A solvent with a comparatively high relative permittivity (or dielectric constant), greater than ca. 15, and a sizable permanent dipole moment, that cannot donate suitably labile hydrogen atoms to form strong hydrogen bonds, e.g. dimethyl sulfoxide. The term (and its alternative "polar aprotic solvent") is a misnomer and is therefore discouraged. Such solvents are usually not aprotic, but protophilic (and at most weakly protogenic). In describing a solvent it is better to be explicit about its essential properties, e.g. dipolar and non-protogenic.
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