Particle size analysis in pharmaceutics and other industries : theory and practice

Table of contents Preface xv 1. Basic principles 1 RANGE OF PARTICLE SIZES AND UNITS 2 MEASURES OF PARTICLE SIZE 2 DISTRIBUTIONS OF PARTICLE SIZES 5 INCREMENTAL AND CUMULATIVE DISTRIBUTIONS 9 NUMBER, AREA AND MASS DISTRIBUTIONS 11 CHARACTERIZATION OF DISTRIBUTIONS 14 Measures of central tendency 14 Moments of a distribution and moment notation 16 Measures of dispersion 18 Measures of distribution shape 19 MODEL DISTRIBUTIONS 19 The normal distribution 21 The lognormal distribution 22 The Rosin-Rammler distribution 23 IDENTIFICATION OF SPECIFIC DISTRIBUTIONS 25 PARTICLE SHAPE 27 Descriptive 27 Descriptors based on direct measurement of dimensions 28 Shape factors 29 Fourier transform methods 30 FRACTAL CHARACTERIZATION OF PARTICLES 31 REFERENCES 33 2. Sample selection and preparation 34 SAMPLE SELECTION 34 SELECTION OF PRIMARY SAMPLE 36 Sampling from flowing powders 37 Sampling from stored powders 37 Sampling from liquids 40 SPLITTING THE PRIMARY SAMPLE 41 Manual methods of sample splitting 41 Mechanical methods of sample splitting 42 DISPERSION OF MATERIALS 44 Wetting 45 Disintegration 47 Stabilization and flocculation 48 PRACTICAL TECHNIQUES FOR SAMPLE DISPERSION 50 CALIBRATION AND REFERENCE STANDARDS 52 REFERENCES 53 3. Sieving 54 SIEVE SIZES AND RANGES 54 What does sieving measure? 55 METHODS OF SIEVE CONSTRUCTION 56 Woven sieves 56 Etched sieves 57 Punched sieves 58 ix TECHNIQUES FOR USING SIEVES 58 Wet sieving 58 Hand sieving 60 Machine sieving 61 Sonic and ultrasonic sieving 63 Airjet sieving 64 Cleaning of sieves 66 Calibration and testing of sieves 67 ERRORS AND PROBLEMS IN SIEVING 69 Errors in the sieve 69 Sieve load 70 Sieving time 70 Properties of the feedstock 71 WHEN TO USE SIEVING 72 REFERENCES 73 4. Electrical zone sensing 74 PRINCIPLE OF OPERATION 74 Sampling head operation 76 APERTURE CONSTRUCTION AND MAINTENANCE 79 CALIBRATION 79 TECHNIQUES FOR THE USE OF THE COULTER COUNTER 82 Overlapping ranges 85 Mass balance checks 86 Electrolyte selection and preparation 87 ERRORS IN ELECTRICAL ZONE SENSING 89 Interference and vibration 89 Coincidence correction 91 Particle path and shape 93 x Flocculation in the electrolyte 95 Particle sedimentation 95 APPLICATIONS 96 Particle counting in parenterals 96 Parenteral fat emulsions 98 REFERENCES 99 5. Introduction to light scattering 101 LIGHT DIFFRACTION 102 SINGLE PARTICLE SCATTERING 103 PHOTON CORRELATION 103 6. The angular distribution of scattered light 106 INTRODUCTION 106 THEORY OF LIGHT DIFFRACTION 107 Optical properties of materials 107 Mie Theory 108 Scattering of polarized light 110 Rayleigh scattering 111 Rayleigh-Gans-Debye (RGD) scattering 113 Fraunhofer scattering 113 Anomalous scattering 114 LASER DIFFRACTION PARTICLE SIZERS 115 Data processing 118 Sample preparation 120 Dry powder feeders 120 Aerosol sizing accessories 121 CALIBRATION ERRORS AND DISADVANTAGES OF DIFFRACTION SIZE ANALYSIS 125 Submicrometre resolution 125 xi 123 Multiple scattering 127 Flow and refractive index fluctuations 127 Computing artefacts 128 Particle shape 128 LASER SAFETY 130 OPTICS CLEANING 131 REFERENCES 132 7. Photon correlation spectroscopy 133 PRINCIPLE OF PHOTON CORRELATION 134 PARTICLE SIZE DISTRIBUTIONS FROM PCS 138 Cumulant analysis 141 Histogram method 143 Exponential sampling method 143 Constrained regularization 145 Multiple angle measurement 145 EQUIPMENT FOR PHOTON CORRELATION 145 The laser 147 The sample optics 148 The detector 149 The correlator 149 SAMPLE PREPARATION 151 ERRORS IN PCS SIZE MEASUREMENT 153 ZETA POTENTIAL MEASUREMENT 154 Overview of zeta potential 154 Zeta potential measurement 155 Experimental aspects 156 Electroacoustic analysis 163 Applications 164 xii REFERENCES 164 8. Particle size analysis of aerosols 166 INERTIAL IMPACTION 167 SAMPLING AEROSOL GASES 170 GENERATION OF CALIBRATION AEROSOLS 172 Impaction particle sizers 173 The two-stage impinger 174 The Andersen sampler 175 Setting up and calibration 179 Errors of Andersen sampler analysis 181 OPTICAL COUNTING METHODS 183 Light scattering intensity measurements 183 AERODYNAMIC PARTICLE SIZERS 185 The Malvern Aerosizer 185 Phase Doppler Anemometry 187 MISCELLANEOUS TECHNIQUES 189 Filtration 189 Nucleation counters 190 REFERENCES 191 9. Sedimentation 192 THEORY 193 Limitations of Stokes’ law 193 THE ANDREASEN PIPETTE 197 Data analysis 199 SEDIMENTATION BALANCES 200 Data analysis 199 PHOTOSEDIMENTATION 203 X-RAY SEDIMENTATION 206 CENTRIFUGAL SEDIMENTATION 208 xiii Determination of density 212 REFERENCES 213 10. Microscopy and image analysis 215 RESOLUTION 215 STATISTICAL CONSIDERATIONS 216 SAMPLE SELECTION AND PREPARATION 217 INSTRUMENTATION 219 ELECTRON MICROSCOPY 220 MANUAL METHODS 221 SEMIAUTOMATIC METHODS 223 AUTOMATIC IMAGE ANALYSIS 224 Image processing instrumentation 225 Image display 229 Image enhancement 230 Image measurement 232 FRACTAL MEASUREMENT 232 REFERENCES 234 Index 237 xiv