Electrostatic double-layer force

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]. 

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... 

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... 

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. 

For the case of purely attractive forces (such as Lon-don-van der Waals forces) the length Sjr over which they act is a useful characteristic. An attractive force which acts over a distance which is much less than Sc will not contribute substantially to the overall rate. When repulsive forces (such as the electrostatic double-layer forces) are also present, they may effectively prevent particles from arriving at the collector, even when they act only over a very short distance. For this reason the decay length alone cannot characterize the relative importance of the joint effect of attractive and repulsive farces. Useful characteristics of their combined effect may be obtained by considering the total potential energy of interaction between the particle and the collector. 

Fig. 8. (A) Measured forces between two charged mica surfaces in 10" M KCl, where beyond 30 A (and out to 500 A) the repulsion is well described by conventional electrostatic double-layer force theory. Below 30 A there is an additional hydration repulsion, with oscillations superimposed below 15 A. (B) Forces between two uncharged lecithin bilayers in the fluid state in water. At long range there is an attractive van der Waals force, and at short range (i.e., below 25 A) there is a monotonically repulsive steric hydration force. (C) Forces between two hydrophobized mica surfaces in water where the hydrophobic interaction is much stronger than could be expected from van der Waals forces alone. From Israelachvili and Marra (1986).

Even though the components of the total interaction potential between such complex adsorbents as solid carbons and a wide range of adsorbates can be grouped in many different ways 315,316], it is convenient and meaningful to consider only the London dispersion (induced dipole) forces and the electrostatic (double-layer) forces [620,621,76,77]. 

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. 

First measurements of the electrostatic double-layer force with the AFM were done in 1991 [9, 10]. The electrostatic double layer depends on the surface charge density (or the surface potential) and the ionic strength. A brief introduction to the theory of the electrostatic force is given in Chap. 4. The electrostatic double-layer force is in many cases responsible for the stabilization of dispersions. An AFM experiment can be regarded as directly probing the interaction between a sample surface and a colloidal particle (or the AFM tip). Since the AFM tip is relatively small, this interaction can be probed locally. The lateral spacial resolution can be of the order of few nanometers. 

With the SFA, the main predictions of the DLVO theory were verified. In particular the electrostatic double-layer force was analyzed for difierent salts and under... 

Analyzing Electric Doable Layers with the Atomic Force Microscope 235 Tab. 1 Measurements of electrostatic double-layer forces with the AFM... 

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. 

When two charged surfaces approach each other at some point, the electric double layers start to overlap and a force, also called disjoining pressure, begins to act [13, 145]. This electrostatic double-layer force decays roughly exponentially. When the surface potentials of both surfaces are below approximately 25 to 50 mV, the force between a spherical tip and a flat sample can be approximated in an analytical form [146-149] ... 

Characteristic decay lengths Xo determined with the SFA, the osmotic stress method, or the AFM range from 0.2 to 1.4 nm. Typical amphtudes are A = 10 to 10 J m . In contrast to the electrostatic double-layer force, hydration forces tend to become stronger and longer ranged with increasing salt concentration, especially for divalent cations. 

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. 

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