chromatograph, re-equilibrated with solvent, and retested. They showed no loss in efficiency. When the short columns are used, precise control of mobile phase water content is required for reproducible column properties when using nonpolar solvents and high flow rates. Recent studies (16) have indicated that with more polar solvents, the control of the mobile phase water content is not so critical. This observation is in agreement with the results of Snyder (8). The silica gel particles used in these experiments are exactly the same particles used on thin layer plates. Efficient extrapolations from TLC to high speed LCshould be madereadily with the added benefit of quantitation and easy sample collection. Silica adsorbents of small particle diameter possess adsorption characteristics similar to conventional silicas. Separations can also be extrapolated from classical gravity-fed column experiments to high speed LC with greatly increased column efficiency. Current experiments involve in situ coating of the packed column with polar liquid phases, resulting in liquid-liquid (16) R. E. Majors, unpublished results, 1972.
partition columns of very good performance. The balanced density slurry packing procedure cannot be used easily with conventionally coated liquid-liquid packing materials because many of the liquid phases are somewhat soluble in the slurry solvents. Small particle silicas with chemically bonded liquid phases, similar to those reported earlier (17), would lend themselves to slurry packing procedures. Kirkland ( 4 ) has applied such techniques to chemically bonded porous layer beads. In addition, columns of kieselguhr have been successfully packed using balanced density slurry packing. Results of these investigations will be presented in forthcoming publications.
RECEIVED for review January 7, 1972. Accepted April 14, 1972. Presented in part at the 13th Eastern Analytical Symposium, New York, N.Y., November 1971. (17) R. E. Majors, 160th National Meeting, ACS, Chicago, Ill., September 1970.
Influence of Column Configuration on Performance in High Efficiency Liquid Chromatography Howard Barth, Erwin Dallmeier, and Barry L. Karger’ Department of Chemistry, Northeastern UnioerSity, Boston Mass. 021 I S The influence of coiling on HETP in high performance liquid chromatography has been shown to depend upon column (ro) and coil radii ( R J . Aluminum columns (ro = 0.95 mm), packed with Corasil I (27-35 pm) and coated in situ with 3,3’-oxydipropionitrile (ODPN), showed significant efficiency losses when coiled to a radius smaller than 13 cm; e.g., when coiled to R, = 1 cm, a sixfold increase in HETP was obtained. No efficiency loss occurred when columns of smaller tube radii (ro = 0.38 mm) were coiled down to R, = 1 cm. Larger diameter columns (ro = 2.4 mm), when coiled (R, = 2.4 cm), gave a fourteenfold increase in HETP. Also column geometries in which the direction of coiling was alternated (figure “8” and ‘5”configurations) gave no efficiency loss when compared to straight columns. Experiments have shown that peak broadening due to coiling in figure “8” columns depends on the extent of lateral mass transfer.
IN HIGH SPEED LIQUIDCHROMATOGRAPHY, it is often desirable to alter the geometry of a long straight analytical column into a compact configuration so that small thermostated baths can be employed. However, as Giddings has shown (1-3), coiling chromatographic columns can have a detrimental effect on efficiency. In a coiled column, a molecule near the inside bend advances more rapidly than one near the outside for two reasons: the shorter path length as well as the higher velocity on the inside. The higher velocity Author to whom reprint requests should be sent. (1) J. C. Giddings, J . Clironwirogr., 3, 520 (1960). (2) J. C . Giddings, J . Gas Chromatogr., 1, 38 (1963). (3) J. C. Giddings, J . Clironiurogr., 16,444 (1964). 1726
results from the inside and outside paths of the bend having different lengths but the same pressure drop. Because of this, the pressure gradient is greater for the shorter, inside path ( 4 ) . A concentration profile is thus set up across the bend, resulting in band broadening and poorer efficiency. The extent of efficiency loss will be dependent on the rates of lateral mass transfer due to diffusion and flow. The influence of coiling on HETP for packed analytical columns in gas chromatography has been found negligible (5-7) because of the high diffusion coefficients of solutes in the carrier gas. The high diffusivity of the solute in the gas phase increases lateral mass transfer and thereby relaxes the concentration profile between the inside and outside bend caused by coiling. In liquids, however, the diffusivity in the mobile phase is about 105 times smaller than in gases; hence, one would expect a much greater influence on HETP by coiling in liquid chromatography. There have been several conflicting reports in the literature on the effect of coiling on efficiency using packed liquid chromatographic columns. Scott et al. (8) and Kirkland ( 9 ) obtained significant increases (up to a factor of 9 (8))in HETP (4) J. C. Giddings. “Dynamics of Chromatography,” Marcel Dekker, New York, N. Y . , 1965, p 213. ( 5 ) E. Bayer, “Gas Chromatography,” Elsevier, Amsterdam, 1961, p 18. (6) R. Villalobos, J . Gus Cliromutogr.. 6, 367 (1968). (7) “Vapor Phase Chromatography,” D. H. Desty, Ed., Academic Press, New York, N. Y . ,1957. (8) R. P. W. Scott, D. W. J. Blackburn, and T. Wilkins, J . Gas Cliromatogr., 5 , 183 (1967). (9) J. J. Kirkland, J . Chrornatogr. Sci.,7, 361 (1969).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 11, SEPTEMBER 1972
on coiling. Both claimed that the increase in HETP was due to a deformation of the packing density upon coiling. Kroneisen (10) on the other hand, reported only a 3@-40% increase of HETP on coiling, and suggested that the large loss in efficiency observed by Scott may have been due to mechanical breakage of soft diatomaceous earth particles. Halasz and Naefe ( 1 2 ) obtained an increase in HETP using coiled stainless steel columns but found no influence on efficiency when using coiled copper columns, in contradiction to Scott and Kroneisen who both used copper tubes. While all these results may at first seem conflicting, it should be pointed out that other factors, besides column and coil diameter, can influence HETP in coiled columns-e.g., the diffusion coefficient of the solute in the mobile phase, the type of solid support and stationary phase, the per cent loading of stationary phase (7), and the technique used in packing the column. Since completion of this work, it has come to our attention that coiled packed columns of porous glass (d, -50 pm) for use in gel permeation chromatography exhibit 40% loss in efficiency (ro = 4 mm, R, = 5.1 cm) (12). However, by using a column with a smaller tube radius (ro = 2.4 mm) and with the same coil radius (R,= 5.1 cm), no loss in efficiency was observed. These authors also studied other column configurations, which we will refer to later in the Results and Discussion section. When open tubes are used in liquid chromatography, an increase in efficiency is obtained on coiling (13, 14). Koutsky and Adler (15) have studied in detail the effect of axial dispersion on coiling open tubes of various column and coil diameters using a liquid mobile phase and have also noted a large decrease of band broadening. This decrease in coiled open tubes is caused by increased lateral mass transfer due to secondary flow (15-19). Secondary flow can be described as a flow perpendicular to the axial fluid stream produced by the action of centrifugal force in a curved tube. This force causes fluid streamlines to be displaced outwardly in a lateral direction. An increased pressure results at the outer bend, causing the fluid to be continuously recirculated toward the inside bend by flow along the walls. As shown in Figure l A , the flow actually divides into two symmetrical circulation patterns. Secondary flow thus decreases band broadening caused by velocity and length inequalities (see Figure 1B) by increasing lateral mixing. Johnson (20) attempted to use secondary flow to reduce band broadening by coiling large diameter (5-cm i.d.) packed columns and operating at high Reynold’s numbers; however, he was unsuccessful in reducing HETP upon coiling. It seems reasonable that in packed columns, where the transcolumn permeability is much lower than in open tubes, ( I O ) A. Kroneisen, Ph.D. Thesis, Universitat Frankfurt/Main, Germany. 1969. (1 I ) I. Halasz and M. Naefe, ANAL.CHEM., 44,76 (1972). (12) L. R. Whitlock, R. S. Porter, and J. F. Johnson, private communication: paper presented at the 163rd National Meeting, ACS. Boston. Mass., April 1972. ( 1.7) C. G. Horvath. B. A. Preiss, and S. R. Lipsky, ANAL.CHEM., 39. 1423 (1967). (14) I . Halasz a’nd P. Walkling. Ber. Birriseirges. Pliys. Cliem., 74, 66 (1970). (15) J. A. Koutsky and K. J. Adler, Cui?.J . Clzem. Eiig., 43, 239 (1964). (16) R. Tijssen. C/rroiircrtogrcr/,/iricr,3, 525 (1970). (17) W. R. Dean. Phi/. M q . , 4,208 (1927). (18) Ihitl.. 5, 673 (1928). (19) M. Adler. Z . A r g e w . M c d r . Meclr.. 14, 257 (1934). (20) G. W. Johnson, 1’h.D. Thesis, Rensselaer Polytechnic Institute. Troy. N. Y..1967.
OUTER BEND
A, SECONDARY FLOW
#
OUTER
w INNER
6, VELOCITY INEQUALITIES IN ACOlL
Figure 1. A . Secondary flow in coiled open tubes B. Velocity inequalities set up in a coiled tube
secondary flow is reduced and therefore plays a less important role than velocity and distance inequalities. However, it does not follow that its role is nonexistent. The purpose of this paper is to examine in detail the influence of column configuration in high performance liquid chromatography. Small diameter porous layer beads (Corasil I) coated with 3,3 ’-oxydipropionitrile (ODPN) have been selected for the packing material. When this type of support is used, peak broadening depends mainly on mobile phase mass transfer effects (21). As described above, the increase in HETP due to coiling is a result of processes occurring in the mobile phase; hence, this column packing should be particularly sensitive to this effect. Since good column reproducibility in HETP was obtained (22), columns were packed with dry support and coated in siru by passing through heptane saturated with ODPN [i.e., steady state columns (21)]. To help facilitate coiling, aluminum columns were used which have been shown to be as efficient as other column tubular materials such as seamless stainless steel (22) using heptane as mobile phase and Corasil I coated with ODPN. EXPERIMENTAL
Apparatus. The high pressure liquid chromatographic system is shown in Figure 2. A three-head membrane pump (Orlita, West Germany, Model M3S4/4) was connected to a reservoir consisting of a two-liter flask thermostated to 25.0 + 0.1 “C using a Haake Constant Temperature Circulator Bath (Polyscience Corp., Evanston, Ill., Model NBS). A pressure controller (23) was operated in parallel with the (21) B. L. Karger, H. Engelhardt, K. Conroe, and I. Halasz, “Gas Chromatography, 1970,” R. Stock and S. G. Perry, Ed., Institute of Petroleum, London, 1971, p 112. (22) B. L. Karger and H. Barth, A n d . Lett., 4,595 (1971). (23) G. Deininger and I. Halasz, J. Clirornarogr., 60, 65 (1970).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 11, SEPTEMBER 1972
1727
TO RESERVOIR
0-600 PSI GAUGE
0-5000 PSI GAUGE
Q
-
ANALYTICAL COLUMN
PRECOLUMN
I
Figure 2. Schematic diagram of chromatographic system
TO REFERENCE CELL OFDETECTOR
RESERVOIR
-1
I
REGULATOR
and removed by opening the valve. Both the analytical and precolumn were thermostated with a water jacket using the Haake constant temperature circulating bath. A Hewlett-Packard strip chart recorder (Model 7127A) was employed. Injections were made using a commercial injector (Waters Associates, Model 904) with a 5-pl high pressure syringe (Hamilton Co., Whittier, Calif., Model HP305SN). Columns and Reagents. The precolumn was constructed from 40 cm of 0.46-cm i.d. stainless steel tubing, containing 3 5 z ODPN (Eastman Organic Co.) on 54-74 pm Porasil D (Waters Associates, Framingham, Mass.). The solid support used in the analytical column was Corasil I, 28-37 pm, which was cleaned before each packing by boiling for several hours in a nitric-sulfuric acid mixture (1 :9). After washing with deionized water, the support was dried for twelve hours at 200 "C. The same packing material was used many times over. The fact that retention times and efficiencies were quite reproducible from column to column, indicates that the washing procedure did not change the characteristics of the support surface. The washed support was packed into 100-cm columns previously cleaned with acetone followed by methylene chloride and then dried with nitrogen. Only 70-cm lengths of 4.8-mm i.d. columns were used since not enough packing material was available to fill 100-cm columns. Various methods of packing were tested, and the most efficient columns were made by adding small amounts (0.3 ml) of dry support with vibrating and tapping the column. The packing procedure for the pre-coiled columns will be discussed later. The Corasil was coated in situ by passing through the column 600-800 ml of heptane saturated with ODPN. This procedure gives a reproducible steady state 1.1 w/w coating of ODPN (21). Column tubings were 4.8-mm and 1.9-mm i.d. aluminum (Altech Associates, Arlington Heights, Ill.), and 0.76-mm and 2.1-mm i.d. stainless steel (Analabs, North Haven, Conn.). The sample size was 2 p1 of 3 mg/ml concentrations of each of the following solutes: toluene, benzyl alcohol, and phenol, dissolved in heptane. The mobile phase consisted of heptane saturated with ODPN. The heptane (Baker Chemical Co., Baker Grade) was purified by mixing it with sulfuric acid for 48 hours, washing with water and then 1N NaOH. It was then dried over KOH pellets and distilled at 98-99 "C.
I
00
.4
.8
1.2
1.6
2.0
2.4
v, cm/aoc
Figure 3. HETP U S . velocity for toluene ( k ' = 0), benzyl alcohol ( k ' = 2.6), and phenol (k' = 7.7) on Corasil I(28-37 pm) coated with 1.1 ODPN using 100-cm straight aluminum column (1.9-mm i.d.)
z
pump. As described previously (23, 2 4 , the liquid pressure was adjusted by applying a back pressure to the controller from a nitrogen tank with a high pressure regulator (Harris Co., Cleveland, Ohio, Model 87-25OOA). Using this controller, it was possible to maintain a constant pressure to better than i1 The controller also served as a pulsation dampener and safety valve. A micro-metering valve (Whitey Research Tool Co., Emeryville, Calif., Model 21RS4) was used to by-pass the solvent stream into the reference cell of a UV detector (Ldboratory Data Control, Riviera Beach, Fla., Model 1205, UV monitor-254). During operation, stagnant eluent was kept in the reference cell and was periodically flushed by opening the needle valve. (Recent experiments have shown that lower base-line drift results from a slow bleed of N, through the reference cell; however, for this work drift was not a problem using a stagnant mobile phase mode.) A 5-pm Teflon (Du Pont) filter (Millipore Corp., Bedford, Mass., LSWG04700) in a high pressure filter holder (Millipore Corp., XX45 04700) was placed in the high pressure supply line. To prevent gas bubbles from entering the precolumn and analytical column, a trap was installed as shown in Figure 2, consisting of a two-way valve attached to four feet of glass tubing extended vertically from the supply line. During operation, bubbles could be trapped in this extension
z.
(24) I. Halasz, A. Kroneisen, H. 0. Gerlach, and P. Walkling, Fresenius' 2.Anal. Chem., 234,81 (1968). 1728
z
RESULTS AND DISCUSSION
Figure 3 shows a typical HETP US. velocity curve using a lOO-cm, 1.9-mm i.d. aluminum column. The capacity factor of toluene was zero while for benzyl alcohol and phenol it was 2.6 and 7.7, respectively. The use of toluene as an unretained peak was checked by comparing its retention to that of npentane using a refractive index detector. Both retentions agreed within 1-2z. Although the capacity factors were
ANALYTICAL CHEMISTRY, VOL. 44, NO. 11, SEPTEMBER 1972
Influence of Coiling on HETP at 1cm/sec for 1.9 mm i.d. Aluminum Columns, L = 100 cm, T = 25 "C, Corasil I, dp = 28-37 pm, Steady State Column-1.1 w/w ODPN HETP, mm Coil radius, cm Number of coils Toluene, k' = 0 Benzyl alcohol, k' = 2 . 6 Phenol, k' = 7.7 0.90 i 0.09 0 . 4 4 f 0.04 0.96 f 0.08 Straight
Table I.
z
1 3
13 4.5
Straightened Straight 4.5
3 13
1 Straightened Straight 2.25
6
Straight 2.25
6
Straight 2.25
6
Straight 1
13
Straight 1
13
Straightened Straight 1
0.94 f 0.08 1.22 C 0.09 0 . 8 4 i 0.09 1 .oo C 0.10 1.18 i 0.11 2.83 f 0.28 0.89 i 0.08 1.25 f 0.10 2.23 i0.14 1.25 f 0 . 0 6 1.99 i0.21 1.02 i0.09 1.83 i 0 . 1 0 1 . 2 1 i0.11 2.73 i 0.11 1.19 1. 0.19 2.80 f 0.47 1.22 f 0.06 1.01 i 0.09 2.77 i 0.30
0.50 f 0.04 0.76 f 0.09 0.36 f 0 . 0 5 0.46 i 0 . 0 4 0.78 i 0.09 2.79 i 0.20 0.44 i0.04 0.54 f 0 . 0 4 1.75 i 0 . 1 4 0.59 f 0 . 0 6 1.64 C 0.09 0.44 =t0.05 1 . 6 5 =k 0.15 0 . 4 6 C 0.04 2.44 i 0.14 0.51 i 0.07 2.78 f 0.17 0.47 f 0.06 0.45 i0.06 2.45 =k 0.23
13
0.86 i0.07 1.14 i 0 . 1 0 0.78 f 0.08 0.93 i 0.10 1 . 1 0 i0.14 3.00 C 0.27 0.84 i 0.07
1 . 2 5 C 0.08 2.45 f 0.38
I
BENZYL ALCOHOL (ki=2.6d 3.2
TOLUENE ( k ' = O )
/
..-
2.8
--.-
.__ c --- Ro*lcm
2.4 I
E 2.0
E.
I
1.6
/'
Figure 4. HETP c's. velocity for toluene (k' = 0) and benzyl alcohol ( k ' = 2.6) using 100-cm aluminum column (1.9-mm i.d.) of different coil radii (&). Columns were packed with Corasil I(28-37 lm) coated with 1.1 ODPN
z
1.2 0.8 STRAIGHT AND Ro* 13cm
0.4
0
I
0.4
I
I
0.8
1.2
1.6
2.0
I
I
0 2.4 v, c m l s s c
0.4
0.8
different, HETP for benzyl alcohol and phenol did not vary greatly. This indicates that mass transfer in the mobile phase, rather than in the stationary phase, is the dominant cause of peak broadening, as expected (21). The influence of coiling on HETP is shown in Figure 4. Column efficiency decreased significantly when the coil radius was less than 13 cm, using 1.9-mm i.d. columns. At a coil radius of 1 cm, the HETP of toluene increased by about sixfold and that of benzyl alcohol and phenol by about threefold. Table I presents some experimental HETP values at constant velocity as a function of coiling 1.9-mm i.d. columns. The relative standard deviation of HETP, as calculated by triangulation, was about 10% for three to six injections and column to column reproducibility in packing and coiling was also about 10% (however, in some cases it was as high as 18%). It is interesting to note that when coiled columns of poor efficiency were straightened, the columns were at least as efficient as originally before coiling. These results on restraightening columns agree with those found in an inde-
1.2
1.6
2.0
2.4
pendent study of the influence of coiling in GPC using 50-pm porous glass beads (12). To show that the changes in HETP in Figure 4 are due to column configuration, 1.9-mm i.d. columns were precoiled to a coil radius of 1 cm. These columns were then packed by vibration and suction from a vacuum line attached at the end of the column. Within experimental error, there was no significant difference of HETP obtained with precoiled columns as compared to columns packed and then coiled. A stainless steel column (2.1-mm i.d.) with a coil radius of 1 cm had the same efficiency as aluminum columns of the same coil radius. When this stainless steel column was straightened, the efficiency was also the same as in the original straight column. Hence, the effect of coiling on HETP appeared to be independent of column tubular material using Corasil I as the solid support. Since there was some indication in Table I of improved efficiency when the coiled columns were restraightened, a single aluminum column, 1.9-mm i d . , was coiled (R,= 1 cm)
ANALYTICAL CHEMISTRY, VOL. 44, NO. 11, SEPTEMBER 1972
1729
Table 11. Continuous Straigthening and Coiling (R, of a 1.9-mm i.d. Packed 100-cm Aluminum Column a t v = 1cmjsec (AI 2 x 2
I B I 3x3
Straight Coiled Straightened Coiled Straightened Coiled Straightened
HETP (mm) -
=
1cm)
Toluene
Benzyl alcohol
Phenol
0.46 i 0.04 2.44 -C 0. I4 0.31 i 0.02 1.84 j=0.14 0.29 i 0.04 2.18 i 0.22 0 . 2 6 C 0.05
I .21 i 0 . I 1 2.73 _L 0.11 0.96 I 0.06 2 . 0 0 f 0.11 0.81 i 0.07 2.21 = 0.01 0 . 7 0 i 0.07
1.25 =t0.08 2.53 I 0.38 1 .OO f 0.01 2.01 f 0.33 0.85 i 0.07 1.88 i 0.12 0.69 i 0.02
IC) 6 x 6
Figure 5. Coil configuration using 100-cm aluminum columns (1.9-mm i.d.) N.B. These are coiled to a small volume in
actual practice. The coils are expanded in the diagram for clarity
and straightened several times. As shown in Table 11, HETP of the final straightened column decreased by about 40% as compared to the original straight column. This final column was highly deformed and following the arguments of Halasz and Walkling (14), who obtained a tenfold decrease of HETP in distorted open tubes (coiled, twisted, and squeezed) as compared to a straight tube, this improved efficiency may be due to increased radial mass transfer caused by a continually changing flow pattern. Alternatively, small changes in the packing density might have occurred in the deformed column, resulting in an improved mobile phase transfer. In addition, it should be pointed out that a decrease of HETP was also observed in the distorted coiled columns, indicating that this increased radial mixing helped compensate somewhat for the velocity and distance inequalities generated in coiled packed columns. Peak broadening in coiled 4.8-mm i.d. columns, as shown in Table 111, gave a threefold increase in HETP for 10.5-cm coil radius and a twelve- to fourteenfold increase for a 2.4cm coil radius. The HETP values obtained for retained components in the wide diameter coiled columns were so great that significant peak asymmetry resulted. We therefore have reported only the results for the unretained componenttoluene. It is reasonable t o assume that transcolumn relaxation of velocity and distance inequalities set up in coiled columns took place to a much less extent in large diameter columns. As seen in Table 111, no significant change in efficiency was observed in coiled 0.76-mm i.d. stainless steel packed columns. The large HETP values for toluene as compared to the retained components were probably due to extracolumn effects. These dead volume effects mainly resulted in the connection between the column and the detector and from the difficulty of injecting into the small bore of the column. The conclusion from Table I11 is that small diameter columns can be safely coiled without loss of efficiency, while it is not advisable to coil large diameter columns. It is not possible to give a definite column diameter a t which no influence due to coiling would occur, for the value will depend on the mobile phase velocity, particle diameter, packing material, and coil radius, along with other factors. However, 1730
narrow tubes and large coil radii will in general diminish the influence of coiling on column efficiency. From the experiments on precoiling and straightening of coiled columns, as described above, it was apparent that zone spreading in coiled columns was not caused to any major extent by the disruption of the packing structure. Turbulence was also negligible since Reynold’s numbers were only about 0.6 at 1 cmisec, and the onset of turbulence occurs at about Re > 10 €or packed columns in liquid chromatography (25). Due to the velocity and distance inequalities between the inside and outside bend, a “slanted” concentration profile will result. It should be mentioned, however, that this profile need not be linear but could be some type of distorted parabola, depending on the transcolumn velocity profile of the straight column. In Tijssen’s model for coiled open tubes (16), the concentration profile is slanted in the opposite direction; ;.e., the molecules near the outside bend are ahead of those in the inside bend because of secondary flow. But since there is a continuous transfer of molecules from one bend of the column to the other with secondary flow, there is no additional zone spreading. In fact, it has been experimentally shown (13-15) that at high velocity, efficiency is better in a coiled open tube than in a straight column because of increased radial mixing. A method which can be used to relax the concentration profile in coiled packed columns is to alternate the inside and the outside bends. In this manner, a slanted profile, which was generated in the first coil, would be reversed in the second loop coiled in the opposite direction. Assuming little or no lateral mixing, the concentration profile at the end of the second coil would be approximately uniform across the column. This alternation would be continually repeated as the solute passed through the coils, and peak broadening due to coiling would be negligible. To test these ideas, columns were coiled into various configurations (see Figure 5), and the results are given in Table IV. As seen in this table, 1.9-mm i.d. columns with twelve alternating loops of coil radius 1 cm (i.e., figure “8” geometry) gave efficiencies equivalent t o straight columns in agreement with the above simple model. Consequently, columns of this i.d. can be safely coiled to a compact form with no loss of efficiency. A less compact geometry was achieved by bending columns into an “S” pattern with each coil having a radius of about 1 cm. These columns were also as efficient as straight ones. Similar trends with figure “8” and “S” columns were observed in GPC using wider diameter columns and larger particle sizes of porous glass ( I 2 ) . (25) I. Halasz and P. Walkling. J . C/rromcr/ogr.Sci., 7, 129 (1969).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 11, SEPTEMBER 1972
Table 111. Influence of Coiling on HETP for Different Tube Diameters Corasil I, c/, = 28-37 pm, Steady State Column-1.1% w/w ODPN, v = 1 cm/sec, T = 25 “C A . Tube diameter = 4.8-mm i.d.; L Coil radius, cm Number of coils Straight
10.5 2.4
=
70 cm
Toluene, k ‘
Coil radius, cm Straight
4
2.25 1
1 4 = 0.76-mm id.; L Number of coils
6 13
Straight I
13
0
0.59 + 0.08 1.63 rt 0.11 8.65 f 0.42 0.60 f 0 . 0 5 1 . 6 0 f 0.16 7.39 i 0 . 6 2
1
Straight 10.5 2.4 B. Tube diameter
=
=
100 cm
Toluene, k‘
Benzyl alcohol, k ’
= 0
1.69 i 0.19 1.33 i 0 . 2 2 1 . 2 7 f 0.15 1.36 i 0.16 1.46 i 0.18
Whether or not figure “8” and “S” shaped columns result in loss in efficiency is dependent on the extent of lateral mixing. Very rapid lateral mass transfer may provide sufficient mixing so that the Concentration profile expected from a coil may not develop. In such a case, columns of the same efficiency as a straight column would result. On the other hand, very slow lateral mass transfer may provide little or no radial mixing as the band traverses a loop. In such a case, the “slanted” profile will result. When this slanted profile reaches the next coil which is looped in a n opposite direction for the figure “8” column, the distance and velocity inequalities become reversed. The solute on the inside track from the first loop slows down and the solute on the outside track speeds up in the second loop. Compensation results so that the concentration profile leaving the second loop is not slanted and minimal broadening due to coiling takes place. In this case, figure “8” columns would be as efficient as straight columns (cf. Table IV). For a n intermediate rate of lateral mass transfer, a partial relaxation of the “slanted” profile will occur (cf., the slow mass transfer case). Reversal of the inside and outside bends will now not result in complete compensation, because many solute molecules will have exchanged lateral positions in their travel through the coil. (N.B. If the molecules exchange completely, as in the fast lateral mass transfer case, the influence of the coil is negligible.) In this case, figure “8” and “S” shaped columns would be less efficient than straight columns. This model can be tested for a given rate of lateral mixing by varying the time available for radial mass transfer. This can be done by changing the number of loops in one direction before reversing the coils. In Table IV, we show the HETP results obtained for 3 column configurations: (a) 2 X 2 [i.e., 2 loops (R, = 1 cm) in one direction, then 2 loops in the opposite direction]; (b) 3 X 3 ; and (c) 6 X 6 (see Figure 5). For R, = 1 cm, a total of 12 loops is possible in a 100-cm column, so for column (a), the 2 X 2 configuration is repeated 3 times, the 3 X 3 configuration ( h ) is repeated 2 times, and the 6 X 6 occurs only once. For columns (a) and (h), HETP values higher than a straight column are obtained (Table IV), while for column (c), HETP values are significantly greater and indeed are similar to those for the analogous coiled column (Table I). For the 6 X 6 column, it is clear that there is sufficient time for lateral mixing t o occur during the solute travel
=
2.6
7.7 0.79 i 0.07 0 . 8 1 + 0.03 0.76 i 0.02 0 . 8 0 & 0.08 0.80 0.03
Phenol, k‘
0.85 =k 0.08 0.88 i 0.11 0.86 f 0.01
=
*
Table IV. 100-cm Packed Aluminum Columns (1.9-mm i.d.) Coiled to Figure “8” Geometries (R, = 1 cm), Corasil I, d, = 28-37 pm, Steady State Column-l.l% wjw ODPN, v = 1 cm/sec, T = 25 “C HETP, mm .Toluene. Benzyl alcohol. I’henol. Geometry X’ = 0 h’ = 2.6 h’ = 7 . 7 ~~
Straight “8”
Straight
2 x 2 loops repeated three times Straight 3 x 3 loops repeated twice
Straight 6
x 6 loops
0.56 + 0.04 0.59 1 0 . 0 5 0.49 .k 0 . 0 6
1 . 1 3 zz 0 . 0 7 1 . 0 3 -L 0.08 1.15 z 0 . 1 5
1 .20 i 0.08 0.53 + 0.05
1 .59 -= 0 . 2 0 0.93 x 0.02
1.24*0.14 0.51 i 0 . 0 4 2.53 0.10
1.34i0.20 1.03 & 0.20 2.73 0.32
1.05::1 0 . 0 8 0.98 :t 0.08
*
through 6 loops. The band entering the 7th coil ( i . c . , the first loop in the opposite direction) will thus be broader at any point across the tube than a band which traveled the same distance in a straight column. It should also be pointed out that the concentration profile at this half-way point in the column will be much less “slanted” than that of a band in which lateral mass transfer is minimal. Little or no compensation can then occur in the 6 loops coiled in the opposite direction. In addition, the band will experience similar broadening to that which took place in the first half of the column, the final result being a column whose efficiency is similar to a fully coiled column. For both the 3 X 3 and 2 X 2 columns, full compensation of the concentration profile in the oppositely coiled loops does not occur. Only for the figure “8” (i.e., 1 X 1) column does full compensation take place. From an understanding of the processes involved in lateral mass transfer in a loop, it should be possible to estimate those conditions under which figure “8” and “S” shaped columns have equivalent efficiency to straight columns. In Table V, we present HETP values of toluene due only to coiling for 1.9- and 4.8-mm i.d. columns of different coil radii. These values were computed by considering the total variance of a coiled column (utot.,l*) to be the sum of the
ANALYTICAL CHEMISTRY, VOL. 44, NO. 11, SEPTEMBER 1972
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Table V. Influence of Coiling on HETP Using Different Column and Coil Radii, L; = 1 cm/sec, T = 25 OC, Corasil I, d p = 28-37 bm, Steady State Column = 1.1% w/w ODPN y o . cm R,, cm Hcoil,amm
a
0.095 0.095 0.095 0.095 0.24 0.24 Equation 2.
2.4 1.4 0.4 0.1 1.1 8.5
1
2.25 4.5 13 10.5 2.4
variances generated by the original straight column (uSt2) and by the effect of coiling ( U ~ ~ ~ I ~ ) . gcoil’ = ctotsl’
- st*
(1)
or, Hcoil
=
(H- HBt)
Lst ~
Lcoil
(2)
where H is the total value obtained from the coiled column, Hst is the peak broadening contribution of the straight column, LSt is the length of the original straight column (70 cm for the 4.8-mm i.d. columns and 100 cm for the 1.9-mm i.d. columns), and Lcoil is the length of the coiled portion of the column (between 61 and 66 cm for the 4.8-mm i.d. columns and between 83 and 90 cm for the 1.9-mm i.d. columns). The HETP values shown in Table V represent averaged values calculated from Tables I and 111. Note that the same column is used to obtain the values of H and Hst (Le., the straight column is coiled to obtain H ) . Two lateral mass transfer mechanisms have been suggested by Giddings (2,26) by which the concentration profile resulting from coiling can be relaxed: diffusion and flow (convection). If band broadening in coiled tubes is the result of slow lateral diffusion, then (2), (3) where L; is linear velocity, ro is the column radius, R, is the coil radius, DM is the diffusion coefficient of the solute in the mobile phase, and y is the obstruction factor to account for the tortuous diffusive paths (-0.6). HDrepresents the plate height contribution to coiling due to this slow lateral diffusion. If lateral mass transfer is limited by flow, then the plate height contribution is (26): (4) where m = 2 ro/dp,dp is the particle diameter. This equation is only approximate, since it is assumed that the lateral movement of one particle diameter occurs on the average after the (26) J. C. Giddings, “Dynamics of Chromatography,” Marcel Dekker, New York, N. Y . , 1965, p 52.
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flow stream has traversed 20 particle diameters. Indeed, it is not altogether certain whether lateral relaxation due to flow takes place (26). For both Equations 3 and 4, H depends on ro4/Ro2. We can test this functionality qualitatively in Table V. The striking point is that for the same coil radius, Hcoilshould be a factor of 35 greater for the 4.8-mm i.d. column. However, for the wider tube, Hcoilis found to be only 6-fold larger. In addition, Heoilseems to depend on Ro-2 for the 13-, 4 . 5 , and 2.25-cm coils with the 1.9-mm i.d. column. Nevertheless, Hooilfor the 1-cm coiled column is only 1.7 times larger than that for the 2.25-cm coiled column where a factor of 5 is expected. A possible explanation for these discrepancies is the presence of an additional lateral mixing effect caused by secondary flow (15, 16). Tijssen (16) has derived an equation for the diffusion coefficient (D,*) due to secondary flow in an open tube where D,*is directly proportional to r 0 3 / 4and inversely proportional to RO1i4. In a packed column, secondary flow would be expected to be much smaller than in an open tube (20). Since the diffusion coefficient of liquids is so small [e.g., 3.7 X cm2/secfor toluene inn-heptane at 25 OC (27)], secondary flow could still enhance mixing in the packed bed. This could account for the lower dependency of Hc0il on ro4/RO2 (Equations 3 and 4). Therefore, it seems reasonable to assume that secondary flow might play a role in reducing band broadening in packed coiled columns. CONCLUSIONS
From the results, certain general conclusions can be drawn. First, the influence of coiling on column efficiency is increased as the tube radius is increased or the coil radius is decreased. In fact, when a column with 0.76-mm i.d. was used, no loss in efficiency was observed even for coils of very small radii (1 cm). Alternative shapes to coiling can be used without loss in efficiency (in comparison to straight columns), if it is desirable to utilize the column in a compact form. Shapes in which the inside and outside bends alternate from one loop to the next can often be successfully employed. Again, however, no hard and fast rules on dimensions can be given, without a better theoretical model. It is clear that while figure “8” and “S” shaped columns have resulted in no loss in efficiency over straight columns, there will be conditions for which these columns may give loss of efficiency. ACKNOWLEDGMENT
The authors would like to thank Armin Haag for discussions on this subject. RECEIVED for review January 11, 1972. Accepted May 16, 1972. Presented at the 161st National Meeting, American Chemical Society, Los Angeles, Calif., April 1971. The authors wish to acknowledge the support of NIH under grant GM15847. B. L. Karger is an Alfred E. Sloan Fellow, 19711973. (27) C. R. Wilke and P. Chang, AICIiE J., 1, 264 (1955).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 11, SEPTEMBER 1972
