Electrostatics electric field

The volumetric charge density is of interest in the study of ionic solutions, in which one can calculate the charge density around a specific ion. This is done by using the Poisson equation, based on electrostatic electric fields or by Boltzman distribution law of classical statistic mechanics. For the simpler case of dilute solutions this approach yields the expression p =... 

The second harmonic contribution from requires an electrostatic electric field E() and is known as electric field induced second harmonic (EFISH). The intensity of the generated second harmonic, assuming that the film is very thin and lossless, is... 

Figure 3.4. Polarization of slab in external electrostatic electric field Eo perpendicular to slab.

Consider the interaction of a neutral, dipolar molecule A with a neutral, S-state atom B. There are no electrostatic interactions because all the miiltipole moments of the atom are zero. However, the electric field of A distorts the charge distribution of B and induces miiltipole moments in B. The leading induction tenn is the interaction between the pennanent dipole moment of A and the dipole moment induced in B. The latter can be expressed in tenns of the polarizability of B, see equation (Al.S.g). and the dipole-mduced-dipole interaction is given by... 

The electrostatic sector consists of two curved parallel plates between which is applied a potential difference producing an electric field of strengtir E. Transmission of an ion tlirough the sector is governed by the following relationship... 

Migration is the movement of ions due to a potential gradient. In an electrochemical cell the external electric field at the electrode/solution interface due to the drop in electrical potential between the two phases exerts an electrostatic force on the charged species present in the interfacial region, thus inducing movement of ions to or from the electrode. The magnitude is proportional to the concentration of the ion, the electric field and the ionic mobility. 

Our discussion of elecfronic effects has concentrated so far on permanent features of the cliarge distribution. Electrostatic interactions also arise from changes in the charge distribution of a molecule or atom caused by an external field, a process called polarisation. The primary effect of the external electric field (which in our case will be caused by neighbouring molecules) is to induce a dipole in the molecule. The magnitude of the induced dipole moment ginj is proportional to the electric field E, with the constant of proportionahty being the polarisability a ... 

Ire boundary element method of Kashin is similar in spirit to the polarisable continuum model, lut the surface of the cavity is taken to be the molecular surface of the solute [Kashin and lamboodiri 1987 Kashin 1990]. This cavity surface is divided into small boimdary elements, he solute is modelled as a set of atoms with point polarisabilities. The electric field induces 1 dipole proportional to its polarisability. The electric field at an atom has contributions from lipoles on other atoms in the molecule, from polarisation charges on the boundary, and where appropriate) from the charges of electrolytes in the solution. The charge density is issumed to be constant within each boundary element but is not reduced to a single )oint as in the PCM model. A set of linear equations can be set up to describe the electrostatic nteractions within the system. The solutions to these equations give the boundary element harge distribution and the induced dipoles, from which thermodynamic quantities can be letermined. 

The source requited for aes is an electron gun similar to that described above for electron microscopy. The most common electron source is thermionic in nature with a W filament which is heated to cause electrons to overcome its work function. The electron flux in these sources is generally proportional to the square of the temperature. Thermionic electron guns are routinely used, because they ate robust and tehable. An alternative choice of electron gun is the field emission source which uses a large electric field to overcome the work function barrier. Field emission sources ate typically of higher brightness than the thermionic sources, because the electron emission is concentrated to the small area of the field emission tip. Focusing in both of these sources is done by electrostatic lenses. Today s thermionic sources typically produce spot sizes on the order of 0.2—0.5 p.m with beam currents of 10 A at 10 keV. If field emission sources ate used, spot sizes down to ca 10—50 nm can be achieved. 

Electrophoresis (qv), ie, the migration of small particles suspended in a polar Hquid in an electric field toward an electrode, is the best known effect. If a sample of the suspension is placed in a suitably designed ceU, with a d-c potential appHed across the ceU, and the particles are observed through a microscope, they can all be seen to move in one direction, toward one of the two electrodes. AH of the particles, regardless of their size, appear to move at the same velocity, as both the electrostatic force and resistance to particle motion depend on particle surface this velocity can be easily measured. 

Response to Electric and Acoustic Fields. If the stabilization of a suspension is primarily due to electrostatic repulsion, measurement of the zeta potential, can detect whether there is adequate electrostatic repulsion to overcome polarizabiUty attraction. A common guideline is that the dispersion should be stable if > 30 mV. In electrophoresis the appHed electric field is held constant and particle velocity is monitored using a microscope and video camera. In the electrosonic ampHtude technique the electric field is pulsed, and the sudden motion of the charged particles relative to their counterion atmospheres generates an acoustic pulse which can be related to the charge on the particles and the concentration of ions in solution (18). 

Electrostatic precipitation Electric-field gradient a. Attraction h. Induction / /5,-n/K D 5,e,2 l5, + 2/l nDtV, / Surface accommodation... 

Noncontacting Electrostatic Measurements These measurements are made by instruments that respond to the electric fields at their sensing electrodes. Gonsiderable care must be taken in the interpretation of the measurements. The three general types of devices are described as follows. 

The continuum electrostatic approximation is based on the assumption that the solvent polarization density of the solvent at a position r in space is linearly related to the total local electric field at that position. The Poisson equation for macroscopic continuum media... 

---