= Solution
For smooth uncharged spheres, the basic attraction is the <Van der Waals force>, arising from correlated electric fluctuations. The <Hamaker constant> $A_H$ incorporates the particles and intervening medium. For equal spheres of radius $a$ separated by a surface gap $h\ll a$, the <near-contact van der Waals attraction of spheres> is
$$
\boxed{U_{\rm vdW}(h)\simeq-\frac{A_Ha}{12h},\qquad F_{\rm vdW}(h)=-\frac{A_Ha}{12h^2}.}
$$
Here positive force means repulsion, and the attractive case has $A_H>0$. At molecular separation, strong short-range repulsion prevents overlap and replaces the continuum divergence with a deep primary minimum. The energy approaches zero from below at large separation; an uncoated, uncharged attractive pair has no electrostatic barrier.
For illustration, $A_H=10^{-20}\,\mathrm J$, $a=100\,\mathrm{nm}$ and $h=1\,\mathrm{nm}$ give $|U|\simeq8.3\times10^{-20}\,\mathrm J\simeq20k_BT$ at $300\,\mathrm K$. These are chosen scales, not universal material constants. Such a well can trap particles after a thermal encounter and cause <particle aggregation>, unless another mechanism such as <steric stabilization> intervenes. The neutral curve in the figure below shows the attraction regularized by an illustrative contact repulsion.
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