Anal. Chem. 2007, 79, 3764-3770
Calculating Optimal Modulation Periods to
Maximize the Peak Capacity in Two-Dimensional
HPLC
Kanta Horie,† Hiroshi Kimura,† Tohru Ikegami,† Akira Iwatsuka,† Nabil Saad,‡ Oliver Fiehn,‡ and
Nobuo Tanaka*,†
Department of Biomolecular Engineering, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan,
and Genome Center, University of California, Davis, Davis, California 95616
Theoretical calculations are presented to optimize modulation period for maximum total peak capacity in comprehensive two-dimensional HPLC (2D-HPLC) taking into
account the effect of modulation on the apparent peak
capacity of the first-dimension (1D) separation. Results
indicate that modulation periods are most favorable when
they are adjusted to ∼2.2-4 times the standard deviation
of a 1D peak in order to avoid excessively short run times
at the second dimension (2D). Data are presented that
effective peak capacities of several thousand in 60 min
can be expected for practical 2D-HPLC conditions, utilizing 1D gradient elution followed by 2D isocratic elution,
that remain at ∼50-70% of the theoretical maximum
peak capacity. This work suggests that lower modulation
frequencies and longer 2D separation times than previously proposed are favorable under realistic chromatographic conditions, alleviating some practical problems
associated with 2D-HPLC.
Separation of complex mixtures consisting of thousands of
components remains a challenge for liquid chromatography.
Recent advances in high-speed separations such as use of
ultrahigh-pressure liquid chromatography1-5 or monolithic silica
columns6,7 considerably increased peak capacities of one-dimensional HPLC separations compared to more conventional HPLC
methods. Today, peak capacities of 350 or greater can be achieved
when long columns and extended gradient run times are employed.7 The next logical step is to combine peak capacities of
two different HPLC separations that are based on largely distinct
* Corresponding author. E-mail: [email protected]. Phone: 81-75-724-7809.
Fax: 81-75-724-7710.
†
Kyoto Institute of Technology.
‡
University of California, Davis.
(1) Wren, S. A. C. J. Pharm. Biomed. Anal. 2005, 38, 337-343.
(2) Gilar, M.; Daly, A. E.; Kele, M.; Neue, U. D.; Gebler, J. C. J. Chromatogr.,
A 2004, 1061, 183-192.
(3) Mellors, J. S.; Jorgenson, J. W. Anal. Chem. 2004, 76, 5441-5450.
(4) MacNair, J. E.; Patel, K. D.; Jorgenson, J. W. Anal. Chem. 1999, 71, 700708.
(5) Patel, K. D.; Jerkovich, A. D.; Link, J. C.; Jorgenson, J. W. Anal. Chem. 2004,
76, 5777-5786.
(6) Kobayashi, H.; Ikegami, T.; Kimura, H.; Hara, T.; Tokuda, D.; Tanaka, N.
Anal. Sci. 2006, 22, 491-501.
(7) Luo, Q. Z.; Shen, Y. F.; Hixson, K. K.; Zhao, R.; Yang, F.; Moore, R. J.; Mottaz,
H. M.; Smith, R. D. Anal. Chem. 2005, 77, 5028-5035.
3764 Analytical Chemistry, Vol. 79, No. 10, May 15, 2007
physicochemical properties, such as normal phase/reversed
phase.8 When all fractions of the first dimension (1D)9 are
comprehensively subjected to a second-dimension (2D) separation,
the theoretical total peak capacity is calculated by multiplying the
peak capacities of both dimensions, assuming total orthogonality
of the two dimensions and no peak broadening or remixing after
1D separation. (Reference 9 was followed for nomenclature related
to 2D-HPLC.) For each dimension, peak capacity is described by
eq 1a (for isocratic elution with t1 and tR giving the retention times
of the first and the last peak in a chromatogram using a column
showing N theoretical plates) or eq 2 (for gradient elutions with
gradient time tG and peak width tW).10-12
n ) 1 + (xN/4) (ln(tR/t1))
(1a)
n ) 1 + tG/tW
(2a)
In reality, however, extra peak broadening effects are common
in 2D-HPLC.13 Effluent from the 1D column is modulated at a
regular interval to form a band of a finite volume to be injected
into the 2D separation system. Any component existing in a band
is broadened to the full volume of the band in a two-dimensional
chromatogram irrespective of its own width at the exit of the 1D
column. It is also unavoidable that some 1D peaks are fractionated
into two or more injections into the 2D separation due to the
modulations of the 1D peaks. Because of these effects, the apparent
total peak volume along the 1D retention axis can be much greater
than the original 1D elution volume. Consequently, the theoretical
total peak capacity of 2D-HPLC as multiplication of the peak
capacities of 1D and 2D will not be reached in practice.
For both 2D-gas chromatography14-17 and 2D-HPLC,13,17,18 it
has previously been suggested that each 1D peak should be
(8) Francois, I.; de Villiers, A.; Sandra, P. J. Sep. Sci. 2006, 29, 492-498.
(9) Shoenmakers, P.; Marriott, P.; Beens, J. LC-GC Eur. 2003, 16, 335-336,
338-339.
(10) Giddings, J. C. Unified Separation Science; Wiley-Interscience: New York,
1991; pp 126-128.
(11) Giddings, J. C. Anal. Chem. 1967, 39, 1027-1028.
(12) Grushka, E. Anal. Chem. 1970, 42, 1142-1147.
(13) Murphy, R. E.; Schure, M. R.; Foley, J. P. Anal. Chem. 1998, 70, 15851594.
(14) Shellie, R.; Marriott, P. J. Anal. Chem. 2002, 74, 5426-5430.
(15) Mondello, L.; Lewis, A. C.; Bartle, K. D. Multidimensional Chromatography;
John Wiley & Sons, Ltd.: Chichester, England, 2002.
(16) Bertsch, W. J. High Resolut. Chromatogr. 2000, 23, 167-181.
(17) Seeley, J. V. J. Chromatogr., A 2002, 962, 21-27.
10.1021/ac062002t CCC: $37.00
© 2007 American Chemical Society
Published on Web 04/17/2007
fractionated into three to four injections or more into the 2D
separation, which enforces a high modulation frequency and very
short 2D run times. Potential difficulties arise from high linear
velocities, insufficient separation times, high-pressure drops, and
reduced separation efficiencies in 2D separations. Fast separations
required for fast modulations are not always possible. Various
approaches were taken in the past to alleviate problems of slow
elution, or a limited frequency of injection, at 2D such as (i) slow
or intermittent elution of 1D columns,19-23 (ii) 2D separation using
two or more chromatographs,24-26 (iii) 2D separation at high
temperatures,27 or (iv) high flow rate at 2D using a monolithic
silica column at 2D.28
Seeley reported a theoretical study of the effect of the
frequency and phase of sampling on accuracy of retention time
at 1D and the effective peak width along 1D retention axis.17 By
averaging the effects of phase and volume of modulation with
respect to 1D separation, it was concluded that a loss in 1D
resolution or the increase in effective 1D bandwidth was less than
20 or 30% if the sampling period was less than 1.5 or 2 times the
standard deviation of a 1D peak, respectively.17
Although it has been proposed to employ short modulation
times for utilizing 1D peak capacity as much as possible,13-18 it is
desirable to develop a method to optimize modulation times in
order to maximize total peak capacity of a 2D-HPLC system taking
into account the peak capacity of 2D and the effect of modulation
of 1D separated peaks. Here results of calculation for optimum
modulation times between 1D and 2D are presented showing the
conditions that maximize the effective total peak capacity of
comprehensive 2D-HPLC.
EXPERIMENTAL SECTION
The HPLC system consisted of a Shimadzu LC-10ADvp pump,
a Shimadzu SPD-10AVvp detector, a Rheodyne 8125 injector, a
GL Sciences EZChrom Elite-2.61 data processor, and columns
maintained at 30 °C. Monolithic silica C18 columns (Chromolith
RP18e, 4.6-mm i.d., 1, 2.5, 5, and 10 cm in length) to be used at
2D as in the previous work28 were evaluated by using reference
compounds (alkylbenzenes) with the HPLC system at 0.5-10 mL/
min to obtain permeability and van Deemter plots. All calculations
including optimization of modulation times were carried out using
Microsoft Excel.
RESULTS AND DISCUSSION
Apparent Peak Capacity at 1D as a Function of Modulation
Time. It is important to understand that the peak capacity that
(18) Schoenmakers, P. J.; Vivo-Truyols, G.; Decrop, M. C. J. Chromatogr., A
2006, 1120, 282-290.
(19) Kohne, A. P.; Welsch, T. J. Chromatogr., A 1999, 845, 463-469.
(20) Holland, L. A.; Jorgenson, J. W. Anal. Chem. 1995, 67, 3275-3283.
(21) Opiteck, G. J.; Lewis, K. C.; Jorgenson, J. W.; Anderegg, R. Anal. Chem.
1997, 69, 1518-1524.
(22) Opiteck, G. J.; Jorgenson, J. W.; Anderegg, R. Anal. Chem. 1997, 69, 22832291.
(23) Kohne, A. P.; Dornberger, U.; Welsch, T. Chromatographia 1998, 48, 9-16.
(24) Haefliger, O. P. Anal. Chem. 2003, 75, 371-378.
(25) Wagner, K.; Miliotis, T.; Marko-Varga, G.; Bischoff, R.; Unger, K. K. Anal.
Chem. 2002, 74, 809-820.
(26) Wagner, K.; Racaityte, K.; Unger, K. K.; Miliotis, T.; Edholm, L. E.; Bischoff,
R.; Marko-Varga, G. J. Chromatogr., A 2000, 893, 293-305.
(27) Stoll, D. R.; Carr, P. W. J. Am. Chem. Soc. 2005, 127, 5034-5035.
(28) Tanaka, N.; Kimura, H.; Tokuda, D.; Hosoya, K.; Ikegami, T.; Ishizuka, N.;
Minakuchi, H.; Nakanishi, K.; Shintani, Y.; Furuno, M.; Cabrera, K. Anal.
Chem. 2004, 76, 1273-1281.
was actually reached in 1D is not maintained in a 2D-HPLC
separation, because a peak or a part of a peak is broadened to a
volume of a band to be injected into 2D in response to the
modulation time, modulation phase, and peak widths. This
phenomenon may contribute more strongly to the reduction of
the total peak capacity than any extracolumn band broadening
effect.
Several operational variables are mutually related in 2DHPLC: the 1D modulation period, PM, 2D retention factor (2k)
range, 2D linear velocity (2u), and 2D column length (2L). A smaller
PM better maintains peak capacity established after 1D separation.
However, it simultaneously dictates 2D parameters, imposing
practical limits upon the 2D operation conditions. For simplicity,
a 2D-HPLC system was examined with 1D gradient elution and
2D isocratic elution in this study. Gaussian peaks with a standard
deviation 1σ at 1D were assumed. In the following calculation, 1D
peak capacity was calculated by eq 2b, indicating peak capacity
actually obtainable within tG including the front half and the back
half of the first and the last peak, respectively.
1
n ) 1tG/1tW
(2b)
Gradient elution at 1D increases the peak capacity per unit time
by reducing 1D peak widths for later eluting peaks, thus maintaining peak widths within narrow ranges across the 1D chromatogram.2,29 For calculations, 1D peak widths (1tW ) 41σ) were
therefore approximated to remain constant. The 2D run times
(2tRmax) were assumed equal to PM. The calculation assumed
random elution of 1D peaks with respect to modulation intervals.17
The apparent 1D peak capacity (1napp) can be calculated from
the 1D gradient time (1tG) and the average apparent 1D peak width
(1tWapp) in two-dimensional chromatograms. The latter was calculated as a function of PM from the average increase in standard
deviation along the 1D retention axis, <σ*>, for a modulated band
taking into account a bandwidth of 81σ of a 1D peak, calculated
by the method of Seeley.17 In this method, an increase in the
standard deviation after the modulation of a 1D peak or a band
broadening factor, σ*, was calculated at a certain phase of the
modulation and the fraction size, assuming a certain PM. The
average of the band broadening factors, <σ*>, was then obtained
for the PM value by averaging σ* obtained for a series of at least
41 different phases per cycle of modulation that evenly divided
one PM. (See ref 17 for the detail of calculation.) The band
broadening factors, <σ*> values, for PM of up to 121σ and the
ratios of 1napp to 1n are plotted against PM/1σ in Figure 1. It can
be noted that the curve representing the band broadening factor
is nearly linear in a region of PM above 31σ.
One can readily get an idea on how much of peak capacity of
1D separations can be utilized in 2D-HPLC by employing a certain
modulation period relative to the standard deviation, PM/1σ, from
this figure. The plot for 1napp/1n indicates the percent remaining
1D peak capacity that can be termed as modulation efficiency (e ).
M
One can use the eM values in Figure 1 in combination with 1n and
2n to obtain total peak capacity of a 2D-HPLC system, which
reflects the reduction of the peak capacity along with 1D retention
axis by modulation. It is important to note that the apparent 1D
(29) Snyder, L. R. Anal. Chem. 1983, 55, 1412A-1430A.
Analytical Chemistry, Vol. 79, No. 10, May 15, 2007
3765
Figure 1. Plot of band broadening factor, <σ*>, and modulation efficiency, eM ) 1napp/1n ) 1/<σ*>, against the modulation period in the unit
of 1σ, PM/1σ. The <σ*> values were calculated by the method of Seeley17.
peak capacities, 1napp, are much smaller than conventionally
calculated. Further, it is clear that 1napp is monotonously declining
with increasing PM as shown in Figure 1.13 With decreasing PM,
1n
1
app approaches the maximal possible peak capacity, n.
Expected Total Peak Capacities in 2D-HPLC. Peak capacity
of the 2D separation is equally important as the 1D separation for
optimizing a 2D-HPLC system. Generally, the shorter the modulation periods are (or the higher the modulation frequency), the
lower peak capacity will be achieved at 2D, because the 2D
separation run time 2tRmax (elution time of the last peak at 2D) is
limited by the modulation period, PM. The 2D linear velocity of
mobile phase (2u), the 2D retention factor (2k) range, and 2D
column length (2L) need to be compatible with the pressure limit
of the pump and the 2D column properties.2,30,31 Peak capacity of
2D, 2n, can be obtained by eq 1a.
The expected total peak capacity of a 2D-HPLC system
(n2D-exp), which takes into account the effect of modulation, can
be calculated by eq 3 as a function of 2tRmax (equal to PM) by using
1n
2
app (Figure 1) and calculated D peak capacities (eq 1) assuming
full utilization of 2D separation from 2tM to 2tRmax, where 2N and 2tM
stand for the number of theoretical plates of the 2D column and
the elution time of an unretained solute in 2D separation,
respectively.
n2D-exp ) (1napp)(2n) ) eM(1n)(2n)
) (1tG/<σ*>1tW)[1 + (x2N/4) ln(2tRmax/2tM)]
(3)
Peak Capacity and Optimum Modulation Periods Observed for a 2D-HPLC with a Particle-Packed Column at 2D.
The following examples show how much peak capacity can be
expected along with an optimum PM value and which PM range
should be considered for practical optimization. Exemplary 2D
peak capacities are calculated for a particle-packed C18 column
by eq 1b for 2D isocratic elution, which is most practical for short
run time. For the calculation of 2N or a plate height (2H) in eq 1b,
(30) Neue, U. D.; Mazzeo, J. R. J. Sep. Sci. 2001, 24, 921-929.
(31) Thompson, J. D.; Carr, P. W. Anal. Chem. 2002, 74, 4150-4159.
3766
Analytical Chemistry, Vol. 79, No. 10, May 15, 2007
the Knox equation (eq 4) was used,32 where a reduced plate height
h is given by 2H/2dp and reduced velocity ν by 2u2dp/Dm (dp,
particle size; Dm, a diffusion coefficient of a solute assumed to be
10-9 m2/s). The 2D column dead time is detailed by 2tM as a
function of 2u and 2L. The resulting calculations for a 2.5-cm
column packed with 2- or 5-µm particles are presented in Figure
2 for a 2u range 0-12 mm/s and 2tRmax range of 0-90 s. (Contour
plots corresponding to Figure 2 are shown in Figure A of
Supporting Information.) Figure 2 indicates that higher 2D peak
capacities can be achieved with longer 2D run times and faster
2D linear velocities.
n ) 1 + (x2N/4) ln(2tRmax/2tM) )
2
1 + [(2L/2H)1/2/4] ln(2tRmax/2tM) (1b)
h ) ν1/3 + 1.5/ν + 0.05ν
(4)
In combination with 1D gradient separations producing 1tW )
5, 10, 30, and 60 s, peak capacities attainable in a 60-min run time
(1tG) were calculated for a 2D-HPLC system using 2D elution
examined in Figure 2 for a particle-packed C18 column. Peak
widths 1tW of 5-60 s in a gradient elution producing 1n of 60-720
in 1tG of 60 min include a commonly obtainable range, 1tW of 1030 s, by gradient elution in reversed-phase HPLC.30
Panels a-j in Figure 3 show practical examples of calculating
the expected total peak capacity (n2D-exp) for 2D-HPLC systems
in a 60-min separation time, calculated for cases 1tW ) 10 and 30
s, and for 2L of 0.5, 1, 2.5, and 5 cm for columns packed with 2- or
5-µm particles, plotted against 2u (1-12 mm/s) and 2tRmax (0-30
or 0-90 s). (Contour plots corresponding to Figure 3 are shown
in Figure B of Supporting Information.) Interestingly, longer
modulation periods can cause greater increases in 2D peak
capacity than decreases in 1napp in a region of PM of up to 2.22.41σ. The expected peak capacity n2D-exp sharply decreases for
PM below 1.51σ, whereas longer than optimal PM only resulted in
gradual decreases in peak capacity.
(32) Poppe, H. J. Chromatogr., A 1997, 778, 3-21.
Figure 2. 2n calculated as a function of 2u and 2tRmax by using eqs 1b, 1c, and 4 for isocratic elution, using a column packed with 2L ) 2.5 cm
for (a) 2-µm particles, (b) 5-µm particles, and (c) a monolithic silica C18 column, for a range 2u ) 1-12 mm/s and 2tRmax ) 0-90 s.
Panels a-c in Figure 3 show the plots of n2D-exp obtainable in
60 min for the case 1tW ) 10 s for a 0.5-, 1-, and 2.5-cm particulate
column at 2D, respectively, packed with 2-µm particles, and panels
d and e in Figure 3 the plots of n2D-exp for the case 1tW ) 30 s for
2.5- and 5-cm column at 2D, respectively. These column lengths
were found to be nearly optimum for each 1tW. The shorter 1tW
favors the shorter PM (or 2tRmax) and the shorter 2L and produces
the greater n2D-exp. Table 1 shows a summary of optimum PM and
n2D-exp for a wider range of conditions than shown in Figure 3.
For 1tW of 10 s, the optimum expected total peak capacity,
n2D-exp, was calculated to be ∼4660 with a high 2u and an optimal
PM of ∼2.41σ of a 1D peak for 2L ) 1 cm. For a linear velocity of
12 mm/s, slightly higher maximal peak capacities can be predicted
for a 1-cm 2L column compared to a 0.5- or 2.5-cm 2L column
(optimum PM at 1.91σ and 3.81σ, respectively), which in turn
provided a higher n2D-exp than a 5-cm 2L column (optimum PM at
∼6.31σ). For 1tW of 30 s, optimum n2D-exp was found at PM of ∼2.31σ
for 2L of 2.5 cm or at ∼31σ for 2L of 5 cm. The maximum estimated
n2D-exp is ∼2620 for 2L of 2.5 cm, greater than for 2L of 5 or 1 cm.
Panels f-h in Figure 3 show the plots of n2D-exp for the case
1t ) 10 s for a 0.5-, 1-, and 2.5-cm particulate column, respectively,
W
packed with 5-µm particles at 2D, and panels i and j in Figure 3
the plots of n2D-exp for the case 1tW ) 30 s for 2.5- and 5-cm column
at 2D, respectively. These column lengths were found to be close
to optimum for each 1tW for a 2D column packed with 5-µm
particles. For 1tW of 10 s, optimum n2D-exp was found for PM of
∼1.91σ for 2L of 0.5 cm, ∼2.31σ for 2L of 1 cm, or at ∼3.61σ for 2L
of 2.5 cm. The maximum estimated n2D-exp is ∼2410 for 2L of 1
cm and slightly higher than for 2L of 0.5 or 2.5 cm. For 1tW of 30
s, optimum n2D-exp was found for PM of ∼2.21σ for 2L of 2.5 cm or
at ∼2.91σ for 2L of 5 cm. The maximum estimated n2D-exp is ∼1330
for 2L of 2.5 cm, slightly greater than for 2L of 5 or 1 cm.
Similarly optimum PM values were calculated to be 2.31σ for
both 1tW of 5 s with a 0.5-cm 2D column and 1tW of 60 s with a
5-cm 2D column packed with 2-µm particles. The optimum PM was
found to be 2.21σ for both 1tW of 5 (2L ) 0.5 cm) and 60 s (2L ) 5
cm) for a 2D column packed with 5-µm particles. The calculated
optimum PM values in Table 1 were obtained with a 40-MPa
pressure limit, while those in parentheses for 2L of 2.5-10 cm
using 2-µm particles and for 2L of 10 cm with 5-µm particles require
greater pressure drop than 40 MPa to be realized. In most cases,
PM values of 1.51σ or smaller showed smaller n2D-exp than PM of
2.2-41σ for the 1tW and 2L range studied with either 2- or 5-µm
particles, or with a monolithic column as shown later.
Peak Capacity and Optimum Modulation Periods Estimated for a 2D-HPLC with a Monolithic Silica Column at
2D. The number of theoretical plates for a monolithic column at
2D was calculated by eq 1c from the experimentally determined
plate height equation for a 5-cm column, H ) 3.4 × 10-5 2u1/3 +
4.6 × 10-9/2u + 11.1 × 10-4 2u (eq 1c). Very similar plate height
values were observed for 1-, 2.5-, 5-, and 10-cm columns in a
methanol-water (80/20) mixture at 30 °C. The results for a 2.5cm column are shown in Figure 2c (and in Figure A of Supporting
Information).
n ) 1 + [{2L/(3.4 × 10-5 2u1/3 + 4.6 × 10-9/2u + 11.1 ×
2
10-4 2u)}1/2/4] ln[2tRmax/(2L/2u)] (1c)
Panels a-c in Figure 4 show the plots of n2D-exp for the case
) 10 s with 1n ) 360 for 0.5-, 1-, or 2.5-cm monolithic silica
column at 2D, panels d and e in Figure 4 the plots of n2D-exp for
the case 1tW ) 30 s for 2.5- or 5-cm column at 2D, and panels f
and g in Figure 4 the plots of n2D-exp for the case 1tW ) 60 s for
1t
W
Analytical Chemistry, Vol. 79, No. 10, May 15, 2007
3767
Figure 3. Expected total peak capacity (n2D-exp, eq 3) calculated for a 2D-HPLC system using gradient elution with 1tG ) 60 min and isocratic
elution of a particle-packed column at 2D packed with 2-µm (a-e) or 5-µm particles (f-j): (a, f) 1tW ) 10 s and 2L ) 0.5 cm, (b, g) 1tW ) 10 s
and 2L ) 1 cm, (c, h) 1tW ) 10 s and 2L ) 2.5 cm, (d, i) 1tW ) 30 s and 2L ) 2.5 cm, and (e, j) 1tW ) 30 s and 2L ) 5 cm.
5- or 10-cm column at 2D, plotted against 2u and 2tRmax. (Contour
plots corresponding to Figure 4 are shown in Figure C of
Supporting Information.) These column lengths were found to be
nearly optimum for each 1tW.
For 1tW of 10 s, optimum n2D-exp was found at PM of ∼2.31σ for
2L of 1 cm. The maximum estimated n
2
2D-exp is 2990 for L of 1
2
cm, slightly higher than for L of 0.5 or 2.5 cm. With the longer
1t of 30 s, the optimum P was found at 2.21σ but with a longer
W
M
2D column. The optimum peak capacity estimated, n
2D-exp, is 1660
3768 Analytical Chemistry, Vol. 79, No. 10, May 15, 2007
for 2L of 2.5 cm, slightly higher than that for 2L of 5 or 1 cm. A
similar tendency was observed with longer 1tW of 60 s, which can
be observed under gradient conditions of relatively low performance. The optimum peak capacity expected is still greater than
1100 with a 5- or 10-cm column at 2D with optimum PM to be 2.31σ
or longer.
For a range of 1tW of 5-60 s, including the range observed in
common gradient elutions, the advantage of employing relatively
long PM at ∼2.2-2.41σ has been observed for achieving maximum
Table 1. Optimum Modulation Period and Total Peak Capacity Expected Taking into Account the Effect of
Modulation in 2D-HPLC Using a Particulate Column or a Monolithic Silica Column (2L ) 0.5-10 cm) at 2D for
Gradient Elutions with 1tG ) 60 min and 1tW ) 5-60 s at 1Da
1t
2D
2L
column
particulate
2 µm
particulate
5 µm
monolithic
(Chromolith)
(cm)
0.5
optimum
PM (1σ)
w
)5s
n2D-exp
1t
w
optimum
PM (1σ)
) 10 s
1t
w
) 30 s
optimum
PM (1σ)
n2D-exp
1t
n2D-exp
w
) 60 s
optimum
PM (1σ)
n2D-exp
2.3
6740
1.9
4530
1.6
2170
1.4
1310
1
2.5
5
10
0.5
3.2
10.2 (6.2)
* (10.7)
* (*)
2.2
6420
3800 (5400)
* (4400)
* (*)
3570
2.4
5.9 (3.8)
* (6.3)
* (10.9)
1.9
4660
3250 (4310)
* (3760)
* (3070)
2360
1.8
2.9 (2.3)
7.5 (3)
* (4.8)
1.5 (2u ) 11.6)
2430
2190 (2620)
1380 (2560)
* (2330)
1110
1.6
2.2 (1.9)
4.5 (2.3)
* (3)
1.5 (2u ) 7.7)
1520
1560 (1750)
1130 (1840)
* (1800)
670
1
2.5
5
10
0.5
3
5.9
10.3
* (*)
2.3
3370
2790
2250
* (*)
4390
2.3
3.6
6
* (10.5)
1.9
2410
2210
1910
* (1550)
2920
1.7
2.2
2.9
5.4 (4.6)
1.6 (2u ) 8.5)
1240
1330
1290
1080 (1170)
1400
1.5 (2u ) 11.6)
1.9
2.2
3.3 (3)
1.5 (2u ) 6.3)
770
880
920
850 (900)
860
1
2.5
5
10
3.1
6
10.5
*
4160
3470
2810
*
2.3
3.7
6.1
10.7
2990
2760
2390
1950
1.8 (2u ) 11.9)
2.2
2.9
4.7
1550
1660
1620
1470
1.7 (2u ) 8.2)
1.9
2.3
3
970
1100
1160
1130
a Calculated with a 0.11σ increment for P of up to 121σ with a pressure limit of 40 MPa, assuming the diffusion coefficient of a solute to be 10-9
M
m2/s, the viscosity of mobile phase 0.001 Pa s, and the flow resistance factor 2φ ) 1000 for the particle-packed columns. Maximum n2D-exp values
2
obtained in a range of u of up to 12 mm/s are listed, unless noted otherwise. The values in parentheses correspond to optimum with an operating
pressure higher than 40 MPa. Asterisks indicate that optimum PM appeared at above 121σ.
expected total peak capacities irrespective of 1tW, as shown in
Figures 3 and 4. The observation is common for both a monolithic
column and a particulate column packed with 2- or 5-µm particles
at 2D. In all cases, a high efficiency 1D gradient separation, or the
shorter 1tW favors the shorter PM (or 2tRmax), but consistently at
2.2-2.41σ, and the shorter 2L, and is expected to produce the
higher n2D-exp based on the higher 1n, as shown in Table 1. The
PM longer than optimum, however, does not cause so much
reduction of n2D-exp as the PM shorter than optimum, as shown in
Figures 3 and 4 (also in Figures B and C of Supporting
Information). In all cases examined, ∼90% of optimum n2D-exp can
be obtained with longer PM of ∼41σ with smaller eM, using a longer
column. Longer PM and the use of a longer column will be
advantageous in terms of extracolumn band broadening and the
frequency of column-switching operation.
The selection of a column length also needs consideration of
column permeability. Monolithic silica columns of 1-10 cm cause
pressure drops of less than 32 MPa at 30 °C at 10 mL/min flow
rates of 80% methanol. More than twice the pressure drop can be
expected for equivalent 5-µm particle-packed columns, and much
higher for 2-µm particles. The region beyond 2u ) 6.4 mm/s in
Figure 3c and d, and beyond 2u ) 3.2 mm/s in Figure 3e (beyond
the dashed lines in Figure B of Supporting Information) cannot
be reached under pressure drop (2P) of 40 MPa, assuming the
viscosity of the mobile phase to be 0.001 Pa s, and a flow resistance
factor 2φ ) 1000 for the particle-packed columns.32 If 2D has to
be operated at a lower pressure, a shorter column and shorter
PM will be preferable. For a particle-packed column to be used
for 2D, attention should also be paid to the stability of a packed
bed. Some problems may be alleviated using monolithic silica
columns due to their high permeability and high stability of
continuous skeletons.6
In practice, (i) it is necessary to know 1tG and 1tW from 1D
gradient elutions and (ii) 2D parameters such as the range of
retention factors, 2k, and the relation of 2D plate height versus 2u.
Then optimizations may proceed as follows: (iii) calculate
expected total peak capacities n2D-exp against 2u and 2tRmax
according to eq 3, (iv) select the optimal column length, 2L, with
respect to achievable linear velocities at given column pressure
drop and pump flow rate parameters, and (v) select optimum
mobile-phase compositions to give high 2D retention,2k. Mobilephase compositions should be selected that enable the elution of
the last peak of interest at around 2tRmax.
Practical optimization should also take into account the effect
of extracolumn band broadening, which is expected to become
serious with a small-sized column. In this sense also, the use of
longer PM together with a longer column at 2D may be preferable,
when a pressure drop permits. A smaller number of fractions of
a single component may also be advantageous for quantification,
although it may be accompanied by ambiguity in 1tR and the loss
of peak shape information.17 On the other hand, shorter PM is
preferable for minimizing injection volume at 2D. The reduction
of the volume and the strength of 1D mobile phase that enters
into 2D should be kept in mind. Band broadening strongly depends
on the strength of 1D effluent as an eluent on the 2D column.
Global optimization of 2D-HPLC for PM,2dp,2k, 2L, and 2u, as well
as 1D gradient conditions, aiming at maximizing total peak capacity
in 2D-HPLC is beyond the scope of the present study. A selection
method for optimized operation conditions of 2D-HPLC has been
reported recently.18 Present study indicates that such an attempt
requires a consideration of a longer modulation period than
previously proposed.
The present results show that (i) modulation efficiency (eM)
calculated by the method of Seeley17 taking into account the
Analytical Chemistry, Vol. 79, No. 10, May 15, 2007
3769
Figure 4. Expected total peak capacity calculated for a 2D-HPLC system using gradient elution with 1tG ) 60 min at 1D and isocratic elution
of a monolithic silica column at 2D. (a) 1tW ) 10 s and 2L ) 0.5 cm, (b) 1tW ) 10 s and 2L ) 1 cm, (c) 1tW ) 10 s and 2L ) 2.5 cm, (d) 1tW ) 30
s and 2L ) 2.5 cm, (e) 1tW ) 30 s and 2L ) 5 cm, (f) 1tW ) 60 s and 2L ) 5 cm, and (g) 1tW ) 60 s and 2L ) 10 cm. Equations 1c and 3 were
used for calculations.
volume and phase of modulation is ∼50-70% at favorable PM of
2.2-41σ and (ii) the shorter 1tW favors the shorter PM (or 2tRmax)
and the shorter 2L, and is expected to produce the higher total
n2D-exp. Total peak capacities of 4600 can be expected after taking
into account the effect of modulations for a typical 2D-HPLC using
1D gradient with 1t of 10 s and 1t of 60 min and 2D isocratic
W
G
elution using a 1-cm column packed with 2-µm particles operated
at 12 mm/s, while a simple multiplication of 1D and 2D peak
capacities results in a potential maximum n2D of ∼6500 irrespective
of PM. The use of a 1- or 2.5-cm monolithic silica column at 2D
can produce n2D-exp of 2750-3000 under similar conditions.
The current method enables researchers with the effective
optimization of a 2D-HPLC separation based on fundamental
chromatographic parameters. Most importantly, it indicates that
in many cases ∼2.2-41σ band widths should be kept for modulation periods for the resolution of the greatest number of peaks as
well as facile operation. It is shown that peak capacities of a few
thousand can easily be achieved with conventional HPLC equipment which then outperforms current one-dimensional applications. The results also indicate that it is very important for an
instrument to be compatible with small-sized columns and fast
3770 Analytical Chemistry, Vol. 79, No. 10, May 15, 2007
gradient operations to be used at 2D for further increasing the
performance of two-dimensional separations. The calculations
presented here will render 2D-HPLC applications and method
development more practical, and thus more attractive, for analytical chemists.
ACKNOWLEDGMENT
This work was supported in part by Grant-in-Aid for Scientific
Research funded by the Ministry of Education, Sports, Culture,
Science and Technology, 14340234 and 17350036. The authors
thank Dr. Cabrera of Merck KGaA for helpful discussion. The
support by GL Sciences and Merck KGaA, Darmstadt, is also
gratefully acknowledged.
SUPPORTING INFORMATION AVAILABLE
Additional information as noted in text. This material is
available free of charge via the Internet at http://pubs.acs.org.
Received for review October 25, 2006. Accepted March 8,
2007.
AC062002T