  In this study, we propose a theoretical framework to investigate the
interactions between flexible polymer chains, specifically polyelectrolytes
(PEs). By calculating the system's free energy while considering
position-dependent mutual interactions and chain conformations, we gain
insights into the local dielectricity as PEs overlap. Our analysis reveals that
the thermodynamic drive for complex coacervation is influenced by factors such
as the number of ions bound to the polymer backbone and the entropy associated
with free ions, challenging earlier assumptions about the relationship between
entropy gain and electrostatic temperature. We demonstrate that global
thermodynamic behavior is strongly influenced by local factors like dielectric
constant, providing clarity on discrepancies between experimental and
computational studies. Additionally, we found that entropy gain is inversely
proportional to the local dielectric constant, assuming a constant
electrostatic temperature. Our findings highlight the importance of considering
polymer-specific parameters when exploring the thermodynamic behavior of
charged polymer complexation.
