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Structural Interpretation in Composite Systems Using Powder X-ray Diffraction: Applications of Error Propagation to the Pair Distribution Function

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ABSTRACT

Purpose

To develop a method for drawing statistical inferences from differences between multiple experimental pair distribution function (PDF) transforms of powder X-ray diffraction (PXRD) data.

Methods

The appropriate treatment of initial PXRD error estimates using traditional error propagation algorithms was tested using Monte Carlo simulations on amorphous ketoconazole. An amorphous felodipine:polyvinyl pyrrolidone:vinyl acetate (PVPva) physical mixture was prepared to define an error threshold. Co-solidified products of felodipine:PVPva and terfenadine:PVPva were prepared using a melt-quench method and subsequently analyzed using PXRD and PDF. Differential scanning calorimetry (DSC) was used as an additional characterization method.

Results

The appropriate manipulation of initial PXRD error estimates through the PDF transform were confirmed using the Monte Carlo simulations for amorphous ketoconazole. The felodipine:PVPva physical mixture PDF analysis determined ±3σ to be an appropriate error threshold. Using the PDF and error propagation principles, the felodipine:PVPva co-solidified product was determined to be completely miscible, and the terfenadine:PVPva co-solidified product, although having appearances of an amorphous molecular solid dispersion by DSC, was determined to be phase-separated.

Conclusions

Statistically based inferences were successfully drawn from PDF transforms of PXRD patterns obtained from composite systems. The principles applied herein may be universally adapted to many different systems and provide a fundamentally sound basis for drawing structural conclusions from PDF studies.

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Abbreviations

DSC:

differential scanning calorimetry

PDF:

pair distribution function

PVPva:

polyvinyl pyrrolidone:vinyl acetate copolymer

PXRD:

powder X-ray diffraction

G :

pair distribution function

r :

inter-atomic radial distance

ρ :

local number density

ρ 0 :

average number density

Q :

scattering vector magnitude

S :

structure function

σ:

standard error

T g :

glass transition temperature

h0 :

statistical null hypothesis

hA :

statistical alternative hypothesis

R :

sum-of-squares difference agreement factor

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ACKNOWLEDGEMENTS

MM would like to acknowledge a pre-doctoral fellowship from the American Foundation for Pharmaceutical Education.

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Authors and Affiliations

  1. Duquesne University Graduate School of Pharmaceutical Sciences, 600 Forbes Ave., Pittsburgh, Pennsylvania, 15282, USA

    Michael D. Moore, Zhenqi Shi & Peter L. D. Wildfong

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  1. Michael D. Moore
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  2. Zhenqi Shi
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  3. Peter L. D. Wildfong
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Correspondence to Peter L. D. Wildfong.

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Moore, M.D., Shi, Z. & Wildfong, P.L.D. Structural Interpretation in Composite Systems Using Powder X-ray Diffraction: Applications of Error Propagation to the Pair Distribution Function. Pharm Res 27, 2624–2632 (2010). https://doi.org/10.1007/s11095-010-0259-7

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  • DOI: https://doi.org/10.1007/s11095-010-0259-7

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