MarkHouwinkBeziehung

The Mark-Houwink relation, also known as the Mark-Houwink-Sakurada equation, is an empirical relation in polymer chemistry that links a polymer’s intrinsic viscosity [η] to its molecular weight M for a given solvent and temperature. It is commonly written as [η] = K M^a, or in logarithmic form log[η] = log K + a log M, where K and a are solvent- and polymer-specific constants.

Historically, the relation was established by Kurt Mark and Dieter Houwink in 1927 and later extended by Sakurada. It provides a practical bridge between solution properties and molecular size, allowing researchers to estimate molecular weights from viscosity measurements or to monitor changes in polymer samples during synthesis or processing. Intrinsic viscosity is typically obtained by extrapolating reduced or specific viscosity measurements to infinite dilution.

The constants K and a depend on the polymer, the solvent, and temperature, and can also be influenced by chain architecture. In good solvents for flexible chains, a is usually around 0.6–0.8; in theta solvents it approaches about 0.5; for rigid or highly structured chains, a can be higher, closer to 1.0. Because K and a are system-specific, the relation must be calibrated for each polymer–solvent–temperature combination.

Applications include estimating molecular weight from viscosity data, characterizing polymer samples, and assessing changes in branching or conformation. Limitations arise from its empirical nature: deviations occur for branched or crosslinked polymers, polydisperse samples, poor solvents, or conditions far from the calibration system. The Mark-Houwink relation remains a foundational tool in polymer characterization when used with appropriate calibration.