**There are several sources of information providing a mathematical description of terms used in light scattering. However, these may not help in understanding their use in the practical application of the technique.**

These terms listed below provide a descriptive definition, with notes on their specific use in the context of Dynamic Light Scattering.

## Z-Average size

The Z-Average mean used in dynamic light scattering is also called the cumulants mean. It is the most stable and primary parameter produced by the technique. While used in a quality control setting, this is probably the best value to report as defined in ISO 13321. More recently ISO 22412 defines this mean as the harmonic intensity averaged particle diameter. Z-average is a hydrodynamic parameter and is hence suited only to particles in a dispersion or molecules in solution.

## Cumulants Analysis

This is a simple technique used to analyze the autocorrelation function generated by a DLS experiment. ISO 13321 and ISO 22412 define the calculation. It can produce several values as it is a moments expansion, however only the first two terms are used practically, a mean value for the size (Z-Average), and a width parameter known as the Polydispersity Index (PdI). The calculation is defined in the ISO standards, so all systems that make use of this calculation as recommended should give comparable results if the same scattering angle is used.

## Polydispersity Index

The polydispersity index is a simple index determined from a simple 2 parameter fit to the correlation data. The Polydispersity Index does not have any dimension and is scaled such that values less than 0.05 are seen very rarely compared with monodisperse standards.

The ISO standard document 13321:1996 E and ISO 22412:2008 define the calculations for these parameters.

## Polydispersity

In the context of light scattering, both polydispersity and % polydispersity are derived from the polydispersity index, which is a parameter calculated from a Cumulants analysis of the DLS-measured intensity autocorrelation function.

A single particle size mode is assumed in the Cumulants analysis and a single exponential fit is applied to the autocorrelation function. Polydispersity describes the width of the assumed Gaussian distribution. In terms of a protein analysis, a percentage polydispersity less than 20% indicates that the sample is monodisperse.

## Diffusion Coefficient

Molecules and particles in solution or suspension are subject to Brownian motion. This is induced via bombardment with solvent molecules, especially as these molecules are moving due to their thermal energy. In the case of the molecules or particles being lit with a laser, the intensity of the scattered light fluctuates at a rate based on the particle size as smaller particles are further kicked by solvent molecules and move more rapidly.

Analyzing these intensity fluctuations can help determine the velocity of the Brownian motion and hence helps determine particle size using the Stokes-Einstein relationship. The diffusion coefficient defines this Brownian motion of the analyte or particle in that particular solvent environment. The translational diffusion coefficient is not based just on the core particle size but also on any surface structure, as well as the concentration and type of ions in the medium.

## Hydrodynamic Diameter

The hydrodynamic size measured by Dynamic Light Scattering (DLS) is defined as the size of a hypothetical hard sphere that diffuses similar to that of a particle being measured. In practice, macromolecules or particles in solution are dynamic, non-spherical and solvated. Due to this the diameter determines from the diffusional properties of the particle indicate the apparent size of the dynamic hydrated/solvated particle.

The hydrodynamic diameter, or Stokes diameter, is that of a sphere that has the same translational diffusion coefficient as the particle being measured, assuming a hydration layer surrounding the particle or molecule.

## Correlation Curve or Correlation Function

The data obtained in a dynamic light scattering (DLS) experiment is mapped as a correlation curve which should be a smooth, single exponential decay function for a mono-size particle dispersion. The correlation curve comprises all data with regards to the diffusion of particles within the sample being measured. The diffusion coefficient D can be determined by fitting the correlation curve to an exponential function.

## Y-Intercept or Intercept

The Y-Intercept or the Intercept in DLS is the intersection of the correlation curve on the y-axis of the correlogram. One can use the y-intercept to evaluate the signal-to-noise ratio from a measured sample and it is often used to judge data quality. It is mostly scaled such that an ideal signal will give a value of 1 - a good system will give intercepts more than 0.6.

## Deconvolution or Deconvolution Algorithm

This is an algorithm-based approach to resolving several exponentials obtained from a polydisperse sample into several intensity values each associated with a discrete size band. A deconvolution of the measured intensity autocorrelation function of the sample helps obtain the particle size distribution from dynamic light scattering (DLS). This is done using a a non-negatively constrained least squares (NNLS) fitting algorithm, a common example being CONTIN.

## Count Rate or Photon Count Rate

In DLS this can be defined as the number of photons detected and is normally stated in a "per second" basis. This helps determine the sample quality by monitoring its stability as a function of time and is used for setting instrument parameters such as the attenuator setting and sometimes analysis duration.

## Intensity Distribution

The first order result obtained from a DLS experiment is an intensity distribution of particle sizes. The intensity distribution is weighted naturally based on the scattering intensity of each particle family or fraction. For biological polymers or materials, the particle scattering intensity is proportional to the square of the molecular weight.

## Volume Distribution

Even though the fundamental size distribution generated by DLS is an intensity distribution, it is possible that this be converted using Mie theory, to a volume distribution or a distribution describing the relative proportion of multiple components in the sample based on their mass or volume rather than based on their scattering (Intensity.)

There are four assumptions that must be accepted while transforming an intensity distribution to a volume/mass distribution. These include the following:

- All particles are spherical
- All particles are homogeneous
- The optical properties of the particles are known, i.e. the real & imaginary components of the refractive index
- There is no error in the intensity distribution

This information has been sourced, reviewed and adapted from materials provided by Malvern Panalytical.

For more information on this source, please visit Malvern Panalytical.