The 3D Model: Explaining Densification and Deformation Mechanisms by Using 3D Parameter Plots

Abstract

The aim of the study was to analyze very differently deforming materials using 3D parameter plots and consequently to gain deeper insights into the densification and deformation process described with the 3D model in order to define an ideal tableting excipient. The excipients used were dicalcium phosphate dihydrate (DCPD), sodium chloride (NaCl), microcrystalline cellulose (MCC), xylitol, mannitol, α‐lactose monohydrate, maltose, hydroxypropyl methylcellulose (HPMC), sodium carboxymethylcellulose (NaCMC), cellulose acetate (CAC), maize starch, potato starch, pregelatinized starch, and maltodextrine. All of the materials were tableted to graded maximum relative densities (ρ_{rel, max}) using an eccentric tableting machine. The data which resulted, namely force, displacement, and time, were analyzed by the application of 3D modeling. Different particle size fractions of DCPD, CAC, and MCC were analyzed in addition. Brittle deforming materials such as DCPD exhibited a completely different 3D parameter plot, with low time plasticity, d, and low pressure plasticity, e, and a strong decrease in ω values when densification increased, in contrast to the plastically deforming MCC, which had much higher d, e, and ω values. e and ω values changed only slightly when densification increased for MCC. NaCl showed less of a decrease in ω values than DCPD did, and the d and e values were between those of MCC and DCPD. The sugar alcohols, xylitol and mannitol, behaved in a similar fashion to sodium chloride. This is also valid for the crystalline sugars, α‐lactose monohydrate, and maltose. However, the sugars are more brittle than the sugar alcohols. The cellulose derivatives, HPMC, NaCMC, and CAC, are as plastic as MCC, however, their elasticity depends on substitution indicated by lower (more elastic) or higher (less elastic) ω values. The native starches, maize starch and potato starch, are very elastic, and pregelatinized starch and maltodextrine are less elastic and exhibited higher ω values. Deformation behavior as shown in 3D parameter plots depends on particle size for polymers such as CAC and MCC; however, it does not depend on particle size for brittle materials such as DCPD. An ideally deforming tableting excipient should exhibit high e, d, and ω values with a constant ratio of e and ω at increasing densification.

Key Words:

• Tableting
• Compaction
• Excipients
• 3D model
• Particle size
• Compression
• Mathematical modeling

Notes

^aThe equation is given in exact mathematical notation; in previous papers2122 the notation was given as used in MatLab®.

^bIn the previously published paper,21 a calculation error influenced the results and influenced particularly e value tendencies (increasing with ρ_{rel, max} in Ref. 21 and decreasing here). This has been corrected and the correct data are now given in this paper.