Bend fluctuation

Shaitan, K.V., Mikhailyuk, M.G., Leont ev, K M.,Saraikin, S.S., and Belyakov, A.A. (2002) Molecular dynamics of bending fluctuations of the elements of protein secondary stmcture, Biofizika 47, 411-419. 

To understand the dynamics of the bending fluctuations associated with these natural modes, a force balance per unit length is required. The force per unit length associated with the bending mode of wavelength A is calculated by differentiating the energy Ux and it is resisted by the frictional dissipation ... 

The basic mechanism for the electric-field-induced instabilities is now quite well understood. The current carriers in the nematic phase are ions whose mobility is greater along the preferred axis of the molecules than perpendicular to it. The ratio of the conductivities is usually about. Because of this anisotropy, space charge can be formed by ion segregation in the liquid crystal itself, as was first pointed out by Carr. The manner in which the space charge can build up due to a bend fluctuation is shown... 

Fig. 3.10.7. Charge segregation in an applied field caused by a bend fluctuation in a nematic of positive conductivity anisotropy. The resulting transverse field is E. ...

First detailed dynamic light scattering (DLS) experiments using bulk liquid crystal samples have confirmed the theoretically predicted existence of two dissipative fluctuation eigenmodes in the nematic liquid crystalline phase the first mode being a combination of splay and bend distortion and the second one a combination of twist and bend fluctuations [55,56]. Both modes are overdamped and the relaxation rate 1/r of each mode depends on the fluctuation wave vector q and viscoelastic properties of the sample [57] ... 

Selection rules for the observation of a given fluctuation mode can also be obtained from (4.26) the twist-bend fluctuation mode can be observed and... 

On the (local) length scale on the order of D, the comblike polymer with densely grafted side chains can be considered as a cylindrical polymer bmsh, that is, an array of polymer chains end grafted with an axial separation to a thin cylinder. This local cylindrical symmetry is ensured by either the intrinsic backbone rigidity or, in the case of flexible backbone, by repulsive interactions between the grafts. This repulsion induces axial tension in the backbone, which maintains locally cylindrical configuration of the comblike polymer in spite of short-scale bending fluctuations in the extended flexible backbone. 

Alternatively, the bending fluctuations can be expanded into local bending modes, the so-called hats [11,12]. In the hat model the membrane is divided into practically circular pieces, which may be chosen as small as a molecular cross-section. The disks fluctuate independently in their curvatures C -F C2. If a single hat is excited, it creates in a flat membrane a cap of spherical curvature C) - C2 with a brim of saddle curvature Cj = —C2, as sketched in Figure 6.4. The brim drops (or rises) logarithmically with the distance p from the hat s center so that the principal curvatures go to zero with 1/p. The hat model gives an idea of the membrane roughness on the... 

Also, mixed membranes were not discussed. They will be bumpy, even in the absence of thermal bending fluctuations, whenever the constituent molecules dilfer by their spontaneous curvatures. This holds for bilayers as well as monolayers, because different pairs of opposite molecules may have different bilayer spontaneous curvatures. 

In the case of mixed membranes it is attractive to solve eq. (32) for the flexibility 1/k and derive this macroscopic quantity from the strength of the mean-square local bending fluctuations. The fluctuations of c, + Cj arise not only from the molecular bending fluctuations but also from the diflusion of the molecules (or pairs of molecules in bilayers) if their spontaneous curvatures are different. Therefore, mixing can lead to a dramatic decrease of the bending rigidity in comparison with one-component membranes [12]. 

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