Inhomogeneous charge distributions

The inner and outer potential differ by the surface potential Xa — (fa — ipa- This is caused by an inhomogeneous charge distribution at the surface. At a metal surface the positive charge resides on the ions which sit at particular lattice sites, while the electronic density decays over a distance of about 1 A from its bulk value to zero (see Fig. 2.1). The resulting dipole potential is of the order of a few volts and is thus by no means negligible. Smaller surface potentials exist at the surfaces of polar liquids such as water, whose molecules have a dipole moment. Intermolecular interactions often lead to a small net orientation of the dipoles at the liquid surface, which gives rise to a corresponding dipole potential. 

The channel-membrane-solution system is characterized by an inhomogeneous charge distribution that conditionally allows mobile ions to cross the strong dielectric barrier imposed by the membrane. Therefore, an accurate representation of the electrostatic forces acting on each component is needed to understand the influence of the system s structural properties on its function. 

The highly inhomogeneous charge distribution of ion channel systems makes them closer to electron devices than to bulk homogeneous systems. 

Figure 6.9 Inhomogeneous charge distribution on the surface of DNA. Phosphates are positively charged, counterions are negatively charged. The strength of attraction depends on the distribution of counterions and on the ratio of the axial shift Az to the helical pitch H. [Reprinted with permission from A. A. Komyshev and S. Leikin, Phys. Rev. Lett., 82, Art. No. 4138. Copyright (1999) the American Physical Society]...

Here, X is th so-called surface potential corresponding with the electrostatic potential step resnlting from the inhomogeneous charge distribution on the surface. This surface dipole can be calculated for metals on the basis of more or less refined theories and depends veiy much on the band stmcture. In order to get some idea of the possible size of snch snrface potentials, one shonld realize that a layer of water molecules with each molecule oriented perpendicular to an atom of a surface with 10 atoms per square centimeter would correspond with a X potential of about 3.8 V. 

Fully Inhomogeneous Charge Distributions and Disordered Polymer Models... 

Out of the class of weakly inhomogeneous charge distributions, the application of coarse graining ideas becomes much less evident. 

The first, and central for this work, example of fully inhomogeneous charge distribution comes from choosing ut as typical configuration of a family of random variables. 

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