Space charge field, definition

Since the electro-osinotic flow is induced by the interaction of the externally applied electric field with the space charge of the diffuse electric double layers at the channel walls, we shall concentrate in our further analysis on one of these 0 1 2) thick boundary layers, say, for definiteness, at... 

Definite collection volumes can be achieved in PIN diodes, where an undoped zone I of an intrinsic semiconductor separates the p- and -regions (Fig. 4.95). Since no space charges exist in the intrinsic zone, the bias voltage applied to the diode causes a constant electric field, which accelerates the carriers. The intrinsic region may be made quite wide, which results in a low capacitance of the p n junction and provides the basis for a very fast and sensitive detector. The limit for the response time is, however, also set by the transit time r = ru/uth of the carriers in the intrinsic region, which is... 

Now integrate over all space. By Gauss theorem, J d rV- ( x TC) may be transformed into a surface integral enveloping all the fields. In order to encompass all charges, the surface integration must be extended to infinitely remote boundaries where the fields definitely vanish. This term therefore drops out, leaving... 

In resolving the apparent paradox of how an antenna with no charge (in free space) can have an electric-dipole moment, one can go back to definitions. In Ref. 14 the fields from a current distribution are evaluated by expanding... 

Where then to look for the Lewis model, a model which in the light of its ubiquitous and constant use throughout chemistry must most certainly be rooted in the physics governing a molecular system If one reads the introductory chapter on fields in Morse and Feshbach s book Methods of theoretical physics (1953), one finds a statement to the effect that the Laplacian of a scalar field is a very important property, for it determines where the field is locally concentrated and depleted. The Laplacian of the charge density at a point r in space, the quantity V p(r), is defined in eqn (2.3). This property of the Laplacian of determining where electronic charge is locally concentrated and depleted follows from its definition as the limiting difference between the two first derivatives which bracket the point in question as defined in eqn (2.2) and illustrated in Fig. 2.2. 

The traditional description of individual properties of molecules is based on the assumption of a definite charge distribution in them determined by the symmetry of the nuclear framework. The light electrons, moving in the field of heavy nuclei, adjust (adiabatically) their space distribution to the nuclear configuration, which results from the self-consistent electrostatic interaction of the electrons and nuclei. 

Thus, Eqs. (12.62), (12.63), and (12.69) give the distribution of the electric field potential in the space around the touching particles. Next, we turn to the definition of the charges qi and and the interaction force between the particles. 

Another unique feature of DEDA [38] is about its calculation of the charge transfer component (Afct)/ which is also calculated variationally based on the net electron flow in real space. This net counting matches classical view of charge transfer more closely and a real space approach leads to a small basis set dependency. Force field development can benefit from these unique features, as each interaction component in DEDA according to the definitions is more consistent with the typical physical picture employed in the classical force field description of intermolecular interactions. 

All science is based on a number of axioms (postulates). Quantum mechanics is based on a system of axioms that have been formulated to be as simple as possible and yet reproduce experimental results. Axioms are not supposed to be proved, their justification is efficiency. Quantum mechanics, the foundations of which date from 1925-26, still represents the basic theory of phenomena within atoms and molecules. This is the domain of chemistry, biochemistry, and atomic and nuclear physics. Further progress (quantum electrodynamics, quantum field theory, elementary particle theory) permitted deeper insights into the structure of the atomic nucleus, but did not produce any fundamental revision of our understanding of atoms and molecules. Matter as described at a non-relativistic quantum mechanics represents a system of electrons and nuclei, treated as point-like particles with a definite mass and electric charge, moving in three-dimensional space and interacting by electrostatic forces. This model of matter is at the core of quantum chemistry. Fig. 1.2. 

Dielectric constant Also called relative permittivity or K. Represented by the variables and k. A measure of a material s ability to store charge under the influence of an applied electric field. Values are given in comparison to a perfect vacuum or "free space, which has a dielectric constant of 1 by definition. 

In a vacuum the electric field E is defined in terms of the force experienced by an infinitesimal test charge that can be placed at any point in space. However this cannot be done within systems like a polymer melt or a polymer solution, since, by definition, the space where we would like to measure the field is already occupied by either a polymer fragment or a solvent molecule. 

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