The Science Behind It

The principle "like dissolves like" is quantified by Hansen Solubility Parameters (HSP). The total cohesive energy of a substance (what holds it together) is divided into three components, which form a 3D coordinate system called **Hansen Space**:

• δD (Dispersion): Weak, universal van der Waals forces present in all molecules, arising from temporary fluctuations in electron clouds. Think of this as a molecule's general "size" or "bulk" attraction.
• δP (Polar): Stronger electrostatic forces between molecules that have a permanent positive and negative end (dipoles). Think of this as the attraction between small magnets.
• δH (Hydrogen Bonding): A very strong, specific type of polar interaction where a hydrogen atom acts as a bridge between two highly electronegative atoms (like Oxygen or Nitrogen). Think of it as tiny, powerful "Velcro" patches on molecules.

A **solute** (what you want to dissolve) is not a single point in this space, but a **Sphere** of compatibility. The sphere's center is the solute's ideal HSP point, and its **Interaction Radius (R₀)** represents its "tolerance" for solvents that aren't a perfect match. A **solvent** (a point) will dissolve the solute if its HSP point falls **inside** this sphere.

The **Hansen Distance (Ra)** measures the "dissimilarity" between a solvent and the solute's center. The formula `Ra² = 4(ΔδD)² + (ΔδP)² + (ΔδH)²` gives extra weight to the dispersion term. This means the Hansen Space is "distorted," and the sphere is visually represented as an **ellipsoid** in our 3D plot, which is the scientifically accurate shape.

How to Use This Tool

1. Enter Experimental Data: In the left column, set the experiment temperature and your definition of a "good" solvent (the solubility threshold). Then, add each solvent you tested and its measured solubility in mg/mL.
2. Get an Initial Guess: Click "Calculate Initial Center" to get a smart starting point for the sphere's center (δD, δP, δH) based on your "good" solvents.
3. Auto-Optimize the Radius: Click "Auto-Optimize Radius" to find the best-fitting sphere size (R₀) for that center.
4. Fine-Tune to Perfection: Manually adjust all four parameters (δD, δP, δH, and R₀) to maximize the **Fit Score**. The final values are your solute's experimentally-determined HSP.
5. Get Advice: Click "Analyze Sphere & Get Advice" to receive feedback on your sphere and suggestions for which solvents to test next to improve your model's accuracy.