Laser diffraction analysis, also known as laser diffraction spectroscopy, is a technology that utilizes diffraction patterns of a laser beam passed through any object ranging from nanometers to millimeters in size [1] to quickly measure geometrical dimensions of a particle. This particle size analysis process does not depend on volumetric flow rate, the amount of particles that passes through a surface over time. [2]
Laser diffraction analysis is originally based on the Fraunhofer diffraction theory, stating that the intensity of light scattered by a particle is directly proportional to the particle size. [4] The angle of the laser beam and particle size have an inversely proportional relationship, where the laser beam angle increases as particle size decreases and vice versa. [5] The Mie scattering model, or Mie theory, is used as alternative to the Fraunhofer theory since the 1990s.
Commercial laser diffraction analyzers leave to the user the choice of using either Fraunhofer or Mie theory for data analysis, hence the importance of understanding the strengths and limitations of both models. Fraunhofer theory only takes into account the diffraction phenomena occurring at the contour of the particle. Its main advantage is that it does not require any knowledge of the optical properties (complex refractive index) of the particle’s material. Hence is it typically applied to samples of unknown optical properties, or to mixtures of different materials. For samples of known optical properties, Fraunhofer theory should only be applied for particles of an expected diameter at least 10 times larger than the light source’s wavelength, and/or to opaque particles. [6] [7]
The Mie theory is based on measuring the scattering of electromagnetic waves on spherical particles. Hence, it is taking into account not only the diffraction at the particle’s contour, but also the refraction, reflection and absorption phenomena within the particle and at its surface. [6] Thus, this theory is better suited than the Fraunhofer theory for particles that are not significantly larger than the wavelength of the light source, and to transparent particles. The model’s main limitation is that it requires precise knowledge of the complex refractive index (including the absorption coefficient) of the particle’s material. The lower theoretical detection limit of laser diffraction, using the Mie theory, is generally thought to lie around 10 nm.
Laser diffraction analysis is typically accomplished via a red He-Ne laser or laser diode, a high-voltage power supply, and structural packaging. [8] Alternatively, blue laser diodes or LEDs of shorter wavelength may be used. The light source affects the detection limits, with lasers of shorter wavelengths better suited for the detection of submicron particles. Angling of the light energy produced by the laser is detected by having a beam of light go through a flow of dispersed particles and then onto a sensor. A lens is placed between the object being analyzed and the detector's focal point, causing only the surrounding laser diffraction to appear. The sizes the laser can analyze depend on the lens' focal length, the distance from the lens to its point of focus. As the focal length increases, the area the laser can detect increases as well, displaying a proportional relationship.
Multiple light detectors are used to collect the diffracted light, which are placed at fixed angles relative to the laser beam. More detector elements extend sensitivity and size limits. A computer can then be used to detect the object's particle sizes from the light energy produced and its layout, which the computer derives from the data collected on the particle frequencies and wavelengths. [5]
In practical terms, laser diffraction instruments can measure particles in liquid suspension, using a carrier solvent, or as dry powders, using compressed air or simply gravity to mobilize the particles. Sprays and aerosols generally require a specific setup. [9]
Because the light energy recorded by the detector array is proportional to the volume of the particles, laser diffraction results are intrinsically volume-weighted. [10] This means that the particle size distribution represents the volume of particle material in the different size classes. This is in contrast to counting-based optical methods such as microspcopy or dynamic image analysis, which report the number of particles in the different size classes. [11] That the diffracted light is proportional to the particle’s volume also implies that results are assuming particle sphericity, i.e. that the particle size result is an equivalent spherical diameter. Hence particle shape cannot be determined by the technique.
The main graphical representation of laser diffraction results is the volume-weighted particle size distribution, either represented as density distribution (which highlights the different modes) or as cumulative undersize distribution.
The most widely used numerical laser diffraction results are:
Harmonized standards for the accuracy and precision of laser diffraction measurements have been defined both by ISO, in standard ISO 13320:2020, [13] and by the United States Pharmacopoeia, in chapter USP <429>. [14]
Laser diffraction analysis has been used to measure particle-size objects in situations such as:
Since laser diffraction analysis is not the sole way of measuring particles it has been compared to the sieve-pipette method, which is a traditional technique for grain size analysis. When compared, results showed that laser diffraction analysis made fast calculations that were easy to recreate after a one-time analysis, did not need large sample sizes, and produced large amounts of data. Results can easily be manipulated because the data is on a digital surface. Both the sieve-pipette method and laser diffraction analysis are able to analyze minuscule objects, but laser diffraction analysis resulted in having better precision than its counterpart method of particle measurement. [23]
Laser diffraction analysis has been questioned in validity in the following areas: [24] [25]
Diffraction is the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660.
Rayleigh scattering, named after the 19th-century British physicist Lord Rayleigh, is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the radiation. For light frequencies well below the resonance frequency of the scattering particle, the amount of scattering is inversely proportional to the fourth power of the wavelength.
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter waves and acoustic waves can also be considered forms of radiative energy, and recently gravitational waves have been associated with a spectral signature in the context of the Laser Interferometer Gravitational-Wave Observatory (LIGO).
In optics, a diffraction grating is an optical grating with a periodic structure that diffracts light into several beams travelling in different directions. The emerging coloration is a form of structural coloration. The directions or diffraction angles of these beams depend on the wave (light) incident angle to the diffraction grating, the spacing or distance between adjacent diffracting elements on the grating, and the wavelength of the incident light. The grating acts as a dispersive element. Because of this, diffraction gratings are commonly used in monochromators and spectrometers, but other applications are also possible such as optical encoders for high precision motion control and wavefront measurement.
Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections of radiation that undergo scattering are often called diffuse reflections and unscattered reflections are called specular (mirror-like) reflections. Originally, the term was confined to light scattering. As more "ray"-like phenomena were discovered, the idea of scattering was extended to them, so that William Herschel could refer to the scattering of "heat rays" in 1800. John Tyndall, a pioneer in light scattering research, noted the connection between light scattering and acoustic scattering in the 1870s. Near the end of the 19th century, the scattering of cathode rays and X-rays was observed and discussed. With the discovery of subatomic particles and the development of quantum theory in the 20th century, the sense of the term became broader as it was recognized that the same mathematical frameworks used in light scattering could be applied to many other phenomena.
The Mie solution to Maxwell's equations describes the scattering of an electromagnetic plane wave by a homogeneous sphere. The solution takes the form of an infinite series of spherical multipole partial waves. It is named after Gustav Mie.
Plate readers, also known as microplate readers or microplate photometers, are instruments which are used to detect biological, chemical or physical events of samples in microtiter plates. They are widely used in research, drug discovery, bioassay validation, quality control and manufacturing processes in the pharmaceutical and biotechnological industry and academic organizations. Sample reactions can be assayed in 1-1536 well format microtiter plates. The most common microplate format used in academic research laboratories or clinical diagnostic laboratories is 96-well with a typical reaction volume between 100 and 200 µL per well. Higher density microplates are typically used for screening applications, when throughput and assay cost per sample become critical parameters, with a typical assay volume between 5 and 50 µL per well. Common detection modes for microplate assays are absorbance, fluorescence intensity, luminescence, time-resolved fluorescence, and fluorescence polarization.
In physics, the phase problem is the problem of loss of information concerning the phase that can occur when making a physical measurement. The name comes from the field of X-ray crystallography, where the phase problem has to be solved for the determination of a structure from diffraction data. The phase problem is also met in the fields of imaging and signal processing. Various approaches of phase retrieval have been developed over the years.
Soil texture is a classification instrument used both in the field and laboratory to determine soil classes based on their physical texture. Soil texture can be determined using qualitative methods such as texture by feel, and quantitative methods such as the hydrometer method based on Stokes' law. Soil texture has agricultural applications such as determining crop suitability and to predict the response of the soil to environmental and management conditions such as drought or calcium (lime) requirements. Soil texture focuses on the particles that are less than two millimeters in diameter which include sand, silt, and clay. The USDA soil taxonomy and WRB soil classification systems use 12 textural classes whereas the UK-ADAS system uses 11. These classifications are based on the percentages of sand, silt, and clay in the soil.
Dynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution. In the scope of DLS, temporal fluctuations are usually analyzed using the intensity or photon auto-correlation function. In the time domain analysis, the autocorrelation function (ACF) usually decays starting from zero delay time, and faster dynamics due to smaller particles lead to faster decorrelation of scattered intensity trace. It has been shown that the intensity ACF is the Fourier transform of the power spectrum, and therefore the DLS measurements can be equally well performed in the spectral domain. DLS can also be used to probe the behavior of complex fluids such as concentrated polymer solutions.
The equivalent spherical diameter of an irregularly shaped object is the diameter of a sphere of equivalent geometric, optical, electrical, aerodynamic or hydrodynamic behavior to that of the particle under investigation.
Static light scattering is a technique in physical chemistry that measures the intensity of the scattered light to obtain the average molecular weight Mw of a macromolecule like a polymer or a protein in solution. Measurement of the scattering intensity at many angles allows calculation of the root mean square radius, also called the radius of gyration Rg. By measuring the scattering intensity for many samples of various concentrations, the second virial coefficient, A2, can be calculated.
In granulometry, the particle-size distribution (PSD) of a powder, or granular material, or particles dispersed in fluid, is a list of values or a mathematical function that defines the relative amount, typically by mass, of particles present according to size. Significant energy is usually required to disintegrate soil, etc. particles into the PSD that is then called a grain size distribution.
Particle size is a notion introduced for comparing dimensions of solid particles, liquid particles (droplets), or gaseous particles (bubbles). The notion of particle size applies to particles in colloids, in ecology, in granular material, and to particles that form a granular material.
Particle size analysis, particle size measurement, or simply particle sizing, is the collective name of the technical procedures, or laboratory techniques which determines the size range, and/or the average, or mean size of the particles in a powder or liquid sample.
Multiangle light scattering (MALS) describes a technique for measuring the light scattered by a sample into a plurality of angles. It is used for determining both the absolute molar mass and the average size of molecules in solution, by detecting how they scatter light. A collimated beam from a laser source is most often used, in which case the technique can be referred to as multiangle laser light scattering (MALLS). The insertion of the word laser was intended to reassure those used to making light scattering measurements with conventional light sources, such as Hg-arc lamps that low-angle measurements could now be made. Until the advent of lasers and their associated fine beams of narrow width, the width of conventional light beams used to make such measurements prevented data collection at smaller scattering angles. In recent years, since all commercial light scattering instrumentation use laser sources, this need to mention the light source has been dropped and the term MALS is used throughout.
Codes for electromagnetic scattering by spheres - this article list codes for electromagnetic scattering by a homogeneous sphere, layered sphere, and cluster of spheres.
Malvern Panalytical is a Spectris plc company. The company is a manufacturer and supplier of laboratory analytical instruments. It has been influential in the development of the Malvern Correlator, and it remains notable for its work in the advancement of particle sizing technology. The company produces technology for materials analysis and principal instruments designed to measure the size, shape and charge of particles. Additional areas of development include equipment for rheology measurements, chemical imaging and chromatography. In 2017, they merged with PANalytical to form Malvern Panalytical Ltd.
Plasmonic nanoparticles are particles whose electron density can couple with electromagnetic radiation of wavelengths that are far larger than the particle due to the nature of the dielectric-metal interface between the medium and the particles: unlike in a pure metal where there is a maximum limit on what size wavelength can be effectively coupled based on the material size.
The characterization of nanoparticles is a branch of nanometrology that deals with the characterization, or measurement, of the physical and chemical properties of nanoparticles. Nanoparticles measure less than 100 nanometers in at least one of their external dimensions, and are often engineered for their unique properties. Nanoparticles are unlike conventional chemicals in that their chemical composition and concentration are not sufficient metrics for a complete description, because they vary in other physical properties such as size, shape, surface properties, crystallinity, and dispersion state.
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