Negative porosity issue in the Heckel analysis: A possible solution

Abstract

A parameterization of compaction simulator generated dynamic compression profile with a few grams of powder provides important information about the material deformation and compact elasticity. The Heckel equation is by far the most popular choice among pharmaceutical scientists for such parametrization. A general approach of Heckel analysis uses pycnometric powder density (ρ_P0) for relative density calculation. However, as 'in-die' tablet bulk density at applied compression pressure (ρ_BP) becomes greater than or equal to the measured ρ_P0, the general approach typically poses a negative porosity challenge at high compression pressure regions. It is only theoretically possible to have a tablet with zero or negative porosity. Negative porosity may be detected during 'in-die' compression analysis, but it will not exist after ejection of the tablet in practical aspect. Thus, the present work proposes a new approach to using pycnometric tablet density (ρ_PP) in the relative density calculations of Heckel analysis. This ρ_PP may be a better representation of actual tablet particle volume, as it is composed of non-accessible intra-particulate pores, which are broken under applied compression pressure. A new approach showed its immunity for Heckel high-pressure negative porosity. It enables the utilization of the compression and decompression phases of dynamic compression profiles to evaluate macroscopic compaction performance. The proposed approach was validated with a reported modified Heckel approach. The Heckel parameters computed with both methodologies for microcrystalline cellulose and lactose were not statistically different. However, a modified Heckel approach was unable to compute Heckel parameters of poorly compacting starch unlike the new approach. A modified Heckel approach became invalid during starch compaction at low compression pressures (below 400 MPa), where starch was forming weaker but still intact tablets. Certainly, a complete Heckel profiling with a new approach could save time and costs in an early development stage for designing and screening scientifically based lead prototype formulations.

Keywords: Heckel analysis; Modified Heckel equation; Negative porosity; Pycnometric powder density; Pycnometric tablet density; Relative density; True density.