Nematic-isotropic entropy transition

Thus on varying the length and parity of the flexible spacer in dimers the nematic-isotropic transition temperature exhibits a dramatic odd-even effect which attenuates as the length of the spacer is increased while the nematic-isotropic entropy also exhibits the same pronounced alternation but which appears not to attenuate as the spacer length is increased. Such behaviour is also observed for semi-flexible main chain liquid crystal polymers for example, Figs. 5 and 6 show the dependence of and ASni/R, respectively, on the length of the flexible spacer for the poly a,co-[4,4 -(2,2 -dimethylazoxy-phenyl)]alkandioates [9],... 

Quite different behaviour is observed if we now compare the ether and carbonate linked series. The nematic-isotropic transition temperatures for the carbonates decrease essentially without alternation as the spacer length is increased while the entropies show a much reduced odd-even effect when compared to the ether linked series [16, 53]. It should be noted, however, that the nematic-isotropic entropies for the carbonate series are still several times larger than those typically observed for conventional low molar mass mesogens. Similar weak odd-even effects in the transitional properties on varying the length of the spacer have also been reported for other dimer series... 

Figure 11 shows the dependence of the transition temperatures on the number of methylene units in the spacer, n, for the CBOnO.lO series [69]. Immediately apparent is that the clearing temperatures show a dramatic alternation which attenuates quite rapidly on increasing n. A dramatic alternation is also exhibited by the nematic-isotropic entropies but which is not attenuated on increasing n (see Fig. 12). As we noted earlier this dependence of the nematic-isotropic transition temperatures and associated entropy changes on varying the length and parity of the flexible spacer is...

Figure 5.18 Illustrating odd-even effects for liquid crystals. Data for the a, o)-bis-(4-cyanobiphenyl-4-yloxy)alkane (BCBOw) series of nematogens, plotted as a function of the number of methylene groups in the flexible spacer, n. (o) Variation of the nematic-isotropic transition temperature ( ) variation of the nematic-isotropic phase transition entropy. [Data from J. W. Emsley et aL, Molec. Cryst. Liq. Cryst. Lett., 102, 223 (1984)]...

Figure 3. Dependence of the entropy change associated with the nematic-isotropic transition (o) on the number of methylene groups in the flexible spacer, n, for the BCBOn series [19]. Also shown are entropy changes associated with the nematic-isotropic ( ) and smectic A-isotropic transition ( ) for the nOCB series for which n now indicates the number of carbon atoms in the terminal alkyl chain, and the nematic-isotropic entropies ( ) for the TCBOn series.

It is natural to ask what effect, if any, the steric interaction might have on the nematic-isotropic phase transition. Onsager recognized that a system of hard rods, without any attractive interaction, can have a first-order transition from the isotropic phase to the anisotropic phase as tbe density is increased. To see how this can come about, we note that in a gas of hard rods there are two kinds of entropy. One is the entropy due to the translational degrees of freedom, and the other is the orientational entropy. In addition, there is a coupling... 

Fig. 2. The dependence of the nematic-isotropic entropy of transition. SjR on the number of methylene groups in the flexible spacer for the poly a,co-[4,4 -(2,2 -dimethy lazoxyphenyl) Jalkandioates.

Fig. 4. The nematic-isotropic entropy of transition for the a,ct)-bis(4,4 -cyano-biphenyloxy)alkanes as a function of the number of methylene groups in the flexible spacer. The theoretical predictions of S/R are joined by the dashed lines.

Fig. 9. The dependence of the entropy change associated with the nematic-isotropic transition on the total number of atoms, n, in the spacer for the cyanobiphenyl dimers linked via ether (O) [18], alkyl ( ) [16] and carbonate groups ( ) [16, 53]...

Figs. 2.1.5-2.1.7 give the reduced temperatures of transition and the corresponding entropy and volume changes as functions of v. For a certain range of v, S/R and AF/F for the nematic-isotropic transition are only very small fractions of the values for the solid-nematic transition. This is indeed a distinctive feature of such transitions in general (table 2.1.2). 

Fig. 5.2.2. Order parameters s and

Curves of the order parameters, entropy and specific heat for three representative values of a are presented in figs. 5.2.1, 5.2.2 and 5.2.3. For a > 0.98, the smectic A transforms directly into the isotropic phase, while for a < 0.98 there is a smectic A-nematic (A-N) transition followed by a nematic-isotropic transition at higher temperature. For a < 0.70 and n/ i < the model predicts a second order A-N transition. Hence... 

Figure 16. Dependence of the nematic isotropic transition entropy ASj on the flexible spacer length m n = 2 O, n = 3 A, A n=4.

A similar analysis can be made for the Landau free energy of a weakly first-order phase transition, for example the nematic-isotropic transition exhibited by some liquid crystals (Section 5.7.1). The free energy (Eq. 1.13), is supplemented by an additional cubic term C T)xlr if the transition is first order. The first-order nature of the transition can be confirmed by calculating the entropy density change at the transition, which turns out to be... 

Figure 17. The dependence of the entropy change, AS/R, at the nematic-isotropic transition on the mole fraction, arf, of the linear conformer in the isotropic phase. The conformational contribution to AS/R is shown as the dashed line.

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