Page 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. NiemczykDepartment of ChemistryUniversity of New Mexico
Page 2
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
Page 3
3500 3000 2500 2000 1500 1000 500
FREQUENCY (cm-1)
-0.1
0.4
0.9
1.4
-LO
G(R
/R 0)
FAFB
Page 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
Page 5
FREQUENCY
AB
SOR
BA
NC
E
Page 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
Page 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
Page 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
Page 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
Page 10
MAKING A 1% SAMPLE
10.0 mgm 1.000 gm
DIFFICULT TO PRODUCE HOMGENEOUS MIXTURE
Page 11
MIX EQUAL AMOUNTS
MAKING A 1% SAMPLE
10 mgm1.00 gm
Page 12
0.990 gm
0.020 gm
SECOND ADDITION
MIX THUROUGHLY
Page 13
CONTINUE ADDING AND MIXING EQUAL AMOUNTS
Page 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
Page 15
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
Page 16
Sample
Nujol
ControlBaselinePathlength
Io I
KBr Mull
b (path length)
Page 17
DRIFT SAMPLINGSample KBr
RD
RS
Ro: KBr, Gold Mirror
RD: Sample
“A” = - log
IO
O
D
RR
Page 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
Page 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)
Page 20
PLS MODEL
A = TB + EA
c = Tv + ec
Spectral Decomposition Maximizes Covariance Between A and c
Unknown Predictiona = tuB + eu
cu = tuV
Page 22
XY
Z
(0,0,0)
PC2
PC1
Page 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
Page 24
EVALUATION OF THE CALIBRATION DATA
CALIBRATION SET VALIDATION SET
Page 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 4 5 6 7 8
Page 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
Page 27
PLS MODEL
A = TB + EA
C = TV + ec
Spectral Decomposition Maximizes Covariance Between A and c
Unknown Predictiona = tuB + eu
cu = tuV
Page 28
NHCH3
HO
H
CH3H
NHCH3
H
HO
CH3H
(1R 2S) ephedrine (1S 2S) pseudoephedrine
Page 29
EPHEDRINE • HCL PSEUDOEPHEDRINE • HCL
R. Bergin Acta Cryst., B27, 381 (1971) Mathew & Palenik Acta Cryst., B33, 1016 (1977)
Page 30
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
Page 31
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
Page 32
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
Page 33
1500 1400 1300 1200 1100 1000
FREQUENCY (cm-1)
INTE
NSI
TY (a
rb. u
nits
)
SPECTRA (base)
SPECTRA (mean centered)
FIRST LOADING VECTOR
Page 34
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%
Page 35
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
Page 36
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%
Page 37
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%)
Page 38
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
Page 39
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
Page 40
1500 1300 1100 900 700 500
FREQUENCY (cm-1)
-0.1
0.3
0.7
1.1
AB
SO
RB
AN
CE
F1F2
Page 41
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
Page 42
3500 3000 2500 2000 1500 1000 500
FREQUENCY (cm-1)
-0.1
0.4
0.9
1.4
-LO
G(R
/R 0)
FAFB
Page 43
1500 1300 1100 900 700 500
FREQUENCY (cm-1)
0.0
0.5
1.0
1.5
-LO
G(R
/R0)
FAFB
Page 44
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
Page 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
Page 46
E.W. Ciurczak, Appl. Spec. Rev. 23, 147 (1987)
J. Bernstein, “Polymorphism is Molecular Crystals”, Clarendon Press, 2002
Page 47
8000 7000 6000 5000 4000
FREQUENCY (cm-1)
0.0
0.2
0.4
0.6
0.8
-LO
G(R
/R0)
EphedrinePseudoephedrine
Page 48
4600 4400 4200 4000FREQUENCY (cm-1)
INTE
NSI
TY (a
rb. u
nits
)
0.1
Spectra (MSC)
Mean Centered
Loading Vector
Page 49
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
Page 50
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
Page 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
Page 52
FREQUENCY
AB
SOR
BA
NC
E
10 1 2 3 4 5
CONCENTRATION
AB
SOR
BA
NC
E
Page 53
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
Page 54
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
Page 55
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