Past exam of the quantum condensed matter course of the University of Cambridge / 2008 / Section A / A2 / c / Solution

DLVO theory combines the attractive Van der Waals force with repulsion between overlapping electrical double layers. A charged colloid attracts counterions; their electrostatic and osmotic response screens its field over the Debye length. Adding salt generally shortens this range and can lower the repulsive aggregation barrier, allowing particles to reach the strongly bound primary minimum. A shallow secondary minimum can instead give weak reversible association. Whether Brownian encounters cause rapid aggregation depends on barrier heights relative to $k_{B}T$, not just on the sign of the force at one separation.

Adsorbed or grafted polymer layers can provide steric stabilization: overlap costs chain entropy and increases the local osmotic pressure. Nonadsorbing smaller particles or polymers can create a depletion force, because bringing large surfaces together increases the volume accessible to the smaller species. Polymer bridging can be attractive when one chain binds more than one particle. A useful comparison experiment varies salt concentration while monitoring scattered light or aggregation, then repeats with a sterically protected suspension. Charge, solvent quality, polymer coverage and particle size determine which interaction dominates; none is a universal constant of all colloids.