Comparison of Statistical Measures Reported by NTA and DLS Techniques

As the Nanoparticle Tracking Analysis (NTA) technique has gained in popularity in recent years, comparison to Dynamic Light Scattering (DLS) results has become more frequent. When comparing results, it is important to understand the differences between the two techniques and what the reported parameters truly mean. This technical note reviews the difference between measures of the center of the distribution (mean and z-average), measures of the width of the distribution (standard deviation and polydispersity index (PDI)) and the different distribution weighting types (number, volume and intensity).

Introduction

As the Nanoparticle Tracking Analysis (NTA) technique has gained in popularity in recent years, comparison to Dynamic Light Scattering (DLS) results has become more frequent. When comparing results, it is important to understand the differences between the two techniques and what the reported parameters truly mean.

DLS has been the most popular sub-micron particle size analysis technique for the past 30-40 years. While each instrument manufacturer has different implementations, the basic principles described here hold true for all types. For a more thorough description of the basic principles behind each technique, the reader is referred to the ASTM and ISO guides on the two techniques [1, 2, 3].

Measures of the center of the distribution

NTA tracks each particle’s position on a frame-by-frame basis, allowing calculation of the diffusion coefficient and thus size of each particle. The data produced is a list of population of single-particle measurements. Common statistical measures of a population are used to represent the final particle size distribution. The mean, mode, median (D50), and standard deviation are standard outputs of NTA software.

DLS analyzes the time-dependent scattered light intensity signal from a single detector. From the analysis of the manner in which this signal fluctuates in time, an autocorrelation function is derived. A polynomial curve is fitted to the logarithmic decay plot of the autocorrelation function to determine size parameters. The basic cumulants model is a simple Taylor series expansion, where the first cumulant corresponds to the intensity-weighted mean, commonly referred to as the z-average particle size. The second cumulant can be related to the width of a hypothetical Gaussian distribution. This is the polydispersity index (PDI).

Log[G] =a++2+3+4….

Where b is the z-average and PDI is calculated by:

PDI = 2c/b2

As the z-average and PDI are direct results of this mathematical approach, rather than a statistical analysis of a population of individually measured particles; they are unique and specific to DLS analyses. In the case of a truly monodisperse size distribution, z-average from DLS measurements and mean or mode sizes from NTA measurements would be equal.

Further reading on PDI:

http://www.materials-talks.com/blog/2015/03/31/pdi-from-an-individual-peak-in-dls/

Measures of the width of the distribution

As described above, the basic technique differences mean that different statistical measures are used to describe the width of the distribution. For NTA, Standard Deviation (SD) is provided by the software. This is reported in units of nanometers and relates to the absolute width of the distribution. It is also common to report a Relative Standard Deviation which is SD*100/mean and expressed as a percentage.

For DLS, the polydispersity index (PDI) is derived as described above for the simple (assumed) Gaussian distribution by the cumulants method. For more advanced deconvolution algorithms where a particle size distribution is actually calculated, the mean size and the standard deviation from that mean can be obtained directly from the statistics of the distribution. Here, the (absolute) width of the distribution can be compared to the mean, and a relative polydispersity = width/mean can be obtained.

 Narrow Distributions Moderate Width Polydisperse Distributions PDI from DLS 0.0-0.1 0.1-0.4 >0.4 %RSD from NTA 0.01-10 10-40 >40

Further reading on polydispersity:

Weighted Distributions: Number, Volume and Intensity

A particle size distribution can be represented in different ways with respect to the weighting of individual particles. The weighting mechanism will depend upon the measuring principle being used.

A counting technique such as NTA will give a number-weighted distribution, in which each particle is given equal weighting irrespective of its size. This is most often useful when knowing the absolute number of particles is important, in aggregate detection for example, or where high resolution (particle by particle) is required.

Static light scattering techniques such as laser diffraction will give a volume weighted distribution. Here the contribution of each particle in the distribution relates to the volume of that particle (equivalent to mass if the density is uniform), i.e. the relative contribution will be proportional to (size)3. This is often extremely useful from a commercial perspective as the distribution represents the composition of the sample in terms of its volume/mass, and therefore its potential worth.

Dynamic light scattering techniques will give an intensity-weighted distribution, where the contribution of each particle in the distribution relates to the intensity of light scattered by the particle. For example, using the Rayleigh approximation, the relative contribution for very small particles will be proportional to (size)6.

When comparing particle size data for the same sample measured by different techniques, it is important to realize that the types of distribution being measured and reported can produce very different particle size results. This is clearly illustrated in the example below, for a sample consisting of equal numbers of particles with diameters of 5 nm and 50 nm. The number-weighted distribution gives equal weighting to both types of particles, emphasizing the presence of the finer 5 nm particles, whereas the intensity-weighted distribution has a signal one million times higher for the coarser 50 nm particles. The volume-weighted distribution is intermediate between the two.

It is possible to convert particle size data from one type of distribution to another; however, this requires certain assumptions about the form of the particle and its physical properties. One should not necessarily expect, for example, a volume weighted particle size distribution measured using image analysis to agree exactly with a particle size distribution measured by laser diffraction.

Further reading on weighting:

http://www.materials-talks.com/blog/2014/01/23/intensity-volume-number-which-size-is-correct/

Intensity - Volume - Number - Technical Note

References

ASTM E2834 - 12 Standard Guide for Measurement of Particle Size Distribution of Nanomaterials in Suspension by Nanoparticle Tracking Analysis (NTA)

ASTM E2490 - 09 Standard Guide for Measurement of Particle Size Distribution of Nanomaterials in Suspension by Photon Correlation Spectroscopy (PCS)

ISO 13321:1996 Particle size analysis -- Photon correlation spectroscopy

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