Particles colloids

The repulsion between two double layers is important in determining the stability of colloidal particles against coagulation and in setting the thickness of a soap film (see Section VI-5B). The situation for two planar surfaces, separated by a distance 2d, is illustrated in Fig. V-4, where two versus x curves are shown along with the actual potential. 

The most familiar type of electrokinetic experiment consists of setting up a potential gradient in a solution containing charged particles and determining their rate of motion. If the particles are small molecular ions, the phenomenon is called ionic conductance, if they are larger units, such as protein molecules, or colloidal particles, it is called electrophoresis. 

For example, a wall or apparatus surface. For example, a colloidal particle. 

There are a number of complications in the experimental measurement of the electrophoretic mobility of colloidal particles and its interpretation see Section V-6F. TTie experiment itself may involve a moving boundary type of apparatus, direct microscopic observation of the velocity of a particle in an applied field (the zeta-meter), or measurement of the conductivity of a colloidal suspension. 

Rowell and co-workers [62-64] have developed an electrophoretic fingerprint to uniquely characterize the properties of charged colloidal particles. They present contour diagrams of the electrophoretic mobility as a function of the suspension pH and specific conductance, pX. These fingerprints illustrate anomalies and specific characteristics of the charged colloidal surface. A more sophisticated electroacoustic measurement provides the particle size distribution and potential in a polydisperse suspension. Not limited to dilute suspensions, in this experiment, one characterizes the sonic waves generated by the motion of particles in an alternating electric field. O Brien and co-workers have an excellent review of this technique [65]. 

The polymer concentration profile has been measured by small-angle neutron scattering from polymers adsorbed onto colloidal particles [70,71] or porous media [72] and from flat surfaces with neutron reflectivity [73] and optical reflectometry [74]. The fraction of segments bound to the solid surface is nicely revealed in NMR studies [75], infrared spectroscopy [76], and electron spin resonance [77]. An example of the concentration profile obtained by inverting neutron scattering measurements appears in Fig. XI-7, showing a typical surface volume fraction of 0.25 and layer thickness of 10-15 nm. The profile decays rapidly and monotonically but does not exhibit power-law scaling [70]. 

Among the many applications of LB films, the creation or arrangement of colloidal particles in these films is a unique one. On one hand, colloidal particles such as 10-nm silver sols stabilized by oleic acid can be spread at the air-water interface and LB deposited to create unique optical and electrooptical properties for devices [185]. 

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... 

The interactions between colloidal particles (see section C2.6.4) are central to tire understanding of suspension behaviour. Aitlrough most work has had to rely on ratlrer indirect ways to characterize tlrese interactions, novel teclmiques are emerging tlrat access tlrese interactions more directly. 

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. 

In particular, in polar solvents, the surface of a colloidal particle tends to be charged. As will be discussed in section C2.6.4.2, this has a large influence on particle interactions. A few key concepts are introduced here. For more details, see [32] (eh 13), [33] (eh 7), [36] (eh 4) and [34] (eh 12). The presence of these surface charges gives rise to a number of electrokinetic phenomena, in particular electrophoresis. 

In electrophoresis, the motion of charged colloidal particles under the influence of an electric field is studied. For spherical particles, we can write... 

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... 

Particularly in polar solvents, electrostatic charges usually have an important contribution to tire particle interactions. We will first discuss tire ion distribution near a single surface, and tlien tire effect on interactions between two colloidal particles. 

More sophisticated approaches to describe double layer interactions have been developed more recently. Using cell models, the full Poisson-Boltzmann equation can be solved for ordered stmctures. The approach by Alexander et al shows how the effective colloidal particle charge saturates when the bare particle charge is increased [4o]. Using integral equation methods, the behaviour of the primitive model has been studied, in which all the interactions between the colloidal macro-ions and the small ions are addressed (see, for instance, [44, 45]). 

The second case involves non-adsorbing polymer chains in solution. It was realized by Asakura aird Oosawa (AO) [50] aird separately by Vrij [51] tlrat tlrese chains will give rise to air effective attraction between colloidal particles. This is kirowir as depletion attraction (see figure C2.6.4. We will summarize tire AO tlreory to explain tlris. 

The depletion picture also applies to otlier systems, such as mixtures of colloidal particles. Flowever, whereas neglecting tire interactions between polymer molecules may be reasonable, tliis cannot be done in tire general case. 

Figure C2.6.9. Phase diagram of charged colloidal particles. The solid lines are predictions by Robbins et al [85]. Fluid phase (open circles), fee crystal (solid circles) and bee crystal (triangles). is tire interaction energy at tire...

In extensively deionized suspensions, tliere are experimental indications for effective attractions between particles, such as long-lived void stmctures [89] and attractions between particles confined between charged walls [90]. Nevertlieless, under tliese conditions tire DLVO tlieory does seem to describe interactions of isolated particles at tire pair level correctly [90]. It may be possible to explain tire experimental observations by taking into account explicitly tire degrees of freedom of botli tire colloidal particles and tire small ions [91, 92]. 

In section C2.6.4.3 it was shown how tlie addition of non-adsorbing polymer chains induces a depletion attraction between colloidal particles. If sufficient polymer is added, tliese attractions can be strong enough to induce a phase separation of tire colloidal particles. An early application of tliis was tire creaming of mbber latex [93]. 

Underwood S M, Taylor J R and van Megen W 1994 Sterically stabilised colloidal particles as model hard spheres Langmuir O 3550-4... 

Rosenbaum D, Zamora P C and Zukoski C F 1996 Phase behaviour of small attractive colloidal particles Phys. Rev. Lett. 76 150-3... 

Kondo A and FllgashItanI K 1992 Adsorption of model proteins with wide variation In molecular properties on colloidal particles J. Colloid Interfaoe Sc/. 150 344-51... 

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