| δd | the dispersion contribution to δ |
| δp | the polar contribution to δ |
| δh | the hydrogen bonding contribution to δ |
The relation δ2=δd2+δp2+δh2 holds. Thus for non-polar solvents δp=δh=0 and δd=δ.
Solutes do also have δd,δp and δh parameters and an additional parameter, the interaction radius, R0. To determine the solubility of a compound the distance Ra is calculated.
| Ra2= 4×Δδd2+ Δδp2+ Δδh2 |
| where |
| Δδd2= (δsolute,d-δsolvent,d)2 |
| Δδp2= (δsolute,p-δsolvent,p)2 |
| Δδh2= (δsolute,h-δsolvent,h)2 |
Please note that the accuracy of using the Hansen parameters to be predict solubility seems to be "moderate".
"Using a data set of 75 polymers, we find that the Hildebrand model displays a predictive accuracy of 60% for solvents and 76% for nonsolvents. The Hansen model leads to a similar performance; on the basis of a data set of 25 polymers for which Hansen parameters are available, we find that it has an accuracy of 67% for solvents and 76% for nonsolvents. … Our analysis shows that while the Hildebrand model has a predictive accuracy of 70–75% for nonpolar polymers, it performs rather poorly for polar polymers (with an accuracy of 57%)."
See: "Critical Assessment of the Hildebrand and Hansen Solubility Parameters for Polymers"; Venkatram S, Kim C, Chandrasekaran A, Rampi Ramprasad R; J. Chem. Inf. Model. 2019 (59) 4188–4194
"Using a data set of 75 polymers, we find that the Hildebrand model displays a predictive accuracy of 60% for solvents and 76% for nonsolvents. The Hansen model leads to a similar performance; on the basis of a data set of 25 polymers for which Hansen parameters are available, we find that it has an accuracy of 67% for solvents and 76% for nonsolvents. … Our analysis shows that while the Hildebrand model has a predictive accuracy of 70–75% for nonpolar polymers, it performs rather poorly for polar polymers (with an accuracy of 57%)."
See: "Critical Assessment of the Hildebrand and Hansen Solubility Parameters for Polymers"; Venkatram S, Kim C, Chandrasekaran A, Rampi Ramprasad R; J. Chem. Inf. Model. 2019 (59) 4188–4194
For a more detailed discussion see →The Official Hansen Solubility Parameter Site or →Solubility Parameters: Theory and Application
The parameters here are given in (cal/mL)½ in order to be consistent with Hildebrand δ. To convert to MPa½ multiply by 2.05.