system. This technical problem should, however, be easily solved. In Table I are given results obtained for carbon monoxide concentrations in laboratory air with the instrument operating without the time derivative attachment. These results are typical of the measurements which can be made with this apparatus.
Organization (WMO). In the near future, we should be able t o evaluate the minimum amount of carbon monoxide which can be measured accurately with this technique. From the chromatograms obtained on air samples, it seems possible that methane could also be measured at the same time as carbon monoxide. Further investigations of these possibilities are proceeding.
DISCUSSION
ACKNOWLEDGMENT
From the results obtained to date with this instrument, it seems feasible t o measure on a routine basis the concentration of carbon monoxide in uncontaminated air and in air samples taken at base-line stations of the World Meteorological
We thank Howard Chung for the art work.
RECEIVED for review July 15, 1971. Accepted September 7, 1971.
Influence of Column Parameters on Peak Broadening in High Pressure Liquid Chromatography Istvan Halasz and Manfred Naefe‘ lnstitut f s r Angewandte Physikalische Chemie der Unioersitbt Saarbriicken, West Germany Brush type stationary phases were produced by esterifying silica, gel with polyethylene glycol (PEG) 200. Two methods of column packing are described, for particle sizes greater and less than 50 I.(, The relative peak broadening h was measured with n-heptane eluent in the linear velocity range between 0.3-5 cm/sec at 26 O C . The influence of column coiling on h depends on the material of construction of the tube and upon the properties of the support. Unexpectedly large errors i n the measurement of h VI. u plots are discussed. A simple method for the measurement of the holdup time f, with UV detectors i n routine work is proposed. The total porosity (6, = 0.71) of our support i s independent of the variations between batches of the particle size d,. The permeability K for this porous support is adequately expressed by K = d,2/ 2000. In the measured velocity range, h = A CU is a good approximation. The constants A and C (and their standard deviations) are calculated. The h VL. u plot i s independent of the column length (L = 25-400 cm) with a sieve fraction of 80-90 p. The influence of the column diameter/particle size ratio on efficiency i s treated. With the conventional column packing methods, the regular packed ones (d,/d, > 10) are to be preferred. The permeability and efficiency are only slightly influenced by the width of the sieve fraction as long as the deviation from the arithmetic mean is smaller than approximately 40%. It is shown, that in the equation h = Dd,@ the constant p is independent of the linear velocity, and of the nature of the sample. The numerical value of p is equal to 1.8 & 11%for different sieve fractions (where d , > 50 p and u = 0.5-5 cm/sec), if 50 p > d, > 20 p, p becomes equal to 1.5 =t 10%. In those sieve fractions where d p is equal to 10-20 p , p becomes zero. The influence of the particle size on the efficiency and on the speed of analysis is discussed quantitatively.
+
SINCE1967, THE USE of liquid chromatography with inlet pressures of up to 500 atm has increased rapidly. The influence of column packing and of column parameters has been experimentally examined (1-13). The results reported 1 Present address, Farbwerke Hoechst AG., Frankfurt/MainHoechst.
(1) D. S. Horne, J. H. Knox. and L. McLaren. Seaaration Sci.. 1, 531 (1966). (2) R. P. W. Scott, D. W. J. Blackburn, and T. Wilkins, “Advances in Gas Chromatography 1967, New York,” A. Zlatkis, Ed., Preston, Evanston, Ill., 1967, p 160. 76
by different authors are in substantial contradiction. It appears that the properties of the material of construction of the tube and those of the stationary phase have a far greater influence than normally would be expected. In this paper we wish t o describe the efficiency of the column as a function of column material and coiling, method of column packing, column length L , column diameter/ particle size ratio, particle size distribution (sieve width), and particle size. A “brush” type stationary phase (14) was used, Le., silica gel esterified with polyethylene glycol 200. We intend t o describe only our experimental results, since it is questionable whether these results can be generalized and applied to all the porous stationary phases now used in high speed liquid chromatography. EXPERIMENTAL Chromatographic Apparatus. Self-built equipment was used (15). The cell column of the home-made UV detector was 4 pl and that of the differential refractometer detector (Waters Associates, Framingham, Mass., Model R 401) 10 pl. The samples were introduced with a 5-pl syringe (Hamilton Company, Whittier, Calif., No. HP 305 N). Because of the temperature dependence of the retention time and the capacity ratio k‘, a copper heat exchanger tube of 2 mm i.d. (3) L. R. Snyder, ANAL.CHEM., 39, 698 (1967). (4) J. F. K. Huber and Y . A. R. Hulsman, Anal. Chim. Acta., 38, 305 (1967). (5) J. J. Kirkland, ANAL.CHEM., 40, 391 (1968). (6) I. HalBsz, A. Kroneisen, H. 0. Gerlach, and P. Walkling, 2. Anal. Chem., 234, 81 (1968). (7) P. Walkling, Ph.D. thesis, Universitat Frankfurt/Main, West Germany, 1968. (8) J. J. Kirkland, ANAL.CHEM.,41, 218 (1969). (9) J. H. Knox and J. F. Parcher, ibid.,p 1599. (10) J. L. Waters, J. N. Little, and D. F. Horgan, J . Chromatogr. Sci., 7, 293 (1969). (11) R. L. Snyder, ibid., p 352. (12) R. P. W. Scott and J. G. Lawrence, “Advances in Chromatography 1969,” A. Zlatkis, Ed., Preston, Evanston, Ill., 1969, p 276. (13) I. HalBsz and P. Walkling, ibid.,p 310. (14) I. Halbsz and I. Sebestian, Angew. Chem. Intern. Ed., 8, 453 (1969). (15) G. Deininger and I. Halbsz, “Advances in Chromatography 1970,” A. Zlatkis, Ed., University of Houston, Houston, Texas, 1970, p 336; or J. Chromatogr. Sci., 9, 83 (1971).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
~~
~
Table I. Properties of the Silica Sieve Batch fraction, PEG moleculesj P g silica gel No. 1 50-200 4 . 0 X lozo 4 . 6 X lozo 2 25-150 3 10-50 2.8 X IOz0
Gel/PEG 200 Brush Organic Re1 retention part %, p-nitrotoluene/ by wt. benzene 13.4 7.3f 1% 15.2 7.312 8.6 18.5 i 3
Table 11. Loadability of 50-cm Columns with 2 mm i.d. Packed with Silica Gel/PEG 200 Brushes (Batch No. 1) Sample Sample size, pg n-Pentane 2,5- 500 Benzene 3,9-1000 Anthracene 0.5- 10 p-Nitrotoluene 0.15 2,6-Xylidine 3.9- 250 Phenylpropanol 100. - 650
and 5 m long was installed between the pump and the sample injection port. This heat exchanger and the chromatographic column were immersed in a water bath having a temperature control better than 10.5 “C. The coil diameter of both the column and heat exchanger tubes was 15 cm. The column temperature used for all measurements was 26 “C. Column Material. I n coiled stainless steel columns, the relative peak broadening h (or height equivalent t o a theoretical plate H E W ) showed a n increase (larger than 20%) compared to the results obtained with a straight one, possibly because the support was squeezed by the unyielding properties of steel in the process of coiling. Unchanged h values were obtained with coiled copper columns where the particle size was greater than 40-50 p , contrary t o earlier results ( 2 ) where copper columns filled with firebrick were packed by another method. For this reason copper tubes were used with noncorrosive mobile phases and samples. These columns varied in length ( L ) between 25 and 400 cm and were cleaned with 2 N HC1 and washed with water and acetone Stationary Phase. The inorganic part of the brush-type stationary phase was silica gel with a specific surface area of 370 m2/g and with a n average pore radius of 40 A. Particle sizes smaller than 50 p were prepared by grinding in a ball mill. Because of this procedure the surface properties were changed. The silica gel was treated with 2 N HC1 and afterwards washed until acid free with water. The silica gel was esterified with polythylene glycol 200 (Schuchard, Miinchen, West Germany). After sieving, the surface of the esterified silica gel was free of silica powder as could be easily observed with a microscope. The properties of 3 batches of these brushes with different features are given in Table I. Mobile Phase and Samples. The eluent was always nheptane (99%) with a viscosity of 0.38 centipoise a t 26 O C and the holdup times of the columns were determined with n-pentane. I n Table 11, minimal and maximal sample sizes are given for unchanged capacity ratios k‘ in a column with a n inner diameter of 2 mm. The loadability as defined above changes markedly with the nature of the sample. However, in Table I1 we list the samples in the order of increasing retention time. COLUMN PACKING
The term “regular packed column” shall be used for columns where the dJd, ratio is greater than 10 (16, 17).
The method used for packing columns depends on the surface properties of the stationary phase and on the particle size of the support. I n comparing different column packing methods it was assumed, that the optimum was achieved if the h/u values were minimal; no tailing effects were observed; and permeabilities of t h e column packed with our porous material were in good approximation t o K N d,*/2000 for the particle size range of d, = 10-200 p . Sieve Fraction 50-200 I.(. With our stationary phase, optimal columns were made with 10% reproducibility of the h os. u curve and permeability, using the method normal for gas chromatography (18). The ends of the column were closed with a metal (copper, stainless steel, etc.) gauze (200 mesh) crushed into ball shape. During filling, the column was vibrated a t about 60 cycles/sec while continuously adding the stationary phase. Afterward the column was tapped on the floor from a 20-cm height and then refilled. If the same method was used t o fill columns with d, < 50 p , the peaks tailed. Sieve Fraction 10-50 p . The best results were achieved with the following method: the column (i.d. = 2 mm), 25 c m long, was packed with 25 equal portions of the “brush.” After adding each portion, the column was vibrated and afterward tapped o n the floor and also vigorously with a rod from the side. The reproducibilities of the h us. u curves and that of permeabilities were again better than 10%. If the columns were coiled, the h values increased by a t least 1 0 % for a given velocity. Linear Velocity of the Eluent. The linear velocity of the eluent can be defined as u = L/t, (1) where u is the migration velocity of the mass center of a n inert sample. In liquid chromatography, the determination of the holdup time of a n inert peak f, is sometimes difficult. It is difficult t o predict if a sample will be inert or not. Sometimes it may be impossible with a UV detector t o detect a n inert peak. It is always possible, however, t o measure the flow rate F . I n a column packed with nonporous support (Le., glass beads) :
where the porosity E, is the ratio of the mobile eluent space t o the volume of the empty column. Experience has shown that in a regular packed column, with the sieve fractions usual for chromatography, eo is independent of the particle size if t h e particles are more or less spherical. In a n acceptable approximation, eo is equal t o 0.4. I n those columns packed with nonporous supports u, and u are identical. Using porous supports (Le., silica gel, alumina, Chromosorb, Porasil, etc.) 4F u=-
adc2ET
(3)
where E T is t h e total porosity, and includes t h e pore volume of t h e support. The pores of the support are filled with immobile eluent; therefore the inert sample is partitioned between the movable eluent and t h e eluent remaining in the pores. Therefore is greater than eo. In regular packed columns with porous supports, the value of E T is, a t a rough approximation, 0.7-0.8. It can be determined experimentally with u, 4Ft, ET = e o - = (4) u irdC2L ~
(16) J. C. Sternberg and R. E. Poulson, ANAL.CHEM.,36, 1492 (1964). (17) I. Halhsz and E Heine, “Advances in Chromatography, Vol. 4,” J. C. Giddings and R. A. Keller, Ed., Marcel Dekker, New York, N.Y., 1967, p 206.
(18) F. H. Huyten, W. van Beersum, and G. W. A. Rijnders, “Gas Chromatography 1960, Edinburg”, R. P. W. Scott, Ed., Butterworths, London, 1960, p 224. ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
77
Table 111. Measured and Calculated Permeabilities of Silica Gel/PEG 200 Brushes with u/u, = 0.56
Batch No. 3 3 3 3
3 3 1 1 2 2 2 1 2 1
Sieve fraction, ~1 11- 16 16- 20 20- 25 25- 30 30- 40 40- 50 57- 63 80- 90 80- 90 7&100 50-1 20 80- 90 25-150 177-200
Kexp[1O-*cm 2] 0.098 0.15 0.25 0.38 0.59 1.12 2.0 3.5 3.9 3.9 3.6 3.4 3.8 20.
d,,C1 13.5 18 22.5 27.5 35 45
60 85
85 85 85
85 87 189
Koaioda[10-8Cm2] 0.091 0.16 0.25 0.38 0.61 1.01 1.8 3.6 3.6 3.6 3.6 3.6 3.8 18.
AK
Z
+7 -6
...
...
-3 +I1 +11 -3 +8 +8
... -5
... - 10
Kcaid = (&)2/2000.
Formally uu can be calculated for a porous support, assuming eo is equal t o 0.4. On the other hand, the u/u, ratio is a column property and it is independent of the detector, if the column of the connecting tubes and that of t h e dead volume of the cell is negligible as compared t o the volume of the eluent inside the column. We determined in all of our columns the u/u, ratio to be 0.56 with a differential refractometer. Consequently, the total porosity eT was equal t o 0.714. These values were independent of the batch and of the particle size of the support. All other measurements were made with a UV-detector. Because the u value includes the column characteristic e T , only this parameter shall be used t o describe the linear velocity of the eluent. Another reason is that u is a n inverse function of the holdup time (Equation l), which itself is an important parameter if the capacity ratio k’ and the relative retention cy are calculated. The Holdup Time t o was determined from the measured flow rate F, with u/u, equal to 0.56 by: L 1.79ae,Ldc2 0.562Ldc2 t 0 -- uv -L - = 1.79- = - -~ ~ u UV UV 4F F
(5)
Specific Permeability Value K is one of the most important parameters in high speed liquid chromatography. Its magnitude determines the maximum column length (Le., the maximum resolution) which can be achieved with a given velocity, a given pressure drop, and a given eluent. The permeability of a regular packed column is only a function of the particle size d, of the support. The permeability is defined here by the integrated form of the Poisseuille equation
I n Table 111, the experimentally determined and calculated permeabilities (and their deviation in %) are shown for different batches and different sieve fractions. It seems t o be that
K dp2/2000 (7) is a n excellent approximation for porous supports. The maximum deviation is about lo%, the average deviation is only =k2% (which of course is accidentally small in this case). Equation 7 gave a good approximation in other experiments using heavy loaded columns (19) where Porasil or silica gel supports were used. N
(19) I. Halhsz, H. Engelhardt, J. Asshauer, and B. L. Karger, ANAL. CHEM.,42, 1460 (1970). 78
ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
Discussion of the h ES. u Curves. In this paper, the linear velocity of the eluent was 0.3-5 cmjsec. In this velocity region, the empirical equation
h=A+Cu (8) was a good approximation-Le., the linear diffusion term Bju of the van Deemter equation was negligible. The coefficients of Equation 8 and tneir standard deviations were calculated from the measured h and u pairs using a linear regression program. Each h/u pair was measured at least three times. Error of Measurement and That of Calculation. The following are the maximal errors in the measurements and calculations used in this work. It is difficult to compare these limits with other work in the literature, because such values are not always given. Errors of the inlet pressure determination up to 5 % were obtained even though a precision manometer (0.6% full scale) was used. The maximum deviation of the calculated holdup time to (between 0.5 and 5 minutes) was 5%, using Equations 1 and 5). Three measurements of the retention times deviated by up t o & 7 % , especially when the capacity ratio k ’ was small, the column was short, or t h e velocity was large. The peak width was determined graphically. The maximum personal error was 10%. Consequently, the errors in the calculation of h can be as high as 20%. The h value due t o sampling, connecting tubes, and the volume of the detector was determined t o be 0.01 cm for L = 25 cm. The A term in Equation 8 was about 0.03 cm for columns packed with small particle sizes. Consequently the term A can represent a calculated error of 30%. INFLUENCE OF DIFFERENT PARAMETERS ON THE RELATIVE PEAK BROADENING / I h as a Function of the Column Length. I n fast liquid chromatography, it is usual to assume that h is independent of L, although there are very few experimental results, which should support this empirical fact. Columns (d, = 2 mm) of 25, 50,100,200, and 400 cm in length were packed with “brushes” having sieve fractions of 80-90 p (batch No. 1). From the h us. u curves measured in these columns, the calculated terms A and C of Equation 8 and their standard deviations are shown in Table IV. Detailed values are tabulated elsewhere (20). In the case of L = 400 cm, the standard devia(20) M. Naefc, Ph.D. dissertation, Universitat Frankfurt/Main,
1970.
Figure 1. h us. u lines as a function of L a t 25 "C Benzene (k' = 0.2) b. p-Nitrotoluene (1.7) c. 2,6-Xylidine (4.9) Symbols for L: 25 cm .,SO cm 0,100 cm v and 200 cm A, 400 cm A K = 3.4 X lo-* cm2, d, = 2 mm Stationary phase: silica gel (370 mz/g) esterified with 13.4 b.w. polyethylene glycol 200; sieve fraction: 8090p; eluent: /?-heptane;U V detector a.
+,
~~~
Peak Broadening as Function of Column Lengtha Constants of the Equation h = A Cu Numberb k' p range, cm/sec L,cm A , 10-3cm, % 25 87.5 f 9 0.2 0.46-3.42 7 50 103. f 13 0.2 0.86-4.37 7 100 97.3+ 6 0.2 0.68-4.92 17 200 106. f 6 0.2 0.72-3.64 6 400 81.4 f 46 0.2 0.94-1.57 3 50 126. f 13 0.86-4.37 7 1.7 100 113. f 11 0.68-4.92 17 1.7 200 104. f 12 6 1.7 0.72-3.64 0.94-1.57 400 131. f 5 3 1.7 i 14 25 121. 0.46-3.42 7 4.8 0.86-4.37 50 122. i 15 7 4.8 100 122. zt 7 0.68-4.92 17 4.8 200 113. i 7 0.72-3.64 6 4.8 400 111. f 25 0.94-1,57 3 4.8 a Stationary phase: silica gel/PEG 200 brush (batch No. 1); sieve fraction: 80-90 p ; samples: benzene (k' 2,6-xylidine (4.9); eluent: n-heptane. Number of measured /7/u values used for the calculation. Table IV.
+
tions of the calculated terms are unusually high, due t o a n insufficient number of measurements. It appears, that the terms of Equation 8 are independent of the column length. I n Figure 1, the h us. u lines are given. The full lines are calculated from the average values of the A and C terms as given in Table IV. The points indicate the experimental results with different column lengths. Two columns were made with L = 100 cm, with different symbols in Figure 1, to indicate the reproducibility of the packing method. The particle sizes (80-90 p ) are unusually large for liquid chromatography. Consequently, the h/u values are high. O n the other hand because of the good permeability of the column, 3 cmjsec linear velocity can be achieved with 230 a t m pressure drop o n the 5.6 meter column using n-heptane as the mobile phase a t 26 "C. At the same time 1330 or 535 theoretical or effective plates, respectively, are generated for k' = 1.7. These are a t least usual efficiencies
=
C,msw, Z 51.2 =!= 8 49.3 f 10 52.8 i 4 50.1 i 5 58.5 i 49 108. f 5 114. f 4 120. f 5 95.9 & 5 149. i 5 151. f 4 149. & 2 153. + 2 156. f 14 0.2), pnitrotoluene (1.7);
compared with published data. The speed of analysis is 2.6 theoretical or 1.0 effective plates per second. The retention time ofp-nitrotoluene (k' = 1.7) is about 8.5 minutes. The speed of analysis increases with increasing linear velocity u as long as A/u becomes smaller, for example, when Alu is about 10% of C. This is the situation with the constants in Table IV if u N 10 cmjsec. At the same time, however, the efficiency decreases, and because of pressure limitations of the equipment the column length must be limited. Peak Broadening as a Function of the dJd, Ratio. With packed columns, deviations from a close packed structure increase with decreasing dJd, ratio. Both in gas (16, 21, 22) and liquid (2, 9, 13) chromatography, the h us. u curves for unretained samples show a sharp increase in h if dJd, is (21) J. C. Giddings, ANAL.CHEM., 34, 1186 (1962). (22) Zbid., 35, 439 (1963).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
79
Table V. Peak Broadening as Function of dJd, Ratio Constants of the Equation h = A Cu Number k‘ K, 10-8 cm2 ~.rrange, cm/sec del4 A , 10-3 cm, % 9 0.2 21 .o 0.70-3.54 20 229 i 26 19 0.2 19.0 0.47-3.88 10 324 i 18 7 0.2 20.0 0.82-3.50 5 285 i 28 5 0.2 20.0 1 .12-3.70 2.5 603 i 18 9 1.7 0.7C-3.54 20 179 f 35 19 1.7 0.47-3.88 10 473 f 18 7 1.6 0.82-3.50 5 376 f 22 S 1.7 1.12-3.70 2.5 858 f 17 9 5.1 0.80-3.54 20 257 f 38 19 5.5 0.47-3.88 10 411 f 12 7 4.9 0.82-3.50 5 308 f 18 5 5.2 1.12-2.66 2.5 700 f 23 Stationary phase: silica gel/PEG 200 brush (batch No. 1); column length: 47-100 cm; sieve fraction: 177-200 (k’ = 0.2), p-nitrotoluene (1.7), 2,6-xylidine (5.2); eluent: n-heptane.
+
p;
C,msec, Z 282 f 9 310 f 8 299 i 12 340 i 13 646 f 4 593 f 6 608 i 6 629 f 10 791 i 5 884 i 2 887 f 3 945 i 9 samples: benzene
Table VI. Peak Broadening as Function of Width of Sieve Fraction Constants of the Equation h = A Cu Number k’ K , 10-8 cm* Fraction, p A, cm, Z C, msec, % 8 0.2 3.8 80- 90 89.1 f 13 52.3 f 10 6 0.2 3.9 70-100 56.7 f 23 65.8 f 9 7 0.2 3.7 50-120 94.4 f 19 69.8 f 12 8 0.2 3.8 25-1 50 208. f 8 98.7 i 8 8 1.4 80- 90 89.2 i 19 110. f 7 6 1.5 7C-100 80.0 i 19 109. f 6 7 1.5 50-120 109. f 8 119. i 4 8 1.4 25-1 50 283. f 6 126. i 7 8 3.1 80- 90 81.0 i 19 153. i 5 6 3.2 70-100 89.0 i 16 149. f 4 7 3.2 50-120 109. i 17 155. i 6 8 3.1 25-150 281. i 5 162. i 4 Stationary phase: silica gel/PEG 200 brush (batch No. 2); d, = 2 mm; column length: 50 cm; samples: benzene (k’ = 0.2), p-nitrotoluene (1.4), 2,6-xylidine(3.1); eluent: n-heptane; velocity range: 0.66-3.5 cmjsec.
+
greater than 5. Columns packed irregularly (Le., d,/d, < 5) with glass beads have been shown to give negative dhjdu values for unretained peaks in liquid chromatography in the velocity range K = 3-10 cm/sec (13), a highly desirable condition for high speed analysis. Similar conditions were not found, unfortunately, for retained samples (13). Irregularly packed glass capillary columns have been used successfully in GC with retained samples (23-25). Such columns have a higher permeability (-10 X ) than a regular column packed with the same sieve fraction. Attempts to increase the diameter of such columns fail because of their low mechanical stability; a problem aggravated in liquid chromatography by the greater shearing forces involved. I n this work irregular packed columns were made by using metal tubes ( i d . >0.5 mm) and conventional packing methods. Some results with such columns have been described (13). Permeabilities were no better than with regular ones and a decrease in the h/u term was observed only when u was greater than 10 cmjsec. The influence of the do/dpratio was studied with brush type packing. Columns with 4, 2, 1, and 0.5 mm inner diameter were packed with a sieve fraction of 177-200 p (batch No. 1). The packing method described earlier was used. The A and
C terms of Equation 8 and their standard deviations are given in Table V for ratios between about 20 and 2.5. The permeabilities of regular and irregular packed columns are in this case more or less equal. The A and C terms are optimal for d,/dp = 20-i.e., for regular packed columns. Consequently, regular packed columns are to be preferred in liquid chromatography unless a new packing method is found which will give a mechanically stable loose packing. Peak Broadening as a Function of Width of Sieve Fraction. Broadening of the sieve fractions results in decreasing efficiency as described in the chromatographic literature. To measure quantitatively this effect, the following experiments were made using brushes of batch No. 2. Sieve subfractions with 10-p width (Le., 50-60, 60-70 . . . 140-150 p ) were prepared. Fractions under 50 p were made on a separator machine (courtesy of Merck AG., Darmstadt, West Germany). The surfaces of the brushes were in all fractions free of silica powder as pointed out earlier. The sieve fractions tabulated below were composed of equal weights of the subfractions :
(23) I. Halhsz and E. Heine, Nature, 194,971 (1962). (24) C. Landault and G. Guiochon, “Gas Chromatography 1964,” A. Goldup, Ed., Butterworths, London, 1965, p 121. (25) I. Halksz and E. Heine, ANAL.CHEM., 37,495 (1965).
The width of the sieve fraction is characterized by the deviation in per cent from the arithmetic mean value. The results are shown in Table VI and Figure 2. Some
80
ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
80-90 p 70-100 p 50-120 p 25-15Op
+
= 85p 6% = 85.5 p f 17z = 85 p i 41 = 8 7 . 5+ ~ 71z
z
8 8
8
A '
8
O A '
PA
8 8
Po
0
'A
0
2
1
Figure 2.
3
u[cm/sj
Peak broadening of 2,6-xylidine as a function of width of sieve fraction Parameters same as in Table VI Symbols for the sieve fractions: 80-9op 70-1OOp 50-12Op
0
A 0
25-150~
Table VII. Peak Broadening as Function of Average Particle Size (50-200 p) Constants of the Equation h = A Cu
+
Number k' K, lo-* cm2 p range, cmjsec Fraction, p A , lO-Vm, 72 C , msec, 72 19 0.2 2.1 0.73-5.04 57- 63 75,041 7 30.1 =t 6 19 1.7 2.1 0.68-4.92 57- 63 64.2 i: 8 67.4 i 3 71.5 i 8 87.0 & 2 19 4.8 2.1 0.47-3.88 57- 63 17 0.2 3.5 0.73-5.04 80- 90 96.1 i: 6 52.4 =I=4 17 1.7 3.5 0.68-4.92 80- 90 112. =t 11 114. f 4 122. =t 7 149. i 2 5.0 3.5 0.47-3.88 8C- 90 17 309. i8 322. i : 18 20. 0.73-5.04 177-200 19 0.2 593. i 6 177-200 473. f 18 20. 0.68-4.92 19 1.7 411. & 12 884. i 2 20. 0.47-3.88 177-200 19 5.5 Stationary phase: silica gel/PEG 200 brush (batch No. 1). dc = 2 mm; column length: 100 cm; samples: benzene ( k ' = 0.2), p-nitrotoluene (1.7), 2,6-xylidine (5.2). Table VIII. Average p Values as Function of Velocity 50-200 p
u, cm/sec
6 , 72
0.5
1.70 i. 9 1.73 1 8 1 . 7 6 3 ~8 1.79 i 10 1.82 & 10
0.75 1 .o
1.5 2.0
u,
cm/sec 2.5 3.0 3.5 4.0 5.0
P,
z
1.83 i 11 1.85 i 12 1.86 i 12 1.87 1 12 1.88 f 12
unexpected results are demonstrated here. Permeability and the h us. u line is practically independent of the width of the sieve fraction as long as the deviation from the arithmetic mean is smaller than about 4 0 x . The conditions became worse with the broad fraction 25-150 p ( 1 7 1 %). It is, however, possible that with another support (especially if its surface is covered with fine powder) and with a n extremely uneven distribution of the subfractions, differing results may be obtained. Peak Broadening as a Function of Particle Size (50-200 p ) . Three sieve fraction, were made of batch No. 1 :
57-60 p
= =
60p
f
5%
i5% 177-2OOp = 188.5 p i 6z
80-9Op
85 p
The usual results are shown in Table VI1 and in Figure 3. I n Figure 3, the empty and full symbols (for example A and A) were obtained with different columns, t o demonstrate again the reproducibility of column packing. It was assumed h = D dpp (9) where 0is independent of the nature of the sample, the linear velocity of the eluent, and the sieve fraction between 50-200 p . This is of course a n extremely rough approximation, and is valid only within a given velocity range, in this instance between 0.5-5 cmjsec. However, this range is of great interest in fast liquid chromatography. In the following procedure, the h values were calculated for 10 velocities with the help of the constants given in Table VII. For a constant velocity and a given sample the /3 value was calculated from a pair of h values. Because of the 3 sieve fractions, 3 values were computed for each velocity and for each sample. Thus for 3 samples, 9 values were calculated for each velocity (every h/u pair was measured at least three times). The average values and their standard deviations are shown in Table VIII. (The /3 values calculated for benzene from the two small particle sizes were neglected because the precision of the measurement was not sufficiently high enough for this type of ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
81
4 A A A
I
I
I
I
I
1
2
3
4
__c
u [cm/s]
Figure 3. h us. u plots of 2,dxylidine as a function of particle size Parameters as in Table VI1 Symbols for the sieve fractions: 57-63p Vand V SO-Wp Oand. 177-200 p A and A
Table IX. Peak Broadening as Function of Average Particle Size Constants of the Equation h = A Cu
+
Number k’ K , 10-8 cmz Fraction, p A , 10-3~m, C,msec, 72 7 0.4 0.10 11-16 41.2 i 13 48.0 f 12 7 1.7 0.10 11-16 5 8 . 0 1 13 48.4 i 17 7 6.6 0.10 11-16 55.8 f 6 35.2 f 11 8 0.4 0.15 16-20 30.1 i 10 47.2 i 6 8 1.7 0.15 16-20 35.8 & 6 57.01 4 8 6.8 0.15 16-20 34.1 i 5 44.7 zt 4 6 0.4 0.25 20-25 31.4 Z!= 19 47.9 f 13 0.25 20-25 39.7 i 15 56.9 f 11 6 2.0 0.25 20-25 36,6+ 9 4 3 . 0 2 ~7 6 7.6 0.60 30-40 56.5 i 10 86.3 i 6 7 0.4 7 2.1 0.60 30-40 86.0 =k 12 95.1 i 10 0.60 30-40 74.3 f 7 70.8 f 7 7 8.0 78.4 2~ 15 130. i 9 8 0.4 1.1 40-50 1.1 40-50 109. i l l 165. i 7 8 1.7 119. i 7 1.1 40-50 111. i 8 8 6.7 Stationary phase: silica gel/PEG 200 brush (batch No. 3); d, = 2 mm; column length: 25 cm; samples: benzene ( k ’ = 0.4), anthracene (1.7-2.1), pnitrotoluene (6.6-8.0); velocity range: 0.30-1.62 cmjsec.
calculation). Although /3 slowly increases with increasing velocity, the agreement in this rough approximation is surprisingly good. By weighing over all the velocities and columns, the following results were computed: for benzene @ = 1.80 i lo%, for p-nitrotoluene /3 = 1.79 f 11 %, for 2,6-xylidine, /3 = 1.83 f12 % and the average of 80 values was /3 = 1.81 i 11%. Particle Sizes between 11-50 p. In Table IX and Figure 4, it is demonstrated that the peak broadening becomes independent of the average particle size, if the sieve fraction is 82
ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
smaller than 20-25 p. This is, of course, the consequence of using the same packing method for the extremely small particle sizes. Probably there are better packing methods for particle sizes under 20 p. In our experience, column packing in this region is best described as a n art. We wanted to demonstrate, that for every packing method there is a lower limit, where h does not decrease with decreasing particle size (i.e., /3 = 0) or sometimes 0becomes negative. In both cases decreasing particle size results in the undesired decrease of column permeability, with no gain in the efficiency of sep-
t
b b
“1
with the constant
b b
b = D a = 2000
A
A
O1
1 I
(13)
if u is constant. For a given eluent 7) and sample k’
0.2
or the speed of analysis
A
I
0 2
A b
b
b
b o +
o
:*e
o*
* 0 *
With constant t R and n, it can be seen from Equations 14 and 14a that the pressure drop A p shall decrease with decreasing d, as long as /3 is greater than one. Small pressure drop is always desirable since sometimes A p is the limiting parameter. Therefore the smallest possible particle size is preferred in chromatography as long as /3 is greater than 1. It is a n experimental fact (11, 26), that with decreasing particle size, p decreases too. The reason for this may be due to the method of column packing. Another reason could be the increasing surface energy of the support with decreasing particle sizes, resulting in agglomeration of the particles or in irreproducible column packing or in the “aging” of the column-i.e., the permeability and (or) the h U S . u curves are changing over the lifetime of the column. As p becomes smaller than one, the pressure drop increases with decreasing particle size (with constant n and t R ) . Therefore there is always a n optimum particle size. The value of the optimum d, depends upon the surface properties of the support and upon the method of column packing. For example, with the system described in this paper, the optimum sieve fraction was 20-25 p .
r 1
Figure 4. ticle size
/z c‘s. u plots of p-nitrotoluene as a function of par-
Parameters same as in Table IX Symbols for the sieve fractions: 11-16
p
16-2Op 20-25p 30-40 p 40-50~
0
+
0
A A
aration. For 10 velocities equidistantly chosen (0.3-1.65 cmisec), ,8 values were calculated with the average particle sizes of 22.5, 35, and 45 p , respectively. These values averaged over all the columns increased with increasing velocity from 1.47 to 1.51. The average of 90 /3 values was 1.50 h 10 for the narrower velocity range compared with that measured for the greater particle sizes. Efficiency and Speed of Analysis as a Function of d,. From Equations 6, 7, and 9 and with L = hn
with the constant a
=
2000 D
(1 1)
if the linear velocity is constant. The most important limitation of a fast liquid chromatographic equipment is its maximum inlet pressure (Le., the maximum pressure drop across the column A p ) . The minimum number of effective plates is defined with the relative retention of the pair of substances which are to be resolved. Consequently, with the capacity ratios of substances, the minimum n is also defined. As can be seen from Equation 10 if the eluent (v), n, and the linear velocity u are constant, the pressure drop across the column is independent of the particle size used if /3 = 2. If p is less than 2, the pressure drop increases with decreasing particle size. The analyst, however, is not interested in the velocity of the eluent, but in the time of analysis t R or in the speed of analysis n/tR. When the particle size is decreased, the required column length decreases with constant velocity and the time of analysis becomes shorter. From Equations 1, 9, and 10 s n d with t R = z,(1 k ’ ) a n d L = hn
+
CONCLUSIONS
The influence of some column parameters on peak broadening in fast liquid chromatography was discussed using a brush type stationary phase (silica gel esterified with PEG 200). Because of the great errors in the calculation of the h values, broad series of precise measurements are required and statistical methods have to be applied for the evaluation of the results. The influence of column packing and that of column coiling o n the peak broadening is co-determined by the surface properties, mechanical stability, and sieve fraction of the support. Important parameters can be calculated in good approximation with simple functions. The permeability increases with the square of the average particle size of the sieve fraction. In the usual range of velocity (0.3-5 cmjsec) and that of particle size (10-200 p ) , the h 1;s.u relationship seems t o be more or less linear. The exponent /3 in the h N dpprelationship is constant over a broad sieve fraction range. O n decreasing d,, however, the exponent /3 decreasing discontinuously with discrete values on the average particle size of the sieve fraction. These values are again determined by the properties of the support. With the stationary phase used in this paper the limits were 50 and 20 p . If p becomes smaller than unity, the decrease of d, results in increasing pressure drop if n and (26) A. Kroneisen, Ph.D. thesis, Universitat FrankfurtiMain, West Germany, 1969.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
83
t R are constant. Consequently, an optimum sieve fraction exists for every kind of support and for every kind of packing method. Narrow sieve fractions, at least for this stationary phase, are not of such great importance as has been assumed.
ACKNOWLEDGMENT
The authors thank Dr. H. Kelker (Farbwerke Hoechst AG., Frankfurt/Main) for the organic analyses. The sieve fractions of the small particle sizes were prepared with the help of E. Merck AG. (Darmstadt). We would like t o acknowledge the help of Dr. P. A. Sewell (Liverpool Polytechnic) in the preparation of this manuscript.
=
K
= (specific) permeability (Equation 6) ( d p ) 2 / 2 0 0 0(Equation 7)
relative peak broadening k' L N
A
=
a
= =
b C
D d, dp dp
F
84
= = =
= = =
constant in Equation 8 constant as defined in Equation 1 1 constant in Equation 1 3 constant in Equation 8, mass transfer constant in Equation 9 inner diameter of the column particle diameter of the support arithmetic mean value of the sieve fraction volume flow velocity of the mobile phase, flow rate
t R ' / t o = capacity (or partition) ratio column length
1 6 ( t ~ ' ) ~ /= w ~n[k'/(l
plates It
AP to tR
tR U
U" W CY
NOMENCLATURE
L ~ ~ / 1 =6 theight ~ ~ equivalent to a theoretical plate or
h
B 9 €0
6T
+ k')]*
=
number of effective
1 6 f ~ ~= / Wnumber ~ of theoretical plates pressure drop across the column holdup time or retention time of an inert peak retention time of peak measured from start t R - to, net retention time linear velocity as defined in Equation 1 linear velocity as defined in Equation 2 peak width at base line kz'/kl' = t ' R Z / f ' R 1 = relative retention constant in Equation 9 viscosity of the eluent interparticle porosity total porosity as defined in Equation 3
Accepted August 20, 1971. Abstracted in part from the Ph.D. dissertation of M. Naefe. The authors thank the Deutsch Forschungsgemeinschaft (Sonderforschungsbereich 52, Analytik, Saarbriicken) for financial furtherance of this research work. RECEIVED for review July 12, 1971.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
