Thickness of the Electric Double Layer

As suggested before, the role of the interphasial double layer is insignificant in many transport processes that are involved with the supply of components from the bulk of the medium towards the biosurface. The thickness of the electric double layer is so small compared with that of the diffusion layer 8 that the very local deformation of the concentration profiles does not really alter the flux. Hence, in most analyses of diffusive mass transport one does not find any electric double layer terms. For the kinetics of the interphasial processes, this is completely different. Rate constants for chemical reactions or permeation steps are usually heavily dependent on the local conditions. Like in electrochemical processes, two elements are of great importance the local electric field which affects rates of transfer of charged species (the actual potential comes into play in the case of redox reactions), and the local activities... 

The microelectrophoretic mobility (jUe) is related to zeta potential ( ) via one of two equations. When the diameter of the particle is small relative to the thickness of the electrical double layer, the Huckel equation applies ... 

For ii) and iii) loosely structured layers are required, and the chains must protrude into the solution over a distance exceeding the thickness of the electrical double layer so that on approach of the surfaces, the adsorbed layers interfere before the electrical double layers overlap. 

Table 1. Effect of buffer concentration c on thickness of the electrical double layer 6 [33]...

The area of an electrode is finite and essentially constant. Similarly, the thickness of the electric double-layer does not vary by a large amount. As an empirical rule, we find that the double-layer capacitance has a value in the range 10-40 pF cm, where F is the SI unit of capacitance, the farad. Note that a capacitance without an area is not particularly useful - we need to know the complete capacitance. 

Equation (1.35) is known as the Debye-Hiickel or Gui-Chapman equation for the equilibrium double layer potential. In terms of the original variable x (1.34), (1.35) suggest e1/2(r(j) is the correct scale of ip variation, that is, the correct scale for the thickness of the electric double layer. At the same time, it is observed from (1.32) that for N 1 the appropriate scale depends on N, shrinking to zero when N — oo (ipm — — oo). This illustrates the previously made statement concerning the meaningfulness of the presented interpretation of relectric potential

(—oo) — 0, < (oo) — —oo). 

Finally, if the thickness of the electrical double layer (diffuse layer) in the droplet is comparable with r, the r dependence of kqbs will be dependent on the TBA+ concentration in the droplet since the spatial distribution of the inner electric potential of the droplet varies with [TBA+TPB ], However, since results analogous with those in Figure 14a ([TBA+TPB ] = 10 mM) have been obtained even at [TBA+TPB"] = 5mM (Aodiffuse layer effect does not contribute to the r effect on kobs at r > 1 /an. 

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... 

What happens when the dimensions are furthermore reduced Initially, an enhanced diffusive mass transport would be expected. That is true, until the critical dimension is comparable to the thickness of the electrical double layer or the molecular size (a few nanometers) [7,8]. In this case, diffusive mass transport occurs mainly across the electrical double layer where the characteristics (electrical field, ion solvent interaction, viscosity, density, etc.) are different from those of the bulk solution. An important change is that the assumption of electroneutrality and lack of electromigration mass transport is not appropriate, regardless of the electrolyte concentration [9]. Therefore, there are subtle differences between the microelectrodic and nanoelectrodic behaviour. 

The potential in the diffuse layer decreases exponentially with the distance to zero (from the Stem plane). The potential changes are affected by the characteristics of the diffuse layer and particularly by the type and number of ions in the bulk solution. In many systems, the electrical double layer originates from the adsorption of potential-determining ions such as surface-active ions. The addition of an inert electrolyte decreases the thickness of the electrical double layer (i.e., compressing the double layer) and thus the potential decays to zero in a short distance. As the surface potential remains constant upon addition of an inert electrolyte, the zeta potential decreases. When two similarly charged particles approach each other, the two particles are repelled due to their electrostatic interactions. The increase in the electrolyte concentration in a bulk solution helps to lower this repulsive interaction. This principle is widely used to destabilize many colloidal systems. 

Debye-Hiickel parameter k (the Debye length), which has the dimension of length, serves as a measure for the thickness of the electrical double layer. Figure 1.5 plots the... 

When the concentration of counterions in the dispersion medium is smaller, the thickness of the electric double layer is larger. Two approaching colloid particles cannot come close to each other because of the thicker electric double layer, therefore, the colloid is stable. Now, visualize adding more counterions. When the concentration is increased, the attracting force between the primary charges and the added counterions increases causing the double layer to shrink. The layer is then said to be compressed. As the layer is compressed sufficiently by the continued addition of more counterions, a time will come when the van der Waals force exceeds the force of repulsion and coagulation results. 

In our earlier work, the mouth diameter of the Au nanotubes was 10 nm, and the rectification observed resulted from electrostatic interactions between cations traversing the nanotube and fixed surface charge (due, e.g., to adsorbed CP) at the nanotube mouth [49]. This mechanism applies only when the mouth diameter is comparable to the thickness of the electrical double layer associated with the fixed surface charge, and this is not the case for the larg mouth-diameter nanotubes used here (Table 24.3). This is proven by the fact that without attached DNA molecules, these nanotubes do not rectify, even though there is adsorbed CP on the nanotube walls (Figure 24.13A). In contrast, the DNA-containing nanotubes rectify the ion current. 

But often more important than the effects of the electrolytes that influence the thickness of the electric double layer are many solutes that, upon adsorption onto the colloid surface, reduce or modify the surface charge. The specific adsorption of H, OH, metal ions, and ligands (as well as the attachment of polymers) to the colloid surface affects the surface charge and the surface potential and, in turn, the colloid stability. 

The extent of dissolution is influenced by the amounts of low-molecular-weight electrolyte present. Excess electrolyte increases the ionic strength outside the humic structures relative to that inside, and it decreases the thickness of the electrical double layer causing the macromolecules to contract. At high salt concentrations hydration is curtailed and dissolution may not take place. 

Electrically charged particles in aqueous media are surroimded by ions of opposite charge (counterions) and electrolyte ions, namely, the electrical double layer. The quantity He represents the energy of repulsion caused by the interaction of the electrical double layers. The expression for He depends on the ratio between the particle radius and the thickness of the electrical double layer, k, called the Debye length. For K.a > 5 (Quemada and Berli, 2002) ... 

Experimental results showed that treatment of CAJ with a cationic resin decreased the zeta ( surface) potential of the particles, decreased the ionic strength, and consequently increased the thickness of the electrical double layer surrounding the particles (Debye length), but did not change cloud... 

The potential energy of repulsion Vr depends on the size and shape of the dispersed particles, the distance between them, their surface potential To, the dielectric constant sr of the dispersing liquid, and the effectiveness thickness of the electrical double layer 1 /k (Chapter 2, Section I), where... 

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