Comparison of core–shell particles and sub-2 μm fully porous particles for use as ultrafast second dimension columns in two-dimensional liquid chtomatography

Journal of Chromatography A, 1386 (2015) 31–38

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Comparison of core–shell particles and sub-2 ␮m fully porous particles for use as ultrafast second dimension columns in two-dimensional liquid chtomatography Imad A. Haidar Ahmad, Arianne Soliven, Robert C. Allen, Marcelo Filgueira, Peter W. Carr ∗ Department of Chemistry, Smith and Kolthoff Halls, University of Minnesota, 207 Pleasant Street SE, Minneapolis, MN 55455, United States

a r t i c l e

i n f o

Article history: Received 29 June 2014 Received in revised form 21 November 2014 Accepted 24 November 2014 Available online 4 December 2014 Keywords: Liquid chromatography High temperature liquid chromatography Ultra fast liquid chromatography Core–shell particles Sub 2 ␮m particles Two dimensional liquid chromatography

a b s t r a c t The peak capacity of small columns packed with 2.7 ␮m core–shell particles and 1.8 ␮m fully porous particles were compared at high temperatures using very steep (fast) gradient conditions and quite high linear velocities using the same instrument configuration as used to transfer first dimension effluent to the second dimension column as done in on-line comprehensive two-dimensional liquid chromatography. The experimental peak capacities of small columns (2.1 mm × 30 mm) packed with both types of particles were measured with fast gradients (9 s to 2 min) at high temperature (95 ◦ C) using both the same flow rate (1.75 mL/min) and then at different flow rates at the same pressure (400 bar). Equal or slightly better peak capacities were achieved with the core–shell particle columns as compared to the fully porous particle columns at the same backpressure or the same flow rate. However, core–shell particles offer a real advantage over the smaller, fully porous particles because they can be operated at higher flow rates thus gradient mixer flush out and column reequilibration can be done in less time thereby allowing a greater fraction of the second dimension cycle time to be dedicated to the gradient time. © 2014 Elsevier B.V. All rights reserved.

1. Introduction In ultrafast on-line comprehensive two-dimensional liquid chromatography (LC × LC), the second dimension column cycle time must be a good deal shorter than the first dimension peak width to restrict the loss in peak capacity arising from the first dimension undersampling effect [1,2]. The goal of this work was to compare the separation performance of fully porous and core–shell particle columns under steep gradient conditions. Small core–shell particles possess several advantages over sub2 ␮m totally porous particles when used under typical second dimension conditions for on-line LC × LC. Core–shell particles used here are made with a 1.7 ␮m impervious solid cores and a 0.5 ␮m porous shell and thus in terms of pressure drop they act as 2.7 ␮m particles. These particles exhibit unusual chromatographic efficiency similar to those of sub-2 ␮m particles but with substantially lower back pressures [3]. Putatively, the presence of the nonpermeable solid core limits the diffusion distance of analytes into the particles and therefore improves the mass transfer process [3]. However, other explanations for their improved performance have

∗ Corresponding author. Tel.: +1 612 624 0253; fax: +1 612 626 7541. E-mail address: [email protected] (P.W. Carr). http://dx.doi.org/10.1016/j.chroma.2014.11.069 0021-9673/© 2014 Elsevier B.V. All rights reserved.

been posited [3]. In any case as a result, separations are significantly expedited. The solid core also acts as a mechanically stable support for the bed at high pressures of up to 600 bar. Such particles are said to form very homogeneous packed beds due to their narrow particle size distribution [3–9]. Previous studies have compared the performance of columns packed with fully porous particles to those packed with core–shell silica under various experimental conditions [3,6,9–12]. In the present study both types of particles were compared under strenuous conditions, as comparable as possible to those used for the second dimension in fast on-line LC × LC. That is, ultrafast gradient separations at high temperature using small columns (30 mm × 2.1 mm) with very short gradients (9–120 s) and high linear velocities (1.75–2.7 mL/min) [1,13–15]. Although others have compared core–shell and sub-2 ␮m particles [9,12] the conditions were quite different from those employed herein. Typically their gradient chromatograms took 1 min to complete. This time scale is well outside that which is optimum for on-line LC × LC [1,13,16]. Additionally we did not use the low dispersion optimized autoinjection of the LC instrument as done in [9,12] but rather samples were injected using the valving system employed to transfer effluent from the first to the second dimension column [13,17,18]. Furthermore the final eluent compositions were adjusted to assure that the last solute eluted quite close to the end of the gradient

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I.A. Haidar Ahmad et al. / J. Chromatogr. A 1386 (2015) 31–38

so that meaningful peak capacities were measured. Additionally quite high flow rates were deliberately used. This is very important in on-line LC × LC. High flow rates and small columns are needed to reduce the gradient mixer and column reequilibration times. In our fast on-line LC × LC work reequilibration times of 3 s are used at flow rates of 2–3 mL/min. Since the system reequilibration time contributes to the second dimension cycle time use of high flow rates is quite important. In prior studies [9,12] flow rates were not higher than 1 mL/min were used except when monolithic columns were studied. A homologous mixture of nitroalkanes was used to evaluate the peak capacity values of columns packed with core–shell and totally porous particles. Both columns had the same diameter and were compared, on the same low dispersion, chromatographic instrument, at both the same total system pressure (P) and at the same flow rate (F) for gradient times that ranged between 9 and 120 s. We deliberately choose a set of solutes ranging in retention from essentially unretained in water to rather strongly retained in organic rich eluents as such mixtures are commonly encountered in LC × LC metabolomic studies [13]. 2. Theory of gradient elution 2.1. Peak width Based on linear solvent strength theory, various groups have used Eq. (1) to predict the peak width at half height (w1/2 ) under linear gradient elution conditions given the requisite parameters which were determined under isocratic conditions. This w1/2 was then used to determine the theoretical peak capacity value based on Eq. (1) [19]. w1/2 = 2.35 =

2.35G(p) · to (1 + ke )



Niso

(1)

G(p) is the “gradient band compression” factor, to is the column dead time, ke is the local solute retention factor when the solute is at the column exit. G(p) and ke are determined using Eqs. (2)–(8). Neue et al. have indicated that there can be several sources of deviations in observed peak widths from Eq. (1) including extra-column peak broadening occurring mainly in the detector and the tubing connecting the column exit and the detector, variations in Niso (the isocratic plate count) with mobile phase composition, and stationary phase diffusion. In the absence of these effects it has been shown that Eq. (1) is basically correct when the gradient compression factor (G(p)) is included. In the presence of these additional effects G(p) is generally closer to unity. In gradient elution LC, the upstream side of a peak travels a little faster than the downstream side resulting in band-compression. This gradient compression of peaks is computed as [19–21]:



G(p) =

1 + p + p2 /3 (1 + p)

2

b (see below)) nearly a factor of 2 improvement in peak width and peak capacity. The change in isocratic retention factor k of nitroalkanes as a function of the percentage-volume of acetonitrile (ACN) in mobile phase was used to determine the S and kw values of individual nitroalkanes according to Eq. (5) [19]. ln k = ln kw − S

(5)

where  is the volume-fraction of ACN and S is the slope of ln k vs. . The dimensionless gradient-steepness (b) is defined in Eq. (6), its role in gradient elution LC is similar to that of the mobile phase strength in isocratic elution [19] b=

to S Vm S = tG F · tG

(6)

where  = final − o and final is the final eluent composition. Vm is the column dead volume. Note that tG is the gradient time and b depends on S but not on kw . Also note that at constant  and tG , b varies with flow rate as the column dead time is inversely related to F. The solute retention factor when the solute is at the column exit, ke , is then calculated (based on the assumption of LSS compliance) according to the following equation [19–21] ke =

ko b(ko − (tD /to )) + 1

(7)

where tD is the system dwell time. Because delayed injection was used in this work (see below) the dwell time can be taken as zero. If we assume that ko is very large then when tD = 0, ke can be approximated as: 1 ke ∼ = b nc ∼ =1+

(8)



Niso

4

×

StG tG + Sto

(9)

We will refer to Eq. (9) as Neue’s approximation. Eq. (9) assumes that the time between the first and last peaks observed is tG and further that G(p) is always unity. While this equation works well with some solute sets, such as tryptic peptides, it is not particularly accurate with small molecules, such as those used here, some of which are insufficiently hydrophobic to be strongly retained under the initial reversed phase chromatographic conditions. It is subject to all of the experimental problems as Eq. (5). However, it indicates the qualitatively correct trend that peak capacity of a given column generally increases as S increases and that the peak capacity at a fixed flow rate approaches a limiting value at long gradient times. 3. Experiments and methods

(2) 3.1. Reagents and materials

where p=

ko b 1 + ko

(3)

and ko = kw exp(−S · o )

(4)

where ko is the isocratic retention time factor at the initial eluent composition of the gradient, kw is the extrapolated solute retention in pure water, and o is the initial eluent composition. G(p) varies from 1 at low values of p, which are equivalent to isocratic conditions, to a limiting value of about 0.58 with very steep gradients. Thus G(p) can cause (for a well retained solute with a large value of

All chemicals used for the chromatographic study were reagent grade or better. HPLC eluents were HPLC grade ACN obtained from Burdick and Jackson (Muskegon, MI) and HPLC grade water from Sigma-Aldrich (St. Louis, MO). Seven standards of nitroalkanes were obtained from Sigma-Aldrich (St. Louis, MO), from which a mixture was prepared. Thiourea from Matheson Coleman and Bell (East Rutherford, NJ) was used to determine the dead time of the chromatographic system. The test solutes were dissolved in pure water at concentrations of: 2.47 (thiourea), 1.39 (nitromethane), 1.48 (nitroethane), 1.70 (nitropropane), 1.81 (nitrobutane), 2.09 (nitropentane), 2.20 (nitrohexane), and 9.87 (nitrooctane), all concentrations are in micrograms per gram of water. In general

I.A. Haidar Ahmad et al. / J. Chromatogr. A 1386 (2015) 31–38

volumes of 2 ␮L were injected. In preliminary work we saw that the injected volume could be varied from 0.5 to 10 ␮L with no observable effect on the peak width under either isocratic or gradient conditions. We believe it does not contribute significantly to any extra-column broadening especially under gradient conditions. A mixture of nine indoles was used in this work, all were synthesized in Professor Wayland Noland’s Lab at University of Minnesota. The names of indoles are listed next along with the concentration in parenthesis in ␮g/mL: (a) 2-(2-(1H-indol-3-yl)acetamido)malonic acid (4.95), (b) 2-aminobenzoic acid (4.92), (c) 2-(1H-indol-3-yl) acetamide (3.9), (d) 4-(1H-indol-3-yl)butan-2-one (1), (e) (E)-3(1,4-bis(methylperoxy)but-2-en-2-yl)-2-methyl-1H-indole (0.7), (f) (E)-3-(1,4-bis(methylperoxy)but-2-en-2-yl)-2-methyl-1Hindole (0.5), (g) (E)-3-(2-nitrovinyl)-1-(pyridin-2-yl)-1H-indole (2), (h) 1-(1H-indol-3-yl)-2,2-diphenylethanone (1), (i) 1,1 (3,3 -(ethene-1,1-diyl)bis(1H-indole-3,1-diyl))diethanone (2). Compounds (a–c) were prepared from stock solutions dissolved in water while for the more hydrophobic compounds (d–i) the indoles were prepared from stock solutions dissolved in ACN. The final composition of the sample solvent was 90% H2 O:10%ACN. This set of solutes was used as it is representative of complex mixtures of maize extracts of interest to us. [13,14] 3.2. Instrumentation 3.2.1. Gradient RPLC instrumentation An Agilent 1290 binary pump Model G4220A (Agilent Technologies, Wilmington, DE, USA) with a JetWeaver model V35 mixer was used. This mixer has a nominal volume of 35 ␮L. The solvent in channel A was pure water and that in channel B was pure acetonitrile. The binary solvent delivery system was connected to an Agilent Thermostatted Column Compartment (TCC) Model G1314 and an Agilent DAD detector Model G4220A equipped with a 1 ␮L, 6 mm path flow cell with a sampling rate of 80 Hz. Data were acquired at a wavelength of 220 nm. In the TCC, the two heat exchangers (3 ␮L and 6 ␮L) were connected together to stabilize the mobile phase temperature at 95 ◦ C. The temperature was checked by use of a calibrated thermistor. It is most important to note that we did not use the system auto-injector rather the samples were introduced using a 10 port-2-position valve (VICI CHEMINERT model 110-0063H, Valco Instruments, Houston, TX, USA) with a 2 ␮L loop volume. This valve is what we use to deliver sample to the second dimension of our 2D-LC system. It is rated to a maximum pressure of 400 bar. For this reason our studies were limited to a system pressure of 400 bar although the Agilent 1290 pump is rated to 1200 bar. For all gradient work the nitroalkane samples were dissolved in 100% water while the indole samples were dissolved in 90%H2 O:10%ACN. For both samples, 2 ␮L were injected. The loop tubing had an internal diameter of 0.005 . All Agilent modules were configured and controlled using OpenLab CDS version, LabVIEW 9.0 software (National Instruments Corporation, Austin, TX, USA) was used to control the 10-port valve and to coordinate the signal between the 10-port valve and the binary pump. The tubing after the injection valve was PEEK 0.005 i.d. tubing; it had a nominal volume of 24 ␮L. Again it is what we use in our on-line LC × LC configuration to connect the valve to the TCC and the second dimension column. 3.2.2. Isocratic RPLC instrumentation An Agilent 1200 liquid chromatograph controlled by version B.04.02 Chemstation software (Agilent Technologies, Palo Alto, CA) was used. The solvent in channel A was pure water and that in channel B was pure acetonitrile. The 1200 Binary pump was connected to an Agilent 1200 degasser and Agilent 1100 autosampler. The chromatography column was placed in a Thermosttated Column Compartment (TCC) Model G1312B. Data were acquired using

33

Table 1 Gradient conditions used in the experiments. Gradient time (s)

9 15 30 60 120 a

% Final ACNa Fully porous 1.8 ␮m

Core–shell 2.7 ␮m

Core–shell 2.7 ␮m

1.75 mL/min; 400 bar

1.75 mL/min; 270 bar

2.7 mL/min; 400 bar

100 100 90 55 45

100 100 90 55 45

85 65 70 50 35

Initial %ACN is 0 at all gradient times.

an Agilent 1200 DAD detector equipped with a 1 ␮L, 5 mm path flow cell with a sampling rate of 80 Hz. Data were acquired at a wavelength of 220 nm. All the tubing connecting the parts of the system is PEEK tubing of internal diameter 0.005 . The system had a nominal volume of 32 ␮L. This instrumentation was used only to measure the retention factors reported not peak widths or peak capacity factors. 3.2.3. Gradient RPLC The separations were carried out on 2.1 mm × 30 mm Zorbax SBC18 1.8 ␮m and on 2.1 mm × 30 mm Poroshell 120 SB-C18 columns. The two columns were operated at 95 ◦ C using the TCC and the flow rates shown in Table 1. In order to reach a stable temperature of 95 ◦ C especially at high flow rates used (nearly 3 mL/min) two TCC heat exchangers had to be chained in series and the columns were placed in the downstream TCC. Please note that in order to fairly compare the two columns or the different flow rates we deliberately varied the final eluent composition to make the last solute elute as close as possible to the end of the gradient as is done in actual practice in on-line LC × LC. The initial composition was pure water to emulate what we find we must do in typical metabolomic studies to get the more hydrophilic compounds to elute just after the dead time. Table 1 shows the various conditions at each gradient time used in this study. It is important to note that the eluent composition at the end of the gradient had to be varied with the gradient time to make the last solute elute close to the end of the gradient. Again this was done to examine the columns under conditions used in on-line LC × LC. Further these compositions were not the same with the two types of particles. In particular they were not the same when the core–shell column was run at 400 bar. We also point out that delayed injection was used to compensate for the dwell volume of the gradient. Thus the samples were injected when the eluent change arrived at the column inlet. 3.2.4. Isocratic RPLC measurements These measurements were performed with a 2.1 mm × 30 mm Zorbax SB-C18 1.8 ␮m column. The column was operated at 95 ◦ C and 1 mL/min, the mobile phase used consisted of different isocratic combinations of water and acetonitrile (ACN). The analytes were eluted at 10% increments of ACN from 10 to 50% (v/v). S and kw values of individual nitroalkanes were determined according to Eq. (5) as explained in the experimental section. The k values were calculated according to the following equation k=

tR − to to − tex

(10)

where tex is the retention time correction due to extra-column volume determined by removing the column and replacing it with a zero dead volume connector. The extra-column volume of the

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Fig. 1. ln k versus  plot for nitroalkanes on 1.8 ␮m SB-C18 particle column (2.1 × 30 mm). F = 1 mL/min, T = 95 ◦ C, k is calculated based on Eq. (10). The slope (−S), and intercept ln kw are the slope and the intercept of the fitted data, respectively. Symbols: ( ) nitromethane, ( ) nitroethane, ( ) nitropentane, ( ) nitrobutane, () nitropentane, ( ) nitrohexane, and ( ) nitrooctane.

Table 2 S and kw values of nitroalkanes determined from Fig. 1.

Nitromethane Nitroethane Nitropropane Nitrobutane Nitropentane Nitrohexane Nitrooctane

S (−slope)

kw a

1.87 3.01 4.28 5.69 7.15 8.61 10.6

0.782 2.06 5.9 18 54 160 1100

R2 b 0.978 0.999 0.999 0.999 0.994 0.991 0.995

a

Note because the initial mobile phase composition was always 100% water ko = kw for all solutes in all experiments. Thus the extent of focusing at the column entrance varies a lot from nitromethane to nitrooctane. b R2 refers to the correlation coefficient of ln k vs. .

system is 32 ␮L. The dead volume of the column corrected for extracolumn volume was 55 ␮L as determined with thiourea.

As expected the S and kw values increase linearly across the homologous series of nitroalkanes, as shown in Fig. 2. The S values of nitroalkanes vary from ∼2 for nitromethane to ∼11 for nitrooctane. These values are in agreement with the expected values for small molecules [22]. 4.1. Peak capacity in gradient elution chromatography 4.1.1. Experimental peak capacity Peak capacity is a theoretical number that represents the maximum number of well-resolved peaks that can be accommodated in the separation range of a chromatogram. In gradient-elution liquid chromatography, the separation range is generally defined as the time between the start and the end of the gradient. The experimental peak capacity can be determined from the average width of the peaks in a chromatogram and was calculated as per Eq. (11) [19]: nc = 1 +

4. Results and discussion We need the S and kw values of the nitroalkanes for our discussion of the peak capacity results. These are shown in Fig. 1 as a function of composition. The plot shows a good correlation between the ln k and , the coefficient of determination (R2 ) of the plots are generally better than 0.990. The extrapolated values of k with water as mobile phase (kw ) and the slopes (S) values are determined from Fig. 1, compiled in Table 2, and plotted in Fig. 2. In general, kw and S values are indicative of the hydrophobicity and non-polar surface area of a molecule. Therefore, kw is higher for more hydrophobic molecules. S values increases with increasing size in a homolog series. It is evident that nitromethane and nitroethane are rather weakly retained even in pure water and thus the assumptions needed to get from Eq. (1) to Eq. (9) will not be valid for these particular solutes. Furthermore, they will not get focused on the top of the column. Nonetheless we include these solutes in our estimate of the average peak width in computing the peak capacity (see Eq. (11) below) thereby getting a conservative estimate of the second dimension peak capacity.

tR,last − tR,first tG ≈ waverage waverage

(11)

where tR,last and tR,first are, respectively, the retention times of the last and first peaks observed in the separation space and waverage is the average 4 peak width based on the assumption of a resolution of 1.0 for all peaks. The first peak to elute was always thiourea (essentially unretained in pure water) and the eluent composition was adjusted so that the last peak eluted coincided with the dead time plus the gradient time. This was done to emulate the conditions imposed on the second dimension column in on-line LC × LC. Thus the numerator in Eq. (11) was always taken simply as tG . Plots of the peak capacity computed from Eq. (11) as a function of gradient time are given in Fig. 3A and B. The curves in this figure were obtained with data acquired using the 2.7 ␮m core–shell material and 1.8 ␮m fully porous particles. 4.1.2. Effect of gradient time and particle type/size The effect of gradient time (tG ) on the measured peak capacities is shown in Fig. 3A and B. In general, the peak capacities increase rapidly with gradient time and then tend to a limiting value at higher gradient times in agreement with Neue’s approximation

I.A. Haidar Ahmad et al. / J. Chromatogr. A 1386 (2015) 31–38

Fig. 2. Plot of S and ln k versus homolog number of nitroalkanes on 1.8 ␮m SB-C18 column.

Fig. 3. (a) Experimental peak capacity as a function of gradient time. T = 95 ◦ C, (2.7 ␮m SB-C18 particle column, F = 2.7 mL/min), (1.8 ␮m SB-C18 P = 400 bar, particle column, F = 1.75 mL/min). Gradient conditions in Table 1. (b) Experimental peak capacity as a function of gradient time. T = 95 ◦ C, F = 1.75 mL/min, (2.7 ␮m SB-C18 particle column, P = 270 bar), (1.8 ␮m SB-C18 particle column, P = 400 bar). Gradient conditions in Table 1.

: refers to ln kw and

35

: refers to the S values.

(Eq. (9)). Based on the variation in the slope with gradient time, each curve can be divided into two parts: the first is for gradient times between 9 and 30 s and the second pertains to times between 30 and 120 s [11,23,25]. Fig. 3A shows that the peak capacity for the 1.8 and 2.7 ␮m particles both at 400 bar (but different flow rates) hardly differ. From 9 to 60 s the core–shell particles (2.7 ␮m) have slightly higher peak capacities whereas at the longest gradient time the fully porous (1.8 ␮m) has a marginally higher peak capacity. Given the differences in operating conditions shown in Table 1 there is scarcely any theoretical reason to prefer one particle over the other when operating at the same pressure even though the core–shell particles are operated at a higher absolute velocity (thus flow rate) and higher reduced velocity. However, if we consider the fact that the system flushout time (including the gradient mixer) will inevitably be longer using the 1.8 ␮m particles at a flow of 1.75 mL/min in contrast to the 2.7 ␮m particles at a flow of 2.7 mL/min. The 2.7 ␮m core–shell particles must be preferred for purely practical reasons. At a flow of 2.7 mL/min we believe that the minimum reequilibration time is close to 3 s [1,13,16]. Thus assuming that the same volume will be needed to reequilibrate and flush the system a time of 4.6 s will be needed at the lower flow rate. While this seems small if we were to keep the cycle time the same for both particle types (say 20 s) the gradient times would be 17 vs. 15.2 s. Given the high slope of plots of peak capacity vs. gradient time that would amount to a significant decrease in peak capacity for the 1.8 ␮m particles to about 44 at 15.2 s gradient time vs. 51 at 17 s gradient time for the 2.7 ␮m particles. In contrast when the particles are compared at the same linear velocities (and of course two different pressures) the two particles produce virtually identical peak capacities at the shortest gradient times but the 1.8 ␮m particles gradually out perform the 2.7 ␮m particles albeit not by much. We point out that in the second dimension gradient time range (12–21 s) where we have shown that the effective peak capacity of on-line LC × LC is at a maximum [16,26], Fig. 4 shows that the 1.8 ␮m particles produce peak capacity at the rate of 2.1/s whereas the 2.7 ␮m particles have a speed of 2.44/s. These are the highest speeds reported using columns, conditions and instrument configurations that are actually employed in online LC × LC. They rival the recently published, purely theoretical limits of speed in LC of 4/s for low molecular weight solutes [9]. Note

Peak Capacity/Cycle Time (s-1)

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3.0 2.5 2.0 1.5 1.0 0.5 0.0

0

20

40

60

80

100

120

Cycle Time (s) Fig. 4. Computed peak capacity per second based on cycle time equal to the sum of gradient time and the reequilibration time as a function of gradient time. T = 95 ◦ C, P = 400 bar, ( ) (2.7 ␮m SB-C18 particle column, F = 2.7 mL/min) assuming ) (1.8 ␮m SB-C18 particle column, F = 1.75 mL/min) a reequilibration time of 3 s, ( assuming a reequilibration time of 4.6 s. Gradient conditions in Table 1.

that the theoretical limit was based on a 4.6 mm id column operated at 15 cc/min and does not include any reequilibration time which inevitably must lower the rate of generation of peak capacity. Fig. 5 shows some interesting phenomena observed when doing very steep gradients. The plot shows the experimental peak halfwidths as a function of gradient time for the different solutes. The data shown is for the 1.8 ␮m SB-C18 particle column; the same general trends were seen for the 2.7 ␮m SB-C18 column at both flow rates (data not shown). The peak widths of the nitroalkanes using the three steepest gradients (tG = 9, 15, and 30 s) actually decrease as the solute carbon number increases. We believe that this results from two factors. First, the more retained solutes are much more highly focused at the column entrance than are the poorly retained peaks. Note (see Table 2) that kw is less than 1 for nitromethane and only 2.0 for nitroethane so not much focusing can happen for these solutes. That is, the contribution of pre-column, extra-column band broadening to the observed peak widths under fast gradient conditions is smaller for the more retained peaks than for the less retained peaks. Second, the gradient compression factor (G(p)) becomes progressively smaller, i.e. there is more band compression of the higher homologs because both ko and b are larger (see Eqs. (8) and (9)) for the higher homologs.

Fig. 5. Experimental peak width at half height for various gradient times (䊉: 9 s, : 15 s, : 30 s, : 60 s, : 120 s), column: 1.8 ␮m SB-C18, index number corresponds to the number of carbons in a nitroalkane with n = 0 value corresponding to the dead marker, thiourea. Gradient final composition ACN ,final are as follows: 100% for tG = 9 s, 100% for tG = 15 s, 90% for tG = 30 s, 55% for tG = 60 s, and 45% for tG = 45 s). 1.8 ␮m SB-C18 particle column, P = 400 bar, F = 1.75 mL/min, and T = 95 ◦ C.

Fig. 6. Plot of experimental ( ) and computed ( ) peak width at half height for tG = 2 min vs. homolog number for 1.8 ␮m SB-C18 particle column, T = 95 ◦ C, F = 1.75 mL/min, P = 400 bar.

At the longer gradient times (tG = 60 and 120 s) the plots are radically different; we now see that the peak widths of the different solutes increase with homolog number. The increase in peak width is overwhelmingly due to the large increase in ke with homolog number at the longer gradient times as shown in Fig. 6. Interestingly at all gradient times ke passes through a maximum vs. homolog number. The maximum in ke is due to the fact that ko is initially quite small at low homolog number and both ko and b increase as homolog number increase. We also point out that G(p) at low gradient times decreases with homolog number from 0.96 by 35% but at gradient times of 60 and 120 s G(p) is very close to 1 and only decreases by less than 5% as homolog number increases. Thus it is clear that the trends seen in Fig. 6 would become much simpler if the early homologs were more strongly retained (say ko > 50). In order to reproduce the values of the peak width at half maximum in Fig. 5 we need a reasonable estimate of the isocratic plate number. We attempted to measure such with our system but became convinced that our columns had such small volumes that extra-column corrections under isocratic conditions were overwhelming [27,28]. Broadening from zero dead volume connections, column entrance effects and other effects could not be deconvolved [27,28]. Thus we resorted to using an estimate of the plate count based on a back calculation from Neue’s equation. Because we had reasonably reliable estimates of the column dead volume and dead time, as well as the solute S factors and the measured value of the peak capacity we used Eq. (9) to compute the Niso value needed to produce the peak capacity observed at tG = 9 s our fastest run. This yielded a value of 5400. This estimate is in rather good agreement with that obtained simply by taking the reduced plate height of the column, at high reduced velocities, to be 3. For a 30 mm long column this gives about 5500 plates. The rather low reduced plate height of 3 at such a high linear velocity supports our contention that there is not much extra-column broadening taking place in our system under gradient conditions for the well retained test solutes. Now that we have an estimate of the isocratic plate count we can compute the peak width under gradient conditions using the peak width equation from Snyder et al. [20]. We took Niso to be 5400, the dead time as 0.032 min and the extra-column peak halfwidth to be 0.0032 min (0.19 s). The extra-column contribution to the observed peak half-width was obtained from the equation:



w1/2,observed =

(w1/2,col )2 + (w1/2,ex )2

(12)

Finally with the same data set we used above we minimized the sum of the squares of the residuals of w1/2,observed from that computed from Eq. (12) by adjusting both Niso and w1/2,ex using

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Fig. 7. Gradient separation of the indole mixture using a 21 s gradient time. Experimental conditions (a) core–shell at 2.7 mL/min (pressure = 400 bar), (b) core–shell at 1.75 mL/min (pressure = 270 bar), (c) 1.8 ␮m fully porous particles at 1.75 mL/min (pressure = 400 bar). Experimental conditions: T = 95 ◦ C, column dimensions 2.1 × 30 mm, intial = 0%, final, (a) = 65%, final, (b) = 75%, and final, (c) = 75%. Letter a → i corresponds to indoles in experimental section and numbers 1 → 3 refer to impurities in the sample.

Eq. (1) to compute w1/2,col . Niso and w1/2,ex were found to be 5900 and 0.29 s respectively. The w1/2,ex agrees well with the observed values of the peak width for the two lowest homologs indicating very little focusing at the column inlet. Our preliminary estimate of Niso and the refined value are in reasonable agreement with one another and with a reduced plate height of about 3. The results of this calculation are given in Fig. 6. We see that the experimental and theoretically estimated peak half widths are in reasonably good agreement. Most importantly we can reproduce from theory the upward trend in the measured peak width with increasing homolog number at the longer gradient time. The computed G(p) with tG = 2 min was very close to 1.0 for all homologs thus the rise in peak width is due primarily to the increase in ke with homolog number (see Eqs. (1) and (7)).

4.1.3. Chromatographic impact of the particle type A mixture of indoles was separated under the same conditions used for the nitroalkane series, at two gradient times, 21 s (Fig. 7) and 12 s (Fig. 8). In Figs. 7 and 8, the letters used to identify peaks (a → i) correspond to the indoles listed in the experimental section. while peaks 1–3 correspond to impurities in the sample. In both figures, it is evident that the chromatographic resolution is better for the core–shell particles at 2.7 mL/min than for the sub 2 ␮m particles at 1.75 mL/min. Obviously the results are better for the core–shell particles at 2.7 mL/min and 400 bar than the core–shell particles at 1.75 mL/min and 270 bar. The improved resolution is clearly seen in the separation of peaks e. and f. under different conditions for the same tG . Also, a better resolution is seen for peaks a. and b. in Fig. 7 (i.e. tG = 21 s) and peaks f and 1 in Fig. 8 (i.e. tG = 12 s).

Fig. 8. Gradient separation of mixture of indoles using a 12 s gradient time. Experimental conditions and symbols are the same as in Fig. 7 except final, (a) = 75%, final, (b) = 90%, and final, (c) = 90%.

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However, the improvements in the chromatograms appear to be due more to changes in selectivity resulting from changes in the gradient slope (b) than from any of the small increases in peak capacity shown in Fig. 3. Based on the comparisons discussed above, the core–shell particles are the better choice for use in the second dimension in 2D-LC under the conditions used here. Compared to the fully porous particle packed column, the core–shell particle column can: (1) operate at higher flow rate and linear velocity without exceeding the 400 bar pressure limit of the sampling valve, (2) be operated with longer gradient times at a fixed cycle time and thus generate better peak capacities at very short cycle times which are of major interest for the second dimension separation in 2D-LC. 5. Conclusions Peak capacity was used to determine whether columns packed with 2.7 ␮m core–shell or with 1.7 ␮m fully porous particle are the better choice for the second dimension in fast on-line 2D-LC separations. In such 2D-LC separations, short very steep gradients, at elevated temperatures and high linear velocities are used for the second dimension separation. The peak capacities of the two types of columns were compared at gradient times from 9 to 120 s with  ≥ 0.7 for tG ≤ 30 s and  ≥ 0.35 elsewhere. Under such conditions, equal or slightly better peak capacities were achieved with the core–shell type columns as compared to the fully porous columns at either the same backpressure or same linear velocity. Given the lower pressure limitations of core–shell particles (typically 600 bar) as compared to sub-2 ␮m fully porous particles (1000–1200 bar) it is not clear which type particle will ultimately be more useful but for the present we believe there is little reason to prefer sub-2 ␮m particles. Clearly the higher flow rate achievable with the core–shell particles means that the system flushoutreequilibration time will be shorter with the core–shell particles. This is a significant advantage in that a greater fraction of the second dimension cycle time can be devoted to generating peak capacity. A second relevant issue is the well-known superior performance of core–shell type particles for the separation of peptides which should make them even more useful as second dimension columns in proteomic applications [24,29]. Acknowledgements The authors would also like to thank professor Dwight Stoll at Gustavus Adolphus College for his helpful discussions and suggestions, and Professor Wayne Noland at University of Minnesota for his kind donation of the indole samples. The authors would also acknowledge financial support from National Institutes of Health (grant number GM 54585-15) and Agilent Technologies for the donation of the columns and loan of equipment. References [1] D.R. Stoll, X. Li, X. Wang, P.W. Carr, S.E.G. Porter, S.C. Rutan, Fast, comprehensive two-dimensional liquid chromatography, J. Chromatogr. A 1168 (2007) 3–43. [2] Y. Huang, H. Gu, M. Filgueira, P.W. Carr, An experimental study of sampling time effects on the resolving power of on-line two-dimensional high performance liquid chromatography, J. Chromatogr. A 1218 (2011) 2984–2994. [3] J.J. DeStefano, T.J. Langlois, J.J. Kirkland, Characteristics of superficially-porous silica particles for fast HPLC: some performance comparisons with sub-2 mm particles, J. Chromatogr. Sci. 46 (2008) 254–260.

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