Compression, electrostatic

This frequency is a measure of the vibration rate of the electrons relative to the ions which are considered stationary. Eor tme plasma behavior, plasma frequency, COp, must exceed the particle-coUision rate, This plays a central role in the interactions of electromagnetic waves with plasmas. The frequencies of electron plasma waves depend on the plasma frequency and the thermal electron velocity. They propagate in plasmas because the presence of the plasma oscillation at any one point is communicated to nearby regions by the thermal motion. The frequencies of ion plasma waves, also called ion acoustic or plasma sound waves, depend on the electron and ion temperatures as well as on the ion mass. Both electron and ion waves, ie, electrostatic waves, are longitudinal in nature that is, they consist of compressions and rarefactions (areas of lower density, eg, the area between two compression waves) along the direction of motion. 

Electrostatic Repulsive Forces. As the distance between two approaching particles decreases, their electrical double layers begin to overlap. As a first approximation, the potential energy of the two overlapping double layers is additive, which is a repulsive term since the process increases total energy. Electrostatic repulsion can also be considered as an osmotic force, due to the compression of ions between particles and the tendency of water to flow in to counteract the increased ion concentration. 

Surface force profiles between these polyelectrolyte brush layers have consisted of a long-range electrostatic repulsion and a short-range steric repulsion, as described earlier. Short-range steric repulsion has been analyzed quantitatively to provide the compressibility modulus per unit area (T) of the poly electrolyte brushes as a function of chain density (F) (Fig. 12a). The modulus F decreases linearly with a decrease in the chain density F, and suddenly increases beyond the critical density. The maximum value lies at F = 0.13 chain/nm. When we have decreased the chain density further, the modulus again linearly decreased relative to the chain density, which is natural for chains in the same state. The linear dependence of Y on F in both the low- and the high-density regions indicates that the jump in the compressibility modulus should be correlated with a kind of transition between the two different states. 

Salts of fatty acids are classic objects of LB technique. Being placed at the air/water interface, these molecules arrange themselves in such a way that its hydrophilic part (COOH) penetrates water due to its electrostatic interactions with water molecnles, which can be considered electric dipoles. The hydrophobic part (aliphatic chain) orients itself to air, because it cannot penetrate water for entropy reasons. Therefore, if a few molecnles of snch type were placed at the water surface, they would form a two-dimensional system at the air/water interface. A compression isotherm of the stearic acid monolayer is presented in Figure 1. This curve shows the dependence of surface pressure upon area per molecnle, obtained at constant temperature. Usually, this dependence is called a rr-A isotherm. 

Best approach toward a general solution of all problems of induced stability appears to be a two-pronged surface treatment involving electrostatic and steric protection. In order to increase repulsion energy, zeta should be increased and to enable the particles to resist compression to a distance of separation less than that at E, a bulky molecule should be attached firmly to the surface. Some systems do not accept both steric and ionic protection but for those that do, the combination shows most promise. Er should not be increased without some assurance that the particles will not be subjected to drastic compressive forces. 

At a finite distance, where the surface does not come into molecular contact, equilibrium is reached between electrodynamic attractive and electrostatic repulsive forces (secondary minimum). At smaller distance there is a net energy barrier. Once overcome, the combination of strong short-range electrostatic repulsive forces and van der Waals attractive forces leads to a deep primary minimum. Both the height of the barrier and secondary minimum depend on the ionic strength and electrostatic charges. The energy barrier is decreased in the presence of electrolytes (monovalent < divalent [Pg.355]

Return to the case of LiF. Lithium ionizes readily, but has little affinity for electrons (I = ionization energy = 5.4 eV and A = electron affinity = 0eV.). On the other hand, fluorine is difficult to ionize, but has considerable electron affinity (I = 17.4eV. and A = -3.6eV.). Thus, when Li and F atoms are close neighbors, electrons can transfer to make Li+ and I. These then attract electrostatically until compression of their ion-cores prevent them from contracting further. In a solid crystal, there are both attractive +/- pairs, and repulsive (+/+ as well as -/-) pairs. However, for large arrays, there is a net attraction. This can be shown most simply by examining a linear chain of +q, and -q charges (Kittel, 1966). 

In the above subsection it was demonstrated that the inclusion of electrostatic interactions into the pressure-area-temperature equation of state provides a better fit to the observed equilibrium behavior than the model with two-dimensional neutral gas. Considering this fact, we would like to devote our attention now to the character of the lipid film under the dynamical, nonequilibrium conditions. In the following we shall describe the dynamical behavior of the phospholipid(l,2-dipalmitoyl-3-sn-phosphatidylethanolamines DPPE) thin films in the course of the compression and expansion cycles at air/water interface. 

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