parison (Table IV), as these components are more representative of typical separations and are suitable for showing the dual-load effect and its dependence on k’. As shown in Table IV, last row, the dual-load effect (decrease in plate height) is less for the lower k’ valuese.g., 15% decrease for k’ = 0.4 us. 27% decrease fork’ = 5. This may be explained by the increased overloading effect expected for early peaks. According to Harris (8), the sample injection volume in microliters for a component should not exceed
.V fi
(3)
where V is the retention volume in milliliters and N is the plate number; for k’ < 1, overloading is dominant over the dual-load effect. On the other hand, the increase in column performance is about the same for k’ values between 0.4 and 5. Apparently, the increased improvement expected for the lower k’ values is compensated, but not dominated, by the overloading effect mentioned above. Of course, a t higher k’ values, the improvement in column performance would decrease to zero, as in the case of packed columns ( I ) . Column Temperature. One means of increasing the validity of column comparison is the use of constant retention time-i.e., time-normalization. As columns varied in load and length, time-normalization was maintained by judicious choice of column temperature, which was found (8) W. E . Harris, J . Chromatogr. Sci., 11, 184 (1973).
to be between 60 and 70 “C. Columns were thus compared at approximately fixed k’ values. When retention and, consequently, k’ is reduced by using a higher column temperature, as in the case of column H, Table IV, where k was reduced from 5 to 0.4, column performance (but not HETP) is improved significantly. Thus, if either a more volatile sample or a higher column temperature were used in this study, column performance might be further increased. Trace Analysis. When large volumes of sample were injected as in the case of trace analysis, dual-load columns were particularly useful as shown in Table V. This lists the average plate numbers obtained when injecting 0.6-pl of the analytical sample (Table U) on four different 35-foot columns of two different liquid loads. At the low liquid load, H E T P is improved by 32%. Even a t the high liquid load (where it may be recalled that there was no dual-load effect for 0.1-11 sample injection volume, Table III),there is an 18% decrease in HETP. CONCLUSION If the amount of‘ liquid phase per unit length is a conveniently variable parameter, as in cases where open tubular columns are made by combining two or more lengths, and particularly where the columns are coated in the laboratory (locally), it may be advantageous to use a higher liquid load in the front length. Received for review July 31, 1973. Accepted October 1, 1973.
Cryostat for Optical Spectroscopy J. Szoke and I. Szilagyi’ Physical Optics Department, Central Research lnstitute tor Physics, Budapest, Hungary
In modern spectroscopic studies, the spectrum under investigation must be measured at different temperatures. While thermodynamic constants can be more accurately determined a t elevated temperatures, for the analysis of spectroscopic fine structure, low-temperature measurements are preferable, because the resolution improves as the temperature decreases; that is, the component bands produce higher and smaller peaks, while the integrated intensity remains constant. However, the increase in the resolution is not continuous, and, especially in electronic spectroscopy, the different types of transition (combinations of electron jump with vibrations, rotations, excitons, phonons, magnons, etc.) often vary selectively with temperature. The temperature range of phase transitions is particularly rich in information. A spectrum therefore needs to be examined over a wide range of low-temperature values, e.g., a t intervals of 5 or 10 “C going from room temperature down to liquid nitrogen temperature. These requirements fix the specifications which must be met by any cryostat used for temperature regulation of samples studied spectroscopically: The sample chamber (in the cryostat) must. be transparent in the spectral region of interest. The windows of the cryostat must be kept Present address, Chinoin Pharmaceutical and Chemical Factory, Budapest, Hungary
292
a t room temperature to protect them from condensation of water vapor. The sample temperature must be constant during the measurement, particularly in the illuminated region. All but the last requirement are easy to achieve. The difficulty of keeping the sample at a constant temperature is due to the fact that the examined area of the sample is exposed to a substantial quantity of light from the radiation field. This is particularly true in the infrared region, where almost all the absorbed energy is converted into heat. The temperature of the illuminated volume (or surface area, in the case of reflection) cannot be locally controlled, so the sample temperature can be cryostated only if the sample is a good conductive material. Usually this is not the case. In heat-conducting cryostats the liquid coolant(s) is in direct contact with the sample, and the heat generated in the sample by radiation from the various sources (mainly the light source) is dissipated by conduction through this medium. The sample temperature is in this case determined by the rates of heat uptake and heat conduction. In the gas-flow-type cryostat cold (usually thermoregulated) gas streams around the sample. The heat absorbed by the sample is taken up by the molecules of the gas, and thus sample temperature is determined by the temperature and flow rate of the gas stream.
ANALYTICAL CHEMISTRY, VOL. 46, NO. 2, FEBRUARY 1974
LIQUID INLET
N2
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L I Q U I D He I N L E T
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-RECUPERATION SYSTEM
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Figure 4. Fluorescence spectra of ammonium uranyl-trisacetate at different temperatures measured in a gas-flow-type cryostat OUTLET
Figure 2. Outline of the gas-flow-type N2 cryostat
It
EXPERIMENTAL The fluorescence spectrum of solid ammonium uranyl-tris-acetate was measured. The microcrystalline sample was prepared by the method of Dieke ( 1 ) and was packed in a vertical target with moderate pressing. The sample was illuminated by focusing the exit slit of the exciting monochromator. The emitted light was dispersed by a high resolution plane-grating monochromator (1200 lines/mm; 100 x 100 mm ruled area; f = 100 cm) in CzernyTurner arrangement. The instrument was developed in this laboratory. The two types of cryostat utilized are depicted schematically in Figures 1 and 2; the points at which the sample temperature was measured are shown in Figure 3. The temperature was measured by using a T-type (copper-constantan) thermocouple to a precision of f l "C between rcam and liquid Nz temperature. The temperature was controlled by a precision proportional regulatory system (2). In the conduction type cryostat, the coolant is transferred through a heating block to the sample holder. The heating current is determined by the difference between the setting and the actual thermo sample signal level. The flow rate of the coolants can be changed by a mechanical valve. (1) W. Lentz,Z. Anal. Chem., 52,90 (1913). (2) J . Balla, K . Tompa. and F . Toth. Cryogenics, 8,47 (1968).
Figure 5. Luminescence spectrum of ammonium uranyl-trisacetate in a thermoconductive cryostat after 8-hr cooling with liquid nitrogen
The temperature can be quickly set 1(: "C/min at the sample holder and it can be controlled easily; while a t the powdered sample, it changes slowly and it is uncontrollable. Therefore, we did not use temperature controller. The temperature of the sample and the sample holder was measured as can be seen in Figure 4.
ANALYTICAL CHEMISTRY, VOL. 46, NO. 2, FEBRUARY 1974
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In the gas-flow type cryostat, the pressure is atmospheric, and the teiaperature can be measured equivalently in the sample at the sample holder or in the chamber and it was controllable in all cases with a precision to fl "C. The spectra measured at the same temperature were reproducible within *270 in intensity.
RESULTS AND DISCUSSION Figure 4 shows spectra taken while using the gas-flow cryostat. The increasingly good resolution is due to the cold effect (The spectroscopic interpretation will be published later). In Figure 5 , the best result obtained with the heat-conducting cryostat can be seen. In this case, the copper transfer block and non-illuminated parts of the sample were kept a t the experimental temperature of -190 "C. The measured spectrum thus corresponds to a spectrum a t about -50 "C. The figures demonstrate clearly that the gas-flow technique is the more effective. With this technique, the tem-
perature can be set in less than 10 seconds per "C.The conductive cryostat does not work satisfactorily if the contact between heat transfer block and sample is imperfect or if the sample material is of poor thermal conductivity. Generally neither of these conditions is fulfilled. It can be concluded that the spectroscopic data obtained a t temperatures cryostated with heat-conducting devices are of questionable reliability. Reports in the literature of small temperature effects may be therefore attributable rather to poor construction of the cryostat than to temperature insensitivity of the material.
ACKNOWLEDGMENT The authors wish to thank J. Balla and I. Peter for helpful discussions and Mrs. B. Szab6 and B. Bencze for the useful technical assistance. Received for review February 1, 1973. Accepted August 17,1973.
Multiclass Linear Classifier for Spectral Interpretation (Pattern Recognition) C. F. Bender Lawrence Livermore Laboratory, University of California, Livermore, Calif. 94550
B. R. Kowalski Department of Chemistry, University of Washington, Seattle, Wash. 98795
Linear classifiers were originally designed to construct decision hyperplanes for binary (yesjno) decisions ( I ) . A linear classifier was the first pattern recognition technique applied to the interpretation of spectroscopic data (2). With this technique, a number of binary decisions were used to predict structural information directly from lowresolution mass spectra. Although the problem is multiclass in nature, a complicated use of the linear classifier gave very encouraging results. Difficulties arise in trying to define multiclass linear machines ( I ) ; hence, a considerable effort has been spent on improving the linear, binary classifier (3). Recently we used a multiclass technique, the K-Nearest Neighbor Rule ( 4 ) , for the interpretation of NMR spectra. For this particular application, the multiclass technique out-performed the technique using linear classifiers as outlined above. The K-Nearest Neighbor Rule is expensive to use and not suited to small laboratory computers. This problem has been partially solved by reducing the number of variables (5, 6), but the K-Nearest Neighbor Rule is still best suited to computers with a large amount of fast storage. (1) N . J . Nilsson. "Learning Machines." McGraw-Hill, N e w York, N . Y . . 1965. (2) P. C. Jurs, 8 . R. Kowalski, and T . L. Isenhour. Anal. Chem., 41, 21 (1969). . (3) L. E. Wangen, N. W. Frew. and T . L. isenhour, Anal. Chem., 43, 845 (1971). (4) 8.R . Kowalski and C. F . Bender, Anal. Chem., 44, 1405 (1972). (5) C. F. Bender and 6.R . Kowalski, Anal. Chem., 45, 590 (1973).
(6) C. F. Bender a n d H. D. Shepherd, and B. R . Kowalski, Anal. Chem., 45, 617 (1973).
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The purpose of this note is to present an efficient multiclass linear classifier which can be easily applied, yet retains the power and simplicity of the binary classifier. This is accomplished by compromising linear separability for interclass separability.
DEFINITIONS AND METHOD A pattern space, X , is a collection of patterns, X, XI, X,,XI, 1.. X,P ... X,P X*l
x,x,
\ X M .............. l where Xil, is the ith variable of the pth pattern. In spectral analysis, each spectrum is a pattern and the variables are related to the spectral intensities and positions of the peaks. A class is a collection of patterns in which all members have a common feature. Pattern recognition methods are used to extract this feature from the variables. Binary decisions are made using a linear classifier by noting the value of the dot product of a weight vector, W, and a pattern X,,
x,+w
s, = (2) Here + denotes matrix transpose. If S, is greater than some number, SO, the decision is yes, and if S , is less
ANALYTICAL CHEMISTRY, VOL. 46, NO. 2, FEBRUARY 1974
