Entropy nematic phase

This can be inserted in equation (02.2.3) to give tlie orientational distribution function, and tlius into equation (02.2.6) to deteniiine the orientational order parameters. These are deteniiined self-consistently by variation of tlie interaction strength iin equation (c2.2.7). As pointed out by de Gemies and Frost [20] it is possible to obtain tlie Maier-Saupe potential from a simple variational, maximum entropy metliod based on tlie lowest-order anisotropic distribution function consistent witli a nematic phase. 

The separation of Hquid crystals as the concentration of ceUulose increases above a critical value (30%) is mosdy because of the higher combinatorial entropy of mixing of the conformationaHy extended ceUulosic chains in the ordered phase. The critical concentration depends on solvent and temperature, and has been estimated from the polymer chain conformation using lattice and virial theories of nematic ordering (102—107). The side-chain substituents govern solubiHty, and if sufficiently bulky and flexible can yield a thermotropic mesophase in an accessible temperature range. AcetoxypropylceUulose [96420-45-8], prepared by acetylating HPC, was the first reported thermotropic ceUulosic (108), and numerous other heavily substituted esters and ethers of hydroxyalkyl ceUuloses also form equUibrium chiral nematic phases, even at ambient temperatures. 

It may be asserted that the fundamental reason arises from the fact that, while parallel arrangements of anisotropic objects lead to a decrease in orientational entropy, there is an increase in positional entropy. Thus, in some cases, greater positional order will be entropically favorable. This theory therefore predicts that a solution of rod-shaped objects will undergo a phase transition at sufficient concentration into a nematic phase. Recently, this theory has been used to observe the phase transition between nematic and smectic-A at very high concentration (Hanif et al.). Although this model is conceptually helpful, its mathematical formulation makes several assumptions that limit its applicability to real systems. 

This is equivalent to saying that the order formed in the nematic phase is not governed by electric dipole interactions but rather by the molecular shape and the van der Waals forces between molecules. Note that, although entropy is also related to the order of a system, the symbol S used here does not refer to entropy. 

While in p-quaterphenyl the nematic phase is only metastable, p-quinquephenyl and p-sexiphenyl, and probaHy also p-heptiphenyl, have stable nematic phases Beyond p-quinquephenyl smectic phases are expected and proven for p-sexiphenyl. The magnitudes of the transition entropies corr ond to the general observations on liquid crystals... 

As expected. Figs. 16 and 17 and Table 8 also demonstrate that the enthalpy and entropy of isotropization from the more ordered smectic mesophase is higher than those from the nematic phase. This discontinuity and/or change in the slope with a change in the type of mesophase can therefore be used as additional confirmation that a phase change has occurred with the addi-... 

The phase separation of the solution is driven by the entropy of forming a liquid-crystalline phase at a high polymer concentration. However, Maier and Saupe [30] concluded that the formation of a nematic phase arises from orientation-dependent interaction of induced dipoles. From these considerations, it appears that both entropy and enthalpy contribute to the stability of mesophases, although in a different ratio for large and small molecules. Asymmetric at-... 

Are all quantitative predictions of the thermodynamics of liquid crystals correct. If not stop here. The reason for this step is that die theory (Flory-Huggins lattice model) also predicts the occurrence of the isotropic to nematic phase transition in liquid crystals. If the theory had predicted correctly the properties of glasses but had failed for liquid crystals we would have had to abandon it, especially since in both cases the cause of the transition is ascribed to the vanishing of the configurational entropy. Alternatively the correctness of the prediction for liquid crystals argues for the correctness of the prediction for glasses. Since we have not been stopped by steps 3 and 4 we proceed to step 5. 

In this article, we first present a brief summary of the entropy of fusion of chain molecules. In the second part, conformational entropy changes associated with the melting via a nematic phase, or the crystallization via a nematic mesophase, will be reviewed. 

The values of y were similarly obtained for dimer CBA- (n = 9,10) and trimer CBA-Tn (n = 9,10). These compounds exhibit the nematic LC phase over a limited temperature range, hampering an accurate estimation of y by the extrapolation from this phase. Accordingly the y values were estimated by method 1 only from higher-temperature phases i.e., y i values are estimated from the isotropic phase, and ycN values from the nematic phase [95]. The ytr values thus derived are all accommodated in Tables 2 and 3, respectively, for the NI and CN transitions. Thermal pressure coefficients of monomer liquid crystals such as 4-cyano-4 -alkylbiphenyls ( CB) and 4-cyano-4 -alkoxybiphenyls ( OCB) are available in the article by OrwoU et al. [112]. The y values applicable to the NI transition of these compounds are cited in Table 4 for comparison. As shown in these tables, use of the volume change A Vtr at the transition (column 4) leads to the estimate of the volume-dependent entropy ASy (column 5) according to Eq. 3. 

The physical definition of the ASa term is still obscure for polymeric systems in which the external degrees of freedom are largely restricted by the chain connectivity. In general, the contribution from this source to the total entropy change is assumed to be small and is often ignored for polymeric chains [ 120]. As stated already, the nematic phase is very much liquidlike, and the component molecules still maintain their translational freedom. The contribution from the residual entropies ASa must be much smaller than those involved in the phase transition between the crystal and the isotropic melt. 

There are several related phenomena that will not be treated in this chapter. They include the well documented transformation of nematic phases into cholesteric (twisted nematic) phases by adding small amounts of optically active molecules to a nematogen [171], creation of smectic phases from mixtures of molecules which alone form only nematic phases [172,173], and the presence of reentrant phases [174] due to molecular reorganizations based upon the relative importances of various short- and long-range intermolecular interactions in different temperature regimes (as mediated by the interplay of entropy and enthalpy terms) [175 -177]. Each has been exploited to create interesting and novel systems and devices based upon mesomorphism. 

The excluded volume theories of Onsager and Flory show that depending on the axial ratio of the rod-like particles, there is a critical concentration above which a nematic phase is formed. This concentration does not depend on the temperature of the system as these theories are essentially athermal, i.e. the part of the free energy leading to the anisotropy is an entropy term. 

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