Electrostatics double-layers

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]. 

Electrostatic double layer interaction, 12 5 Electrostatic effects, in organic separations, 21 660... 

O. Mondain-Monval, F. Leal-Calderon, J. PhUlip, and J. Bibette Depletion Forces in the Presence of Electrostatic Double-Layer Repulsion. Phys. Rev. lett. 75, 3364 (1995). 

Fig. 11. Electrostatic double layer around the charged surface of a particle [14].

Fig. 1.6 DLVO interactions showing the energetics of colloidal particles as a competition between electrostatic double-layer repulsion and van der Waals attractions. The primary minimum is due to strong short-range electron overlap repulsion (shown in Figure 1.4... 

So-called solvation/structural forces, or (in water) hydration forces, arise in the gap between a pair of particles or surfaces when solvent (water) molecules become ordered by the proximity of the surfaces. When such ordering occurs, there is a breakdown in the classical continuum theories of the van der Waals and electrostatic double-layer forces, with the consequence that the monotonic forces they conventionally predict are replaced (or accompanied) by exponentially decaying oscillatory forces with a periodicity roughly equal to the size of the confined species (Min et al, 2008). In practice, these confined species may be of widely variable structural and chemical types — ranging in size from small solvent molecules (like water) up to macromolecules and nanoparticles. 

The invention and refinement of the SFA have been among the most significant advances in experimental colloid science and have allowed researchers to identify and quantify most of the fundamental interactions occurring between surfaces in aqueous solutions as well as nonaqueous liquids. Attractive van der Waals and repulsive electrostatic double-layer forces, oscillatory (solvation or structural) forces, repulsive hydration forces, attractive hydrophobic... 

Interfacial Forces. Neighboring bubbles in a foam interact through a variely of forces which depend on the composition and thickness of liquid between them, and on the physical chemistry of their liquid—vapor interfaces. For a foam to be relatively stable, Ihe net interaction must be sufficiently repulsive at short distances to maintain a significant layer of liquid in between neighboring bubbles, Interfacial forces include ihe van der Waals inieracliun. the electrostatic double layer imeruclion. and disjoining pressure. 

In Chapter 5 we learned that, in water, most surfaces bear an electric charge. If two such surfaces approach each other and the electric double layers overlap, an electrostatic double-layer force arises. This electrostatic double-layer force is important in many natural phenomena and technical applications. It for example stabilizes dispersions.7... 

Please note that the electrostatic double-layer force is fundamentally different from the Coulomb force. For example, if we consider two identical spherical particles of radius R you cannot take Eq. (6.1), insert the total surface charge as Qi and Q2, use the dielectric permittivity of water and expect to get a reasonable result. The main differences are the free charges (ions) in solution. They screen the electrostatic field emanating from the surfaces. 

Figure 6.10 Electrostatic double-layer force between a sphere of R = 3 /um radius and a flat surface in water containing 1 mM monovalent salt. The force was calculated using the nonlinear Poisson-Boltzmann equation and the Derjaguin approximation for constant potentials (tpi = 80 mV, ip2 = 50 mV) and for constant surface charge (i/2/Ad so that at large distances both lead to the same potential.

Roughly 60 years ago Derjaguin, Landau, Verwey, and Overbeek developed a theory to explain the aggregation of aqueous dispersions quantitatively [66,157,158], This theory is called DLVO theory. In DLVO theory, coagulation of dispersed particles is explained by the interplay between two forces the attractive van der Waals force and the repulsive electrostatic double-layer force. These forces are sometimes referred to as DLVO forces. Van der Waals forces promote coagulation while the double layer-force stabilizes dispersions. Taking into account both components we can approximate the energy per unit area between two infinitely extended solids which are separated by a gap x ... 

In an aqueous medium, the electrostatic double-layer force is present. For distances x larger then the Debye length A it decays roughly exponentially F oc exp (—x/A >). 

Within the core region the profile of a drop is modified by surface forces, such as long-range van der Waals and electrostatic double-layer forces [220], These forces affect the profile in a range of 1-100 nm. They can cause a difference between the microscopic contact angle and the macroscopic one (which enters into Young s equation) [268,269], If the liquid is attracted by the solid surface and this attraction is stronger than the attraction between the... 

One of the central questions in the stability of foams is why are liquid films between two adjacent bubbles stable, at least for some time In fact, a film of a pure liquid is not stable at all and will rupture immediately. Formally this can be attributed to the van der Waals attraction between the two gas phases across the liquid. As for emulsions, surfactant has to be added to stabilize a liquid film. The surfactant adsorbs to the two surfaces and reduces the surface tension. The main effect, however, is that the surfactant has to cause a repulsive force between the two parallel gas-liquid interfaces. Different interactions can stabilize foam films [570], For example, if we take an ionic surfactant, the electrostatic double-layer repulsion will have a stabilizing effect. 

The modulation frequency is typically in the range from 100 Hz to 3 kHz, and thus much lower than the resonance frequencies of the cantilever and the scanner. This enables better control of the forces exerted on the sample. The z-mod-ulation amplitude can be varied between 10 nm and 1 pm to ensure that that the tip is retracted from the surface. Shear forces are reduced permitting investigation of soft samples because of the small duration of the tip-surface contact, between 10 3 and 10 4 s. Pulse force mode SFM has been used to map adhesion of heterogeneous polymers in dependence of temperature and molecular weight as well as map electrostatic double-layer interactions [158-160]. 

In the case of Brownian diffusion and interception, particle capture is enhanced by London attractive forces and reduced by electrostatic double layer repulsive forces. 

Across real surfaces and interfaces, the dielectric response varies smoothly with location. For a planar interface normal to a direction z, we can speak of a continuously changing s(z). More pertinent to the interaction of bodies in solutions, solutes will distribute nonuniformly in the vicinity of a material interface. If that interface is charged and the medium is a salt solution, then positive and negative ions will be pushed and pulled into the different distributions of an electrostatic double layer. We know that solutes visibly change the index of refraction that determines the optical-frequency contribution to the charge-fluctuation force. The nonuniform distribution of solutes thereby creates a non-uniform e(z) near the interfaces of a solution with suspended colloids or macromolecules. Conversely, the distribution of solutes can be expected to be perturbed by the very charge-fluctuation forces that they perturb through an e(z).5... 

Because they have so many unexpected features and because they are kind of a hybrid with electrostatic double-layer forces, ionic-charge-fluctuation forces deserve separate consideration. 

Think in terms of a capacitor. With a pure, nonconducting dielectric material there is a constant electric field between plates (see Fig. L3.20). But across a salt solution between nonreactive, nonconducting, ideally bad electrodes (no chemical reactions at interfaces), there is a spatially varying electrostatic double-layer field set up by the electrode walls (see Fig. L3.21). 

The wave equation is built from V E cx pext/ - Because electrostatic double-layer equations are easier to think about in terms of potentials rather than electric fields E = -V0, we set up the problem of ionic-charge-fluctuation forces in terms of potentials. Charges pext come from the potential 0 through the Boltzmann relation... 

In terms of potential, the electrostatic double-layer "wave" equation is... 

The classic 1948 Verwey-Overbeek text is well worth studying even today. E. J. W. Verwey and J. Th. G. Overbeek, Theory of the Stability ofLyophobic Colloids (Dover, Mineola, NY, 1999 originally published by Elsevier, New York, 1948). In 1967 Verwey told me that their studies were done in secret while Nazi soldiers controlled the Philips Laboratories where he and Overbeek pretended to do assigned work. Because they could publish nothing during the war, the world was eventually blessed with a coherent monograph that has defined much of colloid research ever since. This text is especially valuable for its sensitive, systematic treatment of electrostatic double layers. 

It is unfortunate that this macroscopic-continuum limitation is sometimes forgotten in overzealous application. The same limitation also holds in the theory of the electrostatic double layers for which we often make believe that the medium is a featureless continuum. Neglect of structure in double layers is equally risky, though, and even more common than in the computation of van der Waals forces. 

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