Simulation Study of the Origin of Coacervate Density Insensitivity to Polyelectrolyte Length Asymmetry in a Salt-Free Solution

Polyelectrolyte complexes (PECs), formed by the associative phase separation of oppositely charged polyelectrolytes (PEs), are integral to synthetic and biological systems. While length asymmetry between polycation and polyanion is common, its influence on the macroscopic properties of the resulting liquid coacervate phase remains a critical open question. Our recent experimental data show that under salt-free conditions, the density of the coacervate phase formed between oppositely charged PEs with chemically identical backbones is remarkably insensitive to the degree of PE length asymmetry. This observation has not been explicitly described experimentally or theoretically. While an extension of the popular Voorn-Overbeek theory can be sought to understand this departure from length-symmetric systems, a thorough understanding of the underlying physical mechanisms is missing.    

To identify the physical mechanisms driving this insensitivity to length asymmetry, we employed coarse-grained Molecular Dynamics simulations of PEs with explicit nonpolar solvents. These simulations model the phase equilibrium of PE coacervates across various asymmetry ratios (λ=N_short/N_long​). Our systematic study focused on decoupling the contributions of key parameters: counterions, entropic polymer chains, entropic effects from longer chains, enthalpic interactions between monomers, and the non-specific enthalpic interaction between PE end-groups. We observe that a strong, dominant enthalpic interaction specifically localized at the polyelectrolyte end-groups in the presence of counterions could possibly compensate for the entropic costs of packing asymmetric PEs. In summary, our systematic simulation study sheds light on the thermodynamic origin of the coacervate density's insensitivity to polyelectrolyte length asymmetry and provides a possible framework for the rational design of PEC-based materials.