Measurement of column efficiency in whole column detection

Anal. Chem. 1991, 63,575-579

575

Measurement of Column Efficiency in Whole Column Detection Chromatography Kathy L. Rowlen, Kenneth A. Duell,’ James P. Avery,’ and John W. Birks* Department of Chemistry and Cooperative I n s t i t u t e for Research in Environmental Sciences ( C I R E S ) , C a m p u s Box 216, University of Colorado, Boulder, Colorado 80309

The efficiency of a high-performance llquld chromatography (HPLC)column is measured Independently of extra-column contrlbutlons to peak varlance by means of whole column detection (WCD). The apparatus conslsts of a commerclaliy available column Instrumented with 14 lndlvldual UV absorbance detection zones. The variance of the peak at each detector Is determined by flttlng the peak to a y density functlon. A plot of total variance versus column posltlon glves a straight llne whose slope Is equal to the height equivalent to a theoretical plate, H , and whose intercept Is the sum of all contributions to extra-column variance. Variance measurements obtained on column for the three isomers of nltroaniline over the range 20-100% acetonltrlle In water gave the dependences of Hand extra-column variance on the capaclty factor, k’. I t was found that the extratolumn variance Is proportional to q / ( k ’ + 1)*, where q Is the vlscoslty of the mobile phase. This result Is explained in terms of broadening wlthin the Connecting tubing by an amount proportlonalto the viscosity and focusing at the head of the column by l / ( k ’ + 1)2. Contributions to extra-column varlance by the Injector and eiectronlc lntegratlon tlme are calculated from first prlnclpies and found to be small, while the average varlance contribution from the detectors Is deduced from the Intercept of a plot of extra-column variance vs q/(k’ I)*.

+

We recently evaluated the potential advantages of continuously monitoring the progress of a separation at multiple sites along a high-performance liquid chromatography (HPLC) column ( I , 2). Here, it is demonstrated that the technique of “whole column detection” (WCD) chromatography provides accurate measurements of column efficiency in the absence of complications arising from extra-column contributions to band broadening by the injector, connecting tubing, detectors, electronic time constant, etc. All contributions to peak variance in a previously reported WCD instrument (2) are completely characterized by a combination of theory and experiment. Column efficiency, often designated as the height equivalent to a theoretical plate (HETP or H), provides a measure of how peaks broaden as they pass through a chromatographic column. It is a function of particle size and shape, thickness of the stationary phase, diffusion coefficients of the analyte in the mobile and stationary phases, solvent viscosity, flow rate, and uniformity of the packing material. H has been of considerable import since the advent of HPLC, primarily because it provides the chromatographer with an idea of how a particular column can be expected to perform (3). However, with only postcolumn detection, it remains a difficult task to determine column efficiency accurately. The difficulty arises because H is related to the width of a peak o n column. Postcolumn detection measurements of peak width are comPresent address: Department of Electrical and Computer Engineering and CIRES, University of Colorado, Boulder, CO 80309.

plicated by extra-column contributions. Extra-column sources of peak broadening include the injector, connecting tubing, detector(s), and electronic response time. By definitiion, H is given by where upco1is the second moment or variance resulting from eluting a distance x along the column ( 4 ) . Assuming that all contributions to peak width are independent, the total variance of a peak is the sum of all contributions. For most systems, the equation is given by where the subscripts inj, c.t., col, det, and el represent the injector, connecting tubing, column, detector, and electronic contributions, respectively. As discussed by Claessens et al. ( 5 ) ,there are two popular methods for quantitation of extra-column band-broadening contributions. One method involves replacing the column with a zero dead volume union; thus, the total measured variance is due only to the instrument. Another method is to replace the column with a capillary tube. Extra-column variance is then the total measured variance minus the variance contribution from the capillary. Alternatively, the length of the capillary may be varied and a plot of total variance versus capillary length constructed. The instrument variance is then obtained by extrapolating to zero capillary length. However, as Claessens et al. (5)also point out, these methods are limited in their ability to measure true extra-column variance contributions since none accounts for extra-column contributions associated with sample introduction onto the column. Although theoretically difficult to treat, the cohtributions to band broadening associated with frits, the flow profile at the entrance and exit of the column, and the back pressure caused by the column are all thought to be of importance (5, 6). Another method for the measurement of column variance, the “linear extrapolation method” (LEM), is sometimes used as an alternative to those mentioned above. The LEM involves plotting total variance against (1+ k’)2;the slope of the plot ( t o 2 / N )is related to column efficiency, and the intercept is instrument variance. In practice, however, the LEM is accurate only for a very narrow range of conditions and is thus not sufficiently robust for widespread use ( 5 ) . In this work, it is shown that whole column detection allows independent measurements of column efficiency and extracolumn band-broadening contributions. This is accomplished by taking advantage of multiple measurements of peak width along the length of the column. Since uzc0l = x H , a plot of total variance versus column position, x, has a slope of H and an intercept that corresponds to the summation of all extracolumn variance contributions. The benefits of this method include (1)ease of application to a wide range of condtions, (2) independent determination of extra-column sources with the chromatographic system intact, and (3) multiple measurements within a single run. Recently, using laser-induced fluorescence detection at two points on an unpacked capillary tube, Evans and McGuffin

0 1991 American Chemical Society 0003-2700/91/0363-0575$02.50/0

576

ANALYTICAL CHEMISTRY, VOL. 63, NO. 6, MARCH 15, 1991

The circuitry which controls diode sampling is similar to that

Photodiodes (on 1 cm centers)

used in diode array detectors. All of the diodes are sequentially I mm

I

15 cm

I

SIDE VIEW

CROSS-SECTIONAL VIEW

Figure 1. Longitudinal view of the WCD instrument showing the positioning of the photodiodes along the column and cross-sectional view showing light propagation through the column.

(7) demonstrated the separation of extra-column variance from that due to dispersion within the capillary. The work reported here makes use of multiple (14) UV absorbance detection zones on a commercially available, packed HPLC column and demonstrates the behavior of peaks interacting with a stationary phase.

EXPERIMENTAL SECTION Instrument. The chromatographic system is composed of a Kratos Spectroflow 400 HPLC pump, a Rheodyne injector with a 1-pL injection loop, a 15-cm glass cartridge column (Alltech Assoc., 3-mm i.d.) packed with 5-pm of ODs, a Kratos Spectroflow 773 multiple-wavelength absorbance detector, and a Shimadzu CR3A integrating recorder. All of the solvents used were Burdick & Jackson HPLC grade and the chemicals Aldrich Reagent grade. In all experiments, the HPLC solvent flow rate is 0.4 mL/min. As shown in Figure 1, and detailed previously (2), the cartridge system is instrumented with 14 UV-sensitive photodiodes (Hamamatsu 51226-18BQlight sensitive area = 1.0 mm2)mounted within holes at 1-cm intervals along the stainless steel cartridge holder. The metal case for each photodiode is sealed to the steel holder with nonconductive paint. The source light entrance holes (1-mm diameter) are located at points directly opposite (MOO) of each photodiode along the holder. The light source is an 8-W, 25-cm-long backlamp (Sylvania F8T5) having a maximum intensity at 366 nm with an approximate bandwidth of 50 nm. No optical filters were used. Detection Zones. As shown schematically in Figure 1, because of multiple scattering events within the packing material, only a small fraction of the light entering the column reaches the corresponding photodiode detector. The photodiodes were placed 1-cm apart to avoid cross-talk. This distance was arrived at by simple calculations using Snell’s law and assuming an average refractive index for the combined stationary and mobile phases. A more sophisticated random walk calculation, which assumes isotropic scattering at individual particles, indicates that light rays that stray very far from the direct path between the light source and detector seldom reach the photodiode; thus, theory suggests that the effective detection volume is relatively small compared to the total volume illuminated. A major goal of the present study was to determine experimentally the contribution of the detection zones to peak variance. Stray light is also a factor that must be considered. Figure 1 shows how some light rays reach the photodiode by internal reflections within the glass wall rather than by passing through the sorbent. As discussed below, this effect contributes to deviations from the Beer-Lambert law but is corrected for. The experimentally determined limit of detection ( S I N = 3) is approximately absorbance units.

sampled within 4 ms, resulting in a “snapshot” of those positions probed by the detection cells. Diode integration time is variable between 50 and lo00 ms. In all of the experiments reported here, a 650-ms integration time was used. For the narrowest peak measured, an unretained peak having a baseline width ( 8 ~of) 13 s at the inlet of the column, 20 data points were obtained. The widest peak characterized (k’ = 10 at the exit of the column) was sampled 165 times. This sampling rate is faster than required for complete characterization of the frequency components of all peaks, as previously discussed (8). In order to compare peak parameters measured at each point on the column, ideally the response from every diode would be identical and vary linearly with concentration. In a highly scatteringmedium, such as the column packing material, nonlinear absorbance versus concentration plots are observed. For our system, nonlinear absorbance plots are due to a combination of stray light, multiple path lengths (i.e., light scattering), and multiple wavelengths. Linearization and calibration of detector response was achieved with software as described earlier (2); however, in this study, the detector contribution to band broadening was not digitally filtered and peak areas were not normalized. Peak Model. Bidlingmeyer and Warren (3) recently compared nine of the most commonly used methods for determining peak width. They concluded that the use of peak width at half height (2.35~)provides one of the most inaccurate values of plate height, approximately a factor of 2 smaller than the true value. The method of moments (integration of peak with no assumptions about peak shape) resulted in the most accurate measurement of H. However, in a noisy background with no assumptions about peak shape, it is difficult to define start and stop points for integration; as a result, the effectiveness of the method of moments is diminished. Smit et al. (9) have derived the y density function in terms of the plate theory, which is used to describe the process of elution:

where K represents the amplitude of the peak, tois the retention time, 7 is a measure of peak width, and n is the asymmetry factor. The y density function approaches a Gaussian shape as n becomes large. Results from our laboratory indicate that use of the y density function provides a more robust measure of peak parameters than does the method of moments, since a fit to the model allows peak identification in a noisy background. Therefore, in this work, peak parameters are determined by fitting the experimental peak with a y density function via the method of nonlinear least squares. The second moment (variance) of the y density function is 127~.All variances reported herein are in terms of length. For our data, the best fit (relative mean standard error = was achieved by using an asymmetry factor (n)of 6. For comparison, the moment coefficients for skewness (a3)and kurtosis (a4) are 0 and 3, respectively, for a Gaussian and u3 0.8 and u4 z 4 for the peaks reported here (9). The slight deviation from Gaussian peak shape may be due to multiple analyte/stationary-phase interactions, since polar compounds are used. The nitroaniline analytes were chosen for this work because of their strong absorption at the wavelength maximum (366 nm) of the lamp and their lack of fluorescence. The concentrations injected are 1.8,2.6, and 0.75 mg/mL for the ortho, meta, and para isomers of nitroaniline, respectively. Based on a calculation of the maximum loading density occurring at the head of the column (1.4 mg/g of C-18) for the highest concentration analyte (2-nitroaniline) under the most focused conditions, the injected concentrations are estimated to be within the linear region of the adsorption isotherm.

RESULTS AND DISCUSSION Plate Height. By combining eqs 1 and 2, it is clear that the total variance of a chromatographic system is given by (4)


577

I 50 1

1400

800

n

20%ACN

tt

./

J

40

-

30

-

20

-

600

0

2-nlroaniiine

A

3-nnroaniline 4-nnroaniline

400

200

k'+l

plate height ( H )versus retention (k'+ 1) for the three isomers of nitroaniline. Figure 3. Plot of

0

0

~

~

"

2

4

"

"

6

"

"

"

'

~

8 1 0 1 2 1 4

Column Position, cm

Total measured variance versus column position for 2nitroaniline.

Figure 2.

Table I. Plate Height and Extra-Column Variance 7'0 ACN in H 2 0

k'

H,

1 0 - cm ~

Xb2extra-colr

cm2

torr

coeff, r

20 30 40 100

Analyte: 2-Nitroaniline 10.0 14.9 20.0 4.47 14.9 26.9 2.08 20.8 34.9 0.055 32.2 68.1

0.98 0.94 0.94 0.97

20 30 40 100


0.95 0.95 0.93 0.95

20 30 40 100


0.94 0.94 0.95 0.84

xu2extra.col

where is the summation of all extra-column contributions to band broadening. Since WCD provides a measure of u2t,,talas a function of column position (x), a plot of uZtotalversus x has a slope equal to H and an intercept equal Figure 2 is such a plot for 2-nitroaniline in 20%, to ~u2extra.col. 3070, 40%, and 100% acetonitrile (ACN) in water. These plots can be constructed for any resolved peak that has traversed the length of the column. Table I summarizes values of H and of extra-column variance obtained from least-squares fits to plots of u2totalversus x for the three isomers of nitroaniline in the mobile-phase compositions given above. Note that the slope (H) of the line shown in Figure 2 is not independent of mobile-phase composition (i.e., capacity factor). H dependence on k' has been attributed to differing diffusion coefficients for each analyte in the mobile and stationary phases ( 4 ) . A plot of H versus k ' + 1 is given in Figure 3. For all three isomers, H is observed to decrease with increasing retention. The values of H measured here are similar to those cm). reported by the column manufacturer Upon close inspection of Figure 2, it is apparent that there is a much larger slope (plate height H)for lines fitting the variances obtained at the first 3 diodes than for lines fitting

the remaining 11. This is true for all four solvent systems and is also seen in the plots for 3-nitroaniline and 4-nitroaniline. The larger plate height inferred from data a t the first three diodes may be due to (1) less efficient packing of stationary-phase particles at the head of the column or (2) a systematic variation in the effective detection volumes for the first three diodes. In fact, the scatter of the data about the least-squares lines is most likely due to differences in the detector variance for each of the discrete detection zones. The determination of H by detection at numerous sites on the column, rather than at only two sites (7),allows one to observe the variability in H along the column. Extra-Column Variance. As seen in Figure 2 and Table I, the values of extra-column variance, given by the intercepts of plots of uztotalversus x, vary greatly. In the following, we analyze the various contributions to extra-column variance and show that its variability can be completely explained in terms of solvent viscosity effects on peak broadening within the connecting tubing and solvent effects of focusing of the concentration profile at the head of the column. Variance Due t o Electronic Integration Time. The variance contribution resulting from the application of an integration time, t , to a concentration profile may be derived analogous to that for an injector or detector of fixed volume ( 4 ) and is given by L2/12 where L is the distance traveled by the peak during the ihtegration time t (650 ms in this study). Thus, we have

where uo is the velocity of an unretained peak (9.9 cm/min in this study). The maximum contribution occurs for an unretained peak and is calculated to be 9.6 X cm2. In our experiments, however, eq 5 is not exact because the integration time is applied to transmittance data rather than absorbance data. For a Gaussian absorbance profile, for example, the signal processed by the photodiodes has the functional form loGawh and a second moment only 0.61 times that of the Gaus'sian. We have been unable to derive an analytic solution for the contribution to variance of an integration time applied prior to taking the logarithm. Therefore, variance contributions of the integration time were calculated by numerical simulations. It was found that, in the worst case of an unretained peak, the variance is 19% greater than that predicted by eq 5 and that the variance contribution of the

578


integration time converges to that of eq 5 as k’increases. The integration time makes a nearly negligible contribution to total variance: in the worst case of an unretained peak, the contribution is 1.7%.

Variance Due to Injector and Connecting Tubing. Sternberg ( 4 ) has shown that uZinjmay be calculated by a?nj

loo

80

I .

I

Z-nitroan!Pne

8-nitroaniline A

4.nitroanJline

vinj

=A2inj~2

where Vinjis the injection volume (1 pL), Ainjis the crosssectional area of the injection loop, and K is a variable that is determined by the injector input function. For the efficient liquid valve used in this study, the input function should be very nearly ideal; that is, = 12 (4). The worst possible case would be a semiparabolic input function (41, with aZinj approximately a factor of 2 larger than that calculated from eq 6. Sternberg has also shown that the injector variance decreases by a factor of (Ainj/Acol)2 upon entering the column where A,,I is the cross-sectionalarea of the mobile phase within the column. Acol(4.04 X cm2)was calculated from a ratio of the volumetric flow rate (0.4 cm3/min) and the linear velocity of the solvent (velocity of an unretained peak, 9.9 cm/min). Thus, for the system used here, uZinj 5.1 X cm2 and constitutes a negligible (

Measurement of column efficiency in whole column detection

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