QUANTITATIVE ANALYSIS OF POLYMORPHIC MIXTURES USING

INFRARED SPECTROSCOPY

• IR Spectroscopy• Calibration

– Homogeneous Solid-State Mixtures– Multivariate Calibration Concepts– IR Data Collection

• Examples

Thomas M. NiemczykDepartment of ChemistryUniversity of New Mexico

IR SPECTROSCOPY

T = A = - LOG T

A = bC10000 cm-1 → 400 cm-1

4000 → 400 cm-1 Fundamentals10000 → 4000 cm-1 Overtones,

Combinations

OII

Sample

I I0

3500 3000 2500 2000 1500 1000 500

FREQUENCY (cm-1)

-0.1

0.4

0.9

1.4

-LO

G(R

/R 0)

FAFB

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

FREQUENCY

AB

SOR

BA

NC

E

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 1.000 gm

DIFFICULT TO PRODUCE HOMGENEOUS MIXTURE

MIX EQUAL AMOUNTS

MAKING A 1% SAMPLE

10 mgm1.00 gm

0.990 gm

0.020 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 ReflectanceQuick and EasyQuantitative Solids Analysis (?)

• Nujol MullTakes PracticeGood Quantitative Results

• Diffuse Reflectance (DRIFT)Good Quantitative Results

Sample

Nujol

ControlBaselinePathlength

Io I

KBr Mull

b (path length)

DRIFT SAMPLINGSample KBr

RD

RS

Ro: KBr, Gold Mirror

RD: Sample

“A” = - log

IO

O

D

RR

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 + EA

c = Tv + ec

Spectral Decomposition Maximizes Covariance Between A and c

Unknown Predictiona = tuB + eu

cu = tuV

X Y

Z

(0,0,0)

XY

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

1 2

3 4 5 6 7 8

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 + EA

C = TV + ec

Spectral Decomposition Maximizes Covariance Between A and c

Unknown Predictiona = tuB + eu

cu = tuV

NHCH3

HO

H

CH3H

NHCH3

H

HO

CH3H

(1R 2S) ephedrine (1S 2S) pseudoephedrine

EPHEDRINE • HCL PSEUDOEPHEDRINE • HCL

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

4000 3000 2000 1000

FREQUENCY (cm-1)

0.0

0.2

0.4

0.6

0.8

1.0

-LO

G(R

/R0)

EphedrinePseudoephedrine OH---Cl 2.16 A 3273 cm-1

OH---Cl 2.38 A 3330 cm-1

3500 3000 2500 2000 1500 1000 500

FREQUENCY (cm-1)

0.8

1.0

1.2

1.4

1.6

1.8

-LO

G(R

/R0)

E0E25E50

SUMMARY OF 0-50% RESULTS

Frequency Region(cm-1)

Pretreatment CVSEP(wt.%)

No. PLSFactors

400-4000 Baseline 0.75 5

400-4000 MSC 2.27 3

400-4000 1st Derivative 1.46 3

950-1540 Baseline 0.74 3

950-1540 MSC 2.55 5

950-1540 1st Derivative 1.08 3

1500 1400 1300 1200 1100 1000

FREQUENCY (cm-1)

INTE

NSI

TY (a

rb. u

nits

)

SPECTRA (base)

SPECTRA (mean centered)

FIRST LOADING VECTOR

0 10 20 30 40 50

REFERENCE CONCENTRATION (wt%)

0

10

20

30

40

50

PRED

ICTE

D C

ON

CEN

TRAT

ION

(wt%

) CVSEP = 0.74 wt%

SUMMARY OF 0-5% RESULTSFrequency

Region(cm-1)

Pretreatment CVSEP(wt.%)

No. PLSFactors

400-4000 Baseline 0.09 4

400-4000 MSC 0.11 6

400-4000 1st Derivative 0.16 5

400-4000 2nd Derivative 0.13 4

950-1540 Baseline 0.11 4

950-1540 MSC 0.13 6

950-1540 1st Derivative 0.11 3

950-1540 2nd Derivative 0.12 3

0 1 2 3 4 5

REFERENCE CONCENTRATION (wt%)

0

1

2

3

4

5PR

EDIC

TED

CO

NC

ENTR

ATIO

N (w

t%)

20 SAMPLES

950-1540 CM-1

BASELINE

CVSEP = 0.11 wt%

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

10 15 20 25 30 35 40 45 50 55 60

NUMBER OF SAMPLES IN CALIBRATION

AVER

AGE

CVS

EP (w

t%)

REPEAT DETERMINATIONS OF THE 2.67 wt.% SAMPLE

Experiment Std. Dev (wt.%)

No Movement

Sample In/Out

Sample In/Out – Smooth

Sample Cup Repacked

0.02

0.08

0.17

0.12

4000 3000 2000 1000

FREQUENCY (cm -1)

0.0

0.5

1.0

1.5

2.0A

BS

OR

BA

NC

E

F1F2

CC

C

O

C

H H

CH2

N

CH3

CH3 CH2S

CH2

CH2 NH

C

CH NO2

NCH3

H

Ranitidine

1500 1300 1100 900 700 500

FREQUENCY (cm-1)

-0.1

0.3

0.7

1.1

AB

SO

RB

AN

CE

F1F2

0 1 2 3 4

REFERENCE CONCENTRATION (wt%)

0

1

2

3

4

PRED

ICTE

D C

ON

CEN

TRAT

ION

(wt%

) CVSEP = 0.09 wt%

1292-400 cm-1

MSC

3500 3000 2500 2000 1500 1000 500

FREQUENCY (cm-1)

-0.1

0.4

0.9

1.4

-LO

G(R

/R 0)

FAFB

1500 1300 1100 900 700 500

FREQUENCY (cm-1)

0.0

0.5

1.0

1.5

-LO

G(R

/R0)

FAFB

0 1 2 3 4

REFERENCE CONCENTRATION (wt%)

0

1

2

3

4

PRED

ICTE

D C

ON

CEN

TRA

TIO

N (w

t%)

CVSEP = 0.33 wt%

983 - 1262 cm-1

1st Der. Preprocess

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

8000 7000 6000 5000 4000

FREQUENCY (cm-1)

0.0

0.2

0.4

0.6

0.8

-LO

G(R

/R0)

EphedrinePseudoephedrine

4600 4400 4200 4000FREQUENCY (cm-1)

INTE

NSI

TY (a

rb. u

nits

)

0.1

Spectra (MSC)

Mean Centered

Loading Vector

0 10 20 30 40 50

REFERENCE CONCENTRATION (wt%)

0

10

20

30

40

50PR

EDIC

TED

CO

NC

ENTR

ATI

ON

(wt%

) CVSEP = 3.27 wt%MSC Preprocess

3940 - 4742 cm-1

0 1 2 3 4 5

REFERENCE CONCENTRATION (wt%)

0

1

2

3

4

5PR

EDIC

TED

CO

NC

ENTR

ATIO

N (w

t%)

CVSEP = 0.26 wt%

1st Derivative Preprocess

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

AB

SOR

BA

NC

E

10 1 2 3 4 5

CONCENTRATION

AB

SOR

BA

NC

E

0 1 2 3 4 5

CONCENTRATION

AB

SOR

BA

NC

E

AA

AM

CA CM

FREQUENCY

AB

SOR

BA

NC

E

MEASURED, A1

ANALYTE, AA

INPURITY, AI

A1 = AA + AI

1

Conce

ntrati

on

0

1

5

1.5

0 0.5 1.5 2

ABSORBANCE 1

AB

SO

RB

AN

CE

2

FREQUENCY

AB

SO

RB

AN

CE

1 2

0.5

FREQUENCY

AB

SO

RB

AN

CE

1 2

0

0.5

1.0

1.5

0 0.5 1.0 1.5

ABSORBANCE 1

AB

SO

RB

AN

CE

2