Engineering & Science
Mark-Houwink-Sakurada Equation: Intrinsic Viscosity [eta] & Polymer Molar Mass (Mv)
Calculate dilute polymer intrinsic viscosity [eta] = K * Mv^a (dL/g) and invert Ubbelohde viscometer measurements back to viscosity-average molecular weight Mv = ([eta] / K)^(1 / a).
Determine polymer molecular weight and coil conformation from Ubbelohde viscometry!
Capillary viscometry is the fastest QC method for measuring polymer molecular weight in dilute solution! Extrapolating reduced viscosity eta_sp / c to zero concentration yields intrinsic viscosity [eta] (in dL/g), which obeys the Mark-Houwink-Sakurada power law: [eta] = K * (Mv^a), where Mv is viscosity-average molar mass (g/mol) and (K, a) are polymer-solvent-temperature constants!
The Mark-Houwink exponent a directly reveals chain conformation in solution: a = 0.50 defines an unperturbed Flory theta-solvent random coil, 0.65 <= a <= 0.80 indicates a swollen coil in a thermodynamically good solvent (such as polystyrene in toluene at 25 °C with K = 1.1e-4 dL/g, a = 0.725), and a >= 1.0 signals rigid-rod macromolecules! Inverting the power law solves directly for viscosity-average molar mass Mv = ([eta] / K) ^ (1 / a): at Mv = 250,000 g/mol, polystyrene gives [eta] = 0.9014 dL/g!
| Polystyrene in Toluene (K = 0.00011 dL/g, a = 0.725) | Molar Mass Mv (g/mol) | Intrinsic Viscosity [eta] (dL/g) | Solvent Quality Insight |
|---|---|---|---|
| Injection-Molding Grade PS | Mv = 250,000 g/mol | [eta] = 0.9014 dL/g | a = 0.725 -> Good solvent swollen coil |
| High-Impact Extrusion PS | Mv = 500,000 g/mol (2x Mv) | [eta] = 1.4899 dL/g (2^0.725 = 1.653x) | Sublinear coil expansion |
| Inverse Viscometer Assay | Measured [eta] = 0.9008 dL/g | Mv = 249,785 g/mol | ([eta] / K)^(1 / a) inversion |
Intrinsic Viscosity [eta] = K * (Mv ^ a) (dL/g)
Evaluates K * (Mv^a) after checking positive Mark-Houwink parameters K, a, and Mv.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0), "Invalid Viscometry Inputs", ROUND(B2 * (B4 ^ B3), 4))Inverse Viscosity-Average Molecular Weight Mv = ([eta] / K) ^ (1 / a) (g/mol)
Inverts measured intrinsic viscosity B5 (dL/g) into viscosity-average molar mass Mv.
=IF(OR(B2 <= 0, B3 <= 0, B5 <= 0), "Invalid Viscometry Inputs", ROUND((B5 / B2) ^ (1 / B3), 0))Try the example
Use the original values or change them to test your understanding.