Coagulation of colloidal particles

Smoluchowski, who worked on the rate of coagulation of colloidal particles, was a pioneer in the development of the theory of diffusion-controlled reactions. His theory is based on the assumption that the probability of reaction is equal to 1 when A and B are at the distance of closest approach (Rc) ( absorbing boundary condition ), which corresponds to an infinite value of the intrinsic rate constant kR. The rate constant k for the dissociation of the encounter pair can thus be ignored. As a result of this boundary condition, the concentration of B is equal to zero on the surface of a sphere of radius Rc, and consequently, there is a concentration gradient of B. The rate constant for reaction k (t) can be obtained from the flux of B, in the concentration gradient, through the surface of contact with A. This flux depends on the radial distribution function of B, p(r, t), which is a solution of Fick s equation... 

Kinetics is concerned with many-particle systems which require movements in space and time of individual particles. The first observations on the kinetic effect of individual molecular movements were reported by R. Brown in 1828. He observed the outward manifestation of molecular motion, now referred to as Brownian motion. The corresponding theory was first proposed in a satisfactory form in 1905 by A. Einstein. At the same time, the Polish physicist and physical chemist M. v. Smolu-chowski worked on problems of diffusion, Brownian motion (and coagulation of colloid particles) [M. v. Smoluchowski (1916)]. He is praised by later leaders in this field [S. Chandrasekhar (1943)] as a scientist whose theory of density fluctuations represents one of the most outstanding achievements in molecular physical chemistry. Further important contributions are due to Fokker, Planck, Burger, Furth, Ornstein, Uhlenbeck, Chandrasekhar, Kramers, among others. An extensive list of references can be found in [G.E. Uhlenbeck, L.S. Ornstein (1930) M.C. Wang, G.E. Uhlenbeck (1945)]. A survey of the field is found in [N. Wax, ed. (1954)]. 

A sustance that coats the particles of the dispersed phase and prevents coagulation of colloidal particles an emulsifier. 

Peptization is less important in the formation of natural colloidal solutions, inasmuch as conversion of the coagulant into sol again is characteristic of fresh highly dispersed sediments under the influence of special substances — peptizers. Peptization usually is observed when substances capable of forming sols act on sediments formed by coagulation of colloidal particles. 

M. V. Smoluchowski, Phys. Z., 17, 557 (1916). Three Lectures on Diffusion, Brownian Movement, and Coagulation of Colloidal Particles. 

Specific ion Effects, Theory, Fig. 2 Hofmeister series for salt-induced coagulation of colloidal particles as a function of surface polarity and surface charge A direct series is observed when the potency for inducing... 

Particulate organic matter (carbon), operationally distinguished from DOM(C) by filtration with, e.g., 0.45 pm nominal pore size filter. Some POM(C) is created by coagulation of colloidal particles Dissolved organic matter (carbon)... 

When monomer and polymer are mutually insoluble, the loss of radical activity may proceed in several ways 1) Burnett and Melville [59] attributed the abnormal behavior of heterogeneous polymerization of vinyl monomer to the enhanced termination of macroradicals by coagulation of colloidal particles containing growing radicals. Thomas and Pellon [60] have found that the rate... 

The frequency, k, has the units of a second order rate constant, M s", N is Avogadro s number and D, r, are the diffusion constants (in cm" s" ) and the radii of reactions (in cm), respectively, of the two reactants A and B. In keeping with common practice we shall call this the Smoluchowski equation. It is difficult to ascertain the first use of the equation in this form. It has its origins in Smoluchowski s (1916) mathematical treatment of the kinetics of the coagulation of colloidal particles in solution. He derived the equation for the time course of the formation of aggregates of increasing size. His theoretical predictions were found to to fit the results obtained by colloid chemists at that time. Smoluchowski s... 

Equation (2.33) tends to overestimate the particle flocculation rate for the electrostatically or sterically stabilized colloidal dispersions due to the potential energy barrier established between the approaching particles against particle flocculation. Fuchs [45] was the first to introduce the stability ratio (W) to take into account the fact that not aU the collision events lead to successful coagulation of colloidal particles. 

This is the well-known empirical Schulze-Hardy rule of coagulation concentration, which has been confirmed experimentally in many colloidal systems. The above theory of dispersion and coagulation of colloidal particles, based on the repulsive interaction between two diffuse layers and on the attractive interaction owing to the van der Waals-London force, is called the Deijaguin-Landau-Verwey-Overbeek (D.L.V.O.) theory. 

Pan J R, Huang C, Chen S, Chung Y C (1999), Evaluation of a modified chitosan biopolymer for coagulation of colloidal particles , Colloids Surf A, A1, 359-64. 

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