Polarization curvature-induced

For a single, two-dimensional liquid crystal hpid bilayer, or a membrane, in a smectic A-like state, the director field is represented by the membrane normal n. Fiexoelectricity is then defined as a curvature-induced area membrane polarization, or, conversely, as an electric field-induced membrane curvature. Lipids and proteins are oriented parallel to each other along the local membrane normal in the flat state. A curvature of the membrane surface leads, indeed, to a splay type deformation of the molecular local director, with a splay vector S = (si - - S2)n, while a bend deformation along the membrane normal is not allowed because there is no third dimension. Then, obviously, the only polarization component points along the membrane normal. 

Fig. 6.1. Flexoelectric (curvature-induced) polarization Pg and the sign convention for the flexocoefficient / for the case shown / will be positive, fti, R2 are the principal radii of the bilayer curvature (from Petrov, with kind permission from Taylor and FVancis Group).

Fig. 6.2. Flexoelectric polarization of a cylindrical micelle. R is the curvature radius, r is the micelle radius, Pl is the curvature-induced polarization per unit length (from Petrov, with kind permission from Taylor and Francis Group).

Integral proteins could provide a large contribution to the curvature-induced membrane polarization. Both dipolar and quadrupolar contributions could show up, more pronounced than those of lipids. The reason for such an expectation is the very large dipole moment measured for some proteins. Theory also demonstrates that such big molecules with no spherical symmetry may have a very large anisotropy of the quadrupole moment. 

The competition between the polar and steric dipoles of molecules may also lead to internal frustration. In this case, the local energetically ideal configuration cannot be extended to the whole space, but tends to be accomodated by the appearance of a periodic array of defects. For example, the presence of the strong steric dipole at the head of a molecule forming bilayers will induce local curvature. As the size of the curved areas increases, an increase in the corresponding elastic energy makes energetically preferable the... 

In the theoretical section above, the nonlinear polarization induced by the fundamental wave incident on a planar interface for a system made of two centrosymmetrical materials in contact was described. However, if one considers small spheres of a centrosymmetrical material embedded in another centrosymmetrical material, like bubbles of a liquid in another liquid, the nonlinear polarization at the interface of a single sphere is a spherical sheet instead of the planar one obtained at planar surfaces. When the radius of curvature is much smaller than the wavelength of light, the electric field amplitude of the fundamental electromagnetic wave can be taken as constant over the whole sphere (see Fig. 7). Hence, one can always find for any infinitely small surface element of the surface... 

This latter explanation was verified by Webster and Schrank 187 who demonstrated that a transverse polarization of freshly decaptitated avena coleoptiles (containing no auxin ) could be electrically induced symmetrical application of exogenous auxin to the stump after electrical stimulation produced curvature A consistent behavior was exhibited if decapitated stumps, with auxin containing agar blocks on top, were electrically stimulated bending again occurred towards the positive side, similar to the case in which auxin was applied to only one side of freshly decapitated stumps without electrical stimulation (Fig. 12). 

That the electrically induced transverse polarization of the coleoptile is not exerted on the auxin molecule itself, is strongly supported by the fact 3>, that the light-induced lateral EMF is just reversed to the externally applied one, generating the correct curvature the convex side, i.e. the faster growing side, will become the positive side, regardless of the type of curvature (positive or negative, Fig. 13). 

The polar, ionic and even non-ionic head-group interactions of lipid membranes and other surfactants, (as indeed for many polymers and polyelectrolyte intra-molecular interactions) and the associated curvature at interfaces formed by such assemblies will be dependent on dissolved gas in quite complicated ways. Fluctuating nanometric sized cavities at such surfaces will be at extremely high pressure, (P = 2y/r, y= surface tension, and r the radius) resulting in formation of H and OH radicals. The immediate formation of Cl radicals and consequent damage to phospholipids offers em explanation of exercise-induced immunosuppression (through excess lactic acid CO2 production), perhaps a clue to the aging process. 

Tafel Curve Modeling (Ref 4, 5). Equation 6.5 provides the form of the experimental polarization curve when the anodic and cathodic reactions follow Tafel behavior. The equation accounts for the curvature near Ecorr and Icorr, which is observed experimentally. Physically, the curvature is a consequence of both the anodic and cathodic reactions having measurable effects on Iex at potentials near Ecorr. Tafel-curve modeling uses experimental data taken within approximately 25 mV of Ecorr where the corrosion process is less disturbed by induced corro-... 

Oils are solubilized into the interior of micelles where they allow the micelle to swell to a larger radius, hence giving rise to cubic (12) and hexagonal (H2) phases at smaller a values than for the surfactant alone. Polar oils can also reside at the micelle surface to some extent, reducing micelle curvature and inducing the occurrence of lamellar and inverse phases. This behavior is typified by the behavior of the commercial nonionic surfactant nonylphenol-(probably branched)-decaethylene oxide with hexadecane and p-xylene [40]. 

Another example of curvature of van t Hoff plots relates to irreversible changes in the conformation of carbamate-derivatized amylose and cellulose CSP, which was observed for the normal-phase separation of the enantiomers of a dihydropyrimidinone acid and methyl ester. The apparent conformational change was thermally induced and depended upon the polar component of the mobile phase. The irreversible change in the conformation of... 

Flexoelectric polarization of FLC layers should also be taken into account [4, 29]. Reference [29] shows that the total polarization P includes two components, P and P , which are parallel and perpendicular to the C2 axis, respectively. The components P and partially f , are induced by the director curvature in the layers or by the flexoelectric effect (Fig. 7.4)... 

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