Solution (source code)

= Solution

The <saturation concentration> $c_{\rm sat}(T)$ is the dilute-phase coexistence <concentration> at the specified temperature and solution conditions. On increasing the overall <concentration> through this boundary, a macroscopic condensed phase can first coexist with the dilute phase. The other branch gives the dense-phase <concentration> $c_{\rm dense}(T)$.

At the <thermodynamic critical point>, the two branches meet: their <concentration> difference vanishes. Its coordinates define the <critical concentration> $c_c$ and critical temperature $T_c$. In the upper-critical model, $T>T_c$ admits no two-liquid coexistence. Thus \b[$c_{\rm sat}$ is a temperature-dependent branch, whereas $c_c$ is the <concentration> at the endpoint].

Between coexistence <concentrations>, the <lever rule> gives the dense-phase <volume fraction> $v=(\bar c-c_{\rm sat})/(c_{\rm dense}-c_{\rm sat})$, assuming consistent <concentration> and volume definitions. Increasing total <chromatin> then primarily changes phase amounts rather than allowing the dilute phase to increase without bound.