Dynamic Light Scattering – Defined Common Terms

1. Z-Average Size

      The Z-average size or Z-average mean used in dynamic light scattering is a parameter also known as the cumulant mean. It is the most important and stable parameter generated in this technique. As it is defined in ISO 13321 and more recently in ISO 22412, reporting this cumulative mean value is ideal when it is used in quality control regulations, and the ISO standard defines this mean as the ‘harmonic intensity average particle diameter’.

  The Z-average size can be compared with sizes measured by other techniques if the sample is unimodal (i.e., a single peak), spherical or nearly spherical in shape, and monodisperse (i.e., very narrow width of distribution) and is appropriately dispersed in a dispersant, because the Z-average mean size is sensitive even to small changes in the sample, such as the presence of small amounts of aggregates. It should be noted that the Z-average is a hydrodynamic parameter and can only be applied to particles or molecules in solution. 

2. Cumulants Analysis

     This is a simple way of analyzing the autocorrelation function generated by DLS experiments. The outputs are defined in ISO 13321 and ISO 22412. Although it generates many values as it is an expansion of moments, only the first two terms are actually used.

  These terms are known as the mean size (Z-average) and the width parameter, known as the polydispersity index (PdI). The Z-average is a value calculated based on intensity and should not be confused or directly compared with mass or number averages generated by other means. The outputs are defined in the ISO standard. Therefore, any system using these outputs as recommended should present comparable results if the same angle of scattering is used.

3. Polydispersity Index

     This index is a number calculated from a simple 2 parameter fit to the correlation data (cumulants analysis). The polydispersity index is dimensionless and is scaled so that values below 0.05 are rarely seen apart from for highly monodisperse standards. Values above 0.7 indicate that the sample has a very broad size distribution and may not be suitable for DLS methods.

  Various sizing distribution algorithms operate on data that fall between these two limits. The computation of these parameters is defined in ISO standards documents 13321:1996 E and ISO 22412:2008.

4. Polydispersity

     In scattering, the polydispersity or polydispersity % is derived from the polydispersity index, which is a parameter resulting from the cumulants analysis of the intensity autocorrelation function measured by DLS. The cumulants analysis assumes a single particle size mode, applies a single exponential fit to the autocorrelation function, and describes the width of an assumed Gaussian distribution. In protein analysis, a polydispersity % below 20% indicates that the sample is monodisperse. 

5. Diffusion Coefficient

     Particles and molecules in suspension/solution undergo Brownian motion. This is motion caused by the impact of solvent molecules that are moving due to thermal energy. When particles or molecules are exposed to laser light, the intensity of the scattered light varies at a rate that is proportional to the size of the particles because relatively small particles experience more intense collisions from the solvent molecules and therefore move faster.

  Since the rate of Brownian motion can be calculated by analyzing the intensity fluctuations, the particle size can be obtained using the Stokes-Einstein relation. Therefore, the diffusion coefficient defines the Brownian motion of an analyte or particle in a specific solvent environment. This translational diffusion coefficient varies according to the concentration and type of ions in the medium, as well as the size and surface structure of the particles.

5. Hydrodynamic Diameter

     The hydrodynamic size measured by dynamic light scattering (DLS) is defined as the size of a hypothetical sphere that diffuses in the same way as the particle being measured. However, in practice, particles or macromolecules in a solution are not spherical but are dynamic (rotating) and solvated. As a result, the diameter determined by the diffusion properties of the particles represents the apparent size of the dynamic hydrated/solvated particle. Thus, the term hydrodynamic diameter has been established. Therefore, the hydrodynamic or Stokes diameter is the diameter of a sphere that has the same translational diffusion coefficient as the measured particle, assuming the presence of a hydration layer around the particle or molecule.

6. Correlation Curve – or Correlation Function

(Correlation Curve – or correlation function)

     The data measured in a dynamic light scattering (DLS) experiment is a smooth, exponential decay function correlation curve for a monodisperse size particle dispersion. The correlation curve contains all the information regarding the diffusion of the particles in the sample being measured. By fitting the correlation curve to an exponential function, the diffusion coefficient (D) can be derived (D is proportional to the inverse of the decay time).

  Once the diffusion coefficient (D) is known, the hydrodynamic diameter can be calculated using a modified Stokes-Einstein equation. For polydisperse samples, this curve is a sum of exponentials.

7. Y-Intercept or Intercept

     In DLS, the Y-intercept or simply the intercept refers to where the correlation curve intercepts the y-axis on the correlation graph. The y-intercept can be used to assess the signal-to-noise ratio from the measured sample and is often used to judge the quality of the data. It is scaled so that an ideal signal presents a value of 1, a good system provides an intercept above 0.6, and the best systems have an intercept of greater than 0.9.

8. Deconvolution or Deconvolution Algorithm

(Deconvolution or Deconvolution algorithm)

     Algorithm-based approaches to resolve an exponent mixture derived from a polydisperse sample into several intensity values corresponding to individual size bands. The particle size distribution obtained from DLS is derived from the deconvolution of the measured intensity autocorrelation function of the sample. This is typically performed using non-negative least squares (NNLS) fitting algorithms (a common example is CONTIN) that have a constraint to positive values.

9. Count Rate or Photon Count Rate

(Count Rate or Photon Count Rate)

     In DLS, this is simply the number of detected photons, typically expressed as “per second”. It is useful for determining the quality of the sample by monitoring the stability as a function of time and also used to set instrument parameters such as attenuator setting and analysis time. The count rate should be above some minimum value to ensure sufficient signal for the analysis. However, all detectors have a maximum count rate at which their response remains linear. If automated count rate adjustment is not available, follow the manufacturer’s recommendations to adjust the count rate.

10. Intensity Distribution

     The primary result from a DLS experiment is the intensity distribution of particle size. The intensity distribution is naturally weighted by the scattering intensity of each particle fraction or population. For biological materials or polymers, the scattering intensity of the particles is proportional to the square of their molecular weight. Therefore, the intensity distribution may be somewhat misleading as the presence of a small amount of aggregates/agglomerates or larger particle species can dominate the distribution. However, such distributions can serve as a sensitive detector for the presence of larger material within a sample.

11. Volume Distribution

     While the primary size distribution generated by DLS is the intensity distribution, it can be transformed into a volume distribution, which describes the relative proportions of various components in a sample based on mass or volume instead of scattering (intensity), using Mie theory.

  When converting an intensity distribution to a volume/mass distribution, the following four assumptions must be accepted:

• All particles are spherical
• All particles are homogeneous
• The optical properties of the particles, such as the real and imaginary components of the refractive index are known
• There are no errors in the intensity distribution

  Understanding of these assumptions is particularly important because the DLS method itself intrinsically generates distributions with spread peaks.

Therefore, there is always some error in stating intensity distributions.

Thus, volume and number distributions derived from these intensity distributions are best for estimation of relative percentages (not size) for comparative purposes, or when there are multiple modes and peaks, and should not be considered absolute. Therefore, it is good practice to report peak sizes based on intensity analysis and report only relative percentages (not size) from volume distribution analysis.