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 T = A = - LOG T A =  bC 10000 cm -1 → 400 cm -1 4000 → 400 cm -1 Fundamentals 10000 → 4000 cm -1 Overtones, Combinations Sample I I0I0

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 10.0 mgm 1.000 gm DIFFICULT TO PRODUCE HOMGENEOUS MIXTURE

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

12. 0.990 gm 0.020 gm SECOND ADDITION 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 Control Baseline Pathlength IoIo I KBrMull b (path length)

17. DRIFT SAMPLING Sample KBr RDRD RSRS R o : KBr, Gold Mirror R D : Sample “A” = - log IOIO

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 + E A c = Tv + e c Spectral Decomposition Maximizes Covariance Between A and c Unknown Prediction a = t u B + e u c u = t u V

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

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 CALIBRATION SET VALIDATION SET

25. CROSS VALIDATION EVALUATION OF THE CALIBRATION DATA CALIBRATION DATA PREDICTION SAMPLES A.LEAVING OUT HALF THE SAMPLES AT A TIME B.LEAVING OUT ONE SAMPLE SAMPLE AT A TIME 1 2 3 456 78

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 + E A C = TV + e c Spectral Decomposition Maximizes Covariance Between A and c Unknown Prediction a = t u B + e u c u = t u V

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

32. SUMMARY OF 0-50% RESULTS Frequency Region (cm -1 ) PretreatmentCVSEP (wt.%) No. PLS Factors 400-4000Baseline0.755 400-4000MSC2.273 400-40001 st Derivative1.463 950-1540Baseline0.743 950-1540MSC2.555 950-15401 st Derivative1.083

35. SUMMARY OF 0-5% RESULTS Frequency Region (cm -1 ) PretreatmentCVSEP (wt.%) No. PLS Factors 400-4000Baseline0.094 400-4000MSC0.116 400-40001 st Derivative0.165 400-40002 nd Derivative0.134 950-1540Baseline0.114 950-1540MSC0.136 950-15401 st Derivative0.113 950-15402 nd Derivative0.123

38. REPEAT DETERMINATIONS OF THE 2.67 wt.% SAMPLE ExperimentStd. Dev (wt.%) No Movement Sample In/Out Sample In/Out – Smooth Sample Cup Repacked 0.02 0.08 0.17 0.12

39. 4000300020001000 FREQUENCY (cm ) 0.0 0.5 1.0 1.5 2.0 ABSORBANCE F1 F2

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

51. CONCLUSIONS Number of Samples Relative to the Concentration Range is Important Complexity of the Spectral Data is a Factor Sample Prep is Critical –Homogeneous Mixtures –Baseline, Abs. Range NIR Useful

52. FREQUENCY ABSORBANCE 1 012345 CONCENTRATION ABSORBANCE

53. 0123 4 5 CONCENTRATION ABSORBANCE A AMAM CACA CMCM FREQUENCY ABSORBANCE MEASURED, A 1 ANALYTE, A A INPURITY, A I A 1 = A A + A I 1

54. Concentration 0 1 5 1.5 0 0.51.52 ABSORBANCE 1 ABSORBANCE 2 FREQUENCY ABSORBANCE 1 2 0.5

55. FREQUENCY ABSORBANCE 1 2 0 0.5 1.0 1.5 0 0.51.01.5 ABSORBANCE 1 ABSORBANCE 2