Table Of ContentGustav KortUm
Reflectance Spectroscopy
Principles, Methods, Applications
Translated from the German by
James E. Lohr, Philadelphia
With 160 Figures
Springer-Verlag New York Inc. 1969
Professor Dr. Gustav Kortum
Institut f1ir Physikalische Chemie der Universitat
74 Tiibingen, WilhelmstraBe 56
lSBN-13: 978-3-642-88073-5 e-lSBN-13: 978-3-642-88071-1
DOT: 10.1007/978-3-642-88071-1
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Title-No. 1605
Preface
Reflectance spectroscopy is the investigation of the spectral composi
tion of surface-reflected radiation with respect to its angularly dependent
intensity and the composition of the incident primary radiation. Two
limiting cases are important: The first concerns regular (specular)
reflection from a smooth surface, and the second diffuse reflection
from an ideal matte surface. All possible variations are found in practice
between these two extremes. For the two extreme cases, two fundamentally
different methods of reflectance spectroscopy are employed:
The first of these consists in evaluating the optical constants n
(refractive index) and x (absorption index) from the measured regular
reflection by means of the Fresnel equations as a function of the wave
length A. This rather old and very troublesome procedure, which is
incapable of very accurate results, has recently been modified by Fahren
fort by replacing the air-sample phase boundary by the phase boundary
between a dielectric of higher refractive index (n1) and the sample (n2).
If the sample absorbs no radiation and the angle of incidence exceeds
a certain definite value, total reflection occurs. On close optical contact
between the two phases, a small amount of energy is transferred into the
less dense phase because of diffraction phenomena at the edges of the
incident beam. The energy flux in the two directions through the phase
boundary caused by this is equal, however, so that 'total reflection takes
place. On the other hand, if the sample absorbs light, a fraction of the
radiation energy transferred is lost, and the total reflection is attenuated.
This phenomenon has proved extremely valuable in the evaluation of
the absorption spectra of liquid and solid materials, especially in the
infrared region ("internal" reflectance spectroscopy). It is described
in Chapter VIII.
The second method, diffuse reflectance from matte surfaces, assumes
that the angular distribution of the reflected radiation is isotropic;
that is, that the density of the reflected radiation (surface brightness)
is directionally independent. This involves the validity of the Lambert
Cosine Law. Two conceptions are possible for the occurence of this
isotropic angular distribution: For particle diameters much greater than
the wavelength, the radiation is partly reflected by means of regular
reflection at elementary mirrors (crystal surfaces) inclined statistically
at all possible angles to the macroscopic surface. It also partly penetrates
into the inside of the sample where it then undergoes numerous reflec
tions, refractions, and diffractions at the irregularly located particles,
finally emerging diffusely from the surface. For particle diameters of
IV Preface
the order of the wavelength, scattering occurs. This scattered radiation
is angularly distributed according to Mie's theory of single scattering
at gases or colloids and is by no means isotropic. For multiple scattering,
there is no theory at present. It can be shown qualitatively, however,
that for a sufficiently large number and a sufficiently thick layer of
closely packed particles, an isotropic scattering distribution can still
be anticipated. This too can be confirmed by measurements made under
suitable conditions.
As no rigorous theory of multiple scattering exists, many authors
have attempted to develop a phenomenological theory of absorption
and scattering of such tightly packed particle layers. To describe radiation
transfer in a simultaneously scattering and absorbing medium, one
divides the radiation field into two or more opposing radiation paths and
describes the change in radiation intensity in an increment ds by means
of two constants, the absorption coefficient and the scattering coefficient.
These constants are regarded as characteristic properties of the layer
per unit thickness and may be determined from measurements of re
flectance and transmittance on such layers. These two-constant theories
lead in general to related formulas, the most general and comprehensive
of which being that of Kubelka and Munk, which will be thoroughly
treated in the course of this book. Under suitable conditions, this theory
is particularly useful for representing experimental results.
The importance of reflectance spectroscopy for quantitative and
qualitative analysis of crystalline powders, pigments, and solid dyes,
as well as for numerous problems concerning molecular structure, adsorp
tion, catalysis at surfaces, Ligand Field Theory, kinetics of reactions
at surfaces or of solid materials, photochemistry, the determination of
optical constants (n and x), etc., has increased enormously in recent
years. Actually, measurements of diffuse reflectance have been carried
out over several decades, but the method was only rarely fully exploited,
and in many cases was employed rather uncritically.
The purpose of the present book is to investigate theoretically and
demonstrate by means of experimental results the capabilities of diffuse
and internal reflectance spectroscopic techniques. The effects of ex
ternal parameters such as particle size, regular parts of reflection, con
centration of absorbing components, moisture content, effect of addi
tional phase boundaries such as covering glasses, etc, on the results
obtained from these techniques will also be demonstrated. The conclusion
must be that reflectance spectroscopy deserves its proper place among
other spectroscopic methods and is capable of solving numerous problems
only difficultly or not at all soluble by other available methods.
TUbingen, August 1968 G. KortUm
Contents
Chapter I. Introduction
Chapter II. Regular and Diffuse Reflection . . . . 5
a) Regular Reflection at Non-Absorbing Media 5
b) Total Reflection ............ 13
c) Regular Reflectance at Strongly Absorbing Media 21
d) Definition and Laws of Diffuse Reflection 25
e) Experimental Investigation of Diffuse Reflection at Non-
Absorbing Materials . . . . . . . . . . . . . 33
f) Diffuse Reflectance at Absorbing Materials 55
g) Dependence of Remission Curves on Particle Size 58
Chapter III. Single and Multiple Scattering . . . . . . 72
a) Rayleigh Scattering ............. 73
b) Theory of Scattering at Large Isotropic Spherical Particles 81
c) Multiple Scattering ................ 94
d) The Radiation-Transfer Equation . . . . . . . . .. 100
Chapter IV. Phenomenological Theories of Absorption and Scattering
of Tightly Packed Particles . . . . . . . . 104
a) The Schuster Equation for Isotropic Scattering ..... 104
b) The Kubelka-Munk Exponential Solution . . . . . 106
c) The Hyperbolic Solution Obtained by Kubelka and Munk . 116
d) Use of Directed Instead of Diffuse Irradiation . . . .. 127
e) Consideration of Regular Reflection at Phase Boundaries. 130
f) Absolute and Relative Measurements . . . . . . . .. 137
g) Consideration of Self-Emission or Luminescence . . .. 150
h) Attempts at a Rigorous Solution of the Radiation-Transfer
Equation . . . . . . . . . . . . . . . . . . . . . . 156
i) Discontinuum Theories ............... 163
Chapter V. Experimental Testing of the "Kubelka-Munk" Theory. 170
a) Optical Geometry of the Measuring Arrangement .... 170
b) The Dilution Method ................ 175
c) Concentration Dependence of the "Kubelka-Munk" Function
F(Roo) . . . . . . . . . 178
d) The Typical Color Curve . . . . . . . . . . . 186
e) Influence of Cover Glasses .......... 189
f) Scattering Coefficients and Absorption Coefficients 191
VI Contents
g) Influence of Scattering Coefficients on the "Typical Color"
Curve" . . . . . . . . . . . . . . . . . . . . .. 210
h) Particle-Size Dependence of the Kubelka-Munk Function. 213
Chapter VI. Experimental Techniques 217
a) Test of the Lambert's Cosine Law 217
b) The Integrating Sphere . . . . . 219
c) Measuring Apparatus ..... 221
d) Measurements with Linearly Polarized Radiation 231
e) The Measurement of Fluorescent Samples 232
f) Influence of Moisture on Reflectance Spectra 234
g) Preparation of Samples for Measurement . . 237
h) Adsorption from the Gas Phase and from Solution 242
i) Measurements in the Infrared 245
k) Discussion of Errors . . . . . . . . . . . . . 250
Chapter VII. Applications ..... . . . . . . . . 253
a) The Spectra of Slightly Soluble Substances, or Substances
that are Altered by Dissolution. . . . . . . . . ... . . 253
b) Spectra of Adsorbed Substances . . . . . . . . . . . . 256
Acid-Base Reactions between Adsorbed Substance and the
Adsorbent . . . . . . . 257
Charge Transfer Complexes . 262
Redox Reactions ..... 265
Reversible Cleavage Reactions 266
Surface Area Determination of Powders 270
Establishment of Equilibria and Orientation at Surfaces 273
Photochemical Reactions . . . 278
c) Kinetic Measurements . . . . . 281
d) Spectra of Crystalline Powders 285
e) Dynamic Reflectance Spectroscopy 288
f) Analytical Photometric Measurements 290
g) Color Measurement and Color Matching 301
Chapter VIII. Reflectance Spectra Obtained by Attenuated Total
Reflection . . . . . . . . . . . . . . . . . 309
a) Determination of the Optical Constants n and x 309
b) Internal Reflection Spectroscopy 313
c) Methods . . . . . . . . . . . . . . . 319
d) Applications ............. 329
Appendix: Tables of the Kubelka-Munk-Function 337
Tables of sinh-l x; cosh-1 x; coth-1 x 350
Subject Index 357
Chapter I. Introduction
The term absorption spectroscopy is used to denote the qualitative
or quantitative measurement of the absorbance of a material as a func
tion of the wavelenght or wavenumber. With quantitative measurements
using a parallel beam of light the so-called "transmittance" of a plane-
parallel layer, /
= -
T(l) (1)
/0
is measured, where / and /0 denote the radiation flux after and before
the transmission of the radiation through the absorbing layer 1. Even a
measurement of this order of simplicity, however, involves certain com
plications. If a continuous beam of light enters into a homogeneous
medium bounded by plane-parallel windows, it is partially reflected at
each phase boundary, while within the medium it is partially absorbed
and partially scattered.
If we are dealing with gases or dilute solutions, the energy loss due
to reflection at the phase boundaries can be eliminated to a large extent
by suitable experimental measures: the radiation is allowed to pass
successively through two identical cells, one of which contains the ab
sorbing solution or gas, and the other the non-absorbing solvent,
or air at the same pressure. The reflection losses are then identical to
within a very small difference due to the different refractive indices
of the dilute solutions and the solvent, or of the two gases. This small
difference usually lies well within the limits of errors of the measuring
methods. For concentrated solutions, pure liquids or transparent solids
(crystals, glasses, foils, etc.) for which the foregoing is not true, the
reflection losses at the phase boundaries can be eliminated by irradiating
the absorbing material in various layer thicknesses 2. The intensity
ratio A/I/o then, 90rresponding to the difference in the layer thick
ness, gives the true transmittance, since the reflection losses for both
measurements are identiCal. In this case, when the reflection losses
have been eliminated, the value of T defined by means of Eq. (1) is called
the "true" or "internal" transmittance.
It is not possible, on the other hand, to eliminate the radiation loss
caused by scattering by the dissolved molecules or by scattering differ-
1 For methods of spectroscopic measurement see KortUm, G.: Kolorimetrie,
Photometrie und Spektrometrie (Colorimetry, photometry and spectrometry),
4th edition. Berlin-Gottingen-Heidelberg: Springer 1962.
2 Schachtschabel, K.: Ann. Physik 81 (4), 929 (1926).
1 KortUm, Reflectance Spectroscopy
2 I. Introduction
ences by different gases, but these errors also lie within the limits of
error of the measuring methods, provided that we are concerned with
genuine moleculary dispersed solutions, and provided that the trans
mittance does not drop below ca. 0.03 %. Very large errors arise, however,
through scattering in colloidal solutions, where radiation losses due to
absorption and scattering cannot be separated because the scattering
depends on the shape, and particularly on the size and concentration of
the collodial particles as well as on the wavelength of the radiation, and
can only be evaluated theoretically in simple cases (see p. 81 ff.).
The difficulties become still greater when attempts are made to obtain
from scattered transmission the absorption spectrum of solid powdered
materials such as pigments, suspensions, substances adsorbed at solid
surfaces, etc. Recently, infrared spectra of adsorbed molecules have
often been obtained directly in this way. Because of the indefinite layer
thickness, however, only qualitative results can be expected from such
experiments. That satisfactory results can be obtained in this way depends
upon the scattering coefficients being relatively low and the particles
being small compared with the wavelength of the radiation used. This
is particularly true in the range of medium and long-wave infrared
radiation By immersing the powder to be investigated in a suitable
3.
non-absorbing liquid of similar refractive index, it is possible to largely
remove the radiation loss due to scattering. This procedure has often
been employed in the infrared using such immersion liquids as paraffm,
perfluorokerosine, Nujol, and others. Apart from the frequently encounter
ed difficulty in finding suitable liquids, the indefinite thickness of the
layer traversed remains a problem, so that this method also only gives
qualitative results. The so-called KBr-method brought some progress.
4
This involves grinding the finely divided powder under investigation
with an excess of solid potassium bromide (or silver chloride) and pressing
the mixture under high pressure into transparent plates whose absorbance
is measured relative to a plate of the same thickness made from the pure
dilution material. The limitation of this procedure for quantitative evalua
tion arises from radiation losses which are not completely removable,
partly due to the difference in refractive index in the sample and dilution
medium, partly to the inadequate distribution of the sample, and partly
also to traces of moisture which are very difficult to remove 5.
3 This is the reason for the well-known ability of infrared radiation to penetrate
through mist and haze.
4 Stimson, M. M., and M. J. O'Donnell: J. Am. Chern. Soc. 74, 1805 (1952).
Schiedt, U., and H. Reinwein: Z. Naturforsch. 7b, 270 (1952); 8b, 66 (1953).
5 See, for example, Lejeune, R., and G. Duyckaerts: Spectrochim. Acta 6, 194
(1954).
I. Introduction 3
The condition that the particle dimensions must be small compared
with the wavelength is no longer true in the short-wave infrared and
especially not in the visible and ultraviolet region. Scattering then ex
ceeds absorption so greatly that it is no longer possible to obtain a
useful transmission spectrum without taking account of scattering. The
question therefore arises whether it is possible from the measured trans
mittance or diffuse reflectance of a simultaneously scattering and ab
sorbing layer, or from one of these measurements alone, to obtain the
absorption spectrum of the material under investigation.
This question is not merely of theoretical interest, but of the greatest
practical importance for the characterizing and standardizing of in
dustrial products of all kinds (pigments, synthetic plastics, textiles,
papers, paints, etc.); that is, for the quantitative physical analysis of
"color". In addition, the solution of this problem could facilitate the
investigation of numerous other problems for which hitherto suitable
methods have been lacking. Examples which may be mentioned are:
the kinetic investigation of reactions between solid materials, color
changes of solid materials under the influence oftemperature and pressure
(thermochromism and piezochromism), the influence of the adsorption
of molecules on solid ,phases on their spectrum, the catalytic influence
of solid surfaces on the reactivity of adsorbed molecules with gases or
with the surface itself, the photochemistry of adsorbed materials, the
quantitative analysis of mixed solid materials, the quantitative analysis
of paper and thin-layer chromatograms, etc.
To separate the effect of scattering from absorption on the spectro
scopic composition of the radiation flux reflected or transmitted by a
scattering and absorbing layer, a number of theories have been developed,
all of which commence with the transmittance and reflectance of mono
chromatic radiation in an infinitesimal layer. The differential equations
used are then integrated over the total thickness of the"layer. This leads
to suitable formulas which may be tested experimentally, provided that
the initial equations are not too complicated, that is, do not contain
so many constants which must later be evaluated from the measurements
as to be impracticable. This means that simplifying assumptions which
can never be exactly fulfilled in practice must be made. This necessarily
limits the applicability of the formulas developed. In the majority of the
theories, only two constants are introduced, the absorption coefficient
and the scattering coefficient, by means of which transmittance and
reflectance of a layer of finite thickness may be expressed. These so-called
two-constant theories lead in general to similar formulas which may
frequently be converted into each other by interrelating the parameters
used. They are intended to provide a solution for the problem mentioned
above: that is, to determine from the reflectance and scattered trans-
1*
4 I. Introduction
mittance of a simultaneously absorbing and scattering layer the ab
sorption spectrum of the substance in question. They prove in practice
to be useable in this way when suitable measuring conditions are main
tained. In particular success has been achieved in obtaining the so-called
"typical color curve" of the material in question from the diffuse reflectance
of an "infinitely thick" layer (semi-infinite medium) which is no longer
transparent. The curve obtained is frequently in agreement with the true
spectrum after a parallel-displacement in the ordinate. By this means,
it is possible not only to obtain the quantitative physical analysis of
pigments, but also to approach the solution of numerous problems
of the kind already referred to above.
