## 3 Results and Discussion
### Determination of Quercetin and Gallic Acid

Table 5: [PERSON] and Hildebrand parameters of the main bioactive components of blackberry [47, 48] and the used solvents [21]. As the best results were obtained with 90% \(v/v\) acidified acetonitrile, the [PERSON] parameters analysis was performed for the acidified acetonitrile-water solvent mixture as a solvent and cyanidin-3-O-glucose as a solute. The addition of acid shifts the equilibrium towards the more stable flavylium form and conforms to Figure 2, changing the \(\delta_{\rm H}\) value of cyanidin-3-O-glucose. Similar to malvidin, the difference between the Hansen solubility parameters of the flavylium and carbinol pseudobase forms of cyanidin is expected to be equal, as the structural changes between the tautomers don't affect the side structures that differentiate the two anthocyanins [48]. Accordingly, the decrease in the HSPs during the carbinol-flavylium transformation, caused by acidification, could be approximately:  
\(\Delta\delta_{\rm P}\approx 0\) MPa\({}^{0.5}\), \(\Delta\delta_{\rm D}=1.85\) MPa\({}^{0.5}\), and \(\Delta\delta_{\rm H}=6\) MPa\({}^{0.5}\), respectively. The Hansen solubility parameters (HSP) of solvent mixtures differ from pure solvents. Still, they could be the volumetric fraction-weighted average of the components' HSPs, even for solvents in a supercritical state, as seen in Equation (9) [50]. \[\delta_{\rm j,mix}=\Sigma^{\rm n}_{\rm i\,i=1}\Phi_{\rm i}\delta_{\rm j,i} \tag{9}\]  
where: \(\delta_{\rm j,mix}\) the HSPs of the solvent mixture; \(\Phi_{\rm i}\) the volumetric fraction of i-th component; n is the number of components of the mixture, and the j index denoting the different solubility parameters as follows: j = D, P, H\({}^{-}\) dispersion, polar and hydrogen bond partial HSPs. Knowing the HSPs of water and acetonitrile, the solubility parameters of the mixture were calculated for the whole concentration range, as in Equation (10):  
\[\delta_{\rm j,mix}=\Phi_{\rm W}\delta_{\rm W}+\Phi_{\rm AcN}\delta_{\rm AcN} \tag{10}\]  
In water-acetonitrile mixtures, the dispersion Hansen parameter varies minimally (D\(\delta_{\rm D,mix}\approx 0\) MPa\({}^{0.5}\)), as changing the acetonitrile concentration would change the solubility of cyanidin-3-O-glucose only through the other two members. The \(\delta_{\rm P}\) values of water and acetonitrile are also quite close (\(\Delta\delta_{\rm P,mix}\leq 2\) MPa\({}^{0.5}\)), but the variation of \(\delta_{\rm H}\) had a wide variation range (\(\Delta\delta_{\rm H,mix}\leq 36.2\) MPa\({}^{0.5}\)). The value of the polar component of the flavylium cation (\(\delta_{\rm P}=19.48\) MPa\({}^{0.5}\)) doesn't change in comparison to the natural cyanidin-3-O-glucose before the acidification, but this value is near to the values of the acetonitrile-water mixtures (\(\delta_{\rm P}\approx 16\)-18 MPa\({}^{0.5}\)). The value of the dispersive component of the flavylium cation (\(\delta_{\rm D}=23.85\) MPa\({}^{0.5}\)) is closer than of the original form (\(\delta_{\rm D}=25.7\) MPa\({}^{0.5}\)) to the values of the acetonitrile-water mixtures (\(\delta_{\rm D}\approx 15.4\) MPa\({}^{0.5}\)), but the difference remains considerable. In this situation, the solvent optimization task is, mainly, to find the acetonitrile-water ratio with the \(\delta_{\rm H}\) value closest to the \(\delta_{\rm H}\) value of the flavylium ion (\(\delta_{\rm H}=22.08\) MPa\({}^{0.5}\)). As for the acetonitrile, the hydrogen-bond component had a low value (\(\delta_{\rm H}=6.1\) MPa\({}^{0.5}\)), and for water, it had a very high value (\(\delta_{\rm H}=42.3\) MPa\({}^{0.5}\)). Obviously, with the increase in the water amount, the optimum could be reached. In Figure 6, it could be observed that acidification decreases the cyanidin-3-O-glucose point distance, substantially, to the acetonitrile-water curve. The hydrogen-bond component of the solvent mixture increases significantly with water content increase, but the polar component decreases slightly and has an opposite effect on distance.