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Particle Size Analysis by Laser Diffraction
Introduction
3. The scattering pattern at the detectors is the The underlying assumption in the design of laser sum of the individual scattering patterns diffraction instruments is that the scattered light pattern formed at the detector is a summation of the scattering pattern produced by each particle Experimental
that is being sampled. Deconvolution of the Prior to analysis, the dispersion cell is filled with resultant pattern generates information about the clean, deionised water and left to allow thermal scattering pattern produced by each particle and, equilibrium to take place. The instrument upon inversion, information about the size of the automatically aligns so that the incident path of the laser is aligned with the optical arrays. The cleanliness of the system is then checked, and a background is taken. By comparing the signal intensity of the system without a sample present, to the intensity with a sample, the obscuration of the laser beam may be calculated, giving some idea of the material concentration in the dispersal cell. Too high a concentration results in multiple scattering, too low and the signal strength is inadequate to register at the detectors. Figure 2 below illustrates a comparison between the signals obtained from an empty system (red), with that from a particle sample (green). The background signal should always be lower than your sample signal! Data Graph - Light Scattering
Figure 1: Light scattering patterns observed for In essence, each particle scatter pattern is 1 3 5 7 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 comprehensive mathematical solution to the scattering of incident light by spherical particles; Figure 2: Background and sample scattering data the Mie Theory. This theory indicates the necessity for a precise knowledge of the real and Suitable dispersion procedures should be followed imaginary components of the refractive index of to ensure that the powder is dispersed and the material being analysed, to determine particle minimum agglomeration has taken place. Care size and particle size distribution. When a good fit must also be taken to ensure that the dispersal is obtained, then we know all of the relevant cell contains no air bubbles or that particle information in order to deconvolute the Mie fracture is not occurring as the instrument is not pattern into meaningful particle size information. capable of distinguishing between agglomerates, All laser diffraction instruments rely on three basic 1. The particles scattering the light are spherical in Sonification is an option to aid particle dispersion although again, care must be taken to ensure the 2. There is little to no interaction between the light correct intensity and duration of sonification to avoid primary particle breakage. The particle size distribution will depend on the optical model used to calculate it! The real and AN003 Particle size analysis by laser diffraction rev 0.doc Data Graph - Light Scattering
imaginary components of the refractive index are a vital part of the particle characterisation equation. In the case of an unknown particle refractive index (if a literature value is unavailable), the optical properties may be derived by varying the input values and comparing the resultant scatter pattern with the measured Imaginary part of refractive index = 0.1, 20 February 2004 15:32:21 Data Graph - Light Scattering
In figure 3 below, we see the difference the imaginary part of the refractive index makes to the resulting size distribution. The question is which Fit data(weighted)Imaginary part of refractive index = 1.0, 20 February 2004 15:32:21 We clearly see the evolution in scatter pattern as the actual data starts to approach the theoretical, until at an imaginary RI component of 1, the patterns coincide. At this point, we can say that this scatter pattern is the most correct, and in this Imaginary part of refractive index = 0.01 case, the true size distribution will be the blue line Imaginary part of refractive index = 0.1 Imaginary part of refractive index = 1.0 Figure 3: Size distributions using varying Conclusions
If we look at the theoretical scatter pattern 2. Laser diffraction particle sizing requires both compared with the measured data, we get an the real and imaginary components of the instant idea of the goodness of fit. Figures 4, 5 and 6 illustrate the comparison when using an 3. By adjusting RI values manually, the scatter imaginary refractive index of 0.01. 0.1 and 1.0 pattern may be manipulated until actual and theoretical are congruent. At this point, we may say our input RI is correct, and the Data Graph - Light Scattering
resultant size distribution is representative of Imaginary part of refractive index = 0.01, 20 February 2004 15:32:21 Escubed Ltd
AN003 Particle size analysis by laser diffraction rev 0.doc

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