For non-interacting particles, the exponents can be shown to be related by a = 3a – 1. It is important to note, that the k & a values used for the diffusion form of the equation differ from the k & a values used for the viscosity form.
As with the viscosity form of the expression, extensive tables of solvent-particle k & a values are available, many of which are listed in the Help file of the DTS software for the Zetasizer Nano system. Similar to the viscosity form of the Mark-Houwink equation, one can use the above expression to estimate the molecular weight of a particle from the DLS measured diffusion coefficient and known k & a values.
Using the above expression, along with known k & a values, one can estimate the polymer molecular weight from the measured intrinsic viscosity.Īn alternate form of the Mark-Houwink equation, suitable for use with dynamic light scattering (DLS) data, is that shown below, where D is the translational diffusion coefficient, M is the molecular weight, and k & a are solvent-particle dependent fitting parameters. The expression describing this empirical relationship is the Mark-Houwink equation shown below, where h is the intrinsic viscosity, M is the molecular weight, and k & a are solvent-polymer dependent fitting parameters.Įxtensive tables of k & a values for various solvent-polymer pairs are readily available, either through reference publications or simple internet searches.
What_is_the_Mark_Houwink_equation_ What is the Mark-Houwink equation?įor narrow molec ular weight fraction linear polymers, log-log plots of the molecular weight dependence on the intrinsic viscosity are linear.