Chen, Zeng-Ping and Li, Li-Mei and Jin, Jing-Wen and Nordon, Alison and Littlejohn, David and Yang, Jing and Zhang, Juan and Yu, Ru-Qin (2012) Quantitative analysis of powder mixtures by raman spectrometry : the influence of particle size and its correction. Analytical Chemistry, 84 (9). pp. 4088-4094. ISSN 0003-2700 , http://dx.doi.org/10.1021/ac300189p This version is available at http://strathprints.strath.ac.uk/40536/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (http://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge. Any correspondence concerning this service should be sent to the Strathprints administrator: [email protected] The Strathprints institutional repository (http://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. Quantitative Analysis of Powder Mixtures by 1 Raman Spectrometry: the influence of particle size 2 and its correction 3 4 5 6 Zeng-Ping Chen*a, Li-Mei Lia, Jing-Wen Jina, Alison Nordonb, David Littlejohnb, Jing Yanga, 7 Juan Zhanga, Ru-Qin Yua 8 9 10 11 a. State Key Laboratory of Chemo/Biosensing and Chemometrics, College of Chemistry and 12 Chemical Engineering, Hunan University, Changsha 410082, China 13 b. WestCHEM, Department of Pure and Applied Chemistry and Centre for Process Analytics 14 and Control Technology, University of Strathclyde, Glasgow, G1 1XL, Scotland, UK 15 16 17 18 * Corresponding author 19 Tel.: (+86) 731 88821916; Fax: (+86) 731 88821916; 20 E-Mail Address: [email protected] (Z.P. Chen) 21 1 22 Abstract: Particle size distribution and compactness have significant confounding effects on 23 Raman signals of powder mixtures, which cannot be effectively modeled or corrected by 24 traditional multivariate linear calibration methods such as partial least squares (PLS), and 25 therefore greatly deteriorate the predictive abilities of Raman calibration models for powder 26 mixtures. The ability to obtain directly quantitative information from Raman signals of 27 powder mixtures with varying particle size distribution and compactness is, therefore, of 28 considerable interest. In this study, an advanced quantitative Raman calibration model was 29 developed to explicitly account for the confounding effects of particle size distribution and 30 compactness on Raman signals of powder mixtures. Under the theoretical guidance of the 31 proposed Raman calibration model, an advanced dual calibration strategy was adopted to 32 separate the Raman contributions caused by the changes in mass fractions of the constituents 33 in powder mixtures from those induced by the variations in the physical properties of samples, 34 and hence achieve accurate quantitative determination for powder mixture samples. The 35 proposed Raman calibration model was applied to the quantitative analysis of backscatter 36 Raman measurements of a proof-of-concept model system of powder mixtures consisting of 37 barium nitrate and potassium chromate. The average relative prediction error of prediction 38 obtained by the proposed Raman calibration model was less than one-third of the 39 corresponding value of the best performing PLS model for mass fractions of barium nitrate in 40 powder mixtures with variations in particle size distribution as well as compactness. 41 Keywords: Quantitative Raman Spectroscopic Analysis, Particle Size Distribution, 42 Compactness, Multiplicative Confounding Effects, Powder Mixture, Dual Calibration 43 Strategy 2 44 Introduction 45 Powder blending is an important process in the manufacture of many pharmaceutical 46 products 1. Raman spectroscopy has been increasingly applied to the qualitative analysis of 47 powder mixtures 2-6, because of its flexibility of sampling (solids can be analyzed with little 48 or no sample preparation), and exceptionally high chemical specificity and the use of fibre 49 optics for convenient and remote analysis, which facilitate the non-invasive in-line and real 50 time analysis of particulate systems 7-17. However, some issues remain unresolved regarding 51 the quantitative in-line monitoring of particulate systems by Raman spectroscopy. 52 One of the issues is that the Raman intensities of analyte peaks depend on not only the 53 analyte concentration, but also on the intensity of the excitation source, the instrument’s 54 optical configuration and the sample alignment. Therefore, to gain quantitative information 55 requires the use of internal or external standards 18-20. Band ratios between the overall Raman 56 intensities and that of an individual spectral peak arising from internal or external standards 57 are calculated and used in quantitative analysis. But the use of internal or external standards 58 can be difficult to apply accurately in many in-situ process analysis applications. Moreover, 59 for samples involving solids such as powder mixtures, quantitative Raman analysis becomes 60 even more difficult, because the Raman measurements from such samples depend on the 61 particle size and compactness of the mixtures, which hinders the use of an internal or external 62 standard. The application of multivariate calibration methods such as principal component 63 regression (PCR) and partial least squares (PLS) has some advantages over univariate band 64 ratio calibration models in the quantitative analysis of Raman measurements 20, 21. However, 65 when analyzing powder mixtures using Raman spectroscopy, the variations in the physical 3 66 properties such as particle size and compactness of the mixtures have confounding effects on 67 the total Raman intensities. Such confounding effects cannot be effectively modeled by 68 standard multivariate calibration methods, and will significantly affect the predictive 69 accuracy of multivariate calibration models. 70 Although it has long been known that physical properties of powder samples can 71 influence the intensity of the Raman spectrum, and several studies 22-26 have been conducted 72 on the relationship between particle size and Raman intensity, relatively little research 73 focuses on quantitative Raman spectroscopic analysis of powder mixtures. Some of the 74 present authors conducted a preliminary investigation on quantitative Raman spectroscopic 75 analysis of suspension samples 27. However, due to the facility limitations at that time, we 76 were unable to explicitly investigate the effects of particle size distribution and sample 77 compactness on Raman signals of powder mixtures in that work. The objectives of this study 78 are to 1) explicitly investigate the effects of particle size and compactness on Raman signals 79 of powder mixtures, 2) develop an advanced quantitative Raman calibration model for 80 powder mixtures, and 3) eventually achieve accurate quantitative analysis of powder mixtures 81 using Raman spectrometry. 82 83 84 Theory 85 Raman intensities of powder mixtures 86 The intensity of Raman bands depends on a complex expression involving the polarisability 87 tensor of a molecule 28. For analytical purposes, the following less rigorous linear model 4 88 analogous to the Beer-Lambert law can be used. I(v)nr(v)I (1) o 89 Where I((cid:542)) is the Raman intensity at Raman shift (cid:542), I is the intensity of the excitation o 90 radiation, n is the number of molecules of the analyte illuminated by the source and viewed 91 by the spectrometer, and r((cid:542)) is a composite term that represents the overall spectrometer 92 response, and the self absorption and molecular scattering properties of the analyte at Raman 93 shift (cid:542). For K powder samples comprising J constituents with amounts above their Raman 94 limits of detection, their overall Raman intensities can be expressed as the linear combination 95 of the contributions of all J constituents as well as other possible interference(s) such as 96 fluorescence. J I (v)[n r (v)I ]n r ((cid:542))I ; k 1,2,...,K (2) k k,j j o,k k,interf interf o,k j1 97 Where n and n are the number of molecules of the j-th constituent and the k,j k,interf 98 interference(s) in the k-th powder sample illuminated by the source and viewed by the 99 spectrometer, respectively; r ((cid:542)) represents the molecular scattering/fluorescence interf 100 properties of the interference(s) at Raman shift (cid:542). 101 Suppose m and V are the overall mass and volume of the k-th powder sample, k k 102 respectively. V denotes the volume of the k-th powder sample illuminated by the source spec,k J 103 and viewed by the spectrometer. w (w 1) signifies the mass fraction of the j-th k,j k,j j1 104 constituent in the k-th sample. M is the molecular weight of the j-th constituent. The j 105 multiplicative parameter, p , is introduced to account for the effects of the particle size k 5 106 distribution and compactness of the k-th sample on the Raman intensities 24, 27. Equation 2 107 then becomes: J m w V I (v)[p  k k,j spec,k r (v)I ]n r ((cid:542))I (3) k k M V j o,k k,interf interf o,k j1 j k 108 Define q  p m V I V and r*(v)r (v) M . Equation 3 can be simplified as k k k spec,k o,k k j j j 109 follows. J I (v)[q w r*(v)]n r ((cid:542))I (4) k k k,j j k,interf interf o,k j1 110 In equation 4, q is a very important model parameter. It accounts for the variations in Raman k 111 intensities caused by the changes in variables other than the mass fractions of the constituents 112 in the powder mixtures, such as the intensity of the excitation source, the sample’s particle 113 size distribution, sample compactness, the overall mass and volume of the powder sample as 114 well as the volume illuminated by the source and viewed by the spectrometer. 115 Suppose the j-th constituent is the target component in the powder mixtures, and the 116 Raman signals of K calibration samples have been measured over Raman shift range of v ~v . 1 m J 117 As w 1, equation 4 can be rewritten as: k,j j1 J x q w r* q r* [q w r*]n r I k k k,1 1 k 2 k k,j j k,interf interf o,k j3 (5) Where, x [I (v ),I (v ),,I (v )]; r* [r*(v ),r*(v ),,r*(v )], j1, 2, , J k k 1 k 2 k m j j 1 j 2 j m r* r*r*; r [r (v ),r (v ),,r (v )] j j 2 interf interf 1 interf 2 interf m 118 Assumingr*, r*, and r are linearly independent of each other, it can be seen that a j 2 interf 119 straightforward multivariate linear calibration model can be built only between x and k 120 q w (or q ). It is obvious that the multiplicative parameter, q , may be different for each k k,j k k 6 121 of the powder samples. Hence the relationship between Raman spectrum x and the mass k 122 fraction of the j-th constituent (w ) is actually nonlinear; and the multiplicative parameter, q , k,j k 123 has confounding effects on the estimation of w . In order to extract the quantitative k,j 124 information (mass fraction) of any constituent in powder samples from their Raman 125 measurements, it is therefore imperative to estimate the multiplicative parameter, q , for each k 126 powder sample. 127 128 Dual Calibration Strategy (DCS) 27, 29-30 129 For K training samples in which the mass fractions of the target constituent (say, the j-th 130 constituent) are known, the multiplicative parameters, q (k = 1, 2, …, K), can be estimated by k 131 the modified Optical Path-Length Estimation and Correction method (OPLEC ) 30 ( the m 132 Matlab script for OPLEC is provided in supporting information). After the estimation of q m k 133 (k = 1, 2, …, K), the following two calibration models can be built by multivariate linear 134 calibration methods such as PLS. diag(w )qa 1X (cid:533) ; qa 1X (cid:533) j 1 cal 1 2 cal 2 (6) X [x ; x ; ...; x ]; w [w ; w ; ...; w ]; q[q ; q ; ...; q ] cal 1 2 K j 1,j 2,j K,j 1 2 K 135 Where diag(w) denotes the diagonal matrix in which the corresponding diagonal elements are j 136 the elements of w; 1 is a column vector with its elements equal to unity. After the estimation j 137 of model parameters a , a , (cid:533) , and (cid:533) by multivariate calibration methods such as PLS, 1 2 1 2 138 these two calibration models could then be used to predict the mass fraction of the target 139 constituent in any test powder sample (w ) from its Raman spectrum x . test,j test 7 a x (cid:533) q w a x (cid:533) q a x (cid:533) w  1 test 1 (7) test test,j 1 test 1; test 2 test 2; test,j a x (cid:533) 2 test 2 140 The mass fraction of other constituents in the test sample can be obtained in a similar way. 141 142 143 Experimental 144 Materials 145 All chemicals were analytical grade, and were used as received without any further 146 purification. Potassium chromate was obtained from Tianjin Windship Chemistry 147 Technological Co., Ltd (Tianjin, China). Barium nitrate was purchased from Tianjin Kermel 148 Chemical Reagent Co., Ltd (Tianjin, China). 149 150 Equipment 151 Raman spectra were acquired at room temperature on a LABRAM-0101 Laser Confocal 152 Raman Spectrometer equipped with a 1024(cid:215)256 pixels CCD detector. The microscope 153 attachment was based on an Olympus BX41 system with a 10(cid:215) objective. Radiation of 154 632.81 nm from a 17 mW He-Ne laser was used for excitation. The widths of the entrance slit 155 and confocal pinhole were set to 100 (cid:541)m and 1000 (cid:541)m, respectively. Raman spectrum 156 between 200 and 2000 cm-1 was collected with a 5 s exposure time and 3 accumulations for 157 each spectrum. 158 159 Raman measurements of powder mixtures 160 The solids of both barium nitrate and potassium chromate were ground and sorted into 8 161 different particle sizes using standard sieves. The standard sieves were of mesh sizes 40, 60, 162 80, 100, 120, 140, 160 and 200 wires per inch. The hole sizes corresponding to the mesh sizes 163 are 425, 250, 180, 150, 125, 109, 96 and 75 (cid:541)m, respectively. A total of 72 powder mixtures 164 of potassium chromate and barium nitrate powder with different weight ratios (1:0, 0.90:0.10, 165 0.75:0.25, 0.60:0.40, 0.50:0.50, 0.40:0.60, 0.25:0.75, 0.10:0.90 and 0:1) and different particle 166 sizes (425, 250, 180, 150, 125, 109, 96 and 75 (cid:541)m) were prepared by mixing appropriate 167 amounts of the two constituents thoroughly (Table 1). For each of 72 powder mixtures, a 168 sample was randomly taken and loosely packed into a cylindrical sample cup with a diameter 169 of 6.9 mm and a height of 10.7 mm. The laser beam was focused at a point inside the sample 170 so as to ensure the illumination of the whole upper surface of the sample by the laser beam, 171 and then the Raman spectrum was acquired. Following this, each sample was packed more 172 firmly, and a further Raman spectrum was recorded resulting in a total of 144 spectra. 173 Seventy eight spectra (two outliers were removed) from the five mixtures with the ratios of 174 potassium chromate to barium nitrate equal to 1:0, 0.75:0.25, 0.5:0.5, 0.25:0.75 and 0:1 175 formed the calibration data set. The test set comprised the remaining 64 spectra from the 176 other four mixtures. Distinctive Raman peaks of potassium chromate (at around 351, 386.5, 177 396.8(cid:712)853.4, 868.4, 877.8 and 906.8 cm-1) and barium nitrate (at about 1047.5 cm-1) can be 178 readily observed between 292.8 and 1136.6 cm-1 (supporting information, Figure S-1). 179 Therefore, Raman signals in this region were selected for the subsequent data analysis. 9