Solution

ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2019/paper-1/section-a-iii/5/i/solution

charge stabilization of colloids supplies repulsion when like-charged surfaces and their electric double layers approach. steric stabilization uses attached or adsorbed molecular layers whose overlap costs conformational and osmotic free energy. Combining both gives electrosteric stabilization; a solvated coating must remain attached and well solvated. A viscous medium slows encounters but does not by itself create an equilibrium repulsive barrier.
DLVO theory adds screened electrostatic repulsion to Van der Waals force. A representative close-gap form is
for equal spheres of radius , with Hamaker constant and inverse Debye–Hückel screening length . The formula is schematic near molecular contact, where hydration, surface roughness and finite ion size matter. A repulsive barrier many high produces kinetic stability even if the primary attractive minimum is deeper than the dispersed state. Entry into that primary minimum generally gives strongly bound aggregation; a shallow secondary minimum can give reversible flocculation.
Adding electrolyte increases , shortens the repulsion and can remove the barrier, enabling fast diffusion-limited aggregation. The critical coagulation concentration is the approximate salt concentration at which this rapid-coagulation regime begins under specified conditions. It is not a universal property of the salt alone. Test the prediction using time-resolved dynamic light scattering or turbidity at controlled particle concentration, pH and temperature; check that added ions do not specifically adsorb or change the surface chemistry.
Figure 1.
Original schematic DLVO interaction curves showing a stabilizing barrier, secondary minimum and barrier loss on salt addition
. Details.

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