Cooperative Counterion−Polyion Interactions in Polyelectrolyte Chain Dynamics: NMR and Quantum-Chemical Study of Locally Collapsed State in Dilute Poly(N-diallyldimethylammonium chloride) in NaCl/D2O Solutions

Using 1 H and 35 Cl single- and double-quantum NMR spectra, relaxation and pulsed gradient spin echo (PGSE) diffusion experiments combined with quantum-chemical calculations, we studied the molecular dynamics of poly( N- diallyldimethylammonium chloride) (PDADMAC) and its copolymers with acrylamide in D 2 O under conditions of various ionic strength determined by the concentration of the polyelectrolyte itself or an added salt or both. According to absolute signal intensity, only 12−15% of the DADMAC groups are in an actual mobile state, giving rise to detectable signals. Transverse relaxation analysis shows a wide mobility distribution in the mobile groups. Double quantum 1 H NMR signals of N- methyl protons evidence motional anisotropy relative to the NMR time window and thus motional hindering in part of the visible DADMAC groups. Strong dependence of these phenomena on ionic strength, as well as quantum-chemical simulations, indicates that these phenomena are of an electrostatic nature. Probing of the counterion distribution and dynamics by 35 Cl NMR quadrupolar relaxation shows that a majority of counterions behave according to the Halle−Wennerström−Picullel model based on combined Poisson−Boltzmann and Smoluchowski equations, but relaxation of the T 2 3 coherence indicates that a smaller part of the counterions correlate with the polymer motion. Accordingly, the mobile part of the polymer is interpreted as a fluctuation consisting of a locally collapsed chain and condensed counterions. By three independent methods, namely, inversion−recovery, transverse relaxation, and in particular, saturation transfer experiments, the average lifetime of this fluctuation was estimated to be in the range 30−80 ms. Thus, the fluctuation is frozen, that is, it is stabilized by cooperative interaction between the collapsed part of the chain and the condensed counterions. Mutual exchange between groups with different mobility, found by saturation transfer experiment, indicates that the fluctuation can move to-and-fro along the chain.