Nematic-isotropic transition volume change

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). 

The Landau-de Gennes theory for the nematic isotropic transition can be extended to the smectic A-nematic transition. The order parameter for this transition is rl), the amplitude of the density wave describing the formation of layers in the smectic A phase. Since the difference between a value of rlr and -Irlrl only amonnts to a shift of one half layer spacing in the location of all the layers (and therefore no change in the free energy per nnit volume), the expansion in terms of powers of rlr can only contain even powers. Hence the free energy per unit volume in the smectic A phase can be written as... 

Recently Tao et al. extended the MS theory by adding to Eq. (3) the isotropic, density-dependent component of the molecular interactions (/o(r) in the form of the Lennard-Jones potential (/o(r) = 4e [(o-/r) -(o-/r) ]. As a result they obtained a better agreement of the calculated and experimental quantities characterizing the nematic-isotropic transition, for example, volume change at and the values of dT ldp. Chrzanowska and Sokalski considered the case when the parameter Lennard-Jones potential is dependent on the orientation of molecules that allows one to predict properly for MBBA such properties as order parameters, elastic constants, and rotational viscosity coefficients. 

For MBBA (N-(p -methoxybenzylidene)-p-n butylaniline), has the value of 0.85 X 10 over the range of interest. (The volume change at the nematic-isotropic transition is small compared to the thermal expansion and will be neglected.)... 

J.H. Wendorff Yes, but on the other hand you know exactly what the stmctural change, volume change, and everything else is at the nematic isotropic transition. My conclusion is that apparently your method is not very sensitive. 

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 temperature dependence of the density (q) is practically linear, with the exception of jumps near phase transitions. The volume changes are 3-9%, 0.1-0.4%, and 0.01-0.2% for the crystal-mesophase, nematic-isotropic, and smectic A-nematic transitions, respectively. 

J.H. Wendorff (Deutsches Kunststoff-Institut, Darmstadt, Federal Republic of Germany) You reported just a change in slope for MBBA at the nematic isotropic condition. Of course, we know that there is a definite volume change at that transition, whereas for T , you never found a definite volume change or a jump. At there s no jump but you described it in similar terms, and so. I m quite confused. So, this T transition is not a transition ... 

At the nominal melting point Tm there is a first-order phase transition from the crystal to the mesophase with the usual discontinuities in the extensive properties (e.g. volume and entropy). In Fig. 5.7, we schematically illustrate a hypothetical differential-scanning-calorimetry (DSC) trace and the variation in volume of the sample versus temperature for an ideal nematic. The values for the changes in enthalpy (AH 45 kJ mol" ) and volume (A V 10%) at are typical of those changes in extensive properties that occur on melting ordinary organic molecular crystals. However, if you continue to heat the opalescent-looking mesophase, there is a second transition to a transparent isotropic state above Td. Nematic melts... 

Fig. 5.7. An illustration of hypothetical endothermic transitions (DSC trace) and changes in volume that occur on melting a molecular crystal into a nematic mesophase at T, and the subsequent melting of the nematic phase into the isotropic liquid at the clearing temperature T i.

Fig. 1.11. Phase diagram of a melt of long persistent chains [a I) isotropic melt, II) nematic melt, m) high-temperatuie gas phase] and dependence of the order parameter at the point of nematic ordering (b), entropy of the transition calculated for the effective segment (c), and relative change in the volume in the transition (d) on the parameter ltd in a melt of long persistent chains [61].

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