One aspect missing in the Carnahan-Starling result is the effect of connectivity between monomers. There are ways of accounting for the effect of excluded volume due to chains of connected beads, such as the Werthheim approach 124-126 used in models developed by Wang, et al. We will not explore this modification here, but will instead account for the connectivity-based correlations by assuming a tunable factor in front of the excluded volume contribution to the free energy that we will discuss later.