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ANALYTICAL CHEMISTRY, VOL. 50, NO. 4 , APRIL 1978
Band-Broadening Phenomena in Microcapillary Tubes under the Conditions of Liquid Chromatography Takao Tsuda’ and Milos Novotny” Department of Chemistry, Indiana University, Bloomington, Indiana 4 740 1
Chromatographic measurements are described in which band-broadening phenomena were studied under different conditions in glass thick-walled, micron-size capillaries. These experiments were conducted to investigate basic processes involved in (possibly feasible) capillary LC. Measurements carried out with a nonretained solute in microcapillaries of various diameters indicate that the plate height values are considerably better than predicted from the theory. Geometrical characteristics of the inner surface seem to play only a minor role in reducing band-broadening. The “coil effect” and secondary flow phenomena may be important in future attempts to develop capillary LC.
While assessing the theoretical limit of separating ability of gas and liquid chromatography, Giddings ( 1 ) calculated that the theoretical limit to the number of plates is roughly 1000 times higher in liquid than in gas chromatography (LC and GC, respectively). Such numbers are roughly of the same proportion as the products of viscosity and solute diffusivity in t h e respective phases. H e also suggested t h a t the open tubular (capillary) columns in liquid chromatography are worth considering. Although wall-coated capillary columns in gas chromatography are now well-established means to achieve theoretical plate numbers typically between lo6 and lo6, best reported separations in modern liquid chromatography are currently obtained with small-particle packed columns. Mobile-phase viscosity (roughly two orders of magnitude different) and solute diffusivity in mass-transfer processes (typically, five orders of magnitude smaller in LC than in GC) are two basic properties that govern column efficiency. Thus, while the “openness” of GC columns has long been recognized as their beneficial attribute ( 2 ) , the packing tightness is characteristically sought in high-performance LC separations. When considering a translation of Golay’s considerations (3) into the conditions of LC, capillary columns would hardly seem to be worthy of investigation because of the limited radial diffusion possibilities. However, certain additional circumstances must be taken into account. Under the conditions of laminar flow, Taylor ( 4 ) established that the only means of lowering the plate height, H , is a decrease of column diameter:
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where u = flow velocity, r = column radius, and DM= solute diffusivity in the mobile phase. Thus, a decrease of column diameter in LC by approximately one order of magnitude compared t o the currently used GC capillary columns may lead to appreciable gains in column efficiency. While limited practical value of this approach with currently available LC technology is apparent, the same may not hold true for future On leave from the Department of Applied Chemistry, Faculty of Engineering, Nagoya University, Nagoya, Japan. 0003-2700/78/0350-0632$01 0010
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Comparison of plate heights at different mobile-phase velocities for microcapillaries of different internal diameters. (A) plots derived from t h e Taylor equation: (e) experimental curves. (A) column length ( L ) = 11 m: (X) L = 7.5 m; (0)L = 102 m Figure 1.
separations. Such directions were recently advocated by Golay (5). If solute transport by a process other than diffusion can be achieved in the radial direction, separating conditions may be arrived at. Thus, under the conditions of turbulent flow, where the radial component of the total flow is considerably increased and the flow profiles are significantly altered, the plate height should decrease with increasing flow rate, as calculated by Pretorius and Smuts (6). Experiments of Giddings et al. (7) in gas-adsorption capillary chromatography actually demonstrated this phenomenon; an impressive efficiency figure of 3800 plates per second was obtained at a very high Reynolds number. Enormous inlet pressures would be required for turbulent flow capillary LC ( 6 ) . Perhaps, a more attractive route to higher column efficiencies in capillary LC lies in the utilization of secondary flow phenomena induced in helical columns by centrifugal forces. As discussed by Koutsky and Adler (8),this phenomenon has been known for over a hundred years. I n both laminar and turbulent flow regions, the secondary flow inhibits axial dispersion by displacing molecules into perpendicular position. C 1978 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 50, NO. 4 , APRIL 1978
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Figure 2. Effect of surface treatment on the plate height vs. velocity curves. Both columns are 11 m long, with 50-pm i.d. (A) smooth (untreated) wall. (0) capillary lined with “whiskers”
T h e extent of action of t h e centrifugal forces is dependent on both column inner diameter and t h e radius of coil. Although the possible existence of the “coil effect” was not considered by Golay ( 3 ) ,calculations by Tijssen (91, Tijssen and Wittebrood ( I O ) , and more recently Wong e t al. ( 1 1 ) strongly indicate t h a t such phenomenon is existent in GC capillary columns. With higher density of liquids than gases, t h e centrifugal effect will also be greater in LC. While too low theoretical plate numbers were encountered in the earlier work of Horvath e t al. (12) conducted with wide-bore capillary columns under the conditions of highspeed LC, the present study was undertaken to measure the extent of chromatographic band-broadening in t h e range of column diameters with potential utilization. Since Horvath’s work (12) indicated possible beneficial departures from the values predicted by Taylor ( 4 ) ,it has been of some interest to know their magnitude with column diameters approximately an order of magnitude smaller. As the surface factor is likely to play some role in the solute transport phenomena in the micron-size tubes, we have also studied band-broadening phenomena in capillary columns down to 50-pm diameters, provided with silica “whiskers” of micron sizes (13). In addition, the “coil effect” was investigated with glass capillary columns of various diameters.
EXPERIMENTAL Thick-walled glass capillaries of various lengths and diameters were drawn from glass tubes of appropriate dimensions by means of a commercial glass drawing machine (Hupe and Busch, Groetzingen, West Germany). Columns with internal diameters
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down to about 20 pm are readily feasible; for example, common polarographic capillaries make convenient starting materials for glass drawing. Column diameter is occasionally checked under the microscope. If a proper control of drawing parameters is maintained, fluctuations in capillary diameter should be no more than 10% (14) with the micron-size capillaries. The LC apparatus for measuring the extent of band-broadening has been basically described in our recent publication on packed microcapillary columns ( 1 5 ) . The system included a splitting injector and an assembly for additional liquid purge at the column exit, to overcome detector volume problems. A restrictor was added beyond the detector cell to prevent formation of bubbles within the detector. At the present time, investigations were performed only with benzene (a nonretained solute). Injected amounts were kept constant and near the sensitivity limit of the UV monitor. Splitting ratios between 1:lOOO and 1:2500 were typically used. Whereas some measurements were performed with untreated glass capillaries, we also investigated the effects of surface modification. For the latter case, silica “whiskers” were formed inside the columns according to the method of Onuska et al. (13). The “whisker” structures of adequate density were observed microscopically after a double treatment of glass wall with 0.5% solution of NH,F.HF in methanol. Observations of the “whisker” density after LC experiments demonstrated no substantial changes, attesting to good mechanical stability of this surface treatment. In order to investigate an effect of column coiling on plate height values at different velocities, the glass drawing machine was modified with home-made coiling tubes to prepare columns with smaller- or greater-than-usual coil radii. Mobile-phase velocities were evaluated from the retention times of benzene. Hexane was used exclusively as a mobile phase. T o estimate plate height values from the Taylor equation ( 4 ) , the value of diffusion coefficient for benzene in hexane at 23 “C (3.0 x cm2 was calculated from viscosity, molar volume, and heat of vaporization data according to the procedure of Othmer and Thakar (16).
RESULTS AND DISCUSSION Comparisons of theoretical and experimental data, concerning plate height (H) vs. flow velocity ( u ) curves, are included in Figure 1for three different capillary inner diameters. Similarly to the earlier observations of Horvath et al. (12) with wider columns, H values are significantly lower than predicted through the Taylor equation. Although the difference between theoretical and experimental curves appears less pronounced for capillaries of smaller radii, it is of practical importance t h a t this beneficial effect occurs in t h e range of column diameters of potential use. Whereas the presented results were obtained with nonretained solute only and a possible development of capillary LC as an analytical method may still be only a remote
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Figure 3. Plate height vs. velocity curves obtained with glass capillaries of identical internal diameters (195 pm), but different coil diameters. (0) L = 102 m, coil diameter = 23.5 c m . (0)L = 87 m, coil diameter = 5.7 c m
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 4 , APRIL 1978
possibility, these experimental values give rise to certain expectations. I n order to investigate surface effects as possible contributors t o the significant plate height reduction observed above, several columns with different radii were compared in untreated and "whisker" forms. Only minor differences were observed, and these were frequently within the measurement precision of the conducted experiments. This situation is exemplified by Figure 2, where 50-pm columns with two different surface characteristics are compared. The observed difference is indeed small. T h e "coil effect" and possible utilization of the secondary flow present some interesting alternatives. If the earlier theoretical assumptions (8-11) are correct, a decrease of coil diameter can lead to a significant reduction of chromatographic band-broadening. Rather than coil diameter alone, the ratio of such quantity to the column internal diameter must be considered. While reducing the column inner radius, the plate height will decrease. However, the "coil effect" is also likely to be less beneficial. We have made this observation in t h e previously reported work on packed microcapillaries (Is),and the results on open tubes studied in this work show similar trends. Thus, H vs. u curves obtained with different coil radii for both packed (15) and open microcapillaries (of approximately 100 p m and smaller internal diameters) demonstrated no appreciable differences. However, a diameter increase t o 190 pm shows a significant departure of the corresponding curves from each other at high flow rates, suggesting that the "coil effect" is operational here (see Figure 3). Although the plate heights obtained with larger diameters are, regrettably, too high, the flatness of both curves at high velocity values is commendable. Alternatively, the coil radius could be further reduced. However, we find technical difficulties in drawing glass columns with coil diameter smaller t h a n about 4 cm. Whereas coiling and surface treatment could result in minor plate-height reductions in a more or less additive fashion, they still fail to explain the differences between predicted and measured values. While potentially significant for the future of capillary LC, this discrepancy remains to be an interesting theoretical problem. Whether considering achievement of high plate numbers through reduction of column radius, or utilizing secondary flow phenomena in very long columns of somewhat larger diameters, there will be many technical difficulties involved with any future attempts to make capillary LC viable. In fact, it is entirely possible that the columns are considerably better
than our presently crude sampling and detection techniques reveal. Developments of smaller and more sensitive detectors and the high-pressure capabilities beyond the present state, are indeed a challenge. It'hile the presented results are limited to a nonretained solute, suitable column technology is likely to require much additional work. With the limited capacity of small-bore open tubular columns, the recently developed packed microcapillary columns (15) may be a better alternative. In spite of t h e disadvantages of microcapillary columns named above, these columns also possess some unique features: (a) the overall miniaturization of separation processes can be accomplished; and, ( b ) because of the very low flow rates through such columns, a new relationship between the column and detectors or ancillary tools is now available. These considerations appear to provide incentive for further theoretical and experimental studies of capillary LC.
Note Added in Proof. During the 12th International Sbmposium Advances in Chromatography, held in Amsterdam on November 7-10, 1977, we became aware that research along somewhat similar lines has been underway in the Research Laboratories of Shell Oil Company, Amsterdam, by R. Tijssen, the author of the earlier published theoretical papers (ref. 9 and 10).
LITERATURE CITED J. C. Giddings, Anal. Chem., 36, 1890 (1964).
L. S Ettre, "Open Tubular Columns in Gas Chromatography", Plenum Press, New York, N.Y., 1965. M. J. E. Golay, in "Gas Chromatography 1958", D. H. Desty, Ed., Academic Press, New York, N.Y., 1958, p 36. G. Taylor, Proc. R . SOC.(London), 219A. 186 (1953). M. J. E. Golay, Chromatographia. 6, 242 (1973). V. Pretorius and T. W. Smuts, Anal. Chem., 38, 274 (1966). J. C. Giddings, W. A. Manwaring, and M. N Myers, Science, 154, 146 (1966). J. A. Koutsky and R. J. Adler, Can. J . Chem. Eng., 43, 239 (1964). R . Tijssen, Chromatographia, 3, 525 (1970). R . Tijssen and R. T. Wittebrood, Chromatographia, 5 , 286 (1972). A. K. Wong, B. J. McCoy, and R. G. Carbonell, J . Chromatogr., 129, 1 (1976). C. G. Horvath, B. A . Preiss, and S. R . Lipsky, Anal. Chem., 39, 1422 (1967). F. I. Onuska, P. D. Goulden, M. E. Comba, and R. J. Wilkinson, J . Chromatogr., 142, 117 (1977). K. Tesarik and M. Novotny, Chem. Listy, 62, 1111 (1968). T. Tsuda and M. Novotny, Anal. Chem., 50, 271 (1978). D. F. Othmer and M. S. Thakar, Ind. Eng. Chem., 45, 589 (1953).
RECEIVED for review November 9,1977. Accepted December 27, 1977. This work was supported by Grant No. ME'S 7504932 from the National Science Foundation.
