Colloids interparticle forces

In this group of disperse systems we will focus on particles, which could be solid, liquid or gaseous, dispersed in a liquid medium. The particle size may be a few nanometres up to a few micrometres. Above this size the chemical nature of the particles rapidly becomes unimportant and the hydrodynamic interactions, particle shape and geometry dominate the flow. This is also our starting point for particles within the colloidal domain although we will see that interparticle forces are of great importance. 

Once nanoparticles have been formed, whether in an early state of growth or in a more or less final size, their fate depends on the forces between the individual particles and between particles and solid surfaces in the solution. While particles initially approach each other by transport in solution due to Brownian motion, convection, or sedimentation, when close enough, interparticle forces will determine their final state. If the dominant forces are repulsive, the particles will remain separate in colloidal form. If attractive, they will aggregate and eventually precipitate. In addition, they may adsorb onto a solid surface (the substrate or the walls of the vessel in which the reaction is carried out). For CD, both attractive particle-sur-... 

Leong, Y.K., Scales, P.J., Healy, T.W., Boger, D.V. (1995). Interparticle forces arising from adsorbed polyelectrolytes in colloidal suspensions. Colloids and Surfaces A Physicochemical and Engineering Aspects, 95, 43-52. 

We have already introduced the idea that the primary particles of a dispersed system tend to associate into larger structures known as aggregates. The nature of the interparticle forces responsible for this aggregation is one of the most examined areas of colloid science. We defer our discussion of the aggregation (or coagulation) process until Chapter 13, but a few remarks about aggregates — the kinetic units that result from that process —and how their dimensions are represented quantitatively are in order at this time. 

The stability and the structure of dispersions (structure here means the spatial organization of the colloidal particles) are topics of considerable research activity currently there is a lot that we do not know despite the long-standing focus on these topics in colloid science. The first step in approaching problems in this area is to study the origin and the nature of the interparticle forces and how they affect coagulation in dilute dispersions. This is what we focus on in this chapter. 

In Section 13.2, we begin with a closer look at one of the applications we alluded to in Vignette 1.5 in Chapter 1 (colloidal processing of ceramics) in order to gain some perspective on how interparticle forces influence the structure of a dispersion. 

Our objective in this chapter is to establish the quantitative connections between interparticle forces and colloid stability. Before we consider this it is instructive to look at the role of interaction forces in a larger context, that is, the relation between interparticle forces and the microstructure of dispersions and the factors that determine such a relation. These aid us in appreciating the underlying theme of this chapter, namely, the manipulation of interparticle forces to control the properties of dispersions. 

FIG. 13.2 Schematic illustration of the relation between the interparticle forces and the corresponding microstructure observed in dense, monodisperse colloids. (Adapted with permission from D. R. Ulrich, Chem. and Eng. News, 28-35, January 1, 1990.)... 

Clearly, W is a function of any property of the dispersion that affects the strength of the interparticle forces and the energy barrier that slows down (or prevents) coagulation. A classical goal of colloid science has been to develop the equations necessary to predict the extent of stability of dispersions so that the results could be used in combination with the theories of interaction forces developed in previous chapters to promote or prevent the stability of dispersions. 

The question to be discussed is whether saturation of the electric field (asserted by Proposition 2.1) implies saturation of the interparticle force of interaction. Consider for definiteness repulsion between two symmetrically charged particles in a symmetric electrolyte solution. In the onedimensional case (for parallel plates) the answer is known—the force of repulsion per unit area of the plates saturates. (This follows from a direct integration of the Poisson-Boltzmann equation carried out in numerous works, primarily in the colloid stability context, e.g., [9]. Recall that again in vacuum, dielectrics, or an ionic system with a linear screening, the appropriate force grows without bound with the charging of the particles.)... 

Colloidal, interparticle interactions (such as electrostatic forces) can apply additional torques to the particles and influence their motion. 

The DLVO-theory is named after Derjaguin, Landau, Verwey and Overbeek and predicts the stability of colloidal suspensions by calculating the sum of two interparticle forces, namely the Van der Waals force (usually attraction) and the electrostatic force (usually repulsion) [19],... 

Stabilising a colloidal suspension implies that the total interparticle potential decreases with increasing inter particle distance. The different kinds of stabilisation all use some of the above-mentioned interparticle forces. 

Monte Carlo Simulation of Brownian Coagulation over the Entire Range of Particle Sizes from Near Molecular to Colloidal Connection between Collision Efficiency and Interparticle Forces... 

J. H. Clint and S. E. Taylor, Particle size and interparticle forces of overbased detergents a Langmuir trough study, Colloids Surf. 65, 61-67 (1992). 

In Chapter 12 of this book, the mechanical properties of ceramic suspensions, pastes, and diy ceramic powders are discussed. Ceramic suspension rheology is dependent on the viscosity of the solvent with polymeric additives, particle volume fraction, particle size distribution, particle morphology, and interparticle interaction energy. The interparticle forces play a veiy important role in determining the colloidal stability of the suspension. If a suspension... 

FIGURE 12.1 (a) Hydrophilic colloid encased in bound water (b) interparticle forces as a function of interparticle distance. 

Double layers in non-polar media recur in colloid stability (Volume IV). The slow decay dv /dr (or dy//dx) means that the field strength is low. and so is the interparticle force. On the other hand, the range of the Interaction is very high, so that even in dilute sols the particles feel each other s presence. Absence of screening means that the pair interaction between particles is completely described by Coulomb s law. In emulsions and at oil-water Interfaces a "double diffuse double layer may be formed, which is more extended in the oil phase K... 

J. W. Goodwin, Rheological properties, interparticle forces and suspension structure, in D.M. Bloor and E. Wyn-Jones (Eds.), The Structure, Dynamics and Equilibrium Properties of Colloidal Systems. NATO ASI Series C 324, Kluwer, The Netherlands, 1990, pp. 659-679. 

Solvent friction is measured by the Stokes friction coefficient = 6 r)is H- The interparticle forces = — d/dr, U ( rj ) derive from potential interactions of particle i with all other colloidal particles U is the total potential energy. The solvent shear-flow is given by v ° (r) = yyx, and the Gaussian white noise force satisfies (with a,j8 denoting directions)... 

Leong, Y.K., Interparticle forces arising from an adsorbed strong polyelectrolyte in colloidal dispersions Charged patch attraction. Colloid Polym. Sci., 277, 299, 1999. 

Problem 7-24. Sedimentation of a Colloidal Aggregate. Colloidal particles often aggregate because of London-van der Waals or other attractive interparticle forces unless measures are taken to stabilize them. The aggregation kinetics are such that the aggregate formed has a fractal dimension Df, which is often less than the spatial dimension. The fractal dimension measures the amount of mass in a sphere of radius R, i.e., mass R D<. For a fractal aggregate composed of Aprimary particles of radius Op with mass mp, estimate the sedimentation velocity of the aggregate when the Reynolds number for the motion is small. What is the appropriate Reynolds number ... 

The soft (electrostatic) and van der Waals interparticle forces are described in the well-established theory of the stability of lyophobic dispersions (colloidal... 

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