Electrostatic inter-particle force

Abstract. The stability of suspensions/emulsions is under consideration. Traditionally consideration of colloidal systems is based on inclusion only Van-der-Waals (or dispersion) and electrostatic components, which is refereed to as DLVO (Derjaguin-Landau-Verwey-Overbeek) theory. It is shown that not only DLVO components but also other types of the inter-particle forces may play an important role in the stability and colloidal systems. Those contributions are due to hydrodynamic interactions, hydration and hydrophobic forces, steric and depletion forced, oscillatory structural forces. The hydrodynamic and colloidal interactions between drops and bubbles emulsions and foams are even more complex (as compared to that of suspensions of solid particles) due to the fluidity and deformability of those colloidal objects. The latter two features and thin film formation between the colliding particles have a great impact on the hydrodynamic interactions, the magnitude of the disjoining pressure and on the dynamic and thermodynamic stability of such colloidal systems. 

Solid materials have a cohesive stmcture, which depends on the interaction between the primary particles. The cohesive stmcture leads indispensably to a void space, which is not occupied by the composite particles such as atoms, ions, and line particles. Consequently, the state and population of such voids strongly depends on the inter-particle forces. The inter-particle forces are different from one system to another chemical bonding, van der Waals force, electrostatic force, magnetic force, surfece tension of adsorbed films on the primary particles, and so on. Even die single crystalline solid, which is composed of atoms or ions has intrinsic voids and defects. Therefore, pores in solids are classified into intra-particle pores and inter-particle pores (Table 9.6) [80]. 

In this category, among the molecular, electrostatic and magnetic inter-particle bonds, interest is primarily centered on the van der Waals-type attractive forces that may predominate in the absence of liquid and solid bonds. The force of the van der Waals attraction between two spheres of equal size is (R4)... 

In nano materials the porosity is controlled by the interaction of inter-intra particle forces, electrostatic forces and intra-particle forces within the well-defined nanostructural framework. 

A sufficiently dense set of particles (in terms of the number of particles per unit volume) can give rise to clusters (often also called floes), which gather particles together. Inter-particular forces such as the Van der Waals forces and electrostatic forces are responsible for these phenomena. The Van der Waals force is attractive. It therefore promotes the formation of clusters. The electrostatic force is repulsive, and opposes it. We have briefly described in section 13.2.5 the interparticular forces and their effects, but we shall not discuss these issues any further. It is nonetheless useful to recall that, generally speaking, the more spontaneous is the formation of clusters, the smaller is the size of elementary particles. For natural particles, sediments are said to be cohesive (silts) when the elementary particles have a size under 60 am. Particles of a size greater than 60 j,m are non-cohesive they are referred to as sands. 

A key to both methods is the force field that is used,65 or more precisely, the inter- and possibly intramolecular potentials, from which can be obtained the forces acting upon the particles and the total energy of the system. An elementary level is to take only solute-solvent intermolecular interactions into account. These are typically viewed as being electrostatic and dispersion/exchange-repulsion (sometimes denoted van der Waals) they are represented by Coulombic and (frequently) Lennard-Jones expressions ... 

In the theory developed by Derjaguin and Landau (24) and Verwey and Overbeek (25.) the stability of colloidal dispersions is treated in terms of the energy changes which take place when particles approach one another. The theory involves estimations of the energy of attraction (London-van der Walls forces) and the energy of repulsion (overlapping of electric double layers) in terms of inter-oarticle distance. But in addition to electrostatic interaction, steric repulsion has also to be considered. 

In Unit 2.3 we learned about hydrogen bonds. These are inter-molecular electrostatic forces of attraction between certain polar molecules (often water). When an ionic solid is stirred into water, the polar water molecules surround the particles and electrostatic bonds are formed between the oxygen and the metal ion and also between the hydrogen and the anion. These bonds help the solid to dissolve and break into individual ions (Figure 4.6.3). This process is called hydration. 

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