A method of determining sizes of particles suspended in liquids and engaging in Brownian motion involves statistical analysis of counts of photons of laser light scattered by the particles. The method can be implemented by a compact, portable apparatus that can be used, for example, in monitoring of colloidal suspensions, characterization of suspended protein molecules, and the like.
In the prior state-of-the-art light-scattering method for determining particle sizes, one performs a digital correlation followed by an ill-conditioned inversion to obtain a particle-size distribution. The disadvantage of the prior method is that the equipment (especially the computer needed to perform the correlation) is expensive and usually too large and complex to be portable, and the measurements and computations take a few minutes. In the present method, one does not obtain a particle-size distribution; on the other hand, one can estimate the average size of light-scattering particles in a sample after a measurement and computation time of a few seconds.
This method is an instance of photon-correlation spectroscopy (PCS). As such, it is closely related to dynamic-light-scattering (DLS) methods, which are based on the concept of extracting information on the sizes and motions of light-scattering particles from the spatial and temporal dependence of the loss of coherence of scattered laser light. The differences between DLS and PCS arise from the fact that in DLS, one operates photodetectors and associated signal-processing circuits in a photocurrent-measuring regime, whereas in PCS, one operates in a photon-counting regime.
The theoretical basis of the present method is not simple; the mathematical derivation would greatly exceed the space available for this article. However, the underlying theory yields an important benefit: In comparison with other light-scattering methods for measuring particle sizes, this method is relatively simple in practice and involves much less computation.
A typical apparatus used in the present method (see figure) includes a laser diode as the source of light. A monomode optical fiber delivers the light to a probe that is placed in contact with, or proximity to, a sample. A short length of multimode optical fiber with a gradient in the index of refraction is fusion-spliced to the end of the monomode fiber to provide focussing of the light delivered by the probe to the sample. The light emerging from the probe illuminates a small volume in the sample. A portion of the light back-scattered from particles in the sample is collected by the probe, and a second optical fiber couples this collected light to a photomultiplier tube. Under control by a microprocessor, the photomultiplier output is processed by an amplifier/discriminator to obtain equal-amplitude voltage pulses at times that correspond to the times of arrival of the collected scattered photons and then processed by a data-acquisition module.
The aforementioned lengthy mathematical derivation elucidates the relationships among temporal coherence of scattered light, photon-counting statistics, and average particle size. One of the results of the derivation is that the temporal coherence of the scattered light depends on both the integration time and the particle diameter. Consequently, it is possible to estimate the average particle size from the degrees of coherence of the photon counts accumulated during two different integration times - T and KT. The values of T and K are chosen to cover a reasonable range of particle sizes by use of the fastest available electronic circuitry. For example, the choice of T = 200 ns and K = 25 makes it possible to estimate diameters from 5 to 3,000 nm.
This work was done by Harbans S. Dhadwal and Kwang I. Suh of the State University of New York for Glenn Research Center.
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