= Solution
In a <magnesium chloride> <chemical solution>, the principal pair interactions are <hard sphere> exclusion, repulsion of overlapping <electric double layers>, and attractive <Van der Waals forces>. The positive surface attracts <chloride> <counterions> and repels <magnesium> <coions>; mobile <ions> screen the bare <Coulomb's law> interaction. The competition between screened electrostatic repulsion and <Van der Waals force> attraction is described by <DLVO theory>.
For well-separated identical weakly charged spheres, the approximate repulsive pair <potential energy>, at centre separation $R\geq2a$, is
$$
U_{\mathrm{el}}(R)\simeq\frac{Q^2}{4\pi\varepsilon_0\varepsilon_r}
\frac{e^{-\kappa(R-2a)}}{(1+\kappa a)^2R}.
$$
It is a <screened Coulomb pair potential>. An attractive <Hamaker constant> adds a negative short-range contribution, while overlap is forbidden. Very near contact, <solvation> and molecular surface structure can also matter. No polymer-induced interaction should be assumed before polymer is added in part (f).
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