Force double layer

Fig. VI-6. The force between two crossed cylinders coated with mica and carrying adsorbed bilayers of phosphatidylcholine lipids at 22°C. The solid symbols are for 1.2 mM salt while the open circles are for 10.9 roM salt. The solid curves are the DLVO theoretical calculations. The inset shows the effect of the van der Waals force at small separations the Hamaker constant is estimated from this to be 7 1 x 10 erg. In the absence of salt there is no double-layer force and the adhesive force is -1.0 mN/m. (From Ref. 66.)...

Miyatani T, Florii M, Rosa A, Fu]ihira M and Marti O 1997 Mapping of electric double-layer force between tip and sample surfaces in water with pulsed-force-mode atomic force microscopy Appl. Phys. Lett. 71 2632... 

The well-known DLVO theory of coUoid stabiUty (10) attributes the state of flocculation to the balance between the van der Waals attractive forces and the repulsive electric double-layer forces at the Hquid—soHd interface. The potential at the double layer, called the zeta potential, is measured indirectly by electrophoretic mobiUty or streaming potential. The bridging flocculation by which polymer molecules are adsorbed on more than one particle results from charge effects, van der Waals forces, or hydrogen bonding (see Colloids). 

Fig. 3. Attraction—repulsion potentials as a function of distance between particle centers. Curve 1 represents the attractive potential caused by van der Waals forces, curve 2 is the repulsive potential caused by double-layer forces, and curve 3 is the resultant force experienced by the two particles.

Surface forces measurement is a unique tool for surface characterization. It can directly monitor the distance (D) dependence of surface properties, which is difficult to obtain by other techniques. One of the simplest examples is the case of the electric double-layer force. The repulsion observed between charged surfaces describes the counterion distribution in the vicinity of surfaces and is known as the electric double-layer force (repulsion). In a similar manner, we should be able to study various, more complex surface phenomena and obtain new insight into them. Indeed, based on observation by surface forces measurement and Fourier transform infrared (FTIR) spectroscopy, we have found the formation of a novel molecular architecture, an alcohol macrocluster, at the solid-liquid interface. 

FIG. 11 Force profiles between poly(glutamic acid), 2C18PLGA(44), brushes in water (a) at pH = 3.0 (HNO3), (b) at pH 10 (KOH) 1/k represents the decay length of the double-layer force. The brush layers were deposited at tt = 40 mN/m from the water subphase at pH = 3.0 and 10, respectively. 

Althongh van der Waals forces are present in every system, they dominate the disjoining pressnre in only a few simple cases, such as interactions of nonpolar and inert atoms and molecnles. It is common for surfaces to be charged, particularly when exposed to water or a liquid with a high dielectric constant, due to the dissociation of surface ionic groups or adsorption of ions from solution, hi these cases, repulsive double-layer forces originating from electrostatic and entropic interactions may dominate the disjoining pressure. These forces decay exponentially [5,6] ... 

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]. 

Double-jet crystal growth method, 19 179 Double-layer compression, 11 631 Double-layer forces, flocculation and,... 

Double-layer forces are commonly used to induce repulsive interactions in colloidal systems. However, the range of electrostatic forces is strongly reduced by increasing the ionic strength of the continuous phase. Also, electrostatic effects are strong only in polar solvents, which is a severe restriction. An alternative way to create long-range repulsion is to adsorb macromolecules at the interface between the dispersed and the continuous phase. Polymer chains may be densely adsorbed on surfaces where they form loops and tails with a very broad distribution of sizes... 

The contribution of double-layer forces to the osmotic pressure of HIPEs was also investigated [98], These forces arise from the repulsion between adjacent droplets in o/w HIPEs stabilised by ionic surfactants. It was observed that double-layer repulsive forces significantly affected jt for systems of small droplet radius, high volume fraction and low ionic strength of the aqueous continuous phase. The discrepancies between osmotic pressure values observed by Bibette [97] and those calculated by Princen [26] were tentatively attributed to this effect. 

Finally, some studies have been performed on the addition of salt to the aqueous phase of oil-in-water HIPEs [109]. For systems stabilised by ionic surfactants, increasing salt concentration reduces the double-layer repulsion between droplets however, stability is more or less maintained, probably due to steric and polarisation repulsions. Above a sufficiently high salt concentration, emulsions become unstable due to salting-out of the surfactant into the oil-phase. For nonionic surfactants, the situation is similar, except that there are no initial double-layer forces. In addition, Babak [115] found that increasing the electrolyte concentration reduced the barrier to coagulation between emulsion droplets, and therefore increased coalescence. Generally, therefore, stability of o/w HIPEs is not enhanced by salt addition. 

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... 

More detailed and advanced information on these forces can be found in the book by Israelachvili (1991), which is devoted completely to intermolecular and surface forces. Here, we focus on the essential basic information and examples. Before we proceed to a physical explanation of these forces and the necessary equations, it is useful to explore the role played by the van der Waals forces in colloid stability since this theme reappears in our discussions of electrical double-layer forces in Chapter 11 and polymer-induced forces in Chapter 13. 

Electrostatic and electrical double-layer forces play a very important role in a number of contexts in science and engineering. As we see in Chapter 13, the stability of a wide variety of colloids, ranging from food colloids, pharmaceutical dispersions, and paints, to colloidal contaminants in wastewater, is affected by surface charges on the particles. The filtration efficiency of submicron particles can be diminished considerably by electrical double-layer forces. As we point out in Chapter 13, coagulants are added to neutralize the electrostatic effects, to promote aggregation, and to enhance the ease of separation. 

Israelachvili, J. N., Inter molecular and Surface Forces, 2d ed., Academic Press, New York, 1991. (Graduate and undergraduate levels. The objective of this excellent reference is to relate atomic-and molecular-level interactions to surface forces. Chapter 12 discusses electrical double-layer forces and how they can be measured using the surface force apparatus (which we have described in Chapter 1).)... 

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 >). 

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