The nematic-isotropic transition at high pressures II : turbidity measurements

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The nematic-isotropic transition at high pressures II : turbidity measurements

W.J. Lin, P.H. Keyes, W.B. Daniels

To cite this version:

W.J. Lin, P.H. Keyes, W.B. Daniels. The nematic-isotropic transition at high pressures II : turbidity measurements. Journal de Physique, 1980, 41 (7), pp.633-638. �10.1051/jphys:01980004107063300�.

�jpa-00209289�

The nematic-isotropic transition at high pressures II :

turbidity measurements

W. J. Lin (*)

Physics Department, University of Delaware, ^{Newark DE} 19711, ^U.S.A.

P. H. Keyes

Bartol Research Foundation of The Franklin Institute, University of Delaware, Newark, ^DE 19711, ^U.S.A.

and W. B. Daniels

Physics Department, University of Delaware, Newark, ^DE 19711, ^U.S.A.

(Reçu ^{le 28 novembre} 1979, accepté ^{le 13 mars} 1980)

Résumé.

Des mesures de turbidité sous haute pression ^ont été effectuées dans des phases isotropiques ^de MBBA, EBBA ^et CBNA. Dans tous les cas, ^on observe une augmentation de la valeur de Tc 2014 ^{T* avec} la pres- sion. Cependant, ^un comportement anormal de l’amplitude de la turbidité à la transition isotrope-nématique

a été mis en évidence : cette amplitude ^diminue lorsque ^la pression augmente pour le MBBA tandis qu’avec ^son homologue ^le plus proche, EBBA, elle croît et, ^avec le CBNA elle croît d’abord pour diminuer ensuite.

Les valeurs de la turbidité utilisées pour calculer les grandeurs ^des paramètres ^{à la} transition, ^notamment le para- mètre d’ordre Qc, ^ont été déterminées à partir de l’estimation de la discontinuité de volume calculée d’après ^nos

résultats publiés antérieurement et concernant l’équation d’état PVT. La comparaison ^{entre ces résultats et les}

valeurs expérimentales antérieures montre que la validité de la théorie du champ moyen, que ^{nous avons} utilisée pour calculer ^ces paramètres, doit être sérieusement remise en question.

Finalement, les valeurs montrent que Tc 2014 ^{T* est} sensiblement plus élevée suivant l’isochore que selon l’iso- bare, plus classique.

Abstract.

Turbidity measurements at high pressures have been performed ^{in the} isotropic phases ^of MBBA, EBBA, and CBNA. In all cases an increase of the value of Tc 2014 T* with pressure is observed. However, ^rather

unusual behavior is found for the magnitude ^{of the} turbidity ^{at the} isotropic-nematic transition : in MBBA this

magnitude decreases with increasing pressure, in the homologous neighbor ^{EBBA it} increases, and in CBNA it increases and then decreases.

In conjunction with estimates of the volume discontinuity obtained from our previously reported ^PVT data, these turbidity ^{data are used to} calculate the values of the transition parameters, including ⁱⁿ particular ^{the order} parameter Qc. Comparison of these results with previous experimental ^data indicates that the validity ^{of the mean}

field theory, ^{which we have used to} calculate these parameters, ^{must be} seriously questioned.

Finally, the data show that the value of Tc 2014 T* is somewhat larger along ^{an isochoric trace than} along ^{the more}

conventional isobaric trace.

Classification

Physics ^Abstracts

71.30

In a previous paper [1] hereafter, ^{referred to as} I,

we reported ^on the P-V-T equation ^{of state in the} vicinity ^{of the} isotropic-nematic transition. It is well known that this transition displays characteristics of both first and second-order phase changes. ^{In I we}

were chiefly concerned with the first-order character

of the isotropic-nematic transition. In this _paper we

shall present measurements of one of the second- order aspects ^{of this} transition, namely ^{the anomalous} pretransitional increase of the turbidity ^{above the} clearing temperature Tc. ^{These data} yield ^{the effective}

second-order transition temperature ^or spinodal ^tem- perature T*. The difference Tc - ^{T *} provides ^a

measure of the first-order component of the transi- tion.

It is of special ^{interest to examine how the difference}

(*) Present address : Xerox Corporation, ^{Webster, NY 14586,}

U.S.A.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01980004107063300

634

Tc - ^{T * and the} amplitude ^{of the} turbidity ^{and its}

derivative _vary along ^the pressure-temperature phase boundary. ^Each theory ^{for the} nematic-isotropic

transition imposes certain constraints on these varia- tions ; ⁱⁿ some cases a specific functional form is

given ^{for the} temperature dependence. ^{We shall}

examine and test these theoretical predictions ⁱⁿ

detail. We shall also discuss the result of measuring

the pretransitional anomalies under conditions of constant density.

The materials used in this study ^{were :}

N-(p-methoxybenzylidene)-p-butylaniline (MBBA), N-(p-ethoxybenzylidene)-p-butylaniline (EBBA),

and

N-(p-cyanobenzylidene)-p-nonylaniline (CBNA).

MBBA and EBBA were purchased ^{from Eastman} Organics. ^{CBNA was} synthesized following ^a proce- dure similar to that employed by Taylor ^{and Kahn} [2]

and was subsequently recrystallized ^{twice from a}

24 : 1 hexane-benzene solution.

A turbidity measurement is especially ^{well suited}

for a high pressure experiment ^since only ^two optical ports ^are required. Figure ^{1 shows the} high pressure cell body ^{and contents. The cell was} machined from Viscount 44 steel pre-heat ^{treated to a Rockwell}

hardness of 42. Not shown in the figure ^{are the two}

end plug pieces ^{and a} steel annulus which slips ^over

the oil inlet and accomodates the high pressure

tubing ^and fitting.

Fig. ^1.

^The high pressure cell body ^{and contents} for encapsu-

lating liquid crystal samples.

The sample ^was encapsulated in the device shown at the bottom of the figure ^to separate it from the pressure fluid. The stainless steel piece ^{fixes and}

maintains the optical path length. For MBBA and EBBA the path length ^{was 8.7} cm, this rather long

distance being required ^{in order to obtain} easily

measurable attenuations of the light ^{beam near the} phase transition. At about 10 OC above the transition, however, ^the turbidity ^{was found to} have reached its

background ^or non-anomalous value. For CBNA, which has a larger ^intrinsic turbidity, ^similar experi-

mental conditions were achieved by employing ^a path length ^of only ^{1 cm, the excess} length being

taken _up by glass windows. All samples ^{were filtered} through 0.2 u Millipore filters in order to remove

residual dust particles ^which might contribute to the

scattering process.

Figure ² shows the experimental layout. ^The temperature of the cell was measured to a precision

of 0.01 °C by ^{means of a} platinum resistor and Mueller

bridge. ^{A two} stage thermostated oven maintained the constancy ^{of the} temperature ^to within these limits of measurement. The _pressure was measured to a precision ^{of 10 bars} by ^{use of a} Heise bourdon gauge. Octoil S was used as the _pressure transmitting

fluid. The reservoir served as ballast to allow the pressure ^to be adjusted slowly.

Fig. ^2.

Schematic of the experimental setup.

A split portion of the laser beam was monitored

by ^a photocell ^so that corrections could be made for variations in the output power. A neutral density

filter was used to place ^the intensity of the transmitted beam within the linear response range of the photo- multiplier. ^Lenses, pinholes, ^{and an} interference filter collimated the beam and reduced the contri- butions from stray light.

It is well known that the inverse of the scattered

intensity, and hence the inverse of the turbidity,

varies like T - T * as the nematic phase ^is approached

from the isotropic phase ^{at constant pressure} [3].

One can easily imagine approaching ^the isotropic-

nematic phase boundary by increasing pressure while

keeping temperature ^{constant. In this case one should} find -r-1 oc p* - P, or, ^{as one} would _say in the

language of Griffiths and Wheeler [4], ^{the critical}

exponent for the pressure ^scan should be the same as for the temperature ^scan since neither path ^is

tangent ^{to the} phase boundary. Experimentally ^we

find this to be the case, and we can, therefore, ^deter- mine the spinodal ^{line by} finding ^{T* as a function}

of P or by finding ^{P* as a} function of T; ^{the data} obtained from temperature ^{scans are} entirely ^consis-

tent with those from pressure ^scans. As a practical

matter it is usually ^{easier to fix} temperature ^and vary pressure, and ^we have, therefore, ^{used this} approach

in the majority ^{of our runs. For} consistency ⁱⁿ pre-

sentation, however, ^we will exhibit our results as if

we had found T* as a function of P in all cases.

Figure ^{3 shows} the transmitted intensity h ^for

three different pressure ^scans in the isotropic phase

of MBBA. Far from the transition the intensity

assumes a nearly ^{constant value} Io. ^{Closer in to the}

transition the intensity drops abruptly according ^to

the formula It ⁼ Io e-1:L, ^{where L is the} length ^of

the sample ^{and z} is the anomalous portion of ^the turbidity. From these data the inverse turbidity ^i-1

is extracted and is plotted ⁱⁿ figure ^4. A linear fit to the data gives ^{P*. The} pressure for which the sample

became _opaque is taken to be the transition pres-

sure Pc’ ^{When a wider} range of temperatures ^is examined, changes ^{in the} slope ^{of ’t-l v·s. P and in}

the value of P* - Po ^become quite apparent ^as may be seen from figure ^{5 in which some of our EBBA}

data are plotted.

Fig. ^3.

^The transmitted intensity I, ^{ns. P} for three isotherms in MBBA.

Fig. ^4.

The inverse of the turbidity ^1’S. pressure for three iso- therms in MBBA.

Fig. ^5.

The inverse of the turbidity ^ns. pressure for six isotherms in EBBA.

In the de Gennes theory [5] for this transition the free _energy is given by

where Go ^{is the} background ^free energy and

Normally Go, Ao, B ^{and C are} regarded ^as constants, but in our case they, ^{as well as} T*, ^must be considered to be functions of pressure. Or, from the alternate

point ^{of view, we can take A =} a(T) (P* - P) ^and regard Go, ^{B, C and P* as} functions of temperature.

Fluctuations in the order parameter ^{are the source} of the large increase in the light scattering ^{near the}

transition. Formulas for the intensity of the scattered

light ^have already been worked out [5, 6]. ^{The tur-} bidity, being ^{the total cross section, can} be calculated from these formulas by integrating ^{over all} scattering angles with result :

Here ko is the wavenumber of the incident light ^and A8max is the dielectric anisotropy which would result under conditions of complete orientational ordering,

as one has to a good approximation ^{in the} crystalline

state. In deriving eq. (2) ^{we have} neglected ^terms involving ^the gradients of the order parameter. ^This approximation is reasonable since the correlation

length ^is very much smaller than the wavelength ^of

the light [7, 8].

It will _prove to be convenient to re-express ^our inverse turbidity ^{data in terms} of the coefficient A

using eq. (2). ^At any given temperature ^the -r-l data

can be parameterized by ^the slope ^{of -r vs. P and}

by the transition value rc -1. ^{In terms of A this} para-

meterization is equivalent ^to specifying Ac ^and a(T).

636

Table I.

Isotropic-nematic transition parameters for ^MBBA.

Table II.

Isotropic-nematic transition parameters for ^EBBA.

Table III.

Isotropic-nematic transition parameters for ^CBNA.

Values for these parameters, ^{and for} Tc - ^{T * as} well, ^are given in the left-hand columns of tables 1-111.

For all three materials the value of Tc - ^T*

increases with _pressure. Thus it _appears that the transition becomes increasingly first-order at high

pressures. This trend is in qualitative accord with the intuitive feeling ^{that at} higher ^{densities the mole-}

cules should behave more like hard rod systems which have large ^order parameter discontinuities at the transition. All three materials show a decreasing

value for the parameter a(7J with pressure. Such ^a

trend could have been anticipated, ^{as we shall see}

shortly, in view of the fact established in 1 that the

volume discontinuity decreases with _pressure. The

variation of the parameter Ac ^{however could not have}

been predicted in advance. It is difficult to imagine

how the slight difference in molecular structures between MBBA and EBBA could lead to a substantial increase in Ac ^with pressure in one case and an equally

substantial decrease in the other. As if to confirm the fact that the behavior of Ac is extremely ^sensitive

to such subtleties, ^{we find in CBNA a} decreasing

trend followed by ^an increasing ^{one at} higher pres-

sures.

In the right-hand columns of the tables we show other transition parameters ^{which are} derived from the experimental data under the assumption ^{that a}

Landau-de Gennes free _energy expansion ^{is valid.}

Since the nematic is an uniaxial phase [3], ^{the tensor}

order parameter ^involves only ^a single ^order para-

meter Q ^and eq. (1) ^{can be} specialized ^{to :}

(The role of biaxial order parameter fluctuations is

undoubtedly important ^{to a} proper understanding ^of

the isotropic-nematic transition [9, 10]. ^{However, in}

the discussion which follows we are concerned only

with the equilibrium values of the order parameters and hence only the uniaxial parameter ^{need be}

considered.)

As is well known [5], minimization of the free energy of _eq. (3) ^{leads to} the conclusion that ^{a tran-} sition from an isotropic liquid ^{to a} nematic with order parameter

takes place ^{at a} temperature ^{such that}

Furthermore, ^{the free} energy barrier h between the two phases ^{at the} transition [11] ^is given by

And the volume discontinuity, obtained from the

thermodynamic relation V ⁼ (ôG/ôP)T, ^is given by

In deriving eq. (7) ^the pressure variations of B and ^C

are assumed to be negligible compared ^{to that of A.}

The volume discontinuities for MBBA have already

been reported ^{in I.} We have normalized these values

so that 6c calculated from _eq. (7) will be dimension- less and equal ^at atmospheric ^{pressure to the} reported

value [12] of 0.35. With Qc in ^{hand the values} of Bc, Cc, ^{and h can} also be calculated from _eqs. (4), (5),

and (6). The results of these calculations are given

on the right-hand-side of table 1.

Unfortunately ^{we have not} measured the volume discontinuities for EBBA and CBNA, ^{but these two} compounds are, respectively, structurally quite ^simi-

lar to MBBA and CBOOA, ^{which we} have studied.

One of the major conclusions of 1 is that the tempe-

rature variation of 4 V is primarily ^a function of the

degree ^to which end chain flexibility ^is present ⁱⁿ each molecule. Therefore, ^{we make the not unreaso-} nable assumption, ^at least for the purpose of esti-

mating the trends of the transition parameters, ^that the temperature dependence ^{of AV can be taken to}

be the same as that of the structurally similar mole- cule. We have also somewhat arbitrarily ^{set the} atmospheric pressure value of Qc at ^{0.35 as we did}

for MBBA. The resulting values for Qc, Bc, Cc, ^and

h are given in tables II and III.

The phenomenological theory of de Gennes does not make specific predictions ^{for the} temperature variation of these phase transition parameters. ^Mole- cular field theories do make such specific predic- tions, however, and since each theory ^{can in} principle

be cast into the form of ^a Landau free energy expan- sion near the transition, ^{the content of our tables}

can be cômpared ^to these theories. For example, ^the Maier-Saupe theory [13] ^{can be} represented ^{in the}

form of _eq. (3) ^{if we make the} identifications [14] :

Substituting ^into eqs. (4) ^and (5) ^we conclude that :

Therefore, ^{from the} Maier-Saupe theory ^{we would} expect that all three coefficients Ac, Bc, Cc ^{and the}

difference Tc - T * should increase in direct _pro-

portion ^to the absolute temperature of the transition and that the order parameter should be constant.

None of these predictions ^are substantiated by ^the

values in the tables. The failure of the theory ^{to even} qualitatively ^{describe the variation} of Ac ^and Tc - T* ,

which are computed directly from the data without further assumptions, ^is especially damaging. ^{It should}

also be noted that using ^{a volume} dependence ^for A o

other than the V-2 behavior assumed by ^{Maier and}

Saupe ^{will not} remedy ^this deficiency.

638

There are numerous variants of the Maier-Saupe theory, ^{but we will not} discuss their specifics ^because

it _appears that it is not the details of these theories which are in error but the assumption ^{of the} validity

of the mean field or molecular field approximation

- itself. The mean field theory ^has recently been called into question ^{on other} grounds [9], and it has been demonstrated that it gives ^the wrong ^set of critical exponents [15]. ^{Here it will} be shown that mean

field theory ^is apparently incapable ^of parameterizing

and correlating ^the high pressure measurements of

light scattering, ^volume discontinuity, ^{and order} parameter.

Our argument ^centers around the values of Qc in

tables I-III calculated using ^{mean field} theory. ^The

case of EBBA is particularly interesting : ^{at the} highest pressure studied Qc ^has already reached the

degree ^{of order} expected ^{for a hard rod} system ^and is still increasing. ^Such behavior is of ^course unlikely.

Even the trend of increasing ^{order is at variance}

with the direct measurements which have been made of nematic order parameters ^under pressure [16-19].

These experiments ^{show that} Q,, is ^{either constant or}

a slightly decreasing function of _pressure. In order for the EBBA order parameter ^{to even} be constant, it would be _necessary for the volume discontinuity

which enters eq. (7) ^to decrease with _pressure over

the entire _range by about six times more than we

have assumed. Such a volume decrease would be much larger ^{than we} have measured for _any of the

liquid crystals in paper I, including ^{some which we} expect ^{to have} larger pressure variations than should be found for EBBA.

In the case of MBBA the order parameter ^under pressure has been measured [19] up ^{to a} transition temperature ^{of 347 K} (corresponding ^{to a} pressure of 0.90 kbar). ^{Over this} range 6c ^{shows a 7} % ^decrease.

By ^{contrast our mean} field calculated values show an

18 % ^{increase over this same} range. Since the volume

discontinuity ^enters the calculation of 6c ^{as a} square root, it would be necessary for agreement ^{that our} à V’s reported ^{in I be in error} by ^about 50 % ^over

this limited _range and, just ^to keep Qc ^constant, by

about more than a factor of two over our entire

reported range. Such errors are quite inconsistent with _any reasonable estimate of the experimental precision.

The order parameter ^{in CBNA} has been measured under pressure up ^{to a} transition temperature ^of 413 K [18]. Here, ^{for a} change, ^{there is} good agreement between our calculations and the directly ^measured

values. For both sets of values the order parameter

at the transition decreases by ^{about 17} %. ^{In view of}

the large discrepancies for the other two materials,

the agreement for CBNA is probably fortuitous.

Much attention has been drawn to the fact that the value of Tc - ^{T* is so} small. This observation now

loses some of its impact ^since, according ^{to our}

measurements, ^it appears that Tc - ^{T* can be made}

as large ^{as one} pleases by increasing ^the density.

Also, it is true that the value is small only by compa- rison with mean field calculations, ^{such as that of}

Maier and Saupe ^{which seem to have} only ^limited quantitative validity. Nevertheless, in fairness to these theories it must be remarked that the calcula- tions are normally ^{made for a constant volume} system, ^whereas experiments ^have been done at constant pressure. Although ^{we have not} actually performed ^a turbidity measurement at constant

density, ^{we can} compute what the results of such an

experiment would be for MBBA since we have the

complete ^PVT equation ^{of state as} reported ^{in I.}

To permit ^{such a} comparison ^we have calculated the inverse turbidity for nine different isochores spanning

the full _range of densities represented ^{in our} experi-

ments. The results _appear precisely like those in

figure 4, except that the value of T,, - ^{T * is} greater than for an isobaric measurement having ^{the same} Tc by ^{a factor of 1.7} ± 0.2 in all nine ^cases.

Acknowledgments.

^The professional assistance of Dr. Y. T. Lin and Professor H. Kwart in the synthesis

of CBNA is _very much appreciated. ^{This work was} supported ⁱⁿ part by the National Science Founda- tion under grants DMR-7801307 and DMR-7907361 and by the Unidel Foundation.

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