Terahertz time-domain spectroscopy for powder compact porosity and pore shape measurements: An error analysis of the anisotropic bruggeman model

Moritz Anuschek; Prince Bawuah; J Axel Zeitler

doi:10.1016/j.ijpx.2021.100079

Terahertz time-domain spectroscopy for powder compact porosity and pore shape measurements: An error analysis of the anisotropic bruggeman model

Int J Pharm X. 2021 Apr 27:3:100079. doi: 10.1016/j.ijpx.2021.100079. eCollection 2021 Dec.

Authors

Moritz Anuschek^{1

2}, Prince Bawuah¹, J Axel Zeitler¹

Affiliations

¹ Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, CB3 0AS Cambridge, UK.
² Department of Pharmacy, Pharmaceutical Technology and Biopharmaceutics, Ludwig-Maximilians-University, Butenandtstraße, Munich, Germany.

Abstract

Terahertz time-domain spectroscopy (THz-TDS) is a novel technique which has been applied for pore structure analysis and porosity measurements. For this, mainly the anisotropic Bruggeman (AB-EMA) model is applied to correlate the effective refractive index (n _eff) of a tablet and the porosity as well as to evaluate the pore shape based on the depolarisation factor L. This paper investigates possible error sources of the AB-EMA for THz-TDS based tablet analysis. The effect of absorption and tablet anisotropy - changes of pore shape with porosity and density distribution - have been investigated. The results suggest that high tablet absorption has a negligible effect on the accuracy of the AB-EMA. In regards of tablet anisotropy the accuracy of the porosity determination is not impaired significantly. However, density distribution and variations in the pore shape with porosity resulted in an unreliable extraction of the tablet pore shape. As an extension of the AB-EMA a new concept was introduced to convert the model into bounds for L. This new approach was found useful to investigate tablet pore shape but also the applicability of the AB-EMA for an unknown set of data.

Keywords: ϵ ˜ eff , Effective complex dielectric permittivity; ϵ ˜ s , Complex dielectric permittivity of the solid fract; n ˜ , Complex refractive index; AB-EMA, Anisotropic Bruggemen model; API, Active pharmaceutical ingredient; Anisotropy; Bruggeman model; D, Tablet diameter; Density distribution; H, Tablet thickness; Ibu, Ibuprofen formulation; L, Depolarisation factor; L1, Depolarisation factor at the lowest porosity; Lac, Lactose; Lfit, Estimation of the depolarisation factor based on a fitting model; Ll/u, Lower/upper bound of the depolarisation factor; Lmax/min, Maximal/minimal depolarisation factor in the simulation of a tablet set; M, Tablet mass; MCC, Microcrystalline cellulose; Pharmaceutical tablet; Pore structure; RMSE, Root-mean squared error; THz-TDS, Terahertz time-domain spectroscopy; Terahertz; a1, Gradient of the depolarisation factor as a function of porosity; a2, Y-intercept of the depolarisation factor as a function of porosity; c, Speed of light; f, Porosity; f1, Lowest porosity in a set of tablets; n, Refractive index; neff, 1, Effective refractive index at the lowest porosity; neff, Effective refractive index; neff, l/u, Lower/upper Wiener bound for neff; neff, l/u, Lower/upper margin for ns; ns, Intrinsic refractive index of the solid fraction; ns, c, ns estimated with accounting for absorption; ns, fit, Estimation of the intrinsic refractive index based on a fitting model; p, Polar axis of a spheroid, parallel to the wavevector; q, r, Equatorial axes of a spheroid, perpendicular to the wavevector; tablename Str, Starch; αeff, Effective absorption coefficient; κ, Extinction coefficient; κeff, Effective extinction coefficient.