Solid Debye length

The electroviscous effect present with solid particles suspended in ionic liquids, to increase the viscosity over that of the bulk liquid. The primary effect caused by the shear field distorting the electrical double layer surrounding the solid particles in suspension. The secondary effect results from the overlap of the electrical double layers of neighboring particles. The tertiary effect arises from changes in size and shape of the particles caused by the shear field. The primary electroviscous effect has been the subject of much study and has been shown to depend on (a) the size of the Debye length of the electrical double layer compared to the size of the suspended particle (b) the potential at the slipping plane between the particle and the bulk fluid (c) the Peclet number, i.e., diffusive to hydrodynamic forces (d) the Hartmarm number, i.e. electrical to hydrodynamic forces and (e) variations in the Stern layer around the particle (Garcia-Salinas et al. 2000). 

The basic difference between metal-electrolyte and semiconductor-electrolyte interfaces lies primarily in the fact that the concentration of charge carriers is very low in semiconductors (see Section 2.4.1). For this reason and also because the permittivity of a semiconductor is limited, the semiconductor part of the electrical double layer at the semiconductor-electrolyte interface has a marked diffuse character with Debye lengths of the order of 10 4-10 6cm. This layer is termed the space charge region in solid-state physics. 

This same theoretical approach can also apply to the space charge layer formed in solid semiconductors. Instead of the concentration of ions in aqueous solution, however, the concentration of electrons or holes is used with the space charge layer in semiconductors. Then, the Debye length is given by Eqn. 5-7 ... 

In addn, for an ionized gas to be called a plasma, it must have an equal number of pos and neg charges for, by definition, a plasma has no net charge. Regions termed "sheaths , having large (net charges) do develop at the plasma boundaries. Such sheaths are to the plasma what the surface is to a solid or liquid, and their thickness is of the order of the "Debye length ... 

We can observe electro-osmosis directly with an optical microscope using liquids, which contain small, yet visible, particles as markers. Most measurements are made in capillaries. An electric field is tangentially applied and the quantity of liquid transported per unit time is measured (Fig. 5.13). Capillaries have typical diameters from 10 fim up to 1 mm. The diameter is thus much larger than the Debye length. Then the flow rate will change only close to a solid-liquid interface. Some Debye lengths away from the boundary, the flow rate is constant. Neglecting the thickness of the electric double layer, the liquid volume V transported per time is... 

Figure 35. Kroger-Vink diagram of boundary layers for our model substance MX when 5(v m) > 0. The broken lines refer to the ionic defect concentrations at (two) different distances from the interface. The behavior of the electrons in boundary regions is not shown.The approach to the bulk values (printed boldface) for extreme abscissa values is attributable to the disappearing Debye length. The mirror symmetry on compa-rison of v m with Mi follows from Eq. (6S).94 (Reprinted from J. Maier, Ionic Conduction in Space Charge Regions. Prog. Solid St. Chem. 23, 171-263. Copyright 1995 with permission from Elsevier.)...

Figure 36. Defect concentration and conductance effects for three different thicknesses Li L2 Lj. The mesoscale effect on defect concentration (l.h.s.) discussed in the text, when L < 4J, is also mirrored in the dependence of the conductance on thickness (r.h.s.). If the boundary layers overlap , the interfacial effect previously hidden in the intercept is now resolved. It is presupposed that surface concentration and Debye length do not depend on L. (Both can be violated, c , at sufficiently small L because of interaction effects and exhaustibility of bulk concentrations.)36 94 (Reprinted from J. Maier, Defect chemistry and ion transport in nanostructured materials. Part II. Aspects of nanoionics. Solid State Ionics, 157, 327-334. Copyright 2003 with permission from Elsevier.)...

A plane (m) is associated with an excess concentration of elections near the physical surface of the electrode, represented by a solid line. The inner Helmholtz plane (ihp) is associated with ions that are specifically adsorbed onto the metal surface. The outer Helmholtz plane (ohp) is the plane of closest approach for solvated ions that are free to move within the electrolyte. The ions within the electrolyte near the electrode surface contribute to a diffuse region of charge. The diffuse region of charge has a characteristic Debye length. 

Figure 10. Comparison of charge distributions for different types of boundary conditions for the same bulk plasma parameters. The Debye length is rn/o = 10 for (1) and (la), and rD/a = 2 for (2) and (2a). Dashed and solid lines relate to the BC (I) and (II), respectively.

Fig. 4.10. Sketch of adsorption of polydisperse particles at (a) low and (b) high salt concentrations. Dotted lines show the effective particle radius (or interaction distance), (c) Surface coverage of the polystyrene particles versus na ( a is a dimensionless screening parameter, where k is the inverse Debye length and a the particle diameter). The more polydisperse particles (41 versus 107nm) have a slightly increased coverage at high na. Solid curves are approximations derived from the effective hard sphere model (see [89] for further details)...

The contribution of the solid content is frequently forgotten when evaluating the stability of the sols. However, because a number of ions dependent on pH and ionic strength are kinetically bound to the particle surface, the interrelationship between the Debye length and the particle load may be investigated. The example provided is a monodisperse latex sol of 100 mn particle size (Figure 8.32).5 ... 

In Chap. 5, the notion of a Debye length was briefly alluded to, and it was shown that whenever two dissimilar phases come into contact with each other, an electrified interface will result. This so-called double layer acts as a capacitor with properties and responses different from those of the bulk material. The behavior and interpretation of interfacial phenomena are quite complex and not within the scope of this book they fall more in the realm of solid-state electrochemistry and will not be discussed further. 

Nanowires are seen as a solution with which to improve the sensitivity, selectivity, stability and response time of metal-oxide gas sensors. Meier et al (2007) grew Sn02 nanowires of 100 nm in diameter by the vapor-solid growth method. For testing, they were deposited onto micromachined hotplates with a focused ion beam scanning electron microscope (FIB-SEM), as shown in Fig. 6.19. Due to their diameter being similar to the Debye length, a completely depleted conduction channel can be obtained. Maximum response to CO and NH3 occurred at about 260°C. 

This chapter is concerned with the mechanisms of formation of the electrical double layer at a dielectric solid/electrolytic solution interface. When such a contact occurs, the solid s surface acquires a certain charge due to the dissociation of surface ionizable groups and adsorption of ions from solution. Since the whole system is assumed to be electroneutral, the solution has to bear an equal charge of opposite sign. This charge is effectively confined to a thin layer near the dividing surface, termed the diffuse double layer. Its thickness is characterized by the reciprocal Debye length. 

A mmiolayer of ionic species can be adsorbed at the interface with a solid substrate (a Helmholtz monolayer), Fig. 10.10a. A diffuse layer of ions of the opposite sign with density p(z) provides the overall electrical neutrality. This mechanism is not specific for liquid crystals, it takes place in the isotropic liquids as well. However, in liquid crystals the surface field E = 47cPs rf can interact with the director and change orientation of the latter. Qualitatively, the ionic polarization can be estimated as Psurf = where n is the number of charges q and is a characteristic (Debye) length for the charge distribution. 

An important quantity in solid and liquid electrolytes is the Debye length Ld, given by... 

Fig. 4. Effective linear charge density efr of a charged cylinder derived by superimposing the far field (large r) Poisson-Boltzmann potential field onto the potential field predicted by use of the Debye-Hiickel approximation. The solid lines correspond to different values of ax, where a is the cylinder radius and x is the Debye length the electrol3de is monovalent. For comparison, the counterion condensation prediction for is shown as a dotted line. Adapted from Ref. 51.

VOINOV You said the Debye length you calculate in the case of solid electrolyte is smaller than atomic dimension and consequently diffuse layer effects are irrelevant- Presumably, you use for this calculation the Debye length formula developed for the case of aqueous electrolytes. As you have stressed, in many solid electrolytes, only one species can migrate and in that case the solution of Poisson s equation is not the same as in the case of liquid electrolytes. As long as you do not have this solution and have shown it can be approximated by an exponential, and that this exponential is the same as in the case of liquid electrolytes, it seems to me difficult to calculate a Debye length in solid electrolytes. 

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