Research paper On the physical interpretation of the initial bending of a Shapiro–Konopicky–Heckel compression profile Ingvild Klevan a, * , Josefina Nordström b, * , Annette Bauer-Brandl a , Göran Alderborn b a Institute of Pharmacy, University of Tromsø, Tromsø, Norway b Department of Pharmacy, Uppsala University, Uppsala, Sweden article info Article history: Received 30 May 2008 Accepted in revised form 30 September 2008 Available online 7 October 2008 Keywords: Powder compression Heckel Shapiro Fragmentation Powder compression classification system Powder technology abstract The relationship between the natural logarithm of the tablet porosity and the applied pressure is used to describe the compression behavior of a powder. Such a relationship, here referred to as a Shapiro–Konop- icky–Heckel (SKH) profile, is usually divided into three regions, of which the first often is non-linear. The objective of this work was to address the question of the mechanisms controlling the compression and the bending of the first region of a SKH profile for dense particles. In this paper, the first region was described by the Shapiro General Compression Equation, from which a compression parameter was derived as a measure of the bending. The results indicate that for powders undergoing significant particle rearrangement at low applied pressures, the particle rearrangement is the major cause for the initial bending of the SKH profile. For powders showing limited particle rearrangement, the initial bending is mainly caused by the change in particle diameter due to particle fragmentation. It is concluded that the evaluation of the first region of a SKH profile in terms of bending may be used to assess particle frag- mentation. The SKH profile could hence be a useful tool to describe powder compression behavior in terms of particle fragmentation and particle deformation from one single compression analysis. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction The use of the natural logarithm of the tablet porosity or tablet relative density as a function of the applied pressure has evolved as a common means to describe the compression of a powder in dif- ferent fields of powder technology. Shapiro [1] and Konopicky [2] published powder compression data using this approach, but in the pharmaceutical field the type of profile is most commonly re- ferred to as the Heckel equation [3], and the natural logarithm of the inverted tablet porosity is sometimes denoted the Heckel num- ber [4]. In this paper, this relationship is hereafter referred to as the SKH (Shapiro–Konopicky–Heckel) profile. A common approach of interpreting a SKH profile is that the profile can be divided into three regions [5,6]. Firstly, an initial non-linear part with a falling derivative (i.e. a concave compression profile, here denoted region I), followed by a linear part in which the data obey the expression (region II) and finally, a second non-linear part with an increasing derivative (i.e. a convex compression profile, here denoted region III). The physical explanation for these three regions of the profile is normally provided in terms of rate controlling compression mechanisms that vary between the different regions. For region II, it is argued that particle deformation is the con- trolling mechanism, either reversible or permanent [7], and for re- gion III it is proposed that elastic deformation of the whole tablet controls the compression process [5]. For region I finally, Denny [8] has summarized the proposed explanations for the deviation of linearity often observed for different types of particulate solids. Excluding one of the explanations concerning the problem of con- structing a SKH profile for porous, secondary particles (i.e. agglom- erates) [9–11], two main reasons are discussed in the literature. The first, proposed by Shapiro and Heckel, is that the curvature is due to particle rearrangement (powder flow) during compression. This explanation seems to be preferred in the literature for a spec- trum of materials exhibiting ductile to brittle behavior [5,7]. The other explanation is that particles fragment during compression and that this fragmentation causes a gradual change in the deriva- tive of the curve until fragmentation ceases to occur. This explana- tion was suggested by Duberg and Nyström [12] and it has also been used in the modeling of a Heckel profile of a fragmenting (brittle) particulate solid [13]. The conception that fragmentation and deformation are the two processes controlling the compression in region I and II, respec- tively, is interesting since it offers the opportunity to derive indica- tors of both the fragmentation propensity and the deformation propensity of particles in a single compression test. The Shapiro 0939-6411/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ejpb.2008.09.014 * Corresponding authors. Institute of Pharmacy, University of Tromsø, N-9037 Tromsø, Norway. Tel.: +46 (0) 18 4714372 (I. Klevan); Department of Pharmacy, Uppsala University, Box 580, SE-751 23 Uppsala, Sweden. Tel.: +46 (0) 18 4714550 (J. Nordström). E-mail addresses: ingvild.klevan@farmasi.uit.no (I. Klevan), josefina.nord- strom@farmaci.uu.se (J. Nordström). European Journal of Pharmaceutics and Biopharmaceutics 71 (2009) 395–401 Contents lists available at ScienceDirect European Journal of Pharmaceutics and Biopharmaceutics journal homepage: www.elsevier.com/locate/ejpb