## 3 Results and Discussion
### Solubility Parameters  
_Solute._ The LAA solubility parameter of the subcooled liquid state was computed for two different molar volumes (temperatures) according to the HVK scheme using the commercial software HSPiP [9]. At 20 \({}^{\circ}\)C and 25 \({}^{\circ}\)C, the resulting HSP components, as well as \(\delta_{1}\), were the same within less than 0.3% error, so that \(\delta_{1}\) (20 \({}^{\circ}\)C) \(\approx\)\(\delta_{1}\) (25 \({}^{\circ}\)C) = 35.3 (MPa)\({}^{0.5}\) will be used further. To derive an estimate for  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Method** & **V1 (cm\({}^{3}\)/mol)** & **Remark** & **T (\({}^{\circ}\)C)** & **Ref.** \\ \hline X-ray & 103.7 & crystallographic unit cell volume & rt. & [15] \\ aq. solution density & 105.4 & partial molar volume (median), values from 102.38 to 106.49 & 25 & [16; 17; 18; 19] \\ particle density & 106.7 & solid state: purity and crystallinity unknown & 25 & [12; 13; 14] \\ melt density & 109.5 \(\pm\) 4 & subcooled liquid state: values & 20 & [13; 14] \\  & 109.9 \(\pm\) 4 & extrapolated from melt data, presumed & 25 & \\  & & probable error \(\pm\) 4 \% & \\ \hline \end{tabular}
\end{table}
Table 1: Estimates for the molar volume \(V_{1}\) of \(\iota\)-ascorbic acid.  
the uncertainty, the \(\pm 4\%\) error of \(V_{1}\) (25 \({}^{\circ}\)C) was accounted for so that one arrives at an imprecision of \(\pm 0.5\) (MPa)\({}^{0.5}\) for the individual HSP components and about \(\pm 1\) (MPa)\({}^{0.5}\) for \(\delta_{1}\). These values are congruent with precision claims by [PERSON] [9] and [PERSON] [22] on determining HSP from experimental data. Therefore, a margin of \(\pm 1\) (MPa)\({}^{0.5}\) is viewed a realistic lower error boundary for \(\delta_{1}\). Table 2 lists calculation results and literature data.  
While \(\delta_{1}\) by [PERSON] agrees well with the calculations in this study, it remains unclear which thermodynamic conditions [PERSON] et al.'s value is associated with. [PERSON] et al. obtained results by HVK for the solid particle state at 25 \({}^{\circ}\)C, which appear doubtful since we arrive at (\(\delta_{d}\), \(\delta_{p}\), \(\delta_{h}\)) = (18.6, 12.4, 28.2) when using their molar volume (\(V_{1}\) = 106.7 cm\({}^{3}\)/mol), suggesting some error with respect to \(\delta_{p}\) in [24]. This seems likely in view of [PERSON] et al. citing work by [PERSON] et al. that had been relevant to their calculus but was later shown to be substantially erroneous [25].  
_Solvents_. The solubility parameters \(\delta_{2}\) of all solvents relate to 20 \({}^{\circ}\)C or 25 \({}^{\circ}\)C. For methyl hydro peroxide, the Hansen components were not taken from [9] but, instead, calculated by the HVK method yielding at 20 \({}^{\circ}\)C (\(\delta_{d}\), \(\delta_{p}\), \(\delta_{h}\)) = (14.9, 13.1, 21.7) and \(\delta_{2}\) = 29.4, each in units of (MPa)\({}^{0.5}\). With \(\delta_{2}\) = 36.7 (MPa)\({}^{0.5}\), according to [9], the difference stays roughly within the \(\delta\propto V^{-0.5}\) dependency, so that there appear to be no major discrepancies other than those arising from double the molar volume. Like \(\delta_{1}\), an error margin of \(\Delta\delta_{2}\) = \(\pm 1\) (MPa)\({}^{0.5}\) is assumed a reasonable figure for the solvents. All solvent values are presented in the overall results table further below.