Journal of Chromatography A, 1325 (2014) 72–82

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Detailed characterization of the kinetic performance of first and second generation silica monolithic columns for reversed-phase chromatography separations Deirdre Cabooter a,∗ , Ken Broeckhoven b , Roman Sterken a , Alison Vanmessen a , Isabelle Vandendael c , Kazuki Nakanishi d , Sander Deridder b , Gert Desmet b a

KU Leuven, Department of Pharmaceutical Sciences, Pharmaceutical Analysis, Herestraat 49, 3000 Leuven, Belgium Vrije Universiteit Brussel, Department of Chemical Engineering, Pleinlaan 2, 1050 Brussels, Belgium c Vrije Universiteit Brussel, Faculty of Engineering, Materials and Chemistry, Pleinlaan 2, 1050 Brussels, Belgium d Kyoto University, Department of Chemistry, Sakyo-ku, Kyoto 606-8502, Japan b

a r t i c l e

i n f o

Article history: Received 3 September 2013 Received in revised form 20 November 2013 Accepted 26 November 2013 Available online 1 December 2013 Keywords: Second generation silica monoliths Kinetic performance Characteristic length Flow resistance

a b s t r a c t The kinetic performance of commercially available first generation and prototype second generation silica monoliths has been investigated for 2.0 mm and 3.0–3.2 mm inner diameter columns. It is demonstrated that the altered sol–gel process employed for the production of second generation monoliths results in structures with a smaller characteristic size leading to an improved peak shape and higher efficiencies. The permeability of the columns however, decreases significantly due to the smaller throughpore and skeleton sizes. Scanning electron microscopy pictures suggest the first generation monoliths have cylindrical skeleton branches, whereas the second generation monoliths rather have skeleton branches that resemble a single chain of spherical globules. Using recently established correlations for the flow resistance of cylindrical and globule chain type monolithic structures, it is demonstrated that the higher flow resistance of the second generation monoliths can be entirely attributed to their smaller skeleton sizes, which is also evident from the external porosity that is largely the same for both monolith generations (εe ∼ 0.65). The recorded van Deemter plots show a clear improvement in efficiency for the second generation monoliths (minimal plate heights of 13.6–14.1 ␮m for the first and 6.5–8.2 ␮m for the second generation, when assessing the plate count using the Foley–Dorsey method). The corresponding kinetic plots, however, indicate that the much reduced permeability of the second generation monoliths results in kinetic performances (time needed to achieve a given efficiency) which are only better than those of the first generation for plate counts up to N ∼ 45,000. For more complex samples (N ≥ 50,000), the first generation monoliths can intrinsically still provide faster analysis due to their high permeability. It is also demonstrated that – despite the improved efficiency of the second generation monoliths in the practical range of separations (N = 10,000–50,000) – these columns can still not compete with state-ofthe-art core–shell particle columns when all columns are evaluated at their own maximum operating pressure (200 bar for the monolithic columns, 600 bar for core–shell columns). It is suggested that monolithic columns will only become competitive with these high efficiency particle columns when further improvements to their production process are made and their pressure resistance is raised. © 2013 Elsevier B.V. All rights reserved.

1. Introduction The first generation of monolithic silica columns has been on the market for more than a decade now [1–4]. In contrast to packed bed columns, monolithic columns consist of a single, continuous porous skeleton with large throughpores. The large throughpores result in a high external porosity (typically 70–80%,

∗ Corresponding author. Tel.: +32 016 32 34 42; fax: +32 016 32 34 48. E-mail address: [email protected] (D. Cabooter). 0021-9673/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.chroma.2013.11.047

whereas this value is rather around 38% for packed beds) leading to large permeability values, which can be several times larger than that of columns packed with 5 ␮m particles [5]. This high permeability allows monolithic columns to be used at high linear velocities, making them extremely suitable as second dimension columns in e.g. online two-dimensional separation set-ups [6]. Due to their high permeability, monolithic columns can also be coupled to long column lengths resulting in unprecedented efficiencies [7]. The small size of the silica skeletons (1–2 ␮m) on the other hand, results in efficiencies comparable to those of 3–5 ␮m

D. Cabooter et al. / J. Chromatogr. A 1325 (2014) 72–82

particle columns, while the small mesopores give rise to a large sample capacity per unit adsorbent volume [8]. Despite these promising features, monolithic silica columns have not been able to compete with the novel generation of packed particle columns which was commercialized around the same time [9–11]. This lack in performance has mainly been attributed to the fabrication process, which fails to deliver radially homogeneous 4.6 mm inner diameter (I.D.) columns, an observation that was recently confirmed by an in-depth evaluation of the eddy diffusion term in first generation monolithic columns [12]. Macroporous silica monoliths are typically produced from alkoxysilanes using a sol–gel method in the presence of watersoluble organic polymers. The fabrication starts by hydrolysis and polycondensation of high-purity alkoxy silicon derivatives, such as tetramethoxysilane (TMOS) or tetraethoxysilane (TEOS), to form a sol. Adding water and a catalyst starts a reaction process resulting in gel formation. Simultaneously with the gel formation, spinodal decomposition occurs and phase separation takes place between the silica-rich and water-rich phase, representing the future silica skeletons and throughpores, respectively. To manipulate phase separation and thus control the pore size of the gel, a porogen such as polyethylene glycol (PEG) (or polyethylene oxide (PEO)) can be used. By varying the concentration of the porogen, the size of the throughpores can be controlled. Aging in a siloxane solution increases the stiffness and strength of the gel by adding new monomers to the silica skeleton. Adding ammonium to the aging solution, mesopores are formed. The amount and size of the mesopores depend on the concentration of ammonium. The gel is finally dried by capillary pressure, causing the gel to shrink. After drying, the monolithic rod is cladded with PEEK to ensure no void spaces remain around the monolith [13–16]. To improve the performance of the first generation monoliths, alterations to the production process have been made, resulting in the production of so-called second generation monoliths. In 2006, second generation capillary monoliths with an increased structural homogeneity and improved efficiency were obtained by varying the concentration of TMOS and PEG. This resulted in monolithic columns yielding plate heights of 4–5 ␮m [17]. Very recently, the step toward normal bore second generation monoliths has been made by making further modifications to the sol–gel process. Merck launched commercially available 4.6 mm I.D. second generation monoliths in 2011 that were produced using an increasing amount of porogen [18]. The performance of these second generation monoliths has been evaluated for the analysis of small molecules and large biomolecules by several authors [19–23]. Recently, Kyoto Monotech released prototype samples of 2.0 mm I.D. and 3.2 mm I.D. second generation monoliths. These monoliths are produced using poly-acrylic acid (HPAA) as a phaseseparation inducer instead of PEG. PEG is distributed to the silica-rich phase, resulting in the formation of a hydrophobic layer at the surface of the gelling phase due to the specific adsorption of PEG chains onto surface silanol groups of silica oligomers [24]. This process is more pronounced when a hydrophobic mold is used in which case a dense layer, called the skin layer, is formed on the outermost part of the gelled silica rods. The formation of this layer results in a deformation of the framework of the gel before the actual gelation. Deformation of the gelling skeleton beneath the skin layer may also occur, resulting in structural inhomogeneities in the outermost part of the column. Both have a negative effect on the performance of the column. HPAA on the other hand, is distributed to the solvent phase and not the silica rich-phase upon phase separation. This results in less formation of skin layer and deformation of the skeleton in the vicinity of the mold wall, hence resulting in structures with an improved radial homogeneity. It is also easier to produce monolithic columns with a much smaller domain size using HPAA, which will result in improved column

73

efficiency, however, at the cost of an increased column backpressure. The cladding process of the second generation monoliths is also different as it uses a partially molten glass tube, resulting in a less prominent skin layer and hence a smaller loss of efficiency than a hydrophobic tube [25,26]. The present study aims at evaluating the kinetic performance of first and second generation monoliths with similar dimensions by taking efficiency and permeability simultaneously into account, as opposed to other studies were the efficiency and permeability of both generation monoliths has been evaluated separately [19–23]. For this purpose, the kinetic plot method is used. Kinetic plots are obtained by transforming experimentally obtained van Deemter (u0 , H) and permeability (Kv0 ) data using the following equations [27,28]: N=

t0 =

 P   K

v0





u0 H

 P   K  v0



u20

(1)

(2)

wherein u0 (m/s) is the linear velocity of the mobile phase, H is the plate height (m), Kv0 (m2 ) the permeability of the column, P (Pa) the pressure drop and  (Pa s) the viscosity of the mobile phase. A typical kinetic plot of plate count N versus column dead time t0 (min) or retention time tR (min) (tR = (1 + k)·t0 , with k the retention factor of the analyte) shows the efficiency N obtained in a certain time t in a column that is exactly long enough to generate a specific pressure P at a given velocity u0 . The pressure drop P used in Eqs. (1) and (2) is the maximum pressure that can be delivered by the instrument or the maximum pressure the column can withstand and gives an idea of the ultimate performance limit of the support. In the present study, the maximum pressure was set at 200 bar for the monolithic columns. A detailed investigation of the pressure drop characteristics of both generation monoliths is reported as well. For this purpose, total pore blocking (TPB) experiments have been performed to accurately determine the external porosity εe of the columns [29,30] and computationally determined correlations have been used to relate the experimentally determined permeability and porosity values [31]. The accuracy of these correlations is moreover demonstrated experimentally for the first time for monoliths with single globule chain-type skeleton branches and cylindrical skeleton branches. Finally, the performance of first and second generation monoliths is compared to that of state-of-the-art porous particles and evaluated at different operating pressures. 2. Experimental 2.1. Chemicals and columns Propiophenone, butyrophenone and benzophenone were obtained from Sigma–Aldrich (Steinheim, Germany), thiourea from Acros (Geel, Belgium) and potassium iodide (KI) from VWR (Leuven, Belgium). Milli-Q water was prepared using a Milli-Q gradient water purification system from Millipore (Bedford, MA, USA). HPLC grade Acetonitrile (ACN) was purchased from Fisher Chemicals (Erembodegem, Belgium), ammonium acetate from Sigma–Aldrich and glacial acetic acid from Merck (Darmstadt, Germany). The first generation monolithic columns (Chromolith Performance RP-18, 2.0 mm × 100 mm and 3.0 mm × 100 mm) were purchased from Merck. The second generation monolithic columns (3.2 mm × 50 mm, 3.2 mm × 100 mm, 2.0 mm × 50 mm and 2.0 mm × 100 mm) were kindly supplied by Prof. Nakanishi from Kyoto University. All monoliths had a maximum operating

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Table 1 Dimensions and mobile phase compositions used for the different columns. The obtained retention factors of the test compounds are shown. Column

Generation

Length (mm)

I.D. (mm)

Mesopore size (nm)

% ACN

kpropiophenone

kbutyrophenone

kbenzophenone

G1-2.0 × 100-1 G1-2.0 × 100-2 G2-2.0 × 50-1 G2-2.0 × 50-2 G2-2.0 × 100-1 G2-2.0 × 100-2 G1-3.0 × 100-1 G1-3.0 × 100-2 G2-3.2 × 50-1 G2-3.2 × 50-2 G2-3.2 × 100-1 G2-3.2 × 100-2

1 1 2 2 2 2 1 1 2 2 2 2

100 100 50 50 100 100 100 100 50 50 100 100

2.0 2.0 2.0 2.0 2.0 2.0 3.0 3.0 3.2 3.2 3.2 3.2

13 13 12 12 12 12 13 13 17 17 17 17

35.8 35.0 36.5 36.5 36.5 36.5 35.0 35.0 30.0 30.0 30.0 30.0

3.1 3.3 3.0 3.0 3.1 3.1 3.2 3.2 2.6 2.8 2.9 2.8

6.4 6.6 5.9 5.9 6.1 6.2 6.4 6.5 5.9 5.9 6.2 6.2

8.8 9.5 8.3 8.3 8.6 8.8 9.1 9.3 8.4 9.6 9.8 9.7

pressure of 200 bar. Two different columns of every column type (dimensions and generation as specified above) were available (Table 1). A core–shell column (2.1 mm × 100 mm; particle size dp = 2.7 ␮m; Ascentis Express, Supelco (Sigma–Aldrich), Bellefonte, PA, USA) was evaluated as well and was kindly provided by Dave Bell (Supelco). The maximum operating pressure of this column was 600 bar. 2.2. Apparatus 2.2.1. UHPLC instrumentation Column efficiency was studied as a function of flow rate on a Perkin Elmer UHPLC series 275 equipped with an autosampler, a binary pump, a still air oven and a variable wavelength detector with a detector cell of 2.6 ␮l. The maximum operating pressure of the system was 690 bar (10,000 psi). A peeksil viper (75 ␮m I.D.) (Thermo Fisher Scientific, Amsterdam, The Netherlands) was used between the injector and the inlet of the column. Between the outlet of the column and the detector, PEEK tubing with an internal diameter of 125 ␮m was used. The tubing was not altered during the experiments to avoid changing the extra-column volume. The overall system volume was determined to be 13 ␮l. Chromera software (Perkin Elmer, Massachusetts, USA) was used to control the UHPLC system and for data acquisition and analysis. The absorbance was measured at a wavelength of 254 nm. The temperature of the column was kept constant at 30 ◦ C. 2.2.2. HPLC instrumentation Total pore blocking (TPB) experiments were conducted on a Dionex Ultimate 3000 HPLC system equipped with an autosampler, a quaternary pump and a variable wavelength detector with a cell volume of 11 ␮l. The column temperature was controlled at 30 ◦ C with a static air oven compartment (Waters, Bedford, MA, USA). The maximum operating pressure of the system was 400 bar. Peeksil vipers (75 ␮m I.D.) (Thermo Fisher Scientific) were used to connect the column to the injector and detector of the system. The tubing was not altered during the experiments to avoid changing the extra-column volume. Chromeleon software (Thermo Fisher Scientific, Germering, Germany) was used to control the HPLC system and for data acquisition and analysis. The absorbance was measured at a wavelength of 254 nm. 2.2.3. SEM measurements To accurately determine the skeleton size of the studied columns, the first generation monoliths were radially cut in pieces with a thickness of approximately 1–2 mm using a lathe with a titanium nitride coated blade. Representative samples for SEM measurements of the second generation monoliths were made available by Prof. Nakanishi. The employed instrument JSM6400 (JEOL) had a Tungsten filament and was operated at an accelerating voltage of 20.0 kV and

a magnification of 3000× for the first generation monoliths and 6000× for the second generation monoliths. A carbon coating was applied to all samples to increase their conductivity. Of every monolith type, 20 pictures were taken and the size of at least 500 skeleton branches was measured. To determine the skeleton sizes, the SEM pictures were uploaded in a drawing program (Windows Paint) and straight lines, corresponding to the diameter of the skeletons were manually drawn over the skeleton branches. The length of the straight lines was subsequently determined in an automated way using an inhouse written script in Imaq Vision Builder (National Instruments Corporation, Austin, TX, USA).

2.3. Methodology Column efficiency was studied as a function of flow rate under isocratic conditions using a mobile phase composed of ACN/H2 O in varying ratios. The samples used under these conditions contained thiourea, propiophenone, butyrophenone and benzophenone (each 20 ppm), dissolved in the mobile phase. Thiourea was used as t0 -marker. The injection volume was 1 ␮l. Different ratios of ACN/H2 O were used as mobile phase to keep the retention factor k of propiophenone (k = 3.0 ± 0.2), butyrophenone (k = 6.2 ± 0.2) and benzophenone (k = 9.0 ± 0.6) constant on every tested column (Table 1). The column temperature was set at 30 ◦ C. Plate counts were determined using the Foley–Dorsey method to account for any skewness of the chromatographic peaks [32]: N=

41.7(tR /w0,1 ) (b/a) + 1.25

2

(3)

where w0.1 (min) is the peak width at 10% of the peak height and b/a is the asymmetry factor at 10% of the peak height (a (min) is the width of the front and b (min) the width of the tail of the peak at 10% of the peak height). Eq. (3) is only applicable if the asymmetry factor b/a is greater than unity, corresponding to a tailing peak. For fronting peaks, the asymmetry factor was therefore inverted (i.e., the ratio a/b was used). Using the Foley–Dorsey method, one should be aware that it is based on a mathematical model (exponentially modified Gaussian peak shape) which for some peak shapes might not always be the most correct one [33]. However, the Foley–Dorsey method has been proven throughout the years to provide a good first approximation in many cases. All experimental data were corrected for the system variance 2 , s2 ), dead time (t (ext ext , s) and pressure drop (Pext , bar) by removing the column from the system and replacing it with a zero-dead volume connection piece: u0 =

L t0 − text

(4)

D. Cabooter et al. / J. Chromatogr. A 1325 (2014) 72–82

N=

H=

(tR − text )2 2

2 − ext

L N

16

(5)

(a)

14 12

(6)

10

with L (m) the length of the column and  2 (s2 ) the total variance. System peaks were analyzed using the method of moments [34] to account for the asymmetry of the peak profiles encountered at higher flow rates. The signal-to-noise ratio (S/N) was kept >500 by injecting a sufficiently large concentration of analyte to minimize the influence of baseline noise on the calculated variances. System variances were determined to be up to 26% of the total variance for propiophenone, up to 9% of the total variance for butyrophenone and up to 5% of the total variance for benzophenone (depending on the column dimensions and the flow rate). To avoid any misinterpretation that might arise from correction errors, the column performance was assessed from the plate height data obtained for benzophenone. Column permeabilities (Kv0 ) were determined at a column pressure of ∼100 bar using a mobile phase composition of 35/65 ACN/H2 O (v/v %) for all columns. The column temperature was set at 40 ◦ C: Kv0 =

mAU

u0 L ptotal − pext

8 w50%

6 4 2

w10%

0 3.4

30

3.8

4

4.2

4.4

4.6 4.8 time (min)

25 20 15

The viscosity of the mobile phase  was determined according to Li and Carr [35].

10

w50%

5

2.4. Total pore blocking (TPB) experiments for the determination of the external porosity of the columns

w10%

0

The external porosity εe of the columns was determined using the total pore blocking (TPB) method [29,30]. This method consists of filling up the pores of the column with a hydrophobic solvent by first flushing the column with isopropanol and subsequently with the hydrophobic solvent for a sufficiently long time. In the present study, the columns were flushed with decane for at least 50 column volumes. Subsequently, the hydrophobic solvent was flushed out of the interstitial part of the column by rinsing it with 10 mM ammonium acetate buffer (brought to pH = 3 with acetic acid) at a flow rate of 0.22 ml/min for the 2.0 mm I.D. columns, 0.5 ml/min for the 3.0 mm I.D. columns and 0.57 ml/min for the 3.2 mm I.D. columns. The hydrophobic interactions between the C18 chains in the mesopores and the hydrophobic solvent assure that the hydrophobic solvent remains in the mesopores, making these pores inaccessible for the hydrophilic buffer. In the interstitial space, these interactions are not present (certainly not to the same extent), allowing to completely displace the decane by the (immiscible) aqueous buffer. During the flush-out period, heavy distortions of the recorded UV- and pressure signal can be observed, indicating that the decane and aqueous buffer form some kind of an emulsion with immiscible phases. When all the decane is flushed out of the interstitial volume, the UV- and pressure signals completely stabilize again. Subsequently injecting a small marker (1 mg/ml KI, dissolved in the ammonium acetate buffer), capable of exploring even the most minute pockets of the interstitial space, the external porosity can be determined from the elution time of the tracer (ti , min) and the applied flow rate (F, ml/min). The elution time of the KI marker was corrected for the system contribution (text , min), obtained by replacing the column with a zero-dead volume union and injecting the KI-solution under the same conditions as during the TPB experiments: (ti − text )F VG

3.6

(b)

mAU

(7)

εe =

75

(8)

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3 2.4 time (min)

Fig. 1. Representative peak for benzophenone obtained at a flow rate of 0.6 ml/min on (a) a first generation monolith (column G1-2.0 × 100-1) and (b) a second generation monolith (column G2-2.0 × 50-1). The best fitting Gaussian curves are shown in overlay (dashed lines). The lines denoted with w50% and w10% represent the peak widths obtained at 50% and 10% of the peak height, respectively.

where VG (ml) is the geometrical volume of the column, obtained as: VG = r 2 L × 106

(9)

and r (m) is the radius of the column. 2.5. Determination of the total porosity of the columns The total porosity (εT ) was determined from the elution time of thiourea (t0 , min) measured during the plate height measurements, corrected for the system contribution (text , min): εT =

(t0 − text )F VG

(10)

3. Results and discussion 3.1. Plate count determination using the Foley–Dorsey method Fig. 1 shows typical peaks obtained for benzophenone at a flow rate of 0.6 ml/min on a first generation (Fig. 1a) and second generation (Fig. 1b) monolith. Fig. 1a clearly shows the significant fronting that was observed on all first generation monoliths. This peak fronting was noticed for all compounds (k = 3.0–9.0), but was less pronounced at low flow rates (e.g., a/b = 1.2 at 0.2 ml/min for

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D. Cabooter et al. / J. Chromatogr. A 1325 (2014) 72–82

column G1-2.0 × 100-1) compared to high flow rates (a/b = 1.6 at 0.7 ml/min for column G1-2.0 × 100-1). It has been suggested that fronting peaks are only observed when the flow velocity is higher in the wall region than in the center part of the column and the local efficiency is lower near the wall than in the center [36]. The formation of a skin layer in the outermost part of the monolithic rod resulting in deformation of the skeleton and structural inhomogeneities close to the wall of the column could be responsible for both phenomena and hence provide a tentative explanation for the observed fronting behavior of the first generation monoliths. As mentioned previously, the use of HPAA as phase separator in the second generation monoliths results in a less pronounced skin layer and hence less deformation of the skeleton [24]. The resulting improved radial homogeneity is evident from the peaks typically obtained on all second generation monoliths (Fig. 1b) that showed peak tailing rather than peak fronting, which was nonetheless much less pronounced than the fronting observed on the first generation columns. When dealing with asymmetrical (tailing or fronting) peaks, column efficiency can be severely overestimated by analyzing the peak width at half the peak height, as is customarily done. A more precise estimation of the column plate count can be obtained using the Foley–Dorsey method [32]. Fig. 1 shows the best fitting Gaussian curves (dashed lines) overlaid with the actual chromatographic peaks measured on the monolithic columns. Assessing the peak width at half the peak height, a plate count of N50% = 9000 was obtained both for the actual and the Gaussian peak in Fig. 1a. Using the Foley–Dorsey method, the plate count reduced to NFD = 4550 for the actual peak, implying an overestimation of the column efficiency with 50% when analyzing the peak using the half height method. For the Gaussian peak in overlay, a plate count of NFD = 8700 was obtained using the Foley–Dorsey method. The discrepancy between NFD and N50% for the Gaussian peak (∼3%) can be explained by the fact that peak widths were manually read-out. Similar observations were made for the peak shown in Fig. 1b (second generation monolith). The plate count obtained via the half height method was determined to be N50% = 7000 for both actual and Gaussian peak, while this reduced to NFD = 5200 for the actual peak using the Foley–Dorsey method (overestimation of ∼25% using N50% ). The plate count determined for the Gaussian peak using Foley–Dorsey was NFD = 6800. To avoid any overestimation of plate counts and hence misinterpretation of column efficiency data, all plate counts in this study were determined using the Foley–Dorsey method. 3.2. Column evaluation using plate height models Fig. 2 shows all obtained plate height curves for the first and second generation monoliths. The curves in Fig. 2a are obtained for the 2.0 mm I.D. columns, while the curves in Fig. 2b represent the 3.0 and 3.2 mm I.D. columns. As mentioned before, the column performance was assessed using the curves obtained for benzophenone, as for this component the system variance was always less than 5% of the total variance on all columns and at all flow rates. The plots in Fig. 2a show that the second generation 2.0 mm I.D. columns with different lengths display very similar minimal plate heights (Hmin = 7.3–8.2 ␮m, inter-column variability of minimal plate height – calculated as the relative standard deviation – ∼5%), suggesting that the production process of the second generation monoliths leads to reproducible packings both in 5 and 10 cm column formats. A similar reproducibility is observed for the first generation monoliths (Hmin = 13.6–14.1 ␮m, inter-column variability of minimal plate height ∼4%), but these columns were only available in column lengths of 10 cm. The large difference in minimal plate height observed when comparing the first and second generation monoliths (Table 2) suggests that the characteristic

Fig. 2. Van Deemter plots obtained for benzophenone (k = 9.0 ± 0.6) on (a) monolithic columns with an I.D. of 2.0 mm (♦ column G1-2.0 × 100-1,  column G1-2.0 × 100-2,  column G2-2.0 × 50-1,  column G2-2.0 × 50-2, 䊉 column G22.0 × 100-1,  column G2-2.0 × 100-2) and (b) I.D. of 3.0-3.2 mm ( column G1-3.0 × 100-1,  column G1-3.0 × 100-2,  column G2-3.2 × 50-1,  column G23.2 × 50-2, 䊉 column G2-3.2 × 100-1,  column G2-3.2 × 100-2). Open, blue symbols refer to first generation monoliths, closed, black symbols to second generation monoliths. (For interpretation of the references to color in this legend, the reader is referred to the web version of the article.)

length (=domain size (ddom ), sum of the average skeleton (ds ) and through-pore size (dpor ) [37]) of the second generation monoliths must be some 1.8 times smaller than that of the first generation monoliths, at least when assuming that both generations have the same structural homogeneity. Fig. 2b shows the plate height curves obtained for first and second generation monoliths with an inner diameter of 3.0–3.2 mm. Very similar trends are observed as for the 2.0 mm I.D. columns; the inter-column variability for the 2nd generation monoliths is slightly larger (∼11%), whereas the minimum plate heights again indicate a much smaller domain size for the 2nd Table 2 Minimum plate heights (Hmin ) obtained for the different generation monoliths for benzophenone (k = 9.0 ± 0.6) and experimentally determined permeability values (Kv0 ). Column

Hmin (k = 9.0) (␮m)

Kv0 (m2 )

G1-2.0 × 100-1 G1-2.0 × 100-2 G2-2.0 × 50-1 G2-2.0 × 50-2 G2-2.0 × 100-1 G2-2.0 × 100-2 G1-3.0 × 100-1 G1-3.0 × 100-2 G2-3.2 × 50-1 G2-3.2 × 50-2 G2-3.2 × 100-1 G2-3.2 × 100-2

14.1 13.6 7.9 8.1 7.3 8.2 14.1 13.6 6.5 6.7 7.4 8.2

4.67 × 10−14 4.77 × 10−14 1.76 × 10−14 1.76 × 10−14 1.73 × 10−14 1.87 × 10−14 8.53 × 10−14 8.15 × 10−14 1.92 × 10−14 1.96 × 10−14 1.88 × 10−14 1.97 × 10−14

D. Cabooter et al. / J. Chromatogr. A 1325 (2014) 72–82

generation monoliths (Hmin = 6.5–8.2 ␮m) compared to the 1st generation (Hmin = 13.6–14.1 ␮m) (factor 1.9). The 3.2 mm × 50 mm second generation columns (Hmin = 6.5–6.7 ␮m) yielded slightly lower minimum plate heights than all other considered second generation monoliths. This indicates that it is easier to obtain homogeneous packings in short columns (50 mm) with larger I.D. (3.2 mm) than in longer (100 mm) and small I.D. (2.0 mm) monoliths [38]. 3.3. Relation between monolithic column permeability and porosity values Column performance, however, does not only depend on efficiency but also on permeability. Therefore, the permeability values of all columns were determined under identical experimental conditions (§ 2.3). These values are also shown in Table 2. Both I.D. second generation monoliths display very similar permeability values, be it that the values for the 3.2 mm I.D. columns are consistently slightly higher than those of the 2.0 mm I.D. columns. The first generation monoliths on the other hand have much larger permeability values (up to 4 times higher), implying that first generation monoliths can be operated at much higher linear velocities (leading to faster analyses) or in much longer column formats (leading to higher efficiencies) than the second generation, considering the same backpressure is applied. Interestingly, a large difference is also observed between the 2.0 and 3.0 mm I.D. first generation columns, with the 3.0 mm columns having a permeability which is more than 1.7 times higher than that of the 2.0 mm I.D. columns. Very recently, general correlations for the permeability of silica monoliths with varying degrees of globule clustering and different external porosities have been derived based on computational fluid dynamics simulations on simplified mimics of the typical geometry of silica monoliths [31]. For a perfectly ordered tetrahedral skeleton model (TSM) with purely cylindrical branches, the following relation between column permeability Kv0 , skeleton size (ds ) and external porosity εe could be established: Kv0 =

1 εe · ds2 51 εT

 ε 1.59 e 1 − εe

(11)

For monoliths with branches that can rather be represented as a single string of interconnected globules, the so-called single globule chain-type TSM, this correlation reduces to: Kv0 =

1 εe · ds2 51 εT

 ε 1.43 e 1 − εe

(12)

In [31], the correlations in Eqs. (11) and (12) have been applied to some randomly selected literature data to assess their utility. However, no explicit experiments have been performed yet to compare the predictions obtained from Eqs. (11) and (12) to real data. For this purpose, part of the present study has been devoted to evaluating the validity of Eqs. (11) and (12) by experimentally determining each of the structural parameters (ds , εe and εT porosities) appearing in the equations in an independent way. To determine the skeleton size ds , a large number of SEMpictures was taken. Fig. 3 shows some representative SEM pictures of the 2.0 and 3.0–3.2 mm I.D. columns of both generation monoliths. From Fig. 3 it is immediately clear that the first generation monoliths have a larger average skeleton size than the second generation monoliths (note that the scale in Fig. 3a and b is twice as large as in Fig. 3c and d). Interestingly, a clear difference in skeleton size can also be observed for both first generation monoliths (cf. Fig. 3a and b), with the 3.0 mm I.D. columns having a larger skeleton size than the 2.0 mm I.D. columns. These observations are quantitatively confirmed by the average skeleton sizes that were determined for all columns (Table 3) and which

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indicate that ds ∼ 1.0 ␮m for the 2.0 mm I.D. first generation monolith, ds ∼ 1.2 ␮m for the 3.0 mm I.D. first generation monolith and ds ∼ 0.8 ␮m for the second generation monoliths. Comparing the structures of the 1st and 2nd generation monoliths, the branches of the second generation monoliths resemble a single string of interconnected globules and are hence rather of the single globule chain TSM-type, whereas the first generation monoliths are more of the cylindrical TSM-type (see also Fig. 1 in Ref. [31] for a schematic overview of both TSM-type structures). External porosities (εe ) were determined for representative columns of both generation monoliths using the so-called total pore blocking method [29,30]. The results are given in Table 3, showing that all first generation and the 3.2 mm I.D. second generation monoliths have a very similar external porosity of ∼65%, while that of the 2.0 mm I.D. second generation monolith is clearly lower with a value of ∼61%. In a recent study by Gritti and Guiochon [38], external porosities ranging between 61% and 70% were determined for second generation monoliths with dimensions of 3.2 mm × 50 mm and 2.0 mm × 50 mm. The total porosities (εT ) were assessed from the elution time of an unretained marker (thiourea) and are also shown in Table 3, together with the internal porosities (εi ) determined as: εi =

εT − εe 1 − εe

(13)

Table 3 shows that the second generation 3.2 mm I.D. columns have an internal porosity which is much larger than that of all other columns. This large internal porosity is most certainly linked to the much larger mesopore size of these columns (17 nm versus 12–13 nm for all other columns, Table 1). Similarly, these columns also required a lower percentage of ACN to obtain the same retention factor for benzophenone (cf. Table 1). To verify whether permeability and porosity values could be linked to the average skeleton size of the monoliths, Eqs. (11) and (12) were used to calculate ds from the experimentally determined εe , εT and Kv0 -values for the first and second generation monoliths, respectively (Table 3). These values were subsequently compared to the ds -values that were assessed from the SEM pictures. The discrepancy between calculated and experimentally determined skeleton sizes was less than 10% for all columns (except for column G2-3.2 × 50-1 where a discrepancy of 20% was observed). This agreement is deemed to be very good considering that a certain error is anyhow made when manually assessing the length of the skeleton sizes from the SEM pictures. These results confirm that the observed permeability values can be correlated to the skeleton size and porosity values of the columns and demonstrate the general utility of the correlations established in [31]. Considering the external porosity of both generation monoliths is largely the same (εe ∼ 0.65), it can be deduced that the decreased permeability of the second generation is largely attributed to the reduction of the skeleton sizes. The single globule chain-type structure of the second generation monoliths moreover leads to a further reduction in permeability of some 10% compared to the purely cylindrical branches of the first generation (as can be deduced from the permeability values obtained when filling in the values of ds for the first and second generation monoliths in Eqs. (11) and (12)). The difference in skeleton size between the 2.0 mm and 3.0 mm I.D. first generation monoliths (ds = 1.0 versus 1.2 ␮m), explains the large difference in permeability that was observed for these columns. 3.4. Reduced plate height data for an intrinsic column evaluation In Fig. 4 of Ref. [31], correlations are presented that relate the domain size (ddom (m) = dpor + ds , wherein dpor (m) relates to the through-pore size) and the skeleton size (ds , m) of cylindrical and single-globule chain-type TSM monoliths with varying external

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Fig. 3. SEM pictures obtained for the different generation monolithic columns; (a) first generation monolith with an I.D. of 2.0 mm and (b) I.D. of 3.0 mm, (c) second generation monolith with and I.D. of 2.0 mm and (d) I.D. of 3.2 mm.

porosities. Using these correlations, the domain size was determined from the experimental external porosities and skeleton sizes for representative columns of all monolith types (generation and I.D.). The domain sizes are shown in Table 3 and indicate a reduction in domain size of some 25% for the 2.0 mm I.D. columns and some 30% for the 3.0–3.2 mm I.D. columns, going from the first to the second generation monoliths. The domain sizes were subsequently used to convert the van Deemter data shown in Fig. 2 into dimensionless numbers and the resulting plots are shown in Fig. 4. The reduced plate heights (h) and velocities () were obtained as: h=

H ddom

(14)

=

u0 ddom Dmol

(15)

The diffusion coefficient of benzophenone (Dmol , m2 /s) was determined according to the Wilke-Chang equation [39] (Dmol = 6.8–7.0 × 10−10 m2 /s). From Fig. 4, lower minimum plate heights are observed for the second generation 2.0 mm I.D. monoliths compared to the first generation (hmin = 3.8– 4.3 for the second generation versus hmin = 5.6–5.7 for the first generation) when using the domain size to convert the plate heights into dimensionless numbers. This again indicates an improved radial homogeneity for the second generation monoliths due to the improved production process.

Table 3 Experimentally determined skeleton sizes (ds ), external (εe ), total (εT ) and internal (εi ) porosities for representative samples of all column dimensions. The skeleton sizes calculated using the correlations in Eqs. 11(a) and 12(b) and the domain sizes obtained from Fig. 4 in [25] are also shown. Column G1-2.0 × 100-1 G1-2.0 × 100-2 G2-2.0 × 50-1 G2-2.0 × 50-2 G2-2.0 × 100-1 G2-2.0 × 100-2 G1-3.0 × 100-1 G1-3.0 × 100-2 G2-3.2 × 50-1 G2-3.2 × 50-2 G2-3.2 × 100-1 G2-3.2 × 100-2 n.d., not determined.

ds (␮m) (SEM) n.d. 1.0 n.d. 0.8 n.d. n.d. n.d. 1.2 n.d. n.d. n.d. 0.8

εe 0.667 0.641 0.609 0.611 n.d. n.d. n.d. 0.652 0.668 n.d. n.d. 0.641

εT 0.785 0.753 0.760 0.771 n.d. n.d. n.d. 0.743 0.872 n.d. n.d. 0.836

εi 0.355 0.312 0.384 0.411 n.d. n.d. n.d. 0.262 0.615 n.d. n.d. 0.542

ds (␮m) (correlation) (a)

1.1 1.0(a) 0.8(b) 0.8(b) n.d. n.d. n.d. 1.3(a) 0.7(a) n.d. n.d. 0.8(b)

ddom (␮m) 2.5 2.4 1.9 1.9 n.d. n.d. n.d. 2.9 2.0 n.d. n.d. 2.0

D. Cabooter et al. / J. Chromatogr. A 1325 (2014) 72–82

Fig. 4. Reduced form of the van Deemter plots obtained for benzophenone (k = 9.0 ± 0.6) on representative columns of each type (generation and diameter): (a) monolithic columns with an I.D. of 2.0 mm and (b) I.D. of 3.0–3.2 mm. Symbols are the same as in Fig. 2. Experimental plate height data were normalized using the domain sizes shown in Table 3. Diffusion coefficients were calculated using the Wilke–Chang equation.

The same trend is observed for the 3.0–3.2 mm I.D. columns (hmin = 3.3–4.0 for the second generation versus hmin = 4.7 for the first generation). The lowest hmin -values (hmin = 3.3) and hence highest efficiencies are obtained for the 3.2 mm × 50 mm second generation columns, again pointing out the better production quality obtained for these short, larger I.D. columns. This observation is in agreement with the occurrence of transcolumn velocity gradients, in turn caused by a transcolumn gradient of the local external porosity, as it was shown that short and wide columns are much less prone to the transcolumn velocity gradient contribution (see Fig. 9 of Ref. [40]). It must be remarked here that the observed minimum plate heights are considerably above the values that are typically encountered for well-packed columns (hmin = 2 for fully porous columns and hmin = 1.3–1.7 for core–shell particles) [41–44]. 3.5. Kinetic plot evaluation of first and second generation monoliths The data presented so far, have demonstrated that the small domain size of the second generation monoliths results in a much improved efficiency, compared to the first generation. This, however, is achieved at the cost of an increased backpressure (cf. the permeability values in Table 2). To account for both the effect of plate height and permeability on the resulting kinetic performance of the columns, kinetic plots were constructed for all columns evaluated in Fig. 2 (a maximum operating pressure of 200 bar was applied). The resulting plots of analysis time (tR = t0 (1 + k)) versus plate count (N) for benzophenone are shown in Fig. 5.

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Fig. 5. Kinetic plots of analysis time (tR ) versus plate count (N) for benzophenone and for the different evaluated columns obtained at 200 bar: (a) monolithic columns with an I.D. of 2.0 mm and (b) I.D. of 3.0–3.2 mm. Symbols are the same as in Fig. 2. The red curves (×) are obtained for a core–shell column (2.0 mm × 100 mm, dp = 2.7 ␮m) operated at a maximum pressure of 600 bar. Mobile phase conditions used to obtain k = 8.7 on this column were 45.3/54.7% ACN/H2 O. (For interpretation of the references to color in this legend, the reader is referred to the web version of the article.)

From these plots, it is evident that the second generation monoliths perform better than the first generation for N = 10,000–45,000 plates. The curves in Fig. 5 moreover demonstrate that a gain in analysis time of some 1.5–2.5 times can be obtained in this practical range of separations (for the 3.2 mm × 100 mm second generation columns, this gain is slightly lower). For separations requiring more than 50,000 plates, however, the first generation monoliths clearly perform better. This is due to their large permeability, which allows the first generation monoliths te be used in longer columns while still being operated at a sufficiently high velocity, leading to high efficiencies in reasonable analysis times. To compare the performance of first and second generation monoliths to that of state-of-the-art particle columns, kinetic plots were also constructed for chromatographic data obtained for benzophenone on a core shell particle column (2.0 mm × 100 mm, dp = 2.7 ␮m). The mobile phase composition on this column was once again adapted in such a way that a retention factor of k ≈ 9.0 was obtained for benzophenone, to allow for a fair comparison of all column types. To obtain kinetic plots that reflect the actual performance limits of the columns as much as possible, the curves for the core–shell column were moreover constructed for a maximum pressure of 600 bar. The obtained kinetic plots are shown in Fig. 5 (red curves) and demonstrate that, despite the much improved efficiency of the second generation monoliths in the range of N = 10,000–45,000, these columns are still not able to outperform state-of-the-art core shell particles when all columns are evaluated at their own maximum pressure. In fact, the core–shell

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Fig. 6. Kinetic plots of column length (L) versus plate count (N) for benzophenone and for the different evaluated columns obtained at 200 bar: (a) monolithic columns with an I.D. of 2.0 mm and (b) I.D. of 3.0–3.2 mm. Symbols are the same as in Fig. 2.

particles yield an additional gain in analysis time of on average 3 times for plate counts ranging between 10,000 and 150,000. From the plots shown in Fig. 5, kinetic plots of column length versus number of plates can easily be obtained by converting the retention times shown in Fig. 5 as follows: L=

tR u0 (1 + k)

(16)

where u0 is the linear velocity at which each original tR -datapoint was obtained and k = 9.0 for benzophenone (for the exact values of k, please refer to Table 1). Plotting the resulting column lengths versus N, Fig. 6 clearly shows that one of the consequences of the increased efficiency of the second generation monoliths is that much shorter lengths of second generation monoliths can now be used to obtain a similar plate count as in first generation monoliths. For a separation of e.g. 20,000 plates on a 2.0 mm I.D. column, a length of almost 40 cm was required for the first generation monoliths, while the same resolution can now be obtained on a second generation column of only 15 cm (Fig. 6a), which represents a reduction in column length of almost 2.5. Similar observations are made for the 3.0–3.2 mm I.D. columns (Fig. 6b). To assess the kinetic performance of these monolithic columns at higher operating pressures, kinetic plots of tR versus N were also constructed for representative 2.0 mm I.D. and 3.0–3.2 mm I.D. first and second generation monoliths at pressures of 400 bar and 600 bar. These plots were obtained from the van Deemter data in Fig. 2 and by selecting P = 400 bar and P = 600 bar in Eqs. (1) and (2). Since this type of extrapolation does not incorporate the additional band broadening that could originate from trans-column temperature gradients that can develop during a high pressure operation (P > 400 bar), this extrapolation should be approached with the greatest caution and should merely be considered as a qualitative prediction of the performances that are maximally

Fig. 7. Kinetic plots of analysis time (tR ) versus plate count (N) for benzophenone obtained at different pressures for representative columns of each type (generation and diameter): (a) monolithic columns with an I.D. of 2.0 mm and (b) I.D. of 3.0–3.2 mm. Symbols are the same as in Fig. 2. Full lines: 200 bar, dashed lines: 400 bar, dotted lines: 600 bar. The red curves (×) are obtained for a core–shell column (2.0 mm × 100 mm, dp = 2.7 ␮m) operated at a maximum pressure of 600 bar. Conditions same as in Fig. 5. (For interpretation of the references to color in this legend, the reader is referred to the web version of the article.)

achievable under (ultra-) high pressure conditions. The resulting curves are shown in Fig. 7 (the original plots obtained for the monoliths at 200 bar and for the core–shell column at 600 bar are also still shown). As can be seen in Fig. 7, the largest increase in separation performance (hence the largest gain in plate count for a fixed analysis time) will be obtained for performances that are situated (and hence attained at velocities) in the B-term dominated range. This corresponds to the upper-right region of Fig. 7. This large increase in separation performance can be explained by the fact that high pressures allow to bring the velocities at which these performances are attained closer to the optimal velocity, which leads to a strong plate height decrease and hence higher plate count as the main advantage [45]. For performances obtained in the Cterm dominated range of the kinetic plot (lower-left part of the curves), the increase in separation performance is much less pronounced (especially when considering the transition from 400 to 600 bar). Performances obtained at velocities situated in the C-term region, are already attained at velocities in excess of what is needed to operate the support at its optimum [45]. It is therefore logical that the effect of an additional increase of the inlet pressure will generate a much weaker effect in the C-term dominated region. As the performances in the C-term region correspond to plate counts in the practical range of efficiencies (hence corresponding to plate counts that are typically required for standard separations; N = 10,000–50,000), it is clear from Fig. 7 that even if the new generation of monoliths would be able to operate at high inlet pressures (∼600 bar), they would still not be able to compete with stateof-the-art core–shell particle columns. It must, however, also be

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Fig. 8. Reduced kinetic plots of separation impedance (E0 ) versus plate number ratio (Nopt /N) for benzophenone and for the different evaluated columns: (a) monolithic columns with an I.D. of 2.0 mm and (b) I.D. of 3.0–3.2 mm. Symbols are the same as in Fig. 2. The red curves (×) are obtained for a core–shell column (2.0 mm × 100 mm, dp = 2.7 ␮m). Conditions same as in Fig. 5. (For interpretation of the references to color in this legend, the reader is referred to the web version of the article.)

remarked that the performance of the second generation monoliths operated at 600 bar approaches the best performing particle columns much better than what was up to now possible on the first generation monoliths. To investigate the pure performance of the columns in more detail, reduced kinetic plots of separation impedance (E0 ) versus plate number ratio (Nopt /N, obtained by dividing the plate count corresponding to the minimum plate height (Nopt ) by every experimentally determined plate number) were constructed for all considered columns (Fig. 8). These plots allow assessing the pure quality of a packing or support structure without having to specify a reference length (such as a domain or skeleton size) and without taking the effect of pressure into consideration. The separation impedance is calculated from experimentally obtained permeability and plate height data as follows: E0 =

2 Hmin

Kv0

= h2

(17)

with the flow resistance ( = (ds2 /Kv0 )) And the plate number ratio is obtained from experimental van Deemter data: uopt Hmin Nopt opt hmin = = N uH h

(18)

Eqs. (17) and (18) show that the separation impedance and plate number ratio only depend on the dimensionless variables h,  and but can be calculated without having to specify the actual characteristic lengths of the structures.

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Plotting E0 versus Nopt /N, a curve is obtained which goes through a minimum, corresponding to the column’s most advantageous kinetic operating conditions (obtained in a column that is exactly long enough to reach the minimum of the van Deemter curve at the maximal available pressure). The separation impedances on the left-hand side of this minimum are obtained in the B-term region of the corresponding van Deemter plot, whereas the E0 -values obtained on the right-hand side of the minimum are obtained in the C-term region. A reduced kinetic plot therefore contains the same type of information as the reduced form of the van Deemter plot: packings with similar packing quality, intra-particle diffusion characteristics and retention factors, but a different characteristic length, will all have coinciding curves. The lower this curve, the better packed or produced the column will be. Compared to the reduced form of the van Deemter curve, a reduced kinetic plot has the advantage that it also contains information on the column permeability. The reduced kinetic plots in Fig. 8a show a better “packing” or structural quality for the 2.0 mm I.D. second generation monoliths compared to the first generation. For the 3.0–3.2 mm I.D. columns in Fig. 8b, the minimum impedance is more similar, which can be explained by the much higher permeability values that were obtained for the first generation monoliths (and which have an important effect on the obtained impedance values as can be deduced from Eq. (17)). Looking at the minimum E0 -values obtained for all monolithic columns, these are all higher than 2000 (the lowest values are again obtained for the 3.2 mm × 50 mm second generation columns, E0,min = 2200). In contrast, the E0,min -value obtained for the core–shell column is 1800. Considering a value of E0,min = 2000 is the standard for a well-packed column, these plots suggest that the minimum impedance of the second generation monolithic columns comes close to but can still not compete with that of the best performing particle packed columns. This is mainly due to their poorer “packing” or bed quality (which for monoliths should rather be interpreted as “rod homogeneity”). The plots, however, also point out that the optimized production process of the second generation monoliths has already largely improved the rod quality in comparison with the first generation monoliths. From these plots it is clear that, despite the significant improvements in column efficiency and rod homogeneity already achieved on the second generation monoliths, their intrinsic performance will have to be optimized further and their pressure limits should be increased in order for the second generation monoliths to become competitive with state-of-the-art columns.

4. Conclusions A comprehensive evaluation of commercially available first and prototype second generation monoliths has been made. These second generation monoliths are produced using HPAA instead of PEG as phase separator resulting in more homogenous structures (as can be deduced from the improved peak shape obtained on the second generation monoliths) with smaller domain sizes (2.4–2.9 ␮m for the first generation monoliths versus 1.9–2.0 ␮m for the second generation). This results in efficiencies that are considerably higher (some 30–40%) compared to those of the first generation, be it at the cost of an increased backpressure (the permeability of the first generation monoliths is up to 4 times larger than that of the second generation). SEM pictures of representative monolith samples were used to determine the skeleton size of both generation monoliths and revealed more single globule chain-type skeleton branches for the second generation monoliths compared to the more cylindrical skeleton branches marking the first generation. Using theoretical correlations, it was observed that the relatively low permeability of

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the second generation monoliths can be mainly attributed to their smaller skeleton size (0.7–0.8 ␮m for the second generation versus 1.0–1.3 ␮m for the first generation), since the external porosity is largely maintained for both generation monoliths (εe ∼ 0.61–0.65). Interestingly, a large difference in permeability was also observed for first generation monoliths with inner diameters of 2.0 and 3.0 mm (Kv0 = 4.7 × 10−14 m2 for 2.0 mm I.D. versus 8.3 × 10−14 m2 for 3.0 mm I.D. columns). This is due to the significantly larger skeleton size of the 1st generation 3.0 mm I.D. columns investigated in the present study (ds = 1.0 ␮m for 2.0 mm I.D. versus ds = 1.3 ␮m for 3.0 mm I.D.). Combining the experimentally determined plate height data and permeability values using the so-called kinetic plot method, it was observed that the separation performance of the second generation monoliths is only better than that of the first generation in the relevant range of separation efficiencies (N = 10,000–45,000). For more complex separation problems (N > 50,000), the first generation monoliths remain the better choice. This can be attributed to the large permeability values of the first generation columns which allow them to be used in long columns at high operating flow rates, resulting in high separation efficiencies in reasonable analysis times. Comparing the performance of both generation monoliths with that of state-of-the-art core–shell particles, the performance of the latter remains superior, even when all columns are evaluated at the same maximum pressure. This superior performance of the core–shell particles can be attributed to their better packing or production quality, resulting in minimum impedance values