Perturbations slight anisotropy

It is also possible that a membrane might have an even lower symmetry than a chiral smectic-C liquid crystal in particular, it might lose the twofold rotational symmetry. This would occur if the molecular tilt defines one orientation in the membrane plane and the direction of one-dimensional chains defines another orientation. In that case, the free energy would take a form similar to Eq. (5) but with additional elastic constants favoring curvature. The argument for tubule formation presented above would still apply, but it would become more mathematically complex because of the extra elastic constants. As an approximation, we can suppose that there is one principal direction of elastic anisotropy, with some slight perturbations about the ideal twofold symmetry. In that approximation, we can use the results presented above, with 4) representing the orientation of the principal elastic anisotropy. 

The anisotropy of the OH group was obvious from measurements of splittings caused by isotopic perturbation (SIP) values in 2,6-dihydroxy acetophenones . The anisotropy due to the OH group has been calculated in phenol. Depending slightly on the method and the basis set, the difference in chemical shifts between C-2 and C-6 is 3.5 to 5 ppm . ... 

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