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Flory-Huggins Interaction Calculator

Enter the solubility parameters, molar volume, and temperature to find χ.

How it is calculated

The tool uses the solubility-parameter estimate χ = Vm × (δ₁ − δ₂)² / (R × T) + 0.34. The δ values are Hildebrand solubility parameters in MPa0.5, Vm is the molar volume in cm³/mol, T is the absolute temperature in kelvin and R = 8.314 J/(mol·K). Since MPa equals J/cm³, the units cancel and χ is dimensionless. The 0.34 is a fixed empirical term, so identical parameters still give χ = 0.340. The sign of the difference does not matter because it is squared (the difference line shows δ₁ − δ₂ with its sign). The verdict is miscible when χ is below 0.5 and immiscible at 0.5 or above. Molar volume and temperature must be above zero or no result is returned. This is a screening estimate, not a measured interaction parameter.

Worked example

Take a solvent with δ₁ = 20 MPa0.5 and Vm = 74 cm³/mol, and a polymer with δ₂ = 18.6, at 298.15 K. The difference is 1.4, and its square is 1.96. Then Vm × 1.96 = 145.04, and R × T = 8.314 × 298.15 = 2478.8. The ratio is 0.0585, and adding 0.34 gives χ = 0.399. That is below 0.5, so the tool reports the pair as miscible.

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Common mistakes

  • Entering the temperature in degrees Celsius. With 25 instead of 298.15 the same inputs give χ = 1.038 and an immiscible verdict instead of 0.399. The field needs kelvin.
  • Using solubility parameters in other units, such as (cal/cm³)0.5. The formula assumes MPa0.5; values in the older unit are about 2.05 times smaller and need converting first.
  • Entering the polymer's molar volume, or the volume of a repeat unit. Vm is the solvent's molar volume in cm³/mol.
  • Reading χ = 0.340 for identical parameters as a sign of perfect mixing. The constant 0.34 is always added, so χ never falls below it with this formula.
  • Treating the 0.5 cut-off as a sharp boundary. Values near 0.5 are borderline and depend on molar mass, concentration and the accuracy of the δ values.

About this calculator

The Flory-Huggins interaction parameter χ estimates how favorably a polymer will mix with a solvent using χ = (V_m ÷ RT)(δ₁ − δ₂)² + 0.34, where V_m is the solvent's molar volume (cm³/mol), R is the gas constant, T is absolute temperature (K), δ₁, δ₂ are the Hildebrand solubility parameters of the solvent and polymer (MPa^0.5), and 0.34 is an empirical constant added to the result — the closer the two solubility parameters, the smaller χ, and the better the miscibility (even identical parameters leave χ at 0.34).

Polymer chemists and materials scientists use this estimate during solvent selection for coatings, adhesives, membrane casting, and polymer processing: as a rule of thumb, a χ below about 0.5 suggests favorable mixing (good solvent), while higher values point to phase separation or a poor solvent, informing formulation choices before running full solubility trials in the lab.

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Comments (1)

  • Editorial team

    A quick way to screen a list of candidate solvents is to flip the formula around. Since the verdict flips at 0.5, the largest solubility-parameter gap that still passes is the square root of 0.16 × R × T ÷ Vm. With a molar volume of 100 cm³/mol at 298 K that is about 1.99 MPa^0.5, so any solvent within roughly two units of the polymer passes. Which polymer and solvent pairs are you comparing?

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