Characterizing particles with optical techniques: questions to ask first

Miroslaw Jonasz

Introduction
What properties of particles can be sensed?
Are particles to be examined individually or as a suspension?
References

Introduction

Particles in liquids (hydrosols), particles in gases (aerosols), and powders are essentially inclusions in a medium. These inclusions are either of a different composition (e.g. dust in the air) or phase (e.g. water droplets in water vapor). Optical properties of these inclusions are different than those of the medium. This causes light to interact with the inclusions (particles) differently than with the surrounding medium and makes it possible to sense properties of the particles (Jonasz, 1991). The interaction of light with particles, referred to as light scattering, is the basis of many non-contact and non-destructive optical techniques for particle characterization.
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What properties of particles can be sensed?

Interaction of light with particles depends on, and thus enables sensing of

particle size
concentration
composition
shape
orientation of non-spherical and non-homogeneous particles
structures of individual particles
three-dimensional structure of a particle field
flow rate of suspension.

Optical methods of particle characterization can be very efficient and accurate (Jonasz, 1994). Such methods are the basis of optical flow-cytometry and laser diffractometry, important particle sizing techniques that are widely used today.

Even when it is difficult to determine particle properties from light scattering, one can harness the power of optical sensing by using it to monitor deviations from a "standard" particle set. Such deviations can be expressed numerically by adopting an approximate model of light scattering. Parameters of the model serve in this case as useful classification indices and may have little in common with actual physical characteristics of particles.

Particle size and concentration can be combined into particle size distribution which relates the concentration to particle size. The particle size distribution is one of the most important parameters of light scattering by suspensions. Shape, orientation, and structure of a particle tend to be the second order-of-magnitude modifiers. Relative significance of these properties can be set by deciding which aspects of light scattering one wants to observe. For example, the particle composition has relatively less importance than particle size when one observes light scattered into directions close to the direction of propagation of the incident light.
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When particles are homogeneous or coated spheres ...

If particles are homogeneous spheres there is only the size distribution and composition (or the composition-size distribution in general) to determine. This case (for example, water droplets in mist) has been extensively researched and affords extremely accurate measurements of the particle properties. The basis for such accuracy is provided by Mie theory (for example, Bohren and Huffman, 1983 ) that describes scattering of plane monochromatic light wave by a homogeneous sphere. This theory permitted measurements of the diameter of a micrometer-sized spherical liquid droplet to within 1 part in 10,000 (Ashkin and Dziedzic, 1991) and made possible spectroscopy of single micro-droplets. Mie theory and its extension, Aden-Kerker theory of light scattering by a coated sphere, are embodied in our simple stand-alone computer programs and in our subroutines which can be included into your own software. These programs can be used to accurately simulate interaction of light with homogeneous and coated spheres.
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When particles are non-spherical and non-homogeneous …

If a particle is non-spherical and non-homogeneous, several complications arise. First, the particle size is difficult to define. In fact, it is usually defined operationally by the method of particle analysis that one uses. For example, an electro-resistive particle sizing technique (embodied, for example, in the Coulter counter), popularized a concept of an equivalent volume sphere. In this concept, the particle size is defined as a diameter of a sphere with volume equal to that of the particle.

Second, a non-spherical or non-homogeneous particle can be oriented relative to the direction of the incident beam and/or its polarization axis (orientation has no meaning for a homogeneous sphere). Particle shape and orientation may affect interaction of light with the particle. That conclusion follows, for example, from an observation of dust particles in a sunbeam shining through an opening in a window’s curtain: large dust particles (which are usually non-spherical) flash as they tumble drifting across the beam.

Particle size distribution now expands to size-shape-structure distribution. Orientation of particles is typically left out because they are usually randomly oriented. In many applications where the particle shape is random, the users seek merely the particle "size"-distribution, which neglects the shape and orientation information and provides a method-dependent apparent particle size-distribution.

Although Mie theory cannot be used for non-spherical particles, it does provide order-of-magnitude guidelines. Several other models permit interpretation of optical measurements for non-spherical particles (a rigorous solution for the spheroid: Asano and Sato, 1980, as well as approximate techniques: T-matrix: Waterman, 1970, coupled dipoles: Purcell and Pennypacker, 1975, and finite-difference time-domain model (FDTD): Dunn et al. 1997). Jonasz, 1991 provides a more extensive list of relevant pre-1991 references. However, most of these techniques tend to be limited in scope to a range of particle sizes and/or optical properties of the particle material. If the particle volume and composition are the only parameters of non-spherical particles which interest you, it may pay to explore the possibility of "sphering" the particles. This trick, alas possible only with "soft" particles was successfully used to characterize non-spherical red blood cells (Tycko et al. 1985): the cells were treated with a compound that changed their shape to spherical but preserved their volumes.
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Are particles to be examined individually or as a suspension?

Individual (single) particle sensing, frequently referred to as optical flow-cytometry, provides accurate and comprehensive results. However, single-particle sensing technology is relatively complex (for example, Shapiro, 1988). This is a consequence of the very low power of light scattered by a single particle. By sensing suspension one can obtain a much greater signal that is a superposition of signals of all particles in the sensing zone. The tradeoff for such an increased signal magnitude is a difficulty of retrieving characteristics of individual particles from that signal.
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Single-particle sensing

Strictly speaking, the term "flow-cytometry" is reserved for a specific technique of single-particle sensing that makes particles flow in succession in a filament of liquid or gas past the sensing zone of an instrument. Flow-cytometry permits rapid and comprehensive examination of a sample at a rate of thousands of particles per second. Several parameters of the interaction of light with a particle, for example, intensities of light scattered at several angles and/or wavelengths can be measured simultaneously. These measurements can be used to create a multi-dimensional scatter graph in which each data point represents a particle. Data points corresponding to similar particles tend to occupy the same area (n-dimensional volume) in such a graph. If relevant particle properties change, the graph is accordingly modified. Statistical techniques, such as cluster analysis, permit to automate assessment of such changes. This creates a very powerful diagnostic or quality-monitoring tool that can reveal a lot of information about dynamics of a particle population.

Flow-cytometers are versatile but rather expensive instruments, mostly because they need to quickly and accurately measure minute signals generated by individual particles. Flow-cytometers also require skilled operators and are typically confined to laboratory environment. Particles for a flow-cytometric analysis must be sampled from a small volume of suspension that is representative to the whole suspension. This can introduce sampling and contamination errors, as well as modify the suspension in other ways. A narrow orifice leads to or constitutes the sensing zone of a flow-cytometer. Such orifice can be clogged by large particles. Although clogging can be prevented by screening out such particles prior to analysis, the suspension so processed may be inadvertently modified or contaminated.

There are other single-particle sensing techniques, for example, scanning of a volume of suspension with a focused light beam. In this latter technique, electronic processing admits only signals from particles that are within the focus zone. A "time-of-transit" variation of the scanning technique sizes a particle based on the width of the pulse of light scattered as the beam focus travels across the particle. The particle size can aso be determined by measuring light that is scattered forward by a particle.

In all "single-particle" sensing techniques, there is a non-zero probability of coincidence, i.e. of two or more particles being simultaneously within the sensing zone. The signal generated by such particle sets may be interpreted as one generated by single large particle. Accordingly, coincidence can affect particle size distribution measurements: perceived concentration of the large particles will be increased at a cost of the small particle concentration. This effect can be reduced by limiting the particle concentration and/or by minimizing the sensing zone.
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Multi-particle sensing

An alternative to single-particle sensing is to sense suspension "as a whole". Such analysis can frequently be made in situ, without a need for sampling and without related problems. Interestingly, this may alleviate only the sample contamination problem, but not sampling errors. This is because instrumental sampling effects are inevitable as long as the sensing zone volume is smaller than that of suspension.

With multi-particle sensing, the light scattering signal is much stronger than that resulting from each individual particle because it is a sum of signals of all the particles in the sensing volume. This simplifies the design of a sensor and makes the sensor much less expensive than a flow-cytometer.

However, by settling for measurements of light scattering by many particles at a time we face a difficult problem of inversion (extraction) of the particle properties, such as the size distribution, from the combined signal. It turns out that this problem is inherently error-prone: small measurement errors may cause large errors in retrieved particle characteristics. Precision of such inversion may be pretty good, but the value of the inverted property (for example, the size distribution) may be quite different than the actual value. Again, the sensitivity and advantages of optical techniques can still be employed to monitor deviations from a "typical" size distribution. Such deviations can be correlated, for example, with changes in an application’s process quality.
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References

Aden, A. L. and Kerker, M. 1951. Scattering of electromagnetic waves from two concentric spheres. Journal of Applied Physics 22: 1242-1246.

Asano, S. and Yamamoto, G. 1975. Light scattering by a spheroidal particle. Applied Optics 14: 29-49.

Ashkin, A. and Dziedzic, J. M. 1981. Observation of optical resonances of dielectric spheres by light scattering. Applied Optics 20: 1803-1814.

Bohren, C. F. and Huffman, D. R. 1983. Absorption and scattering of light by small particles. Wiley, New York.

Dunn A. Smithpeter C., Welch A. J., Richards-Kortum R. 1997. Finite-difference time-domain simulation of light scattering from single cells. Journal of Biomedical Optics 2: 262-266.

Jonasz, M. 1994. Light scattering: a basis of effective particle characterization techniques. American Laboratory 24: 30-36.

Jonasz, M. 1991. Size, shape, composition, and structue of microparticles from light scattering. In: Principles, methods, and application of particle size analysis. Edited by J. P. M. Syvitski. Cambridge University Press, 143-162.

Purcell E. M., Pennypacker C. R. 1975. Scattering and absorption of light by non-spherical dielectric grains. Astrophysics Journal 186: 705-714.

Shapiro, H. M. 1988. Practical flow-cytometry. Allan R. Liss, New York.

Tycko, D. H., Metz, M. H., Epstein, E. A. and Grinbaum, A. 1985. Flow-cytometric light scattering measurement of red blood cell volume and hemoglobin concentration. Applied Optics 24: 1355-1365.

Waterman P. C. 1970. Symmetry, unitary, and geometry in electromagnetic scattering. Physical Review D 3: 825-839.

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