Ionization and Chain Size of Weak Polyelectrolytes in Semidilute Regime

We present the relations between chain size, correlation length, and degree of ionization for linear weak polyelectrolytes in the semidilute regime. In the semidilute regime, SAXS provides the correlation length(s), ξ, but cannot provide the chain size characteristics. Similarly, pH measurements and the Henderson-Hasselbalch equation do not yield a realistic estimation of the degree of ionization of weak polyelectrolytes in the semidilute regime. On the other hand, simulations provide all these: end-to-end distance R _ee, radius of gyration R _g, degree of ionization α. We measured SAXS profiles of poly-(acrylic acid) at various degrees of neutralization in the semidilute regime. We compared the experimental scattering curves with their counterparts from coarse-grained Hamiltonian Monte Carlo simulations in terms of the position of the polyelectrolyte peak, q*, and the fractal dimension, d _f. Regarding q*, our results not only are in mutual agreement but also obey the previously predicted scaling relations in the limit of high α values. In particular, we obtained R _ee ∝ ξ^0.3 for α  >  0.3, R _ee ∝ α ^4/7 for 0.1 < α < 0.5, R _ee ∝ α^1/7 for α  > 0.5 and R _ee approximately constant for very low values of α.