Particle Size Distribution

Transcription

1 Volume (%) How to choose the correct optical properties for a sample a systematic practical approach Introduction ISO 1332 states that Mie scattering theory should be the only theory used to calculate the particle size distribution when there are particles smaller than 5 micron present in the distribution. Either Mie or Fraunhofer theory can be used for larger material. Fraunhofer theory is an approximation; it assumes the particles are all opaque discs and should be avoided wherever possible. This will not provide accurate answers for small material. Mie theory requires the refractive index and imaginary refractive index / absorption to get a result. For a material of unknown refractive index is Fraunhofer chosen and a possible inaccurate result obtained or does the user spend time working out the refractive index of the sample? Fraunhofer theory is available in the Mastersizer software, although it s use should be carefully monitored. It is far easier to spend a small amount of time researching the correct RI than it is to accept the probably inferior Fraunhofer result. The purpose of this guide is to provide a useful practical guide to determining the correct optical properties. If any additional information on theory is needed the user is advised to read ISO What happens if the incorrect RI is used? Is a choice inappropriate? Errors will start to creep in the proportion of volume subscribed to a given size. Essentially the light scattering data at higher angles (smaller sizes) will start to be badly fitted. This will often overestimate the amount of fine material in the distribution Soybean P5 ABS, 2 Feb 2 16:25:56 Soybean P5 R1.59 abs, 2 Feb 2 16:25:56 Figure 1: Soybean oil emulsion distribution calculated with 2 different RIs. Often this effect will manifest itself as an extra peak at the bottom end of the size distribution with a peak at.2.3 um and a minimum around 1 um (Figure 1). Is the shape of curve what you would expect? If the product is milled it is unlikely to consist of more than one peak a single peak with a tail of fines is what one would expect. The residual (which is a goodness of fit parameter ) provides information on how appropriate a particular optical model is, the lower the residual the more likely it is to be appropriate. However a high residual does not necessarily mean a poor result, a fairly narrow size distribution will only occupy a small proportion of detectors, and hence the residual will be higher than that of a more polydisperse sample. The fit across the whole detector range can also be examined. The imaginary refractive index section later will go into more detail on what to look for on a good fit. Finding the correct RI in the first place The CRC Handbook of Chemistry and Physics and British Pharmocopoeia contain a lot of refractive index information, as does the database in the Mastersizer 2 software (or manual for earlier Mastersizer models). There are also several papers in the literature and some good mineralogy textbooks (for inorganic compounds). However, if you are dealing with novel compounds (generally organic), things may be a little more complex. There are several ways to determine the refractive index optically.

2 Determining refractive indices optically If the material is a liquid, the refractive index can simply be determined in a refractometer (such as an Abbe one). For solids, there a two routes, to use the Becke line test or to use index matching immersion fluids. Both of these are very closely related. A material of high refractive index difference to its surroundings (greater or lower) acts as a lens (a crystal tends to be thicker in the centre and thinner towards the edges like a lens). There will also be internal reflection of light due to internal grain boundaries. Therefore, rays of light coming from the bottom surface of the mineral appear to come from a slightly higher point. Such materials appear to stand out in relief from their surroundings. This phenomenon is responsible for the creation of a Becke line. The Becke line is a band of light visible along a particle boundary in plane-polarised light. There are two thin lines on the grain boundary, one dark and one light. The light line moves into the medium of higher refractive index. If the focus is moved up the line will move into the centre. If the dispersant RI is varied, the crossover point (between the sample having a higher refractive index than the dispersant and vice versa) can be determined. Index matching immersion fluids are available for refractive indices between 1.3 and 2.1. This covers most materials (apart from some pigments and inorganic compounds metal oxides etc). If a liquid is dispersed in a medium of matching refractive index it will be effectively invisible (glass beads in benzene is the classic example of this). These can be used in conjunction with the Becke line test or in a simpler way, just to examine when the particles become effectively invisible. It may be thought that the best way to examine this is actually inside the Mastersizer itself. The only problem with this is that index matching oils are expensive and typically come in small bottles of which many would be required for a measurement. A far more economical solution uses two miscible liquids of differing refractive index. Isopropyl alcohol (RI 1.38) and Methyl napthalene (RI 1.62) are often used. A wide range of different mixtures should be created of which the RI is known (e.g a 4% IPA 6% methyl napthalene mix has a RI of 1.38* *.6 = 1.52). To these an equal weight of sample should be added and a Mastersizer measurement performed. By plotting the obscuration against refractive index the point of minimum obscuration can be easily determined. This is not always zero as if the material has a non zero imaginary refractive index it will scatter even when immersed in a liquid of equal refractive index. If the material being dealt with is a mix of different substances and the refractive indices and proportions of the materials are known, the refractive index of the mixture can be assumed to be a weighted average. How to choose the correct imaginary R.I. The imaginary RI is more difficult to assess but, for the purposes of particle sizing by laser diffraction, this is taken to represent the amount of light absorbed by the particle being measured. A quick estimate of this absorption can be obtained by viewing the particle in the dispersant under an optical microscope. If the particle is a sphere such as a polystyrene latex or an emulsion globule and it appears transparent under the microscope, then it will absorb very little light and the absorption figure will be low. to.1. If the particle is a milled or irregularly shaped transparent particle then light will be absorbed by the irregularities in its surface and the absorption figure will be higher. In such a case, a figure of.1 is likely to be correct. For submicron materials, choosing the correct imaginary RI for a sample can be crucial in getting the most accurate answer.the following sample was milk, and the customer wanted to know why they were not seeing a small tail of large material due to the cream fraction. The optical properties being used were 1.47 R.I. and.1 imaginary R.I is the correct Real R.I. for milk fat but there was some uncertainty as to the correct figure to use for the imaginary R.I.

3 Light Energy Light Energy Volume (%) Lait ecreme, date per 19/2/, Stabilac, 21 Jan 2 13:47:28 Figure 2: Milk, 1.47 and.1 Examination of the light scattering and fit data shows that the RI used is unlikely to be correct since, if they were correct, the red and the green plots should coincide closely to give a low fit error (Residual). In this case the Residual is very high at 16.6% The higher data channels give an indication of where the problem lies Data Graph - Light Scattering Detector Number Fit data(weighted) Lait ecreme, date per 19/2/, Stabilac, 21 Jan 2 13:47:28 Figure 3: Milk, 1.47 and.1 fit. It will be seen that the biggest misfit is in the last few data channels. As a general rule if the red line is higher than the green line on the last few channels, the imaginary RI is too high if it is lower, the imaginary RI is too low. Following this general guideline, the results were calculated with a R.I. of 1.47 and an imaginary RI of.1. 4 Data Graph - Light Scattering This corresponds to the following size distribution. Detector Number Fit data(weighted) Lait ecreme, date per 19/2/, Stabilac, 21 Jan 2 13:47:28

4 Volume (%) Looking at the fit diagram, the weighted residual is now an acceptable 2.7 and the red and green plots coincide well. Figure 4: Milk 1.47,.1 fit Lait ecreme, date per 19/2/, Stabilac, 21 Jan 2 13:47:28 Figure 5: Milk 1.47 and.1 result The result is now exactly what is expected with a peak of casein micelles and a tail due to fat globules present in the cream. The result has changed drastically for the better and agrees with the user s expectations. Confirming the choices The methods described previously (index matching, Becke line tests) can be used to confirm the choice of optical model used in the system. There is also a method involving volume concentration matching. It has been shown by Lips et al. (Lips, A., Hart, P.M. and Evans, I.D., Proceedings of the 5th European Symposium in Particle Characterisation, 1992, 443, Nurnberg Messe, Nurnberg) that the true phase volume of a system of suspended spherical particles whose scattering extinction efficiencies have been correctly predicted by Mie theory can be measured correctly. It was shown that even for oblate spheroids of aspect ratio 5:1 the error was only of the order of %. Experiments confirmed that suspensions of known pre-determined phase volume were correctly reported by the Mastersizer. In addition to the size distribution, the Mastersizer takes a zero angle turbidity measurement that can be used to calculate the volume concentration of particles present. By combining the Mie theory of light scattering with the Beer-Lambert law the following equation is obtained. log e (1- Obscuration) c = -3 ViQi b 2 di (1) where c is the concentration (%), b is the beam length, V i is the volume in size band I, Q i is the extinction coefficient of size band I and d i is the mean diameter of size band I. The extinction coefficient is a measure of how efficient a particle of a particular size is at scattering light. Equation (1) shows the relationship between volume concentration and the obscuration measured as part of a normal experiment. This is used by the machine to calculate a theoretical concentration. For a stable size distribution (with no multiple scattering), comparison of the real and calculated concentrations can be used to establish that an appropriate R.I. has been used.

5 The Mastersizer calculates the theoretical volume concentration using equation (1). To calculate the experimental volume concentration, follow the procedure below. Take the weight of sample added divide by the specific gravity of the material and divide this again by the volume of dispersant liquid used in the measurement. Finally multiply by to give the result as a volume %. Providing the material is a sphere or spheroid the two volume concentrations (real and theoretical) should be within % for the appropriate refractive index. The degree of disparity depends on the sphericity of the material. Obviously for non spherical material, this approach is less useful (although it has been used to calculate the aspect ratio of platey material). However even for a non spherical material, the closest volume concentration should be obtained for the correct R.I. The specific gravity (if unknown) can be calculated by using weighing bottles or by Archimedean displacement. To do a displacement experiment, a large measuring cylinder with a magnetic bead in should be placed on a stirrer. Liquid should be added to a known line on the cylinder. Weigh the container of the sample, then add sample until 1ml of material has been displaced. Weigh the container again. The weight of material needed to displace 1ml of water is the specific gravity. If the material is water soluble the weight should be divided by the density of the liquid (to correct back to water). A final word Remember to keep experimental data from any experiments used to validate optical properties in a safe place, it will be needed if you are ever audited.