Role of Associative Charging in the Entropy–Energy Balance of Polyelectrolyte Complexes

Abstract

Polyelectrolytes may be classified into two primary categories (strong and weak) depending on how their charge state responds to the local environment. Both of these find use in many applications, including drug delivery, gene therapy, layer-by-layer films, and fabrication of ion filtration membranes. The mechanism of polyelectrolyte complexation is, however, still not completely understood, though experimental investigations suggest that entropy gain due to release of counterions is the key driving force for strong polyelectrolyte complexation. Here we perform a comprehensive thermodynamic investigation through coarse-grained molecular simulations permitting us to calculate the free energy of complex formation. Importantly, our expanded-ensemble methods permit the explicit separation of energetic and entropic contributions to the free energy. Our investigations indicate that entropic contributions indeed dominate the free energy of complex formation for strong polyelectrolytes, but are less important than energetic contributions when weak electrostatic coupling or weak polyelectrolytes are present. Our results provide a new view of the free energy of polyelectrolyte complex formation driven by polymer association, which should also arise in systems with large charge spacings or bulky counterions, both of which act to weaken ion–polymer binding.

Recent progress in the science of complex coacervation

“…Whitmer et al, used expanded-ensemble algorithms with coarse-grained Monte Carlo simulations to show that the different complexation mechanisms exist at different linear charge densities, with high charge-density polyelectrolyte complexation being entropically-driven (i.e., counterion release) and low charge-density complexation driven by energetic interactions (i.e., fluctuation-induced attraction). 151 This illustrates the connection between the two different modes of coacervation, and establishes a connection to thermodynamics as measurable by isothermal titration calorimetry. 43,72 Indeed, a number of examples of synthetic polymer complexes in the literature have been measured using calorimetry, 43,50,51,[68][69][70][70][71][72] mostly consistent with an entropic driving force.…”

“…Theory has provided a number of insights into the role of connectivity, from two different perspectives; via fluctuation-induced opposite-charge attraction, or via counterion condensation and release. The current, prevailing view is that both effects can induce coacervation, 151 in the low-and highlinear charge density limits respectively, and this understanding is reinforced by evidence from a combination of theory, simulation, and experiment.…”

Grand-Reaction Method for Simulations of Ionization Equilibria and Ion Partitioning in a Broad Range of pH and Ionic Strength

“…If H + ions are the minority species in the simulation box, then there is a risk that the protonation reaction would be prevented by the absence of explicit H + ions. Similar situation was the bottleneck of simulations by Rathee et al 59,60 , where the absence of OHions prevented them from simulating at pH ≈ 7. In such case, the ionization reaction can be implemented using some other ion as neutralizer.…”

“…this problem can be circumvented by re-formulating the ionization reaction using the OH − ion instead of H + , as has been done by Rathee et al 59 . However, in the intermediate pH range, a different approach is needed.…”

“…H + at pH ≈ 7), its excess chemical potential should be accounted for in the same way. For example, a similar calibration has been used by Rathee et al 59 but they simulated the base (KOH) and salt (NaCl) reservoirs independent of each other. Therefore, their obtained chemical potentials were slightly off from the values that they should attain in a mixture.…”