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We present a theory of the complexation of polyanions by divalent cations. The formation of both mono-and dicomplexes is possible. Monocomplexation locally inverts the charge of the polyelectrolyte and transforms it into a polyampholyte. The formation of a dicomplex creates a bridge between charged monomers. The complexation constants for mono and dicomplexation strongly decrease at high ionic strength. If the complexation constants are large enough, the polyelectrolyte precipitates at moderate salt concentrations. The precipitation is driven either by a Debye-Hückel polarisation energy as in polyampholytes (for almost pure monocomplexation) or by the bridging attraction induced by the dicomplexes. The equilibrium constant for the transformation of two monocomplexes into a dicomplex (at vanishing ionic strength) is a key parameter: - when monocomplexation is favored, the polymer is redissolved by strong charge inversion at moderate salt concentrations. Two successive polymer precipitations and solubilisations can be observed as the divalent salt concentration is increased. - when dicomplexation is favored, the precipitation at moderate salt concentration is followed by a redissolution at high ionic strength where complexation becomes unefficient. Only one precipitation is expected

Precipitation of Polyelectrolytes in the Presence of Multivalent Salts