Anal. Chem. 1988, 6 0 , 1221-1224
venhurst, Ontarlo. June 1987, Paper 1-4; Anal. Chem., In press. (36) Kolthoff, I . M.; Sandell, E. B.; Meehan. E. J.; Bruckensteln, S. Quantitatlve Chemiccrl A n a N k , 4th 4.;Macmlllan: London 1969: p 864. (37) Douglas, D. J.; French, J. B. Spectrochim. Acta, Part 8 1986, 4 7 8 ,
1221
(43) Zhu, G.; Browner, R. F. Appl. Spectrosc. 1987, 4 7 , 349-359. (44) Huang, L.-Q.; Jlang, S.J.; Houk, R. S. Anal. Chem. 1987, 5 9 , 2316-2320.
.-. --..
IP’I-~A
(38) Fulford, J. E.; Douglas, D. J. APPl. SPeChOSc. 1988, 4 0 , 971-974. (39) Houk, I?.S.; Schoer. J. K.;Craln, J. S. J . Anal. At. Spectrom. 1987, 2 , 283-288. (40) Ollvares, J. A.; Houk. R. S. A m / . Spectrosc. 1985, 3 9 , 1070-1077. (41) Ollvares, J. A.; Houk. R. S. Anal. Chem. 1985, 57, 2674-2679. (42) Gray, A. L.; Houk, R. S.; Wllllams, J. 0. J . Anal. At. Spectrom. 1987, 2, 13-20.
R E C E ~ Jfor J review December 8, 1987, Accepted February 9,1988. Ames Laboratory is operated for the U.S.Department of Energy by Iowa State University under Contract No. W-7405-Eng-82* This research was supported by the Director for Energy Research, Office of Basic Energy Sciences.
Quantitative Determination of Organic Compounds by Diffuse Reflectance Fourier Transform Infrared Spectrometry Dietmar Reinecke’ and Anton Jansen Fachhochschule Miinster, Fachbereich Chemie-Ingenieurwesen, 4430 Steinfurt, Federal Republic of Germany Friedrich Fister* and Ulrich Schernau
BASF Lacke
+ Farben AG, 4400 Miinster, Federal Republic of Germany
Dlffuse reflectance Fourler transform Infrared spectrometry can successfully be used for the quantltatlve determlnatlon of small amounts of organlc compounds, e.g. fractions from llquld chromatography. The relatlon between sample concentratlon and reflectance Is-at a flrst approxlmatlondescrlbed by The Kubelka-Munk equatlon. For a correct appllcatlon of the Kubelka-Munk equatlon, the absolute reflectance of the matrlx materlal used as reference also has to be known. A method is descrlbed that petmtts an accurate calculation of the absolute reflectance of the matrlx materlal from experlmental values obtalned wHh conventlonal FTI R equlpment. The procedure Is demonstrated for KBr powder as matrbc materlal and dloctyl phthalate as analyte. ualng the exact value for the absolute reflectance of KBr powder ylelds excellent h e a r correlatlons between the Kubelka-Munk functlon and the sample concentratlon even at low concentratlons.
Applications of diffuse reflectance measurements by infrared Fourier transform spectrometry for the determination of small amounts of organic compounds, including fractions from liquid chromatography,have already been reported some time ago (1,2). To this end the dissolved sample is deposited onto a powdered substrate, e.g. KBr powder, which is also used as reference material. The relation between sample concentration and reflectance is given by the Kubelka-Munk equation. For a correct application of this equation the absolute reflectance of the reference material is needed. For most reference materials these values are not known exactly for the infrared region. Thus, in a first approximation, the reflectance value of the reference material is set to unity. Application of the Kubelka-Munk equation in this way, nevertheless, yields a linear relation between sample concentration and the Kubelka-Munk function for moderate and higher sample Present address: Hewlett-Packard G m b H , 7517 Waldbronn,
FRG. 0003-2700/88/0360-1221$01.50/0
concentrations, while there is a distinct deviation from linearity for lower sample concentrations. In this paper we want to demonstrate, using KBr powder as an example, a way for the determination of the absolute reflectance of the reference material with conventional Fourier transfer infrared (FTIR) equipment. Use of this value, i.e. applying the Kubelka-Munk equation in the correct form, leads to a linear relation between sample concentration and the Kubelka-Munk function even for very low concentrations.
THEORETICAL SECTION The theory of diffuse reflectance, i.e. the relation between sample concentration and reflectance, is given by the solution of the radiation transfer equation (3, 4 ) . Since the exact solution is tedious, several approximations have been used. One of the solutions which has gained general acceptance is known as the Kubelka-Munk theory (4). This theory describes the relation between the absorption coefficient k , the scattering coefficients, and the reflectance R (ratio of reflected to incident radiation) for a semiinfinite medium (“infinitely thick” layer) according to the following equation:
The equation is valid only for systems where no further reflectance at the boundary between the semiinfinite medium (e.g. KBr powder) and the air takes place. So far, the experiments have shown that this assumption is correct for our KBr powder systems. For a mixture of KBr powder and an absorbing analyte, one might assume additivity for k and s (3),such that
- RmrnI2 F(Rmrn) = (1 2Rmrn -
kaca
+ kKBrCKBr
sac,
+ SKBrCKBr
(2)
where k , and kKBrare the molar absorption coefficients of analyte and KBr, sa and smr the molar scattering coefficients, and c, and cmr the respective concentrations. R,, represents the absolute reflectance of the mixture. Since sKBrcKBr >> saca, eq 2 becomes 0 1988 American Chemical Society
1222
ANALYTICAL CHEMISTRY, VOL. 60, NO. 11, JUNE 1, 1988
=
R-m
(4)
(Im/IKBr)R-KBr
where I, and IKBr are the single-beam reflectance spectra of the mixture of KBr powder used as standard, respectively. Using the abbreviation
I
0015
This equation reveals the linear relationship between the Kubelka-Munk function F(R,,) and the analyte concentration c, for the concentration range under study, i.e. c,
