Engineering & Science
Hildebrand Solubility Parameter (delta) & Cohesive Energy Density
Calculate cohesive energy density c = (DeltaH_vap - R * T) / V_m (MPa) and Joel Hildebrand’s SI solubility parameter delta = SQRT(c) (MPa^0.5) to predict polymer-solvent miscibility.
Turn "like dissolves like" into quantitative MPa^0.5 numbers!
Coatings chemists, battery-electrolyte formulators, and pharma crystallization engineers predict whether a solvent will dissolve a polymer or resin using Joel H. Hildebrand’s (1936) Regular Solution Theory! Evaporating 1 mole of liquid at temperature T (K) overcomes internal intermolecular cohesion plus P*V = R*T expansion work, so internal molar cohesive energy is DeltaU_vap = DeltaH_vap - R * T (J/mol). Dividing by liquid molar volume V_m (cm^3/mol) gives Cohesive Energy Density c in J/cm^3 (= MPa), and taking its square root defines the SI Hildebrand Solubility Parameter: delta = SQRT((DeltaH_vap - 8.31446 * T) / V_m) in MPa^0.5!
Non-polar and moderately polar liquids mix spontaneously when their solubility parameters match within |delta_1 - delta_2| <= ~3.5 MPa^0.5! Look at Acetone at T = 298.15 K (DeltaH_vap = 31,300 J/mol, V_m = 74.0 cm^3/mol): c = 389.47 MPa and delta = 19.74 MPa^0.5 (readily dissolving PMMA at delta ~ 19.0 MPa^0.5!), whereas strongly hydrogen-bonded Water (DeltaH_vap = 43,990 J/mol, V_m = 18.07 cm^3/mol) jumps to delta = 47.93 MPa^0.5—explaining why oil/hexane (delta ~ 14.9 MPa^0.5) and water separate completely!
| Solvent at 298.15 K | DeltaH_vap (J/mol) & Vm (cm^3/mol) | Cohesive Energy Density c (MPa) | Hildebrand delta (MPa^0.5) |
|---|---|---|---|
| Acetone (Polar Aprotic Ketone) | 31,300 J/mol, 74.0 cm^3/mol | 389.47 MPa | 19.74 MPa^0.5 (9.65 cal^0.5/cm^1.5) |
| Water (3D Hydrogen-Bond Network) | 43,990 J/mol, 18.07 cm^3/mol | 2,297.24 MPa | 47.93 MPa^0.5 |
| Unphysical Vaporization (DeltaH <= R*T) | Cohesion Guard | "Invalid Thermodynamic Inputs" | Requires DeltaH_vap > R * T |
Cohesive Energy Density c (MPa = J/cm^3) = (DeltaH_vap - R * T) / V_m
Evaluates internal vaporization energy per cm^3 using R = 8.31446 J/(mol*K).
=IF(OR(B3 <= 0, B4 <= 0, B2 <= 8.31446 * B4), "Invalid Thermodynamic Inputs", ROUND((B2 - 8.31446 * B4) / B3, 2))SI Hildebrand Solubility Parameter delta (MPa^0.5) = SQRT(c)
Takes the square root of cohesive energy density (divide by 2.0455 if converting to legacy Hildebrand cal^0.5/cm^1.5).
=IF(OR(B3 <= 0, B4 <= 0, B2 <= 8.31446 * B4), "Invalid Thermodynamic Inputs", ROUND(SQRT((B2 - 8.31446 * B4) / B3), 2))Try the example
Use the original values or change them to test your understanding.