Biaxial nematics reference

In biaxial nematic mesophases, the rotational symmetry of the phase around its director n is broken. It is commonly understood that the term biaxial nematic refers to an orthorhombic nematic phase. With respect... 

However, in 1986, Chandrasekhar [70] published a derivative (Figure 35) which he claimed to show a biaxial nematic phase. This report was interesting because the biaxial nematic phase (Nb), demonstrated in lyotropic systems [71], had been long sought after in thermotropic materials. Further, the molecules were described as bridging the gap between rod- and disc-like materials (a reference perhaps better reserved for polycatenar liquid crystals—vide infra)... 

Fig. 6.6.1. Two examples of molecules which exhibit the biaxial nematic phase (a) (bis-l-(p-n-decylbiphenyl)-3-(p-ethoxyphenyl) propane-1,3-dionatocopper (II))(8i.82) (hereafter referred to as complex A) (b) I,12- >w(pentakis((4-pentyl-phenyl)ethy nyl)pheny loxy)dodecane. ...

As mentioned in Section 3.1, phase biaxiality may be described by a set of microscopic order parameters when the mesogen is a rigid uniaxial particle, where a and (5 refer to the space-fixed axes x y z). Biaxial nematics [3.31], some smectic phases, like smectic C, and certain discotic phases [3.32] exhibit phase biaxiality. The order parameters 5, , and 5, , are different in these phases. NMR may be used to detect phase biaxiality through measurement of a non-zero motionally induced asymmetry parameter in nuclear spin interactions such as dipole-dipole and electric quadrupole interactions. To see how exists in biaxial mesophases, the previous discussion on motional averaging of spin Hamiltonian is gen-... 

Use a computer algebra package such as Maple or Mathematica to show that the Saupe ordering matrix for a biaxial nematic can be written, in the frame of reference for which it is diagonalized, as... 

The phenomenological scalar order parameter q = Qzz is non-zero in nematic phases and vanishes in the isotropic phase. 7] is non-zero in biaxial nematics only and referred to as the biaxial order parameter. The symmetric invariants of may be written as [1,3] ... 

Phase diagram of the potassium laurate (KL)-l-decanol-D20 system, with the Landau point. Nc and Nl are uniaxial nematic phases with cylindrical and lamellar micelle structures, and Nj, denotes the biaxial nematic phase. (Figure reproduced from Reference [8] with permission... 

The macroscopic theory that takes into accoimt the effect of the orientation order was developed by Ericksen, Leslie and Parodi, and usually is referred as ELP theory. A microscopic theory based on correlation functions, which then were "translated" to macroscopic terms and extended to other mesomorphic phases, was developed by the Harvard group. Although usually tire ELP flieory is accepted, it seems that the two approaches are equivalent. A continuum theory of biaxial nematics was developed by Saupe, who followed the description we give with (4.1)-(4.8). In the uniaxial situation, they reproduce the Leslie-Ericksen and Harvard theories. 

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