Nanoadhesion and Micro-scale Interactions of. Pharmaceutical Particles used in Compacting Drug. Tablets

Transcription

1 Nanoadhesion and Micro-scale Interactions of Pharmaceutical Particles used in Compacting Drug Tablets Melissa Merrill Department of Mechanical Engineering The University of Akron, 2010 Akron, OH 44304, USA Advisors: Cetin Cetinkaya, Weiqiang Ding Nanoscale Materials REU Program Department of Mechanical and Aeronautical Engineering Center for Advanced Materials Processing Wallace H. Coulter School of Engineering Clarkson University Potsdam, NY , USA Phone: (315) Version 1.0 August 3,

2 Abstract The most common form of drug delivery in medicine today is the pharmaceutical tablet. The demand for more efficient, consistent, and cost effective tablets is ever increasing, particularly with the recent Process Analytical Technology (PAT) program recommended by the Food and Drug Administration (FDA). This current study targets to link the mechanical properties of tablets on the macro-scale with the mechanical properties of particles and aggregates of particles on the micro-scale and the inter-particle interactions on the nano-scale. To make these connections a study on each scale is conducted with a typical excipient powder, calcium carbonate, in a directly compressible Destab form from Particle Dynamics Inc. On the macro-scale, tablets are compacted using an Instron load frame and cylindrical die, and axial and radial stress and strain data obtained from the compaction experimental setup is used to calculate the average shear modulus, Young s Modulus and Poisson s Ratios of the tablet materials. Then in acoustic contact experiments the time of flight of an acoustic wave through a tablet is used to calculate the average shear modulus, Young s Modulus and Poisson s Ratio. These material properties obtained from the two experiments are found to be in agreement, confirming previous studies. On the micro-scale, aggregates of particles are subjected to micro-scale forces and compacted using an atomic force microscopy (AFM) cantilever and custom nano-manipulation system on an optical microscope, and the applied force and aggregate deformation is tracked. On the nano-scale, acoustic excitation experiments which measure the resonant rocking frequency of an excited particle to calculate the work of adhesion and rolling moment resistance are conducted on individual calcium carbonate particles on a silicon wafer. The possible relationships between the macro, micro and nano length scales examined by this study can be utilized to predict tablet properties from known powder properties, thus facilitating production of pharmaceutical tablets with the desired attributes and functions. 1. Introduction The study of pharmaceutical materials science, a relatively new application of the materials science field, has grown rapidly in the past twenty years [1]. Although pharmaceuticals have been utilized and 2

3 studied for centuries by apothecaries and then pharmacists [2], it has been more recently that engineers and scientists have begun using state of the art equipment and engineering principles to improve the function, accessibility, reproducibility and cost of pharmaceuticals in all forms [1]. The general goal of modern study in the pharmaceutical materials science area of engineering is understanding the connections between properties of pharmaceutical materials at the nano-, micro- and macro-scales and then using such understanding to produce drugs with desired properties and effects [1]. A particularly important aspect of the study of pharmaceutical materials science is the drug tablet. It is the most common, and often most desirable, form of modern drug administration because of its durability, reproducibility, powerful control of active ingredient release and ease of use by patients out of physician care [2,3,4]. An in depth understanding of the mechanical properties of pharmaceutical tablet materials is required for the pivotal roll it can play in increasing the effectiveness of a market facing escalating demands for larger amounts of higher quality products that can be manufactured reliably and withstand the possibly damaging effects of production, packaging and distribution [3]. To assure such an elevated quality standard as consumer demand increases a regulatory program called Process Analytical Technology (PAT) has been recommended by the Food and Drug Administration (FDA). The study and linking of factors that affect tablet compaction and mechanics is thus increasingly imperative. The current study utilizes a popular pharmaceutical excipient powder, calcium carbonate, in three levels of experimentation to examine the adhesive properties of particles on the nano- and micro-scale, the inter-particle interactions on the micro-scale, and compacted tablet properties on the macro-scale aiming to establish connections between the scales. On the macro-scale, tablets are compacted and force and displacement are monitored using an Instron load frame and instrumented cylindrical die. Then mechanical properties of the tablet material are measured using an acoustic contact method. On the micro-scale, aggregates of particles are reconfigured under the force of an atomic force microscopy (AFM) cantilever controlled by a custom nano-manipulation system, and inter-particle interactions are observed with an optical microscope and imbedded camera. On the micro- and nano-scales, single particles are acoustically 3

4 excited by air-coupled and contact transducers and the resonant frequencies of the particles are examined for insight on the irregular particle dynamics and adhesion of calcium carbonate particles. 1.1 Macro-scale In the study of properties of macro-scale drug tablets the methods of C.-Y. Wu, et al. [4] and C.F. Libordi et al. [3] are utilized to extract mechanical properties from stress and strain data measured during uniaxial compaction experiments based on the Drucker-Prager-Cap (DPC) model traditionally used in soil compaction analysis [4]. The model assumes the compacted powder is an effective continuum, allowing the calculation of Young s Modulus and Poisson s Ratio of the material. Critical axial and radial stresses, shown in Figure (1) at points B and D, experienced by the tablet during loading and unloading in the compaction process are used to calculate the shear modulus, G, and the bulk modulus, K, as follows: 4 σ K + G = 3 ε B zz B zz σ ε D zz D zz (1) 2G 3K = B q B p p D (2) where p and q are the two stress invariants 1 p = ( σ zz + 2σ rr ) (3) 3 1 q = σ zz σ rr 3 (4) used in the DPC model [3,4]. σ zz, ε zz, and σ rr are axial stress, axial strain and radial stress respectively as depicted in Figure (2). The shear modulus and bulk modulus can then be used to calculate Young s modulus, E, and Poisson s ratio, v, by 9GK E = 3 K + G (5) 3K 2G v = (6) 2(3K + G) 4

5 [4]. The mechanical properties of compacted tablet materials are then measured by the acoustic contact technique used by C.F. Libordi, et al. [3]. This method measures the time of flight of an acoustic pulse in both the longitudinal ( t L ) and transverse ( t T ) directions, used along with mass density, ρ, to calculate the shear modulus, G, Young s modulus, E, and Poisson s ratio, v, of the tablet material, again assuming the compacted tablet can be considered a continuous volume [3]. Because acoustic contact measurements are nondestructive, confirming its accuracy in determining mechanical properties of tablet materials is valuable for advancements in industrial product monitoring techniques. The velocities of the acoustic pulse through the tablet in the longitudinal (c L ) and transverse (c T ) directions are given by c c L T h = (7) t L h = (8) t T where h is the tablet thickness, and can be used to calculate the Young s modulus and shear modulus of the tablet material as follows: E = 2 ρ (9) c L G = 2 ρ (10) c T [3]. Poisson s ratio can then be calculated with E v = 1 (11) 2 G 1.2 Micro/Nano-scale To study the micro- and nano-scale interactions of irregular pharmaceutical excipient particles the methods used by W. Ding, et al. [5] for measuring rolling moment resistance and adhesion of polystyrene latex particles are applied to the problem of compressing calcium carbonate particles. Because 5

6 pharmaceutical particles are highly irregular in shape, size and texture (Figure 3) the interactions of particles and aggregates of particles during compaction are complex and not yet understood. This technique produces a visual image of the reconfiguration of particle aggregates subjected to an applied load from an AFM cantilever. Force and displacement data are then extracted from the images to quantify the loading effects. 1.3 Nano-scale The acoustic excitation methods of M.D.M Peri and C. Cetinkaya [6,7,8] are used to measure the adhesive properties of single pharmaceutical particles on the nano-scale. Particle adhesion has been subjected to in depth study and many methods have been devised to measure the work of adhesion, but most work has focused on the effect of the axial bond [5,6,7,8]. Acoustic excitation experiments are based on the realization that particle adhesion is determined by the rotational bond, not the stiffer axial bond [5,6,7,8]. In air-coupled excitation and base excitation experiments an acoustic pulse is transmitted to a particle by a focused air-coupled transducer and base excitation of the substrate, respectively, and the frequencies of the particle and the substrate are measured [6,7,8]. Rocking natural frequencies are then found where the particle appears to be resonating separately from the substrate [6,7,8]. The work of adhesion, W a, of a particle is related to the rocking natural frequency, f n, by the following: 1 45W a f n = (12) 3 4ρ 2 2πr where r is the radius of the particle and ρ is the particle density [6,7,8]. Acoustic excitation measurements of rocking frequency and work of adhesion have been effective for ideal, spherical polystyrene latex particles, but as before, the application to the complex adhesion characteristics of irregular particles, such as those found in pharmaceutical powders, has not been explored. 2. Methods and Materials 6

7 All experiments are conducted using the popular pharmaceutical excipient, calcium carbonate, in the Destab 95S Ultra, directly compactable powder form from Particle Dynamics Inc Compaction Experiment The procedure utilized by C.F. Libordi, et al. [3] is used to compact drug tablets made of calcium carbonate powder. The experimental setup pictured in Figure (4) consists of a load frame (Instron 4505), with a 10kN load cell to measure axial force and a linear variable differential transformer to measure axial displacement, and an instrumented die of diameter mm with a static flat-faced lower punch and dynamic flat-faced upper punch (Figure 5) [3]. Radial stress is measured by a radial pressure sensor (PCB X160M01) inserted into the die, with a charge amplifier and custom power supply, and digitizing oscilloscope (Tektronix, TDS 3052) to receive the radial pressure waveform [3]. The die is filled with a height of mm of calcium carbonate powder and is compacted to a tablet thickness between 8.45 mm and 7.92 mm (Figure 6). Axial force and displacement data is collected by the associated Instron load frame software and radial data is collected by the oscilloscope during loading and unloading and then converted to stress and strain under the assumption that the powder bed material can be considered a continuum throughout the compaction process [3]. 2.2 Acoustic Contact Measurements The mechanical properties of the compacted tablets are then measured using the acoustic contact method described by C.F. Libordi, et al. [3] (Figure 7). Ultrasonic coupling gel (Ultragel II, Sonotech Inc.) is applied to two 10 MHz transducers (Panametrics ) and the tablet is pressed between as in Figure (8) [3]. A pulser/receiver unit (Panametrics 5077PR) sends an acoustic pulse to the transmitting transducer that travels through the tablet and is received by the receiving transducer and is sent through the pulser/receiver to the digitizing oscilloscope (Tektronix, TDS 3052) [3]. 2.3 Aggregate Reconfiguration Experiments 7

8 To study the reconfiguration dynamics of aggregates of calcium carbonate particles under a compressive load, particles are deposited onto an epoxy (Pacer Z-Poxy ) coated silicon substrate (wafer, Polishing Corp. of America). The sample is mounted on a piezoelectric bender (Noliac A/S, CMBP 05), connected to a DC power supply (Aglient 6613C, 0-50 V, 0-1 A). The piezoelectric bender and AFM cantilever (Figure 9) (Ti-Pt, MikroMasch NSC 12, 130 µm) are mounted on the custom built nanomanipulator (Figure 10) described in W. Ding, et al. [5] consisting of X, Y and Z motor stages (OptoSigma, Inc., /1155) driven by piezoelectric actuators (New Focus, Inc., MRA 8351). The nanomanipulator system is positioned over an inverted optical microscope with embedded camera (Nikon Epiphot 200) for experimental imaging. Under 50x objective lens magnification the nano-manipulator system is used to bring the tipless edge of the cantilever close to the aggregate on the substrate surface as depicted in Figure 11(a). Then a voltage is applied incrementally to the piezoelectric bender moving the substrate toward the cantilever causing the cantilever to deflect creating a force on the aggregate (Figure 11(b)). Images are taken at each voltage increment and the movement of the substrate and the cantilever is tracked using the changing pixel locations in the images. Force and aggregate deformation can then be calculated and tabulated. 2.4 Air-Coupled Excitation of a Single Particle To measure particle adhesion by air-coupled excitation the procedure described by M.D.M. Peri and C. Cetinkaya is reproduced with the setup depicted in Figure 12 [6]. Calcium carbonate particles are deposited on a silicon substrate (wafer, Polishing Corp. of America) and mounted on a rigid aluminum stub. A 400 khz air-coupled transducer (400 khz, Airmar Technology Corporation) is placed at the focal distance of 5 cm from the sample and receives a pulse from the pulser/receiver unit (Panametrics, model 5077PR) to excite the particle [6]. The laser Doppler vibrometer (Polytek; Vibrometer Controller, OFV 3001; Fiber Interferometer, OFV 551; Ultrasonic Displacement Decoder, OVD 030) integrated into an optical microscope transmits a laser beam through the 100x objective lens which is focused on the top of the particle of interest as depicted in Figure 13(a) [6]. The laser Doppler vibrometer produces a plot of the 8

9 axial motion of the particle in terms of time which is received by the oscilloscope [6]. The same procedure is followed with the laser focused on the substrate near the particle to obtain the axial motion of the substrate (Figure 13(b)) [6]. Signal processing then produces frequency amplitude plots of the axial motion of the particle and substrate. 2.5 Base Excitation of Single Particle To measure particle adhesion by base excitation a procedure very similar to that of air-coupled excitation is used as described by M.D.M. Peri and C. Cetinkaya [7,8]. Instead of excitation by an aircoupled transducer, the silicon substrate with adhered calcium carbonate particles is mounted on a 3.5 MHz transducer (Panametrics V682) with ultrasonic coupling gel (Ultragel II, Sonotech Inc.) and excited with a pulse from the pulser/receiver in the same way (Figure 14(a), (b)) [7,8]. The laser Doppler vibrometer generates a similar axial displacement waveform in the time domain and the experiment is repeated to measure the motion of the silicon substrate. 3. Results 3.1 Compaction Experiments and Acoustic Contact Measurements Seven tablets were compacted in this study and Figures 15 and 16 depict the variation of axial stress with axial strain and the variation of radial stress with time respectively. The critical stress and strain values were taken from these plots and listed in Table 1. From these critical values, bulk modulus, shear modulus, Young s modulus and Poisson s ratio are calculated using Equations 1-6 and listed in Table 2. Acoustic contact measurements were then done on the seven tablets. The time of flight waveform is depicted in Figure 17 with close up images of the arrival times for the longitudinal and transverse waves shown in Figures 18 and 19 respectively. The longitudinal time of flight and an estimated value of the transverse time of flight are read from the waveform and listed in Table 2 along with geometric properties of the tablets. From these critical values and properties the longitudinal and transverse velocity of the 9

10 acoustic pulse in the tablet and shear modulus, Young s modulus and Poisson s ratio are calculated using Equations 7-11 and listed in Table AFM Cantilever Reconfiguration Experiments Three particle aggregates that were reconfigured with the AFM cantilever and nano-manipulation setup are pictured in Figure 20. In each experiment voltage in V increments was applied to the piezo until the maximum voltage of V was reached. Maximum values for substrate displacement, cantilever deflection, aggregate deformation and force on the aggregate are listed in Table 5. The graph of force versus aggregate deformation is depicted in Figure Acoustic Excitation of Single Particles Air-coupled and base excitation experiments were conducted on single calcium carbonate particles and the axial displacement and frequency waveforms were obtained (Figures 22, 23). A predicted rocking resonant frequency is calculated using a value of the work of adhesion, W a, estimated with the Hamaker constant of calcium carbonate, A 0 = 1x10^-20 J. Resonant rocking frequencies were obtained by locating the peaks on the particle frequency waveform that did not have a corresponding peak on the substrate frequency waveform. The observed rocking resonant frequencies were then used to calculate the work of adhesion for each particle using Equation 12 and are reported in Table Discussion 3.1 Compaction Experiments and Acoustic Contact Measurements The compaction experiments and acoustic contact measurements yielded comparable values for the mechanical properties of calcium carbonate tablet materials. The percent difference (Table 7) between the Young s modulus values ranges from 1.72 % to 16.1 % with an average difference of 8.52 % and the Poisson s ratio percent difference ranges from % to % with an average of % confirming the consistency between the two measurement methods discussed by C.F. Libordi et al. [3]. 10

11 The estimated value of the transverse time of flight taken from the acoustic contact measurement waveform is confirmed by back calculation from compaction data. The back calculated values are shown to be within the range predicted by the time of flight waveforms (Table 8). Therefore, although the experimental setup is not ideal for measuring a transverse pulse through a tablet the estimated values for the transverse time of flight are sufficiently accurate for mechanical property extraction. 3.2 AFM Cantilever Reconfiguration Experiments As shown in Figure 21, the force deformation curve shows a generally increasing slope, and is highly rough or irregular with alternating areas of large and small deformation. The roughness can be explained by irregularities on the calcium carbonate particles catching on one another, incurring no deformation as the aggregates are reconfigured, and then releasing suddenly with a large aggregate deformation. When the aggregate reconfiguration force deformation plot is compared to an enlargement of the compaction stress strain curve (Figure 24) it is seen that both graphs exhibit similar irregularity or roughness. Then, after a certain critical stress in achieved the stress strain curve becomes smooth. This is probably when particles are no longer being reconfigured and deformation of individual particles begins. Another interesting feature of the force deformation curve taken from the aggregate reconfiguration experiments is the small segments of negative slope. It is believed that these areas of apparent undeformation are more likely explained by error in tracking the substrate and cantilever movement than actual reconfiguration of the aggregate in such a way that height is increased. The error in measuring pixel location can realistically be 1 to 2 pixels at each point, corresponding to 70 nm to 280 nm overall. All of the observed negative deformation of the aggregates is less than 2 pixels in length so it is probable that such unexpected deformation features can be explained by error. 3.3 Acoustic Excitation of Single Particles The acoustic excitation experiments produced work of adhesion values comparable to the value predicted with the material Hamaker constants suggesting that acoustic excitation could be relatively 11

12 effective in measuring the adhesive properties of irregular calcium carbonate particles on a silicon substrate. Multiple resonant frequencies observed for each particle can be explained by the differing rocking motion of particles in different axial directions. If a particle is highly irregular in shape and surface texture, greater variation of rocking resonant frequencies can be expected. 5. Conclusion The aim of this study to link the macro-scale mechanical properties of pharmaceutical tablets, with the micro/nano-scale inter-particle interactions and nano-scale adhesion of particles was experimentally explored with a series of tests on the common pharmaceutical excipient, calcium carbonate. Calcium carbonate powder was compacted into tablet form with mechanical properties measured both during compaction and with acoustic contact measurements on the compacted tablets and good agreement was confirmed. The micro/nano-scale inter-particle interactions of calcium carbonate aggregates were studied with AFM cantilever aggregate reconfiguration experiments and the adhesive properties of calcium carbonate particles were assessed using acoustic excitation experiments. This experimentation has lead to further insight into the properties of irregular pharmaceutical powders and has generated many more questions to be explored with further research. Acknowledgements I would like to thank my advisors Professor Cetin Cetinkaya, and Professor Weiqiang Ding and all of the students in the Photo Acoustics Research Laboratory and Nanomechanics and Nanomaterials Laboratory particularly Ilgaz Akseli, Andrea Howard, M.D. Murthy Peri, Justin Ricci, and Chris Libordi for their extensive guidance. I would also like to thank Professor Kathleen Issen and Professor John Moosbrugger and Clarkson University for running the Nanoscale Science and Engineering for Materials Systems and Materials Processing REU site, and the National Science Foundation and the Department of Defense for sponsorship. 12

13 References 1. J. Elliot, B. Hancock, Pharmaceutical Materials Science: An Active new Frontier in Materials Research, MRS Bulletin Vol. 31, No. 11, , L.V. Allen Jr., N.G. Popovich, H.C. Ansel, Ansel s Pharmaceutical Dosage Forms and Drug Delivery Systems, Lippincott Williams & Wilkins, C.F. Libordi, I. Akseli, C. Cetinkaya, Non-Destructive Monitoring Techniques: Acoustic Extraction of Young s Modulus and Poisson s Ratio of Drug Tablets, in preparation for Journal of Pharmaceutical Sciences. 4. C.-Y. Wu, O.M. Ruddy, A.C. Bentham, B.C. Hancock, S.M. Best, J.A. Elliot, Modeling the Mechanical Behaviour of Pharmaceutical Powders During Compaction, Powder Technology, 152 (2005) W. Ding, A.J. Howard, M.D.M. Peri, C. Cetinkaya, Rolling Resistance Moment of Microspheres on Surfaces: Characterization of Contact, Submitted for publication in Philosophical Magazine, M.D.M. Peri, C. Cetinkaya, Air-Coupled Excitation of Rocking Motion of Individual Microspheres on surfaces, Applied Physics Letters, 90, (2007). 7. M.D.M. Peri, C. Cetinkaya, Non-contact Microsphere Surface Adhesion Measurement Via Acoustic Base Excitations, Journal of Colloid and Interface Science, 288 (2005) M.D.M. Peri, C. Cetinkaya, Rolling Resistance Moment of Microspheres on Surfaces, Philosophical Magazine, Vol. 85, No. 13, 1 May 2005,

14 Figures B 16 B Axial Stress (MPa) Radial Stress (MPa) D Axial Strain (a) D Time (sec) (b) Fig. 1. (a) Change of axial stress (σ zz ) with axial strain (ε zz ) and (b) the change of radial stress (σ rr ) with time graphs depicting critical stresses at points B and D. Upper Punch σ zz σ rr Tablet Powder Bed z σ zz r Lower Punch Fig. 2. A compacted tablet experiencing axial stress (σ zz ) and radial stress (σ rr ) [3]. 14

15 (a) (b) Fig. 3 (a), (b). Scanning Electron Microscope (SEM) images of calcium carbonate particles exhibiting the irregular shape and texture common among pharmaceutical powders. 15

16 Load Cell Upper Punch Power Supply Powder Bed Die Pressure Sensor Charge Amplifier Load Frame Controller Digitizing Oscilloscope Computer/Signal Processing Load Frame Lower Punch Fig. 4. Tablet compaction experimental setup consisting of a load frame and load cell, instrumented die, radial pressure sensor, and computer control and signal processing equipment [3]. (c) (a) (b) Fig. 5. (a) Cylindrical die with mm diameter, (b) radial pressure sensor and charge amplifier, (c) powder bed filled to height of mm prior to compaction [3]. 16

17 Fig. 6. Calcium carbonate tablets compacted by the compaction experiment procedure in section 2.1. Transmitting Transducer (10MHz) Tablet Acoustic Pulse Pulser/Receiver Unit Digitizing Oscilloscope Receiving Transducer (10MHz) Computer/Signal Processing Fig. 7. Acoustic contact measurement experimental setup [3]. 17

18 Tablet Transmitting Transducer Receiving Transducer Fig. 8. Compacted tablet between transmitting and receiving transducers for acoustic contact measurements. 130 µm cantilever, Force constant = 4.5 N/m Fig. 9. Cantilever used in aggregate reconfiguration experiments 18

19 (a) Substrate, particles (b) Piezoelectric bender Objective lens Cantilevers Fig. 10. (a) Nano-manipulator system used in agglomerate reconfiguration experiments, (b) close up of experimental setup. 19

20 Substrate Displacement Cantilever Particles Cantilever Deflection Epoxy Substrate (a) Piezoelectric Bender (b) Substrate Motion Fig. 11. Diagram of aggregate reconfiguration (a) before subtrate moves and force is applied to aggregate and (b) after force is applied and aggregate begins to reconfigure. 20

21 Transducer Objective Lens Laser spot Substrate Fig. 12. Set up of air-coupled acoustic excitation of a single calcium carbonate particle used to measure adhesive properties. 21

22 Laser focused on calcium carbonate particle 5 µm Fig. 13(a). Laser focused on silicon substrate 5 µm Fig. 13(b). Substrate Transducer Objective lens Laser Spot (a) (b) Fig. 14(a), (b). Experimental set up of base excitation of a single calcium carbonate particle for measuring adhesion. 22

23 Axial Stress (MPa) Axial Strain Fig. 15. Change in axial stress with axial strain during compaction of seven tablets. 23

24 Radial Stress (MPa) Time (sec) Fig. 16. Change in radial stress with time during compaction of seven tablets Amplitude(mV) t (µsec) Fig. 17. Time of flight waveform from acoustic contact measurements of seven tablets. 24

25 Amplitude(mV) t (µsec) Fig. 18. Close up of arrival time of longitudinal time of flight (6.7 µsec -7.6 µsec) Amplitude(mV) t (µsec) Fig. 19. Close up of arrival time of transverse time of flight (10.5 µsec 11.6 µsec) 25

26 70 µm (a) 100 µm (b) 26

27 35 µm (c) Fig. 20. (a) aggregate 1, (b) aggregate 2, (c) aggregate 3. Force (un) Aggregate Aggregate 2 Aggregate Normalized Deformation (aggregate def. / initial height) Fig. 21. Graph of the variation in force on the aggregate as the particle deformation changes for three aggregate samples. 27

28 (a) 28

29 (b) (c) 29

30 (d) 30

31 (e) Fig. 22 (a), (b), (c), (d), (e). Axial displacement and frequency waveforms for five air coupled acoustic excitations experiments in order from 1 to 5. (a) 31

32 (b) 32

33 (c) Fig. 23 (a), (b), (c). Displacement and frequency waveforms for three acoustic base excitation experiments in order from 1 to 5. 33

34 Tables Tablet # σ B zz (MPa) σ D zz (MPa) B ε zz D ε zz σ B rr (MPa) σ D rr (MPa) Table 1. Critical values of stress and strain from compaction experiments. Tablet # K (MPa) G (MPa) E (GPa) v Table 2. Calculated values of bulk modulus, K, shear modulus, G, Young s modulus, E, and Poisson s ratio, v. Tablet # h (mm) d (mm) m (mg) ρ (kg/m^3) t L (µs) t T (µs) Table 3. Tablet properties (height h, diameter d, mass m, density ρ) and time of flight values for acoustic contact experiments. 34

35 Tablet # c L (m/s) c T (m/s) G (MPa) E (GPa) v Table 4. Calculated acoustic and mechanical values of seven tablets from acoustic contact tests. Maximum Cantilever Deformation (µm) Substrate Displacement (µm) Aggregate Deformation (µm) Force (µn) Table 5. Maximum values of cantilever deformation, substrate displacement, aggregate deformation, and force on the aggregate for the three aggregates tested. 35

36 Predicted W a (mj/m 2 ) ρ range (kg/m 3 ) Air Coupled Excitation Particle # d(µm) Expected f n (khz) Observed f n (khz) Experimental W a (mj/m 2 ) Base Excitation Particle # d(µm) Expected f n (khz) Observed f n (khz) Experimental W a (mj/m 2 ) Table 6. Expected and observed values of the work of adhesion and rocking resonant frequencies for five particles measured with the air-coupled excitation experiments and 3 particles measured with the base excitation experiments. Tablet # G (%) E (%) v (%) Table 7. The percent difference between mechanical property values calculated by compaction experiment method and acoustic contact measurement method

37 Tablet # t T (µs) Expected Range (µs) Table 8. Back calculation of the transverse time of flight from the compaction data shown to be in the expected range predicted from the graph. 37