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Light scattering and viscometric measurements on weak polyelectrolytes showtwo important aspects of counterion condensation, namely, non-monotonicvariation in the polyelectrolyte size with the increase in the electrostaticstrength, and, monovalent counterion selectivity in determining the nature ofcollapse transition at high electrostatic strengths. Here, we present aself-consistent variational theory for weak polyelectrolytes which includes theeffects of the polarizability of monovalent counterions. Our theory reproducesseveral experimental findings including non-monotonic conformational size withthe variation in the electrostatic strength and a shift from a continuous to adiscontinuous collapse transition with the increase in the dipole strength ofcondensed ions. At low dipole strength and high electrostatic strength, ourtheory predicts a series of solvent quality driven size transitions spanningthe re-entrant poor, theta and good solvent regimes. At high dipole strength,the size remains that of a compact globule independent of solvent quality. Thedipole strength of the ion-pair formed due to counterion condensation, whichdepends on the size and polarizability of the monovalent counterions, is foundto be an important molecular parameter in determining the nature of collapsetransition, and the size of the collapsed state at high electrostatic strength.

Weak polyelectrolytes in the presence of counterion condensation with ions of variable size and polarizability