Powder densification. 1. Particle-particle basis for incorporation of viscoelastic material properties.

The present investigation was undertaken to examine the basic unit of densification: the particle-particle indentation. The true interparticle contact area that is established during densification ultimately determines the quality of the tablet compact. By examining the interfacial contact between mutually indenting viscoelastic particles, the process of contact evolution may be represented in mathematical form through extension of the classical Hertzian elastic contact description to encompass material viscoelastic terms. In this way, the time-dependent response of materials to applied loads may be addressed explicitly. The effects of rates of applied loading and maximum load levels were also considered. This analysis was based on viscoelastic stress data collected using an instrumented Instron analyzer during the densification of PMMA/coMMA, a pharmaceutical polymeric coating material. A crossed cylinder matrix compaction geometry was used to simulate the geometry of two mutually indenting spherical particles. Numerical and graphical solutions delineating the relationship between contact area evolution and the prescribed loading force are presented. This particle-particle description of the contacting interface serves as a unit basis for describing the entire powder bed. The powder bed may ultimately be modeled as a collection of these particles in contact.

Powder densification. 2. Viscoelastic material properties in modeling the uniaxial compaction of powders.

A micromechanical model for predicting the densification of particulate matter under hydrostatic loading was developed to account for the time-dependent response of materials to applied loads. Viscoelastic material response used in the analysis was based upon a standard three-parameter rheological model. Compaction data under closed die conditions were collected using an Instron analyzer for different rates of applied load. Densification during the loading phase of PMMA/coMMA powder, a pharmaceutical polymeric coating material, was well predicted by the proposed algorithm, which contrasts with the prediction implied through a static indentation model. Secondary factors which affect compaction such as die-wall friction are also briefly discussed.

A comparison of elastic moduli derived from theory, microindentation, and ultrasonic testing.

PURPOSE: The objective of our work was to evaluate the elastic modulus through ultrasonic testing of poly(methyl methacrylate-co-methacrylic acid) (PMMA/coMAA), a viscoelastic polymer similar to the commercial Eudragit, to calculate this modulus, assuming a regular arrangement of interacting groups, and ultimately, assess the accuracy of microindentation as a means of evaluating elasticity in very small samples. METHODS: Knoop indentation testing was performed on cast samples using a Tukon testing apparatus. Solid density and pulse echo testing employing a damped 15 MHz transducer served to quantify the elastic moduli. Using the Hoy method of calculation for molar attraction constants, and assuming pairwise addition, the modulus was calculated and compared with typical experimental values for amorphous and crystalline polymers. RESULTS: Acoustic testing resulted in an average elastic modulus value of 5.67 +/- 0.2 GPa for this copolymer, which concurs with literature values for PMMA. Acoustically derived experimental moduli when normalized and plotted against calculated values, resulted in a relationship, E/(1 - 2v) = 17.0 (Ecoh + xc delta Hm)/V + 6.9, similar to that predicted in theory. CONCLUSIONS: Indentation contact modeling does not adequately describe the real recovery under indentation. In contrast, acoustic testing of pharmaceutical materials affords a simple, reproducible means of characterizing moduli without impairing structural integrity. Acoustically derived moduli further afford insight into the intermolecular interactions, as expressed by the interaction energy terms.

Deformation kinetics analysis of polymeric matrices.

PURPOSE: We hypothesize that if the kinetics and the mechanisms involved in tablet compression are more fully understood and quantified, the parameters which influence tablet behavior in production may be controlled. The objective of our work was to obtain two deformation kinetic parameters for the predominant barrier to deformation, the activation volume (Vact) and the activation energy (Eact) of poly (methyl methacrylate-co-methacrylic acid) (PMMA/coMAA), a viscoelastic polymer similar to the commercial Eudragit. METHODS: Stress relaxation studies were performed and monitored at varying temperatures on compacts using an instrumented Instron testing apparatus. Solid density, microindentation hardness and contact area testing served to quantify the shear stress rates. RESULTS: The Vact was found to be 64.4 +/- 4 b(3), 63.8 +/- 11 b(3) and 79.1 +/- 8 b(3) for the applied strain rates of 1, 2, and 5 mm/min. The Eact for flow was determined to be 145 +/- 7.7, 235 +/- 8.0, and 506 +/- 2.8 x 10(1) kJ/mole(-1) for the applied strain rates of 1, 2, and 5 mm/min respectively. CONCLUSIONS: The average activation energies are indicative of strain hardening effects. The activation volumes and energies obtained will serve as estimates of these state variables for input into a particle deformation model of time-dependent compaction which is underway.

Hardness anisotropy of acetaminophen crystals.

The anisotropy of acetaminophen hardness was demonstrated using both Vickers and Knoop indentation hardness measurements. Based on a model of Knoop hardness anisotropy proposed by Brookes et al. (1), it was concluded that plastic flow in acetaminophen crystals occurs primarily as a result of slip in the (010)<001> system. This conclusion was corroborated with the results of the Vickers indentation tests. The apparent brittleness of acetaminophen was rationalized because only one slip system appeared to be operative. Under these conditions generalized plastic flow cannot occur, since this requires the operation of at least five independent slip systems (2). The high stress concentrations that result from flow lead to fracture. Therefore acetaminophen is more precisely classified as being semiductile. When a material deforms plastically as a result of slip in only one slip system, considerable crystal realignment can occur during compaction. This in turn can facilitate capping during decompression and ejection, since the cleavage plane, (010), would become aligned with the direction of highest tensile stress.

Deformation kinetics of potassium bromide crystals predict tablet stress relaxation.

A model relating the interparticulate contact stress within a tablet matrix with the compaction stress was developed previously to permit the nonlinear deformation kinetic analysis of the viscoelastic behavior of pharmaceutical tablets with the known properties of the tablet constituents. The present research was undertaken to determine whether the inverse operation (i.e., using tablet stress relaxation to determine single crystal properties) was possible. The stress relaxation of potassium bromide (KBr) compacts was evaluated as a function of temperature and relative density, and an attempt was made to calculate the deformation kinetic parameters. The stress relaxation of KBr did not fit the model under ambient conditions for two reasons: (1) KBr has two slip systems with approximately the same shear stress at room temperature; and (2) KBr strain-hardens. When these complications were taken into consideration, the stress relaxation behavior could be explained. Therefore, whereas single crystal tests are capable of yielding parameters that can be used to predict compact behavior, the inverse process of quantifying fundamental material parameters from compact behavior is problematic due to the difficulty of determining, a priori, all the processes that operate simultaneously.

Predicting the postconsolidation relaxation behavior of sodium chloride tablets.

A model that relates the interparticulate contact stress within a tablet matrix with the compaction stress has been developed. The model permits the application of nonlinear deformation kinetic analysis to quantification of the viscoelastic behavior of tablet constituents. Deformation kinetic analysis assumes that stress relaxation is controlled by thermally activated processes similar in character to those associated with chemical reaction kinetics. The model was tested by measuring the stress relaxation of sodium chloride compacts as a function of temperature and relative density. The experimental activation parameters agree with literature values within experimental errors.

Modeling the uniaxial compaction of pharmaceutical powders using the mechanical properties of single crystals. II: Brittle materials.

A model is presented which uses the hardness and elastic moduli of brittle crystals, determined using the Vickers microindentation test, to predict the uniaxial compaction behavior of compacts. A general approach first developed in the materials science field to predict the densification of particulate matter under hydrostatic loading was followed. Modifications to account for the effects of particle geometry and the closed-die loading conditions were considered. The model predicted the densification behavior of sucrose and adipic acid. It did not predict the densification of acetaminophen as well; however, the discrepancy between the experimental and predicted values may arise either from error associated with the evaluation of the elastic modulus using the microindentation test or from error in calculating the relative density of compacts which were observed to have partially laminated. The effects of error both in the hardness value and in the ratio of punch to die-wall stress on the predictive capability of the model were also discussed briefly.

Modeling the uniaxial compaction of pharmaceutical powders using the mechanical properties of single crystals. I: Ductile materials.

A model is presented which uses the Vickers microindentation hardness of ductile crystals such as sodium chloride to predict the uniaxial compaction behavior of compacts. A general approach first developed in the materials science field to predict the densification of particulate matter under hydrostatic loading was followed. However, modifications to account for the effects of particle geometry and the closed-die loading conditions were considered. Using the standard microindentation hardness value of sodium chloride, the model predicted the densification behavior of this material at a punch displacement rate of 1 mm/min. Densification at higher compaction rates was predicted by considering the effect of deformation kinetics on the hardness. Secondary factors which affect compaction, such as particle size effects and die-wall friction, are also briefly discussed.

Evaluating the deformation kinetics of sucrose crystals using microindentation techniques.

The deformation kinetics of sucrose crystals were evaluated using the Vickers microindentation technique. A (100) face of a crystal of sucrose was indented for varying lengths of time at temperatures ranging from 23 to 103 degrees C, and the deformation kinetics analysis proposed by Verrall et al. (1) was employed to calculate the strain rate and stress from the indentation time and the size of the indentation. Two kinetic parameters, the activation volume and the activation energy, were calculated from the experimental data and compared to those of other materials on normalized scales. The results suggest that the deformation kinetics of sucrose resemble those of ice, the crystal lattice of which is highly hydrogen-bonded, similar to that of sucrose.

Evaluating the fracture toughness of sucrose crystals using microindentation techniques.

The brittleness of pharmaceutical crystals influences their ability to form compacts of acceptable quality. While many macroscopic methods are available to elucidate the fracture behavior of materials, the porosity, inhomogeneity, and anisotropy of pharmaceutical compacts render it difficult to interpret the results of these tests. Microindentation techniques may be used to evaluate both the flow and the fracture characteristics of small crystals, so that it is not necessary to test compacts. The flow and fracture behavior of sucrose, the model substance used in this study, were anisotropic. The fracture surface energy, derived from the average fracture toughness value, is of the same order of magnitude as the surface free energy, indicating that sucrose fractures in a brittle manner.