# Particle Size Measurement Short Tutorial

Particle size is a geometric characteristic that is usually assigned to material objects with sizes ranging from nanometers to millimeters. There is a wide variety of real systems that contain particles within this size range. These systems are generally polydisperse, meaning that the particles in a particular sample vary in size. Therefore, in order to adequately characterize such systems, it is not sufficient to simply determine a single particle size. We must instead determine the system’s particle size distribution.

Measurements of the **particle_size** and ** particle size distribution** are extremely important tools for research and development, as well as quality control, in many industries. These industries include pharmaceuticals, cements, ceramics, paints, emulsions, etc. In general, particle size analyzers can be roughly organized into three groups: 1) counters; 2) fractionation methods; 3) macroscopic fitting methods. Below we present links to several International Standards which provide descriptions of some of these methods.

Methods that are classified as macroscopic fitting techniques include light scattering, x-ray scattering, neutron scattering, and acoustic spectroscopy. All of these methods rely on the measurement of a certain property of a sample that contains particles, and then calculating the particle size distribution from this measured raw data using an appropriate theory. For instance, in the case of static light scattering instruments, the raw data measured is the intensity of scattered light versus angle. Calculation of the particle size distribution requires a theory which relates this information to particle size. These theoretical aspects of the light scattering are well known and described in details in the ISO standards referenced below.

Acoustic spectroscopy belongs to the group of macroscopic fitting methods as well. However, it stands alone from other macroscopic methods due to its capability of characterizing concentrated systems without the need for dilution. This method is based on measuring the attenuation of ultrasound at a set of frequencies in the MHz range as a function of distance. This attenuation spectrum is the raw data used for calculating particle size distribution. There is a well-developed theory that takes into account particles’ interactions, which is imperative for extracting particle size distributions from attenuation spectra in concentrated systems. Details of this method are described in the International Standard ISO 20998-1:2006 “Measurement and characterization of particles by acoustic methods — Part 1: Concepts and procedures in ultrasonic attenuation spectroscopy”.

Verification of the theory for acoustic spectroscopy has been conducted by many different groups using a wide variety of samples. Some results of such verification are presented in the book “Characterization of Liquids, Nano- and Microparticulates, and Porous Bodies using Ultrasound” (2017). The verification tests confirm that this method yields particle size distributions that are very close to those determined using other characterization techniques.

Here we present the results of such a verification tests which compare DLS, Centrifugation, ELS, X-ray scattering, and acoustic spectroscopy. All measurements were performed on suspensions of silica Koestrosol. This silica serves as a basis for an EU certified reference material. Details of these experimental tests are described in ref.4.

Method | Particle size value [nm]. |
---|---|

Dynamic light scattering, intensity massed harmonic mean diameter by cumulants method. | 19.0 ± 0.6 |

Centrifuge liquid sedimentation, intensity based modal diameter. | 20.1 ± 1.3 |

Electron microscopy, number based mean diameter. | 19.4 ± 1.3 |

Small X-rays scattering, number based mean diameter. | 21.8 ± 0.7 |

Acoustics, mass based median diameter. | 22.4 ± 0.5 |

Acoustic spectroscopy makes it possible to perform particle size measurements on concentrated dispersions and emulsions with no dilution and no sample preparation. This is critical in many cases when dilution affects particle size distribution. Also, this method can be applied for structured dispersions. Structure, usually in the form of polymer networks, contributes to ultrasound attenuation by itself, but this contribution can be subtracted using appropriate existing theory. In addition, acoustic spectroscopy can resolve particle size distributions of different species of particles in mixed dispersions, assuming that they have different densities.

This method can also be used for continuous monitoring of particle size during milling, crystallization, and other industrial processes. One of the most important applications of acoustic spectroscopy is determining particle size of nano-dispersions and other nano-particulates. Acoustics can monitor the presence of nano-particles with a precision of 1%, whereas nano-particles can be masked by larger particles when other methods are used.

**PARTICLE SIZE DISTRIBUTION.**

In order to characterize the polydispersity of real dispersions and emulsions we use the well-known concept of the “particle size distribution” (PSD). A detailed description of this concept can be found in the publications of Leschonski [5]. There are multiple ways to represent PSD depending on the principles of the measurement and particles’ properties. Usually the independent variable (abscissa) describes the physical property chosen to characterize the size, whereas the dependent variable (ordinate) characterizes the type and measure of the quantity – either number, area, volume, or weight. It is assumed that a unique relationship exists between the physical property and a one-dimensional property unequivocally defining “size”. This can be achieved only approximately. For irregular particles, the concept of an “equivalent diameter” allows one to characterize such entities using a single parameter. This parameter is the diameter of a sphere that yields the same value of any given physical property when analyzed under the same conditions as the irregularly shaped particle.

The different relative amount of particles, measured in certain size intervals, form a so-called density distribution that represents the first derivative of the cumulative distribution*.* The cumulative distribution is usually normalized. This distribution determines the amount of particles (in number, length, area, weight or volume depending on r) that are smaller than the equivalent diameter *X.*

The figure below shows the normalized discrete density distribution or histogram *q _{r}(X_{i},X_{i+1}).* This distribution specifies the amount of particles having diameters larger than x

_{i}and smaller than x

_{i+1}and is given by:

The shaded area represents the relative amount of the particles. The histogram transforms to a continuous density distribution when the thickness of the histogram column limits to zero.A histogram is suitable for presentation of the PSD when the value of each particle size fraction is known. It is the so-called “full particle size distribution”. It can be measured using either counting or fractionation techniques. However, in many cases, full information about the PSD is either not available or not even required. That is why in many cases histograms are replaced with various analytical particle size distributions. There are several analytical particle size distributions that approximately describe empirically determined particle size distributions. One of the most useful, and widely used distributions, is the log-normal distribution. Log-normal distributions require that we extract only two parameters from the experimental data – median size and standard deviation. This is a big advantage in many cases when amount of the experimental data is restricted.

**International Standards for particle sizing**:

International Standard ISO 22412:2008 “Particle size analysis — Dynamic light scattering (DLS)”

International Standard ISO 13320:2009 “Particle size analysis — Laser diffraction methods”

**REFERENCES**.

- Wikipedia Article on “Particle_size”
- Wikipedia Article on “Particle Size Distribution”
- Dukhin, A.S. and Goetz, J.P. “Characterization of Liquids, Nano- and Microparticulates, and Porous Bodies using Ultrasound”, Edition 3, Elsevier, 571 pages, 765 references, (2017).
- Dukhin, A.S., Parlia, S., Klank, D., Lesti, M. “Particle sizing and zeta potential of silica Koestrol (basis for certified reference material ERM-FD100 for Nanoparticles) by Acoustics and Electro-acoustics”,Part.Part.Syst.Charact.,27,pp.165-171, (2010).
- Leschonski, K. “Representation and Evaluation of Particle Size Analysis data”, Part. Charact., 1, 89-95 (1984)