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Isocratic and gradient impedance plot analysis and comparison of some recently introduced large size core–shell and fully porous particles
Journal of Chromatography A, 1312 (2013) 80–86
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Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma
Isocratic and gradient impedance plot analysis and comparison of some recently introduced large size core–shell and fully porous particles Yoachim Vanderheyden a , Deirdre Cabooter b , Gert Desmet a , Ken Broeckhoven a,∗ a b
Vrije Universiteit Brussel, Department of Chemical Engineering, Pleinlaan 2, 1050 Brussels, Belgium KU Leuven, Department of Pharmaceutical Sciences, Herestraat 49, 3000 Leuven, Belgium
a r t i c l e
i n f o
Article history: Received 25 July 2013 Received in revised form 30 August 2013 Accepted 3 September 2013 Available online 7 September 2013 Keywords: Core–shell Fully porous Impedance plot Kinetic performance limit Plate height Permeability
a b s t r a c t The intrinsic kinetic performance of three recently commercialized large size (≥4 m) core–shell particles packed in columns with different lengths has been measured and compared with that of standard fully porous particles of similar and smaller size (5 and 3.5 m, respectively). The kinetic performance is compared in both absolute (plot of t0 versus the plate count N or the peak capacity np for isocratic and gradient elution, respectively) and dimensionless units. The latter is realized by switching to so-called impedance plots, a format which has been previously introduced (as a plot of t0 /N2 or E0 versus Nopt /N) and has in the present study been extended from isocratic to gradient elution (where the impedance plot corresponds to a plot of t0 /np 4 versus np,opt 2 /np 2 ). Both the isocratic and gradient impedance plot yielded a very similar picture: the clustered impedance plot curves divide into two distinct groups, one for the core–shell particles (lowest values, i.e. best performance) and one for the fully porous particles (highest values), confirming the clear intrinsic kinetic advantage of core–shell particles. If used around their optimal flow rate, the core–shell particles displayed a minimal separation impedance that is about 40% lower than the fully porous particles. Even larger gains in separation speed can be achieved in the C-term regime. © 2013 Elsevier B.V. All rights reserved.
1. Introduction The first generation of core–shell particles (also called superficially porous, porous-shell, fused-core or solid core particles) were produced by Horváth and Kirkland in the late 1960’s [1–3]. In 2006, a new generation of core–shell particles was introduced [4]. These 2.7 m particles, with a relatively thick shell of 0.5 m, overcame the low loading capacity which was one of the shortcomings of the earliest generation particles. Compared with fully porous particles, this second generation of core–shell particles shows a slightly lower total mass loadability [5–8]. However, as the loadability appears to vary with column internal diameter (ID) [9] and column performance [5,7,10], the importance of this difference in loadability remains a point of discussion [11]. In the past decade, different vendors commercialized 2.6–2.7 m core–shell particles in a wide variety of column dimensions and stationary phases. Also larger wide pore particles (3.6 m) for the analysis of biomolecules [12,13] and also smaller sizes (1.7 m) [10,14] were developed. In the past year, particles
∗ Corresponding author. Tel.: +32 2629 37 81; fax: +32 2629 32 48. E-mail address: [email protected] (K. Broeckhoven). 0021-9673/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.chroma.2013.09.009
with sizes between 4 and 5 m with a shell of 0.6–0.85 m were introduced [15]. That the research into novel particles with different sizes or shell morphology is still ongoing, is proven by the recent commercialization of very small (1.3–1.6 m) core–shell particles. Core–shell particles offer a huge leap in separation efficiency, compared with their fully porous counterparts [16–20]. Where fully porous particles achieve minimum reduced plate heights of h = 2, core–shell particles consistently achieve values of 1.5–1.8 [4,5,9,10,21–25] and some studies even report values as low as 1.1–1.3 [26,27]. Despite the fact that these high efficiencies could not be reached for the smaller 2.1 mm ID columns [8,12,14,21,24,25,28–30] and also seem to depend on the column length [9], the separation efficiency is significantly better than their fully porous equivalents. The original assumption for the better performance of core–shell particles was the presence of a shorter diffusion path through the porous shell and thus a lower stationary phase mass transfer contribution (Cs -term in the van Deemter equation). The improved performance is however mainly due to the lower A-term (i.e. bed heterogeneity), which also increases the optimal linear velocity u0,opt , and the lower B-term (longitudinal diffusion) [31]. Whether the lower eddy-dispersion (A-term) is due to a narrower particle size distribution or due to better packing
Y. Vanderheyden et al. / J. Chromatogr. A 1312 (2013) 80–86
properties is still a point of discussion [23,30,31]. The lower B-term is a result of the obstruction for diffusion by the solid core [32] and the difference in morphology of the shell structure to that of fully porous particles [33]. The performance of 2.6 m core–shell particles is comparable with sub-2 m fully porous particles but they require a much lower operating pressure and can thus be used on conventional (i.e. 400 bar) LC instrumentation [4,34] if the dead volume of the system is not too excessive to compromise performance. The combination of core–shell particles and ultra-high operating pressures (i.e. 1200 bar) is also feasible and allows even faster and/or more efficient separations [5,35–37]. In fact, where all initially introduced 2.6–2.7 m core–shell particles had an upper pressure limit of 600 bar, several manufacturers now rate their 2.1 mm ID columns up to 1000 bar or even 1200 bar for the new sub-2 m core shell particles. The large core–shell particle columns are however still rated at 600 bar. On the other hand, fully porous particles of 3 m or larger are typically rated at a maximal pressure of 400 bar, whereas smaller particles (2.5 m or below) are typically rated up to 1000–1200 bar. Historically, the efficiency of chromatographic columns is studied via a plot of the plate height H vs. u0 . Very convenient in this type of plot is that it directly reveals the value of the optimal velocity or flow rate [38]. The dimensionless equivalent of this plot, allowing to compare the quality of columns with different particle sizes dp , is the so-called reduced plate height or reduced van Deemter plot of h (h = H/dp ) versus the reduced linear velocity 0 (0 = u0 dp /DM with DM the molar diffusion coefficient) [39]. To compare the kinetic performance (defined as the time needed to achieve a given chromatographic performance) of chromatographic columns, it has become customary over the past few years to use a plot of the elution time of an unretained peak t0 (or tR the retention time of the strongest retained peak) versus the number of theoretical plates or peak count N (or peak capacity np in gradient elution), generally referred to as a kinetic plot [40]. The dimensionless equivalent of the kinetic plot has been introduced in [41] and is obtained by plotting the separation impedance E0 = t0 /N2 ·Pmax / versus Nopt /N (where Pmax is the maximal pressure limit of the column, is the mobile phase viscosity and Nopt is the plate count at optimal linear velocity uopt ). As shown in [41], this plot (further referred to as the impedance plot) is equivalent to a plot of h2 (with the reduced flow resistance as defined in [41]) versus (h·0 )/(hmin ·0,opt ), readily showing that the impedance plot only depends on the dimensionless quantities h, and , and is as such ideally suited to compare the intrinsic kinetic packing quality of columns filled with particles of different sizes. In the present study, comparing several recently commercialized core–shell and fully porous packing materials with diameters ranging between 3.5 and 5 m, this approach has been followed. The concept of impedance plots is also extended to gradient elution mode chromatography.
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acquisition, data handling and instrument control were performed with Agilent Chemstation software. Table 1 summarizes the properties of all columns tested in this study. The Thermo Accucore columns were obtained from Thermo Scientific (Waltham, MA, USA), the Kinetex columns from Phenomenex (Torrance, CA, USA), the HALO column from Advanced Materials Technology (Wilmington, DE, USA), the Ascentis Express columns from Supelco (Bellefonte, PA, USA) and the Zorbax columns from Agilent Technologies (Diegem, Belgium). Since the results obtained on the HALO column were very similar to the results obtained on the Ascentis columns, these results are not shown in this study for reasons of clarity. For each column type, at least two columns were tested and their obtained results averaged. 2.2. Sample and conditions Uracil (t0 -marker) and a mixture of 10 alkylphenones (acetanilide, acetophenone, 3-methyl acetophenone, propiophenone, butyrophenone, benzophenone, valerophenone, hexanophenone, heptanophenone and octanophenone) were purchased from Sigma–Aldrich (Steinheim, Germany). All the test components were dissolved in a mixture of 50/50 ACN/H2 O in a concentration of 0.1 mg/mL. Acetonitrile (Supra-Gradient grade) was purchased from Biosolve (Valkenswaard, The Netherlands). HPLC grade water (H2 O) was prepared in the laboratory using a Milli-Q gradient water purification system (Millipore, Bedford, MA, USA). The sample for the isocratic experiments only contained uracil, butyrophenone, benzophenone and valerophenone. In gradient elution mode, uracil and all 10 alkylphenones were used. The organic modifier content was adjusted such for each column to obtain the same retention factor k for the component of interest (benzophenone, target value of k2 = 6) in isocratic mode. In gradient mode the same ratio of gradient time tG over column void time t0 was used for all experiments (tG /t0 = 12) and the retention factor of acetophenone and octanophenone were fixed at target values of k2 = 2 and k10 = 12 by changing the initial (ϕ0 ) and final (ϕe ) mobile phase composition. The exact mobile phase conditions ϕ and retention coefficient for each column are given in Table 1. To determine column performance the peak widths were measured at half height. Although more accurate methods to determine the exact performance are possible [42], the employed columns, sample and conditions yielded very symmetrical peaks, for which the half width method provides a reasonable good approach especially for the relative comparison in this work. The experimental peak widths and pressure drops were corrected for extra column contributions as described in [43]. All injections were performed in triplicate and the results were averaged in order to counteract statistic variance. 3. Results and discussion 3.1. Plate height analysis
2. Experimental 2.1. Instrumentation and columns All chromatographic experiments were performed on an Agilent 1290 Infinity system (Agilent Technologies, Waldbronn, Germany). The instrument was equipped with a binary pump, a variable wavelength detector with a low dispersion cell (2 L volume and 3 mm path length), an autosampler and a thermostatted column compartment with a mobile phase preheater of 3 L. The oven temperature was set constant to 30 ◦ C for all experiments. The absorbance values were measured at 254 nm with a sample rate of 80 Hz. Data
To evaluate the performance of the fully porous and core–shell particle columns, one can represent the measured plate height as a function of the linear velocity (i.e. van Deemter plot). Since retention has an effect on performance, it was opted to investigate the performance of the components with fixed retention, as was explained before (see Table 1). In Fig. 1A we can see that the minimum plate height of the 5 m fully porous particle column is considerably higher than that of their 3.5 m equivalent, whose plate height curve overlaps with the cluster of core–shell particle columns. The minimal plate height Hmin (at u0,opt ) of the 5 m fully porous particle columns is around 10 m. For the core–shell
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Table 1 Column properties (as provided by the vendor), mobile phase compositions and obtained retention factors for the compounds of interest. All columns have an internal diameter of 4.6 mm. Column
L (mm)
Thermo Accucore XL C-18 Kinetex C18 Halo C18 Ascentis Express C18 Ascentis Express C18 Zorbax C18 Zorbax C18
dp (m)
150 250 250 150 250 250 100
dcore (m)
4 5 5 5 5 5 3.5
Pmax (bar)
2.8 3.3 3.8 3.3 3.3 / /
600 600 600 600 600 400 400
particle columns we observe a minimal plate height between 6 and 8 m. Part of this variation between the different core–shell particle columns results from the fact that they differ in particle size. To rule out the effect of different particle sizes, the reduced plate height plot (h versus v) is used, as shown in Fig. 1B. We can immediately see that the 3.5 m fully porous particle column, which had a minimum plate height comparable with that of the core–shell particle columns, now has a much higher reduced minimum plate height. A clear distinction can be seen between the fully porous particle columns having a hmin of 2–2.1 and the core–shell particle columns having a hmin of 1.4–1.7 (with the Accucore and the 25 cm Ascentis Express columns having the lowest hmin ) which is circa 25% lower than the fully porous particles, consistent with earlier
25
A
H (μm) 20
15
Isocratic
Gradient
ϕACN
k2
ϕ0,ACN
ϕe,ACN
k2
k10
0.425 0.425 0.425 0.452 0.46 0.465 0.48
5.9 6.0 6.1 5.9 5.9 6.2 6.1
0.31 0.36 / 0.35 / 0.43 0.43
0.90 0.727 / 0.675 / 0.76 0.78
2 2 / 2 / 2 2.1
11.8 12 / 11.7 / 11.9 11.8
findings for other particle sizes [7,8,10,12–14,21,23,25]. The core–shell particle columns thus have a lower value than the “theoretically” ideal value of hmin = 2, defined by Knox [44]. Also a much flatter slope in the C-term regime (high velocities) of the core–shell versus the fully porous particle columns can be noticed. As explained in [17,45] this results mostly from the lower A-term contribution of the core–shell particle columns at high velocities, whereas the effect of the decrease in C-term is almost negligible. Due to this flatter slope, the core–shell particle columns can be operated at higher (reduced) velocities without losing too much performance. This effect can be seen in Fig. 2A–D in which chromatograms measured on 5 m core–shell and fully porous particle columns are compared at different flow rates. At the optimal flow rate uopt the number of theoretical plates of the core–shell particle columns is circa 30% higher than the fully porous particle columns, which is of course directly related to the difference in (reduced) plate height. When going to a higher flow rate (e.g. almost three times uopt ) this difference even increases to more than 75%, a direct consequence of the difference in steepness of the C-term. 3.2. Column permeability
10
The column permeability Kv,0 (based on u0 ) can be deduced from a plot of pressure drop P versus linear velocity u0 :
5
Pcol = 0 2
0
4
6
8
10
12
u0 (mm/s) 5
B
h 4.5 4 3.5 3 2.5
u0 · · L 1 ε3 with KV,0 = · dp2 · KV,0 180 (1 − ε)2 · εT
where L is the column length, ε is the external porosity and εT the total porosity. Plots of P as a function of the flow rate F instead of u0 are also common [7]. However, where the flow rate F only includes the effect of the external porosity ε, the linear velocity is based on the residence time t0 of a non-retaining but permeating component (i.e. the t0 -marker). As residence time is directly related to the analysis time (through k, which is kept constant), a plot of P versus u0 is practically more relevant. The column permeability is thus best plotted against u0 which depends on the total porosity εT , which is given by εT = ε + (1 − ε)εint
2
1.5 1 0
10
20
30
40
50
60
70
ν
80
Fig. 1. Comparison of the absolute (A) and reduced (B) plate height as a function of linear velocity u0 or reduced velocity , respectively of all measured fully porous particle (red) and core–shell particle (black) columns: Zorbax 250 mm × 4.6 mm 5 m ( ), Zorbax 100 mm × 4.6 mm 3.5 m ( ), Accucore 150 mm × 4.6 mm 4 m (), Kinetex 250 mm × 4.6 mm 5 m (), Ascentis Express 150 mm × 4.6 mm 5 m () and Ascentis Express 250 mm × 4.6 mm 5 m (䊉); sample compound was benzophenone, for other conditions see Section 2 and Table 1. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
(1)
(2)
with εint the internal porosity. Since columns with different lengths have been used, the pressure drop per column length P/L is plotted as a function of u0 in Fig. 3. The particle size influences the column permeability as can be seen in Eq. (1) and Fig. 3. The column permeability of the investigated core–shell particle columns lies in between those of the 3.5 and 5 m fully porous particle columns. As can be seen in Eq. (1) the porosity influences the u0 based column permeability. If we assume that the external porosity is almost identical for the different columns, the core–shell particles have a lower total porosity due to the solid core which lowers the internal porosity (see Eq. (2)), and this should lead to a larger Kv,0 (see Eq. (1)). The observed pressure drops were, however, significantly larger for the 5 m core–shell particle columns compared to
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83
40
40
A
mAu
B
mAu
t0 = 1.65 min 30
30
t0 = 0.6 min N = 31500
N = 35600 20
10
0
0
Core-shell 0
Fopt = 1.25 ml/min 4
8
N = 23900 N = 25700
10
-10
N = 27400
20
N = 32800
12
t (min)
Core-shell
-10 0
16
F = 3.5 ml/min 1
2
3
4
5
40
40
C
mAu
D
mAu
N = 15400
30
30
t0 = 2.2 min
t0 = 0.7 min
N = 29300
20
N = 25900
N = 15900
20
N = 14400
N = 25200 10
10
0
0
Fopt = 1 ml/min
Fully porous
-10
5
0
6
t (min)
10
15
0
t (min) 20
F = 3 ml/min
Fully porous
-10
2
4
t (min) 6
Fig. 2. Chromatograms and performance recorded on the Kinetex 250 mm × 4.6 mm 5 m core–shell particle column (A and B) and the Zorbax 250 mm × 4.6 mm 5 m fully porous particle column (C and D) at their optimal flow rate (A–C) and a flow rate almost three times higher (B–D).
the fully porous ones, corresponding to a lower Kv,0 . This is probably due to the difference in the nominal particle size given for the columns (e.g. 5 m) as their actual size is closer to 4.6 m [46], which of course strongly affects Kv,0 (see Eq. (1)). After further inquiry with the column vendors, actual particle sizes of 4.65 (instead of 5) m for the Kinetex and Ascentis columns and 4.1 (instead of 4) m for the Thermo Accucore columns were obtained and therefore used in the calculation of reduced parameters in Section 3.2. The advantage of the kinetic plot methodology employed in the following sections is that this does not require to define a characteristic particle size. It should be noticed that the 25 cm Ascentis column exhibited a higher permeability (i.e. lower pressure drop) than its 15 cm equivalent (compare with 䊉 symbols in Fig. 3). This apparent looser packing however results in a poorer performance, as can be seen
ΔPcol / L (bar/m)
in Fig. 1. The effect of column length on packing quality was also observed by [9].
3.3. Impedance plot analysis The kinetic performance limit describes the time needed to achieve a given chromatographic performance. It is customary to present this information using kinetic plots [47] which will be discussed in next section. Given the uncertainties on the exact value of the average particle diameter, we found it instructive to also compare the different particles in an impedance plot, the dimensionless variant of the kinetic plot. In the impedance plot the Knox separation impedance number E0 is plotted as a performance indicator versus Nopt /N: E0 =
2500
2000
1500
1000
500
0 0
2
4
6
8
u0 (mm/s) 10
Fig. 3. Column pressure drop as a function of linear velocity for all measured fully porous particle (red) and core–shell particle (black) columns. The same symbolism is used as in Fig. 1. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
H2 t0 Pmax = h2 0 = 2 · KV,0 N
(3)
As discussed in [41], the Nopt /N ratio is independent of the particle size. This type of plot also incorporates information on column permeability (see Eq. (3)). The big advantage of the impedance plot over the reduced plate height plot is that the exact particle size, which is not always exactly known and is subject to some variation (i.e. particle size distribution or batch-to-batch variability of dp ), does not have to be defined [41]. Note that the maximal mobile phase viscosity max is used to calculate the Knox separation impedance number. Instead of using t0 one can also use the time of the last eluting peak tR,last . Since the retention factor of the peaks of interest is fixed, the choice between t0 and tR,last will not influence the obtained results. The concept of the impedance plot has been extended to gradient elution by replacing the parameter N by the peak capacity np 2
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due to the square root dependency of np with N [48]. The apparent separation impedance number E0,grad will thus be defined as E0,grad =
t0 n4p
·
Pmax
(4)
and will be plotted versus np,opt 2 /np 2 , as the gradient equivalent of Nopt /N. Since np 2 is only proportional with and not equal to N [48], E0,grad will not be equal to E0 , but the same qualitative conclusions can be drawn from both calculation methods. Fig. 4 shows the impedance plot of all investigated columns. Notice that due to the Nopt /N ratio on the x-axis, the data on the left hand side corresponds with the low velocities B-term region and the data on the right hand side with the high velocities C-term region, as in the van Deemter plot. We can once again observe the fully porous and core–shell particles as two distinct groups. The core–shell particle columns display a lower separation impedance and thus better performance over the whole range of velocities. The average minimal separation impedance of the fully porous particle columns is E0,min = 2100 whereas for the core–shell particle columns an almost 40% lower value of E0,min = 1300 is measured (with the lowest value of 1050 for the Accucore column). Since Pmax is chosen at 400 bar as performance limit (see next section) and is also quasi-equal (only small differences in ϕ, see Table 1) for both particle types, E0 varies linearly with t0 /N2 (see Eq. (3)). Hence, in order to achieve the same optimal performance N, the analysis time on core–shell particle columns is around 40% lower
A
7500
E0 6500 5500
4500 3500
compared with their fully porous counterparts. This difference is even higher in the C-term regime, as can be seen by the flatter slope of the core–shell particle columns, an effect which has also been observed in Section 3.1. A difference of 45% in E0 can be seen at velocities circa three times u0 . Fig. 4A also shows that the differences in performance and permeability of the 15 and 25 cm Ascentis columns, as discussed in Section 3.2, almost cancel each other out: E0,min = 1250 for the 15 cm vs. 1400 for the 25 cm column. The impedance plots in gradient elution mode lead to similar results obtained in isocratic mode. This agreement between isocratic and gradient behaviour confirms earlier similar findings reported in [47]. The difference in separation impedance number between both modes is due to a different calculation method. E0,grad,min equals 1600 and 3750 for the core–shell and fully porous particle columns respectively, which is a difference of almost 60%. The lowest value of E0,grad,min = 1450 was measured for the 15 cm Ascentis Express column. As discussed in Section 3.2 we can evaluate the kinetic performance based on the linear velocity u0 or on the superficial velocity us , which is equal to the flow rate F divided by the column cross section A (see Eq. (5)). In the calculation of the impedance number one can also use ts (superficial residence time), which is based on us , leading to a difference of a factor εT since F = us · A = u0 · A · εT
(5)
The superficial velocity based impedance number ES will thus be 1/εT times larger than the linear velocity based impedance number E0 . Due to the lower total porosity of the core–shell particles, this results in a value of ES,min of 2850 and 4100 in isocratic and 3500 and 7200 in gradient elution mode, for the core–shell and fully porous particle columns respectively. The difference between the particle types is hence slightly lower, i.e. circa 30% in isocratic and 50% in gradient mode. 3.4. Absolute kinetic plot analysis
2500
E0,min = 2100
1500
E0,min = 1300
500 0
1
2
3
4
5
6
7
Nopt / N
8
B
9000
E0,grad 7500 6000 4500
E0,min = 3750
3000
1500
E0,min = 1600
0 0
1
2
3
4
np,opt2 / nopt2
5
Fig. 4. Impedance plot showing the behaviour of (A) the separation impedance E0 as a function of Nopt /N for isocratic elution experiments and (B) E0,grad as a function of np,opt 2 /np 2 for gradient elution data of all measured fully porous particle (red) and core–shell particle (black) columns: Zorbax 250 mm × 4.6 mm 5 m ( ), Zorbax 100 mm × 4.6 mm 3.5 m ( ), Accucore 150 mm × 4.6 mm 4 m (), Kinetex 250 mm × 4.6 mm 5 m (), Ascentis Express 150 mm × 4.6 mm 5 m () and Ascentis Express 250 mm × 4.6 mm 5 m (䊉) which is only measured in isocratic elution mode. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
The absolute kinetic plot represents the retention time of an unretained peak t0 or retention time tR of the strongest retained peak versus the number of theoretical plates N [47]. The kinetic performance limit was calculated at the maximal pressure Pmax of 400 bar as this is the upper pressure limit of the fully porous particle columns given by the manufacturers and is also the maximal operating pressure of conventional LC instruments. It should however be noted that the core–shell particle columns have pressure limit specifications up to at least 600 bar. The interested reader can find the kinetic plots with Pmax = 600 for the core–shell particle columns in the Supporting Material, SM (Fig. S-1) where the resulting larger difference between the core–shell and fully porous particle columns under these pressure limits is presented. More information on the calculations of the absolute kinetic performance limits can be found in [35,49]. Once again the parameter N is replaced with np 2 in gradient elution mode. Fig. 5 shows the kinetic plot for both particle types. As the plate number is dependent on the particle size [30], only the large size particles are shown for reasons of clarity. The plot including the smaller 3.5 m fully porous particles can be found in the Supporting Material, SM (Fig. S-2). Since E0 varies linearly with t0 /N2 , the separation impedance can be represented on the kinetic plot as a straight line with a slope of 2 (in log–log scale). The minimal separation impedance has been presented in Fig. 5A for both particle types as dash-dotted lines. This line is also called the Knox–Saleem limit and represents the best possible separation performance with optimized particle size and column length at a given maximal operating pressure [47]. When comparing the plate number at the right hand side,
Y. Vanderheyden et al. / J. Chromatogr. A 1312 (2013) 80–86
100
A
t0 (min)
10
85
rates. At optimal flow rates, the same peak capacity can be reached almost 60% faster with the core–shell particle columns (which is the difference in E0,grad ) or at the same analysis time a circa 25% higher peak capacity can be achieved. Similar relative gains in analysis time or performance are observed in the C-term regime. 4. Conclusions
1
0.1 10000
100000
N
1000000
B
100
t0 (min)
10
The newly introduced large size core–shell particle columns show a clear improvement in separation power over their fully porous counterparts by allowing faster separations (at the same efficiency) or a higher separation resolution (at the same analysis time). Both isocratic and gradient impedance plot yield a similar picture, showing two distinct groups, i.e. core–shell (lowest value of E0 ) and fully porous particles (highest value of E0 ), confirming the intrinsic kinetic advantage of core–shell particle columns, which can also be seen using the absolute kinetic plot. If used around their optimal flow rate, the core–shell particles display a minimal separation impedance that is about 40% lower than the fully porous particles, while even larger gains in the separation speed can be achieved in the C-term regime. Acknowledgements
1
0.1 10000
100000
np2 1000000
Fig. 5. Absolute kinetic plot showing (A) the relation of t0 versus N for isocratic elution experiments and (B) t0 versus np 2 for gradient elution experiments calculated with a maximal pressure limit Pmax of 400 bar of the different measured fully porous particle (red) and core–shell particle (black) columns: Zorbax 250 mm × 4.6 mm 5 m ( ), Accucore 150 mm × 4.6 mm 4 m (), Kinetex 250 mm × 4.6 mm 5 m (), Ascentis Express 150 mm × 4.6 mm 5 m () and Ascentis Express 250 mm × 4.6 mm 5 m (䊉) which is only measured in isocratic elution mode. The dash-dotted lines represent the average Knox–Saleem limit for the fully porous particle column in red and for all core–shell particle columns in black. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
i.e. in the B-term regime corresponding with low velocities and thus long analysis times, we see an overlap between the 5 m fully porous particle column and the core–shell particle columns. When we however go to optimal flow rates, where the lines coincidence with the Knox–Saleem limit, we see a clear difference between the fully porous and core–shell particle columns. The same difference of circa 40% in E0,min can once again be seen. Achieving the same amount of theoretical plates (at optimal flow rates) will thus take 40% less time. Alternatively at the same analysis time a 30% higher plate count can be achieved on the core–shell particle columns compared with the fully porous particle column. At higher flow rates, entering the C-term regime, this difference increases, once again showing that the advantage of core–shell versus fully porous particle columns is even larger when operating at high velocities. At velocities approaching three times uopt we see that the same performance can be reached almost 45% faster by the core–shell particle columns or 35% better performance is achieved in the same analysis time. Fig. 5B shows the kinetic plot of the gradient elution data. E0,grad is plotted versus np 2 instead of N, resulting again in a slope of the Knox–Saleem limit of two. The kinetic plot in which t0 is plotted versus np can be found in the Supporting Material, SM (Fig. S-3). Once again we can see that both fully porous and core–shell particle columns align in the B-term region and the use of core–shell particle columns becomes more advantageous at increasing flow
Y.V. and K.B. gratefully acknowledge Research grants from the Research Foundation Flanders (FWO Vlaanderen). H. Ritchie from Thermo Scientific (Waltham, MA, USA), T. Farkas from Phenomenex (Torrance, CA, USA) and D. Bell from Supelco (Bellefonte, PA, USA) are kindly acknowledged for the gift of the chromatographic columns. 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. 2013.09.009. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
[16] [17] [18] [19] [20] [21] [22] [23]
C. Horváth, B.A. Preiss, S.R. Lipsky, Anal. Chem. 39 (1967) 1422. C. Horváth, S.R. Lipsky, J. Chromatogr. Sci. 7 (1969) 109. J.J. Kirkland, Anal. Chem. 41 (1969) 218. J.J. Destefano, T.J. Langlois, J.J. Kirkland, J. Chromatogr. Sci. 46 (2008) 254. D.V. McCalley, J. Chromatogr. A 1218 (2011) 2887–2897. D.V. McCalley, J. Chromatogr. A 1193 (2008) 85–91. J.J. DeStefano, S.A. Schuster, J.M. Lawhorn, J.J. Kirkland, J. Chromatogr. A 1258 (2012) 76–83. J. Ruta, D. Zurlino, C. Grivel, S. Heinisch, J.-L. Veuthey, D. Guillarme, J. Chromatogr. A 1228 (2012) 221–231. M.M. Fallas, S.M.C. Buckenmaier, D.V. McCalley, J. Chromatogr. A 1235 (2012) 49–59. S. Fekete, K. Ganzler, J. Fekete, J. Pharm. Biomed. Anal. 51 (2010) 56–64. F. Gritti, G. Guiochon, J. Chromatogr. A 1254 (2012) 30–42. S. Fekete, R. Berky, J. Fekete, J.-L. Veuthey, D. Guillarme, J. Chromatogr. A 1236 (2012) 177–188. S. Fekete, R. Berky, J. Fekete, J.-L. Veuthey, D. Guillarme, J. Chromatogr. A 1252 (2012) 90–103. S. Heinisch, A. D’Attoma, C. Grivel, J. Chromatogr. A 1228 (2012) 135–147. S.A. Schuster, B.M. Wagner, B.E. Boyes, J.J. Kirkland, Lecture L-01-04, 35th International Symposium and Exhibit on High Performance Liquid Phase Separations and Related Techniques, HPLC2012, Anaheim, CA, USA, June 17–22, 2012. A. Cavazzini, F. Gritti, K. Kaczmarski, N. Marchetti, G. Guiochon, Anal. Chem. 79 (2007) 5972. G. Guiochon, F. Gritti, J. Chromatogr. A 1218 (2011) 1915–1938. P.W. Carr, D.R. Stoll, X. Wang, Anal. Chem. 83 (2011) 1890. D. Guillarme, J. Ruta, S. Rudaz, J.-L. Veuthey, Anal. Bioanal. Chem. 397 (2010) 1069. D. Guillarme, E. Grata, G. Glauser, J.-L. Wolfender, J.-L. Veuthey, S. Rudaz, J. Chromatogr. A 1216 (2009) 3232. E. Oláh, S. Fekete, J. Fekete, K. Ganzler, J. Chromatogr. A 1217 (2010) 3642–3653. F. Gritti, G. Guiochon, J. Chromatogr. A 1252 (2012) 31–44. D. Cabooter, A. Fanigliulo, G. Bellazzi, B. Allieri, A. Rottigni, G. Desmet, J. Chromatogr. A 1217 (2010) 7074–7081.
86
Y. Vanderheyden et al. / J. Chromatogr. A 1312 (2013) 80–86
[24] D.V. McCalley, J. Chromatogr. A 1217 (2010) 4561–4567. [25] A. Fanigliulo, D. Cabooter, G. Bellazzi, D. Tramarin, B. Allieri, A. Rottigni, G. Desmet, J. Sep. Sci. 33 (2010) 3655–3665. [26] F. Gritti, I. Leonardis, J. Abia, G. Guiochon, J. Chromatogr. A 1217 (2010) 3819–3843. [27] G. Guiochon, F. Gritti, J. Chromatogr. A 1217 (2010) 8167–8180. [28] S. Fekete, E. Oláh, J. Fekete, J. Chromatogr. A 1228 (2012) 57–71. [29] F. Gritti, G. Guiochon, J. Chromatogr. A 1221 (2012) 2–40. [30] G. Desmet, D. Cabooter, P. Gzil, H. Verelst, D. Mangelings, Y. Vander Heyden, D. Clicq, J. Chromatogr. A 1130 (2006) 158. [31] F. Gritti, G. Guiochon, J. Chromatogr. A 1218 (2011) 1592. [32] S. Deridder, G. Desmet, J. Chromatogr. A 1218 (2011) 46–56. [33] A. Liekens, J. Denayer, G. Desmet, J. Chromatogr. A 1218 (2011) 4406–4416. [34] Y. Zhang, X. Wang, P. Mukherjee, P. Petersson, J. Chromatogr. A 1216 (2009) 4597–4605. [35] K. Broeckhoven, D. Cabooter, S. Eeltink, G. Desmet, J. Chromatogr. A 1228 (2012) 20–30. [36] J. De Vos, C. Stassen, A. Vaast, G. Desmet, S. Eeltink, J. Chromatogr. A 1264 (2012) 57–62.
[37] A. Vaast, J. De Vos, K. Broeckhoven, M. Verstraeten, S. Eeltink, G. Desmet, J. Chromatogr. A 1256 (2012) 72–79. [38] J.J. Van Deemter, F.J. Zuiderweg, A. Klinkenberg, Chem. Eng. Sci. 5 (1956) 271–289. [39] J.C. Giddings, J. Chromatgr. A 13 (1964) 301–304. [40] G. Desmet, D. Clicq, P. Gzil, Anal. Chem. 77 (2005) 4058–4070. [41] J. Billen, D. Guillarme, S. Rudaz, J.L. Veuthey, H. Ritchie, B. Grady, G. Desmet, J. Chromatgr. A 1161 (2007) 224–233. [42] F. Gritti, G. Guiochon, J. Chormatogr. A 1218 (2011) 4452–4461. [43] S. Heinisch, G. Desmet, D. Clicq, J.-L. Rocca, J. Chromatogr. A 1203 (2008) 124–136. [44] J.H. Knox, J. Chromatgr. A 831 (1999) 3–15. [45] K. Broeckhoven, D. Cabooter, G. Desmet, J. Pharm, J. Pharm. Anal. 12. (2012), http://dx.doi.org/10.1016/j.jpha.006. [46] F. Gritti, G. Guiochon, J. Chromatogr. A 1280 (2013) 35–50. [47] J. Knox, M. Saleem, J. Chrom. Sci. 7 (1969) 614–622. [48] U.D. Neue, J. Chromatogr. A 1079 (2005) 153. [49] K. Broeckhoven, D. Cabooter, F. Lynen, P. Sandra, G. Desmet, J. Chromatogr. A 1217 (2010) 2787–2795.
Contents lists available at ScienceDirect
Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma
Isocratic and gradient impedance plot analysis and comparison of some recently introduced large size core–shell and fully porous particles Yoachim Vanderheyden a , Deirdre Cabooter b , Gert Desmet a , Ken Broeckhoven a,∗ a b
Vrije Universiteit Brussel, Department of Chemical Engineering, Pleinlaan 2, 1050 Brussels, Belgium KU Leuven, Department of Pharmaceutical Sciences, Herestraat 49, 3000 Leuven, Belgium
a r t i c l e
i n f o
Article history: Received 25 July 2013 Received in revised form 30 August 2013 Accepted 3 September 2013 Available online 7 September 2013 Keywords: Core–shell Fully porous Impedance plot Kinetic performance limit Plate height Permeability
a b s t r a c t The intrinsic kinetic performance of three recently commercialized large size (≥4 m) core–shell particles packed in columns with different lengths has been measured and compared with that of standard fully porous particles of similar and smaller size (5 and 3.5 m, respectively). The kinetic performance is compared in both absolute (plot of t0 versus the plate count N or the peak capacity np for isocratic and gradient elution, respectively) and dimensionless units. The latter is realized by switching to so-called impedance plots, a format which has been previously introduced (as a plot of t0 /N2 or E0 versus Nopt /N) and has in the present study been extended from isocratic to gradient elution (where the impedance plot corresponds to a plot of t0 /np 4 versus np,opt 2 /np 2 ). Both the isocratic and gradient impedance plot yielded a very similar picture: the clustered impedance plot curves divide into two distinct groups, one for the core–shell particles (lowest values, i.e. best performance) and one for the fully porous particles (highest values), confirming the clear intrinsic kinetic advantage of core–shell particles. If used around their optimal flow rate, the core–shell particles displayed a minimal separation impedance that is about 40% lower than the fully porous particles. Even larger gains in separation speed can be achieved in the C-term regime. © 2013 Elsevier B.V. All rights reserved.
1. Introduction The first generation of core–shell particles (also called superficially porous, porous-shell, fused-core or solid core particles) were produced by Horváth and Kirkland in the late 1960’s [1–3]. In 2006, a new generation of core–shell particles was introduced [4]. These 2.7 m particles, with a relatively thick shell of 0.5 m, overcame the low loading capacity which was one of the shortcomings of the earliest generation particles. Compared with fully porous particles, this second generation of core–shell particles shows a slightly lower total mass loadability [5–8]. However, as the loadability appears to vary with column internal diameter (ID) [9] and column performance [5,7,10], the importance of this difference in loadability remains a point of discussion [11]. In the past decade, different vendors commercialized 2.6–2.7 m core–shell particles in a wide variety of column dimensions and stationary phases. Also larger wide pore particles (3.6 m) for the analysis of biomolecules [12,13] and also smaller sizes (1.7 m) [10,14] were developed. In the past year, particles
∗ Corresponding author. Tel.: +32 2629 37 81; fax: +32 2629 32 48. E-mail address: [email protected] (K. Broeckhoven). 0021-9673/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.chroma.2013.09.009
with sizes between 4 and 5 m with a shell of 0.6–0.85 m were introduced [15]. That the research into novel particles with different sizes or shell morphology is still ongoing, is proven by the recent commercialization of very small (1.3–1.6 m) core–shell particles. Core–shell particles offer a huge leap in separation efficiency, compared with their fully porous counterparts [16–20]. Where fully porous particles achieve minimum reduced plate heights of h = 2, core–shell particles consistently achieve values of 1.5–1.8 [4,5,9,10,21–25] and some studies even report values as low as 1.1–1.3 [26,27]. Despite the fact that these high efficiencies could not be reached for the smaller 2.1 mm ID columns [8,12,14,21,24,25,28–30] and also seem to depend on the column length [9], the separation efficiency is significantly better than their fully porous equivalents. The original assumption for the better performance of core–shell particles was the presence of a shorter diffusion path through the porous shell and thus a lower stationary phase mass transfer contribution (Cs -term in the van Deemter equation). The improved performance is however mainly due to the lower A-term (i.e. bed heterogeneity), which also increases the optimal linear velocity u0,opt , and the lower B-term (longitudinal diffusion) [31]. Whether the lower eddy-dispersion (A-term) is due to a narrower particle size distribution or due to better packing
Y. Vanderheyden et al. / J. Chromatogr. A 1312 (2013) 80–86
properties is still a point of discussion [23,30,31]. The lower B-term is a result of the obstruction for diffusion by the solid core [32] and the difference in morphology of the shell structure to that of fully porous particles [33]. The performance of 2.6 m core–shell particles is comparable with sub-2 m fully porous particles but they require a much lower operating pressure and can thus be used on conventional (i.e. 400 bar) LC instrumentation [4,34] if the dead volume of the system is not too excessive to compromise performance. The combination of core–shell particles and ultra-high operating pressures (i.e. 1200 bar) is also feasible and allows even faster and/or more efficient separations [5,35–37]. In fact, where all initially introduced 2.6–2.7 m core–shell particles had an upper pressure limit of 600 bar, several manufacturers now rate their 2.1 mm ID columns up to 1000 bar or even 1200 bar for the new sub-2 m core shell particles. The large core–shell particle columns are however still rated at 600 bar. On the other hand, fully porous particles of 3 m or larger are typically rated at a maximal pressure of 400 bar, whereas smaller particles (2.5 m or below) are typically rated up to 1000–1200 bar. Historically, the efficiency of chromatographic columns is studied via a plot of the plate height H vs. u0 . Very convenient in this type of plot is that it directly reveals the value of the optimal velocity or flow rate [38]. The dimensionless equivalent of this plot, allowing to compare the quality of columns with different particle sizes dp , is the so-called reduced plate height or reduced van Deemter plot of h (h = H/dp ) versus the reduced linear velocity 0 (0 = u0 dp /DM with DM the molar diffusion coefficient) [39]. To compare the kinetic performance (defined as the time needed to achieve a given chromatographic performance) of chromatographic columns, it has become customary over the past few years to use a plot of the elution time of an unretained peak t0 (or tR the retention time of the strongest retained peak) versus the number of theoretical plates or peak count N (or peak capacity np in gradient elution), generally referred to as a kinetic plot [40]. The dimensionless equivalent of the kinetic plot has been introduced in [41] and is obtained by plotting the separation impedance E0 = t0 /N2 ·Pmax / versus Nopt /N (where Pmax is the maximal pressure limit of the column, is the mobile phase viscosity and Nopt is the plate count at optimal linear velocity uopt ). As shown in [41], this plot (further referred to as the impedance plot) is equivalent to a plot of h2 (with the reduced flow resistance as defined in [41]) versus (h·0 )/(hmin ·0,opt ), readily showing that the impedance plot only depends on the dimensionless quantities h, and , and is as such ideally suited to compare the intrinsic kinetic packing quality of columns filled with particles of different sizes. In the present study, comparing several recently commercialized core–shell and fully porous packing materials with diameters ranging between 3.5 and 5 m, this approach has been followed. The concept of impedance plots is also extended to gradient elution mode chromatography.
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acquisition, data handling and instrument control were performed with Agilent Chemstation software. Table 1 summarizes the properties of all columns tested in this study. The Thermo Accucore columns were obtained from Thermo Scientific (Waltham, MA, USA), the Kinetex columns from Phenomenex (Torrance, CA, USA), the HALO column from Advanced Materials Technology (Wilmington, DE, USA), the Ascentis Express columns from Supelco (Bellefonte, PA, USA) and the Zorbax columns from Agilent Technologies (Diegem, Belgium). Since the results obtained on the HALO column were very similar to the results obtained on the Ascentis columns, these results are not shown in this study for reasons of clarity. For each column type, at least two columns were tested and their obtained results averaged. 2.2. Sample and conditions Uracil (t0 -marker) and a mixture of 10 alkylphenones (acetanilide, acetophenone, 3-methyl acetophenone, propiophenone, butyrophenone, benzophenone, valerophenone, hexanophenone, heptanophenone and octanophenone) were purchased from Sigma–Aldrich (Steinheim, Germany). All the test components were dissolved in a mixture of 50/50 ACN/H2 O in a concentration of 0.1 mg/mL. Acetonitrile (Supra-Gradient grade) was purchased from Biosolve (Valkenswaard, The Netherlands). HPLC grade water (H2 O) was prepared in the laboratory using a Milli-Q gradient water purification system (Millipore, Bedford, MA, USA). The sample for the isocratic experiments only contained uracil, butyrophenone, benzophenone and valerophenone. In gradient elution mode, uracil and all 10 alkylphenones were used. The organic modifier content was adjusted such for each column to obtain the same retention factor k for the component of interest (benzophenone, target value of k2 = 6) in isocratic mode. In gradient mode the same ratio of gradient time tG over column void time t0 was used for all experiments (tG /t0 = 12) and the retention factor of acetophenone and octanophenone were fixed at target values of k2 = 2 and k10 = 12 by changing the initial (ϕ0 ) and final (ϕe ) mobile phase composition. The exact mobile phase conditions ϕ and retention coefficient for each column are given in Table 1. To determine column performance the peak widths were measured at half height. Although more accurate methods to determine the exact performance are possible [42], the employed columns, sample and conditions yielded very symmetrical peaks, for which the half width method provides a reasonable good approach especially for the relative comparison in this work. The experimental peak widths and pressure drops were corrected for extra column contributions as described in [43]. All injections were performed in triplicate and the results were averaged in order to counteract statistic variance. 3. Results and discussion 3.1. Plate height analysis
2. Experimental 2.1. Instrumentation and columns All chromatographic experiments were performed on an Agilent 1290 Infinity system (Agilent Technologies, Waldbronn, Germany). The instrument was equipped with a binary pump, a variable wavelength detector with a low dispersion cell (2 L volume and 3 mm path length), an autosampler and a thermostatted column compartment with a mobile phase preheater of 3 L. The oven temperature was set constant to 30 ◦ C for all experiments. The absorbance values were measured at 254 nm with a sample rate of 80 Hz. Data
To evaluate the performance of the fully porous and core–shell particle columns, one can represent the measured plate height as a function of the linear velocity (i.e. van Deemter plot). Since retention has an effect on performance, it was opted to investigate the performance of the components with fixed retention, as was explained before (see Table 1). In Fig. 1A we can see that the minimum plate height of the 5 m fully porous particle column is considerably higher than that of their 3.5 m equivalent, whose plate height curve overlaps with the cluster of core–shell particle columns. The minimal plate height Hmin (at u0,opt ) of the 5 m fully porous particle columns is around 10 m. For the core–shell
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Table 1 Column properties (as provided by the vendor), mobile phase compositions and obtained retention factors for the compounds of interest. All columns have an internal diameter of 4.6 mm. Column
L (mm)
Thermo Accucore XL C-18 Kinetex C18 Halo C18 Ascentis Express C18 Ascentis Express C18 Zorbax C18 Zorbax C18
dp (m)
150 250 250 150 250 250 100
dcore (m)
4 5 5 5 5 5 3.5
Pmax (bar)
2.8 3.3 3.8 3.3 3.3 / /
600 600 600 600 600 400 400
particle columns we observe a minimal plate height between 6 and 8 m. Part of this variation between the different core–shell particle columns results from the fact that they differ in particle size. To rule out the effect of different particle sizes, the reduced plate height plot (h versus v) is used, as shown in Fig. 1B. We can immediately see that the 3.5 m fully porous particle column, which had a minimum plate height comparable with that of the core–shell particle columns, now has a much higher reduced minimum plate height. A clear distinction can be seen between the fully porous particle columns having a hmin of 2–2.1 and the core–shell particle columns having a hmin of 1.4–1.7 (with the Accucore and the 25 cm Ascentis Express columns having the lowest hmin ) which is circa 25% lower than the fully porous particles, consistent with earlier
25
A
H (μm) 20
15
Isocratic
Gradient
ϕACN
k2
ϕ0,ACN
ϕe,ACN
k2
k10
0.425 0.425 0.425 0.452 0.46 0.465 0.48
5.9 6.0 6.1 5.9 5.9 6.2 6.1
0.31 0.36 / 0.35 / 0.43 0.43
0.90 0.727 / 0.675 / 0.76 0.78
2 2 / 2 / 2 2.1
11.8 12 / 11.7 / 11.9 11.8
findings for other particle sizes [7,8,10,12–14,21,23,25]. The core–shell particle columns thus have a lower value than the “theoretically” ideal value of hmin = 2, defined by Knox [44]. Also a much flatter slope in the C-term regime (high velocities) of the core–shell versus the fully porous particle columns can be noticed. As explained in [17,45] this results mostly from the lower A-term contribution of the core–shell particle columns at high velocities, whereas the effect of the decrease in C-term is almost negligible. Due to this flatter slope, the core–shell particle columns can be operated at higher (reduced) velocities without losing too much performance. This effect can be seen in Fig. 2A–D in which chromatograms measured on 5 m core–shell and fully porous particle columns are compared at different flow rates. At the optimal flow rate uopt the number of theoretical plates of the core–shell particle columns is circa 30% higher than the fully porous particle columns, which is of course directly related to the difference in (reduced) plate height. When going to a higher flow rate (e.g. almost three times uopt ) this difference even increases to more than 75%, a direct consequence of the difference in steepness of the C-term. 3.2. Column permeability
10
The column permeability Kv,0 (based on u0 ) can be deduced from a plot of pressure drop P versus linear velocity u0 :
5
Pcol = 0 2
0
4
6
8
10
12
u0 (mm/s) 5
B
h 4.5 4 3.5 3 2.5
u0 · · L 1 ε3 with KV,0 = · dp2 · KV,0 180 (1 − ε)2 · εT
where L is the column length, ε is the external porosity and εT the total porosity. Plots of P as a function of the flow rate F instead of u0 are also common [7]. However, where the flow rate F only includes the effect of the external porosity ε, the linear velocity is based on the residence time t0 of a non-retaining but permeating component (i.e. the t0 -marker). As residence time is directly related to the analysis time (through k, which is kept constant), a plot of P versus u0 is practically more relevant. The column permeability is thus best plotted against u0 which depends on the total porosity εT , which is given by εT = ε + (1 − ε)εint
2
1.5 1 0
10
20
30
40
50
60
70
ν
80
Fig. 1. Comparison of the absolute (A) and reduced (B) plate height as a function of linear velocity u0 or reduced velocity , respectively of all measured fully porous particle (red) and core–shell particle (black) columns: Zorbax 250 mm × 4.6 mm 5 m ( ), Zorbax 100 mm × 4.6 mm 3.5 m ( ), Accucore 150 mm × 4.6 mm 4 m (), Kinetex 250 mm × 4.6 mm 5 m (), Ascentis Express 150 mm × 4.6 mm 5 m () and Ascentis Express 250 mm × 4.6 mm 5 m (䊉); sample compound was benzophenone, for other conditions see Section 2 and Table 1. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
(1)
(2)
with εint the internal porosity. Since columns with different lengths have been used, the pressure drop per column length P/L is plotted as a function of u0 in Fig. 3. The particle size influences the column permeability as can be seen in Eq. (1) and Fig. 3. The column permeability of the investigated core–shell particle columns lies in between those of the 3.5 and 5 m fully porous particle columns. As can be seen in Eq. (1) the porosity influences the u0 based column permeability. If we assume that the external porosity is almost identical for the different columns, the core–shell particles have a lower total porosity due to the solid core which lowers the internal porosity (see Eq. (2)), and this should lead to a larger Kv,0 (see Eq. (1)). The observed pressure drops were, however, significantly larger for the 5 m core–shell particle columns compared to
Y. Vanderheyden et al. / J. Chromatogr. A 1312 (2013) 80–86
83
40
40
A
mAu
B
mAu
t0 = 1.65 min 30
30
t0 = 0.6 min N = 31500
N = 35600 20
10
0
0
Core-shell 0
Fopt = 1.25 ml/min 4
8
N = 23900 N = 25700
10
-10
N = 27400
20
N = 32800
12
t (min)
Core-shell
-10 0
16
F = 3.5 ml/min 1
2
3
4
5
40
40
C
mAu
D
mAu
N = 15400
30
30
t0 = 2.2 min
t0 = 0.7 min
N = 29300
20
N = 25900
N = 15900
20
N = 14400
N = 25200 10
10
0
0
Fopt = 1 ml/min
Fully porous
-10
5
0
6
t (min)
10
15
0
t (min) 20
F = 3 ml/min
Fully porous
-10
2
4
t (min) 6
Fig. 2. Chromatograms and performance recorded on the Kinetex 250 mm × 4.6 mm 5 m core–shell particle column (A and B) and the Zorbax 250 mm × 4.6 mm 5 m fully porous particle column (C and D) at their optimal flow rate (A–C) and a flow rate almost three times higher (B–D).
the fully porous ones, corresponding to a lower Kv,0 . This is probably due to the difference in the nominal particle size given for the columns (e.g. 5 m) as their actual size is closer to 4.6 m [46], which of course strongly affects Kv,0 (see Eq. (1)). After further inquiry with the column vendors, actual particle sizes of 4.65 (instead of 5) m for the Kinetex and Ascentis columns and 4.1 (instead of 4) m for the Thermo Accucore columns were obtained and therefore used in the calculation of reduced parameters in Section 3.2. The advantage of the kinetic plot methodology employed in the following sections is that this does not require to define a characteristic particle size. It should be noticed that the 25 cm Ascentis column exhibited a higher permeability (i.e. lower pressure drop) than its 15 cm equivalent (compare with 䊉 symbols in Fig. 3). This apparent looser packing however results in a poorer performance, as can be seen
ΔPcol / L (bar/m)
in Fig. 1. The effect of column length on packing quality was also observed by [9].
3.3. Impedance plot analysis The kinetic performance limit describes the time needed to achieve a given chromatographic performance. It is customary to present this information using kinetic plots [47] which will be discussed in next section. Given the uncertainties on the exact value of the average particle diameter, we found it instructive to also compare the different particles in an impedance plot, the dimensionless variant of the kinetic plot. In the impedance plot the Knox separation impedance number E0 is plotted as a performance indicator versus Nopt /N: E0 =
2500
2000
1500
1000
500
0 0
2
4
6
8
u0 (mm/s) 10
Fig. 3. Column pressure drop as a function of linear velocity for all measured fully porous particle (red) and core–shell particle (black) columns. The same symbolism is used as in Fig. 1. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
H2 t0 Pmax = h2 0 = 2 · KV,0 N
(3)
As discussed in [41], the Nopt /N ratio is independent of the particle size. This type of plot also incorporates information on column permeability (see Eq. (3)). The big advantage of the impedance plot over the reduced plate height plot is that the exact particle size, which is not always exactly known and is subject to some variation (i.e. particle size distribution or batch-to-batch variability of dp ), does not have to be defined [41]. Note that the maximal mobile phase viscosity max is used to calculate the Knox separation impedance number. Instead of using t0 one can also use the time of the last eluting peak tR,last . Since the retention factor of the peaks of interest is fixed, the choice between t0 and tR,last will not influence the obtained results. The concept of the impedance plot has been extended to gradient elution by replacing the parameter N by the peak capacity np 2
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due to the square root dependency of np with N [48]. The apparent separation impedance number E0,grad will thus be defined as E0,grad =
t0 n4p
·
Pmax
(4)
and will be plotted versus np,opt 2 /np 2 , as the gradient equivalent of Nopt /N. Since np 2 is only proportional with and not equal to N [48], E0,grad will not be equal to E0 , but the same qualitative conclusions can be drawn from both calculation methods. Fig. 4 shows the impedance plot of all investigated columns. Notice that due to the Nopt /N ratio on the x-axis, the data on the left hand side corresponds with the low velocities B-term region and the data on the right hand side with the high velocities C-term region, as in the van Deemter plot. We can once again observe the fully porous and core–shell particles as two distinct groups. The core–shell particle columns display a lower separation impedance and thus better performance over the whole range of velocities. The average minimal separation impedance of the fully porous particle columns is E0,min = 2100 whereas for the core–shell particle columns an almost 40% lower value of E0,min = 1300 is measured (with the lowest value of 1050 for the Accucore column). Since Pmax is chosen at 400 bar as performance limit (see next section) and is also quasi-equal (only small differences in ϕ, see Table 1) for both particle types, E0 varies linearly with t0 /N2 (see Eq. (3)). Hence, in order to achieve the same optimal performance N, the analysis time on core–shell particle columns is around 40% lower
A
7500
E0 6500 5500
4500 3500
compared with their fully porous counterparts. This difference is even higher in the C-term regime, as can be seen by the flatter slope of the core–shell particle columns, an effect which has also been observed in Section 3.1. A difference of 45% in E0 can be seen at velocities circa three times u0 . Fig. 4A also shows that the differences in performance and permeability of the 15 and 25 cm Ascentis columns, as discussed in Section 3.2, almost cancel each other out: E0,min = 1250 for the 15 cm vs. 1400 for the 25 cm column. The impedance plots in gradient elution mode lead to similar results obtained in isocratic mode. This agreement between isocratic and gradient behaviour confirms earlier similar findings reported in [47]. The difference in separation impedance number between both modes is due to a different calculation method. E0,grad,min equals 1600 and 3750 for the core–shell and fully porous particle columns respectively, which is a difference of almost 60%. The lowest value of E0,grad,min = 1450 was measured for the 15 cm Ascentis Express column. As discussed in Section 3.2 we can evaluate the kinetic performance based on the linear velocity u0 or on the superficial velocity us , which is equal to the flow rate F divided by the column cross section A (see Eq. (5)). In the calculation of the impedance number one can also use ts (superficial residence time), which is based on us , leading to a difference of a factor εT since F = us · A = u0 · A · εT
(5)
The superficial velocity based impedance number ES will thus be 1/εT times larger than the linear velocity based impedance number E0 . Due to the lower total porosity of the core–shell particles, this results in a value of ES,min of 2850 and 4100 in isocratic and 3500 and 7200 in gradient elution mode, for the core–shell and fully porous particle columns respectively. The difference between the particle types is hence slightly lower, i.e. circa 30% in isocratic and 50% in gradient mode. 3.4. Absolute kinetic plot analysis
2500
E0,min = 2100
1500
E0,min = 1300
500 0
1
2
3
4
5
6
7
Nopt / N
8
B
9000
E0,grad 7500 6000 4500
E0,min = 3750
3000
1500
E0,min = 1600
0 0
1
2
3
4
np,opt2 / nopt2
5
Fig. 4. Impedance plot showing the behaviour of (A) the separation impedance E0 as a function of Nopt /N for isocratic elution experiments and (B) E0,grad as a function of np,opt 2 /np 2 for gradient elution data of all measured fully porous particle (red) and core–shell particle (black) columns: Zorbax 250 mm × 4.6 mm 5 m ( ), Zorbax 100 mm × 4.6 mm 3.5 m ( ), Accucore 150 mm × 4.6 mm 4 m (), Kinetex 250 mm × 4.6 mm 5 m (), Ascentis Express 150 mm × 4.6 mm 5 m () and Ascentis Express 250 mm × 4.6 mm 5 m (䊉) which is only measured in isocratic elution mode. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
The absolute kinetic plot represents the retention time of an unretained peak t0 or retention time tR of the strongest retained peak versus the number of theoretical plates N [47]. The kinetic performance limit was calculated at the maximal pressure Pmax of 400 bar as this is the upper pressure limit of the fully porous particle columns given by the manufacturers and is also the maximal operating pressure of conventional LC instruments. It should however be noted that the core–shell particle columns have pressure limit specifications up to at least 600 bar. The interested reader can find the kinetic plots with Pmax = 600 for the core–shell particle columns in the Supporting Material, SM (Fig. S-1) where the resulting larger difference between the core–shell and fully porous particle columns under these pressure limits is presented. More information on the calculations of the absolute kinetic performance limits can be found in [35,49]. Once again the parameter N is replaced with np 2 in gradient elution mode. Fig. 5 shows the kinetic plot for both particle types. As the plate number is dependent on the particle size [30], only the large size particles are shown for reasons of clarity. The plot including the smaller 3.5 m fully porous particles can be found in the Supporting Material, SM (Fig. S-2). Since E0 varies linearly with t0 /N2 , the separation impedance can be represented on the kinetic plot as a straight line with a slope of 2 (in log–log scale). The minimal separation impedance has been presented in Fig. 5A for both particle types as dash-dotted lines. This line is also called the Knox–Saleem limit and represents the best possible separation performance with optimized particle size and column length at a given maximal operating pressure [47]. When comparing the plate number at the right hand side,
Y. Vanderheyden et al. / J. Chromatogr. A 1312 (2013) 80–86
100
A
t0 (min)
10
85
rates. At optimal flow rates, the same peak capacity can be reached almost 60% faster with the core–shell particle columns (which is the difference in E0,grad ) or at the same analysis time a circa 25% higher peak capacity can be achieved. Similar relative gains in analysis time or performance are observed in the C-term regime. 4. Conclusions
1
0.1 10000
100000
N
1000000
B
100
t0 (min)
10
The newly introduced large size core–shell particle columns show a clear improvement in separation power over their fully porous counterparts by allowing faster separations (at the same efficiency) or a higher separation resolution (at the same analysis time). Both isocratic and gradient impedance plot yield a similar picture, showing two distinct groups, i.e. core–shell (lowest value of E0 ) and fully porous particles (highest value of E0 ), confirming the intrinsic kinetic advantage of core–shell particle columns, which can also be seen using the absolute kinetic plot. If used around their optimal flow rate, the core–shell particles display a minimal separation impedance that is about 40% lower than the fully porous particles, while even larger gains in the separation speed can be achieved in the C-term regime. Acknowledgements
1
0.1 10000
100000
np2 1000000
Fig. 5. Absolute kinetic plot showing (A) the relation of t0 versus N for isocratic elution experiments and (B) t0 versus np 2 for gradient elution experiments calculated with a maximal pressure limit Pmax of 400 bar of the different measured fully porous particle (red) and core–shell particle (black) columns: Zorbax 250 mm × 4.6 mm 5 m ( ), Accucore 150 mm × 4.6 mm 4 m (), Kinetex 250 mm × 4.6 mm 5 m (), Ascentis Express 150 mm × 4.6 mm 5 m () and Ascentis Express 250 mm × 4.6 mm 5 m (䊉) which is only measured in isocratic elution mode. The dash-dotted lines represent the average Knox–Saleem limit for the fully porous particle column in red and for all core–shell particle columns in black. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
i.e. in the B-term regime corresponding with low velocities and thus long analysis times, we see an overlap between the 5 m fully porous particle column and the core–shell particle columns. When we however go to optimal flow rates, where the lines coincidence with the Knox–Saleem limit, we see a clear difference between the fully porous and core–shell particle columns. The same difference of circa 40% in E0,min can once again be seen. Achieving the same amount of theoretical plates (at optimal flow rates) will thus take 40% less time. Alternatively at the same analysis time a 30% higher plate count can be achieved on the core–shell particle columns compared with the fully porous particle column. At higher flow rates, entering the C-term regime, this difference increases, once again showing that the advantage of core–shell versus fully porous particle columns is even larger when operating at high velocities. At velocities approaching three times uopt we see that the same performance can be reached almost 45% faster by the core–shell particle columns or 35% better performance is achieved in the same analysis time. Fig. 5B shows the kinetic plot of the gradient elution data. E0,grad is plotted versus np 2 instead of N, resulting again in a slope of the Knox–Saleem limit of two. The kinetic plot in which t0 is plotted versus np can be found in the Supporting Material, SM (Fig. S-3). Once again we can see that both fully porous and core–shell particle columns align in the B-term region and the use of core–shell particle columns becomes more advantageous at increasing flow
Y.V. and K.B. gratefully acknowledge Research grants from the Research Foundation Flanders (FWO Vlaanderen). H. Ritchie from Thermo Scientific (Waltham, MA, USA), T. Farkas from Phenomenex (Torrance, CA, USA) and D. Bell from Supelco (Bellefonte, PA, USA) are kindly acknowledged for the gift of the chromatographic columns. 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. 2013.09.009. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
[16] [17] [18] [19] [20] [21] [22] [23]
C. Horváth, B.A. Preiss, S.R. Lipsky, Anal. Chem. 39 (1967) 1422. C. Horváth, S.R. Lipsky, J. Chromatogr. Sci. 7 (1969) 109. J.J. Kirkland, Anal. Chem. 41 (1969) 218. J.J. Destefano, T.J. Langlois, J.J. Kirkland, J. Chromatogr. Sci. 46 (2008) 254. D.V. McCalley, J. Chromatogr. A 1218 (2011) 2887–2897. D.V. McCalley, J. Chromatogr. A 1193 (2008) 85–91. J.J. DeStefano, S.A. Schuster, J.M. Lawhorn, J.J. Kirkland, J. Chromatogr. A 1258 (2012) 76–83. J. Ruta, D. Zurlino, C. Grivel, S. Heinisch, J.-L. Veuthey, D. Guillarme, J. Chromatogr. A 1228 (2012) 221–231. M.M. Fallas, S.M.C. Buckenmaier, D.V. McCalley, J. Chromatogr. A 1235 (2012) 49–59. S. Fekete, K. Ganzler, J. Fekete, J. Pharm. Biomed. Anal. 51 (2010) 56–64. F. Gritti, G. Guiochon, J. Chromatogr. A 1254 (2012) 30–42. S. Fekete, R. Berky, J. Fekete, J.-L. Veuthey, D. Guillarme, J. Chromatogr. A 1236 (2012) 177–188. S. Fekete, R. Berky, J. Fekete, J.-L. Veuthey, D. Guillarme, J. Chromatogr. A 1252 (2012) 90–103. S. Heinisch, A. D’Attoma, C. Grivel, J. Chromatogr. A 1228 (2012) 135–147. S.A. Schuster, B.M. Wagner, B.E. Boyes, J.J. Kirkland, Lecture L-01-04, 35th International Symposium and Exhibit on High Performance Liquid Phase Separations and Related Techniques, HPLC2012, Anaheim, CA, USA, June 17–22, 2012. A. Cavazzini, F. Gritti, K. Kaczmarski, N. Marchetti, G. Guiochon, Anal. Chem. 79 (2007) 5972. G. Guiochon, F. Gritti, J. Chromatogr. A 1218 (2011) 1915–1938. P.W. Carr, D.R. Stoll, X. Wang, Anal. Chem. 83 (2011) 1890. D. Guillarme, J. Ruta, S. Rudaz, J.-L. Veuthey, Anal. Bioanal. Chem. 397 (2010) 1069. D. Guillarme, E. Grata, G. Glauser, J.-L. Wolfender, J.-L. Veuthey, S. Rudaz, J. Chromatogr. A 1216 (2009) 3232. E. Oláh, S. Fekete, J. Fekete, K. Ganzler, J. Chromatogr. A 1217 (2010) 3642–3653. F. Gritti, G. Guiochon, J. Chromatogr. A 1252 (2012) 31–44. D. Cabooter, A. Fanigliulo, G. Bellazzi, B. Allieri, A. Rottigni, G. Desmet, J. Chromatogr. A 1217 (2010) 7074–7081.
86
Y. Vanderheyden et al. / J. Chromatogr. A 1312 (2013) 80–86
[24] D.V. McCalley, J. Chromatogr. A 1217 (2010) 4561–4567. [25] A. Fanigliulo, D. Cabooter, G. Bellazzi, D. Tramarin, B. Allieri, A. Rottigni, G. Desmet, J. Sep. Sci. 33 (2010) 3655–3665. [26] F. Gritti, I. Leonardis, J. Abia, G. Guiochon, J. Chromatogr. A 1217 (2010) 3819–3843. [27] G. Guiochon, F. Gritti, J. Chromatogr. A 1217 (2010) 8167–8180. [28] S. Fekete, E. Oláh, J. Fekete, J. Chromatogr. A 1228 (2012) 57–71. [29] F. Gritti, G. Guiochon, J. Chromatogr. A 1221 (2012) 2–40. [30] G. Desmet, D. Cabooter, P. Gzil, H. Verelst, D. Mangelings, Y. Vander Heyden, D. Clicq, J. Chromatogr. A 1130 (2006) 158. [31] F. Gritti, G. Guiochon, J. Chromatogr. A 1218 (2011) 1592. [32] S. Deridder, G. Desmet, J. Chromatogr. A 1218 (2011) 46–56. [33] A. Liekens, J. Denayer, G. Desmet, J. Chromatogr. A 1218 (2011) 4406–4416. [34] Y. Zhang, X. Wang, P. Mukherjee, P. Petersson, J. Chromatogr. A 1216 (2009) 4597–4605. [35] K. Broeckhoven, D. Cabooter, S. Eeltink, G. Desmet, J. Chromatogr. A 1228 (2012) 20–30. [36] J. De Vos, C. Stassen, A. Vaast, G. Desmet, S. Eeltink, J. Chromatogr. A 1264 (2012) 57–62.
[37] A. Vaast, J. De Vos, K. Broeckhoven, M. Verstraeten, S. Eeltink, G. Desmet, J. Chromatogr. A 1256 (2012) 72–79. [38] J.J. Van Deemter, F.J. Zuiderweg, A. Klinkenberg, Chem. Eng. Sci. 5 (1956) 271–289. [39] J.C. Giddings, J. Chromatgr. A 13 (1964) 301–304. [40] G. Desmet, D. Clicq, P. Gzil, Anal. Chem. 77 (2005) 4058–4070. [41] J. Billen, D. Guillarme, S. Rudaz, J.L. Veuthey, H. Ritchie, B. Grady, G. Desmet, J. Chromatgr. A 1161 (2007) 224–233. [42] F. Gritti, G. Guiochon, J. Chormatogr. A 1218 (2011) 4452–4461. [43] S. Heinisch, G. Desmet, D. Clicq, J.-L. Rocca, J. Chromatogr. A 1203 (2008) 124–136. [44] J.H. Knox, J. Chromatgr. A 831 (1999) 3–15. [45] K. Broeckhoven, D. Cabooter, G. Desmet, J. Pharm, J. Pharm. Anal. 12. (2012), http://dx.doi.org/10.1016/j.jpha.006. [46] F. Gritti, G. Guiochon, J. Chromatogr. A 1280 (2013) 35–50. [47] J. Knox, M. Saleem, J. Chrom. Sci. 7 (1969) 614–622. [48] U.D. Neue, J. Chromatogr. A 1079 (2005) 153. [49] K. Broeckhoven, D. Cabooter, F. Lynen, P. Sandra, G. Desmet, J. Chromatogr. A 1217 (2010) 2787–2795.