Anal. Chem. 1987, 59, 373-376
the polymer chain has an exceptionally weak bond at a periodically occurring site. From our observations with the oligomers of the polyamide and considering the preparation technique in ref 6, it might be conceivable that at least a part of the lines observed in that study is due to preferentially extracted oligomers. For practical investigations of polymers, the laser microprobe method has at any rate the advantage that measurements can be made on the substance itself and that the preparation of a monolayer on specially etched Ag is unnecessary. The availability of laser microprobes with the highest possible detection sensitivity for heavy ions is desirable. An improvement in the spectrum quality for high mass numbers is already possible by summation of a large number of spectra from different pulses. If preparation methods are developed to reduce the molecular weight of high polymers in surface areas to be investigated with the laser microprobe, polymers can be recognized from molecular ions representing the multiples of the monomer unit considerably more easily than from fragment ions that cannot be readily interpreted. ACKNOWLEDGMENT We thank A. Horbach, Bayer AG, ZF-DZA UER, for valuable discussions and his kind assistance in sample characterization. Registry No. Polystyrene, 9003-53-6; polyamide 6,25038-54-4.
373
Hercules, D. M.; Day, R. J.; Balasanmugam, K.; Dang, A,; Li, C. P. Anal. Chem. 1982, 5 4 , 280A. Gardella. J. A.; Hercules, D. M.; Heinen, H. J.; Specfrosc. Lett. 1980, 13, 347. Wilkins, C. L.; Well, D. A.; Yang, C. L. C.; Ijames, C. F. Anal. Chem. 1985, 5 7 , 520. Mattern, D. E.; Hercules, D. M. Anal. Chem. 1985, 5 7 , 2041. Bletsos, J. V.; Hercules, D. M.; Greifendorf, D.; Benninghoven, A. Anal. Chem. 1985, 5 7 , 2384. Bletsos, J. V.; Hercules, D. M.; Benninghoven, A,; Greifendorf, D. Proceedings of the 5th International Conference on Secondary Ion Mass Spectrometry (SIMS V), Washington, DC, 1985; Benninghoven, A., Colton, R. J., Slmons, D. S.,Eds.; Springer: New York, 1966; p 538. Bletsos, J. V.; Hercules, D. M.; van Leyen, D.; Niehuis, E.; Bennlnghoven, A. Proceedings of the 3rd International Conference on Ion Formation from Organic Solids (IFOS III), Munster, 1985; Benninghoven, A., Ed.; Springer: New York, 1986; p 74. Feigi, P.; Schueier, B.; Hilienkamp, F. Int. J. Mass Spectrom. Ion Phys. 1983, 4 7 , 15. Heinen, H. J.; Meier, S.;Vogt, H.; Wechsung, R. I n t . J. Mass Spectrom. Ion Phys. 1983, 4 7 , 19.
Reimer Holm* Bayer AG Central Research and Development D-5090 Leverkusen, Federal Republic of Germany Michael Karas University of Frankfurt Institute of Biophysics D-6000 Frankfurt, Federal Republic of Germany Henning Vogt Leybold-Heraeus GmbH D-5000 Koln, Federal Republic of Germany
LITERATURE CITED (1) Heinen, H. J.; Holm, R. Scanning Nectron Microscopy; 1974, I l l , 1129.
RECEIVED for review April 16,1986. Accepted September 15, 1986.
AIDS FOR ANALYTICAL CHEMISTS Determination of Vanillylmandelic Acid in Urine by Use of Catalytic Maximum Wave in Differential Pulse Polarography Kiyoshi Hasebe,* Teiji Kakizaki, and Hitoshi Yoshida Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060, Japan The need for a fast, simple, and reliable analysis of major metabolites of catecholamines, for example, epinephrine and norepinephrine, is imperative with regard to their important biological roles in order to treat a cancered patient in an early stage ( I , 2 ) . Above all, 3-methoxy-4-hydroxymandelicacid (VMA) and homovanillic acid (HVA) are the main metabolites of epinephrine and norepinephrine, being extremely useful in the diagnosis and treatment of catecholamine-secreting tumors in the case of neuroblastoma and related neural tumors (3, 4 ) . A number of techniques have been used to separate and identify metabolites such as VMA and HVA in urine. These metabolites have been analyzed by a colorimetric method (5) based on a rigorous color-development condition, but it is well-known that many substances existing in urine interfere with color development reaction. Also, a gas chromatographic method (6) requires nonvolatiles to form volatile derivatives. For simultaneous determination of two or more metabolites, high-performance liquid chromatography (HPLC) with UV or fluorescence or electrochemical detection (7,8) has been particularly useful. These obviate the need for pretreatment of the urine sample.
On the other hand, we have studied the differential pulse polarographic (DPP) behavior of several metal ions in the presence of a complexing agent and bromate ions as an oxidant and applied DPP to the determination of microamounts of analytes (9,IO). In the presence of mandelic acid and bromate ions, for example, microamounts of molybdenum(VI) in animal feeds have been determined by use of its catalytic reaction (11). Bardina and Chikryzova (12)reported the indirect determination of mandelic acid at lo4 M by use of the catalytic effect of mandelic acid in sulfuric acid. As a result of the polarographicallycatalytic reaction of the Mo(VI)-hydroxy organic acid complex, an electrode reaction mechanism had been proposed by several workers (IO,13). The mechanism is
Mo(V1)
+ HA
[MoVIA]- + e
[MoVIA]- + H+
(1)
[MoVA]-
(2)
-
+ Red
(4)
where HA is the a-hydroxycarboxylic acid such as mandelic
0003-2700/87/0359-0373$01.50/00 1987 American Chemical Society
374
ANALYTICAL CHEMISTRY, VOL. 59, NO. 2, JANUARY 1987
I I ~
I
o
,
0.1
a2
I
l
03
04
-E, V v s . S C E
os
Figure 1. “Catalytic maximum wave” of VMA in the presence of Mo(V1) and bromate ion by differential pulse polarography: (A) 1 pM Mo(V1) 4- 1 mM KBrO, 4- 0.1 M HCOOH, (B) 0.2 pM VMA 4- A, (C) 0.4 pM VMA A, (D) 0.6 pM VMA 4- A, (E) 0.8 pM VMA 4- A, (F) 1.0 pM VMA A; A€ = -50 mV; scan rate, v = 10 mV s-‘: i,, =
+ +
peak-to-peak current. acid. Ox and Red are the oxidant and its reduced form, respectively. The molybdenum(V1) complex consumed on the electrode is regenerated according to reaction 4. The velocity of the electrode reaction is limited by formation of the active intermediate complex as shown in eq 3. We have already reported the catalytic effect of 11 different kinds of organic compounds containing VMA in the presence of Mo(V1) and bromate ions (14). Thus, an analogous compound like mandelic acid gives a remarkably “catalytic maximum wave” using a dropping mercury electrode (DME) in the DP mode (9), which is about 500-1000 times the oxidation current of VMA on glassy carbon electrode, according to eq 1-4. This paper describes a method for the highly sensitive and selective determination of VMA in urine by differential pulse polarography using the “catalytic maximum wave” technique in the Mo(V1)-VMA-bromate system. EXPERIMENTAL SECTION Apparatus. Polarographic measurements were carried out with a voltammetric analyzer, Model P-1000 (Yanagimoto Mfg. Co. Ltd., Kyoto, Japan) and an X-Y recorder, Model RW-101 (Rika Denki Co. Ltd., Japan) at 25 f 0.5 “C with removal of dissolved oxygen. The DME had the following characteristics: mercury flow rate, m = 1.54 mg s-l in deionized-distilled water at open circuit; naturd drop time, t d = 4.68 s in 0.1 M formic acid solution containing 1 WMmolybdenum(V1)and 1 mM potassium = 53.5 cm. The bromate; and mercury reservoir height, hunCor, cyclic voltammetric measurements were performed with a PAR Model 173 potentiostat equipped with a PAR Model 175 function generator and a PAR Model 303 static mercury drop electrode (SMDE) (Princeton, NJ). Reagents. Vanillylmandelic acid (VMA), 3,4-dihydroxymandelic acid (DOMA),ferulic acid (FA), and 5-hydroxyindoleacetic acid (5-HIM) were obtained from Tokyo Kasei Co. (Tokyo, Japan). Vanillyllactic acid (VLA) and vanillylpyruvic acid (VPA) were from Sigma Chem. Co., (St. Louis, MO). DL-p-Hydroxymandelic acid (HMA), vanillic acid (VA), and the other related compounds were obtained from Nakarai Chem. Co. (Kyoto, Japan). RESULTS AND DISCUSSION Catalytic Maximum Wave of Mo(V1)-VMA-BrO,System. In order to determine a molybdenum content of about M ( I I ) , mandelic acid and bromate ion were used as an activator and a substrate, respectively. In this work, the catalytic ability was examined with the metabolites of catecholamines such as VMA and DOMA. Therefore, 1 pM VMA gave 2.82 WAas the catalytic current under the conditions of Figure 1. Similarly, 1 fiM DOMA and 1 gM HMA were 2.27 p A and 1.18 WAunder the same conditions, re-
Figure 2. Cyclic voltammogram of VMA in the presence of Mo(V1) and bromate ion: (A) 1 pM Mo(V1)4- 1 mM KBrO, 4- 0.1 M HCOOH, (B) 2.0 pM VMA 4- A. Conditions are the same as in Figure 1, except for the scan rate which is v = 200 mV s-’. SMDE was used.
spectively. The catalytic wave of the Mo(V1)-VMA complex in the presence of bromate ion is accompanied by a maximum wave in dc and normal pulse polarography; a typical “catalytic maximum wave” (9-11) is also observed at the reduction potential of the Mo(V1) complex from hexavalent to pentad in the DP mode (Figure 1). But, the reduction wave or peak of the Mo(V) complex to tervalent could not be confirmed because of the overlap of the bromate ion reduction wave with the wave of the Mo(V) complex. Figure 2 shows a cyclic voltammogram of the Mo(V1)-VMA complex in the presence of bromate ion, which is consistent with an EC (heterogeneous electron transfer followed by homogeneous chemical reaction) mechanism (15). From the dependence of mercury height (h = 43.5-63.5 cm) on the wave height in the dc mode, the value of d log i,,,/d log h was 0.121, corresponding to a catalytic reaction (16). Moreover, from the analysis of the i-t curve for the first drop when the potential changes momentarily from the initial potential at 0.2 V to the maximum peak at -0.36 V, the slope of the log i-log t plot was about 0.66, which is the same as the theoretical value for the catalytic current. Supporting Electrolyte. In the determination of molybdenum(V1) by use of the catalytic maximum wave, we have used acetic acid as the supporting electrolyte (11). In this case, we could get much larger catalytic maximum currents in formic acid compared to those in acetic acid. This increase may be due to the difference in the regeneration velocity from the Mo(V) complex to the Mo(V1) complex. The “catalytic maximum current” in the DP mode remains unchanged in the acidic concentration range of 0.05-0.1 M. When the acid concentration becomes higher than 0.1 M, the peak current seemingly decreases because of the increase in the bromate ion reduction current. Namely, the background current apparently increases. The decrease of the catalytic maximum current in formic acid at less than 0.05 M might be due to the decrease of the regeneration velocity of Mo(V1) with increasing pH value (11). The polarographic solution composed of 0.1 M formic acid containing 1pM Mo(V1) and 1 mM potassium bromate had a value of 483 Q cm-l in conductometry. This value is sufficient for the pulse polarographic measurement since it is less than 2000 Q cm-l (17). Effect of Molybdenum(V1) and Bromate Ion Concentrations. The presence of a certain amount of molybdenum(V1) and bromate ion is very important for production of the peak (11,18). The catalytic maximum current increased remarkably with molybdenum(V1) ion concentration up to 1 gM. The bromate ion concentration up to 4 mM also increased the peak current significantly, but the higher the
ANALYTICAL CHEMISTRY, VOL. 59, NO. 2, JANUARY 1987
Table 1. Influence of Catecholamine Metabolites and Related Compounds on the Catalytic Maximum Current of VMA"
Table 11. Mean Values of VMA in Urinary Excretion
compd
concn, pM
recovery, %
diagnosis
concn, pg/mL
Cr concn," wg/mg
3,4-dihydroxymandelic acid DL-p-hydroxymandelic acid vanillylpyruvic acid vanillyllactic acid 3,4-dihydroxyphenylaceticacid caffeic acid 5-hydroxyindoleacetic acid ferulic acid vanillic acid homovanillic acid hippuric acid p-hydroxyphenylacetic acid
0.1 0.4 2.0 1.0 1.0 1.0 10.0 10.0 10.0 10.0 10.0 10.0
110.3 114.0 90.3 109.9 115.8 111.9 100.1 99.4 100.0 97.0 92.4 97.8
normal person (620) normal person (600) neuroblastoma (610) neuroblastoma (571)
3.89 12.3 7.56 10.7
11.4 15.8 34.4 77.9
RSD,b % 2.21 ( n = 4) 3.29 ( n = 3) 6.16 ( n = 3) 5.28 (n = 4)
'
" Creatinine (Cr) content in urine specimens was determined according to the Drocedure in ref 25. Relative standard deviation. oxidation currents. Under optimal working conditions, the corresponding linear regression equation and the correlation coefficient, r, are as follows:
imax/pA = 3.16C/(pM VMA) - 0.328
1 pM VMA in the polarographic solution. Polarographic conditions are the same as in Figure 1.
(5)
r = 0.999 ( n = 21)
~~~
bromate ion concentration, the larger the background current due to the reduction of bromate ion. The optimal concentration of molybdenum(V1) and bromate ion was found to be 1 pM and 1 mM for the determination of VMA in urinary excretions. Effect of Modulation Amplitude. The relationship between pulse amplitude (AE) and the peak potential at positive potential, Ep+can be expressed as follows: -dE,+/dAE = 0.79. This value is somewhat larger than the theoretical value of 0.5 in a reversibly diffusion controlled reaction (19). The dependence of the pulse amplitude on the peak current is given by the slope, di,,,/dAE = 5 X FA mV-'. These results were similar to those observed for the determination of molybdenum(V1) in the mandelic acid-bromate ion system (11). Consequently, we used 50 mV as a pulse amplitude, taking into account the sensitivity and separability for the determination of VMA in urine samples. Effect of Analogous Compounds. Electrochemical study of the redox chemistry of catecholamines and related compounds has been discussed and summarized by Dryhurst et al. (20). It is well-known that the several catecholamine derivatives can be electrochemically oxidized at the carbon electrode under polarographic conditions, but they could not be electrochemically reduced in the ordinary potential region by polarography. In view of the fact that some kinds of a-hydroxycarboxylic acids gave "catalytic maximum" current ( 1 4 ) ,we have studied the effect of catecholamine metabolites and related compounds, which are found in urine and are potential interferences, on the determination of VMA. The results of these experiments are shown in Table I. DOMA and HMA do interfere a great deal with the determination of VMA even in the presence of half the mole ratio (Table I). The recovery of VMA, DOMA, and HMA extracted with ethyl acetate from the authentic solution at below pH 1was examined. The recovery of 5 pg of VMA with ethyl acetate using single-solvent extraction procedures was about 87 % (n = 5, relative standard deviation (RSD) = 0.29%), with the recoveries of 5 pg of DOMA and 5 pg of HMA being 74% (n = 5, RSD = 0.74%) and 83% (n = 5, RSD = 1.2%),respectively. The difference among these recoveries is insignificant. However, according to some workers (21,22),the existence of both DOMA and HMA in urine is a factor of 10 or less compared with that of VMA in urine. The catalytic ability of both compounds is less than that of VMA. Therefore, this assay can selectively analyze VMA only when urine samples are extracted with ethyl acetate. Calibration Curve. As can be seen from Figure 1, the peak currents based on the catalytic reaction are proportional to the VMA concentration range from 0.2 to 1.0 wM. These currents are much larger than the ordinary diffusion-controlled
375
where, i and C are the catalytic maximum peak height (PA) and VMA concentration (pM), respectively. The relative standard deviation at 0.60 pM and calculated detection limits are 2.06% and 6.77 X lo4 M (k = 2, confidence limits 97.2%), respectively. Urine Analysis. This proposed method was applied to the determination of VMA in urines excreted by --'/2-year-old babies. The procedure is as follows: The clean-up of 1 mL of urine sample with 5 mL of ethyl acetate was carried out according to a modification of the method described by Sato et al. (3). After the ethyl acetate extract was centrifuged, an adequate amount of the centrifuged extract was dried by a rotary evaporator at 40 "C. The residue is dissolved into 200 pL of ethyl alcohol, and the aliquots of 5-20 pL are analyzed by DPP under the conditions of Figure 1. The concentration of VMA in urine is determined by the standard addition method (23). The amounts of VMA in urines are shown in Table 11. The relationship between the amounts of VMA obtained by this method (catalytic reaction) and those by HPLC with an EC detector (oxidation reaction) was examined. The results by this method are in good agreement with those by HPLC (correlation coefficient, r = 0.987, n = 10, and slope = 0.996). These values may be compared with the values reported by Soldin and Gilbert Hill (24): r = 0.875, n = 87, and slope = 0.66. This means that this method has excellent characteristics and selectivity. ACKNOWLEDGMENT We thank Yasumasa Sato of Sapporo City Institute of Public Health, at Sapporo, for his constructive comments and supply of baby urine samples. Registry No. VMA, 55-10-7; DOMA, 775-01-9; HMA, 719810-9; VPA, 1081-71-6; VLA, 2475-56-1; 5-HIAA, 54-16-0; FA, 1135-24-6; VA, 121-34-6; HVA, 306-08-1; KOBr, 7758-01-2; p HOC6H,CH2CO2H, 156-38-7; 3,4-dihydroxyphenylaceticacid, 102-32-9; caffeic acid, 331-39-5; hippuric acid, 495-69-2; Mo, 7439-98-7.
LITERATURE CITED Voohess, M. L. Ann. N . Y . Acad. Sci. 1974, 23, 187. Williams, C. M.; Greer, M. JAMA, J . Am. M e d . Assoc. 1983, 163, 836. Satoh, Y . ; Satoh, Y . ; Taguchi. J.; Tsuji, K.; Hayashi, H.; Takasugi, N.; Takeda, T. Pediatr. Jpn. 1983, 2 4 , 1133. NeufOUaStOn'taMass Screening (in Japanese); Boshi aiikukai, Ed.; Okado Shuppan: Tokyo, 1983. Minarni, M.; Mori, K. Ind. Health 1982, 2 0 , 27. Muskiet, F. A. J.; Stratingh, M. C.; Stab, G. J.; Wolthers, B. G. Clin. Chem. (Winston-Salem, N . C . ) 1981, 2 7 , 223. Krstulovic, A. M.; Zakaria, M.; Lohse, K.; Bertani-Dziedzic, L. J . Chromatogr. 1979, 186, 733. Moleman, P.; Borstrok, J. J. M. Clin. Chem. ( Winston-Salem, N . C . ) 1983, 29, 878. Yamamoto, Y.; Hasebe, K.; Kambara, T. Anal. Chem. 1983, 5 5 , 1942.
376
Anal. Chem. 1987,59, 376-379
(IO) Hasebe, K.; Kakizaki, T.; Yoshida, H. Fresenius’ Z . Anal. Chem. (11)
(12) (13) (14) (15) (16) (17) (18) (19)
1985, 322,486. Hasebe, K.; Kakizaki, T.; Tanaka, S.; Yoshlda. H. Nippon Kagaku Kaishi 1984, 557. Bardina, S. M.; Chikryzova, E. G. Zh. Anal. Khim. 1978, 33,358. Zaitsev, P. M.; Zaitseva. 2. V.; Zhdanov, S. I.; Nikolaeva, T. D. Zh. Anal. Khim. 1980, 35, 1951. Hasebe, K.: Kakizaki, T.; Yoshida, H. Anal. Sci. 1985, 7 , 85. Schultz, F. A. J. Nectroanal. Chem. 1984, Lahr, S.K.; Finklea, H. 0.; 763,237. Progress in Inorganic Chemistry; Vicek, A. A,, Cotton, F. A,. Eds.; Interscience: New York, 1963; Vol. 5, p 228. Parry, E. P.; Osteryoung, R. A. Anal. Chem. 1985, 37, 1634. Hemmi, H.; Hasebe, K.; Ohzeki, K.; Karnbara, T. Talanta 1984, 37, 319. Hasebe, K.; Yamamoto, Y.; Ohzeki, K.; Karnbara. T. Fresenius’ Z . Anal. Chem. 1986, 323,464.
(20) Dryhurst, G.; Kadish, K. M.; Schelier, F.; Renneberg, R. Biological Electrochemistry; Academic Press: New York, 1982; Vol. I, pp 116-179. (21) Qwttro, V. D.;Wybenga, D.; Studnitz, W. V.; Brunjes, S. J. Lab. Clin. Med. 1964, 63,864. (22) Dutrieu. J.; Delrnotte. Y. A. Fresenius’ Z . Anal. Chem. 1984, 377, 124. (23) Krstulovic, A. M.; Brown, P. R. Reversed-Phase High-Performance Liquid Chromatography; Wiley: New York, 1982; p 215. (24) Soldin, S.J.; Gilbert Hill, J. Clin. Chem. (Winston-Salem, N.C.)1980, 26,291. (25) Saito, M.; Kitarnura, M.; Niwa, M. Rinsho Kagaku Bunseki; Tokyo Kagaku Dojin: Tokyo, 1971: p 78.
RECEIVED for review April 25, 1986. Resubmitted August 7 , 1986. Accepted September 5 , 1986.
Open-Tubular Mixer for Gradient Preparatlon in Microbore High-Performance Liquid Chromatography Karel Slais’ and Roland W. Frei* Department of Analytical Chemistry, Free University, De Boelelaan 1083, 1081 HV Amsterdam, T h e Netherlands Microbore high-performance liquid chromatography (micro-HPLC) has become a very important separation technique because of its well-documented advantages (1-4). Similar to standard HPLC, gradient elution in micro-HPLC is a powerful technique for eluting solutes with a wide range of polarity, for improving solute detectability, and for increasing the speed of analysis ( 5 ) . However, the miniaturization of devices that can produce precise and accurate gradients is not a simple matter. A number of approaches to this problem have been suggested. One of the most straightforward is to use two high-pressure syringe pumps modified for supplying low flow rates (6-8). These gradient devices are capable of retention time reproducibility of 0.1-0.5 % relative standard deviation (% RSD) (6-8). The solvents delivered by two pumps should be mixed in a static or dynamic mixer if sensitive solute detection is needed (7-9). However, these gradient instruments are not readily available, and they are expensive ( 5 ) . Therefore, a considerable effort was made toward producing gradients for micro-HPLC in an indirect way by using a single high-pressure pump. Ishii et al., in one of the first papers dealing with microHPLC, used an open tube for storing a gradient prepared before the separation (10). In a more recent application of this technique, a retention time reproducibility of 0.9-1.3 % RSD was reported (11). Several authors have used microexponential diluters (12-15). In such a system, the gradient is formed in a stirred mixing vessel. After the initial solvent is introduced via a switching valve, the final solvent is allowed to dilute the initial solvent exponentially. Retention time reproducibilities are reported to be 1.8 (13) or 1-1.5% (14) RSD. A similar approach to gradient elution made use of a series of linked micro-exponential diluters (16, 17). Recently a mixing device consisting of two coaxial tubes was described (18). While the outer tube serves as a mixer and initial solvent container, the inner one has a number of small holes along its length. Thus the solvent of final eluent strength flowing through the inner tube enters the mixer at several places. This leads to a continuously increasing final solvent percentage in the liquid leaving the mixer. The retention time reproducibility for phenols using this device was in range 0.2-0.3% RSD. On leave from the Institute of Analytical Chemistry, Czechoslovak Academy of Sciences, 611 42 Brno, Czechoslovakia.
All the above-mentioned mixing devices suffer from low flexibility in obtaining varying gradient profiles since the geometrical configuration of the mixers must be altered to change the gradient shape. To achieve increased flexibility, a system generating “breakthrough gradients” was introduced (19). Such gradients are produced by eluting the interface between weak and strong eluent from packed “gradient generator” columns. The shape of the gradient can then be changed either by changing the column dimensions and/or the diameter of the packing particles or by altering the refill flow during preparation of the gradient. It was demonstrated that by decreasing the flow rate of the flushing cycle 8-fold, the gradient volume could be diminished to about 50% of its original value, when a 1% solution of acetone in water was mixed with pure water (19). In this paper we describe a device for the inexpensive preparation of continuous mobile phase gradients for micro-HPLC. The device is based on storing and mixing two solvents in an open tubular loop of suitable dimensions and shape. The loop is fitted to a six-port valve in the back-flush mode, so that it can be partially or completely filled by the initial solvent. The final solvent is delivered by a high-pressure syringe pump. With a change of the volume of initial solvent introduced, the length and steepness of the gradient can conveniently be varied. Technical parameters together with performance evaluation under micro-HPLC conditions are given. THEORY Let us consider a tube of circular cross section, which is fitted in the back-flush mode to a six-port valve. While the valve is in the position shown in Figure 1,solvent A, delivered by the pump, moves through the tube from a to b. When the valve is switched, solvent B, which is miscible with solvent A, enters the tube at position b. The boundary between both solvents is thus moving from b to a. When the valve is switched to the original position, the boundary moves in the opposite direction (reversed flush) and leaves the tube at position b for the separation column. While traveling in both directions, the boundary width is continuously increasing. When the procedure described is used to generate boundaries of variable width, the large dependence of boundary width on solvent volume passing through the tube is advantageous. The volumetric variance, av2,for a sigmoidal profile of two very similar miscible solvents can be calculated in the same
C 1987 American Chemical Society 0003-2700/87/0359-0376$01.50/0
