A flat surface is considered. The charge on that surface influences the ion distribution in nearby layers of the electrolyte. The electrostatic potential, y , and the volume charge density, r , which is the excess of charges of one type over the other, are related by the Poisson equation:. This distribution is given by a Boltzmann equation:. The volume charge density at y is:. Thus the combination of this with the Poisson equation gives the Poisson-Boltzmann equation :. Trig relations: ,.
Case 2. Far from a plate of high potential, y 0. Comparing equations 2. The apparent stability of colloids with an electric double layer at their surfaces is due to the repulsive potential energy generated when the double layers overlap. As the two charged surfaces approach each other, the ion concentration between the surfaces increases due to the requirement to maintain electrical neutrality and so a greater osmotic pressure is generated.
For mathematical simplification, consider this situation applied to flat plates. Assume that the electrical potential between the two plates is additive and that overlap is small enough to have constant charge between the plates. The mean excess osmotic pressure, , developed between the plates is. Hence, at the mid-point between the plates, we have:.
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At the mid-point between the plates, , and using equation 2. The repulsive potential energy per unit area due to the overlap of the flat plate electrical double layers, V R , is the work done when the plates are brought closer to each other from an infinite separation. The opposition to this closer movement is provided by. The form of equation 2. In between, however, the behaviour depends critically upon the ionic strength, I , and hence the electrolyte concentration, of the dispersion.
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The concentration of electrolyte at which coagulation becomes rapid is the critical coagulation concentration c. The condition for rapid coagulation can be considered to be that the primary maximum in the total potential energy curve is tangential to the x -axis, i. This gives the concentration of ions, n 0 c.
DLVO theory - Soft-Matter
Hence as the valency of counter ion increases from 1 to 3 we expect the c. The Schulze-Hardy rule, which has been known since the end of the nineteenth century, states that c. Effectiveness of the electrolyte in coagulating the dispersion increases when multivalent ions are contained. Counter ion valency is the important factor in determining c.
For the As 2 S 3 sol, the c.
This is in excellent agreement with the DLVO theory which states that the ratios should be -6 : 3 -6 The polymer adsorbs on to the colloidal particles, forming a protective sheath around the colloidal particle of thickness, d. If colloidal particles are closer than a distance, 2 d , apart, then the adsorbed polymer chains will overlap and hinder the closer approach of the colloidal particles.
The steric potential, V s , may be considered to arise mainly from two contributions:. Entropic term always repulsive due to loss of conformational entropy of polymer chains as they overlap one another. Enthalpic term. Depends upon extent to which polymer segments prefer to be next to solvent compared to themselves depends on Flory-Huggins parameter which you will encounter next year in Prof. Richard's Polymer Course. The ideal polymer for steric stabilisation is a diblock copolymer , AB. The other component B likes to be immersed in solvent maximises d. Alternatively the polymer can be chemically grafted onto the colloidal surface.
As the colloidal particles come closer together, the intercolloidal region consists of a region that is depleted in polymer. Solvent between the colloidal particles then tends to diffuse out to reduce the concentration gradient, causing the colloidal particles to aggregate. A high molecular weight i. The two ends of the polymer may adsorb onto different colloidal particles and then draw them together, leading to bridging flocculation.
This flocculation mechanism can be highly effective; e. The use of polymers in colloidal dispersions to either stabilise steric stabilisation or flocculate bridging or depletion colloidal dispersions is now widespread. There is much interest in producing so-called 'smart' colloids, which are system-responsive colloids that are reversibly flocculating depending upon the conditions, i.
Includes precipitation processes, vapour condensation and chemical reaction to produce an insoluble colloidal dispersion. Examples of the latter include the oxidation of thiosulphate under acid conditions to produce colloidal sulphur:. In forming lyophobic colloids, a stabilising mechanism, e. To produce a colloidal dispersion by condensation, the supply of molecules must run out whilst the particles are in the colloidal size range.
The precipitating colloidal material must be supersaturated , i. At the initial stages of forming the colloidal dispersion by building up molecular aggregates, the small aggregates, or nuclei , will have very large surface area to volume ratios. Hence these nuclei are unstable relative to larger aggregates, and they will tend to dissociate before they can grow to larger sizes. In any thermodynamic system, statistical fluctuations about the normal state occur.
After the nucleation process, growth of the critical nuclei to colloidal and more typically macroscopic sizes occurs.
Theory of the Stability of Lyophobi (Dover Books on Chemistry)
Colloidal dispersions can sometimes be made monodisperse , i. The fast nucleation rate means material is used up rapidly, so the concentration then quickly drops. No nuclei can then be produced supersaturation is too low and the nuclei then grow to colloidal dimensions at all the same rate. Inorganic colloids, and polymer latexes produced by polymerisation of monomers in emulsions, can be monodisperse. The term clay mineral refers to a specific group of silicate minerals.
In terms of tonnage, clays are second only to oil in use. Clay minerals are used in the ceramic industry to make bricks, china and pottery. Clays are extensively used as fillers in paper, paint, polymers etc. The essential feature of clay minerals is the existence of extensive sheets of silicon bonded with oxygen combined with flat sheets of metal usually Al or Mg oxides. Layered crystals are formed. Tucker, J. Corbett, J. Fatkin, R. Jack, M. Kaszuba, B.
MacCreath, F. Pawlik, J. Laskowski, A. Ansari, Journal of Colloid and Interface Science, , , User Username Password Remember me.
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