QUANTITATIVE ANALYSIS OF POLYMORPHIC MIXTURES USING INFRARED SPECTROSCOPY

1. QUANTITATIVE ANALYSIS OF POLYMORPHIC MIXTURES USING INFRARED SPECTROSCOPY • IR Spectroscopy • Calibration • Homogeneous Solid-State Mixtures • Multivariate Calibration Concepts • IR Data Collection • Examples Thomas M. Niemczyk Department of Chemistry University of New Mexico

2. IR SPECTROSCOPY I I0 T = A = - LOG T A = bC 10000 cm-1→ 400 cm-1 4000 → 400 cm-1 Fundamentals 10000 → 4000 cm-1 Overtones, Combinations Sample

4. ADVANTAGES OF APPLYING MULTIVARIATE STATISTICS TO SPECTRAL DATA • Greater Precision (Increased Sensitivity) • Greater Accuracy • Increased Reliability (Outlier Diagnostics) • Quantitative Determination Can be Made in the Presence of Multiple Unknown Interferences • New Range of Problems Can be Addressed

6. QUANTITATIVE ANALYSIS • Design Experiment • Prepare Samples • Collect and Assemble IR Data • Preprocess Data • Mean Center, Baseline • Smoothe, Derivative • Scatter Correct • Frequency Select • Develop Calibration Model • Validate Model • Determine Concentration in Unknowns

7. IMPORTANCE OF STATISTICAL EXPERIMENTAL DESIGNS • Efficient Use of a Limited Number of Samples • Eliminate Spurious Correlations With Orthogonal Designs • Necessary to Avoid Modeling Drift • Can Aid in the Detection of Outliers • Can Assure that Deviations From Linearity are Modeled • Can Yield Realistic Estimates of Future Prediction Ability

8. CALIBRATION DATA • Spectral Calibration Often Limited by Accuracy and Precision of the Reference Methods • Calibration Samples Must Span the Range of Variation Expected in Unknowns • Concentration Range Must be Large Relative to Precision of Reference Method • Avoid Correlation Between Components • Use Statistical Calibration Designs Whenever Possible

9. QUANTITATIVE ANALYSIS • Design Experiment • Prepare Samples • Collect and Assemble IR Data • Preprocess Data • Mean Center, Baseline • Smooth, Derivative • Scatter Correct • Frequency Select • Develop Calibration Model • Validate Model • Determine Concentration in Unknowns

10. MAKING A 1% SAMPLE 1.000 gm 10.0 mgm DIFFICULT TO PRODUCE HOMGENEOUS MIXTURE

11. MAKING A 1% SAMPLE 1.00 gm 10 mgm MIX EQUAL AMOUNTS

12. SECOND ADDITION 0.990 gm 0.020 gm MIX THUROUGHLY

13. CONTINUE ADDING AND MIXING EQUAL AMOUNTS

14. QUANTITATIVE ANALYSIS • Design Experiment • Prepare Samples • Collect and Assemble IR Data • Preprocess Data • Mean Center, Baseline • Smooth, Derivative • Scatter Correct • Frequency Select • Develop Calibration Model • Validate Model • Determine Concentration in Unknowns

15. IR SAMPLING METHODS • KBr Disk Not Appropriate for Polymorphs (?) Poor Quantitative Results • Attenuated Total Reflectance Quick and Easy Quantitative Solids Analysis (?) • Nujol Mull Takes Practice Good Quantitative Results • Diffuse Reflectance (DRIFT) Good Quantitative Results

16. Sample Nujol b (path length) Io I Control Baseline Pathlength KBr Mull

17. DRIFT SAMPLING Sample KBr Ro: KBr, Gold Mirror RD: Sample “A” = - log RD IO RS

18. QUANTITATIVE ANALYSIS • Design Experiment • Prepare Samples • Collect and Assemble IR Data • Preprocess Data • Mean Center, Baseline • Smooth, Derivative • Scatter Correct • Frequency Select • Develop Calibration Model • Validate Model • Determine Concentration in Unknowns

19. MULTIVARIATE CALIBRATION • Focus on Factor Analysis Methods • Partial-Least-Squares (PLS) • Principal Component Regression (PCR) • “Full-Spectrum” Methods • Optimal Number of Factors Determined Empirically • Knowledge of All Spectrally Important Components Not Required • Baseline Variations • Temperature • Unknown Sample Component(s)

20. PLS MODEL A = TB + EA c = Tv + ec Spectral Decomposition Maximizes Covariance Between A and c Unknown Prediction a = tuB + eu cu = tuV

21. Z (0,0,0) Y X

22. Z PC1 (0,0,0) Y X PC2

23. QUANTITATIVE ANALYSIS • Design Experiment • Prepare Samples • Collect and Assemble IR Data • Preprocess Data • Mean Center, Baseline • Smooth, Derivative • Scatter Correct • Frequency Select • Develop Calibration Model • Validate Model • Determine Concentration in Unknowns

24. EVALUATION OF THE CALIBRATION DATA VALIDATION SET CALIBRATION SET

25. 2 1 4 5 6 7 8 3 CROSS VALIDATION EVALUATION OF THE CALIBRATION DATA CALIBRATION DATAPREDICTION SAMPLES • LEAVING OUT HALF THE SAMPLES AT A TIME • LEAVING OUT ONE SAMPLE SAMPLE AT A TIME

26. IMPORTANCE OF CROSS VALIDATION • Needed to Select the Optimal Calibration Model • Determine Prediction Residual Error Sum of Squares (PRESS) • Select Optimal Number of Factors Based on PRESS • Used to Evaluate Precision of the Multivariate Calibration Model • Important for Outlier Detection

27. PLS MODEL A = TB + EA C = TV + ec Spectral Decomposition Maximizes Covariance Between A and c Unknown Prediction a = tuB + eu cu = tuV

29. PSEUDOEPHEDRINE • HCL EPHEDRINE • HCL R. Bergin Acta Cryst., B27, 381 (1971) Mathew & Palenik Acta Cryst., B33, 1016 (1977)

32. SUMMARY OF 0-50% RESULTS

35. SUMMARY OF 0-5% RESULTS

38. REPEAT DETERMINATIONS OF THE 2.67 wt.% SAMPLE

39. 2.0 1.5 F1 F2 ABSORBANCE 1.0 0.5 0.0 4000 3000 2000 1000 -1 FREQUENCY (cm )

45. NIR (~10000 to 4000 cm-1) • Overtone and Combination Bands •  small • Neat samples • Bands Broad and Overlapped • Poor Qualitative Analysis • Good Quantitative Analysis • MVC

46. J. Bernstein, “Polymorphism is Molecular Crystals”, Clarendon Press, 2002 E.W. Ciurczak, Appl. Spec. Rev. 23, 147 (1987)