Colloidal particles, interaction force

We need to understand under which conditions a colloidal system will remain dispersed (and under which it will become unstable). Knowing how colloidal particles interact with one another makes possible an appreciation of the experimental results for phase transitions in such systems as found in various industrial processes. It is also necessary to know under which conditions a given dispersion will become unstable (coagulation). For example, one needs to apply coagulation in wastewater treatment so that most of the solid particles in suspension can be removed. Any two particles coming close to each other, will produce different forces. 

A suspension is a dispersion of solid particles in a liquid. A colloidal suspension is a sol. Colloidal properties become significant when the size of the parhcles is of the order of a few micrometer or less. In suspensions of large particles, for example, of some 10 pm or higher, hydrod5mamic interactions dominate the suspension flow properties emd particle packing behaviour. In colloidal suspensions interaction forces between the particles as well as hydro-dynamic interactions play a role in determining the flow and particle packing properties. 

Zypman FR (2006) Exact expressions for colloidal plane-particle interactions forces and energies with applications to atomic force microscopy. J Phys Condens Matter 18 2795-2803... 

When the colloidal particles interact with the SdFFF channel wall, the potential energy given by Eq. 3 must be corrected, so as to include the potential energy of interaction, forces, and the total potential energy, of a spherical particle in PBSdFFF is given by the relation... 

Colloids are primarily characterized by their dimensions. Several properties—for example, the interfacial area per unit mass of dispersed material and hence the capacity as adsorbent, particle-particle interaction forces, and rheological behavior—are... 

Most suspension particles dispersed in water have a charge acquired by specific adsorption of ions or ionization of surface groups, if present. If the charge arises from ionization, the charge on the particle will depend on the pH of the environment. As with other colloidal particles, repulsive forces arise because of the interaction of the electrical double layers on adjacent particles. The magnitude of the charge can be determined by measurement of the electrophoretic mobility of the particles in an applied electrical field. 

Li Y Q, Tao N J, Pan J, Garcia A A and Lindsay S M 1993 Direct measurement of interaction forces between colloidal particles using the scanning force microscope Langmuir 9 637... 

Colloidal particles can be seen as large, model atoms . In what follows we assume that particles with a typical radius <3 = lOO nm are studied, about lO times as large as atoms. Usually, the solvent is considered to be a homogeneous medium, characterized by bulk properties such as the density p and dielectric constant t. A full statistical mechanical description of the system would involve all colloid and solvent degrees of freedom, which tend to be intractable. Instead, the potential of mean force, V, is used, in which the interactions between colloidal particles are averaged over... 

Surfaces can be characterized using scaiming probe microscopies (see section B1.19). In addition, by attaching a colloidal particle to tire tip of an atomic force microscope, colloidal interactions can be probed as well [27]. Interactions between surfaces can be studied using tire surface force apparatus (see section B1.20). This also helps one to understand tire interactions between colloidal particles. 

Similarly, van der Waals forces operate between any two colloidal particles in suspension. In the 1930s, predictions for these interactions were obtained from the pairwise addition of molecular interactions between two particles [38]. The interaction between two identical spheres is given by... 

In many colloidal systems, both in practice and in model studies, soluble polymers are used to control the particle interactions and the suspension stability. Here we distinguish tliree scenarios interactions between particles bearing a grafted polymer layer, forces due to the presence of non-adsorbing polymers in solution, and finally the interactions due to adsorbing polymer chains. Although these cases are discussed separately here, in practice more than one mechanism may be in operation for a given sample. 

Comprehension of the interactions among microstructures composed of tethered chains is central to the understanding of many of their important properties. Their ability to impart stability against flocculation to suspensions of colloidal particles [52, 124, 125] or to induce repulsions that lead to colloidal crystallization [126] are examples of practical properties arising from interactions among tethered chains many more are conceivable but not yet realized, such as effects on adhesion, entanglement or on the assembly of new block copolymer microstructures. We will be rather brief in our treatment of interactions between tethered chains since a comprehensive review has been published recently of direct force measurements on interacting layers of tethered chains [127]. 

Vakarelski et al. [88] also investigated the adhesive forces between a colloid particle and a flat surface in solution. In their case they investigated a sihca sphere and a mica surface in chloride solutions of monovalent cations CsCl, KCl, NaCl, and LiCl. The pH was kept at 5.6 for all the experiments. To obtain the adhesive force in the presence of an electrostatic interaction, they summed the repulsive force and the pull-off force (coined foe by the authors ) to obtain a value for the adhesive force that is independent of the electrostatic component. 

However, in subsequent studies [23-25,88-90] it was demonstrated that in reality the particle deposition is not a purely geometric effect, and the maximum surface coverage depends on several parameters, such as transport of particles to the surface, external forces, particle-surface and particle-particle interactions such as repulsive electrostatic forces [25], polydispersity of the particles [89], and ionic strength of the colloidal solution [23,88,90]. Using different kinds of particles and substrates, values of the maximum surface coverage varied by as much as a factor of 10 between the different studies. 

The pair potential of colloidal particles, i.e. the potential energy of interaction between a pair of colloidal particles as a function of separation distance, is calculated from the linear superposition of the individual energy curves. When this was done using the attractive potential calculated from London dispersion forces, Fa, and electrostatic repulsion, Ve, the theory was called the DLVO Theory (from Derjaguin, Landau, Verwey and Overbeek). Here we will use the term to include other potentials, such as those arising from depletion interactions, Kd, and steric repulsion, Vs, and so we may write the total potential energy of interaction as... 

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