| | 1 | Author
| W. Helfrich | Requires cookie* | | | Title
|  | | | | Abstract
| In two previous publications1; 2 we have pro posed an elastic theory for simple lipid bilayers which may be viewed as two-dimensional fluids. In particular, we have shown that bilayer spheres in an aqueous medium can be deformed into ellipsoidal bodies if they are submitted to a magnetic field or excess outside pressure. Here we consider a possible deformation by electric fields. It will be seen that the electric effect can be quite strong for large vesicles. As before, we restrict ourselves to small deforma tions, assuming the bilayer to be unstretchable and the sphere to become an ellipsoid of revolution. To calculate the ellipticity we minimize the total ener gy consisting of curvature-elastic and electric parts. The conductivity of the bilayer will in general be very much smaller than that of the aqueous environ ment, so it seems permissible to treat the membrane as a perfect insulator. The electric energy of deformation may be ob tained from the Maxwell stresses. Those inside the membrane will be balanced by equal but opposite elastic stresses. The membrane is likely to sustain the latter without undergoing an appreciable defor mation as they induce neither curvature nor shear flow in the bilayer. The only unbalanced force is due to the Maxwell stress exerted by the electric field just outside the vesicle, since in the enclosed water the field must be identical to zero. We assume here that the membrane is dielectrically isotropic, which implies that the forces caused by the Maxwell stresses are confined to the interfaces with water. If it is not, electrical torque densities may be ex pected within the bilayer. The torques may induce curvature, but this should be negligible as the polarizabilities of the bilayer should be very much smaller than that of water. The standard expression for the electric potential Ue around a sphere in a uniform applied field is Ue= -F eoz + Ae(cos 0/r2). | | | |
Reference
| (Z. Naturforsch. 29c, 182 [1974]; received November 8/December 6 1973) | | | |
Published
| 1974 | | | |
Keywords
| Lipid Bilayer, Deformation, Electric Field | | | |
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| 29 | |
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