Fixed surface potential

Here, is the dimensionless surface potential and is the value of d>j for h o°. Equation 5.179 expresses the dependence riei(/ ) in a parametric form riei(0), hifd). Fixed surface potential or charge means that or s, does not depend on the film thickness h. The latter is important to be specified when integrating H(h) or f(h) (in accordance with Equations 5.162 to 5.165) to calculate the interaction energy. 

FIGURE 5.24 Electrostatic disjoining pressure at (a) fixed surface potential, H. and (b) fixed surface charge density, IIei> both of them plotted vs. the film thickness h. /ji and /j2 are the potentials of the two surfaces Oj, and Os2 are the respective surface charge densities. 

A long thin cylindrical tube of radius a = 5 X 10 m and length L = 0.1 m is closed at both ends by electrodes, across which a voltage drop A(f> = 10 V is applied. The tube contains an ideal dilute aqueous solution of a fully dissociated doubly charged symmetrical binary salt (z = 2) at a concentration Cg = 1 mol m . The tube wall has a fixed surface potential = 1.43x10 V. The temperature T = 25°C, the permittivity e = 7x... 

Figure 4. Electrostatic disjoining pressure versus the film thickness, h a) Ilei at fixed surface potential y/s and b) flei at fixed surface charges and cTs2-...

E. Barouch and S. Kulkarni,/. Colloid Interface Sci., 112,396 (1986). Exact Solution of the Poisson-Boltzmann Equation for Two Spheres with Fixed Surface Potentials. 

Electrophoresis uses the force of an apphed electric field to move molecules or particles, often through a polymer matrix. The electric field acts on the intrinsic charge of a substance, and the force on each substance is proportional to the substance s charge or surface potential. The resulting force on the substance results in a distinct velocity for the substance that is proportional to the substance s surface potential. If two different substances have two different velocities, an electric field apphed for a fixed amount of time results in different locations on the matrix for these substances. 

The reactivity modification or the reaction rate control of functional groups covalently bound to a polyelectrolyte is critically dependent on the strength of the electrostatic potential at the boundary between the polymer skeleton and the water phase ( molecular surface ). This dependence is due to the covalent bonding of the functional groups which fixes the reaction sites to the molecular surface of the polyelectrolyte. Thus, the surface potential of the polyion plays a decisive role in the quantitative interpretation of the reactivity modification on the molecular surface. 

Shear rate When, a melt moves in a direction parallel to a fixed surface, such as with a screw barrel, mold runner and cavity, or die wall, it is subject to a shearing force. As the screw speed increases, so does the shear rate, with potential advantages and disadvantages. The advantages of an increased shear rate are a less viscous melt and easier flow. This shear-thinning action is required to move the melt. 

Austin et al. [132] measured the ionic strength dependence of the liposome-water distribution of several acidic and basic drugs and modelled the data with a combination of electrostatic and ion pair models. They concluded that the increased apparent Dmw values at higher ionic strength were due primarily to the reduction in surface potential and not to ion pairing. Ion pairing was also excluded because the apparent Dmw varied at fixed ionic strength with the... 

Electrocapiilary phenomena on Hg-electrode in presence and absence of an adsorbate (camphor). From a measurement of interfacial tension (a) (e.g., from droptime of a Hg-electrode) or of differential capacity (d) (e.g., by an a.c-method) as a function of the electrode potential (established by applying a fixed potential across tine Hg-electrolyte interface) one can calculate the extent of adsorption (b) (from (a) by the Gibbs Equation) and of the structure of the interface as a function of the surface potential. Figs, a, c and d are interconnected through the Lippmann Equations. 

At oxide surfaces, the surface activities of H+ and OH are not fixed in a similar way. Then the variation in surface potential with solution activity of H+ depends on the chemical and electrostatic properties of the interface. For the many oxides that are insulators, it is much more difficult to obtain a measurement of the surface-solution potential differences than it is for conductors such as Agl. Thus there is uncertainty whether the dependence of surface potential on pH is approximately Nernstian or significantly sub-Nernstian. 

In Eq. 30, Uioo and Fi are the activity in solution and the surface excess of the zth component, respectively. The activity is related to the concentration in solution Cioo and the activity coefficient / by Uioo =fCioo. The activity coefficient is a function of the solution ionic strength I [39]. The surface excess Fi includes the adsorption Fi in the Stern layer and the contribution, f lCiix) - Cioo] dx, from the diffuse part of the electrical double layer. The Boltzmann distribution gives Ci(x) = Cioo exp - Zj0(x), where z, is the ion valence and 0(x) is the dimensionless potential (measured from the Stern layer) obtained by dividing the actual potential, fix), by the thermal potential, k Tje = 25.7 mV at 25 °C). Similarly, the ionic activity in solution and at the Stern layer is inter-related as Uioo = af exp(z0s)> where tps is the scaled surface potential. Given that the sum of /jz, is equal to zero due to the electrical... 

Figure 5-12. Vacancy concentration distribution and the course of oxygen potential during interdiffusion in the AO-BO couple [T. Pfeiffer (1987), T. Pfeiffer, K. Winters (1990)]. The (A, B)0 solid solution is characterized by the following parameters DA/Dn = 3 dR Tin Nv/d In = y Q/u0/QR Tin A, -- 2 t = 5.6x lO11 s. rt, T2, r3 are external surfaces with fixed oxygen potential. tA is a hypothetical internal surface far away from T (/ = 1,..., 3). N indicates a normalized fraction.

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