982
Anal. Chem. 1989, 6 1 , 982-990
Optimization of Sample Size and Sample Volume in Preparative Liquid Chromatography Anita Kattil a n d Georges Guiochon*v2
Department of Chemical Engineering and Department of Chemistry, The University of Tennessee, Knoxville, Tennessee 37996-1600, and Division of Analytical Chemistry, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
The semi-ideal model of chromatography has been used to calculate the influence of the sample amount and volume of a binary mixture on the production rate achieved In preparative liquid chromatography. The optimum condltlons have been found to depend highly on whether one is interested in the production of the first or second eluted component. At low separation factors the sample volume influences the production rate of the first component significantly and low volume, concentrated injections should be used. At large separation factors, the sample volume is of less importance for 1/3 and 1/9 mixtures but of more importance for 3/1 and 911 mixtures. For the second component, the sample vdume influences the production rate to a lesser extent than for the first one; however low volume, concentrated samples give the higher production rates. The maximum production rate for component 7 occurs at very high sample loading so that the displacement effect concentrates and compresses the band. I n contrast, the maximum production rate of component 2 occurs when the front of Its band pushes against the rear boundary of the first component, with little band overlap. If one wants yields exceeding 80% for component 1, It may be necessary to accept production rate losses ranging from 10% to 40%.
INTRODUCTION Presently, there is much controversy and few results of general validity over many practical aspects of preparative liquid chromatography. This state of affairs originates from a combination of the youth of the method (chromatography has become widely used as a separation technique for only a few years), of the relative secrecy which surrounds many applications of preparative chromatography (since the details of a preparation procedure are difficult to patent they are kept confidential), and of the complexity of the process (no empirical study can unravel the intricacy of the relationships between the production rate, the yield and/or the cost of a separation, and the characteristics of the specific application considered). Among the unsolved problems, one of the simplest, yet of highest practical importance, is to know whether large volume dilute samples or small volume concentrated samples, holding the injected amount constant, should be injected into preparative columns for maximum production rate of the desired component. Most separations carried out by preparative chromatography use the overloaded elution mode. In such a case, the higher the sample concentration, the more distorted the profile of a single band and the stronger the degree of interference between closely eluted bands. At high concentrations the band top will sample regions of the isotherm which are farther from the linear range and closer to the saturation 'Department of Chemical Engineering. 2Department of Chemistry. 0003-2700/89/0361-0982$01 SO/O
limit; thus, diluting an extremely concentrated sample could result in lesser band overlap. On the other hand, the larger the sample volume, the larger the elution band volume; diluting excessively the sample will result in linear but very wide elution bands. Intuitively, there seems to be the possibility of an optimum sample volume for which the combination of these two effects on the resolution between two successive bands is minimum. Several approaches have been taken in the study of optimization of experimental parameters in preparative liquid chromatography (1). The semiempirical approach by Snyder (2-4) was based on results of the Craig model calculated with small plate numbers and on correlations of experimental data of various origins. These correlations relate the loading factor to the apparent column capacity factor and efficiency. The scatter of data reflects their uneven quality as well as possible model errors (including deviations from Langmuir adsorption behavior). Knox and Pyper (5) have developed an equation for calculating the conditions for the optimum throughput based on no mixed isotherm effects and 100% yield and 100% purity. Guiochon and co-workers (6-8) have calculated the production rate based on predicted chromatograms obtained from solving the mass balance equations for chromatography with a competitive Langmuir adsorption isotherm and implicitly assuming a constant axial dispersion coefficient. In this work, they assume the effect of the sample volume to be negligible. The influence of the sample volume on the band shape has been studied by previous authors primarily in the linear range of the adsorption isotherm. One of the issues that has been addressed is how the volume affects the column height equivalent to a theoretical plate (HETP) (9). Various authors have calculated the maximum volume that can be injected in order for two peaks to just be resolved, but remaining in the linear elution chromatography (10-12). Snyder (3) points out that there is little influence of the sample volume in overloaded elution when the volume of the injection is less than half the volume of the band. McDonald and Bidlingmeyer (13) have determined the variation of the apparent efficiency of several columns with increasing sample load, at various sample volumes and concentrations. From these results they have derived rules for the optimization of experimental conditions in preparative chromatography. It has been demonstrated, however, that, due to the nonlinearity of the problem, it is erroneous to discuss the optimization of the conditions for the separation of two or more compounds on the basis of data obtained with one pure compound (14). This paper studies the effect of the sample amount and the sample volume on the production rate (given in pmol/(cm2 s)) for selected two-component mixtures having various selectivities and sample compositions. A comparison is made with the Knox and Pyper model (5). The trade-off between yield and production rate will also be discussed. In the following, we have assumed that the column length is constant and that the production rate is proportional to the column cross-sectional area. The first assumption is made 0 1989 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 61, NO. 9, MAY 1, 1989
because this work is a monovariate optimization, reflecting the fact that experimentalists prepare a column and then optimize its operating parameters in order to achieve maximum production rate. The second assumption is made because scaling-up in preparative liquid chromatography is carried out essentially by increasing the column diameter, while keeping constant the column length, packing material, and mobile phase linear velocity. Experience shows that under these conditions the band profiles and the degree of separation between bands are independent of column cross-sectional area, provided that the feed be distributed uniformly over the inlet cross-section of the column, a technical problem equipment manufacturers seem to have solved (14).
THEORY Method Used. This work has been carried out by using the numerical solution to the mass balance equations previously described (15). It is based on the calculation of numerical solutions of the ideal model of chromatography, using the finite difference method and an algorithm that turns the calculation’s errors due to the finite character of the integration increments into the simulation of the effects of the apparent diffusion term, due to the resistance to radial mass transfers (16, 17). Excellent agreement between the chromatographic results predicted by this model and experimental profiles has been reported (18, 19). In previous publications, the sample is injected as a Dirac plug and has a width equal to one time increment. In the present work the injection is rectangular. Characteristics of the Separation Studied. The column length was 25 cm and its H E T P 56 pm (efficiency, 4450 theoretical plates). As suggested (20),the column was operated a t a high mobile phase velocity, 0.625 cm/s. For a column packed with 10-pm particles and a compound with a molecular diffusion in the mobile phase of 6.25 X 10” cm2/s, this corresponds to a reduced velocity of 100. For all of the separations studied, the dead time was 40 s, the retention time for a dilute injection for the first component was 270 s, and the elution time for a dilute injection for the second component was adjusted according to the relative retention. The void fraction was 0.8 and the phase ratio 0.25. In all cases, the production rates and the yields for the two components were calculated assuming a required purity of 99% for the fractions collected. The Langmuir competitive isotherm parameters are al = 23 mL/mL, a2 = 25 mL/mL, bl = 2.38 mM-’, and b2 = 2.56 mM-’. Definitions. Throughput. The throughput is the amount of sample injected in the column at the specified composition, per unit time, per unit column cross-section area. Production Rate. The production rate is the amount of sample recovered at the desired degree of purity, per unit time, per unit column area. Accordingly
where Yiis the yield of component i, fa, is the total amount injected in terms of the fraction of the column saturation capacity, ( a / b )is the ratio of the Langmuir parameters, fi,mmp is the fraction of i in the mixture, L is the column length, t is the void fraction, and tcycleis the cycle time. The ratio a/b is the maximum concentration in the stationary phase of the compound considered, at saturation; it is equal to the amount of solute per unit volume of stationary phase (dimensions, mmol/cm3). Accordingly, the production rate is reported per unit of column cross-sectional surface area. Equation 1is equivalent to the following relationship, which has been used in another paper (21):
983
where u (=F,/S) is the mobile phase flow velocity, F, the mobile phase flow rate and S the column cross-section area, Lf is the loading factor (product off, and and tR,Oand to are the limit retention time at infinite dilution and the dead time, respectively. Cycle Time. The cycle time in our study is considered to be the minimum cycle time required for consecutive, repeated isocratic injections. It is such that the first component of the (n + 1)th injection begins to elute just after the second component of the nth injection has left the column. The end points of the chromatogram are defined (arbitrarily) as the times when the concentration is equal to (femtomole). This definition is different from the one used in our other paper (21), which is tR,O - to. Injection Volume. The injection volume is defined as the width of the sample injection band and is given in units of the standard deviation of a Gaussian injection. Sample Amount. The amount of sample is reported as the loading factor or fraction of the column saturation capacity (3)
Lf is easily derived from the values of the coefficients of the Langmuir isotherm. The numerical values (see above) were selected so that the saturation capacities are the same for the two components.
RESULTS AND DISCUSSION The effect of the sample amount and the sample volume on the production rate (pmol/(cm2 s)) of component 1 and component 2 at 99% purity was studied for six two-component mixtures: three mixtures of identical relative concentration of the two compounds (25% of component 1, 75% of component 2, designed below as 1 / 3 mixture) having relative retentions at infinite dilution of 1.09, 1.25, and 1.7, respectively, and four mixtures having the same relative retention at infinite dilution (1.7) and relative composition of 1/9, 1/3, 3/1, and 9/1, respectively (see Table I). The important features of this study will be presented below. Influence of the Sample Volume on the Production Rate. Figure 1 illustrates the effect of the sample amount and the sample volume on the production rate of components 1 (Figure la) and 2 (Figure lb), respectively, for a sample having a separation factor of 1.09 and a relative composition of 1/3. These are plots of the production rate of each component versus the sample amount (in fraction of the column saturation capacity), for four different values of the sample volume, 1, 3, 5, and 10 standard deviations of the Gaussian peak observed a t infinite dilution of the first component, respectively (Le. 500 pL, 1.5 mL, 2.4 mL, 5 mL). Each curve in Figure l a goes through a maximum and is concave downward. The maxima of all these curves are not critically defined. For an increase or decrease of the sample amount of 25%, the production rate varies by no more than a few percent. The production rate of component 1for a l a injection exceeds the production rate for a 3u, 5u, and 1Ou injection over the entire range of loading factors. It is only very slightly smaller than the production rate for a Dirac injection (not shown, for the sake of clarity). In most cases, however, it would be unrealistic to consider a Dirac injection: the corresponding concentration of the sample in the mobile phase would be beyond saturation. An injection volume of the order of 1 standard deviation of the Gaussian peak obtained a t infinite dilution seems to be a reasonable compromise. Knox and Pyper (5) have already shown that little band broadening is achieved for a pure compound as long as the sample volume does not exceed half the volume of the peak (i.e., two standard deviations), a result confirmed by Guiochon et al. (22).
984
ANALYTICAL CHEMISTRY, VOL. 61, NO. 9,MAY 1, 1989 1.5 1
.+
1.3
12 1.1 1
0.9 I
j
0.0
0.7 0.6
0.5 04
0.3 0.2 0.1
2.4
,
I
Time
(sec)
Flgure 2. Influence of sample vdume on the peak profile. 1,= 2.0 % , 1/3 mixture, Dirac ( l ) , 2s, 3s,4s, 5s (5)injection volumes. I i
.
zj p 12
0.4
I
0.2
I
0 0
2
e
4
8
(b)
10
u (X)
i 4 3 e
Flgure 1. Plot of the production rate versus the loading factor ( % column saturation capaclty). Characteristics of the mixture: relative composltlon, 113;selectivity, a = 1.09. Sample volume (in standard deviation, s , of the Gaussian profile obtained for the first component at infinite dilution): 0,Is, 3s, 0, 5s, A, 10s. (a) Production Rate for component 1. (b) Production Rate for component 2.
+,
Similarly, each of the four curves on Figure I b exhibits a maximum. For a l a sample volume, the maximum production rate for component 2 is rather critically defined. It becomes less sharp for larger sample volumes. At large loading factors all the curves approach a common asymptote, nearly horizontal at approximately 1.2 pmol/(cm2 s). As the sample volume is increased, the production rate decreases over the entire range of loading factors. The optimum loading factor for maximum production rate is approximately equal to 4.5% for the first component and the maximum production rate decreases from 1.5 to 0.75 pmol/(cm2 s) when the sample volume is increased from 1 to 10 standard deviations. For the second component, the optimum sample size at the maximum production rate increases slowly with increasing sample volume from approximately 0.8 for a volume of 1 standard deviation to 5 for a 10 standard deviation volume. The maximum production rates are 2.3 and 1.5 pmol/(cm2 s), respectively. Figure 2 illustrates the influence of the injection volume for a 1 / 3 mixture, a t a selectivity of 1.09, for a loading factor of 2%. This value is intermediate between the optimum loadings for component 2 (0.9%) and for component 1 (4.3%). The elution time for this set of chromatograms is adjusted by subtracting the injection time. Note how the front and the tails coincide. The peak height of component 1 is unaffected by the injection volume while that of component 2 decreases slightly as the injection concentration decreases. The width of the first component decreases with increasing volume which is a consequence of the fact that the front of component two elutes faster under larger volumes as so adjusted. The width of the second component increases with increasing volume. The asymmetry factor for the first com-
(b)
Figure 3. Plot of the production rate versus the loading factor see Figure 1). Characteristics of the mixture: relative composition, 1/3; selectivity, 1.7. Sample volume: 0,1s ; -t 3s : 0 ,5s : A, 1Os. (a) component 1; (b) component 2.
ponent decreases with increasing concentration of the injected solute mixture while for the second component there is very little net effect. Influence of the Selectivity of the Stationary Phase. For the same sample composition, 1/3, the selectivity was increased to 1.25 and to 1.7. The variations of the production rates of both components 1and 2 as a function of the loading factor are qualitatively very similar for these two selectivities. Accordingly, only the results obtained for LY = 1.7 are reported in detail. Those for a = 1.25 are intermediate between those illustrated by Figures 1 and 3. The effect of the sample size for different values of the sample volume on the production rate of components 1 and 2, at cy = 1.7, is shown in Figure 3. The plots of the production
ANALYTICAL CHEMISTRY, VOL. 61, NO. 9, MAY 1, 1989 50
985
Table I. Experimental Conditions for Optimum Production Rate
40
comp no.
30
1 2 1 2 1 2 1 2 1 2 1 2
20
10
0 0
40
(Io
120
le4
200
240
9
8
(Y
1.09
individual mix production comp ratesn yield 1/3
1.25
1/3
1.7
1/3
1.7
3/1
1.7
1/9
1.7
9/1
1.494 2.30 6.99 12.17 16.581 35.059 49.005 92.82 65.27 52.717 64.831 34.64
Lf, %
0.383 4.25 0.983 0.9 0.503 29.2 0.983 5.9 0.590 95.2 0.993 34.0 0.546 104 0.959 29.1 0.649 82.5 0.992 43.1 0.517 122 0.812 33.2
total volb production (a) rateC 1
1
1 1 3 1 5 1 1 1 5 1
3.30 3.20 15.51 16.24 46.5 46.5 57.2 38.1 53.7 58.1 67.9 41.4
"pmol/(cm2 s). bThe injection width in u units. cProduction rate of components 1 and 2 at the optimum, under specified conditions.
7
6 5 1
3 2
11
I
1
0
Flgure 4. Plot of the production rate versus the loading factor (see Figure 1). Characteristics of the mixture: relative composltion, 311; selectivity, 1.7. Sample volume: 0,1s; +, 3s; 0 , 5s; A, 10s. (a) component 1; (b) component 2.
rates of components 1 and 2 versus the sample amount (in fraction of the column saturation capacity) are illustrated in parts a and b of Figure 3, respectively. These plots show that the sample volume has now a very little effect on the production rate for both components, except at very large sample amounts, for the first component (Figure 3a), in which case the production rate falls d o h sharply when the sample volume is reduced. The maximum production rate is achieved for a sample volume of 3 standard deviations. The elution profiles of component 1 a t large sample amounts have the classical L-shape, reported previously (6). Usually, the amount of pure component 1eluted between the two fronts is important, and the yield is of the order of 50%. However, near the maximum production rate, slight increases in the sample amount cause the two fronts to get very close to each other and lead to large drops in the production rate. Unlike the similar curve in Figure l a , the curve corresponding to a 10a injection in Figure 3a is qualitatively different from the others. This is believed to be a consequence of large differences in peak shape due to frontal effects. Figure 3b shows the production rate of component 2 as a function of the sample amount (percent column saturation capacity). Similar to Figure l b , the curve goes through a maximum, but in contrast, this maximum is much less pronounced. An asymptote is seen at large loadings, approaching 26 pmol/(cm2 s). It is remarkable that for this mixture, the optimum loading factor for maximum production rate is nearly the same, whatever the volume of solvent in which it is diluted. This is also true for the 113 mixture with a relative retention of 1.25, which is not shown. For components 1 and 2, (Y = 1.7, the values of the optimum loading factor are approximately 90% and 40%, respectively. The corresponding values of the maximum production rates, also nearly independent of the
sample volume, are approximately 16 and 33 pmol/(cm2 s), respectively. Influence of the Composition of the Binary Mixture. The effect on the production rate of the amount loaded for a 311 mixture having a separation factor of 1.7 is shown in Figure 4. In contrast to the 1/3 mixture, the sample volume influences markedly the values of the maximum production rate of component 1and of the optimum loading factor (see Figure 4a). In this case there is an optimum sample volume, giving the highest production rate for the first component. This optimum volume is 5 standard deviations. The optimum loading factor is nearly equal to the column saturation capacity and the maximum production rate, 49 ccmol/(cm2 s). For component two (see Figure 4b), the production rate increases rapidly at first with increasing value of the loading factor, and then it tends asymptotically toward values of 8.3, 8.1,8.0, and 7.4 pmol/(cm2 s) for lo, 3a, 5a, and 10a injections, respectively. The optimum loading factor is approximately constant, at 40% of column saturation capacity corresponding to a maximum production rate of 9.3 pmol/(cm2 s). Similar studies to the ones described above were carried out for a 1/9 and a 911 mixture. The qualitative trends observed for the influence of the loading factor and the sample volume on the production rate are similar to those already reported for the 1 / 3 and 3/1 mixtures. Table I summarizes the conditions under which the maximum production rate is achieved for the first or the second components, for all the mixtures investigated. The first observation, and a most important one, is that the values of the maximum production rate, the optimum sample volume and amount injected corresponding to this maximum production rate, are different for the two components of a binary mixture. The loading factor which gives the maximum production rate for component one is always much greater than that for component two. This is because, in order to optimize the production rate for component one, it is important to take advantage of the displacement effect, which tends to concentrate this compound. In contrast, in optimizing the production rate for component two, one should use displacement effects only to a limited degree and avoid tag-along effects. Clearly, the larger the separation factor, the more the column has to be overloaded in order to achieve the higher production rates and throughputs. The values of the total production rates corresponding to the maximum production rate of either component 1 or 2 are very close, except for mixtures containing more component 1 than 2. In this case the throughput corresponding to the maximum production rate of compound 1 is much larger (about 50%) than the
986
ANALYTICAL CHEMISTRY, VOL. 61, NO. 9, MAY 1, 1989 0
a O 1
223
260
530
190
140
343
290
24:
3.1:)
9
d
C
m
9 0
t
0
F 0
0 0
ICC
'5'2
230
253
3 '30
100
150
200
250
300
3
Figure 5. Chromatograms obtained under simulated experimental conditions corresponding to the optimum production rate in different cases. (a)component 1: selectivity, cy = 1.09; mixture composition, 113; sample amount, L , = 4.25%; sample volume, 1s. (b) component 2: selectivity, cy = 1.09; mixture composition, 113; sample amount, L , = 0.90%; sample volume, 1s. (c) component 1: selecthrity, cy = 1.25; mixture composition, 1/3; sample amount, L , = 29.2%; sample volume, 1s. (d) component 2: selectivity, cy = 1.25; mixture composition. 113; sample amount, L , = 5.90%; sample volume, 1s
throughput corresponding to maximum production rate of component 2. The difference between the two throughput values is large when the lesser concentrated component elutes last because the competitive effect, which leads to the second component being dragged (tag-along effect (6)), increases the amount of this second component to be recycled and reduces the throughput. Elution B a n d Profiles u n d e r Optimum Conditions. Elution band profiles of the two components of the mixture simulated under different sets of experimental conditions (different values of the selectivity and composition) are shown on Figures 5-7. For the sake of clarity of these figures, the sum of these two profiles (i.e., the chromatogram which would be registered by an ideal nonselective detector) is not shown. In each case the values of the loading factor and the sample volume corresponding to the maximum production rate of either component 1 or 2 have been selected. On each chromatogram the cut points for 99% purity are also shown. The area between the two vertical lines is the portion which re-
quires recycling. It should be emphasized that the optimum experimental conditions, especially the optimum value of the loading factor, corresponding to the maximum production rate of one component are very different from those corresponding to the maximum production rate of the other. Accordingly, when both compounds have to be recovered pure, a compromise involving the operation cost and the value of the production rate has to be found. Discussion of this problem is beyond the scope of the present work. Figure 5 shows the chromatograms corresponding to the optimum conditions for 1/3 mixtures having separation factors of 1.09 (parts a and b of Figure 5 ) and 1.25 (parts c and d of Figure 5 ) , respectively. If component 1 is the product of interest (Figure 5a,c), the second component which is in a higher concentration is employed to displace and concentrate the first component. The amount injected and processed is large, but the yields are moderate or low. For component 1, the yields vary between 40 and 60% (see Table I), depending on the characteristics of the mixture. The yield increases with
ANALYTICAL CHEMISTRY, VOL. 61, NO. 9, MAY 1, 1989 '9
a
987
b
9
L
0 60
60
n
160
260
360
160
260
360
I" _,
c
0
d
0
0
0 0
60
'60
260
360
i
Figure 8. Chromatograms obtalned under simulated experimental conditions corresponding to the optimum production rate in different cases. (a) component 1: Selectivity, a = 1.7; mixture composition, 113; sample amount, L , = 95.2%; sample volume, 3s. (b) component 2: selectivity, a = 1.7; mixture composition, 113; sample amount, L , = 34.0%; sample volume, 1s. (c)component 1; selectivity, CY = 1.7; mixture composition, 311; sample amount, L , = 104%; sample volume, 5s. (d) component 2: selectivity, CY = 1.7; mixture composition, 311; sample amount, L , = 29.1 % ; sample volume, 1s.
increasing selectivity. If component 2 is the product of interest, on the contrary, more modest degrees of column overload permit a marked reduction of the relative importance of the intermediate zone of overlap in the chromatogram (see Figure 5b,d). The yields achieved for the component of interest are much larger than in the previous case. Most yields exceed 95% (see Table I). It is interesting to compare parts b and d of Figure 5, which illustrate the chromatograms corresponding to the optimum conditions for maximum production rate of component 2, for CY = 1.09 (Figure 5b) and for a = 1.25 (Figure 5d). Since the separation factor is small in the former case, there is band overlap and at the cut point the displacement effect is still small, barely sufficient for the band of component two to begin pushing the tail of component one. On the other hand, when the separation factor is increased to 1.25 for the same mixture composition, the chromatogram corresponding to the optimum conditions for the production rate of component 2 (Figure 5d) exhibits nearly complete separation of the two bands, although considerable interaction
between them still takes place. The tail of the first component band is almost completely displaced and the little part that is eluted after the second shock of the band system (23) is small enough that the fraction cut may be placed at the second shock and allows the achievement of 99% purity of component 2, 100% yield for the second component, and 99% yield for the first component at a purity largely exceeding 99%. Figure 6 shows the chromatograms obtained for the 1/3 and the 3/1 mixtures at a separation factor of 1.7. With larger separation factors, much larger injected amounts are required to achieve equivalent displacementeffects. This in turn means higher band velocities. Thus, concentration shocks of the first component are eluted nearly at the dead time: the elution time of the front of the first component (60 s) is very near the dead time (40 s), as seen in the case of the optimization of the production rate of the first component from both the 1/3 and the 3/1 mixture (see Figure 6a,c). This is in contrast with the elution time of the first component front observed with a separation factor of 1.25, 100 (Fig. 5c), and 200 (Fig. 5d) for the optimization of the production rate of components
ANALYTICAL CHEMISTRY, VOL. 61, NO. 9, MAY 1, 1989
988
9
a m 0
L4
e, 0
?
0
9 0
260
60
3bC
‘60
260
360
?
P
C
d
r?
t 0
N
CI
0 c
C 0
C
6C
’60
263
160
260
360
Figure 7. Chromatograms obtained under similar experimental conditions corresponding to the optimum production rate in different cases. (a) component 1: selectivlty, CY = 1.7; mixture composition, 119; sample amount, L, = 82.5%; sample volume, 1s. (b) component 2: selectivity: CY = 1.7; mixture composition, 119; sample amount, L, = 43.1%; sample volume, 1s. (c) component 1: selectivity, a = 1.7; mixture composition, 911; sample amount, L , = 122%; sample volume, 5s. (d) component 2: selectivity, CY = 1.7; mixture composition, 9/1; sample amount, L , = 33.2%; sample volume, 1s.
1and 2, respectively. For the production of component two, on the contrary, displacement effects are used minimally to achieve the highest production rate with just enough band overlap to permit the achievement of the purity requirements (Figure 6b,d). Lastly, the chromatograms for the maximum production rate of either components 1 or 2, for a 9/1 and a 1/9 mixture, are presented in Figure 7. In general, the displacement effects are used to squeeze and concentrate the band of component 1,which permits a large production rate if a moderate yield is acceptable. The experimental conditions become rapidly critical, however. If the amount injected is increased slightly beyond the optimum in the case of Figure 7a, the front of component two would soon catch up with that of component one and be eluted nearly at the same time, which would thus result in a severe loss of production rate (see Figure 3a). In the case of component two, the column should be overloaded only up to the point where the front of the second component is eluted just before the end of the tail of the f i t one, allowing
moderate overlap only. This permits in the same time the achievement of a high (98%) yield and of the purity specifications. Moreover, this shows that recycle techniques are not always necessary nor even useful, at least in the case of the second component for which it would not lead to an increased production rate. Comparison with t h e Results of t h e Optimization Procedure of Knox a n d Pyper. Knox and Pyper (5) have presented a method for finding the optimum throughput which uses a very simple model. They consider that the adsorption behavior of the two components of a binary mixture follows the Langmuir isotherm but neglect solutesolute interactions. Later Snyder et al. have attempted to improve over this model by going to the other extreme assumption (4). The “blockage effect” assumes that there is no competition, but that the molecules of the first eluted component do not “see” the stationary phase in the first part of the column which is “saturated” by the molecules of the second component. The profiles shown on Figures 5 to 7 demonstrate that the actual
ANALYTICAL CHEMISTRY, VOL. 61, NO. 9, MAY 1, 1989 1
Table 11. Comparison between Throughputs Calculated by Knox and Pyper and in This Work
0.9
0.8
throughput,’ Mmoll(cm2s) this work after ref 5
a
mixture composition
1.09
113
0.32
1.25
113
5.69
1.7
119
51.5
113
51.5
311
51.5
989
0.7 0.6
911
51.5
15.5 (1) 4.5 (2) 55.3 (1) 16.6 (2) 100.5 (1) 59.1 (2) 112.0 (1) 47.1 (2) 119.9 (1) 38.7 (2) 139.2 (1) 42.7 (2)
0.5
0.4
0.3 0.2 0.1
(a)
0
o
40
Im
120
M
2m
2.0
u (9
“Amount injected per cycle time. behavior of the eluites is intermediate between those considered in these two models. Even for a selectivity of 1.7, there is some significant degree of competition between the molecules of the two components for adsorption. The optimum throughput was calculated according to the equations in ref 1 and are presented in Table 11. Since this model does not include solute-solute interactions there is no discrimination between mixtures of different composition (1/3, 3/1, 1/9, 9/1). Knox and Pyper (5) predict values of the optimum throughput which are much lower than ours for mixtures haiing a separation factor of 1.09 and 1.25. However, for the mixtures with a separation factor of 1.7, there is a good agreement for component 2 between their approximate value for the optimum throughput and the set of our more precise values (which depend on the mixture composition). For component 1,values of the throughput are still approximately double those of Knox and Pyper, because we have shown that the optimum for component two is not near the value of the throughput corresponding to a resolution of 1. The close agreement at high values of the selectivity may be due to the fact that competitive effects are less significant than at lower separation factors. This is in agreement with the fact that the “blockage effect” accounts reasonably well for results obtained at high values of the selectivity (i.e., above ca. 1.7 to 2) (24). Moreover, Knox and Pyper assume rectangular band profiles that permit the achievement of 100% pure fractions while we consider the production rate of 99% pure compounds, taking the apparent diffusion into account. Finally, we find that their assumption that the optimal production rate is achieved with a 100% yield is acceptable only for component 2 at large values of the selectivity. The Trade-off between Yield and Production Rate. The yield was studied as a function of the loading factor (fraction of column saturation capacity) for various mixture compositions (1/9, 1/3, 3/1,9/1) and at four different sample volumes (i.e. 1, 3, 5, and 10 standard deviations of the solute Gaussian band at infinite dilution). In all cases we observed that all of the yield versus loading factor curves were monotonically decreasing and concave up. More specifically, a pattern can be seen for components 1and 2 for all the different types of sample mixtures, Figure 8 (cy = 1.7). For component 1 and a l a injection (Figure 8a), the yield is practically unaffected by the mixture composition as long as the sample amount is lower than the saturation capacity of the column. At constant values of the loading factor in excess of unity, the yield increases with increasing relative concentration of component 1,as one proceeds from a 1/9 mixture to a 9/1 mixture. Figure 8b illustrates the relationship between yield and loading factor for component 2. As the relative concentration of component 1 increases, the yield decreases at all loading
I
:
0.5
4
O . l ! ,
,
o
40
,
,
,
m
,
I
120
I
I
I
,
m
160
I
2.0
u (9
Figure 8. Plot of the yield as a function of the loading factor for binary mixtures of different composition (selectivity, a = 1.7). Mixture composition: 0, 1/9; +, 1/3; 0 ,3/1; A, 911. (a) component 1, injection volume, 1s ; (b) component 2, injection volume, 3s. 1
0.9
08 07
06 05
04
03 02 01
0 0
40
80
120
160
200
240
Lf (X)
Figure 9. Plot of the yield of component 1 as a function of the loading factor for samples of different volumes. Characteristics of the mixture: selectivity, 1.7; composition, 1/3. Sample volume: 0, 1s; +, 3s; 0 ,
5s; A, 10s.
factors, over the entire range of loading factors. We observed also (results not shown) that a t any given sample composition, the sample volume does not affect the yield for component 2. This statement is valid for all sample compositions studied, for selectivities of 1.25 and 1.7. In contrast, the sample injection volume greatly affects the yield for component 1. Figure 9 shows a typical example of this effect for a 3/1 mixture. The yield remains nearly the same for all sample volumes up to a loading factor equal to unity. Beyond this point, it falls down rapidly for small sample volumes, less so for moderate values of this volume. The curve for a 100 sample volume injection is qualitatively different from those calculated for the other values of the injection band widths. This is because with a large sample volume frontal
990
ANALYTICAL CHEMISTRY, VOL. 61, NO. 9, MAY 1, 1989 1
,
0.0 0.8
0.7 0.8
0.1 0.4
0.3
0.2 0.1
0
I,
,
,
,
2
0
,
,
,
I
6
4
,
,
I
10
u (X) 1
0,s
ACKNOWLEDGMENT The authors thank Samir Ghodbane (Merck, Rahway, NJ) for fruitful discussions.
0.8
0.7 0.6 I I
f
LITERATURE CITED
0.1 0.4
0.3 0.2
0.1
o
at maximum value of the production rate tends to lie between 30% and 70%, while for component two the yields are usually greater than 98%. Even in the difficult case of a 9/ 1mixture, the yield is still higher than 80%. Thus, if one wants to meet the yield criteria, losses of component 2 are not much of a problem as long as one operates under the optimum experimental conditions or even under conditions somewhat less than optimum. However, if component 1 is the product of interest, meeting the yield criteria can result in a considerable loss of product or in high production costs, due to the large amount of material to be recycled. The reduction in sample amount injected during each cycle time can be calculated by comparing the data in Figures 1 and 10. This shows that, for a 113 mixture with a selectivity of 1.09, a 40% loss in the production rate is incurred to obtain a 80% yield. When the selectivity is 1.7, the losses range between 10% and 20% depending on the sample composition.
I
,
0
,
,
2
,
,
,
,
6
4
,
,
I
8
10
Lf (%)
Flgure 10. Plot of the yield as a function of the loading factor for samples of different volumes. Characteristics of the mixture: selectivity, 1.09; composition, 1/3. Sample volume: 0,1s; 3s; 0 , 5s; A, 10s. (a) component 1; (b) component 2.
+,
effects are taking place. Results similar to those shown on Figure 9 are obtained for the 113, 119, and 911 mixtures as well. When the selectivity becomes small, for example equal to 1.09, the yield is strongly affected by the sample volume over a much wider range of sample loadings, i.e., at values well below unity, as illustrated by Figure 10 which shows this effect for components 1 (Figure loa) and 2 (Figure lob). For both components the yield increases with decreasing sample volume. For component 2, the yield is unaffected by the sample volume at values of the loading factor in excess of 0.03 (3%); however, the recovery yields are very low at such high loadings, which are well above the optimum value for maximum production rate (see Figure 1). In preparative liquid chromatography at the process scale, a yield in excess of 80% is often considered desirable. Table I presents the yield obtained at the optimum production rate for the various mixtures studied. For component 1,the yield
(1) Guiochon, G.; Katti, A. Chromafographia 1987, 2 4 , 165. (2) Eble, J. E.; Grob, R . L.; Antle, P. E.: Snyder, L. R. J. Chromafogr. 1987, 384, 25. (3) Eble, J. E.: Grob, R. L.; Antle, P. E.; Snyder, L. R. J. Chromafogr. 1987. 384, 46. (4) Snyder, L. R.; Cox, G. 6.; Antle, P. E. Chromafographia 1987, 2 4 , 82. (5) Knox, J. H.; Pyper, H. M. J. Chromafogr. 1988, 363, 1. (6) Ghodbane, S.; Guiochon, G. J. Chromfogr. 1988, 440, 9. (7) Katti, A. M.: Guiochon, G. J. Chromafogr. 1988, 449, 25. (8) Guiochon, G.; Ghodbane, S.; Golshan-Shirazi, S.; Huang, J.-X.: Katti, A.; Lin, 6.-C.; Ma, 2. Taianfa, in press. (9) Done, J. N. J. Chromafogr. 1976, 125, 43. (10) Coq, 6.; Cretter, G.: Rocca, J. L. J. Chromafogr. 1979, 186, 457. (11) Coq. 6.; Cretier, G.; Rocca, J. L. Anal. Cbem. 1982, 5 4 , 2271. (12) Personnaz, L.; Gareil, P. Sep. Sci. Technol. 1981, 16, 135. (13) McDonald, P. D.; BMlingmeyer. B. A. I n Reparaffve Liquid Chromefography; Bldllngmeyer. B. A., Ed.; Elsevier: Amsterdam, The Netherlands, 1987; pp 26-30. (14) Colin, H. Sep. Sci. Techno/. 1987, 2 2 , 1851. (15) Guiochon, G.; Ghodbane, S. J. Phys. Cbem. 1988. 9 2 , 3682. (16) Rouchon. P.; Schonauer, M.; Valentin, P.; Guiochon, G. I n The Science of Chromafography; Brunner, F., Ed.; Elsevier: Amsterdam, The Netherlands, 1985; p 185. (17) Lin, B. C.; Guiochon, G. Sep. Sci. Technol. 1988, 2 4 , 31. (18) Golshan-Shirazi, S.; Guiochon, G. Anal. Chem. 1988, 6 0 , 2634. (19) Golshan-Shirazi, S . ; Guiochon, G. J. Chromafogr. 1989. 451, 1. (20) Ghodbane, S.; Guiochon, G. J. Chromatogr. 1988, 452, 209. (21) Golshan-Shirazi, S.; Gulochon, 0. Anal. Chem., in press. (22) Guiochon, G.; Golshan-Shirazi, S.; Jaulmes, A. Anal. Cbem. 1988, 6 0 , 1856. (23) Lln, B. C.; Goshan-Shirazi, S . ; Ma, 2.: Gulochon, G. Anal. Chem. 1988, 6 0 , 2647. (24) Ghodbane, S.: Guiochon. G. J. Chromatog. 1988, 450, 27.
RECEIVED for review September 28,1988. Accepted January 23, 1989. This work has been supported in part by Grant CHE-8715211 of the National Science Foundation and by the cooperative agreement between the University of Tennessee and Oak Ridge National Laboratory.
