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/D 2 O Solutions J. Kr ˇ ı ´z ˇ ,* J. Dybal, and D. Kurkova ´ Institute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic, HeyroVsky Sq. 2, 162 06 Prague 6, Czech Republic ReceiVed: January 30, 2002; In Final Form: May 14, 2002 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 - Wennerstro ¨m-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. Introduction Despite intensive research spanning 4 decades, 1-4 the struc- ture and dynamics of polyelectrolytes has continued to attract a lively interest. This may be partly because a number of biologically important macromolecules such as nucleic acids and some proteins are polyelectrolytes and thus can be influenced by electrostatic interactions. From a more general point of view, some of the features of polyelectrolytes remain somewhat elusive. This holds in particular for their dilute solutions. Because their experimental study in a dilute regime is exceptionally difficult and prone to various artifacts of the used methods, most of the recent studies were done either in theory 5-10 or in simulation. 11-18 Neither of these approaches is quite undisputable: the polyion is frequently assumed to be a stiff rod or cylinder with symmetrically distributed charges or alternatively a flexible string of beads interacting by simple (such as Lennard-Jones) potentials; its length is taken either as infinite or, in most simulations, as quite short; the electrostatic potential is usually described in the mean-field Poisson- Boltzmann or cruder approximation, not taking the charge correlations into account; often, energy rather than Gibbs free energy (including entropy) is considered as the final criterion of the probability of a given state. Despite these limitations, which are quite understandable considering the scope and complexity of the problem, various predictions seem to converge to some important conclusions concerning polyelectrolyte molecular dynamics. In a dilute solution (the concentration of charged monomer units being on the order of 10 -3 mol/L), the counterion space distribution strongly depends on the charge density of the polyion. For a weakly charged polyion, that is, one with the charge separation exceeding the Bjerrum length, λ B (λ B ) e 2 /(ǫk B T), ǫ being the dielectric constant, e the elementary charge, and k B the Boltzmann constant), the coun- terions are distributed more or less uniformly throughout the space (although the popular Manning hypothesis apparently is not literally fulfilled), whereas for a strongly charged one, the radial counterion density increases with decreasing distance. In the latter case, a fraction of polyions is condensed on the polyion, that is, either intimately bound to it or distributed in its vicinity, effectively increasing its mean charge distance approximately to λ B . Considering now the polyion itself, electrostatic repulsive interaction between the like charges forces its backbone into a more extended conformation, thus increasing its electrostatic persistence legth 19 (due to short-range interac- tions), as well as end-to-end distance (due to long-range interactions) of the chain. Expectedly, this effect is weakened by counterion condensation, as well as salt additions to the solution. According to simulations, the added electrolyte does * To whom correspondence should be addressed. kriz@imc.cas.cz. 7971 J. Phys. Chem. A 2002, 106, 7971-7981 10.1021/jp020282k CCC: $22.00 © 2002 American Chemical Society Published on Web 08/07/2002