1408
AY’M d , do
Ps, pso U
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AHID cp, c y a in eq
J. Phys. Chem. 1983, 87,1406-1408
value of AYM at 25 ‘C density of the solution and of the solvent isentropic compressibility of the solution and the solvent in bar-l sound velocitv freezing point depression integral heat of dilution specific heat capacity at constant pressure and at constant volume coefficient of thermal expansion
P
36
isothermal compressibility Registry NO. C~DAO,20762-86-1;C ~ A O3, u i w - 7 ; C ~ A O ,
2605-78-9; CIODAO, 2605-79-0.
Supplementary Material Available: Full-sized photocopies of the Appendix giving all the original data are available (8 pages). Ordering information is available on any current masthead page.
Pressure-Volume-Temperature Relations and Isotropic-Nematic Phase Transitions for a 4’-n-Alkyl-4-cyanobiphenyl Homologous Series Torhlakl Shlrakawa, Takao Hayakawa, and Tanekl Tokuda Department of Chemistry, Facuity of Science, Tokyo Metropol/tan University, Setagaya-ku, Tokyo 758 Japan (Received: August 13, 1982; In Final Form: November 18, 1982)
The P-V-T relations were measured for a 4’-n-alkyl-4cyanobiphenyl homologous series near the phase-transition point from the nematic to the isotropic phase. Log-log plots of the transition temperature vs. molar volume at the transition points gave linear relations for three homologues. The slopes d In T,/d In V, are found to be -7.62, -6.10, and -5.15 for 5CB, 6CB and 7CB, respectively. The first numerals in the abbreviated codes refer to the carbon number in the alkyl chain. Agreement was not good either qualitatively or quantitatively between the observed values of d In T,/d In V, and those calculated by the extended hard-rod theory hitherto presented, which suggests that the “softness”of the intermolecular potential should be taken into account for these systems.
Introduction The molecular shape asymmetry is an important factor which determines the properties of a particular substance whether it exhibits the liquid crystalline phase or n0t.l The effect of molecular shape on the potential function has attracted considerable interest from several investigators. The theory of the liquid crystalline phase is divided into three classifications: (1)order-disorder theory, (2) hard-rod theory, (3) mean-field theory. We have previously shown2 that the experimentally observed value of -d In T,/d In V, agreed with that calculated by the Pople-Karasz t h e ~ r ywhich , ~ was extended order-disorder theory, where T,is the transition temperature and V, is the molar volume at the transition points. The PopleKarasz theory, however, is not the one which takes into account the molecular shape factor, while those theories which are based on hard-rod models account for the effect of the length and the width of molecules. The theory of fluid structure based on hard-rod models was first discussed by Onsager.* Zwanzig6 proposed a version of Onsager’s theory which enabled the estimation of the virial coefficients to a much higher order. Alben,G Kimura,’ and Savithramma and Madhusudana8 also pro(1)Gray, G. w. ’Advances in Liquid Crystals”; Brown, G. H., Ed.; Academic Press: New York, 1976;Vol. 2, p 1. (2)Shirakawa, T.; Inoue, T.; Tokuda, T. J. Phys. C k m . 1982,86,1700. (3)Pople, J. A.;Karasz, F. E. J . Phys. Chem. Solids 1961, 18, 28. (4)Onsager, L. Ann. N. Y. Acad. Sci. 1949,51,627. (5) Zwanzig, R. J. Chem. Phys. 1963,39, 1714. (6)Alben, R.Mol. Cryst. Liq. Cryst. 1971, 13, 193. (7)Kimura, H.J.Phys. SOC. Jpn. 1974,36, 1280.
posed an extension of the hard-rod-model theory. They introduced the spherocylinder system which involves attractive forces as well as repulsive ones. With the hard-rod systems, the length-to-width ratio of a molecule determines the thermodynamic properties of the liquid crystalline phase. In a previous paper,2 we have suggested that the value d In T,/d In V, is a useful measure for testing theories. The value d In T,/d In V, is one of the calculable properties in hard-rod-model theory for the nematic liquid crystalline phase. If we measure the d In T,/d In V, value for compounds varying in length-to-width ratio, then we can check the theories easily. The homologous series of 4’-n-alkylcyanobiphenyl has four nematogenics. They are 5CB, 6CB, 7CB, and 8CB. In this paper, we have measured d In TJd In V, for three homologues of 4’-n-alkylcyanobiphenyl,and we compare these values with the theoretical values and discuss the applicabilities of the theories to the present system. Experimental Section The compounds of the 4’-n-alkyl-4-cyanobiphenylhomologous series (alkyl = pentyl (5CB), hexyl (6CB), and heptyl (7CB)) were obtained from Tokyo Oka Industry, Ltd., and were used without further purification. The clear points of 5CB, 6CB, and 7CB were measured with a differential scanning calorimeter. The density of the materials was measured with a Lipkin-Devison type picnometer. (8)Savithramma, K.L.; Madhusudana, N. V. Mol. Cryst. Lzq. Cryst. 1980,62,63.
0022-3654/83/2087-1406$01.50/0 63 1983 American Chemical Society
P - V-T Relations and Isotropic-Nematic Phase Transitions
The Journal of Physical Chemistry, Vol. 87, No. 8, 7983 1407
1 .01
20
D
E
. m a
rn L
1.00
E \
a,
10 13.99
295
305
300
31 0
31 5
245
243
247
TI K
F w e 1. Densky as a function of temperature for SCB, 6CB, and 7CB.
P-V-T relationships were measured with a piston-cylinder apparatus. A differential transformer attached to one end of the piston detects the degree of compression of the fluid, which is indicated on a digital voltmeter. The volume of the cylinder was about 14 cm3. The pressure was measured with a Manganin pressure gauge. The pressure measured was corrected by using the melting points of benzene at high pressure and the compression measured was corrected by using ethylene glycol. The precision of the pressure measurements was better than f0.15 MPa and that of compression measurements was better than f0.1%. The temperature could be read with a precision of 0.02 K and the stability of the temperature controller was better than fO.O1 K in the range from 290 to 340 K.
Results and Discussion Figure 1 shows density vs. temperature curves for 5CB, 6CB, and 7CB at atmospheric pressure. The clear points were found to be 308.53, 302.77, and 315.61 K for 5CB, 6CB, and 7CB, respectively. The volume changes which accompanied the phase transitions were found to be 0.2090, 0.19%,and 0.22% for 5CB, 6CB, and 7CB, respectively. The clear points measured by differential scanning calorimeter were found to be 308.8,302.8,and 315.7 K for 5CB, 6CB, and 7CB, respectively. These values were slightly higher than the clear points by density measurement. For this reason, density measurement is a more stationary measurement than differential scanning calorimeter measurement for clear points. Near the nematic-isotropic transition temperature, the density curves were concave, suggesting the influence of the changing of order. Figure 2 shows typical P-V isotherms for 5CB, 6CB, and 7CB near the phase-transition points from isotropic to nematic. When we increased the pressure of the isotropic phase, the molar volume decreased continuously up to the point beyond which the volume change accompanied phase transition. The molar volume at which the phase transition occurs decreased with increasing temperature. In the previous paper: we suggested that the value -d In T,/d In V , is an excellent indicator for testing the volume-dependent part of the intermolecular potential function for nematic liquid crystals. For 8CB, we obtained -d In T,/d In V, = 4.7, which agreed with the value derived from the theory of Pople and Karasz. This relation is expected from theory and is observed for some compounds.*l' Figure 3 shows log-log plots of the transition (9) McColl, J. R.; Shih, C.
S.Phys.Rev. Lett. 1972,29,85.
(10)Keyes, P. H.; Daniels, W .b. J. Phys.(Orsay, Fr.) 1979,40,C3-
380. (11)Hanawa, C.;Shirakawa, T.; Tokuda, T. Chem. Lett. 1977,1223.
20
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256
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.
.
.
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.
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258
20 m
v/cm 3 mol - 1 Flgure 2. Typical pressure-volume isotherms for 5CB (A), 6CB (E), and 7CB (C). 5CB: (a) 320.85, (b) 317.77, (c) 316.05, (d) 313.55 K. 6CB (a) 313.45, (b) 311.62, (c) 309.70, (d) 307.14, (e) 303.75 K. 7CB: (a) 324.12, (b) 321.99, (c) 319.91, (d) 318.02, (e) 315.89 K.
temperature and the molar volume at transition points for 5CB, 6CB, and 7CB. The plot of In T, - In V, is linear for each compound. The slopes -d In T,/d In V, calculated are 7.62, 6.10, and 5.15 for 5CB, 6CB, and 7CB, respectively. These values are larger than those of some compounds in Keyes and Daniels' study.l0 However, we have also measured the value of -d In T,/d In V , for MBBA, 3.9. This value agree with Keyes and Daniels' study. For the CB series, the larger values of -d In T,/d In V, suggest that the volume-dependent part of the intermolecular potential is harder than the repulsive part of the Lennard-Jones potential but softer than the hard-rod potential. Figure 4 shows the relation between the number of carbon atoms in the alkyl group and -d In T,/d In V ,
1400
The Journal of Physical Chemistty, Vol. 87, No. 8, 1983
5 . 78
Y
-
5.76
b-
c
5.74
5.72
mol-')
I"(V'/"
Figure 3. Log-log plots of the molar volume at the transition points and transition temperature for 5CB, 6CB, and 7CB.
5
6
7
8
9
Number o f carbons i n alkyl group
Figure 4. 4 In T,/d In V , plotted against the number of carbon atoms in alkyl chains for 4'-n -alkylcyanobiphenyl homologues.
values for four homologues of cyanobiphenyl. The -d In T,/d In V, value decreased with increasing chain length. Tranfield and Collings12 first observed -( V/ T)(dT/d V) values for alkoxyazoxybenzene. They observed also that -( V/T)(dT/dV) decreased with increasing alkoxyl chain length. No odd-even effect was observed for -d In TJd In V, for RCB while the odd-even effect is generally known for various thermodynamic properties such as dPldT, volume discontinuity at transition, etc. This means that (12) Tranfield, R. V.; Collings, P. J. Phys. Reu. A 1982, 25, 2744.
Shirakawa et ai.
the variation of -d In T,/d In V, for alkyl chains is not due to alkyl chain conformation. Onsager first proposed the hard-rod-model theory for the anisotropic phase. Theories which extend Onsager's treatment have been presented by many In these theories, the thermotropic properties of the liquid crystals were expressed as a function of the length ( L )to width ( D ) ratio (LID)of molecules. In an extension of the hard-rod-model theory, the -d In T,/d In V, value was calculated by Alben, Andrew, Kimura, Savithramma, and Madusudana as a function of the LID ratio. A common feature of these theories is that the value of -d In T,/d In V, decreases as LID decreases. Our experimental value of -d In T,/d In V,, on the contrary, decreases with increasing molecular length. These results imply that the variation of -d In T,/d In V, with the carbon number of the alkyl chain for CB's is not due to the length-to-width ratio. Since -d In T,/d In V, did not show the so-called odd-even effect, it is almost certain that the variation of -d In T,/d In V, with the number of carbon atoms does not originate with only variation in the alkyl chain length. A nematogenic molecule has a hard-rod part such as a biphenyl ring and a flexible chain such as an alkyl chain or an alkoxyl chain. Cutler, McMickle, Webb, and Schie~sler'~ measured the compressibiltiy of 13 hydrocarbons and observed that the compressibilities of liquid hydrocarbons were strongly dependent on molecular structure. The order of compressibility was as follows: benzene ring < cyclohexyl ring < short alkyl chain < long alkyl chain. In our results for the CB series, -d In T,/d In V, decreased with alkyl chain carbon atoms. This means that the long alkyl chain of CB is softer than the short alkyl chain. Tranfield et a1.12observed that the value of -( V/ T)(dT/dV) for alkoxyazoxybenzene is smaller than our observed value of -d In T,/d In V, for the RCB series. These results are also explained by the softness of the molecular structure. There is a ON=N bond in the hard-rod part of alkoxyazoxybenzene while RCB has no bonds other than C-C bonds. Since the ON=N bond is more flexible than the biphenyl C-C bond, alkoxyazoxybenzene is softer than RCB molecules. We may conclude from the present studies that the theory of nematics should involve the concept of softness. Registry No. 4'-Pentyl-4-cyanobiphenyl, 40817-08-1;4'4'-heptyl-4-cyanobiphenyl, hexyl-4-cyanobiphenyl, 41122-70-7; 41122-71-8. (13) Cutler, W. G.; McMickle, R. H.; Webb, W.; Schiessler, R. W. J. Chem. Phys. 1958,29, 727.
