Quantitative Infrared Spectroscopy for Understanding of a Condensed Matter

207 Pages·2017·7.427 MB·English

by  Takeshi Hasegawa (auth.)

Takeshi Hasegawa
Quantitative Infrared
Spectroscopy for
Understanding of a
Condensed Matter
Quantitative Infrared Spectroscopy
for Understanding of a Condensed Matter
Takeshi Hasegawa
Quantitative Infrared
Spectroscopy
for Understanding
of a Condensed Matter
123
Takeshi Hasegawa
ICR
KyotoUniversity
Uji, Kyoto
Japan
ISBN978-4-431-56491-1 ISBN978-4-431-56493-5 (eBook)
DOI 10.1007/978-4-431-56493-5
LibraryofCongressControlNumber:2017935560
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Preface
Infrared (IR) spectroscopy strongly attracted the attention of theoretical physicists
from the 1930s until the 1970s, and most of the important fundamentals were
comprehensively organized in terms of molecular vibrations and rotations along
with the rapid progress of quantum mechanics and chemistry. For experimental
chemists, commercial IR spectrometers played a great role in the latter half of the
twentieth century, and theoretical fundamentals were confirmed quantitatively by
usingaspectrometer.Forexample,thetheoreticalpredictionoftheFermiresonance
was experimentally recognized for many organic compounds.
At this early stage of IR spectroscopy, theoretical and experimental chemists
madegreateffortstoestablishfundamentalsforanalyzingIRspectraforchemistry.
Some textbooks were devoted to summarizing IR bands characteristic of chemical
groups in many organic and inorganic compounds in various chemical environ-
ments involving solvents and temperature. Correlations of some IR bands to
hydrogenbonding,molecularconformation,andcrystallinitywerealsostudied,and
IR spectroscopy was thus recognized as one of the most powerful analytical tools
for discussing chemical compounds.
The accurate measurements of IR spectra were boosted by introducing the
Fourier transform infrared (FT-IR) spectrometer, which guarantees both accuracy
and precision in principle for both ordinate and abscissa axes thanks to the
laser-basedinterferometerandstabledigitalelectriccircuits.SinceFT-IRhasgreat
sensitivity, which can be used even for a monolayer analysis, many optical con-
figurations were proposed, represented by the transmission, reflection–absorption
(RA), attenuated total reflection (ATR), external reflection, and specular reflection
techniques,sothatthemolecularorientationinanultrathinfilmwouldbediscussed
by comparing it to the spectrum of a bulky sample. The great sensitivity of this
“surface spectroscopy” is still outstanding in our current age. The power of
molecular orientation analysis is also outstanding since it can be performed no
matter how the crystallinity is in the film.
During the progress of FT-IR applications, another important theoretical
frameworkwasestablishedinelectrodynamicsforsurfacespectroscopy.Sincemost
of the analytical targets of FT-IR are condensed matter, electrodynamics
v
vi Preface
considering electric permittivity plays many crucial roles for revealing the surface
selectionrulesofsurfacespectroscopies.Thetheoreticalexpressions ofthesurface
spectrometryareparticularlyimportantforastrongabsorbingmatterrepresentedby
the carbonyl, nitrile, and perfluoroalkyl groups.
Unfortunately, education of electrodynamics in school is very far from popular
in chemistry, and the aspect of “science of measurements” is not widespread even
among vibrational spectroscopists. As a result, the overall picture of IR spec-
troscopy has long been oriented to quantum chemistry only, and surface spec-
troscopy has been forgotten except for some simple surface selection rules.
In recent years, nonlinear spectroscopic technique represented by the
sum-frequencygenerationhasrapidlybeenrecognizedevenbyanon-spectroscopist
tobeapowerfultechniquefordiscussingadetailofaninterface.Theproblemisthat
such a user blindly relying on nonlinear spectroscopy alone is not aware of the
intrinsic power of linear spectroscopy. The lack of an overall picture of IR spec-
troscopyis oneof thereasons for the problem.
The goal of this book is, therefore, to summarize the overall picture of IR
spectroscopy with respect to quantitative understanding of condensed matter. In
particular, surface spectroscopy based on electrodynamics is described in detail in
Chap. 3, so that a physical logic would not be omitted. In addition, the concept of
convolution and the Kramers–Kronig relations are also described from a funda-
mental concept in Chap. 4. These concepts should not be introduced as formulae,
since they comprise the essence of linear spectroscopy.
For a quantitative study using IR spectroscopy, in recent years multivariate
analysis, i.e., chemometrics, is quite often employed. Therefore, the theoretical
framework of chemometrics is presented in Chap. 5.
In Chap. 6, application studies of IR spectroscopy are presented. In particular,
chemometrics and surface spectroscopy are merged to yield a new spectroscopic
technique of p-polarized multiple-angle incidence resolution spectrometry
(pMAIRS). This technique enables us to discuss the molecular orientation of each
chemical group as well as the polymorph in a very thin film even with a surface
roughness. As a good example to get beyond the analytical limit constrained by
Maxwell equations, pMAIRS is introduced to provide an overall picture of IR
spectroscopy.
Inaddition,quantitativediscussionofIRspectraofperfluoroalkyl(Rf)compounds
isadded.AnRfcompoundhaslongbeenregardedasacompoundsimilartoanormal
hydrocarbon,andtheparticularityofanRfcompoundinvibrationalspectroscopyhas
beenmissed.AspresentedindetailinChap.6,theoverallpictureofIRspectroscopy
worksverypowerfullytodiscussanRfcompound.Moreover,theknowledgefrom
factor group analysis based on quantum chemistry to surface spectroscopy inelec-
trodynamicsisnecessaryforfullydiscussingRfcompounds.
This book is a summary of my IR study with my colleagues, whom I thank
greatlyandappreciatedeeply.Inparticular,thecorepartofChap.3istheresultof
an invaluable contribution of a former student, Dr. Yuki Itoh.
Preface vii
Iwouldbemosthappyifmanyscientistsandengineersinthecominggenerations
re-recognizethegreatintrinsicpowerofIRspectroscopy.SinceFT-IRiswidespread
inlaboratories,itspowerwillhelpverymuchinstudyingmaterialchemistry.What
we need isonly theoverallpicture ofIR spectroscopy.
Kyoto, Japan Takeshi Hasegawa
Contents
1 Infrared Spectroscopy as a Vibrational Spectroscopy . .... ..... .. 1
1.1 Molecular Vibrations.. ..... .... .... .... .... .... ..... .. 1
1.2 Normal Coordinate and Normal Modes. .... .... .... ..... .. 2
1.3 Light Absorption by a Molecule: 1. Understanding
by a Quantum Mechanical Approach... .... .... .... ..... .. 12
1.4 Selection Rule of IR Spectroscopy. .... .... .... .... ..... .. 16
1.5 Another Selection Rule on the Group Theory .... .... ..... .. 20
1.6 Light Absorption by a Molecule: 2. Understanding
on Electrodynamics for a Bulk Matter Toward
Beer’s Law . .... .... ..... .... .... .... .... .... ..... .. 30
References ... .... .... .... ..... .... .... .... .... .... ..... .. 36
2 Fundamentals of FT-IR .... ..... .... .... .... .... .... ..... .. 37
2.1 Principle of Spectral Measurements.... .... .... .... ..... .. 37
2.2 Introducing an Interferometer: FT-IR... .... .... .... ..... .. 39
2.3 Laser and FT Spectrometer .. .... .... .... .... .... ..... .. 42
2.4 Apodization Function.. ..... .... .... .... .... .... ..... .. 45
Reference.... .... .... .... ..... .... .... .... .... .... ..... .. 46
3 Surface Spectroscopy Using FT-IR .... .... .... .... .... ..... .. 47
3.1 Fundamentals of Ordinate Scale of FT-IR Spectra. .... ..... .. 47
3.2 Absorbance Spectra of a Weakly Absorbing Matter.... ..... .. 50
3.3 Boundary Conditions in Electrodynamics.... .... .... ..... .. 51
3.4 A Model-Based Approach to Generate the TO Energy
Loss Function ... .... ..... .... .... .... .... .... ..... .. 56
3.5 Fresnel Equation and Optical Anisotropy.... .... .... ..... .. 60
3.6 Transfer Matrix Method..... .... .... .... .... .... ..... .. 65
3.7 Calculation of Single-Beam Spectra of the Background
and the Sample Measurements.... .... .... .... .... ..... .. 68
ix
x Contents
3.8 TO and LO Energy Loss Functions: Introduction
of the Thin-Film Approximation .. .... .... .... .... ..... .. 71
3.9 Analytical Expression of a Transmission Spectrum .... ..... .. 77
3.10 Preparation for the Analytical Expression of a Reflection
Spectrum ... .... .... ..... .... .... .... .... .... ..... .. 82
3.11 Analytical Expression of an RA Spectrum... .... .... ..... .. 85
3.12 Analytical Expression of an ER Spectrum... .... .... ..... .. 89
3.13 Analytical Expression of an Attenuated Total
Reflection (ATR) Spectrum .. .... .... .... .... .... ..... .. 92
3.14 Specular Reflection Spectrum. .... .... .... .... .... ..... .. 96
3.15 Surface Selection Rules of IR Surface Spectroscopy ... ..... .. 96
3.16 Sampling Techniques.. ..... .... .... .... .... .... ..... .. 110
References ... .... .... .... ..... .... .... .... .... .... ..... .. 113
4 IR Absorption of a Dielectric Matter: Phase Retardation
of the Polarization Density.. ..... .... .... .... .... .... ..... .. 115
4.1 Dielectric Matter and Electric Permittivity... .... .... ..... .. 115
4.2 Electric Susceptibility and Linear Convolution ... .... ..... .. 116
4.3 Electric Susceptibility and Green’s Function . .... .... ..... .. 120
4.4 Complex Electric Permittivity .... .... .... .... .... ..... .. 122
References ... .... .... .... ..... .... .... .... .... .... ..... .. 126
5 Chemometrics for FTIR.... ..... .... .... .... .... .... ..... .. 127
5.1 Beer’s Law and a Single-Constituent System. .... .... ..... .. 127
5.2 Extended Beer’s Law for a Multi-Constituent System:
CLS Regression.. .... ..... .... .... .... .... .... ..... .. 130
5.3 Least Squares Solution of a Regression Equation . .... ..... .. 133
5.4 Intrinsic Limitation of CLS Regression . .... .... .... ..... .. 136
5.5 Inverse Beer’s Law: ILS Regression (or MLR)... .... ..... .. 139
5.6 Principal Component Analysis (PCA) .. .... .... .... ..... .. 142
5.7 Merge of ILS and PCA: PCR .... .... .... .... .... ..... .. 153
5.8 Independent Residual Terms: PLS. .... .... .... .... ..... .. 154
5.9 Efficient Removal of Spectral Noise Using PCA.. .... ..... .. 157
5.10 Alternative Least Squares (ALS) for Spectral Decomposition . .. 159
5.11 Factor Analytical Resolution of Minute Signals (FARMS) ... .. 161
References ... .... .... .... ..... .... .... .... .... .... ..... .. 163
6 Applications: Various Techniques to Make the Best
Use of IR Spectroscopy .... ..... .... .... .... .... .... ..... .. 165
6.1 Specular Reflection and KK Analysis .. .... .... .... ..... .. 165
6.2 IR pMAIRS Technique: Quantitative Molecular Orientation
Analysis in a Thin Film..... .... .... .... .... .... ..... .. 170
6.3 Fluorocarbon-Specific IR Spectroscopy . .... .... .... ..... .. 184
References ... .... .... .... ..... .... .... .... .... .... ..... .. 193
Contents xi
7 Appendix.... .... .... .... ..... .... .... .... .... .... ..... .. 195
7.1 Fundamental Parameters in Electrodynamics . .... .... ..... .. 195
7.2 Continuity of Electric and Magnetic Fields at an Interface.... .. 197
7.3 Factor Group Analysis of PTFE Having the 13 Helix
6
Conformation.... .... ..... .... .... .... .... .... ..... .. 199
References ... .... .... .... ..... .... .... .... .... .... ..... .. 200