Dynamics, site binding, and distribution of counterions in polyelectrolyte solutions studied by electron paramagnetic resonance spectroscopy

A microscopic picture of counterion condensation in liquid and glassy frozen solutions of the cationic polyelectrolyte poly(diallyldimethylammonium chloride) (PDADMAC is derived from data obtained by a combination of continuous-wave and pulse electron paramagnetic resonance techniques. The condensation of such divalent anions to the polyelectrolyte chain in the presence of a large excess of polyelectrolyte and monovalent counterions can be described by a dynamic equilibrium between specifically site-bound and nonspecifically territorially bound counterions with exchange between the two states proceeding on time scales significantly shorter than 1 ns. No free divalent counterions are detected. The dynamic electrostatic attachment is manifest in an axially symmetric rotational diffusion tensor, with the unique axis of fast rotation corresponding to the electrostatic bond between one sulfonate group of Fremy's salt and the quaternary ammonium group of the PDADMAC repeat unit. A distance of 0.43 nm between the electron spin and the N-14 nucleus of the ammonium group is found by electron spin-echo envelope modulation spectroscopy, suggesting that the site-bound state corresponds to contact ion pairs. The same experiment provides an estimate of 20% site-bound and 80% territorially bound divalent counterions in glycerol/water glassy frozen solution. Pulse electron-electron double resonance measurements show that on nanometer length scales the counterions are virtually homogeneously distributed in three dimensions for high polyelectrolyte concentration but linearly distributed along stretched chains at low polyelectrolyte concentrations where no overlap of chains is expected.