Effect of Charge Regulation and Conformational Equilibria in the Stretching Properties of Weak Polyelectrolytes

Weak polyelectrolytes can modulate their charge in response to external perturbations, such as changes in the pH, ionic strength (I), or electrostatic interactions with other charged species, a phenomenon known as charge regulation (CR). On the other hand, it is well established that CR is highly coupled with the conformational degrees of freedom. In this paper, the influence of CR in the stretching properties of weak polyelectrolytes is analyzed, and the possibility of CR induced by mechanical stretching is explored. With this aim, we make use of a minimal model, which captures the fundamental aspects present in the stretching of a flexible weak linear polyelectrolyte: internal angle rotation, bond stretching, bond bending, and proton binding, which is the paradigmatic mechanism of CR The angle rotation is described by using the rotational isomeric state approximation, while for protonation, the site binding model is assumed. Mechanical stretching is studied by performing semi-grand canonical Monte Carlo simulations at different pH and ionic strength conditions. The simulations simultaneously provide both conformational (bond state probabilities, persistence length l(p), and chain elongation) and protonation properties (degree of protonation theta and the effective protonation constant K-c). The obtained force-extension curves suggest that the pH value and the ionic strength I have a significant effect on polyelectrolyte stretching. Three different force regimes can be observed. For large forces (F > 100 pN for typical force constants), the force-extension curve is almost independent of the pH and I. For low forces, the persistence length 1p is force-independent, although it strongly increases with the pH value. Under this regime, linear and Pincus scaling behaviors are observed. Finally, in the intermediate-force regime, both rotational and protonation degrees of freedom are mechanically activated, and the picture becomes more complicated. It is found that l(p) increases with F and, under certain conditions, a significant increase of theta with F is observed, indicating that CR could in principle be induced by means of mechanical stretching. This fact can be explained by analyzing the coupling between theta and the probability of a bond to be in the gauche state P(g). P(g) decreases with F as the bonds adopt the trans conformation so that the electrostatic repulsion is reduced and theta increases. Finally, the intricate interplay between short-range and long-range interactions is analyzed, leading to apparently contradictory behaviors (P(g) and l(p) simultaneously decrease with I), which can only be explained by CR and the presence of complex spatial correlations.