Figure 3.

The mapping from the solvent accessible volume fraction ${\eta }_k^i$ to the solvation state ${\upsilon }_k^i$. In panel A, the naïve choice ${\upsilon }_k^i={\eta }_k^i$ is shown along with corrections introduced by the natural bounds of ${\eta }_k^i$ (see text). In panel B, the generalized, sigmoidal interpolation is shown. At τ_d=0.25 and χ_d=0.5, the curve is very similar to the linear case using the same bounds. Shifting χ_d to 0.1 and 0.9, respectively, shifts the mid-point of the transition accordingly, but leaves the overall curvature largely unaffected. Conversely, values of χ_d=0.5 and τ_d=0.1 increase curvature and yield a more step-like transition. See Equation 4 for details.