Mechanical Properties of Single Microparticles and their Compaction Behavior

• School of Chemical Engineering, The University of Birmingham

Pharmaceutical tablets are produced by compacting feed particles consisting of active ingredients and excipients. The tablets should have adequate mechanical strength to withstand the various handling operations in the logistic chain from producer to patient, and the active ingredients should be delivered and released reproducibly to the stomach or intestines in a specified time period. To make sufficiently strong tablets, high-compaction pressures are often required. Initially this involves a rearrangement of the feed particles and then they undergo deformation and possibly breakage. These events can occur sequentially or in parallel. Elastic and plastic deformation and also the rupture of particles during the consolidation of a powder bed contribute to the formation of a coherent mass in a tableting process. The properties of a compact depend strongly on the mechanical characteristics of the individual feed particles and the evolving particle-particle interactions. Hence, it is important to understand the mechanical properties of such feed particles as a basis for predicting the compaction behavior, which is the focus of this short review.

Micromanipulation

The mechanical properties of single particles can be measured by diametric compression between two rigid platens. This method has been applied to relatively large agglomerates (> 500 μm), e.g. prepared from quartz sand and polyvinyl-pyrrolidone as a binder [1], spherical polystyrene colloids binderless granules (~ 2 mm) [2] and soft detergent based agglomerates (1 – 2 mm) [3]. However, the implementation for microparticles in the rangeThe force applied on a particle is measured using a commercial force transducer and the displacement and speed of the probe acting as the upper platen is controlled by a fine micromanipulator. Typical loading data for a single microparticle are shown in Figure 2.

Figure 1. Schematic diagram of the micromanipulation rig [7]

The technique can be applied to both constant velocity loadingunloading and transient measurements. The data can be modelled analytically or by finite element analysis (FEA) to determine the intrinsic material parameters of the test particle. For elastic microspheres, the Hertz or Tatara model has been used to fi t the non-linear loading data corresponding to small or large deformations respectively in order to determine the Young’s modulus [6]. Plastically deforming particles exhibit linear loading data and the hardness, which is related to the uniaxial yield stress, may be calculated from the gradient [9]. Stress relaxation measurements may be used to characterize viscoelastic particles in terms of the instantaneous and equilibrium Young’s moduli, and relaxation times [10, 11]. The linear viscoelastic properties of microspheres have been measured in this way using an extended Hertz model [10]. The non-linear viscoelastic properties of microhydrogel particles have been determined using FEA to model the stress relaxation data [11].

Figure 2. Typical compression force (F) data to rupture as a function of displacement (δ) for a single methacrylic acid - ethyl acrylate copolymer particle (Diameter = 20.0 μm). The compression speed was 2 μm/s [8].

Figure 3. Typical loading data for a spray-dried maltose particle (Diameter = 60.0 μm) showing multiple fracture events.

In order to exemplify the approach, the results of a study involving pharmaceutical excipients [8] will be described in more detail. The excipients were three enteric polymer particles and three different powders in the form of agglomerates. Their diameters ranged from 20 to 90 μm. The enteric polymer particles and the agglomerates had distinct morphologies. The methacrylic acid-ethyl acrylate copolymer particles exhibited a single rupture mode under compression (Figure 2) that involved a single axial crack as observed by video-microscopy. However, the compression of spray-dried maltose particles resulted in fragmentation that was characterized by multiple rupture events (Figure 3). The mechanical properties directly determined from the micromanipulation of these microparticles are summarized in Table 1.

Tableting

The excipient particles discussed in the previous section were compacted in a 6 mm diameter cylindrical tableting die using a universal testing machine at pressures up to 60 MPa [8]. The loading data were analyzed to calculate the parameters of the Heckel [12, 13] and Kawakita [14] models. These parameters were compared with each other, and with the mechanical properties of the individual component particles. The Heckel equation provided a poor fit to the bed compression data. Denny [15] suggested that this was due to the yield stress of particles in the bed being dependent on the bed pressure. However, the reciprocal of the Heckel parameter was found to show some correlation with the yield stress of the single particles but with considerable scatter. The Kawakita equation may be written in the following form:

 where σ is the applied compressive stress, ε is the degree of volume reduction, which is equivalent to the nominal uniaxial strain and the parameters a and b are constants. It has been shown theoretically that 1/b is a measure of the single particle strength [16]. There was a reasonable linear correlation between this parameter and the nominal rupture stress of single particles [9], which was also the case for larger detergent particles [16].

Table 1. Mean Yong’s modulus, hardness, nominal rupture stress and strain at rupture of the particles. The value after ± represents the standard error.

The above data demonstrate that the micromanipulation technique is a powerful tool for determining the mechanical properties of individual microparticles, which can be used to predict their compaction behavior. Recent work of Bashaiwoldu et al. [17] showed that the Kawakita parameter b obtained from compaction of pellets into a tablet is a function of the surface tensile strength of the pellets made from different formulations with different film coating thicknesses. This is another evidence of a relationship between the micromechanics of feed particles and their compressibility.

Compaction of Binary Mixtures

Pharmaceutical tablets usually contain multiple components so that understanding the compaction behavior of mixtures is important. This has been investigated for binary mixtures [18], and the compaction data were related to the individual mechanical properties of the constituents based on a simple micromechanical model. In principle, the approach could be extended to a greater number of components. It has also been found that the Kawakita parameter 1/b for binary mixtures of particles exhibited non-ideal mixing; the value was constant for mixtures of methacrylic acid-methyl methacrylate with the stronger methacrylic acid-ethyl acrylate copolymer particles until the phase volume of the stronger methacrylic acid-ethyl acrylate copolymer particles was greater than 50%, which may correspond to a percolation threshold [18]. Moreover, the compaction of Hertzian methacrylic acid-ethyl acrylate copolymer particles exhibited a Hertzian response during tableting up to nominal strains of ~30%, which corresponds to a value that is much greater than that of the feed particles [18]. Such Hertzian persistence has been observed previously for the compaction of spherical glass ballotini and was interpreted in terms of percolating chains of particles with a defined constant spacing [19]. In the case of the methacrylic acid-ethyl acrylate copolymer particles, it was observed that the spacing decreased with increasing strain that could be the result of their greater deformability leading to more uniform stress transmission at greater pressures.

Summary and Perspectives

A micromanipulation technique has been demonstrated to be effective in characterizing the elastic, plastic, viscoelastic and fracture properties of single microparticles. The Heckel and Kawakita models are able to describe the bulk compression of powders to different extents and the associated model parameters can be related to the mechanical properties of the single particles. The Kawakita equation provides a relatively close fit to compaction data for binary mixtures over a large range of strains and provides an interpretation of the data at the particle length scale that could be extended to multi-component powders. At strains up to ~ 30%, the compaction data for spherical elastic particles may also be described by a Hertzian relationship. The apparent Hertzian persistence can be rationalized by employing a percolating linear force chain model for which the spacing between the chains decreases with increasing strain – tending to homogeneous stress transmission. The micromechanical model provides an insight into the compaction behavior of single and multi-component powders, and this approach may be further exploited to guide the development of novel tablet formulations with desirable performance, particularly those containing active ingredients susceptible to high pressure [20, 21]. Moreover, the mechanical properties of feed particles can have a profound impact on the feasibility of process scale-up, but many commonly used particle types remain largely uncharacterized [22]. Understanding the mechanical properties of feed particles, including active ingredients, in relation to their chemical composition and molecular structure, will become increasingly important in formulating new drug carriers, i.e. there is a considerable potential in understanding the interrelationships between the morphological, chemical, surface and mechanical properties of the feed particles and those of the tablets such as the dispersion and dissolution characteristics and integrity of the active ingredients.

Author Biographies

Zhibing Zhang, Professor of Chemical Engineering, is a leader of Micromanipulation Group in the School of Chemical Engineering, University of Birmingham, UK. He has an international reputation in mechanical characterization of single micro-particles based on micromanipulation and in encapsulation and controlled release of active ingredients for various industrial applications. He has published over 150 refereed academic papers, 6 book chapters and 180 other publications.

Professor Michael Adams joined the School of Chemical Engineering at the University of Birmingham in 2004. His research interests include product engineering, particle technology, the properties and processing of soft solids, materials science, complex fluids, interfacial engineering, tribology and adhesion. He has published over 180 scientific papers and co-edited four books.

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