Debye shielding distance

A collection of electrons and ions, usually at a high enough temperature so that the ionization level is about 5% and at densities such that the Debye shielding distance is much smaller than the macroscopic dimensions of liie system. See also Fusion Energy. 

The quantity is termed the Debye shielding distance or, more frequently, the Debye length. 

While much of his reputation was based on nonpolymeric accompHshments, such as demonstrated by the Debye-Huckel theory, the Debye-Scherrer x-ray diffraction technique, the Debye-Sears effect in liquids, the Debye temperature, the Debye shielding distance, the Debye frequency and the Debye unit of electric moment, his development of the hght scattering technique for the determination of the molecular weight of polymers resulted in his also being recognized as a world class polymer scientist. 

For ionic concentration of 1 mol/m and a dielectric constant equal to that of water, e = 78 0, we have Xjj 9.5 nm at standard ambient condition where Xd is termed as the Debye shielding distance or Debye length. 

PLASMA (Particle). 1 An assembly of ions, electrons, neutral atoms and molecules in which the motion of the particles is dominated by electromagnetic interactions. This condition occurs when the macroscopic electrostatic shielding distance (Debye length) is small compared to the dimensions of the plasma. Because of the large electrostatic potentials... 

From the above considerations we can now define what is meant by electrically neutral solutions. If the dimensions of the system L are much larger than Aj3, then whenever local charge concentrations arise or external potentials are introduced into the solution they are shielded out in a distance short compared with L, leaving the bulk of the solution free of large electric potentials or fields. Based on a Debye length of 1 to 10 nm, the assumption of electrical neutrality is generally justified for the problems so far considered. However, as we shall discuss in the next section, in the case of very small charged microscopic capillaries, such as are characteristic of membranes and finely porous media, the double layer is central to the calculation of the solute and ion fluxes. 

The Debye radius gives the characteristic plasma size scale required for the shielding of an external electric field. The same distance is necessary to compensate the electric field of a specified charged particle in plasma. In other words, the Debye radius indicates the scale of plasma quasi-neutrality. There is the correlation between the Debye radius and plasma ideality. The non-ideality parameter F is related to the number of plasma particles in the Debye sphere, For plasma consisting of electrons and positive ions,... 

The typical space-size characterizing a plasma is the Debye radius, which is a linear measure of electroneutrality and shielding of external electric fields. The typical plasma time scale and typical time of plasma response to the external fields is determined by the plasma frequency illustrated in Fig. 3-19. Assume in a one-dimensional approach that all electrons at X > 0 are initially shifted to the right on the distance xq, whereas heavy ions are not perturbed and remain at rest. This results in an electric field, which pushes the electrons back. If = 0 at X < 0, this electric field acting to restore the plasma quasi-neutrality can be found at x > xq from the one-dimensional Poisson equation as... 

A basic parameter of plasma collective phenomena is the Debye Iraigth that provides a measure of the distance over which an extrinsic charge introduced into j ma is shielded [13], In the simplest case ... 

The Debye-Bueche theory, on the other hand, considers the partially draining coil as a sphere that is more or less permeable, within which a number of smaller beads is homogeneously distributed. The beads correspond to the monomeric units. The drag which one bead produces on the others is calculated, and this resistance is then expressed in terms of a length L, which corresponds to the distance from the surface of the sphere to where the flow rate of the solvent is reduced to 1 /e times what it is at the surface of this sphere. The shielding ratio, or shielding factor, is given by... 

Figure 12.12. Variation of the diffusion coefficient as a function of the distance (p) from the center of the pore (i.e. p = 0 A) to within 1 A of the -SOs groups. The calculation is for Nafion with 6 H2O/ SOs" with inclusion of either Debye-Huckel or Attard models for the shielding. At the center of the pore the Attard formulation results in the most significant screening of the sulfonate groups and hence the higher proton self-diffusion coefficient.

AcAc, acetylacetonate EPR, electron paramagnetic resonance DPM, dipivaloylmethane Tc, Correlation time for molecular tumbling A/x, concentration of spins X (per unit volume) D, mutual translational self-diffusion coefficient of the molecules containing A and X a, distance of closest approach of A and X ye, magnetogyric ratio for the electron C, spin-rotation interaction constant (assumed to be isotropic) Ashielding anisotropy <7 <7j ) coo, Debye frequency 0d, the corresponding Debye temperature Fa, spin-phonon coupling constant. 

Calculate the root-mean-square end-to-end distance for a polystyrene with molecular weight 2 x 10 in benzene with an intrinsic viscosity of 107 mL/g. According to Debye and Bueche s analysis, the shielding ratio is in the vicinity of 0.836 with a = 3.92 (Debye and Bueche, 1948). 

One key quantity of the contribution A is the ion-specific inverse Debye screening length k which compares to the MSA F [Eq. (4)] k describes the reciprocal distance within which the long-range forces among ions are shielded by water, expressed as ... 

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