Lyotropic liquid crystals elasticity

For an approximate quantitative comparison of our theoretical results with the experiments on lyotropic liquid crystals we make a number of assumptions about the material parameters. As we have shown in Sect. 3.2 the different approaches cause only small variations in the critical wave number. For this estimate it suffices to use the critical wave number obtained in our earlier work [42], For lyotropics it is known [56, 57], that the elastic constants can be expressed as... 

Good physical stability can, however, be obtained by developing a viscoelastic network in the continuous phase. The elastic component acts as a net that prevents the droplets from settling or creaming. Viscoelastic networks can be obtained with high-molecular-weight water-soluble polymers or lyotropic liquid crystals. 

Polyim-phenylene isophthalamide) forms lyotropic liquid crystals. Fibers can therefore be spun at lower concentration from isotropic solutions and at higher concentrations from nematic solutions. Because of their high degree of chain segment orientation, fibers spun from nematic solutions show, as expected, higher moduli of elasticity, tensile strengths and lower elongation at rupture values than those spun from isotropic solutions. 

Where po is the zero field pitch, A (m, the diamagnetic anisotropy of the liquid crystal, K22, the twist elastic constant. As the field increases the pitch is predicted to oncrease slowly at first and then diverge logarithmically as the critical field is ap>proached. The theory has been verified for lyotropic liquid crystals of PBG in a number of different solvents (Chandrasekhar, 1977, lizuka, 1973, DuPre Duke, 1974,1975, DuPre et al., 1976,1977, Patel DuPre, 1979). Molecules of liquid crystals orient themselves in the magnetic field so that their long chains are oriented parallel to the magnetic field lines (Miller, 1978). This orientation is associated with the molecular anisotropy of macromolecules rather than the existence of permanent magnetic moments. 

The structure of the BPIII phase actually resembles the L3 (so-called sponge) phase of lyotropic liquid crystals/ and the smectic blue phases observed and studied recently. Both the sponge and smectic blue phases are optically isotropic, and the smectic blue are optically active as well. Theoretical arguments show that the reason for the defect structure is the negative value of tire saddle-splay elastic constant, K24, which makes the defects energetically favorable. A sketch of the sponge phase and of the smectic blue phase is shown in Figure 6.24. 

The elastic bending modulus Kc for lipid bilayers was found to be of the order of 10 x 10-20 J.6 For the lyotropic lamellar liquid crystals, the additional presence of a cosurfactant at the interface shouldleadto smaller values. Various experimental measurements21 provided values ranging between 0.08 and 5 x 10-20 J. 

Structural forces due to long-range positional order are quite easily observed in the smectic A liquid crystals. SFA measurements have been performed on lamellar lyotropic smectics [42,43] and in thermotropic smectics [44-46]. These works extend to a nanometer scale the early studies on elasticity, viscoelastic response and layers instability of smectic A, observed in macroscopic wedge-shaped piezoelectric cells [47,48]. 

The three elastic constants of a liquid crystal are important physical parameters which depend on the interaction between the molecules in the liquid crystalline state. While a large number of theoretical and experimental investigations on the elastic constants are contained in the literature for thermotropic liquid crystals, very little is known about them in the case of lyotropic polymer liquid crystals such as those formed by poly-Y-benzyl-L-glutamate (PBLG) in various organic solvents. Some theoretical investigations have been carried out 3 the experimental data is limited largely to measurements of the twist elastic constant and a few recent measurements of the bend and splay constants. ... 

The strain tensor must conform to the symmetry of the liquid crystal phase, and as a result, for nonpolar, nonchiral uniaxial phases there are ten nonzero components of kij, of which four are independent ( i i, 22> A 33 and 24)- These material constants are known as torsional elastic constants for splay (k, 1), twist ( 22) bend ( 33) and saddle-splay ( 24) terms in 24 do not contribute to the free energy for configurations in which the director is constant within a plane, or parallel to a plane. The simplest torsional strains considered for liquid crystals are one dimensional, and so neglect of 24 is reasonable, but for more complex director configurations and at surfaces, k24 can contribute to the free energy [7]. In particular 24 is important for curved interfaces of liquid crystals, and so must be included in the description of lyotropic and membrane liquid crystals [8]. Evaluation of Eq. (16) making the stated assumptions, leads to [9] ... 

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