The diffusion interaction parameter kD is a useful parameter to assess weak inter-particle interactions and is generally employed to understand and predict colloidal protein stability. For instruction on setting up a kD experiment please refer to the article How to perform kD measurements. 

kD is calculated via a concentration-dependent measurement of the diffusion constant D. Fitting the D(c) curve with a straight line yields the first order diffusion interaction parameter kD :

where D is the translational diffusion coefficient, D₀ the diffusion coefficient at infinite dilution, k_D the first order diffusion interaction parameter, and c the particle concentration.

In a Size Analysis experiment using Prometheus Panta, two different diffusion coefficients can be obtained per sample, as the raw autocorrelation function (ACF) data is processed using two distinct fitting approaches.

The cumulant fit provides a diffusion coefficient that is used to calculate the cumulant hydrodynamic radius via the Stokes-Einstein equation. The diffusion coefficient is derived from the average ACF of all 10 acquisitions within a single capillary and is directly displayed in the results table of a Size Analysis experiment. Outlier acquisitions are automatically excluded from averaging.

The size distribution fit provides an intensity-weighted size distribution, from which hydrodynamic radii for up to four discrete peaks can be determined. The diffusion coefficient for kD analysis is directly calculated from the intensity-weighted size distribution's harmonic mean hydrodynamic radius via the Stokes-Einstein equation, where the distribution's y-values serve as weights in the calculation of the harmonic mean hydrodynamic radius. In Panta Control, diffusion coefficients from all acquisitions are used in a linear regression for kD analysis. The software also allows users to set a lower radius cutoff, enabling the exclusion of smaller particles - such as buffer components like sugars - from the analysis.

For homogeneous samples without small particles, the cumulant fit provides the most accurate diffusion coefficient and should be used for kD analysis. However, since the software allows for the exclusion of small particles from the analysis, the kD analysis in Panta Software is based on the size distribution model. As a result, the displayed diffusion coefficient may differ from the diffusion coefficient shown in the table of a Size Analysis experiment. 

At high sample concentration, secondary effects like restricted diffusion or multiple scattering may lead to an under- or overestimation of the diffusion constant and the concentration-dependency becomes non-linear. With lower concentrations, the noise or the influence of small buffer peaks may increase. Both effects tend to lead to an overestimation of the diffusion constant. Capillaries showing secondary effects at high concentration or noisy data at low concentration can be removed from the kD calculation by using the exclude function. Capillaries with additional buffer peaks do not have to be excluded completely. If the particles disturbing the signal are smaller than 2 nm, it is possible instead to filter out their contribution to the output diffusion coefficient. Because it is more intuitive to remove particles based on their size than on their diffusion coefficient, a cutoff of 1, 1.5, or 2 nm can be applied to the lower radius limit of a capillary in the acquisition details tab. Filtering out the diffusion coefficients below the threshold does not eliminate the scattering of those particles, it merely removes the scattering signal of those particles from the kD analysis.

If performing the analysis outside the software, users should consider these differences and select the diffusion coefficient that best represents the sample. When using the cumulant fit diffusion coefficients, applying a weighted linear regression can further enhance data reliability.