Thin double layer systems

The anomalous surface conduction was studied extensively by O Brien and by Hunter, and they could show that the Stem layer conduction is about thirty times larger than the diffuse layer conduction at low salt concentration. This explains substantial discrepancies between the electrophoresis and the conductance estimates of zeta potential. For thin double-layer systems such as this, the zeta potential is usually calculated from the electrophoretic mobility using Smoluchowski s formula, which in O Brien s case corresponds to a zeta potential of 50 mV [8]. Complex conductivity measurements result in f = —160 mV. 

The Dynamic Mobility for Thin Double Layer Systems 63... 

The above discussion also applies to the thin double layer systems with surface conductance considered in the previous section. The surface conductance alters the double layer charge distribution, and so it gives rise to double layer distortion. 

The EMS can be applied to concentrated suspensions (>1 vol%) of particles above 50 nm and below 10 microns (Hunter 1998). Exact analytical models are available for solid concentrations below approximately 3 vol% and for thin double layers. Although there has been considerable progress in theoretical treatment of higher concentrated systems, empirical correction terms are usually used to account for the hydrodynamic and electrostatic particle-particle interactions. Depending on the quality of the data basis used for deriving these interpolating equations, very satisfactory results can be obtained (Knosche 2001 Babick et al. 2001). 

Where s is an integral number. For a very thin double layer, i.e., I/k r, Eq.(lO) returns to either Eq.(8) or (9), indicating that those two equations are only valid for a very thin double layer ease, most likely happened in aqueous systems. For a very thick double layer, even 1/(sk) r, Eq.(lO) becomes ... 

The actual value of the double-layer capacitance depends on many variables including electrode type, electrochemical potential, oxide layers, electrode surface heterogeneity, impurity adsorption, media type, temperature, etc. [1, pp. 45-48]. Capacitance of the double layer also largely depends on the intermolecular structure of the analyzed media, such as the dielectric constant (or high-frequency permittivity), concentration and types of conducting species, electron-pair donicity, dipole moment, molecular size, and shape of solvent molecules. Systematic correlation with dielectric constant is lacking and complex, due to ionic interactions in the solution. In ionic aqueous solutions with supporting electrolyte ("supported system") the values of -10-60 pF/ cm are typically experimentally observed for thin double layers and solution permittivity e - 80. The double-layer capacitance values for nonpolar dielec-... 

Numerical solutions to predict EO flows for all relevant length scales in complex geometries with arbitrary cross-sections are difficult for Debye lengths much smaller than the characteristic dimensions of the channels (e.g., the hydraulic diameter). Indeed, this is the case for typical microfluidic elec-trokinetic systems, which have Debye length-to-charmel-diameter ratios of order 10 or less. For these cases, thin double-layer assumptions are often appropriate as approximations of EO flow solutions in complex geometries. For the case of thin double layers, the electric potential throughout most of the cross-sectional area of a microcharmel is zero, and the previous equation, for the case of zero pressure gradients, reduces to ... 

Here we briefly discuss the dynamic mobility of particles that do not have thin double layers, that is systems in which the double layer thickness is more than about l/20th of the particle radius. In Section 4.4 we pointed out that double layers are usually thin in aqueous based systems, for the salt concentration is often higher than 1 mM and so double layers are typically less then 10 nm thick. However, such double layers are not thin compared to nanoparticle radii and it is these systems that we are concerned with here. 

In most electrochemical systems, the double layer is very thin (1—10 nm). The thickness is characterized by the debye length, X,... 

The surface forces apparatus (SEA) can measure the interaction forces between two surfaces through a liquid [10,11]. The SEA consists of two curved, molecularly smooth mica surfaces made from sheets with a thickness of a few micrometers. These sheets are glued to quartz cylindrical lenses ( 10-mm radius of curvature) and mounted with then-axes perpendicular to each other. The distance is measured by a Fabry-Perot optical technique using multiple beam interference fringes. The distance resolution is 1-2 A and the force sensitivity is about 10 nN. With the SEA many fundamental interactions between surfaces in aqueous solutions and nonaqueous liquids have been identified and quantified. These include the van der Waals and electrostatic double-layer forces, oscillatory forces, repulsive hydration forces, attractive hydrophobic forces, steric interactions involving polymeric systems, and capillary and adhesion forces. Although cleaved mica is the most commonly used substrate material in the SEA, it can also be coated with thin films of materials with different chemical and physical properties [12]. 

The system developed by O Grady is reproduced in Fig. 9. A key element of this arrangement is the electrochemical thin layer cell, using a combined Pd-hydrogen reference and counter electrode, thus minimizing the amount of electrolyte necessary for the electrochemical treatment. This type of cell is particularly useful for double layer studies but cannot be used for gas evolution or corrosion experiments at higher current densities. For a collection and discussion of other transfer systems the reader is referred to the review article by Sherwood [43]. 

To a first approximation, the BLM can be considered to behave like a parallel plate capacitor immersed in a conducting electrolyte solution. In reality, even such a thin insulator as the modified BLM (designated by and R, in Fig. 108) could block the specific adsorption of some species from solution and/or modify the electrochemical behavior of the system. Similarly, System C may turn out to be a semiconductor(l)-insulator-semiconductor(2) (SIS ) rather than a semiconductor(l)-semiconductor(2) (SS ) junction. The obtained data, however, did not allow for an unambiguous distinction between these two alternative junctions we have chosen the simpler of the two [652], The equivalent circuit describing the working (Ew), the reference (Eg), and the counter (Ec) electrodes the resistance (Rm) and the capacitance (C of the BLM the resistance (R ) and capacitance (Ch) of the Helmholtz electrical double layer surrounding the BLM as well as the resistance of the electrolyte solution (RSO ) is shown in Fig. 108a [652],... 

Ottewill and co-workers106,200 have used a compression method to measure the double-layer repulsion between the plate-like particles of sodium montmorillonite. This is a particularly suitable system for such studies, since the particles are sufficiently thin (c. 1 nm) for van der Waals forces to be unimportant and surface roughness is not a problem. The dispersion was confined between a semipermeable filter and an impermeable elastic membrane and an external pressure was applied via a hydraulic fluid so that the volume concentration of particles and, hence, the distance of separation between the particles could be measured as a function of applied pressure. 

Fig. 73. Dynamic behavior in S-NDR systems with high conductivity under galvanostatic conditions [22]. (a) Stable stationary domains for two values of the imposed current density, (b) 7/(4 DL plot showing stable and unstable states. The thin lines denote the homogeneous solutions, the thick ones domain solutions. Solid line stable state dashed line unstable state. The arrows indicate the transitions between homogeneous and domain states that would be observed in a galvanodynamic experiment, (c) Chaotically breathing domains that exist in small parameter regions if the characteristic time of the autocatalytic chemical variable is much faster than that of the double layer potential.

The concept of emulsion liquid membranes (ELM) was first proposed by Li in 1968 [1]. Since their inception in the late 1960s they have been referred to as surfactant liquid membranes, double emulsion membranes or ELM. Regardless of the terminology used, the workings of such systems are as follows they consist of an emulsion formed by an organic solvent and water, which can be stabilized by the addition of surfactant. This emulsion is then contacted with a continuous phase containing the desired solute, stirred to yield globules, and transported across the extremely thin membrane layer that separates internal phase droplets... 

A linear relationship exists between the ESA or CVP amplitude and the volume fraction of the suspended particles. At relatively high-volume fractions, hydrodynamic and electric double-layer interactions lead to a non-linear dependence of these two effects on volume fraction. Generally, non-linear behavior can be expected when the electric double-layer thickness is comparable to the interparticle spacing. In most aqueous systems, where the electric double layer is thin relative to the particle radius, the electro-acoustic signal will remain linear with respect to volume fraction up to 10% by volume. At volume-fractions that are even higher, particle-particle interactions lead to a reduction in the dynamic mobility. 

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