Reasonable values for $B_2$ and $B_3$:

We have not completely explored the entire range of values for $B_2$ or $B_3$ at present. Currently, we set the range for $B_2$ such that $-10 < B_2 < 10$ Å$^3$. The parameter $B_3$ is much less sensitive to size, although because this is a kind of mean field theory, there are transition points where the relationship between $N$ and $\nu$ (or $B_2$ and $B_3 )$ hits what resembles a phase transition. As with all mean field results, there is a region of coexistence there, and this can lead to some very interesting physics. For $B_3$, I have left the following options available with certain restrictions: $0 < B_3 < 500$. Perhaps some negative values exist in some systems when $B_2$ is positive, but the physical meaning of a negative $B_3$ is a bit strange to me. How would you get the two-body term to be repulsive and the three-body term attractive?

An important point to consider is that we cannot have both $B_2 < 0$ and $B_3 < 0$. A reasonable guess for the relative magnitude of $B_2$ and $B_3$ is probably $B_3 \sim 10\vert B_2 \vert$, where the $\vert \vert$ means ``absolute value''. Probably values of $B_2 < -5$ or $B_2 > 5$ are a little extreme. In the future, I hope to add some useful experimental data for solvent-polymer interactions to get a clearer handle of the magnitude of $B_2$ and $B_3$. I also plan to add some figures to help a little in the explanation here.