= Solution
Without stabilization, the <potential energy> is predominantly attractive outside the molecular core and drops into a deep primary minimum. With the charging treatment, the <DLVO theory> sum develops a positive barrier between distant particles and that primary minimum. The barrier must be large compared with $k_BT$ to inhibit aggregation on the experimental timescale. A shallow secondary minimum can remain at larger separation, depending on parameters.
\Image[/past-exam-of-the-soft-condensed-matter-course-of-the-university-of-cambridge/2021-q5-pair-potentials.png]
{title=Attractive and electrostatically stabilized <colloidal> pair potentials}
{description=Original illustrative curves for two equal spheres. The unstabilized curve uses the nonretarded sphere–sphere attraction; the stabilized curve adds screened electrostatic repulsion. The molecular core is excluded and the deep near-contact well is clipped by the plotting range. Potential depths and screening parameters are illustrative, not data supplied by the paper.}
The horizontal axis is the surface gap, so the molecular exclusion boundary is at its origin. Both interactions tend to zero at large separation. Raising salt concentration shortens the <Debye–Hückel screening length> and can reduce the barrier, allowing particles to stick again.
Back to article page
