Two fitting models are available for fitting the autocorrelation function (ACF) derived from dynamic light scattering (DLS) measurements with PR.Panta Control. The data of each DLS acquisition is automatically analyzed with both algorithms.

Cumulant fit

The cumulant analysis was developed by Koppel in 1972 and is one of the most commonly used methods for DLS data analysis. It models the ACF using an average diffusion coefficient to obtain a single averaged hydrodynamic radius rH with a single polydispersity index (PDI). More specifically, the ACF is fit by a polynomial series expanding around the mean decay rate G:

where B is the baseline, b is the amplitude, m₂ is a factor for polydispersity, and t is the time increment. The mean decay rate G is proportional to the mean translational diffusion coefficient D which is used to calculate rH.

The cumulant analysis is defined in the ISO 22412 on DLS measurements and is the method of choice for the analysis of monodisperse samples.

Size distribution fit

The size distribution fit (or regularization) models the ACF with a sum of exponential functions. Each of the exponential functions relates to one particle size, which is why the output is a distribution of particles with discreet hydrodynamic radii. Several regularization methods exist and there is no standardized algorithm defined in the ISO norm for DLS measurements. The algorithm implemented in PR.Panta Control belongs to the group NNLS (non-negative least squares) methods.

Due to noise in the data and the fact that many solutions exist which can fit the data to a similar accuracy, size distribution fits often yield very "spiky" distributions with many different particle sizes. To obtain results that better reflect a real particle distribution, the regularizer comes into play. It is a tool that controls the smoothness of the distribution, favoring clusters of particle sizes at the cost of increased fitting error, which helps to alleviate the problem of multiple fit solutions and noise. The magnitude of the regularization parameter is proportional to the smoothness of the distributions. PR.Panta Control uses a fixed regularization parameter which has been optimized for the analysis of biological samples such as protein solutions. Note that the output size distribution will always be one of many possible solutions and care should be taken to not over-interpret the results, especially if several particle populations are observed.

In PR.Panta Control, the result of this fit is displayed as a size distribution plot. In the tabulated results, the size distribution model reports the hydrodynamic radii and PDI for up to three discreet peaks (the model can fit more than three peaks, but only the three largest ones will be summarized in the results table). Furthermore, the average diffusion coefficient across all particle populations from the size distribution fit is used to calculate the diffusion interaction parameter kD.

The size distribution fit works best for polydisperse samples.