Concentration dependence of the Flory-Huggins interaction parameter in aqueous solutions of capped PEO chains

The dependence on volume fraction $\varphi$ of the Flory-Huggins $\chi_{\mathrm{wp}}\left(\varphi\right)$ describing the free energy of mixing of polymers in water is obtained by exploiting the connection of $\chi_{\mathrm{wp}}\left(\varphi\right)$ to the chemical potential of the water, for which quasi-chemical theory is satisfactory. We test this theoretical approach with simulation data for aqueous solutions of capped PEO oligomers. For CH$_3$(CH$_2$-O-CH$_2$)$_m$CH$_3$ ($m$=11), $\chi_{\mathrm{wp}}\left(\varphi\right)$ depends strongly on $\varphi$, consistent with experiment. These results identify coexisting water-rich and water-poor solutions at $T$ = 300K and $p$ = 1atm. Direct observation of the coexistence of these two solutions on simulation time scales supports that prediction for the system studied. This approach directly provides the osmotic pressures. The osmotic second virial coefficient for these chains is positive, reflecting repulsive interactions between the chains in the water, a good solvent for these chains.