Dilute-Solution Viscometry
Dilute-solution viscometry measures how a dissolved polymer thickens its solvent, and the resulting intrinsic viscosity gives a simple, classic estimate of molar mass through the Mark-Houwink relation.
Definition
Dilute-solution viscometry is the determination of a polymer's intrinsic viscosity from measurements of solution viscosity at low concentration, used to estimate molar mass and to probe chain dimensions in solution.
Scope
This topic covers the measurement and interpretation of dilute polymer-solution viscosity: relative, specific, reduced, and inherent viscosities, extrapolation to the intrinsic viscosity at infinite dilution, the link between intrinsic viscosity and hydrodynamic volume, and the Mark-Houwink equation relating intrinsic viscosity to molar mass with parameters that depend on polymer, solvent, and temperature.
Core questions
- How is intrinsic viscosity obtained from solution-viscosity measurements?
- How does intrinsic viscosity relate to chain hydrodynamic volume?
- How does the Mark-Houwink equation convert intrinsic viscosity to molar mass?
- What do the Mark-Houwink exponents reveal about solvent quality and chain shape?
Key theories
- Intrinsic viscosity and hydrodynamic volume
- Extrapolating the concentration dependence of solution viscosity to infinite dilution gives the intrinsic viscosity, which is proportional to the chain's hydrodynamic volume divided by its molar mass and so reflects coil size in solution.
- Mark-Houwink relation
- Intrinsic viscosity scales with molar mass raised to an exponent between about 0.5 at theta conditions and near 0.8 in good solvents, so calibrated Mark-Houwink constants yield a viscosity-average molar mass and report on chain conformation.
Mechanisms
A dissolved coil perturbs the flow around it, raising the solution viscosity in proportion to the volume fraction the coils occupy. Measuring efflux times in a capillary viscometer at several low concentrations and extrapolating the reduced viscosity to zero concentration isolates the intrinsic viscosity, free of chain-chain interactions. Because intrinsic viscosity tracks hydrodynamic volume, and hydrodynamic volume grows with molar mass, the empirical Mark-Houwink power law converts intrinsic viscosity into a viscosity-average molar mass; the value of its exponent indicates whether the chain is in a theta, good, or rigid-rod environment.
Clinical relevance
Dilute-solution viscometry remains a fast, inexpensive method for estimating molar mass in research and industry, used to monitor synthesis, specify grades of commercial polymers, and assess degradation. Its sensitivity to hydrodynamic volume also underlies the universal calibration that converts size-exclusion chromatograms across different polymers.
History
Staudinger first linked solution viscosity to chain length in the 1930s, and the empirical power-law relation between intrinsic viscosity and molar mass was established by Mark, Houwink, and Sakurada in that decade; Flory's later treatment connected intrinsic viscosity to chain dimensions and the theta state, putting the method on a firmer theoretical footing.
Key figures
- Hermann Staudinger
- Herman Mark
- Roelof Houwink
- Paul Flory
Related topics
Seminal works
- hiemenz2007
- flory1953
Frequently asked questions
- What is intrinsic viscosity?
- It is the limiting contribution of a polymer to its solution's viscosity per unit concentration, found by extrapolating dilute-solution measurements to zero concentration. It reflects the size of the individual coils in that solvent.
- How does viscometry give a molar mass?
- The Mark-Houwink equation relates intrinsic viscosity to molar mass through two constants specific to the polymer-solvent-temperature system. With those constants, a single intrinsic-viscosity measurement yields a viscosity-average molar mass.