} might ^{well be} possible, ^{for a} pure

sample, ^to plot S2 ^versus (p-p e) ^{at a} succession of constant temperatures ^and thereby ^obtain points

on a single ^curve, which could then be made to match the curve in figure ⁴ by adjustment ^{of the abscissa}

scales, ^{as in} figure ^{3. But our results were too much}

affected by contamination, ^and by consequent ^drift of the transition curve, to be worth presenting ⁱⁿ

detail.

5.4 5 CB. - Horn [1] ^{and Horn} and Faber [2]

deduced their values for the order parameter ^{in 5 CB} from a quantity 1 (= (ne - n 2)/(& _ 1)), ^{where ne}

and _no are refractive indices. If both 1 and AH are

indeed proportional ^{to S2, then the ratio} (AHIZ)

should of course be _constant, and it appears ^to be

so along ^the clearing ^curve within the limits of experi-

mental error, as may be seen from figure ^{5. To} compute

most of the points ^{in this} diagram ^{we have used our}

measurements of (AH),, ^{and have taken} Le ^{from the} polynomial expressions ^{which Horn used to fit his}

data, ^{and the estimated error} of ± ² % ^comes largely

from the latter ; ^{but to} compute ^the point ^at T,

^{35 OC} (i.e. ^for atmospheric pressure) ^{we used for} Le ^the

accurate data which Horn obtained directly ^{with a}

Chatelain wedge, ^{and the estimated error in this case}

is contributed largely by (AH),,, ^{which, at} atmospheric

pressure, ^{we can} deduce only by extrapolation.

In figure ^{6 we} show values of (AHIZ) ^at pressures above the clearing ^{curve for four different} tempe-

ratures at which we made nmr measurements, again computed using ^Horn’s polynomials ; ^{in this} figure

the points ^are plotted against 1 (in ^effect against ^the

order parameter), ^this proving ^a convenient _way to

spread ^{them out.} Figure ⁶ confirms the impression given by figure ⁵ that there is no significant ^variation

of (AHIZ) ^with temperature, ^for given ^{1. But it}

looks as though ^{as one moves} away from the clearing

curve (AHIZ) ^falls slightly, from about 7.45 to 7.2 G.

The fall seems to occur over the _range of I from 0.2 to 0.25, which would correspond ^{to a} temperature

range of about 3 OC at constant pressure.

The nmr line shape ^{for 5} CB varies with tempe-

rature along ^{lines of constant I in the} p-T plane,

Fig. ^5.

(AII/Z)

^T along clearing ^{curve in 5 CB.}

Fig. ^6.

(All/1) ^{l’s. 2.’ in 5 CB at four} temperatures : ^{+ 55.0} °C, 0 74.2 °C,

94.8 °C.. 117.0 °C.

and the fact that (AH/2:) ^{does not do so} suggests that this ratio is insensitive to changes ^{in the mean} conformation of the molecules. Since there is no reason why ^the effect of such changes ^on (AHIS2)

and (ZIS2) should be the same, ^we conclude that it is

probably negligible ^{for both. To} explain ^{the apparent} sensitivity ^of (AHIZ) ^to changes ^{in ¿ near the} clearing

curve we must therefore turn to other possibilities.

Errors in the procedure ^{we have used to reconcile}

Horn’s _pressure readings ^{to ours can} scarcely ^{be to} blame, ^as these would be most significant ^at points

far from the clearing ^{curve. It} is conceivable that the customary assumption that nematic molecules ^rotate

freely enough about their long ^{axes to} be treated

ns axially symmetric breaks down in the case of 5 CB.

In that case 1 and dll should both be proportional

not to S2 ^but (see [2]) ^to (S2 ^+,c ( ^{sin 20 cos 2} y )) ^and (S2 ^{+ e’} ( sin2 D ^cos 2 y )) respectively, ^where y is

an angle of rotation of the molecule about its long

axis with respect ^{to the} plane ^that contains the director and e, e’ are small numerical coefficients, and the variation of (All/1) ^{could be} interpreted by postu- lating that ( ^{sin 2 0 cos 2 y} )/ S2 ^{is at its} largest ^near

the clearing ^curve (see Luckhurst et al. [15]) ^{and that}

e and -’ are not the same. It is also conceivable, however, that (ZIS2), ^{and hence} (AIIII), ^is perturbed

close to the clearing ^curve by local field corrections [2].

Finally, Horn’s fitted surfaces for ne(T, p) ^and no(T, p)

may be slightly ^{distorted in this} region.

Horn and Faber [2] ^have reported ^that, along ^the clearing ^{curve for 5 CB,} S2, ^{decreases on} compres- sion, being ^about 15 % ^{smaller at 150 °C than at}

35 °C. The present ^work evidently confirms that result. If Sherrell and Crellin’s estimated value for

S2/AX(’) ^{in 5 CB is correct} [8] ^then (¿/S2) ^{is about} 15 % less than the value used by ^{Horn and Faber,}

i.e. 0.625 rather than 0.72. In that case (AIIIS2) ^is

about 4.6 G, ^as stated in table II.

5.5 6 CB, ^{7 CB AND} 8 CB. - Our results for these

materials are shown in figure 7, ^{where All is} plotted

against pressure for a number of temperatures. ^The

lowest point ^{on each} isothermal represents ^a reading

Fig. ^7.

^The line width AH plotted against pressure tor (a) ⁶ CB, (b) ^{7 CB and} (c) ⁸ CB, ^{at different} temperatures. The lowest point

each isothermal represents ^the reading ^taken

^the clearing ^curve.

The

in figure (c) represent ^the S-N transition in 8 CB.

taken on the critical curve, i.e. (Al/),. ^The readings

were not extended upwards ^{as far as the} melting

curve for fear that crystallization might damage ^the

rf coil, but the nematic-smectic transition is detec- table for 8 CB ; ^{it is indicated} by ^{arrows in} figure ^7.

The decrease of S2, ^on compression ^{is if} anything

more marked for 7 CB and 8 CB than for 5 CB, but no such decrease is apparent ^{in the case of 6 CB.}

6 CB also seems to be the odd one out where the

scaling ^factor (AIIIS2) ^is concerned. The estimates for this quantity ^{shown for} 6 CB. 7 CB and 8 CB in table II were obtained by extrapolating ^{the curves}

of (AIl), ⁱⁿ figure ^{7 back to} atmospheric pressure and making ^use of Sherrell and Crellin"s atmospheric

pressure values for S2, [8]. ^{Relative to one another} they ought ^{not to be in error} by ^{more than 0.1 G.}

We have no explanation ^{to offer for the} apparently

anomalous behaviour of 6 CB.

At present ^{we do not know how the} density ^varies

with _p and T for _any of the homologues ^{of 5} CB,

so we are not in a position ^{to use our data for AH}

to discuss the temperature and volume dependence

of S2 in detail. To make such a discussion easier in the future, however, ^{it seems worth} recording

that for 6 CB and 7 CB our values for AII _may be

accurately ^fitted by ^the polynomial expression

using ^the coefficients listed in table III. Here

where Te ^{is taken to} vary with _pressure along ^each

isotherm in the manner described by equation (1).

The isothermal curves drawn through ^the points ⁱⁿ figure ^{7 for 6 CB and 7 CB are based} upon equation (2)

and illustrate the _accuracy of the fit achieved. No such fit was possible ^{for 8} CB, ^even in its nematic range, because of the anomalous rise in S2 ^{and AH}

which precedes ^the nematic-smectic transition.

Table 1I1.

Coefficients ⁱⁿ equation (2).

Acknowledgments.

The authors are very grateful

to Dr. T. E. Faber for guidance ^of the work and for

all of the help ^{he has so} generously ^offered.

1172

References [1] HORN, ^R. G., ^J. Physique ³⁹ (1978) 105 ; ^J. Physique ³⁹ (1978)

167.

[2] HORN, R. G. and FABER, T. E., ^Proc. R. Soc. London 368

(1979) 199.

[3] DELOCHE, B., CABANE, ^{B. and} JEROME, D., ^Mol. Cryst. Liq.

Cryst. ¹⁵ (1971) ^197.

[4] McCOLL, ^{J. R. and} SHIH, ^C. S., Phys. ^{Rev. Lett. 29} (1972) 85.

See also : McCOLL, ^J. R., Phys. ^{Lett. 38A} (1972) ^55.

[5] GRAY, ^G. W., The molecular physics of liquid crystals, ^ed.

G. R. Luckhurst and G. W. Gray (Academic, London) 1979.

[6] McCOLL, ^J. R., ^{J. Chem.} Phys. ⁶² (1975) ^1593.

[7] SHERRELL, P. L. and CRELLIN, ^D. A., ^J. Physique Colloq.

40 (1979) ^C3-211.

[8] WALLIS, ^G. P., ^{Ph. D.} Thesis, Cambridge University (1978).

[9] SHASHIDHAR, ^{R. and} VENKATESH, G., ^J. Physique Colloq. ⁴⁰ (1979) ^C3-396.

[10] LIEBERT, ^{L. and} DANIELS, ^W. B., ^J. Physique ^{Lett. 38} (1977)

L-333.

[11] SPRATTE, ^{W. and} SCHNEIDER, ^G. M., Bezichte der Bunsen-

Gesellschaft für Physikalische ^{Chenie 80} (1976) ^886.

[12] WEBER, K. H., ^Ann. Phys. ⁷ (1959) ^1.

See also : GHOSH, K. S., Solid State Commun. 11 (1972) 1763 ; DIEHL, ^{P. and} TRACEY, A. S., Mol. Phys. ³⁰ (1975) ^1917.

[13] ROWELL, J. C., PHILLIPS, W. D., MELBY, ^{L. R.} and PANAR, M., J. Chem. Phys. ⁴³ (1965) ^3442.

[14] ^See e.g. : DELOCHE, B., CHARVOLIN, J., LIEBERT, L. and STRZE- LECKI, L., J. Physique Colloq. ³⁶ (1975) ^C1-21.

EMSLEY, J. W., LINDON, J. C. and LUCKHURST, ^G. R., ^Mol.

Phys. ³⁰ (1975) ^1913.

DELOCHE, B. and CHARVOLIN, J., ^J. Physique ³⁷ (1976) ^1497.

[15] LUCKHURST, ^G. R., ZANNONI, C., NORDIO, ^{P. L. and} SEGRE,

U., Mol. Phys. ³⁰ (1975) ^1345.