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Characterization of the Viscoelastic Behavior of Pharmaceutical Powders A Thesis Submitted to the Faculty of Drexel University by Barbara Jane Robinson in partial fulfillment of the requirements for the degree of Master of Science in Materials Engineering June 2009 ii ACKNOWLEDGEMENTS The author would like to thank her thesis advisor, Dr. Antonios Zavaliangos, for the opportunity to work on this research and the encouragement throughout. The author would also like to thank Johnson & Johnson Pharmaceutical Research and Development for providing their facilities and equipment for this research. Thanks are due to the staff at J&J PRD for their support in this project, especially Dr. Denita Winstead, Dr. John Cunningham, and Mr. Tracey Mascaro. Thanks are due to the faculty, staff, and students in the Department of Materials Science & Engineering, as well. Finally, the author would like to specially thank her parents and family for their continued encouragement, inspiration, and support. iii Table of Contents LIST OF TABLES ...............................................................................................................v LIST OF FIGURES ........................................................................................................... vi ABSRACT ...........................................................................................................................x 1. Introduction ......................................................................................................................1 1.1 Powder Compaction ...........................................................................................1 1.2 Viscoelasticity ....................................................................................................5 1.3 Shear versus Bulk Viscoelasticity ....................................................................11 1.4 Viscoelastic Models .........................................................................................13 2. Literature Review of Viscoelastic Behavior of Pharmaceutical Compacts ...................17 2.1 Radebaugh et al ................................................................................................18 2.2 Hancock et al....................................................................................................23 2.3 Welch et al .......................................................................................................27 2.4 Rippie and Danielson et al ..............................................................................34 3. Motivation ......................................................................................................................41 4. Materials and Methods ...................................................................................................43 4.1 Materials ..........................................................................................................43 4.2 Experimental Method.......................................................................................44 4.2.1 Capabilities of the Compaction Simulator ........................................44 4.2.2 Description of Experiment ................................................................45 4.3 Raw Data ..........................................................................................................48 4.4 Data Processing ................................................................................................53 5. Investigation of Frictional Effect on Energy Dissipation ..............................................55 iv 5.1 Mathematical Calculations of Frictional Energy Loss.....................................55 5.2 Experimental Investigation into Frictional Effect on Energy Dissipation .......57 5.3 Numerical Simulations of Frictional Energy Dissipation ................................62 6. Experimental Results and Discussion ............................................................................65 6.1 In Die Experimentation and Results ................................................................65 6.2 Out of Die Experimentation and Results .........................................................77 7. Conclusions ....................................................................................................................81 8. Future Work ...................................................................................................................83 LIST OF REFERENCES ...................................................................................................84 APPENDIX A: Calculation of Energy Dissipation Caused By Friction .........................87 v LIST OF TABLES 1. Rippie and Danielson’s results from their work in [17] ................................................36 2. Rippie and Danielson’s results from their work in [18] ................................................38 3. Material Information for Selected Materials..................................................................44 4. Starch Compaction Heights and Die Fill Depths for Desired Relative Densities..........46 5. MCC Compaction Heights and Die Fill Depths for Desired Relative Densities ...........47 6. Sequence of Frequencies during DMA on Each Specimen ...........................................48 7. Achieved Amplitude versus Programmed Amplitude for Starch ..................................49 8. Achieved Amplitude versus Programmed Amplitude for MCC....................................50 vi LIST OF FIGURES 1.01. Schematic of the Compaction Cycle ..........................................................................2 1.02. Schematic of a Rotary Tablet Press ...........................................................................4 1.03. Schematic of a Hydraulic Tablet Press (Compaction Simulator) ...............................5 1.04. Visual Representations of (a) Creep, (b) Stress Relaxation, and (c) Hysteresis ........7 1.05. Graphic Representations of Cyclic Stress-Strain Behavior of an Elastic Material (a), a Viscous Material (b), and a Viscoelastic Material (c) .......................................9 1.06. Differences between Young’s Modulus (E), Shear Modulus (G), and Bulk Modulus (K) ..............................................................................................................11 1.07. Graphical Representation of (a) the Kelvin-Voigt Model and (b) its Creep and Recovery Behavior ...................................................................................................14 1.08. Graphical Representation of (a) the Maxwell Model and (b) its Creep Recovery Behavior ....................................................................................................................15 1.09. Graphical Representation of the Four Parameter Model ..........................................16 1.10. Graphical Representation of the Creep and Creep Recovery Behavior of the Four Parameter Model ..............................................................................................16 2.01. Dynamic Mechanical Tester and Experimental Setup Used by Radebaugh et al .....18 2.02. Plot of Storage Modulus versus Frequency for Compacts of Microcrystalline Cellulose, at a Porosity of 0.195, 0.01% strain, and 22°C. Each Point Represents the Average taken over Six Compacts ...................................................20 2.03. Plot of Storage Modulus versus Solid Volume Fraction from results of Radebaugh et al. Each Point Represents the Average taken over Six Compacts. ....21 2.04. Plot of Tan versus Solid Volume Fraction from Results of Radebaugh et al. Each Point Represents the Average taken over Six Compacts .................................21 2.05. Plot of Reciprocal Porosity versus Storage Modulus from Results of Radebaugh et al. Each Point Represents the Average taken over Six Compacts. .......................23 2.06. Experimental set up from Hancock et al. for Dynamic Tension Experiments (a) and Dynamic Three-Point Beam-Bending Experiments (b). ....................................24 vii 2.07. Variation of Storage (diamonds) and Loss (circles) Moduli of MCC with Specimen Porosity (a) and Frequency (b) from Hancock et al by Dynamic Tension Tests ............................................................................................................27 2.08. Variation of Storage (diamonds) and Loss (circles) Moduli of MCC with Specimen Porosity from Hancock et al. by Dynamic Three-Point Beam-Bending Tests ..........................................................................................................................27 2.09. Experimental Setup for the Split Hopkinson Bar Method used by Welch et al .......29 2.10. Variation of Storage (dashed line) and Loss (dotted line) Modulus with Frequency from SHBM of Welch et al. Note that the range of the vertical axis varies among the materials........................................................................................30 2.11. Fitted Parametric Curves for Welch et al. Complex Modulus Data .........................31 2.12. Variation of Experimental (dashed line) and Parametrically Fit (solid line) Dissipation Factor with Frequency from SHBM of Welch et al. ............................32 2.13. Tensile Strength versus Frequency of Maximum Dissipation for the Materials Tested by Welch et al. Error Bars Represent the 1 Standard Deviation Interval for n=3. ........................................................................................................32 4.01. Experimental Setup of Huxley Bertram
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