This expression is used to be consistent with the semiflexible chain used in the simulations performed in this and previous works. Finally, the last two terms are associated with the Carnahan-Starling expression for the free energy of hard spheres; 123 the second of these terms simply removes the quadratic contributions that would arise from the pairwise interactions already included in the TM and RPA terms. This is almost certainly an underestimation of this free energy, due to the correlations associated with the connected polymer chains.