Electrostatic correlation free energy for finite polymer chains

Electrostatic correlation free energy (ECF) is the basis for modeling the thermodynamic behavior of polyelectrolyte solutions. In the past, it has mainly been estimated using the Edwards approximation, valid for infinite chains. Here, we show that the leading contribution due to finite molecular size is of order N^-1, regardless of the fractal dimension d, where N is proportional to molecular weight. This contribution is a local effect, originating from the missing correlations among connected charges near chain ends. In contrast, the contribution from the long-wavelength or infrared regime is weaker, of order N^-3/d ln N. Closed-form expressions for the free energy are provided for polyelectrolytes exhibiting either coil- or rod-like statistics, in the absence or presence of small ions. The consequence of the end effect is demonstrated by evaluating the phase diagram, surface tension, and molecular weight-driven partitioning.