Computer retrieval of infrared spectra by a correlation coefficient

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Computer Retrieval of Infrared Spectra by a Correlation Coefficient Method Kazutoshi Tanabe and Shinnosuke Saeki National Chemical Laboratory for Industry, Honmachi, Shibuyaku, Tokyo 15 1, Japan

The possibility of retrieving IR spectra by making use of an electronic computer is experimentally examined on a small number of reference spectra stored in computer memory as a miniature model of spectral data compilation. Transmlttance data measured at a constant wavenumber Interval for 110 kinds of liquid compounds were punched into paper tapes, and the similarity of two spectra was judged by computing a correlation coefficient between them. The effects on correlation coefficients of wavenumber range, wavenumber interval, wavenumber shift, ordinate scale, sample thickness, and sample purity were investigated. When spectra from 1200 to 650 cm-I in the absorbance scale are measured at an interval of 10 cm-' and when the purity of unknown samples used for the retrieval exceeds 95%, correlation coefficients between the same compounds are computed to be above 0.95 in almost ail cases. The practicability of this method for the retrieval of IR spectra among numerous reference spectra is discussed.

factors found in the first category, such as the shift of peak positions and the change of peak intensities, may be reduced. However, a main difficulty in the second category lies in the fact that IR spectra of the same compounds do not always show the same patterns, because experimental conditions differ from spectrum to spectrum. Thus, when different spectra of the same compound are compared, transmittance values of absorption peaks and base lines (non-absorbing lines) are, of course, not always in agreement with each other on a chart paper. Such difficulty also holds, though perhaps to a lesser degree, for the first category, but it might be more severe for the second. It is difficult for a retrieving machine to judge such dissimilar patterns as being those of the same substance. In this paper, the possibility of retrieving IR spectra is examined by a method where correlation coefficients are computed to reduce such difficulty in pattern recognition (16).

PROCEDURE IR Measurement. A Perkin-Elmer Model 180 grating infrared

In order to identify chcmical substances by IR spectra, it is necessary to retrieve the same spectrum as that of an unknown compound from numerous reference spectra. A t present, several mechanical methods for retrieving IR spectra have been proposed. Those may be classified into the following two categories. In the first category, the retrieval of spectra is achieved by making use of only position data of main absorption peaks in spectra. This category includes the Specfinder of the Sadtler Spectra, the DMS and IRDC edge-notched cards, and the Wyandotte-ASTM punched cards. Recently, several authors proposed retrieval systems by making use of electronic computers, mainly based on the Wyandotte-ASTM cards (1-15). However, information included in spectra consists not only of peak positions of absorption bands, but also of intensities, widths, and shapes of absorpt,ion bands. In the first category, peak position data are used for the retrieval, but the other spectral information is not sufficiently utilized for the retrieval. I t was a correct choice of information in the age of prism spectrophotometers several years ago. At that time, peak intensities, widths, and shapes of IR absorption bands could not be obtained with sufficient accuracy because of the shortage of spectral resolution and reproducibility of prism spectrophotometers. However, a t the present time, as almost all of prism spectrophotometers have been replaced by grating spectrophotometers, and photometric techniques have been much improved, observed peak intensities, widths, and shapes of absorption bands are sufficiently accurate to be used as keys for the retrieval of IR spectra. In the second category, taking the above-mentioned facts into account, spectra are retrieved by making use of all spectral information such as peak positions, intensities, widths, and shapes of absorption bands. The collation by ocular inspection is the most primitive method in this category. These methods are closely connect,ed to pattern recognition, where it can be expected that many disturbing 118

spectrophotometer equipped with a digital recorder, and a sealed liquid cell 0.015 mm thick with KBr windows were used to measure spectra of 110 kinds of liquid compounds in hand. Transmittance values of four figures measured a t a constant wavenumber interval were punched into paper tapes by means of the digital recorder. The number of reference spectra, 110, is quite small compared to the number of spectra in data compilation usually encountered. However, since the digital measurement of spectra is so time-consuming, it was considered better to take all possible combinations of these 110 spectra than to increase the number of reference spectra. As described below, the number of every possible pair among 110 spectra amounts to about 6000, which may be sufficient enough for investigating the possibility of retrieving spectra by this method. Computer Programming. A FACOM Model 270-30 electronic computer was used to compute the correlation coefficient between two spectra

(where x , , yL are the ordinate values a t i t h abscissa value of reference and unknown spectra, respectively, and n is the number of sampling points) and to print out serial numbers of reference compounds which show correlation coefficients above a threshold value. The program was written in FORTRAN IV language.

RESULTS AND DISCUSSION Effect of Wavenumber Range. Generally speaking, in order to increase the number of reference spectra stored in computer memory and to reduce machine time necessary for the retrieval, it is necessary to decrease the number of sampling points n. For this purpose, the effect of wavenumber range on computed correlation coefficients was examined. Among usual wavenumber ranges of IR spectra, the range above 2000 cm-1 is of little use for the identification by IR spectra. Thus, two wavenumber ranges 1750-650 and 1200-650 cm-l were tested. Histograms which show the distributions of correlation coefficients computed for about

ANALYTICAL CHEMISTRY, VOL. 47, NO. 1, JANUARY 1975

1

i_ 0.5

01 02 0.5 1

1.c

2 5 10 20 53 103

Wavenumber interval (cni')

Correlation coefficient

Figure 1. Histogram of correlation coefficients for the wavenumber range of 1750-650 cm-'

Figure 3. Dependence of correlation coefficients on the wavenumber intervals for ( a ) hexane-heptane, ( b ) cumene-sec-butyl benzene, ( c )hexane-sec-butyl benzene, and ( d )heptane-cumene

1000n

L

LL

Cxrelatton coefficient

Figure 2. Histogram of correlation coefficients for the wavenumber range of 1200-650 cm-'

Wavenumber shift (cm-')

Figure 4. Dependence of correlation coefficients on the wavenum-

6000 pairs-that is, for every possible pair among 110 kinds of reference spectra- for the two ranges are shown in Figures 1 and 2. For the wavenumber range 1750-650 cm-l, a maximum point of the histogram lies at r of about 0.1, and pairs which show correlation coefficients above 0.95 amount to ten, while for the wavenumber range 1200-650 cm-', a maximum lies a t r around -0.1, and only one pair shows a correlation coefficient above 0.95. This indicates that the wavenumber range below 1200 cm-l, which is called a finger-print region, is of more use for the retrieval of IR spectra than the range above 1200 cm-l. Here it should be noted that, when the correlation coefficient is utilized, a wavenumber range with no or little absorption does not make positive, but negative contributions to the ability of identification, as is easily understood from the above equation. Thus the wavenumber range was set a t 1200-650 cm-' in this study. Effect of Wavenumber Interval. As another method to decrease the number of sampling points, the dependence of computed correlation coefficients on the wavenumber interval was examined. Correlation coefficients for several pairs among spectra of hexane, heptane, cumene, and secbutyl benzene were computed for various wavenumber intervals from 0.1 to 100 cm-l. The result is shown in Figure 3. For intervals from 0.1 to 10 cm-l, the computed correlation coefficients do not vary significantly, while for intervals larger than 10 cm-', the correlation coefficients vary notably. This means that these larger intervals are not suitable for the retrieval of spectra. Spectral band widths of liquid compounds treated here are in general larger than 5 cm-l, but some of solid compounds, measured by the KBr disk method sometimes show band widths smaller than 5 cm-l. For such solid compound spectra, it may be desirable to compute correlation coefficients using spectral data measured at an interval

ber shifts for (a) anisole and ( b ) cyclohexyl bromide

smaller than 10 cm-l. However, it seems probable that solid compounds showing such narrow absorption bands are not so often encountered, and that the wavenumber interval 10 cm-l is not-unsuitable for such solid compound spectra, taking into account the result shown in Figure 3. Hence, the wavenumber interval was set at 10 cm-l in this study. Since the wavenumber range was set at 1200650 cm-l as described above, the number of sampling points per one spectrum is equal to fifty-six. This number leads to the fact that spectral data for more than seventy thousand kinds of substances can be stored on a reel of magntic tape which is usually available (2400-feet long, 800 BPI). Effect of Wavenumber Shift. In order to examine the effect of wavenumber shift of peak positions due to errors in spectral measurement, correlation coefficients between the spectra of the same substances mutually shifted by 1 to 10 cm-' were computed for cyclohexyl bromide and anisole. The results are shown in Figure 4. As the wavenumber shift increases, the computed correlation coefficients necessarily decrease from a value of 1.0, but the rate of decrement is faster for cyclohexyl bromide than for anisole, consistent with the fact that the former compound shows narrower absorption peaks than the latter. These results prove that, in order to obtain computed correlation coefficients above 0.95, it is necessary t o keep the wavenumber shift below 3 cm-I, and that, when the wavenumber shift is greater than 3 cm-1, an appropriate wavenumber correction has to be carried out. This restriction may be rather rigorous, because it is not easy to maintain the abscissa precision of IR spectrophotometers within 3 cm-l. Furthermore, for solid compounds which were not treated in this study, band widths of IR absorption peaks are sometimes smaller than for liquid compounds and, for

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I

Table I. Dependence of Correlation Coefficients on Sample Thickness in the Case of Spectra of Cyclohexyl Bromide ( a ) Absorbance scale

0.025(mm) 0.05(mm) O.l(mm)

0.015(mm)

O.OZS(mm]

O.OS(mm)

0,999 0.996 0.988

0.998 0.992

0.996

( b ) Transmittance scale O.OlS(mm)

0.025(mm) 0.05(mm) O.l(mm)

0.992 0.963 0.877

0.025(mm)

O.OS(mm)

0.989 0.927

0.970

401

Figure 6. Correlation coefficients between ( a ) pure and impure propyl chloride, and ( b )pure and impure propyl bromide

I

I

,

,

0

20

4dOO 40 60 80 Purity (7,)

100

Figure 5. Correlation coefficients between ( a ) pure and impure oxylene, and ( b )pure and impure m-xylene

such solid compounds, the restriction for the wavenumber shift may be more rigorous than 3 cm-l. Therefore, operators should be sufficiently careful to keep the abscissa precision within 2 or 3 cm-l by calibrating their spectrophotometers from time to time. Effect of Ordinate Scale a n d Sample Thickness. As a guideline for good laboratory practice in collecting reference data as well as in measuring unknown data, the Coblentz Society Class I11 specifications (17) would be pertinent. That is, it seems appropriate to put a specification on sample thickness so that the absorbance of most of absorption bands should not exceed 1.0 or 1.5 but the absorbance of a t least one band should exceed 1.0. However, such a specification will not always be satisfied in practical cases. It is very often the case that sample thicknesses are very different between reference and unknown spectra. Even if sample thickness varies from 0.015 to 0.1 mm, spectral patterns in the absorbance scale change linearly with the sample thickness, while spectral patterns in the transmittance scale do not. Since the correlation coefficient intrinsically does not vary depending on such a proportional variation in spectral pattern, the correlation coefficient computed for spectral data in the absorbance scale is expected to be insensitive to the change of sample thickness. In fact, the result given in Table I shows that the computed correlation coefficients in the absorbance scale are rather insensitive to the change in the sample thickness; while, in the transmittance scale, the dependence of the computed correlation coefficients on the sample thickness is considerable. However, almost all of conventional IR spectrophotometers cannot provide a spectrum in the absorbance scale. In the transmittance scale, when the difference between sample thicknesses is large as 0.015 and 0.1 mm, the computed correlation coefficients between them are proved to be somewhat lower than 0.95. But, in the observed spectra of 120

3000

2dOO

15bO

sdo

Figure 7. Spectrum of mixture of 10% o-xylene and 90% m-xylene (sealed liquid cell 0.015 mm thick with KBr windows)

cyclohexyl bromide measured with the sealed liquid cell 0.1-mm thick, several absorption peaks reach the 0% transmittance line, and thus the sample thickness of 0.1 mm is not pertinent to spectral measurement of cyclohexyl bromide. So, in order to obtain correlation coefficients above 0.95 in the transmittance scale, it is necessary to measure spectra with an appropriate sample thickness. On the other hand, computed correlation coefficients in the absorbance scale are insensitive to the change in sample thickness and, thus, operators need not pay much attention to the choice of sample thickness, because the spectral data a t very low transmittance can be neglected in computing correlation coefficients in order to avoid a matter of overflow in computer. Hence, it is concluded as follows. It is desirable to measure spectra in the absorbance scale and, if that is not possible, transmittance data should be converted into absorbance data in the computer. Then computed correlation coefficients between the same compounds will always be obtained above 0.99, irrespective of the sample thickness used in the experiment. Effect of Sample Purity. Although the retrieving procedure treated here is proposed for the identification of chemical substances, not for qualitative analysis of mixtures, it should be taken into account that most of the unknown substances encountered in the real world contain a greater or lesser amount of impurities. Hence, the effect on the retrieval process caused by the presence of impurities should be experimentally examined here. In order to examine the applicability of the correlation coefficient method to impure unknowns, mixtures of various concentrations of o-lm- xylene and of propyl chloride/ bromide were investigated. The results are shown in Figures 5 and 6. When the concentration of 0-xylene increases and the purity of m- xylene decreases in solution, the computed correlation coefficients between pure and impure m-xylene decrease quite remarkably. On the other hand, even if the purities of 0-xylene, propyl chloride, and bro-

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mide are reduced to a passable degree, the computed correlation coefficients between pure and impure samples are larger than 0.95. The sensitive reduction of the correlation coefficients in the case of m- xylene mixed with o- xylene can wholly be attributed to the extremely strong 740 cm-l band assigned to the CH out-of-plane bending mode of o- xylene. For example, the mixture of 10% o- xylene and 90% m- xylene shows the 740 cm-1 band at the 6% transmittance for the 0.015mm thickness (Figure 7). In such a case, even for existing methods which use only peak position data, it would not be easy to retrieve a correct spectrum of m- xylene. In order to obtain computed correlation coefficients above 0.95, the purity of unknown samples is required to exceed 80, 96, 53, and 9OOh for the four cases in Figures 5 and 6. Taking into account the fact that peak intensities of IR absorption bands differ remarkably from compound to compound, it is not easy to specify the necessary purity for unknowns. However, it may tentatively be concluded that, when the purity of unknown samples is higher than 959'0, correlation coefficients will be computed to be above 0.95 in almost all cases. Effect of O t h e r Factors. Spectral resolution of IR spectrophotometers, ordinate shift of base line, and the difference of sample preparation method may be considered as other factors affecting computed correlation coefficients. The effect of spectral resolution of spectrophotometers would be of little significance, at least as far as grating instruments are used. As the spectral slit widths of any grating spectrophotometers are usually 1 or 2 cm-' at 1000 cm-I, the difference in spectra of liquid or solid compounds is comparatively small, and its effect can be ignored. Even if spectral resolutions differ between reference and unknown grating spectra, this gives rise only to imperceptible changes in peak intensities and band widths, and thus computed correlation coefficients between them may hardly be affected. As far as the ordinate shift of base line (non-absorbing line) is parallel in the wavenumber range concerned, its effect on computed correlation coefficients can be neglected completely. That is, when base lines of both reference and unknown spectra are parallel to the 0% transmittance lines, correlation coefficients between them are computed to be nearly equal to 1.0, even if the absolute value of the base lines differs considerably between those two spectra. However, when the base line of either spectrum inclines as is often encountered in spectra of solid compounds measured by the KBr disk method, correlation coefficients may be computed to be somewhat lower than 1.0. Hence, in order to retrieve a correct spectrum easily, it is necessary to make use of refined spectra with no or little inclination of base lines. Since the wavenumber range in computing correlation coefficients is as narrow as 1200-650 cm-', it may not be difficult to obtain spectra of fine quality even for solid compounds. The difference of sample preparation methods may affect computed correlation coefficients quite critically. Especially, spectra measured in the vapor phase differ significantly from those measured in the liquid or solid phase, and computed correlation coefficients between them will be considerably lower than 1.0. In the case of liquid compounds, correlation coefficients between spectra measured in the pure liquid state and in solution may be somewhat lower than 1.0. In the case of solid compounds, sampling techniques such as the KBr disk method, the mull method, or the solution method may affect computed correlation coefficients quite critically. Hence, to obtain computed correlation coefficients above 0.95, it is necessary to measure

spectra by specified sampling methods, or to store into computer memory a variety of spectral data of the same substances measured by various sampling methods. But, as the latter procedure is not desirable in respect to the increase of computer memory and machine time for the retrieval, it would be reasonable that liquid compounds be measured by the capillary method, and solid compounds be measured by the KBr disk method, because spectra measured by these methods seem to be free from disturbances caused by absorption bands of medium. If sampling techniques are standardized in such a manner, correlation coefficients between the same compounds are always computed to be nearly equal to 1.0, and thus correct spectra will easily be retrieved. Reproducibility of Correlation Coefficients. To examine the effect of reproducibility in IR spectral measurement, the spectrum of cyclohexyl bromide was measured several times under the same experimental conditions, and correlation coefficients between those spectra were computed. The result is: the maximum is 0.9997, the minimum is 0.9977, the average is 0.9992, and the standard deviation is 0.0006. When experimental conditions in spectral measurement are fixed, computed correlation coefficients can be obtained with high reproducibility. Practicability of This Method. As a result of the above considerations, it is proved that, when spectra from 1200650 cm-l are measured at an interval of 10 cm-', and when the purity of unknown samples exceeds 95%, correlation coefficients in the absorbance scale between the same compounds are computed to be above 0.95 in almost all cases. On the other hand, the probability that a pair of different chemical substances gives a correlation coefficient higher than 0.95 is very low. Thus, it may be expected that correct spectra will be retrieved with passable rapidity by this method. However, the data set used in the present experiment is indeed small, i.e., only 110 liquid compounds, while most laboratories have actual need of treating a compilation of one to two orders of magnitude more materials in a variety of physical states for analytical purpose. In fact, existing methods which use only peak position data are based on about 100,000 reference spectra stored on magnetic tape. So, it is necessary to consider whether it is possible to retrieve unknowns from 100,000 file data by this method. For that purpose, it would be necessary to confirm that among 100,000 reference spectra, a relatively small number of compounds, say, fewer than twenty, show correlation coefficients above a threshold value (0.95), and that the machine time necessary for such a search is short enough for the practice of retrieval. Although the data set used here is quite small, the number of every possible pair among them amounts to about 6000. Figure 2 shows the distribution of the correlation coefficients computed for those 6000 pairs, but there is only one pair which shows a correlation coefficient above 0.95. This leads to the estimation that, if an unknown spectrum is collated with 6000 reference spectra, only one spectrum will, on an average, show a correlation coefficient above 0.95. From this, it is statistically expected that, if collated with 100,000 reference spectra, about fifteen spectra will show correlation coefficients higher than 0.95. In such a case, correct spectra will easily be found among those picked out. Consequently, it will probably be possible to retrieve unknown samples from 100,000 reference spectra by this method. Next, it would be interesting to examine how much time a search of, say, 100,000 reference spectra would take to run. For the small-scale electronic computer used in this

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experiment with 64 kilo-bytes of core memory, it took about 3 seconds for a search of 110 reference spectra. This speed requires about 45 minutes for a search of 100,000 reference spectra, but this time can be reduced sharply by using the following three procedures. The first is the speed-up owing to utilization of largescale computers. Computing speeds of existing large-scale computers are five to ten times greater than that of the one used here. The second is the speed-up by the improvement in the retrieving program. The computer program in this study was written in FORTRAN IV language, but programming in machine languages such as BASIC ASSEMBLER will lead to at least two or three times speed-up. The third is the speed-up owing to utilization of some preliminary retrieving methods. Making use of data of the average and the standard deviation of spectral patterns will be available for such a preliminary retrieving method, which may give some reduction of machine time for the retrieval. Consequently, these procedures will produce a t least one order of magnitude speed-up in machine time for the computer retrieval, and a search of 100,000 reference data by this method will take only a few minutes, which is quite practicable for the retrieval of unknown spectra. From these considerations, it can be concluded that the correlation coefficient method studied here will be sufficiently practicable for the retrieval of unknown samples from numerous reference spectra. For existing methods which use only peak position data, a key to the success in the retrieval predominantly lies in the correct choice of absorption peaks used for the retrieval, and much attention has to be paid to the treatment of weak or shoulder bands associated with strong absorption bands in spectra. On the other hand, the correlation coefficient method calls to account spectral data a t every wavenumber point, and there may be no room for human deliberation on spectral data of

unknown samples in the retrievl. In this respect, the correlation coefficient method does not require much skill for the retrieval, and it will be successful even for inexperienced users. When the compilation of digitized IR spectra is carried out for numerous chemical substances, this will be a promising method for the identification of chemical substances using their IR spectra.

LITERATURE CITED ( 1 ) R. A. Sparks, "Storage and Retrieval of Wyandotte-ASTM Infrared Spectral Data Using an IBM 1401 Computer, ASTM, Philadelphia, Pa., 1964. (2) L. D. Smithson, L. B. Fall, F. D. Pins, and F. W. Bauer, "Storage and Retrieval of Wyandotte-ASTM Infrared Spectral Data Using a 7090 Computer," Technical Documental Report No. RTD-TDR-63-4265, Research and Technology Division, Wright-PattersonAir Force Base, Ohio, 1964. (3) T. A. Entzminger and E. A. Diephaus, "Storage and Retrieval of Wyandotte-ASTM Infrared Spectral Data Using a Honeywell 400 Computer." US. Public Health Service, Robert Taft Sanitary Engineering Center, Cincinnati, Ohio, 1964. (4) D. H. Anderson and G. L. Covert, Anal. Chem., 39, 1288 (1967). (5) D. S. Eriey, "Fast Searching System for the Wyandotte-ASTM Infrared Data File," Chemical Physics Research Laboratory, The Dow Chemical Company, Midland, Mich., 1967. (6) D. S.Erley, Anal. Chem., 40, 894 (1968). (7) L. H. Cross, J. Haw, and D. J. Shields, "Retrieval of Infrared Data," Mol. Spectrosc., Proc. Conf. 4th 189 (1968). (8) Yu. P. Drobyshev, R. S. Nigmatullin, V. I. Lobanov. I. K. Korobeinicheva, V. S. Bochkarev, and V . A. Koptyug, Vestn. Akad. Nauk SSSR, 40, 75 (1970). (9) D. S. Eriey, Appl. Spectrosc., 25,201 (1971). (10) G. A. Massios, Amer. Lab., 3, 55 (1971). ( 1 1 ) R. W. Sebesta and G. G. Johnson, Jr., Anal. Chem., 44, 260 (1972) 44. 1669 11972). (121 C. S. Rann. , Anal. . Chem.. ~. (13) S. Shimizu, Annual Meeting of the Chemical Society of Japan, 2F14, Hiroshima, 1973. (14) S. Kihara, K. Takahashi, K. Fukaya, and J. Ishida, Tokyo Conference on Applied Spectrometry, 1B11, Tokyo, 1973. (15) K. Tanabe, S.Saeki, and T. Tamura, Jap. Anal., 23,626 (1974). (16) J. C. Reid and E. C. Wong, Appl. Spectrosc., 20, 320 (1966). (17) The Coblentz Society Board of Managers, Anal. Chem., 38 (9), 27A (1966). \

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RECEIVEDfor review February 19, 1974. Accepted October 1, 1974.

Ligand-Exchange Chromatography of Amino Sugars James

D. Navratil, Eduardo Murgia, and Harold F. Walton

Department of Chemistry, University of Colorado, Boulder, Colo. 80302

The amino sugars, glucosamine, galactosamine, and mannosamine, are retained strongly on copper- and nickel-loaded ion-exchange resins and eluted selectively with aqueous ammonia in the order quoted. They are easily separated from carbohydrates and all but one or two amino acids. Detection and measurement are done by ultraviolet absorbance of the copper complexes eluted from the resin. Best results were obtained with an acrylic-type resin, but resins based on polystyrene were also used. To test the analytical method, glucosamine was determined in chitin from lobster shells. The method is simpler and faster than published methods and can detect one microgram of amino sugar.

Studying the ligand-exchange chromatography of ethanolamines, we noted that glucosamine and galactosamine were retained strongly by a nickel-loaded cation-exchange resin ( I ). We decided to investigate the ligand-exchange chromatography of amino sugars more thoroughly for two 122

reasons. First, they are important biochemically. They occur as units of natural polymers in the shells of crabs and lobsters ( 2 ) ,marine biological adhesives ( 3 ) , and bacterial cell walls ( 4 ). Mucopolysaccharides, containing hexosamine units, are excreted in the urine of patients with liver disorders and diseases of connective tissue ( 5 - 7 ) ;hepatitis is induced experimentally by feeding d- galactosamine (8). Second, the amino sugars are ideal subjects for ligand-exchange chromatography. Their strong binding by metalloaded resins, due apparently to a synergistic effect of amino and hydroxy groups, offers the possibility of selectively absorbing them from complex mixtures. The analytical method for hexosamines most often mentioned in the literature is that of Elson and Morgan (9) modified by Boas ( 1 0 ) . It uses a color-producing reaction that is hard to control and does not distinguish between different hexosamines. The hexosamines are separated beforehand from sugars and amino acids by cation exchange. Glucosamine and galactosamine can be separated from one

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