Pharmaceutical powders deformation

The equation of Heckel has been discussed again and again. One main issue of critique is that pharmaceutical powders are not purely plastically deforming materials and thus particle size and deformation mechanisms influence the derived parameters [129, 130]. Already very small errors in displacement determination or the measurement of true density can induce huge errors in the derived parameters [75-77, 129, 131, 132], Spnnergaard [126] referred the equation of Walker and Bal shin for his characterization of materials. He criticized further that the yield strength derived from the Heckel equation is directly dependent on the true density of the powders [127]. 

Even with the gaps in the theory, the fundamental concepts developed for continuum systems are substantially the same for systems of pharmaceutical powders. Powders confined and subjected to a compressive stress will rearrange until there is insufficient free volume to allow translation of particles. As the stress increases, particles make contacts which increase in area with stress, they will deform elastically (i.e.. reversibly) with Young s modulus (E) as the linear proportionality constant. The normal strain (eO in the loading direction for a material undergoing elastic deformation under uniaxial tension (cr) may be expressed as (2) ... 

The constant c represents the effect of change in applied pressure on the compact porosity. The authors examined several pharmaceutical powders (Acetaminophen, Emcompress or DCP, lactose, MCC, and com starch) to estimate the value of c and determine if it is a true representation of the compressibility of a given material (Fig. 10) (94). It was found that the parameter, c, provides a good representation of material compressibility for single- and multi-component systems. Thus, the relationship promises to be a useful quantitative descriptor of deformation behavior of pharmaceutical powders (94). 

Rheology is the study of flow and deformation of materials under the influence of external forces. It involves the viscosity characteristics of powders, liquids, and semisolids. Rheological studies are also important in the industrial manufacture and applications of plastic materials, lubricating materials, coatings, inks, adhesives, and food products. Flow properties of pharmaceutical disperse systems can be of particular importance, especially for topical products. Such systems often exhibit rather complex rheological properties, and pharmaceutical scientists have conducted fundamental investigations in this area [58-64],... 

The deformation behavior of many pharmaceutical materials is time-dependent and the nature of this time dependency is often related to the mechanism of compaction for a given material. It is thought that time dependency or speed sensitivity arises from the viscoelastic or viscoplastic characteristics of a material. In contrast, studies have shown that brittle materials are much less speed dependent that ductile materials because yielding and fragmentation are not as dependent on the rate of compression. It is also believed that the particle size and size distribution of the powder or granules have an important role in the speed sensitivity due to the fact that this property affects the predominant mechanism of deformation (6,58-60). 

Hiestand Tableting Indices Likelihood of failure during decompression depends on the ability of the material to relieve elastic stress by plastic deformation without undergoing brittle fracture, and this is time-dependent. Those which relieve stress rapidly are less likely to cap or delaminate. Hiestand and Smith [Powder Technol., 38, 145 (1984)] developed three pharmaceutical tableting indices, which are applicable for gener characterization of powder com-pactiability. The strain index (SI) is a measure of the elastic recovery following plastic deformation, the bonding index (BI) is a measure of plastic deFormation at contacts and bond survival, and the brittle fracture index (BFI) is a measure of compact brittleness. 

The limitations of the Jenike shear cell are that it is not very useful for measuring bulk solids with large shear deformations, e.g., plastic powders. The level of consolidation stresses required are inappropriate for pharmaceutical materials, and the quantity of material required is often beyond that available in the early stages of development. Alternative shear cells that have been used include annular shear cells (Nyquist and Brodin 1982 Irono and Pilpel 1982) and ring shear testers (Schulze 1996). 

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