2002
Anal. Chem. 1980, 52, 2002-2008
Comparison of the Theoretical Limits of Separating Speed in Liquid and Gas Chromatography Georges Guiochon Ecole Polytechnique, Laboratoire de Chimie Analytique Physique, Route de Saclay, 9 7 728 Palaiseau Cedex, France
The performances of GC and LC cdumns are compared; these performances are defined as the time needed to generate a peak having a given efficiency (plate number). A comparison can be made by using columns of different lengths but otherwise identical, except for a different mobile phase velocity. The fastest analysis is then achieved when the inlet pressure is the maximum pressure at which the available equipment can work. Calculations have been made for a number of different combinations of particle size, diffusion coefficient, HETP equation coefficients, maximum pressure available, etc. both in LC and GC. Combinations of realistic values of these parameters result in curves which are in a restricted area of a time vs. plate number graph characterizing typical column performances.
Fifteen years ago, under a title very similar to the above, Giddings investigated the principal factors affecting the separating speed in gas and liquid chromatography ( I ) . High-performance liquid chromatography, however, was yet to be developed, and although the author predicted correctly in this foreseeing paper the trends which this development was going to follow and the range of optimum operating conditions of the new technique, he had little experimental data to introduce in his equations. Furthermore the concept of reduced plate height and velocity, introduced by the same author hardly a year before (2) had not yet led to the derivation of the simplified reduced height equivalent to a theoretical plate (HETP) equation (3) and of the theory of optimization of column design and operating parameters. Now that the kinetics of band spreading in chromatography and the optimization of chromatographic separations are well understood and that the state of the art in column packing for either gas or liquid chromatography has reached a level that we can hardly expect to improve markedly in the future, it seems appropriate to revisit Giddings theoretical approach, using our present experimental knowledge. Admittedly gas chromatography (GC) and liquid chromatography (LC) are not largely competitive. In the few cases where they are, the decision to use one or the other will be based more on consideration of either relative retention of some critical compounds or detection limits rather than of relative speed of analysis. It is interesting, however, on a purely theoretical ground to know whether and if so why one chromatographic technique is more powerful, efficient, or faster than the other one. It also turns out that this same theoretical approach can be used to compare the speed of packed and capillary columns and that this sheds new light on the presently controversial issue regarding the practical interest of capillary columns in LC . In this approach we draw largely on two discussions recently published on the possibilities of achieving extremely large efficiencies in gas ( 4 ) and liquid ( 5 ) chromatography. The equations used below have been extensively discussed in these papers to which the reader is referred for their detailed de0003-2700/80/0352-2002$0 1.OO/O
rivation and an evaluation of their range of validity. Finally it should be emphasized that analysis times in excess of a day, sometimes considered below, are of academic interest and are quoted merely for the sake of comparison or for illustrating the practical impossibility of some separations. PRINCIPLE OF T H E METHOD OF COMPARISON The fundamental concept in this discussion is the available maximum pressure of the equipment. Let us assume that we have a convenient chromatographic system allowing the separation of the compounds of a mixture and that we can prepare columns with different lengths but identical characteristics: the same permeability, the same coefficients of the plate height equation, etc. As pointed out by Knox (6),if we have already achieved a separation, we can still do it faster by using a longer column and a larger flow velocity, which requires a higher inlet pressure. The longer column offers a larger efficiency a t a given flow rate, and this excess efficiency is lost by operating at a larger velocity. It is shown that in doing so we decrease the analysis time. Eventually the maximum pressure a t which the equipment can work is reached (or the maximum velocity, with some detectors). The fastest analysis with any column design will be achieved with a column operated a t the maximum available pressure and having such a length as to give the plate number necessary to perform the desired separation. For columns of different design, used with different equipment, the comparison between the speed of separation is conveniently obtained by comparing plots of the shortest analysis time ( t ) vs. the necessary plate number (N), derived for these columns; some columns with poorer values of the coefficients of the H E T P equation but large permeability may permit the achievement of larger plate numbers while being slower at moderate efficiencies (cf. below). For a given technique, LC or GC, the curves corresponding to the range of conditions observed in current practice will determine a zone of the t , N plane. The comparison between the speed of separation of the two techniques is obtained from the relative positions of these zones. The equations relating efficiency and analysis time to the design and operation parameters of the columns are different for gas and liquid chromatography because gases are compressible (7) and liquids are not, or more exactly it has been shown that their compressibility has no effect on analysis time (8). The derivation has to be made in each case. In both cases, however, we shall use the same equation (3) for the reduced plate height h = 2 y / v Au1l3 Cu (1)
+
+
with
h =H/d, and u =
ud,/D,
(3)
where h is the reduced height of the column, H the actual plate height, d, the average particle size ( 5 ) ,v the reduced velocity 0 1980 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 52, NO. 13, NOVEMBER 1980
Ilrn 1.5
2003
: 8-
L
:c I c
Flgure 1. Plot of reduced plate height vs. reduced velocity: curve 1, very good packed column ( A = 1, C = 0.01); curve 2, fair packed
column ( A = 3, C = 0.05); curve 3, capillary column ( A = 0, C = 0.2). Straight lines 4-6 give the three contributions to curve 2 (respectively axial diffusion, packing unevenness, and resistance to mass transfer).
of the mobile phase, u its actual velocity, and D , the diffusion coefficient of the studied sample in the mobile phase. The coefficients A and C are dimensionless parameters, characteristic of the quality of the packing and of the quality of the stationary phase, respectively. C measures the rate of mass transfer in the stationary phase. Figure 1 shows three H E T P curves used in the numerical applications. One corresponds to an excellent column ( A = 1, C = 0.01); it seems it will be difficult to do much better. The second corresponds to a fair column ( A = 3, C = 0.05); it is most often possible to achieve that kind of performance. The third corresponds to a very good capillary column. These kinds of performances have been reported in GC but not yet in LC. In fact we shall not consider LC capillary columns here. Curves 4-6 show the variation of the three contributions to eq 1 in the case of curve 2 and how the third term remains small for v < 100 and negligible for v < 20. By definition of the plate height, we have L=NH (4) which combines with eq 2 to give L = Nhd, The flow rate is related to the pressure gradient by the Darcy equation u =
Bo d P B dx
(6)
where Bo is the column permeability and 7 the mobile phase viscosity. The column permeability is proportional to the square of the particle diameter for packed columns.
Bo =
ked,'
(7)
The integration of eq 6 is different in gas and liquid chromatography. LIQUID CHROMATOGRAPHY The pressure gradient is assumed to be constant. The liquid flow rate is given by u = (Bo/d(.@/L) Combination of eq 2, 3, 5, 7, and 8 gives
(8)
N = (k,/?Dm)(dp2/hv)*
(9) The analysis time is obtained by integration of the equation
dt = dl/u and in LC it is given by the relationship t = (L/u)(l k?
+
(10) (11)
Figure 2. Performances of packed LC columns. Plots of analysis time vs. plate number obtained for packed columns. The design and operating parameters of these columns are given in Table I.Straight line 1’ is the asymptote to curves 1 and 4. The parameters of the other asymptotes are given in Table I, as well as the vertical ones (time becomes infinite).
Figure 3. Performances of packed LC columns. Plots of analysis time vs. plate number obtained for various columns (Table 11). The numbers on each curve give the column length ( m ) which permits the achievement of the corresponding performances ( t , N).
where k ’ is the column capacity factor, a function only of the thermodynamics of the interaction between the sample and the components of the chromatographic system and to a limited degree of the column design (phase ratio, specific surface area, etc.) Combination of eq 3, 5, and 11 gives t =
N-
1+k’h -dP2 Dm v
The combination of eq 1,for the chromatographic system considered, and eq 9 and 12 permits the determination of the t vs. N plots corresponding to a given column and instrument. A few such curves are given in Figures 2 and 3. The sets of parameters corresponding to each curve are given in Tables I and 11. As the values of the parameters h and v in eq 9 and 12 are related by eq 1,for the sake of simplicity the derivation of the curves in Figures 2 and 3 is made as follows. Values of the reduced velocity in geometrical progression are selected, because the plots are in logarithmic scales. The reduced plate height is calculated from eq 1. This set (h,v ) of reduced values is then introduced into eq 9 to calculate the plate number, and into eq 4 and 12 to calculate the analysis time and column length. Curve 1 in Figure 2 corresponds to a set of parameters which represent conditions currently considered as very favorable in LC. The other curves illustrate the effect of a large change in one of the column parameters: particle size (curves 1 and 2), pressure (1-41, diffusion coefficient (1-5), parameters of the H E T P equation (1-6). Before discussion of whether i t
ANALYTICAL CHEMISTRY, VOL. 52, NO. 13, NOVEMBER 1980
2004
Table I. Parameters Used t o Calculate the Performances of Columns in LC4 (Figure 2) curve no. 1
A C
2
1
cp D,, cm2/sx I),
lo6
20
d,, I.tm A P , atm
5 1000
Nld,
2.08 0.50
l o 6 plates
(Nlt)lm,ms-' no. of plates achieved in 1 min
1
2 103 ~
1.7 X y
1000 33.3
8.0
8.0
0.50
2.1 x 103 5.0 x 104 4.3 x 105
23 x 103 5 o x 104 3 6 x 105
6.3 x 103 i 5 x 104
1.3 X
9.1 x
2.7 X
3 x 103
8.3 x 7.4 x 2.6 X
lo6
io4 105 lo6
curve no.
A C I),
cp
D,,
cm*/s X
lo6
d,, IJm A P , atm
NIh,
l o 6 plates
(N/thd,m-' In all cases k'
2
4b
3
3
4
0
1 0.01 0.4
0.05 0.10
20 5
2 20
2 0.5
1
50
5b 0
0.20 0.20 1
1
20 20
20 5 200
1000 200
50
20 0
2.08
26.7
62.5 3.9
0.50
400
83 2~
= 1X
20.8
lo6
lo6
3
0.05 0.4 20
5 5
5 1000
1000 8.33 2.0
2.08 2.5
i i x 105
lo6
3.8 x 1 0 3 7.9 x l o 4 4.9 x 105 1.0 x l o 6
= 0.75, k ' = 3.
Table 11. Parameters Used to Calculate the Performances of Columns in LC4 (Figure 3 ) 1
1 0.01 0.4
1 0.01 0.4 20 5 10000
20 20
22 x i o 4 10.5 x 105
l h 1 day 1 week a In all cases k , = 1 x
6
1 0.01 0.4 20 20 200 6.67
1 0.01 0.4
0.01 0.4
5
4
3
io4
160
10
OTC.
would be realistic to consider conditions more favorable than those corresponding to curve 1 or what set of parameters represents the most unfavorable conditions which is possible t o find in current practice, a discussion of the shape of these curves is in order. At very low velocities, the analysis time becomes very long, since the maximum pressure permits the operation of a very long column: when the velocity is reduced, an increasingly long column is operated a t a decreasing speed and the elution time eventually becomes infinite. The plate number is inversely proportional to hv, which, according to eq 1, tends toward 2y; hence its upper limit is
On the other hand when the velocity becomes very large, hv is equivalent to Cv2 and the plate number tends toward 0 as does the elution time, but the ratio tends toward a limit.
In the case of packed columns, however, this limit is approached only a t very large reduced velocities. As shown in Figure 1, the second term of the HETP equation remains the major contribution up to reduced velocities well in excess of 100, unless C is unusually large (9). As long as h can be considered as equivalent to the second term, Av1f3,of eq 1, the ratio t / N is proportional to v-2/3and decreases with increasing velocity. A favorable analytical technique offers the achievement of a large efficiency in a given time or conversely the achievement of a given plate number in a short time; accordingly the corresponding curve tends to be in the lower right part of
Figure 2. This also means a large upper limit of the plate number as given by eq 13 and a low limit of the ratio t / N as given by eq 14. Accordingly we want a low solvent viscosity, a large inlet pressure, and a small mass transfer coefficient. The tortuosity y and the permeability vary in a very narrow range and cannot be controlled. The demands regarding d;/D, are conflicting, and this has very important consequences. If the emphasis is on fast analysis, then we need fine particles and a large diffusion coefficient. Moderate plate numbers are achieved in a very short time, but the limit plate number (cf. eq 13) will be rather small. On the other hand, if the emphasis is on very high efficiency, this can be achieved only through the use of rather coarse particles and a low diffusion coefficient, if possible. This may seem paradoxical, but it comes from the fact that it is not the actual velocity of the mobile phase but its reduced velocity which controls the HETP. At a constant, given pressure, the use of large particles permits the operation of very long columns a t still significant reduced velocities, hence the achievement of high efficiencies, but with very long analysis times. On the other hand, with fine particles a moderate value of the reduced velocity corresponds to a large actual velocity; hence with a given inlet pressure, only a small column can be used and a moderate number of plates achieved, but the analysis time is very short. It should be noted that eq 13 is also the equation for the critical inlet pressure, the lowest inlet pressure which permits the achievement of a given plate number (1, 3, 5). These results are illustrated in Figure 2, by comparison between c w e s 1and 4, where the pressure is raised from 103 to lo4 atm, and between curves 2 and 3, where the pressure is decreased from lo3 to 200 atm. Curves 1 and 4 have the same asymptote, line 1; curves 2 and 3 also have the same asymptote, but it is not shown on the figure, for the sake of clarity. The difference between the two curves of each set is important mainly a t large efficiencies. It is not very important in current practice. The use of the enormous pressure of 104 atm, well beyond any practical possibility, would permit the achievement of only 3.5 times more plates in 1 day (and 2.3 times more plates in 1 h). Similarly increasing the inlet pressure from 200 to 103 atm while using 20-pm particles would increase by only 50% the number of plates achieved in 1 day (cf. curves 3 and 2). In both cases, a better use of the larger pressure is achieved through the operation of columns packed with finer particles, as shown by the difference between curves 1 and 3. Even in this case the difference is important only for moderate efficiencies and short analysis times. As explained above, a marked reduction in the diameter of the particles (curves 2 to 1) permits the faster achievement of
ANALYTICAL CHEMISTRY, VOL. 52, NO. 13, NOVEMBER 1980
small or moderate efficiencies, while it reduces the maximum possible efficiency. Comparison between curves 1 and 5 illustrates the effect of a large decrease in the diffusion coefficient. Very similar plate numbers are achieved in 1 day (about 1 X lo6 plates). For analysis times of less than 1 day, the lower diffusion coefficient leads to a longer analysis time through unfavorable influence on the t / N ratio a t high flow velocities (cf. eq 14); for analysis times longer than 1 day, it permits the achievement of better performances. The difference between the two curves is small, however, and the ratio of plate numbers obtained in a given time does not exceed 2 between 0.5 min and 1 week. Finally the comparison between curves 1 and 6 illustrates the effect of the HETP parameters, especially of parameter A . At very large efficiencies, the two curves, which have the same upper limit (cf. eq 13), are very close. At lower efficiencies the difference remains moderate, since under the conditions of curve 1, 2.1 more plates are obtained in 1 day and 2.75 more in 1 h than under the conditions of curve 6 (cf. the H E T P curves in Figure 1). While any change, even important, of one of the parameters of the column has a moderate effect on the performance, a combination of several changes would drastically modify the picture. T o represent the range of conditions in which LC can currently be performed, we have selected for the curves in Figure 3 the values of the parameters given in Table 11. The parameter sets for curves 1 and 2 on this figure have been chosen so as to describe the most favorable and most unfavorable conditions probable while assuming good laboratory practice. This choice results from the previous discussion. It is seen in Table I1 that the maximum plate number with curve 1 is 10 times smaller than with curve 2 , while the limit of the t / N ratio is 800 times smaller. In practice, however, the conditions of curve 1 always permit the achievement of faster analysis (25 times more plates in 1 day, still 10 times more in 1 week). The hatched area between curves 1 and 2 corresponding to analysis times of less than 1 week corresponds to the performances which can currently be achieved by LC. Curve 3 shows the effect of conditions much more adverse than those corresponding to curve 2. They tend to become rare in current LC practice but still are found in gel permeation chromatography (GPC). Columns with A = 3 or 4 are poorly packed since the minimum reduced plate height is between 5 and 6. Anyway calculations show that the effects of particle size and diffusion coefficient are dominant, while those of A and C are smaller. Accordingly, we can consider that only the points between curves 1 and 2 correspond to performances characteristic of present day LC. We can also restrict the figure to analysis times less than 1 week. The numbers on each curve on Figure 3 represent the corresponding column lengths in meters. The comparison shows that another advantage of columns packed with fine particles over those packed with coarse particles is that shorter columns are used, which is very important for the achievement of large efficiencies. The packing of very long columns would be very impractical or even impossible although it has been possible to prepare and operate 1&12 m long packed columns and to obtain excellent results (10). Open tubular columns for liquid chromatography will not be considered here. They will be discussed in another paper (11). From current literature (12) it seems that the performances of columns having an inside diameter of 100 pm or more are still much inferior to those of GC open tubular columns h- is well above unity) and there is considerable development work to be carried out before they approach the theoretical
2005
performances which can be calculated from the Golay equation (13). On the other hand recent discussions (14) have shown that only open tubular columns with diameters between 5 and 20 hm can be expected to be competitive with conventional columns packed with 5-10 pm particles. The development of such open tubular columns is obviously plagued with such enormous technological difficulties in connection with sample introduction and detection that there is serious doubt whether they will ever be available to the analyst (11). Therefore, the exclusion of open tubular columns for LC from this discussion seems of little importance. GAS CHROMATOGRAPHY Because of the compressibility of gases, the pressure gradient is not constant along the column. It has been shown that if the carrier gas behaves ideally, the outlet gas velocity is given by
where Pi and Poare the column inlet and outlet pressures, respectively (7). The analysis time is given by t = ( L / j u o ) ( l+ k’) (16) with
j is the compressibility factor. Combination of eq 15 and 17 gives
In this work we are interested in ultimate performances, and we consider that any column is operated at maximum inlet pressure, the adjustment in efficiency being made not as in current practice by changing the flow rate but by changing the column, replacing it by a similar one of different length. With most equipment currently available, the maximum pressure is 4 or 5 atm and the outlet pressure is atmospheric. It would not be difficult to operate a GC a t 20 atm. Then we can neglect Pocompared to Pi in eq 15 and 18 and write
u, = B,-,P~/2vLPo
(19)
Combination with eq 2-4 and 7 gives
or, by combining eq 21 and 22
t=N
2(1 -t k? hPi - -dP2 30, UP,
Comparison between eq 9 and 21 and 12 and 23 respectively shows the importance of the effect of the compressiblity of the mobile phase on the performances of the column. We have seen above that in LC if the pressure gradient (APIL) is kept constant, the velocity of carrier liquid is constant (cf. eq 8); hence the plate height and the analysis time increase in proportion to the plate number. This is not so in GC. If Pi/L is kept constant, the outlet velocity increases in proportion to Pi (cf. eq 19). Thus the plate height increases and the plate number increases more slowly than the column
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ANALYTICAL CHEMISTRY, VOL. 52, NO. 13, NOVEMBER 1980
Table 111. Parameters Used to Calculate the Performances of Columns in GCa column no. 2
1
A C
1 0.01
ko
l/800
PP cmz/s d,, lJm atm N h , l o 6 plates
90 0.5 50 50 0.58 6.6 X 10.’
rir
D,,
(tIWlim, ms
a In all cases k ’ = 3, y = 0.75 except when A standard pressure gauge gives Pi- Po.
3
3
0.05 l/lOOO 24 0 0.05 200 4 0.18
0.83
4.3
3.2
=
4
3
1 0.01 l/SOO 90 0.5 20 150 X
10.’
0.05 l/lOOO 240 0.05 200 150 250 160
0 ( O T column, y = 1)Po = 1 atm.
length. On the other hand, the average velocity j u , = (3Bo/2q)(Pi/L) remains constant and the analysis time increases in proportion to the column length. So the retention time increases faster than the plate number (15). If the outlet velocity is kept constant, the plate height remains nearly constant or decreases slightly with increasing column length, since the term of resistance to mass transfer in the stationary phase decreases with increasing pressure drop (16). Then the plate number increases in proportion to the column length, but to keep u, constant we must keep Pi2/L constant (cf. eq 19) and then t R increases as L3I2(cf. eq 20) or practically as MI2 (13). Equations 21 and 23 are used to draw the curves in Figure 4 much in the same way as eq 9 and 12 were used to draw the curves in Figures 2 and 3. The same reduced plate height equation was used (eq 1) with the same sets of values of the coefficients A and C. The numerical values used for the other parameters are given in Table 111. As in LC, when the column length is increased progressively, the velocity becomes very small and the efficiency tends toward a limit while analysis time becomes infinite. In GC the limit is given by
This is derived from eq 21, the limit of hv for Y = 0 being 27Dm. When the velocity becomes very large, both the efficiency and analysis time tend toward 0 and the ratio t / N toward
Equations 24 and 25 differ from eq 13 and 14 by the respective factors of Pi/2Po and 2Pi/3P,. At large inlet pressures these factors become very important. The corresponding values of these limits are also given in Table 111. The asymptotes of curves 1, 2, and 5 are shown in Figure 4. Curves 1 and 2 do not come close to their asymptotes because the rather small pressures used do not permit the operation of the columns at large enough velocities and, within the limits of the figure, the third term of eq 1 remains too small compared to the second one. The parameters of these curves 1and 2 have been chosen to represent extreme experimental conditions, so that in most cases GC analyses are run under intermediate conditions and the hatched region between curves 1 and 2 represents GC performances. The influence of the parameters is similar to what is discussed for LC, but there are some important differences. In GC the limit of t / N at high carrier gas velocity is a function of the inlet pressure, so columns of the same design operated at different inlet pressures do not have the same asymptote for their characteristic lines (cf. curves 2 and 4 and 6 and 7 ) .
5
6
7
0 0.2 1/32 90 0.5 250 10 10.8
0 0.2 1/32 90 0.5 100 10 1.74 1.1
0 0.2 1/32 90 0.5 100 50 43.4 5.33
6.67
Pi is the absolute inlet pressure. A
Performances of columns in GC. Plots of analysis time vs. plate number obtained for various columns (Table 111). Straight lines l’, 2’,and 5’ are the asymptotes to curves 1, 2,and 5, respectively. The number on each curve gives the corresponding column length (m). Flgure 4.
The larger pressure results in better performance with long columns and poorer performance with short columns. Optimization is more complicated in GC and it is only interesting to increase the inlet pressure beyond some optimum value if at the same time the particle size is decreased (cf. curves 2, 1,and 3 or 5 and 7 ) . The conditions which lead to the fastest achievement of a given plate number are such that the flow velocity is around the optimum, for which the plate height is minimum. The hatched area between curves 1 and 2, for analysis times between 1 min and 1 week, corresponds to the performances typical of current GC techniques using packed columns. The advantage of open tubular columns (OTC) over packed columns (PC) in GC (compare curves 2 and 5 or 1 and 6) results from the much higher permeability of the OTC. The reduced plate heights of PC and OTC are of the same order of magnitude; hence the column length needed to achieve a given plate number is very close for PC and OTC; the optimum velocity of carrier fluid is also similar in P C and OTC. Because of the much larger permeability of OTC, however, the inlet pressure necessary to achieve this flow velocity is much lower with OTC and the average velocity corresponding to a given outlet flow velocity is much larger, so the analysis time is shorter with OTC. Elimination of Pi between eq 21 and 22 gives
On the assumption that the experimental conditions are otherwise identical, the analysis time would be smaller by a
ANALYTICAL CHEMISTRY, VOL. 52, NO. 13, NOVEMBER 1980
Flgure 5. Comparison between the ultimate performances of packed columns in GC and LC. Curves 1 and 2 are the same as curves 1 and 2 of Figure 3; curves 1' and 2' are identical with curves 1 and 2, respectively of Figure 4. a-d are the lines calculated by Giddings ( 7 ) to limit the LC (a, b) and GC (c, d) ranges, respectively, using experimental data available in 1965.
factor of l/kol/z( l 5 , 1 7 ) . Since for an OTC h3/vis also smaller than for a PC, the open tubular columns are about 20 times faster than PC columns (same carrier gas, same plate number; particle diameter = inner diameter of column). The same advantage does not appear in LC where the compressibility of the mobile phase is negligible, so the large permeability of the open tubular column results only in the need for a lower inlet pressure, which is convenient but does not result in a decrease in the analysis time (11). COMPARISON BETWEEN GAS A N D LIQUID CHROMATOGRAPHY The curves numbered 1 and 2 on both Figures 3 and 4 are reproduced in Figure 5 for easy comparison. I t can be seen t h a t there is considerable overlap between the two regions corresponding to current performances obtained with packed columns in LC and GC, respectively, which means that the two techniques offer very similar performances. For a surprisingly large range of performances it can be said that these two techniques perform identically well. LC tends to be somewhat slower for very easy analyses and faster for very difficult ones, but the differences are significant only when unrealistic problems are considered, like the achievement of 100 plates or of more than 5 X lo5, which is almost impossible with packed columns in GC because of the limited pressure available. T h a t of course is valid for a comparison between packed columns; in gas chromatography the performances obtained with capillary columns are certainly much better than those achieved with packed columns, and the use of the former columns has become standard for the achievement of more than 1 to 2 X lo4 plates. The explanation is shown in the discussion of eq 26 and of Figure 4. Curve 5 corresponds to a good but standard capillary column while curve 1 corresponds practically to the utmost performances available with packed columns, as columns of this kind have been prepared and used only by Huber and co-workers (18). Efficient capillary columns are not yet used in LC and much work has to be devoted to their development before they will become available for practical applications. Accordingly they have been excluded from the present discussion. I t is too early to draw definitive conclusions, but some trends are easy to derive from the above equations ( 1 1 ) . Finally one may not necessarily be interested in achieving the fastest possible analysis by operating the columns at the highest possible pressure, and it may be more realistic to compare columns working at their optimum flow rate and
2007
Flgure 6. Comparison between performances of GC and LC columns operated at the optimum flow rate. Conditions are as given in Table V. The area between curves 1 and 2 corresponds to performances currently achieved with LC columns packed with 5-ym particles and the area between curves 4 and 5 to performances achieved with GC columns packed with 100-ym particles. Curve 3 corresponds to an actual, good GC,OT column (i.d. 250 ym). Each straight line is solid as long as the pressure Is below 1000 atm in LC, 50 atm in GC. Point A on line 1 correspond to AP = 1000 atm for a column packed with 5-ym particles and D, = 5 X lo-' cm2/s. The same line also corresponds to a column packed with 1Gym particles and D, = 2 X 10" cm2/s. Point B would then correspond to 1000 atm.
Table IV. Optimum Values of the Reduced Plate Height Equationsu curve no. 1
A 1 3 0
2 3 a
B 1.5 1.5 2
C 0.01 0.05 0.2
hmin
Uopt
2 4.5 1.25
3 1.3 3.2
Cf. Figure 1.
Table V. Characteristics of the Columns Discussed in Figure 6a curve no 1
PC,LC h*in
uopt d p , Pm tRYCh
APor Pi, atrn
2 3 5 3.70 60
2 4 PC, 3 PC, 5 LC OT,GC GC PC,GC 4.5 1.3 5
19.2 58
1.25 3.2 250 b b
2 3 100 0.5 10.5
4.5 1.3 100 2.6
10
k ' = 3, k , = 1 x Dm = 5 x cm2/sin LC, 0 . 2 cm2/sin GC, Po = 1 atm, ri = 90 pP for H, in GC. Column type: PC = packed column; OT = open tube. LC = liquid
chromatography. GC = gas chromatography. lo6. Equation 1 9 is not a For N = 1 X l o s plates.
3 . 5 h and 2 atm for N = 1 x valid approximation of e q 1 5 .
merely increase the length and inlet pressure to increase the plate height. The performances would not be as good, but the experimental conditions would be less demanding. Of course when the column becomes longer, the maximum pressure is eventually reached, which sets the upper limit of the plate height which may be achieved under the corresponding conditions. Figure 6 shows such a set of diagrams. Now eq 12 is used in LC, where h and v are the minimum reduced plate height and optimum reduced velocity, respectively (cf. Table IV). In GC eq 26 is used. The parameters selected are given in Table V. The value of D, = 0.2 cm2/s in hydrogen corresponds to rather high molecular weight compounds.
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ANALYTICAL CHEMISTRY, VOL. 52, NO. 13, NOVEMBER 1980
It is obvious that in such a case LC loses part of its advantage, which is the easier use of large inlet pressures: 200 atm is quite conventional in LC whereas 1000 atm is about the upper practical limit. In GC the corresponding values would be 10-20 and 100-150 atm, respectively. Under the conditions of this figure GC is faster than LC for all analyses requiring less than a few hundred thousand plates (and about 10 h). On the other hand, because of the difference between eq 12 and 26, showing that the analysis time under the conditions of the comparison increases in proportion to the plate number in LC and to the power of 1.5 of the plate number in GC, LC will eventually become faster than GC. Unfortunately this happens for analyses requiring several months, which most probably will remain a rather academic problem. CONCLUSION Gas chromatography appears in practice to be a somewhat faster separation technique than LC. It could in fact be made faster than it is in current practice by the use of larger inlet pressures and of columns packed with smaller particles (18) or of open tubular columns of smaller inside diameter (4,19). The availability of capillary columns which have a very large permeability makes the use of these advanced PC attractive only when both high efficiency and a large sample size are required, which happens in some applications like positive identification of traces by GC/MS (18) or preparative applications. The difference in speed between the two chromatographic techniques is explained by the difference in mechanical properties of the mobile phases used, and there is little hope of observing a change in that situation since the present technology of column preparation results in columns having similar coefficients for the reduced plate height equation in GC and LC. Finally a comparison between the data given by Giddings in his early publication (1) and those used here show that progress in GC over the span of 15 years has been rather limited: Giddings only considered packed columns. The use of hydrogen, some improvements in packing technology, the use of smaller particles, and larger pressures explain the difference, which if we exclude the work of Huber et al. (18) is rather small. On the other hand LC has made considerable progress: it is now possible to generate 1x lo5plates in 0.5-1 h while the experimental data available to Giddings led him t o predict 24 h, a gain of 30 on the analysis time. Further progress on both techniques will probably be limited in the future. At least it is clear now that the advantage in speed of GC over LC is small a t present and there is no general reason to strive for the preparation of volatile derivatives of thermally unstable or high-boiling compounds in order to analyze them by GC, unless there is a very specific reason for doing so, such as the different selectivity of retention mechanisms or the lower detection limits due to the availability of much more sensitive detectors in GC.
A
BO C
GLOSSARY coefficient in the H E T P equation (eq 1) column permeability (eq 6) coefficient in the H E T P equation (eq 1) diffusion coefficient in the mobile phase (eq 3) particle diameter (eq 2) height equivalent to a theoretical plate (HETP) (eq 21
re&ced H E T P (eq 1) compressibility coefficient in GC (eq 16) specific permeability of packed columns (eq 7) column capacity factor (eq 11) column length (eq 4) number of theoretical plates (eq 4) limit or maximum plate number (eq 13) pressure (eq 6) column inlet pressure (eq 15) column outlet pressure (eq 15) Pi - Po (eq 8) time (eq 11) flow velocity of the mobile phase (eq 3) outlet flow velocity, in GC (eq 15) abscissa along the column (eq 6) tortuosity factor of the packing (eq 1) viscosity of the mobile phase (eq 6) reduced flow velocity (eq 1)
LITERATURE CITED Giddings, J. C. Anal. Chem. 1965, 37, 60-63. Giddings, J. C. Anal. Chem. 1963, 35, 1338-1341. Knox, J. H.; Saleem, M. J . Chromatogr. Sci. 1969, 7 , 614-622. Guiochon, G. Anal. Chem. 1978, 50, 1612-1821. Guiochon, G. J . Chromatogr. 1979, 785, 3-26. Knox, J. H. J . Chem. Soc. 1961. 433-441. Guiochon, G. Chromatogr. Rev. 1966. 8 , 1-47. Martin, M.; Blu, 0.; Guiochon, 0. J . Chromatogr. Sci. 1973, 7 7 , 641-654. (9) Colin, H.; DiezMasa, J. C.; Czaykowska, T.; Miedziak, I.; Guiochon, G. J . Chromatogr. 7978, 767, 41-65. (IO) Scott, R. P. W.; Kucera, P. J . Chromatogr. 1979, 769, 51-72. (11) Guiochon. G., submitted for publication in Anal. Chem. (12) Ishi, D.; Tsuda. T.; Takeuchi, T. J . Chromatogr. 1979, 785, 73-78. (13) Golay, M. J. E. "Gas Chromatography 1958"; Desty, D. H., Ed., Butterworths: London, 1958; pp 36-53. (14) Knox, J. H.; Gilbert, M. T. J. Chromatogr. 1979, 786, 405. (15) Guiochon. 0. Adv. Chromatogr. ( N . Y . ) 1969, 8 , 179-270. (16) . . Glddinas. J. C. "Dynamics of ChromatwraDhv": Marcel Dekker: New York, i 9 6 s ; p 39.(17) Halasz, I.; HerbMnn, K.; Heine, E. "Gas chromatography 1964"; GokJup, A., Ed.; Instiiute of Petroleum: London, 1965; pp 38-80. (18) Huber, J. F. K.; Lauer, H. H.; Poppe, H. J. Chrometogr. 1975, 772, 377-388. (19) &spar, G.; Annino, R.; Vidal-MadJar, C.; Guiochon, G. Anal. Chem. 1978, 50, 1512-1518. (1) (2) (3) (4) (5) (6) (7) (8)
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RECEIVED for review May 1, 1980. Accepted June 30, 1980. Presented at the Symposium on the ACS Award in Analytical Chemistry a t the 179th National Meeting of the American Chemical Society, Houston, TX, March 1980.
