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

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

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

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

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

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

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

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

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

0.990 gm gm SECOND ADDITION MIX THUROUGHLY

CONTINUE ADDING AND MIXING EQUAL AMOUNTS

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

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

Sample Nujol Control Baseline Pathlength IoIo I KBrMull b (path length)

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

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

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)

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

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

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

EVALUATION OF THE CALIBRATION DATA CALIBRATION SET VALIDATION SET

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

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

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

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

SUMMARY OF 0-50% RESULTS Frequency Region (cm -1 ) PretreatmentCVSEP (wt.%) No. PLS Factors Baseline MSC st Derivative Baseline MSC st Derivative1.083

SUMMARY OF 0-5% RESULTS Frequency Region (cm -1 ) PretreatmentCVSEP (wt.%) No. PLS Factors Baseline MSC st Derivative nd Derivative Baseline MSC st Derivative nd Derivative0.123

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

FREQUENCY (cm ) ABSORBANCE F1 F2

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

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

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

FREQUENCY ABSORBANCE CONCENTRATION ABSORBANCE

CONCENTRATION ABSORBANCE A AMAM CACA CMCM FREQUENCY ABSORBANCE MEASURED, A 1 ANALYTE, A A INPURITY, A I A 1 = A A + A I 1

Concentration ABSORBANCE 1 ABSORBANCE 2 FREQUENCY ABSORBANCE

FREQUENCY ABSORBANCE ABSORBANCE 1 ABSORBANCE 2