ANALYTICAL CHEMISTRY, VOL. 50, NO. 8, JULY 1978
value can be made equal to the number of points in the spectrum, or any subset, provided it is larger than the number of points contained in a peak. N F should be estimated small enough to follow the changing slope in the background. N B is the number of points that are overlapped for each linear segment. This number is harder to estimate and is used to assure continuity between the calculated linear background segments. NB has to be less than NF. N is the number of points in the data, and B is the matrix containing the intensity values. MAX and MIN are the maximum and minimum values in the matrix B. The BKGR subroutine requires approximately 2K bytes of core storage, excluding the data matrix B. The size of the data matrix would be determined by the number of data points and whether the data is stored in a two byte, or four byte matrix. If the data matrix is a two byte integer and 2000 points are needed, the core storage requirements would be increased by 4K bytes for a total storage of 6K bytes. The current BKGR routine was written to be overlayed to minimize the storage required by the program. The algorithm
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converges very rapidly on the background, usually within four iterations. Thus when using a time-sharing or minicomputer, the calculations are completed without a noticeable delay. BKGR has been found to be a very effective tool in the analysis of spectral data. This FORTRAN Iv subroutine uses an iterative sliding least square background stripping algorithm. The subroutine is presently used to remove the background before a second derivative peak search is done on the data (3). This makes the determination of peak heights and intensities from the search much more reliable. A listing of BKGR is available from the author.
LITERATURE CITED (1) 8.D. Cullity, "Elements of X-Ray Diffraction", Addison-Wesley Publishing Company, Reading, Mass., 1967, pp 335-338. (2) E. J. Sonneveld and J. W. Visser, J . Appl. Crystallogr., 8, 1-7 (1975). (3) R. P. Goehner, SFECPLOT An Interactive Data Reduction and Display Rogram, unpublished work, 1977.
RECEIVED for review January 13, 1978. Accepted March 1, 1978.
Dynamic Range Improvement in Fourier Transform Infrared Spectrometry Tomas Hirschfeld Block Engineering, Cambridge, Massachusetts 02 139 T h e dynamic range of absorption measurements is limited by the increase in the relative absorbance error a t extremely high or low transmittances. T o keep this error within reasonable bounds, the sample concentration, pressure, or path must be set by trial and error. Beyond the time consumed in these trials, repeated measurements of the entire spectrum may be required if both strong and weak bands must be measured. T h e time lost here is more than an inconvenience if the sample cannot stay around long enough, as in ppb air pollution measurements ( I ) , GC-IR ( 2 ) ,or transient studies ( 3 ) . T h e actual measurement dynamic range can be derived from the customary relative absorbance error expression ( 4 ) , which may be written as
SNRA = A In 10
SNR,
X 2
-0."
10-l
0
1
REAL M J P J R N C E
Figure 1. Minimum, maximum, and mean absorbances and their ratio for a given minimum absorbance SNR relative to the 100% transmission line SNR
(1)
/
where A is the absorbance, SNRAits signal noise ratio, and SNRT that of the 100% line for the prevailing measurement conditions. As is well known, SNRA peaks for A = log e at (SNRA)MAX = e SNRT. If we set a measurement threshold (SNRA)MIN = a SNRT, the range of A is limited by both roots of the transcendental equation
A In 10
-a=0
(2)
Figure 1 shows AMIN,AMAX,and their ratio the dynamic range D as functions of a. Obviously, in order to maximize D we should aim for the largest possible SNRT (FT-IR!) and thus the smallest possible a. Furthermore, the "target" value of A should be made approximately (AMINAMAX)1/2 by adjusting the sample concentration, pressure, or absorption path. However, when the possible range of sample absorbances exceeds D, multiple measurements become necessary. These can be avoided by simultaneously measuring the sample at two path lengths. Experimentally, a stepped window may be used in a n absorption cell, or a multiple path cell can be maladjusted so that part of the beam traverses it only once.
10-5
lo.^'
10-2
1D.i
1
13
REAL ABSDRSANCE
Flgure 2. Apparent absorbance for a two-step cell as a function of the real absorbance for path ratios of 50 and 250
The effective absorbance of such a cell will be, for equal energy in both pathlengths:
A,= log
2
10-A
+ 10-Ar
(3)
where A, is the effective transmission and r is the pathlength ratio of both cell regions. Since A, does, of course, not obey Beer's law, Equation 3 can be numerically inverted point by
0003-2700/78/0350-1225$01.00/00 1978 American Chemical Society
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ANALYTICAL
CHEMISTRY, VOL. 50,
NO. 8, JULY 1978 DYNAPIC RANGE
point to restore the A spectra. This can also be done starting from the effective transmittance spectra. The appearance of the A, vs. A curve for r = 50 and 250 can be seen in Figure 2. For the regenerated A spectrum, we have now, by derivation
SNR,'
A h 10 (lowA+ r 2
=-
SNR,
10'
102
103
10'1
105
136,
lo\
(4)
and the limits of the A range are then the two or four roots of the transcendental equation:
where a' = (SNRA')MIN/SNRT. The limits of absorbance as a function of a'can be seen in Figure 3 for r = 50 and r = 250. Clearly, r should be kept small enough that the chosen a'can be exceeded over one continuous range of absorbance. Comparison with Figure 1 then shows that this range is far wider than a conventional cell's for any given a'. Higher improvements, probably not worth the effort, can be obtained from cells with > 2 simultaneous pathlengths. The computational capabilities of FT-IR instrumentation can thus be used to supplement their high SNR levels in order
Figure 3. Minimum and maximum absorbances and their ratio for a given minimum absorbance SNR relative to the 100 % transmission line SNR in a two-step cell for path ratios of 50 and 250
to greatly extend their dynamic range, by using specially designed sample cells.
LITERATURE CITED (1) P. C. Hanst, A. Lefohn, and 6.Gary, Appl. Spectrosc., 27,188 (1973). (2) A. W. Mantz, Ind. Res., Feb. 1977. (3) A. W. Mantz, Appl. Spectrosc., 30, 459 (1976). (4) R. P. Baurnan, "Absorption Spectroscopy", Wiley, New York, N.Y., 1962,
p 378.
RECEIVED for review October 25, 1977. Accepted April 13, 1978.
Two-Phase Sample Preparation and Concentration Technique for Sugar Derivatives Maria Martinez, David Nurok, and Albert Zlatkis" Chemistry Department, University of Houston, Houston, Texas 77004
There is a considerable advantage in preparing samples for gas chromatography in as concentrated a form as possible. This is of particular importance when determining trace components using an open tubular column where the sample is usually split before being introduced onto the column. In the analysis of nonvolatile compounds, such as sugars, it is necessary to derivatize before chromatography. This results in the compounds of interest being dissolved typically in 0.5 to 1 mL of reagent. Concentration can be effected by evaporation but this can lead to sample losses. These problems have been overcome by one of us ( 1 ) in the analysis of the kestoses, which are three isomeric trisaccharides that occur in low concentration in sugar cane molasses. Derivatives are prepared in a two-phase system such that essentially all of the silylated kestose is found in the top phase. The.& lylating reagent used is trimethylsilylimidazole which had previously been shown to be an excellent reagent for derivatizing sugars ( 2 ) . The top phase consists of hexamethyldisiloxane which is formed in situ or which may be added after silylation. The top phase occupies about 5 to 10% of the volume of the bottom phase and results in the sugar derivatives being concentrated by a factor of 10 to 20 times. For the kestoses, the error in using this technique as opposed to a single-phase technique is less than 3% when considering the same sample. This technique has proved useful for the analysis of trisaccharides in molasses (3) and also for the analysis of sugar impurities included in sucrose crystals ( 4 ) . T o illustrate the wider application of this technique, the analysis of sugars in beer, honey, sherry, and raisins is discussed in this note.
EXPERIMENTAL Reagents. The following were used Trimethylsylilimidazole 0003-2700/78/0350-1226$01 .OO/O
(Ohio Valley Speciality Chemicals, Inc., Marietta, Ohio). Hexamethyldisiloxane (Fluka AG, Tridom Chemical Inc., Hauppauge, N.Y.). Hexanes (Spectroanalyzed, Fisher Scientific Co., Fair Lawn, N.J.). Pyridine (Certified ACS, Fisher Scientific Co., Fair Lawn, N.J.), dried over Potassium Hydroxide (J. T. Baker Chemical Co., Phillipsburg, N.J.). Imidazole (99%, Aldrich Chemical Company, Milwaukee, Wis.) dried in a desiccator over silica gel. Samples. Samples were derivatized in the following forms: Honey in a 20% solution in distilled water, beer as a freeze dried solid, sherry and raisins without any prior treatment. Derivative Preparation. The silylating reagent consists of four volumes of trimethylsilylimidazole and one volume of dry pyridine. Reagent, 0.5 mL, is added to 8 mg of sample in a 1-mL mini-vial (Alltech Associates, Arlington Heights, Ill.) fitted with a Teflon-faced liner. The reaction is vigorous for samples containing appreciable quantities of water and care should be exercised. The mixture is shaken and allowed to stand for 10 min. The mixture is then saturated with imidazole and the double phase formed by adding 40 fiL to 100 fiL of either hexamethyldisiloxane or hexane. The vial is shaken and then centrifuged to separate the two phases. The top phase contains nearly all of the silyl derivative and is used for injection. The single-phase run refers to the derivitized sample before addition of imidazole. Chromatography. A Perkin-Elmer Model 900 gas chromatograph (FID) was used. Separation was on a 12 m X 0.25 mm glass open tubular column coated with SE 30. The carrier gas was nitrogen, introduced at a pressure of 5 psi. The inlet was set at 330 "C, the interface at 300 "C, and the oven was programmed at 4"/min from 150 t o 270 "C at which temperature it was maintained for 20 min.
RESULTS AND DISCUSSION The concentrating effect of the two-phase system is significant and is illustrated by a consideration of the chromatograms of a derivatized sample before and after formation 0 1978 American Chemical Society
