456 GRADIENT ELUTION Table 9.4 Separation Conditions for Optimized Conditions in Figure 9.21a t G (min) d p (μm) L (mm) F (mL/min) k* PC a 1 0.6 10 1.8 3 170 3 0.8 30 1.4 3 230 10 1.1 80 1 3 310 30 1.4 170 0.8 3 400 100 1.9 420 0.6 3 540 300 2.5 960 0.4 3 710 1000 3.4 2400 0.3 3 960 Note: Column diameter of 4.6 mm is assumed, with a pressure of 6000 psi a Calculations based on h = v 0.33 + 2/v + 0.05v. The examples of Figure 9.21b can be more fully appreciated in terms of a relationship for gradient time. From Equation (9.5) we have t G = 1.15k ∗ V m ΔφS F (9.24) so a reduction in k ∗ results in a decrease in gradient time, and vice versa. A decrease in column length L (proportional to V m ) while holding pressure and k ∗ constant requires a proportionate increase in flow rate F, resulting in a decrease in gradient time that is proportional to L/F (or to L 2 ). In most cases, maximum or optimum values of PC for a given gradient time will require an intermediate particle size (e.g., 2.2 μm) or column length (e.g., 65 mm) that are unavailable, especially for a limited range of columns from a preferred source. However, the use of a moderately different particle size (2- or 3-μm) can be compensated by the use of sub-optimum values of k ∗ as above, with only a moderate loss in peak capacity. Similar plots as in Figure 9.21a,b result for the separation of higher molecular-weight samples, but with generally higher peak capacities and a need for still smaller particles. 9.3.9.2 Fast Gradient Separations Gradient separations with run times of a few min or less (sometimes referred to as ‘‘ballistic gradients’’ [59]) are needed for high-volume testing, where thousands of samples must be analyzed at acceptable cost—and therefore minimum run time. Short run times are also needed in two-dimensional HPLC (Section 9.3.10) for the second-dimension separation, in order to analyze a large number of fractions from the first-dimension separation, during the time required by the initial separation. As run time for a given assay is decreased below a few minutes, the performance of the equipment becomes limiting. Aside from previously discussed requirements of column length, flow rate, and particle size (in connection with Fig. 9.21), fast separations require (1) very small values of the dwell-volume V D ,(2)sample injections that can be performed within a second or two, (3) fast detector response 9.3 METHOD DEVELOPMENT 457 for peaks with W < 1 sec, (4) an ability to carry out very steep gradients (e.g., 1–2%B/sec; Fig. 17.28), and (5) rapid or off-line data processing (Section 3.8.4). Fast separations are normally limited to small values of the column plate number N ∗ or peak capacity PC, because possible values of PC decrease for shorter gradients (Fig. 9.21). However, small values of N ∗ or PC are still acceptable in many cases: • samples with fewer, easily separated components • following the extensive optimization of separation selectivity, especially the use of two or more conditions that affect selectivity (Table 2.2) • separations with a tolerance for small values of R s , because of either selective detection (e.g., LC-MS) or an acceptance of reduced accuracy in assay results • the second separation in 2D-HPLC Samples with only a few easily separated components can be assayed using smaller values of N ∗ . This can also be true for samples that contain a larger number of components, when separation selectivity has been extensively optimized (resulting in maximum values of α), and for separations with a tolerance for small values of R s .Thesecond separation in 2D-HPLC can often be carried out with a smaller value of N ∗ because the number of sample components will have been drastically reduced, their values of α tend to be larger for the second, orthogonal separation, and MS is often used for detection. Apart from the equipment needed for fast separation, the choice of column dimensions, particle size, and flow rate and the maximum allowable pressure for the system determine (in theory) the minimum separation time for a required value of PC. Thus the smallest available particles and highest possible pressure will (in principle) allow the fastest separation for some required sample resolution; see Figure 9.21a and the discussion of [60]. However, practical constraints for a given gradient system will qualify the latter conclusion to some extent (column lengths may be limited to some minimum value, flow rates cannot be greater than some maximum value, and extra-column effects cannot be entirely avoided). Finally, the equilibration time t eq between successive gradient runs must be made as short as possible (Section 9.3.7), which is predominantly a function of the equipment (its dwell volume and gradient rounding). Several reports [43, 59, 61–65] provide both examples and further experimen- tal details for ‘‘fast’’ gradient elution. Figure 9.22a shows the separation of a model sample in 1.6 minute, while Figure 9.22b shows the result of successive injections every 1.6 minute (arrows mark the time of each injection). The 5-μm-particle col- umn used in this example is not especially well suited for fast separation, but in this case fast separation is favored by large α-values—as might result from an extensive optimization of selectivity. Separation speed can also be enhanced by the use of higher temperatures (Section 2.4.1). 9.3.10 Comprehensive Two-Dimensional HPLC (with Peter Schoenmakers) Section 9.3.9 examined conditions (particle size, column length, flow rate) for maximum peak capacity within a given gradient time. Other conditions can be varied further to optimize relative retention and maximize critical resolution, as discussed in Section 9.3.3. However, even these steps will be insufficient for samples that contain hundreds or thousands of individual compounds—as in the case of 458 GRADIENT ELUTION 1 2 3 4 5 6 7 8 9 0 0.5 1.0 1.5 2.0 (min) 0 2 4 6 (min) (a) (b) #1 #2 #3 #4 #5 Figure 9.22 Example of fast gradient separation. Sample: 1, uracil; 2, acetone; 3, N-benzylformamide; 4–9,C 2 -C 7 alkylphenones. Conditions: 50 × 2.1-mm (5-μm) C 18 col- umn; 0 − 100% B in 1 min; A-solvent is 3/7/90% n-propanol/acetonitrile/water; B-solvent is 3/97/0% n-propanol/acetonitrile/water; 1.0 mL/min; 40 ◦ C. (a) single chromatogram; (b)suc- cessive injection of five samples at 1.6-min intervals. Arrows mark the time of each sample injection. Figures adapted from [43]. proteolytic digests of the human proteome (Section 13.4.5). In the latter case we require a considerable increase in peak capacity over that which can be achieved by a single separation (as in Figure 9.21). This increase in peak capacity can be achieved by two-dimensional HPLC (2D-LC), in which some or all fractions from an initial (first-dimension) gradient separation are collected and injected into a second (second-dimension) HPLC system with subsequent gradient separation. 2D-LC separation can be carried out off-line (collecting fractions) or on-line (column switching [Section 2.7.6] with one or two switching valves). If all fractions are subjected to the second-dimension separation, and if fractions are taken so frequently that the first-dimension separation is largely maintained, we have comprehensive two-dimensional liquid chromatography, conveniently abbreviated to LC × LC [66]. 9.3.10.1 Principles of LC × LC Some aspects of comprehensive 2D-LC are illustrated in Figure 9.23, where a portion (two peaks) from the first-dimension chromatogram is shown. A number of fractions (shaded rectangles) are collected across each peak, and each of these fractions is then injected into the second-dimension column—resulting in the chromatograms shown at the top of Figure 9.23 for each fraction (in this example, the second peak from the first separation is resolved into two peaks [i and j] by the second separation). The latter chromatograms are obtained using a single detector, which is positioned after the second-dimension column. The series of chromatograms (one for each fraction from the first-dimension separation) is stored in the computer, and the data can then 9.3 METHOD DEVELOPMENT 459 Second-dimension separation First-dimension separation Fractions i j Figure 9.23 Hypothetical example of comprehensive 2D separation of a single analyte. Sev- eral fractions are collected in the first-dimension separation for each peak; each fraction then occurs in several second-dimension chromatograms. Peaks i and j are present in the second peak of the first-dimension separation. be presented in various ways; for example, (quasi) three-dimensional, contour, or color plots. An example of a three-dimensional plot is shown in Figure 9.24a, where each peak or solute is defined by its retention time in the first- and second-dimension separations; peak absorbance (proportional to concentration) is shown by the height of each peak. In this case some of the data are obscured (small peaks behind larger peaks), but this can be overcome by computer-rotation of the plot. An example of a two-dimensional plot is shown in Figure 9.24b, with the data (as in Fig. 9.24a, but a different sample) now observed from above. Different shades represent different peak intensities (darker spots correspond to higher peaks, as in Fig. 9.24a). If a comprehensive two-dimensional analysis is performed automatically and in real time, the second-dimension separation must be much faster than the first-dimension separation. For example, if the first separation has a gradient time of 250 minutes, and 500 fractions (not an excessive number) are collected, the second separation can take no longer than 0.5 minute. If the fractions are collected by a fraction collector, they can be analyzed more slowly in the second dimension, but in that case the total analysis time can be very long. As can be seen in Figure 9.21a, a faster second-dimension separation means a much lower peak capacity; shorter columns, smaller particles, and higher flow rates are favored for the second separation. To achieve the full potential of 2D-LC (as measured by peak capacity), any separation accomplished in the first dimension must not be undone when the second-dimension separation is implemented [67]. That is, no remixing of the materials separated in the first dimension is allowed (even though each fraction from the first column can be assumed to be remixed during its transfer to the second column). An initial conclusion [68] was that each first-dimension peak must be sampled at least 4 times, in order to avoid a considerable loss in 2D peak capacity. However, this can lead to a very large number of collected fractions, 460 GRADIENT ELUTION 500 400 300 200 100 0 0 10 15 20 25 0 5 10 15 20 0 5 10 15 20 25 30 20 15 10 5 0 First dimension retention time (min) Second-dimension retention time (min) First-dimension retention time (min) mAU 2 nd Dimension retention time (sec) (a) (b) Figure 9.24 Examples of 2D separation. (a) Three-dimensional representation of a compre- hensive two-dimensional chromatogram of a mutant-maize extract; (b) gray-scale 2D plot from a comprehensive LC × LC separation of an indolic-metabolite standard mixture. with a corresponding increase in effort. A subsequent analysis of the effect of sampling frequency on peak capacity suggests that a better compromise is a sam- pling rate of two fractions per first-dimension peak [69], which still results in a 2-fold loss in total peak capacity [57] because of the smaller number of collected fractions. For a well-designed LC × LC separation (Section 9.3.10.4), a given component will be present in several of the serially collected fractions, and will therefore 9.3 METHOD DEVELOPMENT 461 appear in several sequential second-dimension chromatograms (as in Fig. 9.23). Each component must be correctly identified in the adjoining chromatograms, and its peak areas must be added for quantitative analysis [71]. Because (1) the peak is split into several fractions, (2) each fraction is diluted during the second-dimension separation, and (3) fast-gradient baselines are often problematic, detection can be a serious bottleneck for LC × LC. UV detectors have been popular for LC × LC, but detection with a mass spectrometer is much more powerful because of its advantages of peak identification and deconvolution (Section 4.14). 9.3.10.2 Peak Capacity As a rule of thumb, high-resolution one-dimensional LC allows peak capacities in the hundreds, whereas LC × LC provides peak capacities in the thousands. For example, by reference to Figure 9.21b, consider a 200-minute first-dimension separation, followed by 100 separations for 2 minutes in the second dimension. Assume a maximum column-pressure of 6000 psi; then the peak capacity PC for the first dimension will be about 650. Similarly, for the second dimension, PC ≈ 130, from which PC ≈ 650 × 130 ≈ 85, 000. However, the effective peak capacity n c will be much smaller for several reasons: • separations in the first and second dimension that are non-orthogonal • use of only part of the chromatogram • under-sampling of the first dimension When peak capacity for a 2D separation is calculated as the product of peak capacities for the two separations, it is assumed that the two separations are completely orthogonal (retention times in the first dimension independent of the retention times in the second dimension). In practice, this is never even approximately thecaseinLC× LC, especially for any non-ionizable compounds that are present in the sample [72]. Because only part of the chromatogram is filled with peaks, a further reduction in effective peak capacity results (as discussed in Section 9.3.9). Finally, it is impractical to collect enough fractions in the first dimension to completely avoid undersampling. Little control is possible over the above contributions to a loss of effective peak capacity; as a result values of n c for LC × LC have seldom exceeded ≈ 2000 at the time the present book was published. The latter number can be effectively increased, however, by the use of selective detection (e.g., LC-MS). The main challenge is to select two separations that are as nearly orthogonal as possible. This normally requires the use of two different separation modes (Section 9.5); for example, ion exchange for the first dimension, followed by RPC for the second dimension. Alternatively, if separation conditions can be made sufficiently orthogonal (as discussed in Chapters 5–7), two RPC separations may represent a comparable choice for maximum orthogonality in LC × LC. 9.3.10.3 Instrumentation for LC × LC Off-line LC × LC can be carried out with conventional instrumentation, as described in Section 13.4.5. LC × LC with valve-switching is a bit more complicated but more convenient. While one fraction is being analyzed on the second-dimension column, 462 GRADIENT ELUTION Loop 1 Waste Injector Pump 1 Pump 2 Loop 2 Column 1 Column 2 Detector Loop 1 Detector Waste Injector Pump 1 Pump 2 Loop 2 Column 1 Column 2 (a)(b) Figure 9.25 Possible valve configuration for LC × LC. In the first stage (a), loop 1 is loaded with effluent from the first-dimension column, loop 2 is connected between pump 2 and the second-dimension column. During the next stage (b), the contents of loop 1 are injected into the second-dimension system, while loop 2 is filled with effluent from the first-dimension column. a second fraction from the first separation is being collected, ready for the next injection. One popular arrangement employs a two-way, ten-port switching valve, as illustrated in Figure 9.25. In Figure 9.25a, loop 1 is loaded with effluent from column 1. When the valve is switched, the contents of loop 1 are flushed by pump 2 onto column 2. Thus a (second-dimension) chromatogram is obtained for the contents of loop 1. At the same time, loop 2 is being filled with the next fraction from column 1. When the valve is switched again (Fig. 9.25b), a second-dimension chromatogram is obtained for the contents of loop 2. If the loop size is significantly greater than the volume of a fraction, all of the fraction is collected in the loop and the total sample is separated and analyzed. If 2 t an is the second-dimension analysis time (also called the cycle time)and 1 F the flow rate in the first-dimension separation, the volume of the loop (V loop ) should meet the following criterion: V loop > 2 t an 1 F (9.25) An LC × LC system consists of two pumping systems, but only one detector is required. The detector must be both fast (small time constant) and sensitive—because of the dilution of the sample that occurs during two consecutive separations. 9.3.10.4 Method Development for LC × LC The selection of conditions for LC × LC proceeds differently than for 1D separation, where the primary goal is the optimization of separation selectivity for some 9.3 METHOD DEVELOPMENT 463 minimum resolution (e.g., R s ≥ 2) for all peaks of interest. For various reasons, this is not be practical for LC × LC. The main goals in developing a fully automated 2D separation include the following: • orthogonal conditions for the two separations • compatibility of the two mobile phases • selection of conditions for maximum peak capacity for each separation, within the constraints that the gradient time for the second separation will be limited to a small fraction of that for the first separation Orthogonal Conditions. RPC separates mainly on the basis of solute hydropho- bicity, while ion exchange chromatography (IEC) separates on the basis of molecular charge or ionization—the two separations can therefore be regarded as roughly orthogonal. For this and other reasons discussed below, these two separation modes are often used together for 2D-LC. Two RPC separations can also be made near-orthogonal, by selecting two orthogonal columns (Sect. 5.4.3) with different B-solvents, temperature, and especially pH [73]. Other possible combinations of separation conditions or modes are possible, but are subject to some of the problems discussed below. Mobile-Phase Compatibility. The sample solvent for the second dimension is the first-dimension mobile phase. Two important characteristics of the mobile phases for the first- and second-dimension separation are miscibility and elution strength. The injection of a significant volume of a solvent that is immiscible with the mobile phase—as when combining RPC with nonaqueous normal-phase chromatography—can lead to severe peak broadening and/or distortion. If the mobile phase associated with the fraction from the first dimension is a strong solvent for the second dimension (resulting in a small value of k), peak distortion and broadening can again occur in the second separation (Section 17.4.5.3). The use of IEC followed by RPC largely avoids problems with mobile-phase compatibility because the aqueous IEC mobile phase is (1) miscible with RPC mobile phases and (2) is a very weak RPC mobile phase. A starting point for the design of an LC × LC system is to select an acceptable first-dimension separation time (t G ) and pressure. From this we can estimate PC for this separation, as well as suitable conditions (particle size, column length, and flow rate; see Fig. 9.21a, Table 9.4, and the discussion of Sections 9.3.9.1). The resulting peak capacity allows an estimate of average peak width W (Eq. 9.20), which is of critical importance if we are to take several fractions for the first-dimension peak (as in Fig. 9.23). A good recommendation [69] is to choose two fractions for each peak (i.e., a collection time equal to w/2); for further information on the effect of fraction size on peak capacity, see [74]. If we know the time and the pressure available for the second-dimension separation, we can optimize the column and separation conditions in the same way as for the first separation. A possible optimized configuration for LC × LC is described in Table 9.5, which is somewhat more ambitious than contemporary practice at the time this book was published. Because the first-dimension separation of Table 9.5 is slow, the corresponding optimum column is long; ≈950 mm—or four 250-mm columns in series. In contrast, 464 GRADIENT ELUTION Table 9.5 Representative Conditions for an LC × LC Separation Parameter First Dimension Second Dimension a Pressure drop (psi) 6000 6000 Eluent viscosity (cPoise) 0.75 0.75 Analyte diffusivity (cm 2 /sec) 10 −5 10 −5 Gradient time 300 min 30 sec Column diameter (mm) 1 4.6 Injection volume (μL) 5 20 Flow rate (μL/min) 20 1500 Particle size (μm) 5 1.5 Column length (mm) 950 25 k ∗ 43 Peak capacity 700 100 Peak width (sec)/number of fractions 26 sec/1400 Dilution factor k = 011 k = 33.51 Injection band broadening (%) k = 021264 k = 3133 a Alternative choices are possible, with similar gradient times and peak capacities. the second-dimension column should be short (about 25 mm in the present example). Theparticlesizeisconventional(5μm) for the first dimension, but very small (1.5 μm) for the second dimension, because fast separations are favored by smaller particles (Fig. 9.21). Band broadening in the second dimension can be reduced by minimizing the volume of fractions from the first column—which is favored by a smaller diameter of the first column, relative to the second. However, this implies that peaks will be greatly diluted in the second separation (because the first, narrow-diameter column will have a smaller sample capacity). Thus selecting the column diameters means striking a balance between peak width and detection sensitivity. For further details, see [58]. 9.4 LARGE-MOLECULE SEPARATIONS The gradient separation of large molecules (peptides, proteins, nucleic acids, syn- thetic polymers, etc.) occurs in essentially the same way as for small molecules (100–1000 Da) [2]. Consequently changes in gradient or column conditions (t G , φ 0 , φ f ,F,L, etc.) will affect the separation of large-molecules in the same general way as discussed in Sections 9.1 through 9.3 for small molecules. Large molecules do have some special characteristics that play a role in their gradient separation 9.5 OTHER SEPARATION MODES 465 (Sections 13.3, 13.4.1.4). In this section we will examine one of these characteristics: the increase of values of S as solute molecular weight M increases, as described approximately by Equation (9.23) (see also Fig. 13.11 for some examples). The main consequence of an increase in S with M is its effect on values of k ∗ (Eq. 9.4). If gradient conditions are selected to give a value of k ∗ = 5fora small-molecule sample (as in Table 9.3), the same conditions for a large-molecule sample will result in a smaller value of k ∗ (because of larger values of S)and poorer resolution. To achieve the same value of k ∗ = 5 for a large-molecule sample, the gradient time must be increased, by the ratio of S-values for the two samples. For example, if M = 10,000 Da for the large-molecule sample, S will be about 0.25 × (10, 000) 0.5 ≈ 25 (Eq. 9.23). As S ≈ 4 for small molecules, the gradient time should be (25/4) = 6-fold larger for the large-molecule sample. If the gradient time for the small-molecule samples is 10 minutes (Table 9.3), this should be increased to about one hour for the large-molecule sample, in which case, k ∗ will also equal 5 for the large-molecule sample. Gradient separation of large-molecule samples thus require more time, or larger values of t G , other factors equal. Chapter 13 provides a detailed discussion of the separation of large-molecule samples (in most cases by gradient elution). 9.5 OTHER SEPARATION MODES Our discussion of gradient elution in Sections 9.1 through 9.4 has assumed RPC separation. Other separation modes exist, as summarized in Table 9.6. The gradient separation of small molecules by any of the procedures of Table 9.6 takes place in similar fashion as for RPC, so changes in gradient or column conditions will affect separation in approximately the same way as discussed in Sections 9.1 through 9.3 for RPC. For example, an increase in gradient time t G or flow rate F, or a decrease in column volume V m or gradient range Δφ, will increase k ∗ —with predictable consequences for average resolution or peak width (Eq. 9.4). 9.5.1 Theory For each of the separation modes of Table 9.6, isocratic values of k as a function of %B are given either by Equation (9.1) or by log k = log k B − n log φ (9.26) where log k B is defined in Table 9.6, n is a constant for a given solute and experimental conditions (also see Table 9.6), and φ refers to the volume fraction of the B-solvent (= 0.01% B; see Table 9.6 for a definition of the B-solvent for different separation modes). For linear-gradient separations that are described by Equation (9.26), the gradient retention factor k ∗ is given by [2] k ∗ = t G F 1.15[V m n log(φ f /φ 0 )] (9.27) . are subjected to the second-dimension separation, and if fractions are taken so frequently that the first-dimension separation is largely maintained, we have comprehensive two-dimensional liquid chromatography,. then injected into the second-dimension column—resulting in the chromatograms shown at the top of Figure 9.23 for each fraction (in this example, the second peak from the first separation is resolved into. second-dimension column, 462 GRADIENT ELUTION Loop 1 Waste Injector Pump 1 Pump 2 Loop 2 Column 1 Column 2 Detector Loop 1 Detector Waste Injector Pump 1 Pump 2 Loop 2 Column 1 Column 2 (a)(b) Figure