Debye screening

Explicit calculation of this sum shows that it is the Debye screened potential... 

This has the fomi of a second virial coefficient in which the Debye screened potential has replaced the Coulomb potential. Expressions for the other excess themiodynamic properties are easily derived. 

This is an inverse lengtli k is known as tire Debye screening lengtli (or double layer tliickness). As demonstrated below, it gives tire lengtli scale on which tire ion distribution near a surface decays to tire bulk value. Table C2.6.4 gives a few numerical examples. 

Table C2.6.4 Debye screening lengtli k for aqueous solutions of a 1-1 electrolyte at 298 K (equation (C2.6.7)).

Fig. 1. Electron temperature and density regions for plasmas (7—9) where the numbers and the diagonal lines represent (—) the Debye screening length,...

Also shown in Figure 1 are the Debye screening length and Debye sphere size. For gaseous plasmas, A)-, 1 (11). SoHd-state plasmas or... 

D. Brydges, P. Federbush. Debye screening in classical Coulomb systems. In G. Velo, A. S. Wightman, eds. NATO Advanced Science Institutes. Series No. B 74. New York Plenum Press, 1981, pp. 371-385. 

Here, x and y are the dimensionless distance and potential defined by x = xr and y = e

elementary charge, T the absolute temperature, k the Boltzmann constant, and x the Debye screening parameter defined by x = (8jtne2/skT)1/2. 

In the second group of models, the pc surface consists only of very small crystallites with a linear parameter y, whose sizes are comparable with the electrical double-layer parameters, i.e., with the effective Debye screening length in the bulk of the diffuse layer near the face j.262,263 In the case of such electrodes, inner layers at different monocrystalline areas are considered to be independent, but the diffuse layer is common for the entire surface of a pc electrode and depends on the average charge density <7pc = R ZjOjOj [Fig. 10(b)]. The capacitance Cj al is obtained by the equation... 

Daikhin, double layer capacitance of solid at rough electrodes, 52 Debye screening and diffuse layer near the surface, 50... 

Diffuse layer near the surface, Debye screening and, 50... 

K = Debye screening length 4 = model parameter n = osmotic pressure p = density T = tortuosity factor <1> = swelling ratios... 

Using the equation, very strong concentration effects in small systems have been calculated. For instance, if the macroaqueous phase contains 1 M NaCl and 1 /rM NaTPB, the concentration of this electrolyte in the micro-organic phase at partition equilibrium is 1390/rM [14] This approach is valid if the phases in small systems are thick enough (> 1 /rm), in comparison to the Debye screening length, to fulfill the electroneutrality conditions. 

FIGURE 11.32 Flow profiles in microchannels, (a) A pressure gradient, - AP, along a channel generates a parabolic or Poiseuille flow profile in the channel. The velocity of the flow varies across the entire cross-sectional area of the channel. On the right is an experimental measurement of the distortion of a volume of fluid in a Poiseuille flow. The frames show the state of the volume of fluid 0, 66, and 165 ms after the creation of a fluorescent molecule, (b) In electroosmotic flow in a channel, motion is induced by an applied electric field E. The flow speed only varies within the so-called Debye screening layer, of thickness D. On the right is an experimental measurement of the distortion of a volume of fluid in an electroosmotic flow. The frames show the state of the fluorescent volume of fluid 0, 66, and 165 ms after the creation of a fluorescent molecule [165], Source http //www.niherst.gov.tt/scipop/sci-bits/microfluidics.htm (see Plate 12 for color version). 

Chazelviel treated departures from electroneutraltiy in growth from binary solution by dividing the electrolysis cell into zones [40]. In the bulk of the cell he assumed electroneutraltiy, while he allowed departures from electroneutraltiy in a region larger than the Debye screening length. A scale x defines the extent of the transport-induced space charge. 

Because the inverse Debye length is calculated from the ionic surfactant concentration of the continuous phase, the only unknown parameter is the surface potential i/io this can be obtained from a fit of these expressions to the experimental data. The theoretical values of FeQx) are shown by the continuous curves in Eig. 2.5, for the three surfactant concentrations. The agreement between theory and experiment is spectacular, and as expected, the surface potential increases with the bulk surfactant concentration as a result of the adsorption equilibrium. Consequently, a higher surfactant concentration induces a larger repulsion, but is also characterized by a shorter range due to the decrease of the Debye screening length. 

The function on the right hand side of Eq. (34) consists of a series of elliptic integrals, which depend not only on the unknown electrostatic force but also on the surface charge densities, q and on the interface and protein surface, respectively, and on the inverse Debye screening length (1/K). 

As the ionic strength increases, the Debye screening length decreases, resulting in interparticle electrostatic interactions of shorter range. The theoretical surface potential can be further related to the net protein charge Q (Home et al, 2007) ... 

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