Determination of the Refractive Index of Water ...

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Part. Part. Syst. Charact. 19 (2002) 426 ± 432

Communication

Determination of the Refractive Index of Water-dispersible Granules for Use in Laser Diffraction Experiments* Hans Saveyn**, Dries Mermuys**, Olivier Thas***, Paul van der Meeren** (Received: 2 January 2002; accepted: 23 April 2002)

Abstract Modern laser light scattering equipment can cover a very broad particle size range by using complex algorithms, such as the Mie theory. A disadvantage of this theory, however, is that it requires the knowledge of the refractive index of the particles, which is not straightforward for powdered organic substances. In this study, thiram, a common dithiocarbamate fungicide, was used as a model compound. In a first part, a method was elaborated to determine the refractive index, based on refractive index measurements of solutions of the compound of interest in a range of solvents. Two different extrapolation techniques were

compared. Both techniques were validated by applying them to the determination of the refractive indices of poly(vinyl acetate) and poly(methyl methacrylate). Secondly, the influence of the refractive index value on the generated particle size distribution in the laser diffraction software was investigated. It was observed that widely different particle size distributions can be generated by the laser diffraction software for a single experimental data-set. Therefore, accurate refractive index information is required to obtain reliable particle size distribution results.

Keywords: differential refractometry, laser diffraction, laser light scattering, refractive index, submicron particles

1 Introduction During recent decades, laser diffraction has proven to be a powerful technique for particle sizing [1, 2]. Thanks to the development of accurate opto-electronics and fast computing devices, this sizing technology has been implemented in many control and research laboratories [3, 4]. The technique is mainly based on static light scattering. It can be used for measuring particles whose diameters range from the submicron level up to several millimeters [5]. In the determination of the particle size distribution (PSD) from the experimentally determined light scattering pattern, either the Fraunhofer theory or the Mie * **

Presented at Partec 2001 (March, 27 ± 29th 2001, N¸rnberg). ir. H. Saveyn, ir. D. Mermuys;, Prof. Dr. ir. P. van der Meeren, Particle and Interfacial Technology Group, Ghent University, Faculty Agricultural and Applied Biological Sciences, Coupure Links 653, 9 000 Ghent (Belgium). E-mail: [email protected] *** Dr. ir. O. Thas, Biomath, Ghent University, Faculty Agricultural and Applied Biological Sciences, Coupure Links 653, 9 000 Ghent(Belgium). ¹ 2002 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

theory may be used. Most recent laser diffraction devices are able to use both algorithms. As a result of the refinement of the Mie theory versus the Fraunhofer theory, more accurate PSD measurements can be made. Mainly the size distribution of smaller particles can be obtained with higher precision [6]. Knowledge concerning the presence of these small particles is of primary importance in the risk evaluation of powdered materials. One of the disadvantages of the Mie algorithm is the requirement that both the refractive index of the particles and of the dispersion medium should be known. Although for many substances the refractive index is given in the literature, nevertheless for even more substances the refractive index is not known. For liquid substances, measuring the real refractive index can be readily done using an Abbe¬-type refractometer. For solid substances, determining the refractive index is more problematic [7]. In the case of larger particles, i.e. > 50 mm, this can be accomplished by using the Becke line method, which requires that the particles are observed microscopically in a range of liquids of varying refractive index in which the particles do not dissolve [8]. When the particles are rather small, i.e. < 50 mm, or 0934-0866/02/0406-0426 $ 17.50+.50/0

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2 Theory

Eq. (3) is applicable to polymers, and also to other organic solutes, provided that dissociation of the solute does not occur; the latter happens e.g. when dissolving salts in water. If the refractive index of the solute is equal to that of the solvent, the refractive index of a solution of the solute in this particular solvent would be the same as the refractive index of the pure solvent and hence the SRII equals zero. Eq. (3) allows us to determine at which solvent refractive index the value of the SRII becomes zero, i.e. to determine which solvent refractive index equals the solute refractive index. As in this particular case the refractive indices of the solvent and of the solute are the same, the latter is calculated as

2.1 Determination of the Refractive Index from Specific Refractive Index Increment Measurements

nsolute

dissolve in most organic liquids, the Becke line approach is useless. Some alternative methods have been proposed [7], but are often rather complicated. Other, less complicated, methods have not been validated for organic particles [9]. In this paper, two techniques are introduced to measure the real refractive index of water-dispersible organic particles. The model substance studied was thiram, a common dithiocarbamate fungicide.

For polymers, much research has been carried out in the past concerning the specific refractive index increment (SRII) dn/dc, since this value is required in determining the molecular weight of polymers by static light scattering techniques [10, 11]. The SRII, henceforth denoted by n, stands for the small increment of refractive index dn between a solution and the pure solvent when a solute is dissolved in the solvent at a very low concentration dc: n

dn Dn lim dc c!0 c

1

where c is expressed as the mass of solute per unit volume of solution. Alternatively, the concentration of the solute may be expressed as the volume of solute per unit volume of solution. In this case dn/dc is dimensionless. To distinguish between these two concentration expressions, another SRII is defined, denoted by n', for a volumetric concentration c': dn Dn : n 0 lim c0 !0 dc c0 0

2

2.1.1 Extrapolation from Multiple Solvent Data (Technique 1) When a solute is dissolved in different solvents, the absolute value of the SRII will logically decrease as the refractive indices of the solute and of the solvent approach each other. In this respect, it has been observed earlier that the SRII is linearly related to the refractive index of the solvent [12]: n a b ¥ nsolvent .

(3)

a : b

4

It is clear that the same reasoning is valid for SRII values expressed as n'. In this case, Eq. (3) becomes n' a' b' ¥ nsolvent

(5)

and hence nsolute

a0 : b0

6

2.1.2 Extrapolation from Single Solvent Data (Technique 2) The refractive index of a solution may be estimated from the solute concentration (c) and the refractive index of the solvent (nsolvent) [13]: nsolution nsolvent n ¥ c a ¥ c2.

(7)

For very low concentrations, i.e. below 1% (v/v), the square term can be neglected and Eq. (7) becomes nsolution nsolvent n ¥ c.

(8)

This is a general equation which can be assumed to be valid for a broad spectrum of non-dissociating solutes and solvents. Therefore, assuming additivity of the refractive index of solvent and solute, the latter may be obtained by extrapolation of the refractive index of a concentration series towards a concentration of 100% (v/v) solute. In the latter, purely hypothetical case, the refractive index of the solution becomes equal to the refractive index of the solute. A purely hypothetical solution containing 100% (v/v) of solute will have a density equal to the density of the solute. As a further consequence, the solute concentration, expressed as

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mass per unit volume of this 100% (v/v) solution, equals the density of the pure solute, 1solute. Hence Eq. (8) becomes nsolute nsolvent n ¥ (csolute; at 100% (v/v) solute) nsolvent n ¥ 1solute .

(9)

When the dimensionless parameter n' is used, the extrapolation equation will be nsolute nsolvent n' ¥ (c'solute; at 100% (v/v)solute) nsolvent n' ¥ 1.

The densities of PVA (poly(vinyl acetate)) and PMMA (poly(methyl methacrylate)), used in extrapolation technique 2, were 1PVA 1.05 g/ml and 1PMMA 1.19 g/ ml [11]. For the statistical evaluation of the refractive indices of PVA, PMMA and thiram by technique 1, the Bootstrap model was applied. The confidence interval on the intersection with the horizontal axis was calculated by using the Bootstrap model with 1 500 Bootstrap sample series taken from the solvent data points [14].

(10)

In the latter case, the concentration of the solute is expressed as a volume per volume ratio, which is equal to 1 in the case of a 100% (v/v) solute concentration. For the sake of completeness, it should be mentioned that this procedure is based on a linear increase in the refractive index of the solution with increasing solute concentration over the whole concentration range, which seems to be justified for most solutions [11]. However, if the solute and solvent are strongly interacting, deviations from linearity may occur, as exemplified by aqueous ethanol solutions [10]. Therefore, the validity of this technique should always be checked by performing measurements with at least two different solvents, which must lead to very similar results.

3 Materials and Methods 3.1 Materials All chemicals (bromonaphthalene, iodobenzene, quinoline, aniline, acetone, chloroform) were of analytical grade (> 96% purity) and supplied by Merck-Eurolab (Belgium). Thiram, IUPAC name bis(dimethylthiocarbamoyl) sulfide, was supplied by UCB, Ghent (Belgium) and was of > 99% purity. The remaining part consisted of a dispersant and a wetting agent.

3.2 Measurement of the Refractive Index Six solvents of widely different refractive index were selected for the experimental determination of the refractive index of thiram. With each solvent, a concentration series including five different concentrations of thiram was prepared with a maximum of 1% (v/v) thiram dissolved. The refractive indices of the pure solvents and of the thiram solutions were determined using a temperature-stabilized (20.0 0.1 8C) Abbe¬ refractometer (Model ATAGO 3T) with a range from n 1.3 to 1.7 and a precision of 0.0001 units.

3.3 Analysis of Laser Diffraction Patterns A Malvern Mastersizer S laser diffraction apparatus was used, in combination with an MS-17 wet sample dispersion unit. The dispersions were made by adding thiram to doubly deionized water in the dispersion unit. Pumping and stirring were set at 20% of maximum power. No sonication was used and the dispersion bath was emptied and cleaned between consecutive measurements. The sample amount was chosen to obtain 15 ± 30% obscuration during measurement. A 300 RF lens was used. The light source was an He-Ne laser with a wavelength of 632.8 nm and a polarization angle of zero. Regarding the software, the polydisperse model was chosen for PSD determination. On measuring one thiram sample, 15 particle size distributions were generated by the Malvern Mastersizer software by varying the real refractive index in the software from n 1.40 to 2.10 in increments of 0.05. Additionally, a 16th value of n 1.76 (being the average determined value for the refractive index of thiram) and a 17th higher value of n 2.5 were selected. The imaginary part of the refractive index of thiram as determined with a Shimadzu UV-1205 spectrophotometer, according to the method described by van de Hulst [6], was smaller than 10 5 and therefore set equal to zero for all experiments.

3.4 Particle Sizing by Centrifugal Photosedimentometry As an independent particle sizing technique, centrifugal photosedimentometry, was applied, with a Shimadzu SA-CP2-10 centrifugal particle size analyzer operating at 1 500 rotations per minute. For the calculation of the PSD from the experimentally determined extinction data, the deconvolution routine CONTIN was used as described by Putman et al. [15].

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4 Results and Discussion 4.1 Determination of the Refractive Index of PVA and PMMA In order to check the validity of the two techniques described, literature refractive index data for solutions of PVA and PMMA in a range of solvents [11], as summarized in Table 1, were first used for the determination of the refractive index of a solute from solution data. By using data for these well-known compounds, the calculated values of the refractive index could be compared with the known refractive index from independent measurements.

Fig. 1: Linear regression for the determination of the real refractive index of PVA and PMMA from multiple solvent data, based on literature data from Brandrup and Immergut [11].

4.1.1 Refractive Index of PVA and PMMA from Multiple Solvent Data

4.1.2 Refractive Index of PVA and PMMA from Single Solvent Data

From Figure 1, it can be clearly derived that the different SRII values for both PMMA and PVA follow a linear course as a function of the refractive index of the pure solvent, as predicted by Eq. (3). The intersection of the regression line with the horizontal axis indicates the hypothetical solvent for which the SRII value is equal to zero, i.e. for which the refractive index of the polymer, npolymer , becomes equal to the refractive index of the solvent, nsolvent . This returns a value of 1.5017 for PMMA with the 95 % Bootstrap confidence interval ranging from 1.4932 to 1.5100. This fits reasonably well with the literature value of 1.492 for PMMA [11]. Similarly good agreement was also found between the calculated mean value of 1.4796 for PVA, with a 95% Bootstrap confidence interval ranging from 1.452 to 1.505, and the literature value of 1.4665 [11].

Table 1 shows the extrapolated refractive indices for PMMA and PVA, based on Eq. (9). The table indicates good convergence for all extrapolations for both PVA and PMMA. The mean value for PMMA is n 1.5076 0.0117 (95% confidence interval) and for PVA is n 1.4666 0.0183 (95% confidence interval). These values agree very well with the tabulated values of n 1.492 for PMMA [11] and n 1.4665 for PVA [11]. The maximum deviation between an extrapolated value and the literature value for PVA is 2.6% and for PMMA 2.2%.

4.2 Determination of the Refractive Index of Thiram In the same way as was done for PVA and PMMA, measured data for thiram solutions, as summarized in

Table 1: Refractive indices, specific refractive index increment data and extrapolated refractive index values for PMMA and PVA in a range of solvents, based on literature data from Brandrup and Immergut [11]. Solvent

nsolvent ( )

Methanol Acetonitrile Acetone Ethyl formate Ethyl acetate Methyl ethyl ketone n-Butyl acetate Methyl isobutyl ketone Tetrahydrofuran MMA Dioxane DMF Chloroform Carbon tetrachloride Toluene Benzene Chlorobenzene

1.3288 1.3442 1.3588 1.3598 1.3723 1.3788 1.3941 1.3962 1.4050 1.4140 1.4165 1.4305 1.4459 1.4601 1.4961 1.5011 1.5241

nPMMA (ml/g) ± 0.1385 0.1310 ± 0.1196 0.1066 0.0987 ± ± 0.0934 0.0712 0.0624 0.0602 0.0230 0.0072 0.0043 0.0233

nPVA (ml/g) 0.1262 0.1040 0.1043 0.0950 0.0870 0.0800 0.0716 0.0680 0.0582 ± 0.0280 ± ± ± ± 0.0038 0.0458

nPMMA ( )

nPVA ( )

± 1.5090 1.5147 ± 1.5146 1.5057 1.5116 ± ± 1.5251 1.5012 1.5048 1.5175 1.4875 1.5047 1.5062 1.4964

1.4613 1.4534 1.4683 1.4596 1.4637 1.4628 1.4693 1.4676 1.4661 ± 1.4459 ± ± ± ± 1.5051 1.4760

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Table 2: Measured refractive indices and specific refractive indices increment data for thiram solutions in a range of solvents and extrapolated refractive index values for thiram. Solvent

Refractive index of pure solvent ( )

Measured n' for solution of thiram ( )

Extrapolated value of nthiram ( )

Acetone Chloroform Aniline Iodobenzene Quinoline Bromonaphthalene

1.3616 1.4467 1.5870 1.6203 1.6270 1.6582

0.4296 0.3061 0.1792 0.1678 0.1390 0.0893

1.7912 1.7528 1.7662 1.7881 1.7660 1.7475

Table 2, were evaluated for the determination of the refractive index of thiram. 4.2.1 Refractive Index of Thiram from Multiple Solvent Data Figure 2 shows that the refractive index increment values (n') follow a linear course when plotted as a function of the refractive index of the pure solvent. The intersection of the regression line with the horizontal axis yields a refractive index of 1.7573 with a 95% Bootstrap confidence interval ranging from 1.7274 to 1.8130. 4.2.2 Refractive Index of Thiram from Single Solvent Data Table 2 shows the extrapolated refractive index values for thiram as determined by Eq. (10). The mean value for the six solvents is nthiram 1.7686 0.0179 (95% confidence interval). The narrow confidence interval indicates the good agreement of all extrapolations. Moreover, this estimate of the refractive index of thiram corresponds very well with the value obtained by extrapolation of multiple solvent data. These results support the validity of the two proposed techniques for the determination of the refractive index

Fig. 2: Linear regression for the determination of the real refractive index of thiram from multiple solvent data.

of unknown organic substances. Indeed, chemically it seems very reasonable to assume that polymers, which are large organic molecules consisting of smaller organic units, will have the same optical behavior in a solvent as small organic compounds. Therefore, the described method for the determination of refractive indices may be extended to other organic molecules, provided that the molecules dissolve well in the chosen solvents and do not dissociate.

4.3 Analysis of Laser Diffraction Patterns In order to check the influence of the estimated value of the refractive index of the particles in laser diffraction experiments, 17 particle size distributions were generated from a single experimental data-set for the thiram sample, by applying 17 different values for the refractive index of the particles in the Malvern Mastersizer software. Figure 3 indicates that pronounced submicron peaks were obtained, including 10 ± 62% of the total volume fraction of the particles, for low values of the refractive index (i.e. n 1.40 to 1.50). For higher values of the refractive index, no or very few submicron particles were observed in the particle size distributions.

Fig. 3: Different particle size distributions generated by the Malvern Mastersizer S instrument from a single data-set as a result of different refractive index values.

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Therefore, in general, for a sample of unknown refractive index, it is very hard to decide whether submicron particles are really present in the sample or whether they are artefacts due to an inappropriate estimate of the refractive index of the material. For the supermicron fraction, it is noticed that about the same range of particle sizes is observed in each of the 17 particle size distributions, independent of the chosen value of the refractive index. Moreover, Figure 4 gives an overview of the most commonly used average diameters obtained for the 17 generated particle size distributions. The error bars show the standard deviations from five independent measurements. Considering both the weighted average surface diameter (x1,2) and the weighted average volume diameter (x1,3), Figure 4 indicates that widely different results are obtained when the value of the refractive index of the particles specified in the software deviates significantly from its real value (i.e. less than 1.55 or above 2.10). The pronounced decrease of the average diameter observed at these extreme values corresponds well with the observations of Hayakawa et al. [9]. On the other hand, these authors suggested that the refractive index of the particles could be determined from the analysis of experimental laser diffraction data because the correct value of the refractive index of the particles would give rise to the highest value of the weighted average volume diameter. However, Figure 4 reveals no significant differences in weighted average volume diameter over a very broad range of refractive index values from about 1.55 to 2.10. Hence the refractive index of the particles cannot be accurately determined from Figure 4. As a further consequence of the relatively constant average particle size over a fairly broad region, it can be concluded that it is not worthwhile to spend extra effort to increase the accuracy of the

refactive index estimation beyond the second decimal place. As far as the arithmetic average length diameter (x1,0) is concerned, a rather irregular pattern is observed for refractive index values ranging from 1.55 tot 2.10. This behavior is due to the extreme sensitivity of this particular average diameter to even a very slight fronting tendency of the monomodal distributions. In this particular case, the high standard deviations clearly demonstrate that the variations of the average diameters between consecutive measurements, due to sample handling, are more pronounced than the variations due to slight changes in particle refractive index. In conclusion, Figure 4 clearly demonstrates that erroneous results may be obtained if no information is available about the refractive index of the particles. On the other hand, it is obvious that a precision of three or more decimal places for the refractive index is not required in laser scattering experiments.

4.4 Centrifugal Photosedimentometry Centrifugal photosedimentometry was performed as an independent measurement technique to check the presence of submicron particles in thiram dispersions in water. By application of the algorithm proposed by Putman et al. [15], the intensity-weighted PSD of the thiram sample was measured in triplicate. These measurements revealed a PSD with a diameter ranging from 2 to 20 mm. Hence this independent measurement technique proved that the generated particle size distributions that contained submicron peaks were not valid, and that in these cases the submicron peak was clearly an artefact: the submicron peaks were generated because of incorrect refractive index input parameters.

5 Conclusions

Fig. 4: Overview of the average diameters of the particle size distributions generated by the Malvern Mastersizer S instrument as a result of different refractive index values. The data points are average values of five independent measurements and the error bars represent the standard deviation on each value.

It is clear from our investigations that for a single experimental data-set, widely different particle size distributions (both monomodal and bimodal) can be generated. Therefore, correct refractive index information concerning the particles to be measured is required to obtain accurate PSD results, as only the first two decimal places have an important effect on the generated PSD. For organic compounds, this refractive index information may be obtained with sufficient precision (i.e. up to the second decimal place) by the extrapolation of refractive index measurements of solutions of the organic compound in a range of solvents, according to two different techniques.

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6 Acknowledgements

8 References

Jo Demeester (Laboratory for General Biochemistry and Physical Pharmacy, Faculty of Pharmaceutical Sciences, Ghent University) is gratefully acknowledged for his help and comments on the determination of refractive index increments. Thanks are also due to Eddy Devos and Marc Demuynck (UCB, Ghent) for supplying us with chemicals and the Abbe refractometer.

[1] J. Z. Knapp, T. A. Barber, A. Lieberman: Liquid- and Surface-borne Particle Measurement Handbook. Marcel Dekker, New York 1996. [2] M. Rhodes: Introduction to Particle Technology. Wiley, Chichester 1998. [3] A. Annapragada, A. Adjei: An analysis of the Fraunhofer diffraction method for particle size distribution analysis and its application to aerosolized sprays. Int. J. Pharm. 127 (1996) 219 ± 227. [4] E. Brewer, A. Ramsland: Particle size determination by automated microscopical imaging analysis with comparison to laser diffraction. J. Pharm. Sci. 84 (1995) 499 ± 501. [5] A. R. Jones: Light scattering for particle characterization. Prog. Energ. Combust. 25 (1999) 1 ± 53. [6] H. C. van de Hulst: Light Scattering by Small Particles. Dover Publications, New York 1981. [7] C. F. Bohren, D. R. Huffman: Absorption and Scattering of Light by Small Particles. Wiley, New York 1998. [8] G. Breuer, R. Rath: Investigation of the Becke line as a Fresnel diffraction phenomenon. Neues Jb. Min. Abh. 145 (1982) 115 ± 133. [9] O. Hayakawa, K. Nakahira, J. I. Tsubaki: Estimation of the optimum refractive index by the laser diffraction and scattering method. Adv. Powder Technol. 6 (1995) 47 ± 61. [10] M. B. Huglin: Light Scattering from Polymer Solutions. Academic Press, New York 1972. [11] J. Brandrup, E. H. Immergut: Polymer Handbook. Wiley, New York 1989. [12] M. Hert, C. Strazielle: Determination of increase in index of refraction dn/dc of polymers in solution in mixtures of solvents ± Relation between dn/dc and partial specific volume of polymer. Eur. Polym. J. 9 (1973) 543 ± 557. [13] J. W. Lorimer: Refractive-index increments of polymers in solution. 3. Dependence on concentration. Polymer. 13 (1972) 274 ± 276. [14] B. Efron, R. J. Tibshirani: An Introduction to the Bootstrap. Chapman & Hall, New York 1993. [15] B. Putman, P. Van der Meeren, J. Vanderdeelen: A CONTINbased approach towards the data analysis of particle sizing experiments by centrifugal photosedimentometry. Part. Part. Syst. Charact. 14 (1997) 73 ± 78.

7 Symbols and Abbreviations a a' b b' c c' n PMMA PSD PVA SRII v/v dn n dc dn 0 n 0 dc

(ml/g) ( ) (ml/g ) ( ) (g/ml) (ml/ml) ( )

a Dn

(ml2/g2) molecular polarizability ( ) difference in refractive index between solvent and solution (g/ml) density

1

(ml/g)

intercept intercept slope slope mass/volume concentration volumetric concentration real refractive index poly(methyl methacrylate) particle size distribution poly(vinyl acetate) specific refractive index increment volume/volume ratio specific refractive index increment

(ml/ml) specific refractive index increment