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Flow-Cell-induced Dispersion in Flow-through Absorbance Detection Systems. True Column Effluent Peak Variance. Purnendu K. Dasgupta, Charles Phillip Shelor, Akinde Florence Kadjo, and Karsten G. Kraiczek Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b04248 • Publication Date (Web): 28 Dec 2017 Downloaded from http://pubs.acs.org on December 30, 2017
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Analytical Chemistry
Flow-Cell-induced Dispersion in Flow-through Absorbance Detection Systems. True Column Effluent Peak Variance. Purnendu K. Dasgupta*, Charles Phillip Shelor, Akinde Florence Kadjo Department of Chemistry and Biochemistry, University of Texas at Arlington, Arlington, Texas 76019-0065, United States. Karsten G. Kraiczek Agilent Technologies, Hewlett-Packard Strasse 8, D 76337 Waldbronn, Germany. ABSTRACT: Following a brief overview of the emergence of absorbance detection in liquid chromatography, we focus on the dispersion caused by the absorbance measurement cell and its inlet. A simple experiment is proposed wherein chromatographic flow and conditions are held constant but a variable portion of the column effluent is directed into the detector. The temporal peak variance ( , , which increases as the flow rate (F) through the detector decreases, is found to be well-described as a quadratic function of 1 /F. This allows the extrapolation of the results to zero residence time in the detector and thence the determination of the true variance of the peak prior to the detector (this includes contribution of all preceding components). This general approach should be equally applicable to detection systems other than absorbance. We also experiment where the inlet/outlet system remains the same but the path length is varied. This allows one to assess the individual contributions of the cell itself and the inlet/outlet system.to the total observed peak. The dispersion in the cell itself has often been modeled as a flow-independent parameter, dependent only on the cell volume. Except for very long path/large volume cells, this paradigm is simply incorrect.
INTRODUCTION Millikan was the first to describe a “photoelectric colorimeter”.1 Using 1-2 mm i.d. tubes containing stationary samples, he demonstrated the sensitive measurement of various hemoglobins. Liquid phase flow-through optical absorption measurements using an in-situ phototransducer was reported shortly thereafter by Roughton, in the context of kinetic measurement of rapid reactions following the mixing of two reactants.2 By the early 1950’s, Chance made great improvements in the speed and accuracy of accelerated and stopped-flow spectrophotometric measurements, attaining error levels of 20 µAU.3 The late 1950’s and the early 1960’s saw a succession of major developments in liquid phase analysis. In 1957, Skeggs4 described the automated colorimetric measurement of discrete samples conveyed by a segmented carrier fluid. Spackman, Stein, and Moore’s automated amino acid analyzer was the first liquid chromatograph (LC);5 optical absorbance was the first detection method used in LC. Stein and Moore ultimately won the Nobel for this work, which relied on absorbance measurement of the ninhydrin-amino acid reaction products. Their instrument design seemingly anticipated future variable wavelength and path length needs: it utilized three serial photometric cells, two terminal ones monitored absorption at 570 nm using different path lengths to accommodate greatly differing sensitivities (and concentrations) of different amino acids and a middle one monitored absorption at 440 nm for proline/hydroxyproline. The same separation is presently accomplished on high efficiency columns in 1/50th the time but the principle remains the same.6 High performance liquid chromatography made its commercial debut in 1963 as a gel-permeation chromatograph with a refractometer as the first detector.7 In 1966, Horvath and Lipsky8 modified a commercial UV-
visible spectrometer with a 5-mm path (3.9 µL) flow cell for the first LC-UV experiment. In 1967, the first analytical liquid chromatograph was introduced with an UV absorbance detector as an option.7 In the intervening half century, LC has not only climbed to the pinnacle of commercial success, the speed and efficiency has remarkably increased: separations can be accomplished in less than a second.9 The observed results are influenced by all extracolumn components: injector, connecting tubing, the cell and its inlet/outlet system, the nature of detector signal processing and even the data acquisition system.10 Absorbance detection has not only remained a mainstay in HPLC, it presents a unique dilemma. The sensitivity of absorbance detection improves with increasing pathlength but increasing pathlength typically increases the volume of the cell, which increases the cell-induced dispersion. In recent years, the advent of liquid core waveguide (LCW) cells11 have made possible very small diameter cells, a 10 mm path cell is available for Ultra HPLC applications with a volume of only 100 nL (~100 µm bore).12 Regardless, there are limits to reducing the cell diameter: light throughput controls shot noise which ultimately determines the attainable signal to noise ratio. For LCW cells, Kraiczek et al.13 have considered the relationship between chromatographic resolution and absorbance detection limits in HPLC. Such considerations obligatorily must assume a point of compromise: no additional dispersion is wanted by a chromatographer but no external detection is possible if detectorinduced dispersion must be zero. The choice of this point of compromise is arbitrary. In addition, a reduction in cell volume does not result in a proportionate reduction in the cell-induced dispersion: Cell inlet/outlets will typically contribute a fixed and appreciable
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level of dispersion. Entrance and exit to/from the cell involve abrupt changes in flow direction, and often, changes in the flow geometry and/or hydraulic diameter. These contribute to the dispersion beyond that due to the cell itself. The relative magnitudes have not been studied. Mathematical transform/deconvolution approaches have previously been advanced to determine individual dispersion contributions.14,15 The present paper reports on a simple method to determine the overall contribution of the detection cell to the dispersion of a chromatographic band and hence to correct for it. The approach relies on carrying out chromatography under constant conditions but directing a variable portion of the column effluent flow to the detector while the rest is directed to waste. Under constant chromatographic conditions, the dispersion of individual peaks exiting the column remain the same. But the temporal peak dispersion as observed by the detector varies considerably, increasing with decreasing flow rate through the detector. If the measured peak variance can be extrapolated to zero detector residence time, the true efficiency of the band prior to entering the detector may be computed. We also use a specially constructed absorbance detection cell where the inlet/outlet remain unaltered but the pathlength can be varied by moving the receiver fiber optic. If the dispersion from the detector cell can be ascertained as a function of the cell path length, the user can choose the best path length for a given application. The pathlength dependent dispersion data allows an estimate of the zero-path dispersion, which can be attributed to the cell inlet/outlet. EXPERIMENTAL SECTION Chromatography. The chromatography system consisted of a G4204A quaternary pump, G1316C column compartment set to 30 °C, and a G4226A high pressure autosampler (all chromatographic equipment and supplies hereinbelow from www.agilent.com). The test solution containing dimethyl phthalate, diethyl phthalate, biphenyl, o-terphenyl, and bis(2ethylhexyl) phthalate (0.15, 0.15, 0.01, 0.03 and 0.32% w/w, respectively) in 50% acetonitrile was injected (0.5 µL) onto a 2.1 x 150 mm Poroshell (120 EC-C18, 2.7 µm) column, using 100% acetonitrile as eluent @350 L/min. Injector/injection details are given in the Supporting Information (SI). Referring to the top panel of Figure 1, the column outlet was connected with a 20 cm length of 0.12 mm i.d. stainless steel tubing (Tube 1) to a zero dead volume tee. The opposing arm of the tee was connected to the detector inlet with a 6, 12 or 18 cm length of a 20 µm i.d. fused silica tube (Tube 3). The tee-port was provided with a restriction capillary (Tube 2) to direct a controlled amount of flow to waste. Table S1 lists the combination of tubes that allowed 47-176 µL/min to proceed through the detection cell. Initially, the tee arm was simply plugged to allow all of the column effluent to flow through the detector cell to attain a cell flow rate (F) of 350 µL/min. Subsequent experiments showed that even for the sharpest peak, the results could not be distinguished from a configuration where the column was directly connected to the detector with Tube 1. The results were used interchangeably but the vast majority of the F=350 µL/min data were obtained in the latter (no tee) configuration. Cells. Three fixed path length cells (3.7, 10, and 60 mm, P/N G4212-60032, G4212-60008, and G4212-60007, respectively; see Figure S116 in the Supporting Information (SI)) were used
in various experiments. The majority of the experiments, however, were conducted with a modified 60 mm base-path cell in
Figure 1. Top: System schematic. Bottom: Five analyte chromatogram obtained using the conditions given in the experimental section. No split, F = 350 L/min, 3.7 mm path cell. which the receiver fiber optic (also the liquid exit end) could be placed at any location inside the cell by a micrometer to create any pathlength from zero (input and receiver fibers touching) to 60 mm (maximum length permitted by the tube), referred to as the variable path length (VPL) cell hereinbelow (Figure 2). The VPL and fixed path cells are constructed similarly with a 535 µm i.d. fused silica tube as the main body with 440 µm o.d. (400 µm core) fused silica optical fibers protruding into the tube and custom PEEK tees with the tee arms serving as the inlet/outlet. The output of the G7117A Detector was recorded at 80 Hz with a response time of 63 ms. A 4 nm slit width was used. The 254 nm signal was referenced to the 360 nm signal averaged over 100 nm pixel bandwidth.
Figure 2. Variable path length cell (based on the cell block 3, Figure S1 in SI, with a 60 mm base path). The light exit fiber EF is movable via a feed-through micrometer drive, reading out the path length. Light is focused on the inlet fiber IF. The EF output is focused on the Array Detector (Figure S1). Experiments and Peak Variance Calculation. The 5-analyte mixture was chromatographed with detector cell flow rates of
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Analytical Chemistry 47.4, 76.9, 111, 176 and 350 µL/min for the three fixed path length cells and at 47.4, 111, 176 and 350 µL/min with the VPL cell, using path lengths of 0.025, 0.100, 0.250, 0.500, 1.00, 2.50, 5.00, 10.0, 15.0, 20.0, 30.0, 40.0, 50.0, and 60.0 mm, each chromatogram was run in triplicate. Without counting replicates, this would in principle result in 45 and 280 peaks to analyze for the fixed path and the VPL cells, respectively. Peak standard deviation reported in the main text was computed as the Gaussian ideal (half-width at 60.65% of the peak height17,18). For peak 5, a comparison based on the second statistical moment is also reported. However, since the analytes were not singly injected, half-widths could not be measured for poorly resolved peaks. Only peak 5 could be analyzed under all combination of cell pathlengths and flow rates. At the other extreme, peaks 1 and 2 could be analyzed only for short pathlengths and generally only at higher flow rates. While large dispersion conditions resulted in non-Gaussian peaks; most highly dispersed peaks were automatically excluded due to poor resolution. PRINCIPLES Detector-Induced Dispersion. We formulate the overall observed peak dispersion ( ) as: =
+
=
+
+
...(1)
is the variance of the peak as it enters the detecWhere tor (this includes all preceding components, including the inconsists of jector, column and connecting tubing), and ) and the cell itself contributions from both the cell inlet ( ). The peak standard deviation can be expressed either in ( time ( ) or volume ( ), the latter simply being F where F is the flow rate. Volumetric dispersion is typically more discussed but most chromatograms are depicted in time. We have chosen to use both temporal and volumetric dispersion in different sections of this paper. The caveats are that using and as the dependent variables results respectively in greater weighting of data at lower flow rates and larger volume cells. Inlet/outlet geometries are typically mirror images. One may wonder why the outlet, by which point measurement is complete, should have any effect. The combination of the inletoutlet geometries governs the flow dynamics that contributes to hydrodynamic dispersion in the cell. With the present geometry, for very short path cells, there may be poor overlap of the flow path and theoretically probed volume. For long cells, the inlet-outlet interaction is increasingly decoupled. In the present experiments by maintaining constant chromatois held constant. But as flow graphic conditions, , through the detector changes, , and hence , changes. If the dependence of , on F (specifically meaning flow rate through the detector) can be established, the data can potentially be extrapolated to infinite flow rate to render , to zero. While there is universal agreement that to prevent apparent deterioration of chromatographic efficiency, the maximum cell volume should be a “small” fraction of the sharpest peak volume, quantitative descriptions differ. This is not a new problem; we refer to the erstwhile classic by Snyder and Kirkland.19 They suggested a value of 10%, citing Sternberg,20 albeit how consideration of Sternberg leads to this value is unclear to us. Sternberg treated manifold causes of extracolumn dispersion. While his focus was on gas chromatography, the
same principles apply. Sternberg considered the finite response volume of the cell (Vcell) that acts to integrate the measured signal, thus deriving , as: ,
=
(Vcell/F)2 ...(2)
Sternberg’s treatment computes the second moment of a rectangular plug entering and leaving the cell without any mixing or dispersion (perfect plug flow) for which K is 12. Subsequent efforts to include effects of mixing invoke that K can have different values. In this paradigm, zero mixing provides K=12 whereas K=1 corresponds to the behavior of an ideal mixer21 (see also the Supporting Information for derivation of K for the zero and ideal mixing cases). One would readily appreciate that K=1 results in , equaling the nominal cell residence time. The problem with this terminology of an unity K connoting an ideal mixer is that a poorly swept cell would have K 15 mm, r2 for fit remains at 1.000, even at L = 10 mm it is 0.997. It degrades some in shorter path cells for reasons that will be discussed later. The relative standard deviation in reduces from 4% to 3% if considerations are confined ,
to L > 10 mm. Table S2 in the SI presents all relevant regression statistics for all 5 peaks. Instead of taking , as the half-width at 0.6065 h, we also calculated , as the second moment following the computational algorithm outlined by Morton and Young.25 The results are shown in Figure S4 in the SI for the same chromatographic peaks analyzed in Figure 4. As the peak is not perfectly Gaussian, the , values calculated as the second moment are predictably higher but otherwise the pattern is identical. The extrapolated intercept has a higher uncertainty (1.4230.357 s2) but in the end, this is barely statistically distinguishable from that obtained by the half-width-based assessment of , .
Figure 4. Quadratic fit of the observed temporal variance of peak 5 for thirteen different path lengths in the VPL cell. The intercept (sd) averages 1.0230.037 s2 compared to the lowest , value of 1.354 s2 noted for the L = 0.50 mm cell at F = 350 L/min. The inset shows an ordinate magnified view, the full original abscissa scale is presented. Note curvature change with L, the dependence being essentially linear at L = 20 mm. peaks, data could be For the earlier eluting, smaller , processed only for smaller L cells due to insufficient resolution at longer pathlengths. For peaks 1 and 2, data for all flow rates were usable for at least four different values of L. For peaks 3 and 4, this increased to eight values of L. The fits to eq 4 for peaks 1-4 are presented in Figures S5-S8; the minimum r2 values for individual L values were 0.98, 0.98, 0.97, and 0.96 for peaks 1-4. Values Much Efficiencies Based on Extrapolated , Better Compared to Any Actual Cell. The smallest , observed for peak 5 was 1.340 s2 (F = 350 µL/min, L = 0.1 mm). This is respectively 31 and 35% higher than the average intercept of 1.023 s2 for all cell paths and specific intercept of 0.994 s2 for the L = 0.1 mm cell. The computed efficiency for the peak thus suffers by >30% from cell-induced dispersion. Confidence in the robustness of the method comes from the close correspondence of the data to the quadratic model across the path length range. We considered the data for an altogether
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Analytical Chemistry different fixed path 60 mm cell obtained on a different day, the r2 for a fit to eq 4 for peak 5 (5 flow rates) was 0.9999. The observed , at the highest flow rate was 2.415 s2 compared to an intercept of 1.1400.321 s2 (the 95% uncertainty limits are those of the fit, there is only one data set) which overlaps the 1.0230.037 s2 value reported for all the L values taken together in Figure 4. In this case, the large cell is causing a more than a factor of two loss in the observed efficiency, even with the significant intrinsic variance for peak 5. Predictably, peaks with less intrinsic variance are more affected, the effect being significant even with short cells. Consider the case for peak 1 for the 3.7 mm fixed path cell, the shortest of this family in commercial use. The observed , for F = 350 µL/min was 0.2924 s2 compared to the extrapolated intercept ( , ) of 0.19380.0215 s2 (r2 0.9970, n=5), equivalent to ~50% lower efficiency for the peak. For peak 5 @350 µL/min (nominal velocity u 1.68 mm/s, tR 163.1 s.), a variance of 1.023 s2 leads to N = 26,000 for a 150 mm column. The plate height and the reduced plate height are 5.77 µm and 2.14, respectively. Van Deemter behavior reported in the literature26 for 2.7 µm superficially porous particles showed a hmin of 5.53 µm and uopt of 0.35 mm/s. By u = 1.68 mm/s, h increased 1.51x to 8.37 µm. Assuming the same degree of change in the present case, the best case reduced plate height at uopt would be 1.42. Physical Significance of Eq 4. While eq 4 is empirical, it is tempting to relate at least the quadratic term to one akin to eq 2, i.e., as being response volume related. The first-degree coefficients may relate to cell inlet/outlet plus hydrodynamic dispersion. Plots of p and q as a function of Vcell2 are presented in Figure 5 for L 15 mm (see below for reasons for limiting the data to higher Vcell values, all data appear in Table S2).
Figure 5. Plot of best fit 1 coefficients p (blue diamonds) and 2 coefficients q (red circles) in eq 4 for peak 5 as a function of the square of the nominal cell volume. The slope of the q vs Vcell2 plot corresponds to 1/K in eq 2. While the q values for L 20 mm are reasonably linear with Vcell2 (r2 = 0.9952), and the reciprocal slope indicates a reasonable value for K (9.2), by L 15 mm, q becomes negative. the
slope calculated for data comprising of even lower Vcell2 values produce a K far exceeding 12. Obviously, over a large range of Vcell, especially small values, simile with eq 2 is not meaningful. Note that, compared to the q values, the p-values are nearly constant with Vcell2, even to lower values, the meansd for p in the entire L = 0.10-60 mm (Table S2) range is 2.970.57. The constancy suggests that this term arises largely from a Vcell-independent component, likely the cell inlet/outlet system. At either extreme of L or Vcell, this paradigm correctly predicts the observed behavior: for a large Vcell when the dispersion is dominated by that in the cell rather than the inlet, is expected to linearly increase with 1/F2 as seen in Fig, ure S9 (peak 5 in L = 60 mm cell). Conversely inlet/outlet effects may be dominant in a small volume cell, resulting in a linear dependence of , on 1/F (see e.g., data for peak 2 in a 3.7 mm fixed path cell, Figure S10). The overall dispersion thus represents a competition for dominance between the inlet/outlet, and the cell itself. This is reflected in the Figure 4 inset where the ordinate scaling is magnified. The curvature of each trace is a balancing act: when the cell inlet/outlet dominates as with short path cells, the plot approaches a plateau at high 1/F. When the cell volume is the dominant cause for dispersion (as with high L), there is a steep upward curvature. A near straight line results when these two effects balance each other, in this case at L = 20 mm. For intrinsically narrower peaks, this balance point is reached at a lower L. Short and Very Short Path Cells. Flow Dynamics, Dispersion and Reproducibility. Much of the discussion in this section may be unique to the geometry of the present cells, which involve a transition from the connecting tube (0.12 mm ) to a right-angle change in flow direction to an annulus (inner 0.440 mm, outer 0.535 mm, annular gap 47.5 µm) to the principal flow channel of 0.535 mm , then the outlet geometry presents a mirror image. Especially for very small L, some of the inlet flow can pass from the inlet annulus to the outlet annulus without ever entering the optical path, making a poorly swept cell. We hasten to add that the VPL cell was intended to study parametric behavior, not to create a very short path cell to be actually used. Even without fluid dynamic modeling it is obvious that the smaller the separation between the optical fibers, the greater is the fraction of the inlet flow to pass directly to the outlet without traversing the optical path. The smallest path (L = 0.025 mm) cell did not produce the smallest dispersion for any peak at any flow rate. For a given peak, one would normally expect a monotonic increase in the observed temporal dispersion (after all, Vcell is increasing) but this is not observed in the small L domain. See Figure S11 for the behavior of peak 1 at various flow rates for L 10 mm. A monotonic increase of , with the cell path length, would suggest that the flow dynamics has attained a stable pattern. This was not observed at least until L = 1 mm for F = 47.4 and 111 µL/min and L = 2.5 mm for F = 350 µL/min. For the extreme case of the 0.025 mm path cell, the instability in the flow pattern shows up in variations in peak height and even in the peak standard deviation. The relative standard deviation values of the peak half-width (measured in triplicate at all flow rates), were well below 1% (averaging 0.21, 0.28, 0.27, 0.26, and 0.29% for peaks 1-5, respectively) for all other cells, while those for the L = 0.025 mm cell averaged 2.43, 2.87, 1.82, 1.96, and 7.13% for peaks 1-5, respectively. The data are graphically displayed in Figures S12-S16.
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Short cell paths are used to reduce dispersion. The inlet/outlet contributions become an irreducible minimum at some point, however, regardless of the specific geometry, except for an on-column cell. An excessively short path may result in poor sweepout and greater, rather than less, dispersion. The exact behavior may depend on inlet/outlet geometries, often proprietary. Separating the Variance Contributions of the Cell and the Cell Inlet. Once we have determined the , (as in Figure (hereinafter termed , ) is obtained 4), , , (eq 1). The VPL cell provides a unique opas , - , portunity to hold the inlet/outlet system constant while readily varying L or Vcell. For further consideration, it will be advantageous to consider the volumetric variance , , obtained as F2( , - , ). , is expected to vary monotonically with L past the minimum length (hereinafter called Lmin) needed to establish the same flow pattern along the remainder of the cell length. Knowing , as a function of L or Vcell, extrapolation to zero L can determine , as the intercept. An important validation is that the projected value should be independent of the peak we are consid, compared to the othering. Peak 5 has a much larger , by subtraction is larger, ers, the error in computing , these are separately considered later.
Figure 6. Dispersion caused by the cell (including the inlet) as a function of length at a fixed flow rate of 176 L/min. The solid lines are best fits to a quadratic function of L, the best fit r2 values are listed. The lower set of data represents , , the individual values of the L=0 intercept were subtracted from each data set. Figure 6 shows the results for peaks 1-4 for the F = 176 L/min flow rate; similar data respectively appear in Figures S17-S19 for F = 47.4, 111, and 350 L/min. All the fits depicted are quadratic functions of L; these corresponds to the data much better than linear fits with L. The mean (SD) of the intercepts computed for peaks 1-4 in Figure 6 is 0.866
(0.146) L2. The data for peaks 3 and 4 only produce an intercept of 0.9880.065 L2. and , should be independent of the specific Both , peak (but not of the flow rate) and this is largely observed. In principle only path lengths > Lmin should be included in this analysis; Figure 6 does include smaller L values as variance of peaks 1 and 2 could only be measured for relatively short path cells. Without discounting any of the data in Figures 6 and (meanSD) values for F = 47, S17-S19, the respective , 111 176 and 350 L/min are 0.2390.013, 0.4910.107, 0.8660.146, and 1.330.22 µL2 This dependence of , on flow rate is graphically depicted in Figure S20. Flow Rate Dependence of Cell Dispersion, , . Is Eq 2 Valid? For peak 5 with L > 5 mm, , becomes large enough compared to , to reliably calculate , by difference. From these, the average , values at each flow rate (foregoing paragraph) can be subtracted to obtain the corresponding , values. These are shown plotted in Figure 7 for three different flow rates. 47, 111 and 350 µL/min, the data for the 176 µL/min partially obscures the 111 µL/min values and are not shown.
Figure 7. The variance from the cell and the inlet/outlet, approximately equal to , , for peak 5 at three different flow rates. If the lower 4 cell volumes (L = 5-20 mm) are considered separately from the higher 4 cell volumes (L = 30-60 mm), there is always greater linearity for the higher volume set. At the lowest flow rate, it would appear that there is a linear relationship as would be expected from eq 2. The reciprocal of the slope (tantamount to K therein) is 9.700.26 (the uncertainty indicates 95% standard error of the fit coefficient). On the other hand, the data for the highest flow rate is clearly nonlinear. In Table S3, where the data are divided into two separate groups (L = 5-20 mm, and L = 30-60 mm), illustrates that none of the traces are strictly linear; for each flow rate, there is a statistically different slope for each of the two groups. There is better linearity at higher values of L. While for the larger L or larger Vcell domain, K becomes statistically constant; for the
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Analytical Chemistry smaller L domain, K is not a constant with flow rate. In smaller volume cells, K decreases (greater mixing) steeply with increasing flow rate. A flow-independent K paradigm (eq 2) is inapplicable. CONCLUSIONS We provide a simple method to correct for detector-induced dispersion. While this still does not give the true column efficiency (injector and connecting tubing dispersion contributions remain), detector-induced dispersion is often the largest contributor to extracolumn dispersion.21 While the approach is demonstrated utilizing data from an absorbance detection system, the method would be generally applicable to any detector. The use of a cell where the pathlength can be varied while maintaining the same inlet/outlet system also allowed us to assess the individual contributions of the inlet/outlet system and the cell itself, to the total observed peak variance. The flow rate dependence on both parameters suggests that the inlet/outlet dispersion pattern as a function of flow rate in the present cell closely resembles that of an open tube, this may not, however, be applicable to other cell inlet/outlet geometries. The dispersion in the cell itself has often been modeled as a flowindependent parameter that is dependent only on the cell volume. Except for long path/relatively large volume cells, this is simply wrong.
ASSOCIATED CONTENT Supporting Information Optical system of detector cell, tube dimensions for flow diversion, flow cell variance in time and volume domain, numerical summary of eq 4 fit parameters, etc. The Supporting Information is available free of charge on the ACS Publications website. ac17b04248q_si_001.pdf
AUTHOR INFORMATION Corresponding Author *E-mail:
[email protected]. Fax: 817-272-3808.
ORCID
Purnendu K. Dasgupta: 0000‐0002‐8831‐7920
Notes The authors declare no competing financial interest.
ACKNOWLEDGMENT
The US National Science Foundation is acknowledged for support (CHE-1506572). The experimental data were generated by C.P.S. at Agilent (Waldbronn, Germany) under the aegis of Agilent University Relations and External Research Gift No. 3819.
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