Elastic Properties of Liquid Crystalline Polymers

According to the elastic continuum theory of liquid crystals which was introduced in Chapter 1, the three kinds of deformations can be described by three elastic constants, An(splay), / (twist) and / (bend). In the case of small molecular mass liquid crystals, the three constants are mainly determined by the chemical composition of the liquid crystalline molecules. Among them, K22 is the smallest while the other two are approximately close. All three elastic constants are of the order of 10 12 N. The elastic constants of some important liquid crystals are listed in Table 6.1. Each kind of liquid crystals is a mixture of R5-pentyl and R6-hexyl homologues in the ratio of 40 60. The data are obtained at the temperature of T = Tc — 10 °C where Tc is the clear temperature. 

The above qualitative description illustrates that the molecular length has an important effect on the elastic constants of liquid crystalline polymers. 

Priest (1973) and Straley (1973), in terms of the classical virial expansion, the Onsager theory (referred to in Section 2.1) and the curvature moduli theory, derived the elastic constants of rigid liquid crystalline polymers. The free energy varies according to the change of the excluded volume of the rods due to the deformation. The numerical calculation of elastic constants (Lee, 1987) are shown in Table 6.2. 

The three elastic constants are reduced by ksT/D (D is the diameter of the rod). They are the functions of the dimensionless parameter Q = cf L/D with cf) the volume fraction of the liquid crystalline polymers and L the molecular length. It is shown in the Table 6.2 that the three elastic constants increase as Q and the order parameter S increase. Among them the bend elastic constant K33 varies dramatically, and finally becomes infinite as S approaches unity in the perfectly ordered state. 

Assume that the degree of the ordering of liquid crystalline polymers is high and the orientational distribution function is simply Gaussian, Odijk (1986) developed the analytical formulae for elastic constants 

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