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Protic solvents can form a tight shell around a nucleophile. But what's stopping any polar solvent from doing so? Shouldn't a polar solvent surround negatively charged $\ce{F-}$ with its partially positive side?

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Found a good explanation in Oxford University presentations.

It appears that partially positive side of aprotic solvents is hindered in the middle of the molecule. Only negative charge is on the surface. I've looked at DMSO, DMF, acetone, acetonitrile - all of them share this feature. So in case of a negatively charged ion - such solvents are not good at surrounding it.

It looks like elements that end up partially positive (except for $\ce{H}$) are those that can have 3+ bonds ($\ce{C}$, $\ce{S}$), so they are mostly surrounded by other atoms. It's only $\ce{H}$ who has 1 bond and therefore ends up at the surface of the molecule and can interact with negatively charged nucleophiles.

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