Theory of band formation

The elastic storage in a nematic is either in the molecules themselves and/or in the macroscopic texture of the nematic phase. A mechanism for the storage of elastic energy in the texture of the liquid crystal 

In the same paper Picken et al [13] also describe a more general two-dimensional lattice model to deal with this additional aspect. In this model only splay and bend deformations are allowed to occur. The longitudinal relaxation (i.e. the band spacing) will be determined mainly by the bend elastic constant K, as used in the one-dimensional model, and the lateral relaxation is driven by the splay modulus K, They find the result of this model to be not completely satisfactory.. .. it is clear that from the present model the aspect ratio of the bands Lj /L l is expected to be a constant (and equal to (iC /K ) ). This is not in agreement with the experimental results where the lateral correlation length seems to depend on the applied preshear rate, (and the longitudinal correlation length does not). They speculate that Possibly, the applied shear rate influences the details of the initial texture that is formed upon cessation of flow.  

Gleeson et al [60] agree that the only two possible sources of elastic energy which could drive the band formation phenomenon are molecular 

Note that molecular elasticity does not refer to energy actually stored in the molecules i.e. in bond distortions or non-equilibrium conformations. 

The second source. ..is the elasticity stored in the texture, i.e. the micron-scale orientational inhomogeneities created or amplified by the previous shearing flow. Like molecular elasticity, the influence of texture elasticity can be quantified by a dimensionless number, in this case an Ericksen number. 

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The problem may be analysed in terms of the theory of band formation outlined in Chap.2, using the more accurate formalism of Chap.3. The origin of the disease can be traced to the pole at P = 1/y in the w(P) function (4.18). Usually, this pole is not seen in an energy-band calculation because 1/y is outside the range of P or S values given by (2.23), where bands are formed... 

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