Mark-Houwink equation

The Mark-Houwink equation (also known as the Kuhn-Mark-Houwink-Sakurada equation or Staudinger-Kuhn equation )

${\displaystyle \lbrack \eta \rbrack =K\cdot M^{\alpha }}$

is an empirically found form of the relationship between two quantities of a polymer , namely

• the molar mass mean M ( viscosity mean , corresponds approximately to a weight mean ) and
• the limiting viscosity [η] ( Staudinger index : limit value of the reduced viscosity , extrapolated to a concentration and a shear gradient of zero; determined experimentally via viscosity measurements at different polymer concentrations ).
• K and α are constants that cannot be calculated exactly theoretically and therefore have to be determined empirically for each polymer- solvent pair.

In their logarithmic form

${\displaystyle M^{\alpha }={\frac {\lbrack \eta \rbrack }{K}}}$

the equation is often used to determine the molecular weight average of a polymer from the Staudinger index.

The values ​​of K and α depend on the geometric shape of the polymer (hydrodynamic volume) and thus also on its interaction with the solvent. They are determined with the help of calibration samples, which should have a very narrow molecular weight distribution with a known viscosity average. The constants K and α for many polymer-solvent pairs are published in the specialist literature.

The equation is named after Hermann F. Mark and Roelof Houwink .

Individual evidence

1. ↑ Herbert Stricker (Ed.): Martin Swarbrick Cammarata, Physikalische Pharmazie . Wissenschaftliche Verlagsgesellschaft, Stuttgart, 1987, pp. 455 f.
2. ^ Gary Patterson, "Polymer Science from 1935-1953: Consolidating the Paradigm," Springer 2014, p. 64