(38c) Contact Mechanics of Single Particle Compression and Bulk Compression of Single Component and Binary Mixtures of Particles

The compression of pharmaceutical powders into tablets for oral administration is widely used in the industry. During this process, the particles undergo elastic and plastic deformation and also breakage. The resulting extensive areas of true contact between the particles those that are formed during compaction, and that remain after release of the tablets from the die, are critical to the formation of a coherent mass. The current paper described a micromechanical analysis of the confined uni-axial compaction of an assembly of spherical particles used in pharmaceutical tablets. A binary mixture of particles of different hardnesses was used for this study. This is because practical tablet formulations comprise a number of different types of particles and an understanding of the factors affecting their response in a tabletting process is important for optimising the formulation and tabletting conditions.

The particulate materials used were Eudragit® L100-55 (Degussa Rohm, UK) and Eudragit® S100 (Degussa Rohm, UK). Eudragit® refers to a range of synthetic cationic and anionic block copolymers in the form single particles that are synthesised from dimethylaminoethylmethacrylates, methacrylic acid and methacrylic acid esters in varying ratios. They are commonly used as enteric coating materials. The mechanical properties of the individual particles were determined by a micromanipulation technique that had been developed for characterising the mechanical properties of single biological (Zhang et al. 1992) and non-biological particulate materials (Sun and Zhang 2001). The technique is based on diametrical compression between two parallel surfaces. The samples were also compacted in a cylindrical tableting die.

The compression of single Eudragit® L100-55 and S100 particles showed elastoplastic deformation and brittle fracture characteristics. That is, the initial deformation corresponded to Hertzian (elastic) deformation (Johnson 1985) and the Young's moduli were calculated to be 1.6 ± 0.1 and 0.5 ± 0.1 GPa respectively. At nominal compressive strains of 2.9 ± 0.3 and 0.8 ± 0.1 % respectively, the particles deformed plastically with hardness values of 95.1 ± 6.9 and 10.4 ± 0.8 MPa respectively. The particles were also compressed to failure and the nominal fracture stresses were 20.8 ± 1.6 and 1.0 ± 0.1 MPa with corresponding nominal strains of 13.1 ± 0.7 and 5.7 ± 0.5 % respectively; the nominal stress is defined here as (force/cross-sectional area of the particle) and the nominal strain as (total displacement/particle diameter). Thus the Eudragit® L100-55 particles were significantly harder and stronger than Eudragit® S100.

The powders were mixed such that the mass percentage of Eudragit® L100-55 was 0, 25, 50, 75 and 100 %. The nominal stress as a function of the compressive strain data from the die compaction measurements of these mixtures could be accurately represented by the Kawakita equation (Kawakita and Ludde 1971). The micromechanical analysis described by Adams and McKeown (1996) suggested that the value of one of the parameters in the equation, 1/b, is a measure of the mean strength of the particles. It was also shown that an important factor is that the stress required to compact a bed increases with increasing aspect ratio (ratio of initial bed height and the diameter of the die) due to wall friction imposed by the die. They were able to obtain close agreement between the two values of nominal strength by extrapolating the bed data to a zero aspect ratio. The same approach was adopted in the current study. The variation of the extrapolated 1/b values as a function of mass percentage of Eudragit® L100-55 showed a negative deviation from ideal mixing behaviour. This suggests that the Eudragit® S100 particles were preferentially compressed, which is consistent with electron micrographs of the compressed powders and also the hardness and fracture strains of the individual particles. For large compressive strains, beds of Eudragit® L100-55 showed plastic deformation and cracks, whilst Eudragit® S100 fractured to fine debris.

The loading data were compared with a micromechanical analysis of an assembly of Hertzian particles (Adams et al. 1997). In this work, it was assumed that the stress was transmitted by percolating load bearing strings separated by particles that did not carry any load. The key point about this model is that the compression characteristics of the bed will be identical to the single particles provided that the number of contacts remain constant. By assuming an affine deformation, it was then possible to determine the number density of the chains from a knowledge of the Young's modulus of the individual particles. In the current work it was found that the Hertzian deformation characteristics persisted to strains of 32.7 ± 0.7 and 21.0 ± 0.4 % for single component Eudragit® L100-55 and S100 beds. This is considerably greater than the yield and fracture strains of the individual particles. The paper will describe the results of electron micrographic studies that were undertaken in an attempt to understand this behaviour and also the way in which the number density of the strings varied with the composition of the mixtures, which corresponded to typically 0.1-0.5 particle diameters between the strings.

Reference

Adams, M. J. & McKeown, R. (1996) Micromechanical analyses of the pressure-volume relationship for powders under confined uniaxial compression. Powder Technology 88: 155-163.

Adams, M. J., McKeown, R., & Whall, A. (1997) A micromechanical model for the confined uni-axial compression of an assembly of elastically deforming spherical particles. Journal of Physics D-Applied Physics 30: 912-920.

Johnson, K. L. (1985) Contact mechanics Cambridge University Press, Cambridge.

Kawakita, K. & Ludde, K. H. (1971) Some considerations on powder compression equations. Powder Technology 4: 61-68.

Sun, G. & Zhang, Z. (2001) Mechanical properties of melamine-formaldehyde microcapsules. Journal of Microencapsulation 18: 593-602.

Zhang, Z., Ferenczi, M. A., & Thomas, C. R. (1992) A micromanipulation technique with a theoretical cell model for determining mechanical properties of single mammalian cells. Chemical Engineering Science 47: 1347-1354.