This expression, with a few minor differences, recovers Equation . The first two terms account for the combinatoric entropy of counterion 'binding', defining the fraction ξ P + = N * B /N P + . The subsequent terms account for the decrease in translational entropy for the bound states, which is related to the terms in Equation 32 that account for the charge fraction-dependent terms in the mixing entropy. The final terms are the effective change in free energy of binding, ∆G P ±,± that are given by: ∆G P ±,± = -ln 1 2ν 0 * Dr P + P P + dr ± {A P +,-