Long-range repulsion

The DLVO theory [88,89], a landmark in the study of colloids, interprets stability as dependent on the competition between the long-range repulsion forces of similarly charged... 

That is, it also reduces the long-range repulsions between the orbitals as much as possible. Thus, this localization method achieves three objectives concentration of the molecular orbitals, short-range separation of different orbitals, and long-range separation of different orbitals. 

Double-layer forces are commonly used to induce repulsive interactions in colloidal systems. However, the range of electrostatic forces is strongly reduced by increasing the ionic strength of the continuous phase. Also, electrostatic effects are strong only in polar solvents, which is a severe restriction. An alternative way to create long-range repulsion is to adsorb macromolecules at the interface between the dispersed and the continuous phase. Polymer chains may be densely adsorbed on surfaces where they form loops and tails with a very broad distribution of sizes... 

The thicknesses of free soap films and liquid films adsorbed on surfaces (Figs. 1.26d and 1.26e), which can be measured using optical techniques such as reflected intensity, total internal reflection spectroscopy, or ellipsometry as functions of salt concentration or vapor pressure, can provide information on the long-range repulsive forces stabilizing thick wetting films. We see an example of this in Chapter 11. 

A series of theoretical papers have recently investigated the structure and thermodynamic stability of CL/ DNA complexes (May and Ben-Shaul, 1997 Dan, 1998 Bruinsma, 1998 Bminsma and Mashl, 1998 Harries et al., 1998 O Hem and Lubensky, 1998 Golubovic and Golubovic, 1998). Analytical and numerical studies of DNA-DNA interactions bound between membranes show the existence of a novel long-range repulsive electrostatic interaction (Bminsma, 1998 Bruinsma and Mashl, 1998 Harries et al., 1998). 

Resonances unassociated with eigenstates of Feshbach s QHQ are often associated with the shape of some effective potential in an open channel, normally a combination of short-range attractive and long-range repulsive potentials, forming a barrier, within which a large part of the wavefunction is kept. These resonances are called "shape resonances" or "potential resonances." They occur at energies above and usually close to the threshold of that open channel. 

Since the Hamaker constant for proteins in a physiological solution is of the order of 10 20 J, Eq. (18) provides a concentration of approximately 2 M even for the large value of /(=31 X10 50 Jm3 corresponding to Cl- ions [14]. This corresponds to an ideal gas pressure of approximately 50 atm. Consequently, the long-range repulsion or attraction between plates due to the van der Waals interactions between a gas of neutral particles and the plates is expected to be negligible in most cases. 

The long-range repulsion induced by the electrolyte concentration (see Figure 4c) can be explained as follows. At zero surface charge, the total charge of the electrolyte... 

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