Retention and bandwidths prediction in fast gradient liquid chromatography. Part 2—Core–shell columns

Journal of Chromatography A, 1337 (2014) 57–66

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Retention and bandwidths prediction in fast gradient liquid chromatography. Part 2—Core–shell columns ˇ Pavel Jandera ∗ , Tomáˇs Hájek, Kateˇrina Vynuchalová Department of Analytical Chemistry, Faculty of Chemical Technology, University of Pardubice, Studentská 573, CZ-53210 Pardubice, Czech Republic

a r t i c l e

i n f o

Article history: Received 15 November 2013 Received in revised form 7 February 2014 Accepted 10 February 2014 Available online 18 February 2014 Keywords: Prediction of retention with fast gradients Gradient peak capacity Flavones Phenolic acids Core–shell columns

a b s t r a c t Recently, we confirmed that the well-established theory of gradient elution can be employed for prediction of retention in gradient elution from the isocratic data, method development and optimization in fast gradient chromatography employing short packed fully porous and monolithic columns and gradient times in between 1 and 2 min, or even less. In the present work, we extended this study to short core–shell reversed-phase columns. We investigated the effects of the specification of the stationary phase in the core–shell structure on the prediction of gradient retention data. Two simple retention models describing the effects of the mobile phase on the retention by two-parameter equations yield comparable accuracy and can be used for prediction of elution times. The log–log model provides improved prediction of gradient bandwidths, especially for less retained compounds. A more sophisticated three-parameter model did not offer significant improvement of prediction. We compared the efficiency, selectivity and peak capacity of fast gradient separations of alkylbenzenes, phenolic acids and flavones on seven core shell columns with different lengths and chemistry of bonded shell stationary phase. Within the limits dictated by a fixed short separation time, appropriate adjustment of the range of the composition of mobile phase during gradient elution is the most efficient means to optimize the gradient separation. The gradient range affects sample bandwidths equally or even more significantly than the column length. Both 5-cm and 3-cm core–shell columns may provide comparable peak capacity in a fixed short gradient time. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Speed of separation is crucial issue in improving the productivity of an analytical laboratory. Fast generic gradient methods are required for high throughput in food safety control, in environmental analysis and especially in pharmaceutical laboratories throughout the whole drug analysis process, including drug discovery screening, raw material analysis, impurity profiling, pharmacokinetic studies and final product stability tests. In two-dimensional comprehensive LC × LC, fast second-dimension separations (preferably using gradient elution) are especially important because of the limited second-dimension separation time [1,2]. Fast gradient separations can be achieved by using short columns packed with small particles. Reduction in the particle size improves separation efficiency, but at a cost of increased pressure drop across the column, proportional to second power of decreasing particle size. Clearly, the speed of separation increases at a higher

∗ Corresponding author. Tel.: +420 466 037 023; fax: +420 466 037 068. E-mail address: [email protected] (P. Jandera). http://dx.doi.org/10.1016/j.chroma.2014.02.023 0021-9673/© 2014 Elsevier B.V. All rights reserved.

flow rate of the mobile phase, but is traded for either decreased resolution or increased operation pressure. Extremely fast efficient separations can be achieved on columns packed with sub-2 ␮m particles in so-called ultra high performance liquid chromatography (UHPLC) setup, at very high operation pressures over 100 MPa [3]. Alternative solutions enabling fast efficient separations using a conventional HPLC instrumentation are possible using new column formats. One approach relies on using monolithic columns, which consist of a single-piece continuous separation media (rod), allowing approximately three-times faster analyses than the particulate packed columns of the same length at the same operating pressure [4]. Columns packed with non-porous or superficially porous (core–shell) particles offer increased efficiency at a cost of weaker retention and lower sample load capacity [5]. Superficially porous fused-core (core–shell) 2.7 ␮m silica-based particles with sub1 ␮m active porous layer [6] are prepared by depositing silica-sol particles onto a spherical non-porous solid core. Core–shell materials provide reduced band broadening and outstanding efficiency (height equivalent to a theoretical plate) lower than monolithic columns even at high mobile phase velocities, while sufficient outer particle size allows moderate permeability to accomplish very fast

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separations without significant loss in efficiency at relatively moderate operation pressure, in contrast to the columns packed with sub-2 ␮m fully porous particles [7–9]. A short diffusion path in a thin surface layer offers a very flat C term of the van Deemter plot due to fast mass transfer kinetics in the shallow pores. Recently, it was suggested that the actual advantage of core–shell column lies mainly in the diminution of the longitudinal diffusion, B, and eddy diffusion, A, terms rather than in a smaller C term [10,11]. Typical 2.6–2.7 ␮m core–shell particles contain a 1.9 ␮m nonporous core surrounded by a 0.35–0.5 ␮m porous shell. Narrow-bore columns packed with 1.7 ␮m [12,13] and 1.3 ␮m [14] core–shell particles provide peaks that have a variance of 2.1 ␮m. Recently introduced columns packed with 5 ␮m core–shell particles with 0.5–0.7 ␮m thick porous shell provide faster separations [15] and were claimed to provide reduced extra-column broadening effects in comparison to smaller particles [9]. Mass-transfer kinetics in chromatographic columns packed with core–shell particles was studied in detail by Guiochon and co-workers [7,16,17]. In fast gradient chromatography, columns packed with fused-core columns generally perform better than monolithic columns for separations of low-molecular compounds [18]. The reason is that retention factors of the last eluted compounds largely decrease during gradient elution as the analytes migrate along the column, and the superficial flow velocities imposed to the monolithic columns are twice or thrice larger than optimum [19]. Various 3 and 5 cm commercial core–shell columns can be used for fast gradients in the second dimension. Besides the type of the shell stationary phase, also the column length, hold-up volume, mobile phase flow-rate and the gradient retention range affect the quality of fast gradient separation. Recently, we studied the effects of the injected sample volume and solvent, of the gradient ramp, gradient range and mobile phase flow-rate on the fast seconddimension gradient separations of model alkylbenzenes and of phenolic and flavonoid antioxidants on several short commercial columns [20,21] and developed a new approach to the optimization of second-dimension gradient in two-dimensional LC × LC [22]. In the present work, we extended our previous study of fast gradients on short packed fully porous and monolithic columns to short core–shell columns. We investigated the effects of the solid core volume on the determination of retention factors and we compared two simple retention models describing the effects of the mobile phase on the accuracy of prediction of elution volumes and bandwidths in fast gradients. Finally, we studied the effects of the column length, chemistry of the stationary shell phase and of the gradient composition range on the bandwidths, efficiency, selectivity and peak capacity of seven commercial core–shell columns.

the bulk mobile phase is immobilized by occlusion (adsorption) at the solid adsorbent surface and forms thus a part of the stationary phase, which may participate in the sample distribution process by partition mechanism. During gradient elution, the volume of the liquid immobilized by adsorption may change, depending on the actual composition of the mobile phase. Hence, it is difficult to fix the boundary (dividing surface) between the stationary and the mobile phase [23]. The practical solution to this problem is by adopting a convention, defining the volume of the stationary phase, VS , as the part of the column, which is inaccessible to a non-retained marker compound (“nothing is adsorbed in terms of volume”). The volume of stationary phase, VS = VC − Vm = VC (1 − εT ), is given by the difference of the volume of the empty column VC , and the volume of the mobile phase in the column (Vm = VC εT ), where εT is the total column porosity. Molecules differing in size may penetrate into different proportion of pores; hence every specific sample compound theoretically has its own (thermodynamic) dead volume [24]—and consequently its own column phase ratio. However, practical comparison of the retention of various solutes requires a single hold-up volume marker compound, which is neither retained nor excluded from the column (kinetic) dead volume [25]. Various methods were proposed for the determination of the column dead volume using various markers [26,27]: marked components of the mobile phase (2 H2 O, needing refractometric detection), or inorganic salts (KBr or KNO3 , which may be subject to ion exclusion from absorbent pores), or small neutral compounds (uracil or thiourea), which are most frequently used. It has been noted that a small error in the determination of the column phase ratio and hold-up volume may lead to wrong conclusions about the retention mechanism [28]. However, there is still the issue of the correct phase boundaries in the column. Anyway, the selection of the dead volume seems less critical issue, if the main task is the prediction of gradient data from the experimental isocratic data, as in this study. The most important in practice is using consequently the same dead volume marker both for the data acquisition and for the prediction of retention. The vNA convention does not imply any concrete physical model of retention mechanism, neither adsorption nor partition. In core–shell columns, the solid core is impervious to both the sample and the mobile phase and does not participate in the chromatographic distribution process. If we do not include the core volume, Vcore , into the corrected volume of the stationary phase, VS,cor = VC − Vm − Vcore = VS fcor . and assume that the sample distribution is controlled by the same thermodynamics as with fully porous particles, we can re-write the definition equation for the retention factor as:

2. Theory

kcor = KD

2.1. Retention factors and phase ratio The column phase ratio, ˚, i.e., the ratio of the volume of the stationary phase, VS , and of the mobile phase, Vm , in the column, relates the distribution constant, KD , (the concentration ratio of the analyte in the stationary phase, cS , and in the mobile phase, cM ) and the retention factor, k, (the ratio of the sample molar masses in the two phases, nS and nM ), which can be evaluated from the experimental retention times, tR , measured under isocratic conditions at a constant mobile phase composition and flow rate, Fm : k=

tR Fm − Vm nS cS VS VS = = = KD = KD ˚ Vm nM cM Vm Vm

(1)

To relate the chromatographic retention data to the distribution constant, the phase ratio in the column, ˚, should be known. Usually a more or less thick liquid layer of different composition than

VS fcor VC − Vm − Vcore = KD Vm Vm

(2)

The core correction factor, fcor , accounts for the ratio of the thickness of the shell layer, dshell and the mean particle radius, rpartic ,  = dshell /rpartic :

 fcor =

 1−

d 1 − shell rpartic

3  (3)

The non-porous inner core represents between 25% and 36% of the core–shell particle volume; however the loading capacity was found comparable to that of fully porous sub-2 ␮m particles and better correlated to the pore volume or surface coverage than to the shell thickness [28]. In the present work, we studied the effects of the corrections for the core volume on the accuracy of prediction of the gradient retention data.

P. Jandera et al. / J. Chromatogr. A 1337 (2014) 57–66

2.2. Isocratic retention models as the basis for prediction of gradient retention data In reversed-phase chromatography (RPLC), where non-localized adsorption or partition is assumed to control the retention, a simple semi-logarithmic model is widely used to describe the effect of the volume fraction of the organic solvent, ϕ, on the retention factor, k, in aqueous–organic mobile phases [29,30]: VS log k = log KD + log = a − mϕ VM

log kcor = a − m ϕ = log k + log fcor − m ϕ = a + log fcor − mϕ (5) In comparison to Eq. (4), the intercept a of Eq. (5) is lower, a = a + log fcor , as kcor < k and fcor < 1, but the slope m should not be not affected by the correction. In the normal-phase liquid chromatography, sorption on localized adsorption centers is assumed to control the retention [31]. Simplified theoretical models of adsorption chromatography lead to Eq. (6) describing the effects of increasing concentration of the stronger (more polar) solvent, ϕ, on decreasing retention factor, k in a binary (mostly mixed organic) mobile phase [29,32]: (6)

k0 , a and m are experimental constants, k0 being the retention factor in pure strong solvent. As both Eqs. (4) and (6) represent simplified semi-empirical models, the goodness of the fit of either equation to the isocratic experimental retention data alone is not sufficient proof for the validity of retention model in particular separation systems, even though it has been occasionally used for distinguishing whether the chromatographic system is controlled by partition (non-localized adsorption) or by localized adsorption [29,33,34]. As can be expected, the fit of the experimental data is usually improved by using second-order [29,35] or more complex [36–41] retention model equations. These model equations generally need higher number of isocratic scouting experiments, less convenient non-linear regression data analysis and the best-fit parameters are more likely to be affected by experimental errors. Anyway, both log k versus ϕ (or log k versus log ϕ) twoparameter equations may be useful for retention prediction, method development and optimization of fast gradient elution [42–45]. 2.3. Prediction of gradient elution times (volumes) from the isocratic retention data In gradient reversed-phase chromatography, the volume fraction of a polar organic solvent (acetonitrile, methanol) in water, ϕ, increases with time, i.e., with the volume of the mobile phase that flowed through the column in time t from the start of the gradient, V = t × Fm : ϕ =A+B×V

VG = tG × Fm is the gradient volume, i.e., the volume of the mobile phase from the start to the end of the gradient. Assuming the validity of isocratic model equation, Eq. (4), the elution volumes, VR(g) , in gradient reversed-phase chromatography can be predicted using Eq. (8) [30,42,43,46,47]: VR(g) =

  1 × log 2.31mB × Vm 10(a−mA) − VD + 1 + Vm + VD mB (8)

(4)

The parameters a (log k in water) and m (the organic solvent strength parameter) of Eq. (4) depend on the solute, stationary phase and type of the organic solvent and usually are determined by regression analysis of the experimental retention factors measured in several mobile phases. This approach can be also applied to the corrected retention factors for core–shell columns:

log k = log k0 − m log ϕ = a − m log ϕ

59

(7)

B = (ϕG − A)/VG is the gradient steepness (ramp), independent of the flow-rate of the mobile phase, Fm ; tG is the gradient time, A is the ϕ at the start gradient, ϕG is ϕ at the end of the gradient and

Vm is the column hold-up volume, A and B are the gradient parameters, Eq. (7), a and m are the best-fit regression constants of Eq. (4), VD is the instrumental dwell volume (which comprises the volume of the gradient mixer and of the connecting tubing between the mixer and the column inlet where pre-gradient sample migration may occur). In chromatographic systems where Eq. (6) applies, the gradient elution volumes can be calculated using Eq. (9) [43,44,48]: VR(g) =

 1/(m+1) A 1 − + Vm + VD (m + 1) B k0 Vm − VD Am + A(m+1) B B (9)

After the end of the gradient, the column must be re-equilibrated to the initial. The time required is governed mostly by flushing out the system dwell volume, VD , and the column hold-up volume, Vm . Re-equilibration can occur quickly, with less than three column volumes of conditioning solvent [49]. This is very important in on-line comprehensive two-dimensional HPLC, where fast gradient analysis is used in each of the numerous repeated cycles in the second dimension. Core–shell columns allow faster re-equilibration of initial conditions after the end of the gradient, in comparison to fully porous particles [50]. 2.4. Sample migration along the column and gradient bandwidths The gradient bandwidths, wg , are generally considerably narrower than the widths of the peaks eluted under isocratic conditions. This is due to continuously changing composition of the mobile phase during gradient elution. As the elution strength increases, the speed of the migration of sample zone along the column, ui , gradually increases, too. The migration velocity depends on the solute retention factor, k, which is directly proportional to the distribution constant, KD (Eq. (2)). The retention factor k is constant during the whole time of isocratic elution. On the other hand, in gradient elution, the retention factor can be considered constant only in a very small (differential) section of the column length, dL, for a very short (differential) time interval, dt. This local instantaneous retention factor, ki , at any actual position in the column is rapidly changing (continuously decreasing) as the elution strength (the local concentration of the strong eluent, ϕi ) is increasing during gradient elution. The sample zone migration velocity, ui = u/(1 + ki ), is slower than the linear velocity of the mobile phase, u, and increases as ki , is decreasing with time at any place in the column. The dispersion by diffusion is directly proportional to the time the solute spends in each column section, hence inversely proportional to ki and it decreases as the solute moves through the subsequent sections from the top to the end of the column. Furthermore, when an already dispersed zone moves from the section with a lower solvent strength of the mobile phase to the next section with a higher concentration of the strong solvent and lower ki , the solute zone is focused, much like as the on-column focusing of a sample dissolved in a weaker solvent injected on the column equilibrated with a stronger mobile phase. That is why the contribution of dispersion to band broadening is lower in comparison to sample migration under isocratic conditions (ki = const, ui = const). The local change

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Table 1 Sample compounds. No.

Compound

No.

Compound

No.

Compound

1 2 3 4 5 6 7 8 9 10 11 12 13

Gallic acid Protocatechuic acid p-Hydroxybenzoic acid Salicylic acid Vanillic acid Syringic acid 4-Hydroxyphenylacetic acid Caffeic acid Sinapic acid p-Coumaric acid Ferulic acid Chlorogenic acid (−)-Epicatechin

14 15 16 17 18 19 20 21 22 23 24 25 26

(+)-Catechin Flavone 7-Hydroxyflavon Apigenin Lutheolin Quercetin Rutin Naringin Biochanin A Naringenin Hesperetin Hesperidin Apigenin

27 28 29 30 31 32 33 34 35 36 37 38

Myricetin Esculin Esculetin Scopoletin 4-hydroxycoumarin 7-hydroxycoumarin Benzene Methylbenzene Ethylbenzene Propylbenzene Butylbenzene Pentylbenzene

of the local instantaneous retention factors, ki , in gradient elution can be calculated at any time and sample zone position at the fractional distance, Li , from the top of the column. The volume of the mobile phase that has passed through from the top of the column to the center of the sample zone at the distance Li , can be determined as the “proportional” contribution to the net gradient elution volume, V Ri = VRi − Vmi = V R (Li /L), where L is the total column length and Vmi is the proportional part of the column hold-up volume: Vmi = Vm (Li /L) [44]. Combining the semi-logarithmic model retention equation, Eq. (4) and the gradient Eq. (8), we obtain Eq. (10) for ki : ki =



1



(10)

2.31mBVm Li /L + 10(mA−a)

The log–log model Eq. (6), combined with Eq. (9) provides Eq. (11):







ki = k0 (m + 1) Bk0 Vm Li /L + A(m+1)

−m/m+1

(11)

Using Eqs. (10) or (11), as appropriate, the retention factor at the elution time of the peak maximum, ke , can be calculated, setting Li = L. Assuming strongly retained compounds and gradients starting at a very low concentration of the organic solvent (A ≈ 0), Eq. (10) can be simplified to Eq. (12), introduced by Snyder in the LSS model for calculation of ke elution [51]: kei,LSS =

1 2.31mBVm

(12)

Assuming that the band dispersion is principally controlled by the mobile phase at the time of elution (ϕ − ϕe ), the gradient bandwidths, wg , can be – to first approximation – estimated as the bandwidths under isocratic conditions, with the instantaneous retention factor ke [42,44,46,51,52]: 4Vm wg = √ (1 + ke ) N

(13)

wg is in volume units; ke in Eq. (13) can be inserted from Eq. (12), or calculated from Eqs. (11) or (12) for Li = L [43,44]. It should be noted that the number of theoretical plates, N, to be used in Eq. (13) must be determined under isocratic conditions. At increasing gradient steepness, B, and (or) the starting concentration of the organic solvent, A, both the gradient retention times and bandwidths decrease. The experimental bandwidths may be slightly narrower than the wg , calculated from Eq. (13), This effect has been attributed to the “additional gradient bandwidth compression”, which may occur as the trailing edge of the sample moves slightly faster in a mobile phase with higher elution strength than the leading edge in a weaker mobile phase [53]. Poppe et al. [54] introduced a correction factor taking into account the effect of decreasing solvent strength across the sample band in gradient elution, which was later studied in more detail [55,56]. However

this additional band compression has minor effect on very narrow peaks in fast gradient elution. In the present work, we compared the experimental gradient elution volumes and bandwidths with the values predicted on the basis of the semi-logarithmic and log–log retention models (Eqs. (8)–(11) and (13)), to evaluate the suitability of the two models for fast gradients on core–shell columns. 3. Experimental 3.1. Materials Acetonitrile, LiChrosolv grade, was purchased from Merck (Darmstadt, Germany). Water was purified using a SG Ultra Clear UV water purification system (SG, Hamburg, Germany). Ammonium acetate and formic acid (≥98%) were purchased from Sigma-Aldrich (St. Louis, MI, USA). Buffered mobile phases containing 10 mM CH3 COONH4 were prepared by dissolving the appropriate weighed mass of ammonium acetate in water and adjusting the pH to 3.1 by adding a few drops of formic acid. The mobile phases were filtered using a Millipore (Bedford, MA, USA) 0.45 ␮m filter and degassed by ultrasonication. Alkylbenzene standards (benzene to n-pentylbenzene), phenolic acids and flavonoid compounds (Table 1) were obtained from Sigma-Aldrich (St. Louis, MI, USA). The stock solutions of n-alkylbenzene standards (20 g/L), of phenolic acid and flavonoid standards (100 mg/L) were prepared in 1:1 aqueous acetonitrile. The working standard solutions were obtained by dilution with the mobile phase. Seven core–shell columns with different stationary phases were tested for fast gradient operation. The bonded stationary phases included octadecyl, octyl, phenyl-hexyl, amide and pentafluoropropyl ligands: three Ascentis Express, 2.7 ␮m, 30 × 3.0 mm i.d. columns (C18, C8, phenyl-hexyl, all from Supelco, Bellafonte, PA, USA), a Poroshell SB-C18 column, 2.7 ␮m, 30 × 3.0 mm i.d., (from Agilent, Palo Alto, CA, USA) and three Kinetex columns, 2.6 ␮m, 50 × 3.0 mm i.d., (C18, XB-C18, PFP, 2.6 ␮m, 50 × 3.0 mm i.d., from Phenomenex, Torrance, CA, USA) were used. Table 2 lists the properties of the eight core–shell columns tested, all 3 mm i.d., 50 or 30 mm long, containing silica-based 2.6 ␮m (Kinetex) and 2.7 ␮m (Ascentis Express, Poroshell) particles with 0.5 or 0.35 ␮m porous-shell layer. The separation efficiencies of the columns in 50% acetonitrile, in terms of height equivalent to a theoretical plate, ranged from 6 ␮m (Kinetex XB C18) to 12 ␮m (Kinetex C18), at the flow-rates employed for fast gradient separations, which were close to the instrumental pressure limits. 3.2. Equipment A 1200 series rapid resolution LC liquid chromatograph (Agilent, Palo Alto, CA, USA) equipped with a micro-flow binary pump,

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61

Table 2 Properties of the columns. Column no.

Trade name (manufacturer)

Dimensions (L × i.d.), particle size (␮m)

%C

S

P.D.

Vm

εT



fcor

1 2 3 4 5 6 7 8

Kinetex C18 2.6 ␮ (Phenomenex, Torrance, CA, USA) Kinetex PFP (Phenomenex, Torrance, CA, USA) Kinetex XB C18 (Phenomenex, Torrance, CA, USA) Poroshell 120 SB-C18 (Agilent, Palo Alto, CA, USA) Ascentis Express C8 (Supelco, Bellefonte, PA, USA) Ascentis Express C18 (Supelco, Bellefonte, PA, USA) Ascentis Express phenyl-hexyl (Supelco, Bellefonte, PA, USA) Ascentis Express RP-Amide (Supelco, Bellefonte, PA, USA)

50 × 3, 2.6 50 × 3, 2.6 50 × 3, 2.6 30 × 3, 2.7 30 × 3, 2.7 30 × 3, 2.7 30 × 3, 2.7 30 × 3, 2.7

12 9 10 N.A. N.A N.A. N.A. N.A.

150 200 200 120 150 150 150 150

100 100 100 120 90 90 90 90

0.212 0.224 0.215 0.204 0.153 0.160 0.140 0.152

0.599 0.633 0.607 0.962 0.722 0.755 0.660 0.717

0.27 0.27 0.27 0.37 0.37 0.37 0.37 0.37

0.61 0.61 0.61 0.75 0.75 0.75 0.75 0.75

L—column length (mm), i.d.—inner diameter (mm), %C—carbon load, S—specific surface area (m2 /g), P.D.—pore diameter (Å), Vm —hold-up volume (mL), εT —total column porosity,  = dshell /rparticle , fcor —core–shell factor.

a degasser, an auto-sampler, a diode-array UV detector and a thermostated column compartment was used in all experiments. 3.3. Methods The isocratic retention data used for the determination of the parameters a, m, k0 of Eqs. (4)–(6), were measured in premixed mobile phases at different concentrations of acetonitrile in aqueous–organic mobile phases. The column hold-up volumes (Vm ) were measured as the elution volumes of uracil as a non-retained marker (Table 2). The temperature was set to 40 ◦ C in all experiments. The predicted gradient elution volumes were corrected for the VD in Eqs. (8) and (9). The experimental gradient delay volume of the 1200 series RR chromatograph (VD = 1.15 mL) was measured by running a linear gradient of 0.1% acetone in pure acetonitrile, as suggested elsewhere [48]. The bandwidths evaluated by the chromatography data station at the half peak heights were re-calculated to the bandwidths at the baseline (4), w(g)meas , from which the extra-column contributions to band broadening, we , were subtracted to obtain corrected experimental gradient bandwidths, w(g)exp : w(g)exp =



w(g)meas 2 − we 2

(14)

4. Results and discussion 4.1. Retention models and band migration along the core shell columns Core–shell particles with a relatively shallow active stationary phase layer may seem to be more likely to provide adsorption than the fully porous particles. Hence we compared the semilogarithmic and the log–log models as the basis of prediction of retention in gradient LC for alkylbenzenes and flavonoid compounds on various types of core–shell columns. Eq. (4) describes the semi-logarithmic model of retention factors versus acetonitrile volume fraction in the mobile phase, generally used in reversed-phase chromatography. Fig. 1 shows that the experimental log k versus ϕ plots of alkylbenzenes on the Ascentis Express C18 column deviate from linearity of Eqs. (4) and (5). The linearity of the plots described by the two-parameter log–log equation, Eq. (6), significantly improved in comparison to the semilogarithmic model in Fig. 1. We investigated the effects of including the core volume into the stationary phase on the prediction of the retention data. The retention factors, kcor , corrected by core-correction factor, fcor , calculated using Eq. (3), are lower than the uncorrected k (Eq. (4)), as they include only the porous shell layer into the stationary phase. The best-fit intercepts a of the plots of the log k versus the volume fraction of acetonitrile, ϕ, corrected for the core volume are shifted by a constant decrement to lower values, but the slopes m of the

plots are not affected by the correction, as illustrate the plots for uncorrected k (full lines) and the plots after the correction for the solid core volume (dashed lines) on an Ascentis Express C18 column (Fig. 1). The same behavior was observed on all core–shell columns. Table S1 in the Supplementary internet files gives the values of the best-fit regression parameters and correlation coefficients of the two models for the individual alkylbenzenes and flavonoid samples on seven core–shell columns. The parameters a include the corrections for the inert core volume for all columns. Both semi-logarithmic and log–log models show good data fit and were employed as the basis for prediction of gradient retention data. The local instantaneous retention factors, ki , in gradient elution gradually decrease at increasing fractional distance Li from the column top, as the sample bands move along the column during gradient, as illustrates Fig. 2 for methylbenzene (MB) and pentylbenzene (PeB) in fast 1-min gradients (from 0% to 100% acetonitrile) on a 5-cm Kinetex C18 column ((A) and (B)) and on a less retentive, 3-cm Ascentis Express C8 column ((C) and (D)). At the first glance, both the semi-logarithmic (Eq. (10)) and log–log (Eq. (11)) models provide similar plots. The log–log model predicts lower local instantaneous retention factors ki than the semi-logarithmic model at the early stage of the gradient in the upper parts of the columns. The differences between the models are less significant for the more retained pentylbenzene. At the start of the gradient, the sample zones are strongly retained and migrate very slowly along the column in the upper 5–10% of the column length (ki > 30 for pentylbenzene). The ki decrease more rapidly for the semilogarithmic model, with increasing concentration of acetonitrile. Similar ki versus Li plots were measured on the other core–shell columns. The local instantaneous retention factors continuously decrease down to minimum values, ki = ke , at the time of elution, where L = Li . ke are used for prediction of bandwidths in gradient elution from Eq. (13). The ke calculated for benzene and methylbenzene from the semi-logarithmic model (Eq. (10)) and the ke,LSS determined from the simplified Eq. (12) [48], are considerably higher than the ke of pentylbenzene, whereas the ke predicted on the basis of the log–log model (Eq. (11)) are almost equal for all alkylbenzenes in fast 1 mingradients (as shows Table 3 for a 3 cm-Ascentis Express C18 column and for a 5 cm-, but less retentive Kinetex PFP column and Table S2 in the Supplementary internet information material for the other five columns). Of course, the volume fractions of acetonitrile at the time of elution, ϕe , increase for more retained higher alkylbenzenes. In comparison to the semi-logarithmic model, the ϕe predicted by the log–log model are similar or only slightly higher for more retained alkylbenzenes, but significantly higher for benzene and toluene. With 1 min gradients, both the log–log and the semilogarithmic models predict higher retention factors at the time of elution, ke , for shorter (3 cm) Ascentis and Poroshell columns, obviously due to less steep gradient ramps, B = 0.222–0.250, Eq. (7), in comparison to longer (5 cm) Kinetex columns (B = 0.333–0.4).

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Fig. 1. Effects of the volume fraction of acetonitrile, ϕACN , on the retention factors, k, of benzene (B), methylbenzene (MB), ethylbenzene (EB), propylbenzene (PrB), butylbenzene (BB) and pentylbenzene (PeB) on an Ascentis Express C18 column (30 × 3.0 mm i.d.). Full lines -uncorrected k; dashed lines k after subtraction of the solid core volume (Eq. (5)). Left: semi-logarithmic model (Eq. (4)); right: log–log model (Eq. (6)).

4.2. Prediction of the elution times and bandwidths in gradient elution on core–shell columns Table 3 shows the experimental and predicted gradient retention times and bandwidths of alkylbenzenes in fast gradients on a 3 cm Ascentis Express C18 and a 5 cm Kinetex PPF core–shell columns. Table S2 in the Supplementary internet information material shows the data for the remaining 5 core–shell columns tested. The selection of the two-parameter isocratic retention model is not very critical for the accuracy of prediction of the retention times (volumes) in fast broad-range gradient elution (0–100% acetonitrile in 1 min) on core–shell columns. The differences of the predicted from the experimental data are in the range of 0.01–0.10 min (Table S3). For the seven core–shell columns studied, the retention times

of alkylbenzenes and flavones predicted using the semi-logarithmic (Eq. (8)) model, differ from the experimental values at 3.8–7.3% and the log–log (Eq. (9)) model at 4.6–11.1% (Table S5). We tested the effect of employing a three-parameter isocratic model [36], which was earlier successfully used for direct prediction of gradient retention data [57,58]: log k = −m log (a − bϕ)

(15)

The three-parameter model did not provide any improvement in the prediction of gradient data in comparison with the twoparameter models (data not shown). For better accuracy, we corrected the measured gradient bandwidths, w(g)meas , for the extra-column contributions to band broadening, we , using Eq. (14). The corrected experimental gradient

Fig. 2. Changes in the local instantaneous retention factors of methylbenzene (MB—(A) and (C)) and pentylbenzene (PeB—(B) and (D)) at the sample zone centers, ki , in the column at the distance Li from the top, during a 1 min gradient, 0–100% acetonitrile in water. L is the column length, ke are the retention factors at the sample elution times. Columns: Kinetex C18 (50 × 3.0 mm i.d., 2.5 mL/min—(A) and (B)); Ascentis Express C8 (30 × 3.0 mm i.d., 4.5 mL/min—(C) and (D)).

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63

Table 3 Experimental (exp) and calculated values of retention times, tR(g) , min (Eqs. (8) and (9)), and peak widths, w(g) , min (Eq. (13) for the semi-logarithmic (log k − ϕ) and log–log (log k − log ϕ) retention models. tR(g)

exp

w(g)

meas

w(g)

exp

log k − ϕ

ke,LSS tR(g)

BE MB EB PB BB PeB

0.62 0.72 0.79 0.86 0.92 0.98

0.010 0.010 0.010 0.012 0.012 0.012

0.009 0.009 0.009 0.011 0.011 0.011

4.89 4.31 3.85 3.44 3.09 2.83

BE MB EB PB BB PeB

0.80 0.89 0.94 0.99 1.03 1.06

0.014 0.013 0.011 0.011 0.011 0.010

0.012 0.011 0.008 0.008 0.008 0.007

2.34 1.95 1.68 1.46 1.29 1.16

w(g)

Express C18, 4.5 mL/min 0.63 0.015 0.75 0.013 0.84 0.012 0.92 0.011 0.98 0.010 1.03 0.009 Kinetex PFP, 2.8 mL/min 0.81 0.013 0.95 0.011 1.02 0.009 1.08 0.008 1.12 0.008 1.15 0.007

log k − log ϕ ke

ϕe

tR(g)

w(g)

ke

ϕe

5.22 4.45 3.91 3.46 3.09 2.83

0.34 0.46 0.55 0.63 0.69 0.74

0.72 0.79 0.86 0.92 0.98 1.03

0.010 0.010 0.010 0.010 0.010 0.010

2.99 3.15 3.23 3.29 3.29 3.29

0.43 0.50 0.56 0.63 0.69 0.74

2.84 2.12 1.74 1.48 1.29 1.16

0.32 0.46 0.53 0.59 0.63 0.66

0.91 0.98 1.03 1.08 1.12 1.16

0.009 0.009 0.009 0.009 0.008 0.008

1.58 1.61 1.59 1.55 1.50 1.45

0.42 0.49 0.54 0.59 0.63 0.67

ke —retention factors at the time of elution, (Eqs. (10)–(12), ϕe —volume fractions at the time of elution, gradient: 0–100% ACN in 1 min, w(g)meas —measured peak width, w(g) exp —peak widths corrected for the extra-column contribution, we —corresponding to the volume of 0.02 mL, according to Eq. (14).

Table 4 Efficiency, average bandwidths, optimum gradient range and peak capacity of the core–shell columns. Column

HETP(iso) (␮m)

N(iso)

HETP(grad) (␮m)

N(g)

w(g)meas (min)

w(g)exp (min)

nc(g)

ϕopt (% ACN)

Ascentis Express C18 (30 × 3.0 mm, 2.7 ␮m) Ascentis Express C8 (30 × 3.0 mm, 2.7 ␮m) Ascentis Express phenyl-hexyl (30 × 3.0 mm, 2.7 ␮m) Poroshell 120 SB-C18 (30 × 3.0 mm, 2.7 ␮m) Kinetex 2.6 ␮ C18, 100A (50 × 3.0 mm, 2.6 ␮m) Kinetex 2.6 ␮ XB-C18, 100A (50 × 3.0 mm, 2.6 ␮m) Kinetex 2.6 ␮ PFP, 100A (50 × 3.0 mm, 2.6 ␮m)

7 (3.0 mL/min)

4500

9 (4.5 mL/min)

3300

0.018

0.017

111

3–33

8 (3.0 mL/min)

3600

10 (4.5 mL/min)

3000

0.033

0.033

61

0–28

11 (3.0 mL/min)

2800

24 (4.0 mL/min)

1300

0.021

0.020

93

7–31

9 (3.0 mL/min)

3500

11 (4.0 mL/min)

2600

0.017

0.016

120

4–31

12 (2.0 mL/min)

4300

9 (2.5 mL/min)

5900

0.018

0.016

110

8–41

6 (2.0 mL/min)

8400

3 (3.0 mL/min)

18,200

0.013

0.012

150

6–39

9 (2.8 mL/min)

5600

6 (2.8 mL/min)

9000

0.019

0.018

101

6–36

Height equivalent to a theoretical plate of a column and number of theoretical plates under isocratic conditions (for butylbenzene in 50% acetonitrile) – HETP(iso) and N(iso) – and in broad range fast gradient elution (3–60% ACN in 2 min, except for 3–40% ACN in 2 min on the Express C8 column) – HETP(grad) and N(g) for alkylbenzenes – Eq. (16); w(g)meas —average measured peak width of flavones (gradient; w(g)exp —corrected experimental peak width of flavones (Eq. (14)); nc(g) —peak capacity of core–shell columns in 2-min gradients, calculated from the average measured peak width of flavones—Eq. (17); ϕopt —optimized gradient range of acetonitrile volume fraction for the separation of phenolic acids and flavone compounds (tg = 2 min).

bandwidths, w(g)exp , were approximately 0.001 min, i.e., 0.06 s, narrower than w(g)meas ; for the Ascentis Express C8 column the effects of correction did not exceed the experimental error (Table 4). For accurate prediction of the gradient bandwidths from Eq. (13), the correct determination of the plate number under isocratic conditions is essential. The height equivalent to a theoretical plate, H, depends on the composition of the mobile phase, which changes during the gradient [51,52]. To correct for this effect, “the apparent gradient number of theoretical plates”, N(g) , can be determined from re-arranged Eq. (13), assuming an approximately constant average experimental gradient bandwidth, wg,(av) (in time units) and ke for various sample compounds during a gradient run [52]:

N(g) ∼ = 16

t0 (1 + ke ) wg(av)

2

(16)

Fig. 3 illustrates the effects of the retention factors at the elution times of alkylbenzenes (benzene to pentylbenzene), ke , on the “apparent gradient plate number” on seven 30-mm (1–4) and 50-mm (5–7) core–shell columns, in fast gradients (0% to 100% acetonitrile in 1 min). On each column, the experimental gradient bandwidths, w(g)exp , were almost the same for alkylbenzenes (Table 3, Table S2) and similar for flavones (Table S4). Hence we used the mean experimental bandwidths for the alkylbenzenes to calculate N(g) from Eq. (16), with ke determined using

Fig. 3. Effects of the retention factors at the elution times of alkylbenzenes (benzene to pentylbenzene), ke , calculated using the semi-logarithmic and log–log (values inside the dotted limits) models on the “apparent gradient plate number”, N(g) , calculated from Eq. (20) using the mean experimental gradient bandwidths, w(g)exp (Table 4) for 30 mm (1–4), and 50 mm (5–7) core–shell columns. Gradients: 0–100% acetonitrile in water in 1 min; Fm —mobile phase flow rate (mL/min); B = (ϕG − A)/VG —the gradient ramp (Eq. (7)). The log–log model data for all alkylbenzenes are grouped within the dotted circled areas.

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occurs in the mobile phase with high concentration of acetonitrile, toward the column end, the length of the column has only minor effect on the bandwidths. This may explain lower “gradient HETP” with respect to the “isocratic HETP”, observed with the longer, 5 cm columns (Table 4). 4.3. Separation selectivity, optimum gradient range and peak capacity in fast gradient chromatography on core–shell columns

Fig. 4. Van Deemter plot (H = A + B/u + C × u) for butylbenzene on a Kinetex XB-C18 column (2.6 ␮m, 50 × 3.0 mm i.d.) in 50% acetonitrile/water. H—height equivalent to a theoretical plate (HETP), u—mobile phase velocity, mm/s. A = 0.00253 ± 0.00016 mm; B = 0.00438 ± 0.00011 s; C = 0.00036 ± 0.00002 mm2 /s; R2 = 0.9974.

the semi-logarithmic (Eq. (10) and log–log (Eq. (11) models, setting Li = L. The semi-logarithmic model predicts significantly higher bandwidths for weakly retained benzene and toluene, resulting in wide spread of the data (points) on the N(g) ) versus ke plots in Fig. 3 However, the log–log model data for all alkylbenzenes group closely together within the dotted circled areas in Fig. 3, showing only minor effects of the sample on the N(g) and gradient bandwidths (Table 4). The log–log model probably is more suitable to describe the effects of the sample migration on the ultimate retention at the time of elution and provides very similar values of ke for all alkylbenzenes and N(g) almost independent of the sample (Fig. 3), hence is more consistent and useful for the determination of the “apparent gradient plate number” than the semi-logarithmic model, at least for fast gradients on core–shell columns. The core–shell columns generally show very low contribution of the mass-transfer resistance term, C, to band broadening, especially at high mobile phase velocities [59]. The N(g) calculated from Eq. (16) for the 3 cm columns at 4–4.5 mL/min are approximately at 20–30% lower than the numbers of theoretical plates determined at isocratic conditions for butylbenzene in 50% ACN at 3 mL/min, N(iso) —Table 4. On the 5 cm core–shell columns, the N(g) were higher than on the 3 cm columns, as it could be expected,. From among the 3 cm core–shell columns, the Ascentis Express C18 shows the best efficiency, whereas the Kinetex XB-C18 is the most efficient 5 cm column, showing isocratic H = 5–6 ␮m in the mobile phase velocity range 1.5–10 mm/s (0.5–3 mL/min) (Fig. 4). In comparison to the bandwidths predicted with the N(iso) directly measured under isocratic conditions, the accuracy of prediction of the bandwidths from Eq. (13) considerably improved when using the average apparent number of theoretical plates, N(g) , calculated from Eq. (16),. When using the N(g) , determined for alkylbenzenes, differences in bandwidths between 0.002 and 0.004 min were observed both for alkylbenzenes (Table S2) and for flavones (except for the Ascentis Express C8 and phenyl-hexyl (Table S4 in the Supplementary internet files). For alkylbenzenes, the log–log model showed the mean differences between the experimental and the predicted peak widths in between 4.8% and 13.7%, which was better than the differences of prediction for the semi-logarithmic model (12.7–28.4%), whereas the mean standard deviation of repeated measurement of peak widths was 0.0003 min, i.e., 3% (Table S5). As the main part of the band migration obviously

To optimize fast gradient separations, a short gradient time can be fixed (e.g., to 1–2 min for the second-dimension separations in comprehensive 2D LC × LC) and the mobile phase flow rate should not exceed the limits imposed by the instrumental pressure tolerance., At a constant limiting gradient time, tG , and flow-rate of the mobile phase, Fm , predictive optimization of fast gradients should be focused on the gradient concentration range ϕ = ϕG − A, where A is the volume fraction of the organic solvent in the mobile phase at the start, and ϕG at the end of gradient elution [60]. The starting composition of the mobile phase can be adjusted to optimize the resolution of “critical pairs” of sample compounds in minimum analysis time avoiding excessively long elution times of weakly retained compounds, and ϕG should allow the elution of strongly retained sample compounds before the end of a fast gradient [61]. This strategy was employed for the optimization of comprehensive 2D LC × LC gradient separation of phenolic and flavonoid compounds [20]. Table 4 lists the optimum gradient concentration range of acetonitrile, ϕopt for seven core–shell columns. The final gradient concentration of acetonitrile, ϕG , was calculated to achieve the elution of the most strongly retained flavones, flavone and biochanin A, in 2-min gradient time; the initial concentration, A, to elute the least retained gallic acid at VR = 1.5 Vm [20]. Generally, the optimum gradient range depends on the column length and is shifted to higher % acetonitrile for 5-cm columns with respect to shorter, 3cm columns, to compensate for simultaneously increasing column hold-up volume and decreasing flow-rate dictated by maximum instrumental pressure. From among the 3-cm columns, the lowest starting concentration of acetonitrile (pure aqueous buffer) should be used with the least retentive Ascentis Express C8 column, whereas on the phenyl-hexyl column, which shows the strongest retention, the gradient can be started at relatively high acetonitrile concentration (7%). Assuming that the whole chromatogram is regularly covered by sample peaks, stacked side-by-side within the pre-set gradient time with the gradient range, ϕ, optimized to cover the interval between the expected elution times of the first peak, 1, and of the last one, z, tG = tR = tR,z − tR,1 , introducing N = L/H, and tm =  r2 LεT , the theoretical peak capacity, n(g), under reversed-phase gradient conditions can be predicted from Eq. (17), assuming approximately constant average bandwidth, wg , (Eq. (13)):



n(g) ∼ =

tR,z − tR,1 +1∼ = w(g)

+1 ∼ =

Fm tG √ +1 √ 4r 2 εT H (1 + ke ) L

tR L H 4tm (1 + ke ) (17)

here tm is the column hold-up time, which may be considered equal to the elution time of the first solute, εT is the total column porosity, r the column inner radius and Fm the mobile phase flow rate., Similar expressions for peak capacity in gradient LC were obtained using the “average” retention factor under gradient conditions, kg = V R /Vm [62–65]. n(g) in gradient elution is considerably higher than in the isocratic mode. The gradient peak capacity, n(g) of the seven core–shell columns in the full time range 2-min gradients, calculated from Eq. (17) using the average measured (uncorrected) gradient peak widths,

P. Jandera et al. / J. Chromatogr. A 1337 (2014) 57–66

65

combined with various core–shell columns in the second dimension [66]. 5. Conclusions

Fig. 5. Chromatograms of 24 phenolic and flavone compounds on a 5-cm Kinetex XB-C18 Ascentis Express, a 3-cm Ascentis phenyl-hexyl and a 5-cm Kinetex PFP column in 2-min gradients from 3% to 60% acetonitrile (+0.05 mol/L ammonium acetate). The numbers of peaks are as in Table 1.

w(g)meas is given in Table 4. The peak capacity is proportional to the square root of the number of theoretical plates, N = L/H, hence one would expect increasing peak capacity for longer columns. Indeed, the most efficient 5-cm Kinetex XB-C18 column provides the highest n(g) from among the columns tested. However, Eq. (17) predicts secondary effects of the column length, L, on the gradient peak capacity. At a constant column diameter and a fixed gradient time, tG = tR , the column hold-up time, tm increases, but the retention factor at the time of elution, ke , decreases with increasing column length L (Fig. 3, Table 3 and Table S4). Further, the mobile phase flow-rate, Fm , should be adjusted when increasing L, not to exceed the instrumental pressure limits. When decreasing the flow-rate, the column efficiency, H, may improve to some extent, even though the effect is less significant with core–shell than with fully porous column packing materials (Fig. 4). Hence the effect of the core–shell column length is not straightforward and high peak capacity can be achieved on both 3-cm and 5-cm core–shell columns when running fast gradients. The chemistry of the shell stationary phase controls the selectivity of separation and affects the column efficiency (HETP), the optimum gradient range, and ke (Table 4), Consequently, the peak capacity depends on the stationary phase. All core–shell C18 columns studied show higher peak capacity (nc(g) = 110–150) than the columns with less lipophilic bonded stationary phases (nc(g) = 60–100). Fig. 5 compares fast gradient separations of a test mixture of 24 phenolic acids and flavones in 2-min gradients from 3% to 60% acetonitrile on three core–shell columns with different separation selectivities. The most efficient 5-cm Kinetex XB-C18 non-polar core–shell column shows the best resolution (except for vanillic and caffeic acids). On a 3-cm Ascentis phenyl-hexyl and a 5-cm Kinetex PFP column several co-eluted peaks were observed. Complex mixtures of phenolic and flavone antioxidants can be readily separated by comprehensive two-dimensional LC × LC, on a monolithic zwitterionic polymethacrylate column in the first dimension,

The present work provides deeper insight into the factors affecting fast gradient separation on core–shell columns and possible sources of errors in prediction of gradient retention times and peak widths from the isocratic data: selection of a suitable retention model, determination of the phase ratio in the column, column plate number, extra-column contributions to band broadening. Correcting the volume of the stationary phase for the solid core volume provides more realistic retention factors, but does not affect significantly the accuracy of the prediction of gradient elution data. It is important that the same convention for the definition of stationary phase is used for the acquisition of the retention model parameters under isocratic conditions and for the prediction of the gradient retention data. Based on the fit of the model equations alone, it is not possible to decide whether the retention on core–shell columns is based on adsorption or on partition. Most probably, the two effects may combine, depending on the sample and chemistry of the stationary phase. The two-parameter semi-logarithmic (LSS) retention model provides slightly better prediction of retention times, whereas the log–log retention model characterizes more accurately the instantaneous changes in retention as the sample migrates along the column and yields more better agreement of predicted peak widths with experiment in fast gradients on core–shell columns. Employing the “apparent gradient number of theoretical plates” for calculation of gradient bandwidths considerably improves the agreement between the experimental and the predicted bandwidths. Correction for the experimental extra-column contributions improves the agreement between the predicted and experimental gradient peak widths. High peak capacity in fast gradient elution on core–shell columns can be achieved both on longer (5-cm) and shorter (3cm) columns, with optimized gradient range of the mobile phase to suit the stationary phase chemistry and the column length. Acknowledgments This work was supported by the Czech Science Foundation, project No. P206/12/0398. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.chroma. 2014.02.023. References [1] L.W. Potts, D.R. Stoll, X. Li, P.W. Carr, Chromatography A 1217 (2010) 5700. [2] G. Guiochon, N. Marchetti, K. Mriziq, R.A. Shalliker, Chromatography A 1189 (2008) 109. [3] M.E. Swartz, J. Liq. Chromatogr. Related Technol. 28 (2005) 1253. [4] H. Minakuchi, K. Nakanishi, N. Soga, N. Ishizuka, N. Tanaka, Chromatography A 762 (1997) 135. [5] J.J. Kirkland, Anal. Chem. 41 (1969) 218. [6] J.J. Kirkland, T.J. Langlois, J.J. DeStefano, Am. Lab. 39 (2007) 18. [7] A. Cavazzini, F. Gritti, K. Kaczmarski, N. Marchetti, G. Guiochon, Anal. Chem. 79 (2007) 5972. [8] E. Olah, S. Fekete, J. Fekete, K. Ganzler, Chromatography A 1217 (2010) 3642. [9] J.J. DeStefano, S.A. Schuster, J.M. Lawhorn, J.J. Kirkland, Chromatography A 1258 (2012) 76. [10] F. Gritti, I. Leonardis, D. Shock, P. Stevenson, A. Shalliker, G. Guiochon, Chromatography A 1217 (2010) 1589. [11] F. Gritti, G. Guiochon, Chromatography A 1218 (2011) 1915.

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