Adiabatic calorimetry measurements in the vicinity of the nematic-smectic A-smectic C multicritical point

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Adiabatic calorimetry measurements in the vicinity of the nematic-smectic A-smectic C multicritical point

M.A. Anisimov, V.P. Voronov, A.O. Kulkov, F. Kholmurodov

To cite this version:

M.A. Anisimov, V.P. Voronov, A.O. Kulkov, F. Kholmurodov. Adiabatic calorimetry measurements

in the vicinity of the nematic-smectic A-smectic C multicritical point. Journal de Physique, 1985, 46

(12), pp.2137-2143. �10.1051/jphys:0198500460120213700�. �jpa-00210162�

Adiabatic calorimetry measurements in the vicinity

of the nematic-smectic A-smectic C multicritical point

M. A. Anisimov, ^{V. P.} Voronov, ^{A. O. Kulkov and F.} Kholmurodov (*)

Institute of Petrochemical and Gas Industry Moscow, 117917, U.S.S.R.

(Reçu ^{le 24 mai} 1985, accepté ^{le 24} juillet 1985)

Résumé.

La calorimétrie haute résolution a été utilisée pour étudier la ^nature du point multicritique ^des phases nématique-smectique A-smectique ^C (NAC) ^dans un_mélange ^de 4-n-hexyloxyphényl-4’-n-octyloxy-benzoate (608) ^{et de} 4-n-hexyloxyphényl-4’-n-décyloxybenzoate (6010). Les transitions nématique-smectique ^{C sont faible-}

ment du premier ordre, cependant l’entropie de transition disparaît ^au point NAC. La forme des anomalies des chaleurs spécifiques ^au voisinage ^du point ^{NAC est} plus compliquée ^{que celle} prédite ^{par la théorie de} champ

moyen. Ce résultat ainsi que la topologie ^du diagramme ^de phase révèlent la pertinence des fluctuations au point

NAC.

Abstract

High-resolution ^adiabatic calorimetry has been used for the study ^{of the nature of the NAC} (nematic-

smectic A-smectic C) multicritical point in the mixture ^of 4-n-hexyloxyphenyl-4’-n-octyloxybenzoate (608) ^and 4-n-hexyloxyphenyl-4’-n-decyloxybenzoate (6010). ^{The N-C} transitions are weak first order however the transition entropy disappears ^{at the NAC} point. ^The forms of the heat capacity anomalies in the vicinity of the NAC point ^are

more complicated then those predicted by ^the simple mean-field theory. This result as well as the phase diagram topology manifest the fluctuation nature of the NAC point.

Classification

Physics ^Abstracts

b1.30 - 64.70E

1. Introductioa

Since the NAC (nematic-smectic ^A-smectic C) ^multi-

critical point ^was discovered experimentally [1, 2]

significant efforts both of the theorists [3-5] ^and experimentalists [6-8] ^{were made for} understanding ^the

nature of this phenomenon. ^The description ^{of the}

NAC point ^{as a Lifshitz} point [9] implies the first order character of the N-C transition ^{as a} result of the tilt fluctuations in the nematic phase; furthermore the N-C latent heat has ^to disappear ^{at the NAC} point [3]. ^This prediction ^{has been} supported by experiment [6, 7]. ^{However there were} important disagreements

between the observed experimentally phase diagrams topologies [6-8].

In any model with the director tilt depending ^{on the}

existence of the smectic ordering [5, 9] the N-A and N-C lines are continuous at the NAC point ^while

the A-C line is coming ⁱⁿ obliquely. ^The previously

observed phase diagrams [6, 7] ^{seemed to have an} opposite behaviour : the A-C and N-C lines were

continuous, ^{while the N-A line} approached ^{the NAC} point obliquely. Therefore the simple ^mean-field

model by Benguigui [4], ^who proposed ^{the tilt to be}

an independent ^order parameter coupled ^{with the}

smectic density ^{wave, seemed to be} preferable [6, 7].

Recently Brisbin et al. [8] have studied accurately ^the phase diagrams ^{of four} liquid crystals ^{mixtures near}

NAC points and obtained a universal behaviour which is in evident contradiction with _any mean-field

theory. ^{In view of this} important result it was

interesting ^to investigate ^the vicinity ^{of a NAC} point by high-resolution ^adiabatic calorymetry (see ^also

Ref. [10]). Previously only ^{DSC and AC} calorymetric techniques ^were used in the study ^{of NAC} points [1, 6, 7].

2. Experimental procedure.

We have carried out enthalpy ^{and heat} capacity

measurements on the mixture 4-n-hexyloxyphenyl-4’- n-octyloxybenzoate (608) ^and 4-n-hexyloxyphenyl-4’-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198500460120213700

2138

n-decyloxybenzoate (6010) ( 1). ^The precise ^adiabatic technique reported ^elsewhere [11] ^{has been} improved especially ^for measurements on small samples ^of liquid crystals [12]. ^The sample (0.2 gram approximately)

was contained into a titanium alloy calorimetric cell.

The microcalorimeter was surrounded with two thermal screens. This system ^was placed ^{in a vacuum}

bulb. A thermocouple battery ^{with a} sensitivity ^of

200 gV/K ^{was used for} measuring ^the temperature difference between the cell and the internal screen.

A platinum resistor thermometer was placed ^{on the}

internal screen. Heat losses in the calorimeter did not exceed 5 x 10-’ W. Far from the phase ^transition points ^{the heat} capacity ^{of the} empty calorimetric cell

was about a half of the total heat capacity. ^{We carried}

out measurements in the puls-heat (the ^minimum step

was 0.01 °C) ^and scanning regimes. ^{The rate of} heating

could be changed ^{in the} range of 2 ^x 10-30C/h ^to

20 °C/h. ^The scanning regime ^{was used for} determining

the temperatures ^and enthalpies ^{of the} phase ^tran-

sitions.

_ _ _ _

Both the 6010 and 608 were chemically ^{stable and}

rather _pure (2). ^The two-phase region ^{for the} isotropic-

nem atic phase transitions was less than 0.06 °C. The calorimetric cell was being ^filled carefully ^{in a} dry nitrogen atmosphere. ^{In the mixtures} especially ^near

the NAC point, ^the equilibration ^{time was much} larger ^{than it was} in the pure liquid crystals. ^Therefore

after filling, ^the calorimetric cell was heated to 130 OC, shaked and left a day ^{at this} temperature.

The phase diagram ^{of the} 608-6010 mixture is shown

on figure ^{1. The NAC} point is located somewhere between 32.5 and 32.7 % ^mol. 6010. Furthermore one can note the peculiarity ^{on the} nematic-isotropic ^line

at the concentration corresponding ^{to the NAC} point.

3. Results and discussion

3.1 N-C TRANSITIONS LINE.

The N-C transitions

are first order however their latent heat is drastically decreasing upon approaching ^{the NAC} point (Figs. ²

and 3). Whereas the N-C transition entropy ^{in the} pure 608 is about 0.1 R (R ^{is a} gas constant), ^{it is only}

4 x 10-1 R in the 32.5 % 6010 mixture ! Such a

paltry latent heat becomes noticeable only ^{when the}

slowest scanning ^{rate is used} (Fig. 3b). Otherwise the transition looks as a second order ^one (Fig. 3a). ^The change of the concentration only ^{in 0.1} % ^{leads to the}

second order transition within the limits of our

(1) ^Other conventional abbreviations ^{are HOPOOB and}

HOPDOB. The structural formula for 6010 is

and for 608 is

(~) ^The liguid crystals ^{were made} and kindly given ^{to us} by

D. Demus (6010) and B. M. Bolotin (608).

- -- -

Fig. ^1.

^Phase diagram of the 608-6010 mixture.

Fig. ^2.

Temperature dependence of ^the enthalpy ^{near the}

N-C transition in the 30.6 % 6010 mixture. The rate of

scanning ^{is 1.4 x 10- 5} °C/s.

accuracy (Fig. 4). ^The extrapolation ^{with a} square ^root law of the transition entropy depression gives the

NAC point position between 32.5 and 32.6 % 6010

(Fig. 5). Of course, ^{the non obvious} assumption ^{that the} point of the latent heat disappearence ^{and the NAC} point ^are identical has to be made.

The results of the heat capacity measurements near

the N-C transitions on two samples (pure 608 and the closest to the NAC point) ^are presented ^on figure ^6.

The heat capacity ^{anomalies can be} qualitatively explained ⁱⁿ the framework of the mean-field Landau

theory [13] ^{with a} negative fourth-order term in the

Fig. ^3.

Temperature dependence ^{of the} enthalpy ^{near the}

N-C transition in the 32.5 % 6010 ^{mixture : a) the rate of}

scanning ^{is 1.4 x 10- 5} °C/s ; b) ^{2.2 x 10- 6} oC/S.

Fig. ^4. = Temperature dependence ^{of the} enthalpy ^{in the}

32.6 % 6010 mixture. The rate of scanning ^{is 1.4}

free _energy expansion :

where Fo ^{is the} background molar free _energy, TNc

is the N-C transition temperature, ^T* is the absolute

stability limit of the nematic phase, ~ is the smectic C

Fig. ^5.

^N-C transition entropy ^{and heat} capacity jumps

near the NAC point.

6.

Heat capacity near the ^N-C transition in the pure 608 (crosses) ^{and 32.5} % 6010 ^mixture (dots).

order parameter, a ^{and c are} positive constants, ^{b is a}

negative ^{one. From the} expansion (1) ^{one can obtain}

the expressions for the anormalous part of the heat

capacity ⁱⁿ the ordered phase :

2140

where

to

and for the transition entropy :

According ^{to the} prediction of the Landau theory

we approximated the results of the heat capacity

measurements in the smectic C phase with the for- mula :

and obtained for the _pure 608 a good fit in interval

t ⁼ 5 ^x 10- 2-4 ^x 10 - 5 when the value of ^{a =} 0.5

was fixed and to ^{was taken as} ajustable parameter.

Assuming a - ^{1 we} obtained reasonable estimates for the coefficients b, ^c and the shift to ^{of the} pure 608 :

b rr - 0.05, ^{c ~ 0.25} and to ~ ^{8 x 10-4. One can see}

howevt!’r from figure 6 that fluctuation corrections ^to

the heat capacity ^{in the nematic} phase ^{of the} pure 608

are noticeable. Therefore a more attentive analysis ^is probably necessary.

Close to the NAC point the transition latent heat becomes extremely ^{small. In 32.4} % 6010 it is about 10- 3 RTNC. According ^{to formulae (3) and (4) it means}

that b ~ - 5 x 10-4 and t £r 8 x ^{10-8. So one}

would think the heat capacity ^{had to manifest a tricriti-}

cal behaviour. On the contrary ^{we could not obtain a} good fit with fixed a ⁼ 0.5 anywhere ^{close to the NAC} point. ^{If one used a as an} ajustable parameter ^and

fixed to ^{= 0, an} unexpected very small value of the effective exponent ^{a was} obtained The better fit was

obtained with the help ^{of the crossover formula :}

however the ajustable ^value of to appeared ^{to be too}

large (Table I). ^{One can} notice that the good ^{fit with}

the ajustable ^{value of a £r 0.4 in the} asymptotic region

of t 10-3 is identical with that in t ⁼ 5 x 10-2- 3.6 x 10 - If t 10- 3 the term + t0)-0.5 - 1] plays the role of a background ^{which is much} larger

than the real background of the heat capacity. ^Unfor- tunately ^{we have not} yet ^{been able to} study ^{in detail}

the heat capacity behaviour in the disordered phase

near the NAC point. ^In spite of the smallness of the

anomaly ^a large scattering ^{of the date is observed there.}

Most probably ^{it is} because of the N-A transition

neighbourhood and further study is necessary.

Another peculiarity of the N-C transition near the NAC point ^{is a} non-linear concentration dependence

of the transition entropy (see Fig. 5). ^{This fact can be} explained ^{with an account} of the nonlinear shape ^of

the transition line in the vicinity of the NAC point (Fig. 7). According ^{to the Landau} theory [13] ^the

coefficient b and hence the transition entropy ^AS

are proportional ^to TNAC. ^However

- -- -

Fig. ^7.

^Phase diagram of the 608-6010 mixture near the NAC point.

Table I.

Fit with formula (6) of ^{the smectic C heat} capacity. ^{Data obtained on the 32.4} % 6010 mixture.

T Nc(x) - TNAC ^is proportional ^to (XNAC - x)", ^where

n ^most probably is between 0.5 and 0.6 [8]. ^Therefore

AS is also proportional ^to (XNAC - x)~.

3.2 A-C TRANSITIONS LINE.

The results of the heat capacity measurements near the A-C transitions

are shown on figure ^8. Only ^{two curves are} presented

as examples. Like in the case of the N-C transition we

could not obtain a good ^fit by the formula (5) ^{with the}

fixed value a ⁼ 0.5 (see ^Table II). ^{A small but} positive

effective exponent ^{a was} obtained for the 32.6 % 6010 mixture; for the 32.66 % mixture the exponent ^a is negative but also small (Table III).

One can see that the crossover approximation provides ^a good fit. The results for the 32.6 % ^mixture (A-C transition) ^are very close to those for 32.4 % (N-C transition) (see ^Table I). ^{In the} asymptotic region (t ^10- 3) ^{a fit} involving ^{a = 0.5} only, ^{cannot be}

ruled out (see ^Table III), however it involves an

anomalously large background.

The most striking ^{result of our heat} capacity ^mea-

surements is a failure of the mean-field description

at the A-C transition even for those samples ^{which are}

not close to the NAC point. ^{We could not obtain a} good

fit with the formula (5) for the A-C transitions even for 70 % 6010 mixture, ^{whereas the crossover formula} (6)

was adequate everywhere.

The Landau theory [ 13] predicts ^{for a} second order transition close to a tricritical point (the coefficient b in the expansion (1) ^is positive ^but small) ^{the same heat} capacity ^{behaviour as for a} weak first order one (see

formula (2)). ^{However the} temperature shift to ^{is four}

times less :

Indeed we could describe only ^the background part ^of the heat capacity by ^formula (2) using ^reasonable

values of a, b and ^{c. The existence} of the heat capacity sharp cusp in addition to the mean-field background

is clearly seen ^{if one compares the pure 608} (Fig. 6) ^and

the 48 % 6010 ^mixture (Fig. 8).

Fig. ^8.

^Heat capacity ^near the A-C transition in 32.6 % (dots) ^{and 48} % 6010 mixtures (crosses).

We are not able to report ^{the exact} value of the critical exponent ^{a in the immediate} vicinity ^{of the A-C}

transition. Even the mean-field value a ⁼ 0.5 is not excluded At present ^further measurements and fitting

are in _progress. Nevertheless the results presented ^here

show that the mean-field interpretation of A-C transi- tions [14,15] should be revised at least in the vicinity

of the NAC point.

3.3 N-A TRANSITIONS LINE. - In the 608-b010

mixtures as well as in the _pure 6010 the N-A transitions

are second order. Furthermore there is a drastic decrease of the heat capacity anormalies upon appro-

Table II.

Fit with formula (6) of ^{the smectic C heat} capacity. ^{Data obtained on the 32.6} % 6016 mixture.

2142

Table III.

Fit with formula (6) of ^{the smectic C heat} capacity. ^{Data obtained on the 32.66} % ^{6010 mixture.}

ching ^{the NAC} point (Fig. 9). ^Therefore it is difficult to know the exact shape of the N-A line in the imme- diate vicinity ^{of this} point. Nevertheless our results

are in qualitative agreement ^{with the} phase diagrams topology ^found by Brisbin et al. [8]. The results of the heat capacity ^data analysis ^near the N-A transition in 48 % 6010 mixture are presented ^{in table IV. For}

this mixture the value of the exponent ^{a is close to the} renormalization _group result 03B1 ~ - 0.03 for two-

component order ^parameter universality ^{class. For}

the _pure 6010 we obtained a ⁼ 0.24 ± 0.01 ⁱⁿ the interval t ⁼ 5 ^x 10- 3-2 x 10- 5. Our results can

be explained by ^{a crossover} from the critical (a ~-- 0)

to the tricritical behaviour (a ⁼ 0.5) [16-18]; ^indeed

the N-A tricritical point ^is expected if the N-A and N-I transitions are sufficiently ^{close to} each other.

However an additional effect must be taken into account if one analyses ^critical phenomena in mixtures.

It is the effect of renormalization of the critical _expo- nents if measurements are carried out at constant concentration. The heat capacity Cp at constant concentration does not diverge ^{at the N-A transition} point ^{in a} mixture and its critical exponent ^renorma- lizes from a to - a/(I - ^{a) (for a} > 0). ^The range of

the temperature ^{where a is} already renormalized Fig. ^9.

^Heat capacity ^{near the N-A} transitions.

Table IV.

Fit with formula (5) of the ^heat capacity. ^{Data obtained in the} vicinity of ^{the N-A} transition (*).

(*) 1) ^index (1) ^{marks the} parameters in the smectic A phase;

2) ^{in all runs =} 0 ;

3) ^{x = 0.48 mf.} 6010.

(t ~ to) ^can be estimated by ^formula [19] :

r (8)

t° ^N Ac x{ ¹ x) (1/T ^{c dx}

where Ac ^{is a critical} amplitude ^{of a} non-renormalized heat capacity (in ^{units of} R), T~ ^{is a critical} tempe- rature, ^x is a concentration. The slope ^{of the N-A}

line becomes large ^{near the NAC} point ^{For the 33} % 6010 6010 mixture the value mixture the value TNA ⁱ - d 2013dTNA/dx ~ 0.15. ^{TNA dx} _0.15.

If one imagines [5] that the NAC point is Gaussian for the N-A line (a ⁼ 0.5) ^{one can} obtain, assuming Ac ~ 1 [16], ^that to ^~ 10- 3 ; i.e. the renormalization must be taken into account.

Acknowledgments.

We thank E. Gorodetskii and V. Podnek for comments related to the nature of the NAC point ^{in their mo-}

del [5]. ^{One of us} (M. Anisimov) ^is greatful ^{to J. Prost}

for helpful ^and stimulating discussions at the Centre de Recherche Paul Pascal in Bordeaux.

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