Electrolytes electrostatic double-layers

It is well-known that free films of water stabilized by surfactants can exist as somewhat thicker primary films, or common black films, and thinner secondary films, or Newton black films. The thickness of the former decreases sharply upon addition of electrolyte, and for this reason its stability was attributed to the balance between the electrostatic double-layer repulsion and the van der Waals attraction. A decrease in its stability leads either to film rupture or to an abrupt thinning to a Newton black film, which consists of two surfactant monolayers separated by a very thin layer ofwater. The thickness of the Newton black film is almost independent of the concentration of electrolyte this suggests that another repulsive force than the double layer is involved in its stability. This repulsion is the result of the structuring of water in the vicinity of the surface. Extensive experimental measurements of the separation distance between neutral lipid bilayers in water as a function of applied pressure1 indicated that the hydration force has an exponential behavior, with a decay length between 1.5 and 3 A, and a preexponential factor that varies in a rather large range. 

Sample Preparation. The polystyrene spheres to be used should be monodis-perse with a particle radius i of about 50 nm, although any size in the range i = 30 to 100 nm is suitable. Such nanospheres are available commercially as aqueous latex suspensions with 1% to 10% PS by weight. A small amount of this latex suspension should be diluted 100- to 1000-fold. Using a microsyringe, take 0.1 mL from the PS stock, deliver this into a rinsed dilution bottle, and then add 10 mL of a hltered lO-mM solution of NaCl or other 1 1 electrolyte. The purpose of this electrolyte is to partially suppress coulombic interactions (electrostatic double-layer repulsion) that can influence the diffusion constant and lead to R values that are artificially high by —10%. The electrolyte solution should be prepared from distilled water and stored at room temperature. Before use, it must be hltered through a suitable membrane (0.1-jum pore size) to remove dust particles. Avoidance of dust is cracial, and capped dilution bottles should be used. 

A simplification to this for low surface potential where the electrostatic double layers only have weak overlap leads to an exponential expression for the force between two flat interfaces (in the case of a symmetric electrolyte and symmetric surfaces)... 

For similar micellas concentrations, the effect of electrolyte will be more severe for the anionic surfactant as it will suppress the electrostatic double-layer repulsive forces acting between the micelles. For nonionic surfactant, the repulsive force between micelles is a steric force rather than an electrostatic force, such that electrolyte has less of an effect. 

Figure 7.1 Schematic diagram of interaction potential versus separation distance D for van der Waals and electrostatic double-layer interactions. The lower inset shows the collapse of the repulsive barrier as the electrolyte concentration is increased or the surface potential is decreased. At a separation distance of zero, there is an infinitely steep hard-core repulsive (or positive) interaction. (From Israelachvili 1991, reprinted with permission from Academic Press.)...

First we consider the electrostatic (double layer) interaction between two identical charged plane parallel surfaces across a solution of symmetric Z Z electrolyte. The charge of a counterion (i.e., ion with charge opposite to that of the surface) is -Ze, whereas the charge of a coion is +Ze (Z = +1, +2,. ..) with e the elementary charge. If the separation between the two planes is very large, the number concentration of both counterions and coions would be equal to its bulk value, n, in the middle of the film. However, at finite separation, h, between the surfaces the two EDL overlap and the counterion and coion concentrations in the middle of the film, io and 2o> longer equal. Because the solution inside the film is supposed to be in electrochemical (Donnan) equilibrium with the bulk electrolyte solution of concentration q, we can write 20 0 or, alternatively,... 

Electrostatic Component of AGads A major contribution to AGads in colloidal systems arises from the interaction of electrostatic double layers that form about charged particles immersed in electrolyte solutions. Oxide and protein surfaces principally develop charges by ionizing prototropic groups on their surfaces (27). 

Soon after the invention of the AFM, it was reahzed that by taking force-versus-distance measurements, valuable information about the surfaces could be obtained [2, 3]. These measurements are usually known as force measurements. The technique of force measurements with the AFM is described in detail in the third chapter. Force measurements with the AFM were first driven by the need to reduce the total force between tip and sample in order to be able to image fragile, biological structures [4, 5], Therefore it was obligatory to understand the different components of the force. In addition, microscopists tried to understand the contrast mechanism of the AFM to interpret images correctly. Nowadays most force measurements are done by surface scientists, electrochemists, or colloidal chemists who are interested in surface forces per se. Excellent short [6] or comprehensive [7] reviews about surface force measurements with the AFM have appeared. Also an older review about surface force measurements in aqueous electrolyte exists [8], This overview focuses on electrostatic double-layer forces. 

Note AFM measurements of electrostatic double-layer forces in aqueous electrolyte. Force measurements between surfactant layers are not included. They are discussed in the text. PEEK Poly(etheretherketone) EBfilm Langmuir-Blodgett film. 

Since the first measurements of the electrostatic double-layer force with the AFM not even 10 years ago, the instrument has become a versatile tool to measure surface forces in aqueous electrolyte. Force measurements with the AFM confirmed that with continuum theory based on the Poisson-Boltzmann equation and appKed by Debye, Hiickel, Gouy, and Chapman, the electrostatic double layer can be adequately described for distances larger than 1 to 5 nm. It is valid for all materials investigated so far without exception. It also holds for deformable interfaces such as the air-water interface and the interface between two immiscible liquids. Even the behavior at high surface potentials seems to be described by continuum theory, although some questions still have to be clarified. For close distances, often the hydration force between hydrophilic surfaces influences the interaction. Between hydrophobic surfaces with contact angles above 80°, often the hydrophobic attraction dominates the total force. 

Electrostatic double-layer forces are always present between charged particles or emulsion droplets in electrolyte solutions. Counterions to the emulsion droplet (ions with opposite charges to that of the drop) are attracted to the surfaces and coions are repelled. Hence, outside the charged emulsion droplet, in the so-called diffuse layer, the concentration of ions will be different to that in bulk solution, and the charge in the diffuse layer balances the surface charge. 

As an illustration, Fig. 8a shows a typical DLVO-type disjoining-pressure isotherm Tl h) (see Refs 3,4 and 62 for more details). There are two points, h = hy and h = h2> at which the condition for stable equilibrium, Eq. (42), is satisfied. In particular, h = h-y corresponds to the so-called primary film, which is stabilized by the electrostatic (double layer) repulsion. The addition of electrolyte to the solution may lead to a decrease in the height of the electrostatic barrier, IIjjj j (3,4) at high electrolyte concentration it is possible to have < P, then the primary film does not... 

The electrostatic double-layer force can be calculated using the continuum theory, which is based on the theory of Gouy, Chapman, Debye, and Hiickel for an electrical double layer. The Debye length relates the surface charge density of a surface to the electrostatic surface potential /o via the Grahame equation, which for 1 1 electrolytes can be expressed as... 

The total interaction between any two surfaces must also include the van der Waals attraction, which is largely insensitive to variations in electrolyte concentration and pH, and so may be considered as fixed for any particular solute-solvent system. Further, the van der Waals attraction wins out over the double-layer repulsion at small distances, since it is a power-law interaction, whereas the double-layer interaction energy remains finite or rises much more slowly as 0. This is the theoretical prediction that forms the basis of the so-called Derjaguin-Landau-Verwey-Over-beek (DLVO) theory (illustrated in fig. 7.2) [15]. In the DLVO theory, the interaction between two particles is assumed to consist of two contributions the van der Waals attraction and the electrostatic double-layer repulsion. At low salt concentration, the... 

Eirst, we consider the electrostatic (double layer) interaction between two identical charged plane parallel surfaces across solution of symmetrical Z Z electrolyte. The charge of a counterion (i.e., ion with charge opposite to that of the surface) is —Ze, whereas the charge of a coion is +Ze (Z = 1, 2,. ..) with e being the elementary charge. If the separation between the two... 

Figure 10.18 Electrostatic double-layer interactions and the simplest mathematical expression for two equalsized spheres under simplifying conditions (Debye-Huckel approximation). The repulsive forces decrease exponentially with distance and added electrolyte...

Part of the discrepancy between the calculated and experimental electrochemical oxidation rates of Fe(OH2)6 is due to electrostatic double-layer effects upon the apparent rate constants for electrochemical exchange. The standard rate constants measured at the formal potential for the redox couple concerned must be corrected for double-layer effects to obtain the corrected rate [45]. Such corrections depend on the electrode, electrolyte, Tafel coefficient, potential and charge of the redox couple. For the electrochemical exchange of the Fe(OH2)6 couple at the mercury/aqueous surface at 25 °C, the correction for the double-layer effects increase the rate from 2 x 10" to 1 x 10" cm sec" [38]. Thus, the disaepancy noted above is reduced to a factor of 200. 

Experimentally, electrostatic double-layer forces versus distance were first quantitatively measured in foam films [444—446]. Aqueous foam films with adsorbed charged surfactant at air-liquid interfaces are stabilized by double-layer forces, at least for some time. Voropaeva ef al. measured the height of the repulsive barrier between two platinum wires at different applied potentials and in different electrolyte solutions [447]. U sui et al. [448] observed that the coalescence of two mercury drops in aqueous electrolyte depends on the applied potential and the salt concentration. Accurate measurements between solid-liquid interfaces were first carried out between rubber and glass with a special setup [449]. In the late 1970s, DLVO force could be studied systematically with the surface forces apparatus [424,450,451]. With the introduction of the atomic force microscope, DLVO forces between dissimilar surfaces could be measured [198, 199, 452, 453]. 

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