LS Instruments

This method enables the determination of the average particle size and width of the particle size distribution (PSD) in a colloidal (nanoparticle) sample from a Dynamic Light Scattering (DLS) measurement. CUMULANT is however based on the assumption that only one particle population is present (monomodal), which must have a gaussian distribution around the average particle size.

As in all the DLS experiments, the particle radius  is computed from the diffusion coefficient D.  

Where k_B is the Boltzmann-Konstant, T  the temperature, and η the viscosity.

To obtain the diffusion coefficient from a DLS measurement the intensity correlation function must be analyzed. The standard procedure for this is the application of the CUMULANT method. By fitting a polynomial of third degree to the logarithm of the intensity correlation function, the decay rate  is obtained (1. cumulant).

The decay rate is directly related to the diffusion coefficient D :

Where is q is the wave vector, which depends on the scattering angle. Higher orders of the fitting result (2. and 3. cumulant) give the polydispersity index of the sample. Most modern DLS instruments perform CUMULANT analysis automatically. The quality of the result, however, depends significantly on the quality of the data and the constraint settings of the fitting procedure. CUMULANT can only determine the particle size distribution of a Gaussian distribution around one mean particle size. This is often referred to as the Polydispersity Index (PDI). For bi- or polymodal particle size distributions more complex analysis methods such as the CONTIN or CORENN method are required.