We perform extensive molecular dynamics (MD) simulations between pairs of ions of various diameters (2-5.5 angstrom in increments of 0.5 angstrom) and charge (+1 or -1) interacting in explicit water (TIP3P) under ambient conditions. We extract their potentials of mean force (PMFs). We develop an interpolation scheme, called i-PMF, that is capable of capturing the full set of PMFs for arbitrary combinations of ion sizes ranging from 2 to 5.5 angstrom. The advantage of the interpolation process is computational cost. Whereas it can take 100 h to simulate each PMF by MD, we can compute an equivalently accurate i-PMF in seconds. This process may be useful for rapid and accurate calculation of the strengths of salt bridges and the effects of bridging waters in biomolecular simulations. We also find that our data is consistent with Coffins' "law of matching affinities" of ion solubilities: small-small or large large ion pairs are poorly soluble in water, whereas small-large are highly soluble.