Lipid bilayers, elastic propertiesA theory of the elasticity of lipid bilayers is proposed. Three types of strain, i. e. stretching, tilt and curvature, are distinguished and the associated stresses are identified. It is argued that in the case of vesicles ( = closed bilayer films) the only elasticity controlling nonspherical shapes is that of curvature. Euler-Lagrange equations are derived for the shape in magnetic fields and under excess outside pressure. It is shown that magnetic fields can deform spherical vesicles into ellipsoids of revolution. Under excess outside pressure the spherical shape becomes unstable at a certain threshold pressure. Both effects can be influenced by a spontaneous curvature of the bilayer. Some possible experiments to determine the elastic properties are also discussed.Brought to you by | University of Manitoba Authenticated Download Date | 6/17/15 6:31 PM

It has been proposed in the discussion that the energy balance in an electric field is satisfied simply by momentum changes of the neutral particle causing the electron drag. Such an interpretation is not possible, as may be readily seen in the ring model. Here an electron keeps its wave vector when accelerated by a field, thus the total wave vector of the system consisting of the neutral particle and the electrons will also be conserved. Therefore, a change in the wave vector of the neutral particle requires that at least one electron alters its wave vector. Because of the exclusion principle this electron has to be excited into an empty band.As to the calculations we found that the result for {(0] Nv [ 2)+ (2] Nv [0)} has to be corrected to give approximatelyWe wish to emphasize, however, that repeated checks and further simplifications of the model confirmed that (Nv~ 2 can be made nonzero. Only two possible explanations for this admittedly strange result appear to be left: (1) Divergence of the perturbation calculation in higher than second order. (2) Excitation of electrons into the conduction band by the combined action of the neutral particle and the electric field.

Electrical conductivity measurements were performed with thin (50 μ) single crystals of p-terphenyl, p-quaterphenyl, and anthracene supplied with aqueous electrodes, one of which was an iodine-iodide solution (acceptor electrode), and the other an iodide solution. The results strongly indicate that the acceptor electrode can form ohmic contact for hole injection into these crystals and that space-charge-limited currents can be drawn through them. The crystals were found to contain hole-trapping states the location-in-energy of which can be approximated by a decreasing exponential distribution above the valence band. The measurements showed that the hole mobility in p-terphenyl is about 3×10−2 cm2/v sec, is independent of the field at least up to about 4×104 v/cm, and that the hole-trap concentration is at least 1013 cm−3. The acceptor electrode used does not form ohmic contact to crystals of naphthalene and diphenyl; an explanation for this is proposed. Some theoretical aspects of ohmic contact formation to organic crystals and space-charge-limited current flow in insulators are also discussed.

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The out-of-plane fluctuations of fluid membranes are sterically hindered in multilayer systems. The repulsive interaction associated with the steric or excluded-volume effect is studied theoretically by two methods. The interaction energy per unit area of membrane is derived as a function of temperature, membrane curvature elasticity and mean membrane spacing; it is inversely proportional to the square of the latter. Steric repulsion is estimated for lecithin bilayers in water. There and in other cases, it may compete with van der Waals attraction.