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Submitted on 1 Jan 1975
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THERMAL EXPANSION AND SPECIFIC HEAT OF A NEMATIC LIQUID CRYSTAL
H. Gruler, F. Jones
To cite this version:
H. Gruler, F. Jones. THERMAL EXPANSION AND SPECIFIC HEAT OF A NE- MATIC LIQUID CRYSTAL. Journal de Physique Colloques, 1975, 36 (C1), pp.C1-53-C1-54.
�10.1051/jphyscol:1975108�. �jpa-00215885�
JOURNAL DE PHYSIQUE Colloque Cl, suppliment au no 3, Tome 36, Mars 1975, page C1-53
Classification Physics Abstracts 7.130 - 7.500 - 7.520
THERMAL EXPANSION AND SPECIFIC HEAT OF A NEMATIC LIQUID CRYSTAL
H. GRULER (*) and F. JONES
Gordon McKay Laboratory, Harvard University, Cambridge, Mass 02138, U. S. A.
RBsumB.
-On donne l'expression de I'energie libre de Gibbs en fonction d'une temperature rkduite. Les coefficients d'expansion thermique a et les chaleurs sptcifiques C devraient &re iden- tiques pour tous les nkmatiques. La loi de Griineisen (invariance du rapport a/C en fonction de la tempkrature) est vkrifiee pour le PAA.
Abstract. - The Gibbs free energy of a nematic liquid crystal is expressed in a reduced tempera- ture scale. Therefore the derived thermal expansion coefficient a and specific heat C should be similar for all nematics. Furthermore the ratio of a / C should be temperature independent. This Griineisen law holds at least for PAA where a complete set of data is available.
The Gibbs free energy of a nematic liquid crystal can be expressed with the mean field approximation of Maier and Saupe [I]. Here we use another way of describing the nematic phase by making the good approximation that the degree of order versus reduced temperature is an universal curve. Actually this univer- sal curve was first calculated by Saupe [2] and in a more generalized form by Humpheries et al. [3]. For such corresponding states the Gibbs free energy can be expressed (as in solids [4]) as :
GN = GI + Bf(7) (1) where z = T/O.
Such a form of the Gibbs free energy does not allow us to calculate the degree of order of the nematic phase.
The characteristic temperature 19 is a temperature where the degree of order would be zero. This temperature can be calculated by the Maier-Saupe theory.
The free energy given by eq. (1) gives very accurate results in calculating the thermal expansion coefficient a and the specific heat C,. For the thermal expansion we find that
a = - (ve2)-I ~ ( a e / a ~ ) f ' ~ . (2)
Similarly we get an expression for the specific heat : Cp = - T8-l f " . (3) Comparing eq. (2) and (3) we obtain the following relation :
./cP = (ve)- ( a e l a ~ ) . (4) Thus within the limits of applicability of the law of corresponding states, the ratio of the coefficients of thermal expansion and the specific heat is independent
(*) Present address : University of Ulm, Experimental Physics 111, Oberer Eselsberg, 0-7900 Ulm, West-Germany.
of the temperature. In solid state physics this effect is known as Griineisen's law [4]. We have the possibility of comparing Griineisen's law with experiment. For 4,4'-di(methoxy) azoxybenzene (PAA) we have all the data we need in order to check eq. (4). We use the specific heat from Arnold (see Fig. 1) and the thermal
-0 Y C - O - ~ - ~ + N.Q- O.CH,
-NEMATIC PHASE -
I I 9