Essentials of Pharmaceutical Preformulation 1st edition by Simon Gaisford, Mark Saunders ISBN 0470976365 978-0470976364

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ISBN 10: 0470976365
ISBN 13: 978-0470976364
Author:  Simon Gaisford, Mark Saunders 

Essentials of Pharmaceutical Preformulation is a study guide which describes the basic principles of pharmaceutical physicochemical characterisation. Successful preformulation requires knowledge of fundamental molecular concepts (solubility, ionisation, partitioning, hygroscopicity and stability) and macroscopic properties (physical form, such as the crystalline and amorphous states, hydrates, solvates and co-crystals and powder properties), familiarity with the techniques used to measure them and appreciation of their effect on product performance, recognising that often there is a position of compromise to be reached between product stability and bioavailability.

This text introduces the basic concepts and discusses their wider implication for pharmaceutical development, with reference to many case examples of current drugs and drug products. Special attention is given to the principles and best-practice of the analytical techniques that underpin preformulation (UV spectrophotometry, TLC, DSC, XRPD and HPLC). The material is presented in the typical order that would be followed when developing a medicine and maps onto the indicative pharmacy syllabus of the Royal Pharmaceutical Society of Great Britain

Undergraduate-level pharmacy students and R&D / analytical scientists working in the pharmaceutical sector (with or without a pharmaceutical background) will find this text easy to follow with relevant pharmaceutical examples.

• Essential study guide for pharmacy and pharmaceutical science students
• Covers the pharmaceutical preformulation components of the Royal Pharmaceutical Society of Great Britain’s indicative syllabus
• Easy to follow text highlighted with relevant pharmaceutical examples
• Self-assessment assignments in a variety of formats
• Written by authors with both academic and industrial experience
• Companion website with further information to maximise learning

Essentials of Pharmaceutical Preformulation 1st Table of contents:

1 Basic Principles of Preformulation Studies

1.1 Introduction

Table 1.1 Total market sales in the pharmaceutical sector from 2003 to 2010 (data from IMS Health).

Table 1.2 Top ten drugs by sales worldwide in 2010 (data from IMS Health).

1.2 Assay design

1.2.1 Assay development

Table 1.3 Molecular sample properties and the assays used to determine them.

Table 1.4 Macroscopic (bulk) sample properties and the techniques used to determine them.

1.3 Concentrations

1.3.1 Units of concentration

Summary box 1.1

1.4 UV spectrophotometry

Table 1.5 UV absorbance maxima for a range of common functional groups (data from Wells (1988)).

Table 1.6 The effect of auxochromes on the UV absorbance of the parent compound C6H5–R (data from Wells (1988)).

Study question 1.1

1.4.1 Method development for UV assays

Table 1.7 Suitable solvents for UV analysis.

Table 1.8 Specifications for a UV spectrometer (data from Wells (1988)).

Summary box 1.2

1.5 Thin-layer chromatography (TLC)

1.5.1 TLC method development

1.5.1.1 Preparation of the plates

1.5.1.2 Spotting

Figure 1.1 Layout of a typical TLC plate used for stability testing during preformulation. Key: A, 2% impurity standard; B, 50 °C stability sample; C, 1% impurity in laboratory reference sample of drug; D, 37 °C stability sample; E, 1% impurity; F, 30 °C stability sample; G, 0.5% impurity; H, 4 °C stability sample; I, Laboratory reference standard (redrawn from Wells (1988), with permission from John Wiley & Sons, Inc.).

1.5.1.3 Separation

1.5.1.4 Mobile and stationary phase selection

Table 1.9 Derivatised silica stationary phases used in reverse-phase TLC.

Table 1.10 Solvent strengths in normal- and reverse-phase TLC.

Table 1.11 Mobile-phase solvents for TLC method development (data from Poole and Dias (2000)).

1.5.2 High-performance TLC

Summary box 1.3

1.6 High-performance liquid chromatography

1.6.1 Normal- and reverse-phase HPLC

Table 1.12 Stationary phases used in reverse-phase HPLC.

Table 1.13 Buffer solutions for reverse-phase HPLC.

1.6.1.1 Solvent gradients

1.6.2 HPLC method development

Summary box 1.4

1.7 Differential scanning calorimetry

1.7.1 Interpreting DSC data

1.7.1.1 Effect of heat capacity

Table 1.14 Certified reference materials (CRM) for calibration of DSC instruments (data from Haines (2002)).

Figure 1.2 Effect of heat capacity on DSC data (solid line – sample material, dotted line – reference material).

Figure 1.3 The three DSC experiments required to calculate the heat capacity of a sample material.

1.7.1.2 Effect of phase transitions

Figure 1.4 Effect of heating rate on DSC data (solid line – sample material, dotted line – reference material).

Figure 1.5 Information that can be derived from DSC data (in this case, melting of indomethacin).

1.7.2 Modulated-temperature DSC

Figure 1.6 Sample temperature as a function of time for MTDSC (solid line, calculated using Equation (1.15)) and the corresponding underlying linear heating rate (dotted line).

1.7.3 DSC method development

1.7.3.1 Instrument selection

1.7.3.2 Pan type

1.7.3.3 Experimental parameters

Summary box 1.5

1.8 Dynamic vapour sorption

1.8.1 DVS method development

Summary box 1.6

1.9 Summary

References

Answer to study question

Additional study questions

2 Ionisation Constants

2.1 Introduction

Table 2.1 Solubility and pKa data for the 10 best selling drugs of 2010.

2.2 Ionisation

Figure 2.1 Change in percent ionisation as a function of pH for weak acids and weak bases.

Figure 2.2 Increase in solubility with increasing pH for an acidic drug (pKa 7.4, So 10 mg mL−1).

Figure 2.3 Increase in solubility with decreasing pH for a basic drug (pKa 4.5, So 10 mg mL−1).

Figure 2.4 Solubility data for metronidazole, showing the difference between experimentally measured solubility data and the curve predicted using Equation (2.18) (solubility data from Wu and Fassihi (2005)).

Study question 2.1

Study question 2.2

Summary box 2.1

2.2.1 Percent ionisation

Table 2.2 Percent ionised for weak acids and bases as a function of pH.

Study question 2.3

2.3 Buffers

2.4 Determination of pKa

Table 2.3 IUPAC descriptions for error in pKa values.

2.4.1 Determination of pKa by potentiometric titration

Figure 2.5 A plot of volume of titrant added versus solution pH for a potentiometric pH titration.

2.4.2 Determination of pKa in nonaqueous solvents

Table 2.4 Measured (in water) and extrapolated (from the Yasuda–Shedlovsky plots) pKa values for three drugs (data from Takács-Novák et al. (1997)).

Figure 2.6 Yasuda–Shedlovsky plots for three drugs (redrawn from Takács-Novák et al., Copyright (1997), with permission from Elsevier).

2.4.3 Other factors affecting measurement of pKa

Summary box 2.2

2.5 Summary

References

Answers to study questions

Additional self-study questions and answers

3 Partition Affinity

3.1 Introduction

3.2 Partitioning

Study question 3.1

Summary box 3.1

3.2.1 Effect of partitioning

3.2.2 Determination of log P

3.2.2.1 Shake-flask method

Figure 3.1 The shake flask method for determination of partition coefficient.

Study question 3.2

Figure 3.2 Discriminating power of various partitioning solvents (redrawn from Wells (1988), with permission from John Wiley & Sons, Inc.).

Summary box 3.2

3.2.2.2 Chromatographic methods

Figure 3.3 Log P versus log retention factor correlation (linear regression coefficients are shown as r2 values) for three series of barbituric acids (data courtesy of Richard Prankerd).

3.2.3 Effect of salt formation on partitioning

Table 3.1 The effect of salt formation on the partition coefficient of weak bases.

Summary box 3.3

3.3 Summary

References

Answers to study questions

4 Solubility

4.1 Introduction

Table 4.1 BCS categories based on solubility and intestinal permeability.

Table 4.2 Table of USP and PhEur terms for describing the solubility of drugs.

4.2 Intrinsic solubility

Summary box 4.1

4.2.1 Ideal solubility

Table 4.3 Ideal (calculated) solubility for aspirin compared with experimentally determined solubilities in a range of solvents (at 25 °C, assuming MP 137.23 °C, ΔfH 29.8 kJ mol−1) (data from the RSC Open Notebook Science Challenge).

Table 4.4 Ideal (calculated) solubility for paracetamol compared with experimentally determined solubilities in a range of solvents (at 30 °C, assuming MP 170 °C, ΔfH 27.6 kJ mol−1) (data from Granberg and Rasmuson (1999)).

Table 4.5 Dielectric constants of some common pharmaceutical solvents at 25 °C.

4.2.2 Solubility as a function of temperature

Figure 4.1 Solubility as a function of temperature for paracetamol in three solvents (data from Granberg and Rasmuson (1999)).

Figure 4.2 A schematic plot showing the change in solubility with temperature for drugs with endothermic and exothermic enthalpies of solution.

Figure 4.3 A plot of ln x2 versus 1/T for three drugs in water (solubility data from Mota et al. (2009)).

4.2.3 Solubility and physical form

Figure 4.4 Concentration versus time profile for dissolution of a metastable (ms) form of a drug. The system is in equilibrium until excess drug is removed by filtration, after which the solution is supersaturated with respect to the stable (s) form. Subsequently the stable form precipitates and a new position of equilibrium is reached.

Study question 4.1

Summary box 4.2

4.2.4 Measurement of intrinsic solubility

Figure 4.5 Phase–solubility diagram for a pure compound.

Figure 4.6 Phase–solubility diagram for a compound with one impurity.

Figure 4.7 Effect of the drug:solvent phase ratio when the drug is impure (redrawn from Wells, 1988, with permission from John Wiley & Sons, Inc.).

Figure 4.8 DSC thermal traces for benzoic acid of varying purity.

Figure 4.9 Melting endotherm for indomethacin recorded by DSC and the integration of partial areas to allow calculation of sample purity.

Figure 4.10 van’t Hoff plot for melting of indomethacin.

Figure 4.11 van’t Hoff plot for melting of indomethacin, corrected using Sondack’s method.

4.2.5 Calculation of pKa from solubility data

4.3 Summary

References

Answer to study question

Additional self-study questions and answers

5 Dissolution

5.1 Introduction

5.2 Models of dissolution

Figure 5.1 A schematic representation of the boundary layer adjacent to the surface of a dissolving solid and the change in concentration of solute across it.

5.3 Dissolution testing

Table 5.1 The number of USP monographs for immediate release oral dosage forms requiring dissolution tests (reproduced from Dokoumetzidis and Macheras, Copyright 2006, with permission from Elsevier).

Table 5.2 Pharmacopoeial dissolution apparatus.

Figure 5.2 Dissolution apparatus 1 (basket, right) and apparatus 2 (paddle, left).

Figure 5.3 Dissolution curves for indomethacin tablets stirred at 50 and 100 rpm (data redrawn from Klein (2006)).

Study question 5.1

Figure 5.4 Concentration versus time profile for a solute undergoing dissolution following addition to water and (inset) the linear rate region when C = St//10 (i.e. sink conditions).

Study question 5.2

Summary box 5.1

5.3.1 Intrinsic dissolution rate (IDR)

Study question 5.3

5.3.2 IDR as a function of pH

Figure 5.5 pH across the diffusion layer for dissolution of salicylic acid in various media, showing that the pH at the surface of the dissolving solid can be significantly different from that of the bulk solvent (redrawn from Serajuddin and Jarowski (1985), with permission from John Wiley & Sons, Inc.).

5.3.3 IDR and the common ion effect

Summary box 5.2

5.4 Summary

References

Answers to study questions

6 Salt Selection

6.1 Introduction

Table 6.1 Possible advantages and disadvantages of salt formation.

6.2 Salt formation

Table 6.2 Physicochemical properties of some diclofenac salts (data from Fini et al. (1996)).

Table 6.3 Descriptions of acid and base strength (data from Stahl and Wermuth (2011)).

Figure 6.1 Solution pH as a function of concentration for a basic salt.

Table 6.4 Values for the self-ionisation constant of water as a function of temperature (data from Bandura and Lvov (2005)).

Figure 6.2 Solution pH as a function of concentration for an acidic salt.

Study question 6.1

Summary box 6.1

6.2.1 Selection of a salt-forming acid or base

Figure 6.3 Percentage of salt formed as a function of acid pKa when reacted with a basic drug of pKa 7.5.

Table 6.5 Values of pKa for selected pharmaceutical acids (data from Stahl and Wermuth (2011)).

Table 6.6 Values of pKa for selected pharmaceutical bases (data from Stahl and Wermuth (2011)).

Table 6.7 Frequency of pharmaceutical anions and cations of drugs in USP 29-NF24 (data from Kumar et al. (2008)).

Study question 6.2

6.2.2 Salt screening

Table 6.8 Properties of some common solvents used for salt screening (data from Huang and Tong (2004)).

Figure 6.4 A decision tree for salt selection based on characterisation of physicochemical properties (data from Morris et al. (1994)).

Summary box 6.2

6.3 Salt solubility

Table 6.9 Solubilities of various procaine salts as a function of temperature (data from Guerrieri et al. (2010)).

6.3.1 Solubility of basic salts

Figure 6.5 Solubility profile for a basic salt as a function of pH (pKa 6.7).

6.3.2 Solubility of acidic salts

Figure 6.6 Solubility profile for an acidic salt as a function of pH (pKa 5.6).

6.3.3 The importance of pHmax

Figure 6.7 Solubility profiles for a basic drug (pKa 6.7) in three salt forms (solubilities 5, 2 and 0.5 mg mL−1).

Figure 6.8 Effect of a change in pKa on the solubility profile of a basic salt (original pKa 6.7).

Figure 6.9 Effect of free base solubility on the solubility profile of a basic salt (St 0.01 mg mL−1).

Figure 6.10 Effect of salt solubility on pHmax for a basic salt.

Summary box 6.3

6.4 Dissolution of salts

Figure 6.11 Schematic representation of the boundary layer surrounding the surface of a dissolving solid and (inset graph) the change in pH with distance from the surface of the dissolving solid.

Figure 6.12 pH across the diffusion layer as a function of dissolution medium for haloperidol (redrawn from Serajuddin. Copyright (2007), with permission from Elsevier).

6.4.1 Modification of pHm

Table 6.10 Measured pH microenvironment of a number of excipients.

6.5 Partitioning of salts

Table 6.11 Log P and solubility data for ibuprofen sodium (data from Sarveiya et al. (2004)).

Table 6.12 Log P and flux values (across a polydimethylsiloxane model membrane) for various salts of ibuprofen (data from Sarveiya et al. (2004)).

Summary box 6.4

6.6 Summary

References

Answers to study questions

7 Physical Form I – Crystalline Materials

7.1 Introduction

7.2 Crystal formation

7.2.1 Crystal formation from the melt

Figure 7.1 Thermodynamic representation of the change in enthalpy as a material crystallizes from a liquid to form a solid phase (reproduced from Glicksman (2011), with kind permission from Springer Science + Business Media B.V.).

7.2.2 Crystal growth from solution

Study question 7.1

Summary box 7.1

7.3 Crystal structure

Table 7.1 Axis and angle rules for the seven Bravais unit cells.

Figure 7.2 The 14 distinct Bravais lattices.

Figure 7.3 The six basic habits described in the USP.

Summary box 7.2

7.4 Polymorphism

Figure 7.4 Thermodynamic representation of the formation of polymorphs.

Study question 7.2

7.4.1 Thermodynamics of polymorphism

Figure 7.5 Schematic representation of the change in free energy with temperature for two monotropic polymorphs.

Figure 7.6 Schematic representation of the change in free energy with temperature for two enantiotropic polymorphs.

Summary box 7.3

7.4.2 Physicochemical properties of polymorphs

Figure 7.7 Schematic representation of polymorphic forms of a drug (top left and right) as well as a monohydrate or solvate (bottom left) and a co-crystal (bottom right).

Study question 7.3

Figure 7.8 Blood plasma concentrations versus time for two polymorphs of chloramphenicol palmitate (redrawn from Aguiar et al. (1967), with permission from John Wiley & Sons, Inc.).

Study question 7.4

7.5 Pseudopolymorphism

Figure 7.9 Overview of crystalline forms.

Summary box 7.4

7.6 Polymorph screening

Figure 7.10 DSC thermal traces showing the melting of paracetamol form I (initial heat), quench cooling to form a glass (cool) and crystallisation to and melting of the metastable form II (second heat) (data courtesy of Asma Buanz).

7.7 Characterisation of physical form

Figure 7.11 XRPD diffractograms for two polymorphs of sulphapyridine (data courtesy of Asma Buanz)

7.7.1 Characterisation of polymorphs

Figure 7.12 Schematic DSC thermal trace showing melt of the stable form of a polymorph.

Figure 7.13 Schematic representation of the DSC thermal traces for a metastable polymorph on its first (top) and second (bottom) heating runs.

Study question 7.5

Figure 7.14 DSC thermal trace for an enantiotropically related pair of sulphathiazole polymorphs (top, courtesy of Asma Buanz) and a series of monotropically related premafloxacin polymorphs (bottom, redrawn from Schinzer et al. (1997)).

Study question 7.6

Figure 7.15 Schematic representation of the DSC thermal traces for a metastable polymorph at slow (top) and fast (bottom) heating rates.

Figure 7.16 Schematic representation of the theoretical position of the crystallisation exotherm when a very fast heating rate is used.

Figure 7.17 Determination of the minimum heating rate required to inhibit a kinetic event.

Study question 7.7

Summary box 7.5

7.7.2 Characterisation of pseudopolymorphs

Figure 7.18 Schematic DSC thermal traces for an irreversible hydrate (top) and a reversible hydrate (bottom).

Study question 7.8

Figure 7.19 DSC and TGA thermal traces for a metastable polymorph (top) and an irreversible hydrate (bottom).

Summary box 7.6

7.8 Summary

References

Answers to study questions

Table 7.2 Properties that may change with polymorphic form (adapted from Grant (1999)).

8 Physical Form II – Amorphous Materials

8.1 Introduction

8.2 Formation of amorphous materials

Figure 8.1 Schematic representation of the formation of a glass, showing the glass transition temperature, the Kauzmann temperature, ageing and recovery.

Summary box 8.1

Study question 8.1

Study question 8.2

Summary box 8.2

8.3 Ageing of amorphous materials

Summary box 8.3

8.4 Characterisation of amorphous materials

Figure 8.2 XRPD ‘halo’ seen for amorphous powders.

Figure 8.3 The glass transition as seen by DSC and the analysis for Tg and heat capacity.

8.4.1 Measurement of ageing

Study question 8.3

Figure 8.4 Decay function data versus annealing time and the fit to the KWW equation (dotted line).

Figure 8.5 Effect of τ on the decay function (Ta = 25°C, β = 0.5).

Figure 8.6 Effect of Ta on the decay function (τ = 10 h−1, β = 0.5).

Figure 8.7 DSC thermal trace for the glass transition of an aged glass (top) and the second heat (bottom).

Figure 8.8 Schematic DSC thermal traces for an amorphous material that crystallises and melts, showing the effect of the scan rate.

Summary box 8.4

8.5 Processing and formation of amorphous material

8.5.1 Spray-drying

Figure 8.9 A scanning electron micrograph of spray-dried particles.

8.5.2 Freeze-drying

Figure 8.10 The stages of freeze-drying with reference to the phase diagram of water (see the main text for an explanation of the processes at points 1 to 4).

Figure 8.11 A scanning electron micrograph of a freeze-dried material.

8.5.3 Quench-cooling

8.5.4 Milling

Table 8.1 Surface energy of various lactose samples determined with inverse phase chromatography (data from Newell et al. (2001)).

Study question 8.4

8.5.5 Compaction

Summary box 8.5

8.6 Amorphous content quantification

8.6.1 Calibration standards

Study question 8.5

Study question 8.6

Figure 8.12 A calibration line for the amorphous content in salbutamol sulphate showing deviation from linearity as the amorphous content approaches 100% (redrawn from Gaisford and O’Neill, Copyright 2011, with permission from Elsevier).

8.6.2 DSC for amorphous content quantification

Figure 8.13 Separation of MTDSC data into reversing and nonreversing signals for a sample of trehalose.

8.6.3 DVS for amorphous content quantification

Figure 8.14 DVS data for a sample of amorphous salbutamol sulphate, showing water absorption and then crystallisation at a critical RH of 75%.

Summary box 8.6

8.7 Summary

References

Answers to study questions

9 Stability Assessment

9.1 Introduction

Table 9.1 ICH storage conditions for general, refrigerated and frozen drug substances and products (ICH Guideline Q1A).

Table 9.2 ICH climatic zones and their associated long-term storage conditions.

Summary box 9.1

9.2 Degradation mechanisms

9.2.1 Hydrolysis

Figure 9.1 V-shaped pH–stability profile for hydrolysis of atropine (redrawn from Connors et al. (1986)).

Figure 9.2 Sigmoidal pH-stability profile for hydrolysis of cycloserine in dilute solution (redrawn from Kondrat’eva et al. (1971), with kind permission from Springer+Business Media B.V.).

Figure 9.3 Double bell-shaped pH–stability profile for hydrolysis of aztreonam (redrawn from Connors et al. (1986)).

Figure 9.4 pH profile for the hydrolysis of aspirin, showing V-shaped behaviour at extremes of pH and sigmoidal behaviour in between (redrawn from Connors et al. (1986)).

Study question 9.1

9.2.2 Solvolysis

9.2.3 Oxidation

Figure 9.5 The effect of various antioxidants, chelating agents and antioxidant/chelating agent mixtures on the formation of peroxides in oil of terebinth (redrawn from Fryklöf (1954)).

Study question 9.2

9.2.4 Photolysis

Summary box 9.2

9.3 Reaction kinetics

9.3.1 Solution-phase kinetics

9.3.2 Zero-order reactions

Figure 9.6 Decomposition profile for a drug substance degrading via zero-order kinetics.

Study question 9.3

9.3.3 First-order kinetics

Figure 9.7 Decomposition profile for a drug substance degrading via first-order kinetics and (inset) the linear plot of ln (drug remaining) versus time.

Study question 9.4

9.3.4 Second-order reactions

Figure 9.8 Decomposition profile for a drug substance degrading via second-order kinetics and (inset) the linear plot of 1/drug remaining versus time.

9.3.5 Solid-state kinetics

Study question 9.5

Figure 9.9 Definition of hygroscopicity profiles.

Summary box 9.3

9.4 The temperature dependence of reaction kinetics

Figure 9.10 Energy diagrams for exothermic and endothermic reactions at a given temperature.

Figure 9.11 Maxwell–Boltzmann distribution of energies at two temperatures (T2 > T1). The fraction of molecules (area under the curve) possessing energies above Ea will react upon collision.

Figure 9.12 An Arrhenius plot constructed with rate data determined at 40, 50 and 60 °Cand the extrapolation to room temperature.

Figure 9.13 Increase in temperature required to increase the rate of reaction (relative to the rate at 25 °C) for reactions with activation energies of 50, 75 and 100 kJ mol−1

Table 9.3 Increase in temperature required to raise the reaction rate relative to the rate at 25 °C as a function of activation energy.

Summary box 9.4

9.5 Stress testing

9.5.1 Stress testing in solution

Table 9.4 A scheme to determine the mechanism of degradation. Key: O2 store under oxygen; N2 store under nitrogen; L + store under light; L –store protected from light; T increase temperature (data from Wells (1988)).

9.5.2 Stress testing in the solid-state

Table 9.5 A typical storage and testing protocol for preformulation stress testing (data at the lower temperatures are useful to check the validity of data extrapolation from high temperatures).

Table 9.6 The relative humidities maintained by various saturated salt solutions at 15, 20 and 25 °C (data from Greenspan (1977)).

9.5.3 Drug–excipient compatibility testing

Figure 9.14 Work-flow diagram for performing a drug substance–excipient compatibility screen with DSC.

Study question 9.6

Summary box 9.5

9.6 Summary

References

Answers to study questions

10 Particle Properties

10.1 Introduction

10.2 Microscopy

10.2.1 Light microscopy

10.2.2 Hot-stage microscopy

Study question 10.1

10.2.3 Electron microscopy

10.2.4 Atomic force microscopy

Summary box 10.1

10.3 Particle shape

10.3.1 Habit

Figure 10.1 Effect of preferential growth on different faces of a hexagonal seed crystal.

Figure 10.2 Three of the possible planes (and Miller indices) in a cubic unit cell.

Figure 10.3 Effect of preferential growth on crystal planes on the habit of an orthorhombic crystal.

Summary box 10.2

10.3.2 Particle sizing

Figure 10.4 Definitions of some common particle shapes.

Table 10.1 Surface areas for three geometric shapes of equivalent volume.

Figure 10.5 Some statistical measures of particle size for an irregular particle measured against a standard circle. Key: C, maximum horizontal chord (or intercept); ECD, equivalent circle diameter; F, Feret’s diameter; M, Martin’s diameter.

Summary box 10.3

10.3.3 Particle size distributions

Figure 10.6 Particle size data as a frequency distribution histogram and cumulative percentage by number and weight.

Figure 10.7 Determination of the median diameter of a powdered material from cumulative percentages.

Figure 10.8 Narrow and wide particle size distributions illustrated by cumulative percentage undersize plots.

Figure 10.9 Gaussian (or normal) distribution relative to a typical powder distribution.

Figure 10.10 Determination of geometric mean standard deviation for narrow and wide particle size distributions.

Summary box 10.4

10.4 Summary

References

Answer to study question

11 Powder Properties

11.1 Introduction

11.2 Powder flow and consolidation

Summary box 11.1

11.2.1 Carr’s index

Figure 11.1 An automated jolting volumeter for determination of fluff and tapped density.

Table 11.1 Relationships between Carr’s compressibility index, Hausner ratio and powder flow.

11.2.2 Hausner ratio

11.2.3 Angle of repose

Figure 11.2 Determination of the angle of repose from a powder cone.

Table 11.2 Relationship between angle of repose and powder flow.

Study question 11.1

Study question 11.2

Study question 11.3

Study question 11.4

Figure 11.3 Relationship between Carr’s index and angle of repose and the consequence for powder flowability.

Summary box 11.2

11.2.4 Mohr diagrams

Figure 11.4 Forces acting on an uncompressed powder contained in a cylinder (left) and the forces acting on a plane through the powder (right).

Figure 11.5 A Mohr diagram representing the normal and shear forces for all possible planes through a powder.

11.2.4.1 Mohr diagrams and consolidation

Figure 11.6 Mohr circles (only the positive shear stress values are shown) for an uncompressed powder (C) and three samples after a vertical force has been applied. T1 and T2 are below the yield value while the yield value has been reached at T3.

11.2.4.2 Determination of the yield locus

Figure 11.7 Plots of shear stress as a function of time for two samples undergoing shear testing. The samples are consolidated under the same preload stress, but sheared under different normal loads.

Figure 11.8 Shear stress versus normal stress plot for consolidated samples showing construction of the yield locus.

Summary box 11.3

11.3 Compaction properties

Figure 11.9 Tablet strength as a function of storage time (at 57% RH) for spray-dried lactose (redrawn from Sebhatu et al. (1994) with kind permission from Springer Science+Business Media B.V.).

Study question 11.5

Table 11.3 Interpretation of the compression data suggested by Wells (1988).

Study question 11.6

11.3.1 Compaction simulators

Summary box 11.4

11.4 Summary

References

Answers to study questions

Back Matter

Index

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