56 BASIC CONCEPTS AND THE CONTROL OF SEPARATION 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Time (min) 02 Time (min) 80% methanol (0.3 ≤ k ≤ 0.8) 70% methanol (0.8 ≤ k ≤ 2.3) 60% methanol (1.8 ≤ k ≤ 6.6) 50% methanol (4 ≤ k ≤ 19) (a) (b) (c) (d ) 1 2 3 4 5 1 2 3 4 5 t 0 0246 Time (min) 1 2 3 4 5 51015 1 2 3 4 5 0 Time (min) Figure 2.18 Separation as a function of mobile phase %B. Herbicide sample: 1, monolinuron; 2, metobromuron; 3, diuron; 4, propazine; 5, chloroxuron. Conditions, 150 × 4.6-mm, 5-μm C 18 column; methanol-water mixtures as mobile phase; 2.0 mL/min; ambient temperature. Recreated chromatograms from data of [7]. R s reported in this book are always calculated from Equation (2.23). Equation (2.24) will be used mainly for an understanding of how resolution depends on various experimental conditions, and as a guide for systematic method development. An alternative expression for R s in Equation (2.24) is R s = 1 4  k 1 + k  α − 1 α  N 0.5 (2.25) The derivations of Equations (2.24) and (2.25) are based on different approximations concerning the widths of the two peaks, and each equation has a similar accuracy. Equation (2.24) has the advantage of greater simplicity for use in guiding method development. The development of an isocratic HPLC method proceeds by systemati- cally adjusting (‘‘optimizing’’) experimental conditions until adequate separation is achieved, preferably with a critical resolution R s ≥ 2. Equation (2.24) provides a 2.5 RESOLUTION AND METHOD DEVELOPMENT 57 useful guide for isocratic method development, as will be explored in Sections 2.5.1 through 2.5.3. Each of terms a–c of Equation (2.24) can be controlled by varying certain separation conditions (Table 2.2). Usually the first step is to choose a column with a sufficient plate number that is likely to separate a sample of the required com- plexity. In many cases, N ≈ 10, 000 is a good starting point, and this can be achieved either with a 150-mm long column packed with 5-μm particles, or a 100-mm, 3-μm column. The solvent strength (%B) is next varied to achieve an appropriate range in values of k (e.g., 1 ≤ k ≤ 10), followed by optimizing selectivity (α). Finally, the column plate number N can be adjusted for a best compromise between the conflicting goals of increased resolution vs. a shorter run time. The final separation conditions we select are hardly ever truly optimum (the best possible). However, the term ‘‘optimized’’ is often used in the literature to indicate a relatively improved or preferred separation rather than an absolute best separation. We should also note the difference between ‘‘local’’ and ‘‘global’’ optimizations. Local optimization refers to obtaining best values of one or two (seldom more) separation conditions over a limited range in values of each condition, while other (usually nonoptimal) conditions are held constant. Global optimization refers to best-possible values for all conditions that can affect separation or resolution. When chromatographers report an ‘‘optimized’’ procedure, they almost always are using this term to describe an improved separation or local optimum. We will continue this usage in the present book; that is, ‘‘optimum’’ will not be the same as a global best value of resolution. 2.5.1 Optimizing the Retention Factor k (Term a of Eq. 2.24) Sample retention k in isocratic elution is usually controlled by varying the mobile-phase composition (%B). The first step is to achieve values of k for the sample that are neither too small nor too large. Relative values of resolution R s (Eq. 2.24) and peak height h p (Eq. 2.11) are plotted against k in Figure 2.19, as a way of showing how these two quantities vary with k (assuming no change in α with k). Two peaks at the bottom of Figure 2.19 illustrate how resolution and peak height change when %B is decreased so as to change the average value of k from 1 to 10. The usual separation goal is k ≤ 10 for all peaks because this corresponds to narrower, taller peaks for improved detection, as well as short run times so that more samples can be analyzed each day. Values of k<<1 can result in poor resolution, especially from the possible overlap of analytes with matrix interferences that typically accumulate near t 0 (as in the ‘‘junk’’ peak of Fig. 2.5b). Therefore 1 ≤ k ≤ 10 is usually a goal for all peaks in the final separation (when method development has been completed). However, at the option of the chromatographer, it is possible to expand this preferred retention range somewhat, for example, to 0.5 ≤ k ≤ 20. Alternatively, regulatory agencies may recommend k ≥ 2 for all peaks of interest in the chromatogram [46], in order to minimize possible interference from sample excipients or other non-assayed (‘‘junk’’) peaks that elute near t 0 . Similarly, for separation with mass spectrometric detection (LC-MS), it is recommended that k ≥ 3 because of the possibility of ion-suppression effects. When it is found that all peaks of interest cannot be accommodated within some maximum range in k (e.g., 0.5 ≤ k ≤ 20), it is then necessary to use gradient elution (Section 2.7.2, Chapter 9). 58 BASIC CONCEPTS AND THE CONTROL OF SEPARATION R s , h p 1.0 0.8 0.6 0.4 0.2 0.0 0246810 k relative R s [k /(1 + k)] relative peak height h p , [1/(1 + k)] k = 1 k = 10 Figure 2.19 Relative resolution R s andpeakheighth p as a function of k orruntime.Runtime is proportional to the value of 1 + k for the last peak, and α is assumed constant. The effect of a change in %B on separation is illustrated in Figure 2.18 for RPC. With 80% methanol/water (80% B) as the mobile phase (Fig. 2.18a), values of k are small (0.3 ≤ k ≤ 0.8), and as a result the sample is poorly resolved (R s = 0.8). With 50% B (Fig. 2.18d;4≤ k ≤ 19), the sample is very well resolved (R s = 3.9), but the run time is longer than necessary, and later peaks are wide (and short)—with reduced detection sensitivity. An intermediate mobile phase (60% B; Fig. 2.18c) provides an acceptable range in k (1.8 ≤ k ≤ 6.6) with a reasonable compromise among resolution (R s = 2.6), detection sensitivity, and run time (6 min). A mobile phase between 60% and 70% B might be an even better choice, offering R s > 2.0 with a shorter run time and increased detection sensitivity. Changes in RPC retention with change in %B (as in Fig. 2.18) can be described by the empirical relationship [47] log k = log k w − Sφ (2.26) where φ is the volume fraction of the B-solvent (equal to 0.01 × %B), k w is the extrapolated value of k for solute X with water as the mobile phase (for φ = 0), and S is a constant for a given compound when only φ is varied. For a review of the historical development of Equation 2.26, see [48] and references therein. For ‘‘small’’ molecules with molecular weights of 100 to 500 Da, S ≈ 4 [49]. An increase in φ by 0.1 unit (e.g., a change in the mobile phase by +10% B) will therefore result in an average decrease in k for all peaks in the sample by a factor of approximately 10 (0.1×4) , or about 2.5-fold. The latter relationship suggests a systematic procedure for arriving at a satisfactory value of %B so that 1 ≤ k ≤ 10 (or any other desired range in k)isachieved. By this procedure, an initial separation or ‘‘run’’ can be carried out with 80% or 90% B, which usually ensures that the entire sample will be eluted from the column in a short time. In the separations of Figure 2.18, for example, the initial 2.5 RESOLUTION AND METHOD DEVELOPMENT 59 run (Fig. 2.18a) with 80% B gives a retention range for the sample of 0.3 ≤ k ≤ 0.8. Applying the rule of a 2.5-fold increase in k for each 10%B decrease, we can estimate values of k for lower %B as follows: for 70% B, 2.5 × 0.3 ≈ 0.8for peak 1 (first peak) and 2.5 × 0.8 ≈ 2.0 for peak 5 (last peak), or 0.8 ≤ k ≤ 2.0. For 60% B, a similar calculation based on the run with 70% B gives 2.0 ≤ k ≤ 5. The latter predicted range in k is well within the desired range of 1 ≤ k ≤ 10 (as is the observed range of 1.8 ≤ k ≤ 6.6); therefore the second method development experiment should use 60% B as mobile phase (other conditions being the same). For samples that are much less strongly retained than this sample, the initial experiment with 80% B might yield k ≈ 0 for all peaks in the chromatogram (i.e., a single peak that comprises all of the sample components). In this case a decrease in %B of at least 30% B will be required for acceptable values of k; the second experiment might therefore substitute (80–30% B) = 50% B as mobile phase, followed by further changes in %B for 1 ≤ k ≤ 10—as in the example above based on Figure 2.18. Because of the approximate nature of the ‘‘rule of 2.5,’’ it is best not to change %B by > 30% B between experiments, or late-eluting peaks may be missed for values of %B that are too low. An alternative (usually preferred) approach for selecting a suitable value of %B makes use of gradient elution for the initial experiment in method development (Section 9.3.1). 2.5.2 Optimizing Selectivity α (Term b of Eq. 2.24) When a further improvement of the separation is needed, relative retention (peak spacing, selectivity, or separation factor α) is next adjusted by varying any of the first seven conditions of Table 2.2: %B, the choice of B-solvent (usually methanol or acetonitrile), temperature, column type, or—for samples that contain acids or bases—mobile phase pH, buffer concentration, and ion-pair reagent concentration. Note in Table 2.2 that changes in each of these conditions can also result in changes in k, so the mobile phase %B may require simultaneous, further adjustment in order to maintain values of k within an acceptable range in k (usually no greater than 0.5 ≤ k ≤ 20). Figure 2.20 provides an illustration of varying selectivity for the separation of a sample that contains six components. In this example, %B was initially varied to achieve 2 ≤ k ≤ 4 for the separation of Figure 2.20a. We will further vary %B and temperature as means for improving selectivity and resolution. For a mobile phase of 45% B and a temperature of 30 ◦ C (Fig. 2.20a), peak-pairs 1–3 and 5/6 are poorly resolved (R s = 0.3). A decrease in %B (30% B, Fig. 2.20b)resultsina better separation of all six peaks, an acceptable retention range (4 ≤ k ≤ 12), but with marginal resolution of peaks 3 and 4 (which were well resolved in Fig. 2.20a). A reversal of the positions of peaks 5 and 6 also occurs in Figure 2.20b.Wecan see from these two chromatograms that an intermediate value of %B is likely to improve resolution, by moving peaks 3 and 4 apart—before peak-pairs 1/2 or 5/6 come together. In fact a mobile phase of 33% B (and 30 ◦ C) for this sample results in a significant increase in resolution (R s = 2.1, not shown). If temperature is increased from 30 to 45 ◦ C (Fig. 2.20c,same%BasFig.2.20a), further changes in relative retention or selectivity result, but the overall separation is poor (R s = 0.4). If the resolution of this sample is explored further, by trial-and-error 60 BASIC CONCEPTS AND THE CONTROL OF SEPARATION 45% B, 30°C 2 ≤ k ≤ 4, R s = 0.3 30% B, 30°C 4 ≤ k ≤ 12 R s = 1.4 45% B, 45 1 ≤ k ≤ 34 R s = 0.4 C 20% B, 47 4 ≤ k ≤ 20 R s = 4.0 1 024 Time (min) 0246810 Time (min) 1 + 2 + 3 4 6 2 3 4 6 5 1 02 Time ( min ) 0 2 4 6 8 10121416 18 Time ( min ) 1 + 2 3 4 5 + 6 2 4 3 6 5 (a)(b) (c)(d ) t 0 5 C Figure 2.20 Effect of mobile phase %B and/or temperature on the isocratic separa- tion of a six-component sample. Sample: 1, 3-phenylpropanol; 2, 1-nitropropane; 3, oxazepam; 4, p-chlorophenol; 5, eugenol; 6, methylbenzoate. Conditions: mobile phase is acetonitrile-water; 150 × 4.6-mm C 18 column (5-μm particles); 2.0 mL/min; see figure for values of %B and temperature (changed conditions bolded in Figs. 2.20b–d). Note that peak heights are normalized to 100% for tallest peak in each chromatogram. Simulated chro- matograms based on data of [50, 51]. changes in both %B and temperature, it is possible to achieve a maximum resolution of R s = 4.0 for 20% B and 47 ◦ C (Fig. 2.20d), provided that we allow a k-value as high as 20. The goal of improving selectivity (as in the examples of Fig. 2.20) can be an increase in resolution, a decrease in run time, or (usually) both. The selection of conditions for acceptable separation (i.e., method development) should emphasize changes in selectivity, which can be used for simultaneous improvements in both resolution and run time. This will be especially true for samples that are more difficult to separate—those with a large number of components (and a crowded chromatogram), or peaks with very similar retention (e.g., isomeric compounds). 2.5.2.1 ‘‘Regular’’ and ‘‘Irregular’’ Samples The present section can be useful as an aid in interpreting separation as a function of %B (especially in gradient elution). However, this topic is not essential for using or developing RPC methods. For that reason some readers may prefer to skip to Section 2.5.3, andreturntothissectionatalatertime. Samples for reversed-phase separation can be classified as either ‘‘regular’’ or ‘‘irregular’’ [52]. When only %B is varied for a ‘‘regular’’ sample, the chromatogram appears to expand and contract like an accordion, with little, if any, change in the spacing of peaks within the chromatogram. The separations of Figure 2.18 provide a good example for this ‘‘regular’’ sample (a mixture of herbicides). The sample of Figure 2.20, on the other hand, shows a reversal of retention for peaks 5 and 6 when %B is changed (Fig. 2.20b vs.Fig.2.20a), as well as less pronounced changes in the relative retention of peaks 1 to 4. This sample can therefore be described as 2.5 RESOLUTION AND METHOD DEVELOPMENT 61 ‘‘irregular,’’ in contrast to the ‘‘regular’’ sample of Figure 2.18. A change in %B affects relative retention (or selectivity) for ‘‘irregular’’ samples but not for ‘‘regular’’ samples. Because of the possibility of peak reversals and peak misidentification for ‘‘irregular’’ samples, peak tracking (Section 2.6.4) becomes more difficult for such samples. ‘‘Regular’’ samples are usually mixtures of structurally related compounds, whereas ‘‘irregular’’ samples are mixtures of more dissimilar molecules—as in Figure 2.20 for this mixture of several compounds of unrelated structure. Never- theless, predictions of whether a sample is regular or irregular are often uncertain; experiments where %B is varied as in Figure 2.18 are required for reliable answers to this question. Regular and irregular samples can also be defined by means of Equation (2.26). Regular samples will show a strong correlation of values of S and log k w for a given sample (i.e., diverging, near parallel plots), whereas irregular samples will show a poor correlation (i.e., intersecting plots). Many samples show a behavior that is intermediate between the examples of Figures 2.18 and 2.20, with less pronounced changes in relative retention as %B changes. For further informa- tion concerning regular and irregular retention behavior, see Section 6.3.1 (isocratic elution) or Section 9.2.3 (gradient elution). 2.5.3 Optimizing the Column Plate Number N (Term c of Eq. 2.24) 2.5.3.1 Effects of Column Conditions on Separation When selectivity has been adjusted for optimum peak spacing and maximum sample resolution (Section 2.5.2), an adequate separation will often result. Yet a further improvement in separation may be possible by varying column conditions (column length, flow rate, particle size), so as to improve the column plate number N (term c of Eq. 2.24). Note that relative retention and peak spacing (values of k and α) will remain the same when only column conditions are changed for isocratic separation; as a result the optimized peak spacing achieved previously by varying α (term b of Eq. 2.24) will not be compromised. An increase in N leads to an increase in resolution (Eq. 2.24), and usually a longer run time. Conversely, a decrease in N can provide a shorter run time—which may be of interest when R s  2 after optimizing selectivity (see below). Other factors equal, values of N are proportional to column length (Eq. 2.12) and generally increase for a decrease in flow rate or particle size. Run time is proportional to t 0 (Eq. 2.5 ) when k does not change, and t 0 is proportional to L/F (Eq. 2.7). Therefore run time increases proportionately for an increase in column length or a decrease in flow rate. Similarly the pressure drop P increases for an increase in column length or flow rate, or a decrease in particle size (Eq. 2.13a). Consequently we need to balance run time, resolution, and pressure when we vary column conditions in order to improve separation (Section 2.4.1.2). As an example of an increase in sample resolution by a change in column conditions, consider the separation of Figure 2.20b,whereR s = 1.4. In the absence of an improvement in selectivity (as in Fig. 2.20d)—which may not be readily possible for some samples—an increase in column length can always be used to increase resolution. Figure 2.21a shows the result of an increase in column length from 150 mm in Figure 2.20b to 300 mm (e.g., by using two 150-mm columns connected in series). Baseline separation is now achieved, with R s = 1.9. 62 BASIC CONCEPTS AND THE CONTROL OF SEPARATION 010 20 Time (min) (a) (b) (c) 024 Time (min) 0.2 0.4 0.6 0.8 Time (min) 300-mm column, 5-μm particles 2 mL/min, P = 1700 psi R s = 1.9, run time = 20 min 50-mm column, 5-μm particles 3.0 mL/mi, P = 480 psi R s = 2.0, run time = 4 min 30 × 1.0-mm column, 1.5-μm particles 0.5 mL/min, P = 11,000 psi R s = 2.0, run time = 0.7 min Figure 2.21 Use of a change in column length or flow rate to either increase resolution or decrease run time. (a) Separation of Figure 2.20b with an increase in column length from 150 to 300 mm, other conditions the same; (b) separation of Figure 2.20d with a decrease in col- umn length from 150 to 50 mm, and an increase in flow rate from 2.0 to 3.0 mL/min, other conditions the same; (c)sameas(b) except high-pressure operation and a 30 × 1.0-mm col- umn with a flow rate of 0.5 mL/min; column conditions are noted in the figure. Simulated chromatograms based on data of [50, 51]. Although the latter resolution is marginally less than our recommended minimum value (R s ≥ 2.0), it should prove acceptable for most applications. The cost of this increased resolution is a doubling of both run time (to 20 min) and pressure (to 1700 psi). In this example the increase in pressure is acceptable. When optimizing α as in Section 2.5.2, it is often advisable to strive for excess resolution, since this can later be traded for a shorter run time, by using a shorter column and/or a higher flow rate. An example of a change in column conditions that can reduce run time is provided by the separation of Figure 2.20d,whereR s = 4.0. By shortening the column 3-fold (from 150 to 50 mm) and increasing the flow rate 1.5-fold to 3 mL/min, the run time is decreased 4.5-fold to 4 minutes (Fig. 2.21b). At the same time the resolution is acceptable (R s = 2.0), and so is the pressure (P = 480 psi). Many samples will have fewer, more widely separated peaks than in this example, allowing their separation in less than a minute by a suitable choice of column conditions. 2.5 RESOLUTION AND METHOD DEVELOPMENT 63 In the past many laboratories have preferred columns packed with -5μm particles. Such columns are less demanding in terms of equipment (Section 3.9), and are less likely to be plugged by particulates. Today, however, there is increasing use of columns packed with 3-μm particles or smaller (see following Section 2.5.3.2). If a change in column conditions is made for either higher resolution or a faster run time, the same column packing (e.g., Symmetry C18) is strongly recommended,in order to avoid any change in column selectivity (Section 5.4). For further details on the choice of column conditions, see Section 2.4.1.2. 2.5.3.2 Fast HPLC There is increasing emphasis on very fast separations; for instance, with run times of less than a minute for relatively simple samples (<10–15 components), or a few minutes for more complex mixtures. Assuming the availability of suitable equipment and optimized column conditions, the time required by a separation depends on the value of k for the last peak and the value of α for the least resolved (‘‘critical’’) peak-pair. Once ‘‘best’’ values of k and α have been established (optimization of selectivity), resolution and run time depend only on N. Conditions that favor fast separation include small particles, short columns, and high flow rates. Further decreases in run time (with no loss in N) can be achieved by one or more of the following options: • ultra-high pressure ( > 6000 psi) • higher temperature • particles of special design High-Pressure Operation. It should be clear from Figure 2.15 and the discussion of Section 2.4.1.1 that a higher pressure can be used to decrease run time, with no loss in N (or resolution). As in the case of separations at lower pressures, small particles should be combined with (relatively) short columns and higher flow rates for fast separation. The use of higher pressures than can be achieved by conventional HPLC systems (with maximums of 6000 psi or 400 bar) is referred to as ultra–high-pressure liquid chromatography, or U-HPLC. U-HPLC, with pressures > 6000 psi can be used for either better resolution (higher values of N) or reduced run time, as first reported by Rogers [53] and more fully developed by Jorgenson [54]. Commercial HPLC equipment was later introduced that allows operation at pressures of 15,000 psi or more. As an example of how run time can be reduced with the help of high-pressure operation, Figure 2.21c shows the separation of the sample of Figure 2.20d,usinga 30 × 1.0-mm column, packed with 1.5-μm particles, and a flow rate of 0.5 mL/min; the resulting pressure is 11,000 psi. A run time of only 0.7 min is achieved (vs. 17 min originally), while maintaining a resolution of R s = 2.0. When this result is compared with the separations of Figs. 2.21a,b, the potential value of higher pressure operation should be apparent. (Note that some commercial U-HPLC systems are limited to flow rates of ≤ 5 mL/min, so smaller diameter columns generally are used to enable high mobile-phase linear velocities for fast separations.) Several similar examples have been reported [21], where reductions in run time of 2- to 6-fold were achieved by the use of ultra–high-pressure operation. 64 BASIC CONCEPTS AND THE CONTROL OF SEPARATION However, it should be noted that certain assumed relationships begin to fail significantly as the column pressure increases beyond 5000 psi [55]. Mobile-phase viscosity increases with pressure, so pressure no longer increases proportionately with flow rate. Values of k and α become pressure dependent [1], and therefore dependent on column conditions; this is less noticeable at lower pressures. Finally, heat is generated when a liquid flows through a packed column, and this heat is proportional to the pressure drop across the column. Changes in temperature within the column can have adverse consequences on peak shape and plate number [56], as well as further change values of k and α (undesirable!). While higher pressure operation has very definite potential advantages, it requires special equipment (Section 3.5.4.3) and columns (Section 5.6.2). High-pressure operation has also been claimed to complicate method development [1, 55]. This is because values of k, diffusion coefficients D m , mobile-phase viscosity, and other properties that affect separation, are more dependent on pressure, which usually increases during column use (at lower pressures, these properties can be regarded as essentially independent of pressure). For these and other reasons (safety, regulatory, cost, and special problems associated with the use of very high pressures), the extent to which U-HPLC is likely to replace HPLC in the routine laboratory was not clear at the time this book was published. High-Temperature Operation. HPLC separation is usually carried out at tem- peratures between ambient and 50 ◦ C. The selection of a specific temperature within this range is often made on the basis of optimum selectivity (as in the example of Fig. 2.20d). The use of higher separation temperatures (e.g., > 100 ◦ C) has been suggested as a means of shortening run time and improving resolution, as a result of an increase in N per unit time for a given pressure [57–59]. If we consider Figure 2.15 again, we recall that run time, the plate number N, and column pressure are all interrelated. Provided that we select a particle size, column length, and flow rate for maximum plates per unit time (i.e., ‘‘optimum’’ use of the column, with ν ≈ 3), the value of N increases for higher temperatures. An increase in temperature results in both a decrease in mobile-phase viscosity (Appendix I) and an increase of the solute diffusion coefficient D m . A lowering of mobile-phase viscosity allows a higher flow rate for the same pressure (Eq. 2.13a), which is equivalent to an increase in pressure (as in U-HPLC). An increase in D m results in the same value of N at a higher flow rate and shorter run time (Fig. 2.11b). Consequently an increase in temperature can, in principle, be used to shorten run time while maintaining the same value of N—or increase N while maintaining run time the same. The advantages of high-temperature operation are offset by some correspond- ing disadvantages. First, HPLC at near-ambient temperatures was often selected in the past because of a concern that sample degradation might occur during separa- tion at higher temperature. Although this is a potential complication which many chromatographers might prefer to avoid, the probability of such sample degradation is undoubtedly low for most samples [60–62]. A second problem in the use of higher separation temperatures is the possibility of radial temperature gradients within the column. Without careful thermostating of both the column and the entering mobile phase, severe peak distortion can result (Section 3.7.1). Radial temperature gradients represent a more serious problem when column temperature is increased, although 2.5 RESOLUTION AND METHOD DEVELOPMENT 65 the problem can be minimized by the use of narrower diameter columns that allow faster equilibration of the column temperature. A third problem is column instability at higher temperatures, especially for a mobile phase pH outside the range of 2 to 8. Finally, selectivity generally decreases for higher temperatures, although this may not be true for selected peak-pairs in the chromatogram. The ‘‘best’’ temperature will often represent a compromise between maximum N and maximum α. Particles of Special Design. A number of column configurations exist, apart from the commonly used fully porous particles: columns packed with either pellicular or shell (superficially porous) particles (Section 5.2.1.1), and monolithic columns (Section 5.2.4). The relative advantages of each of these different column types will be discussed (Section 5.2). Pellicular and shell particles can be especially advantageous for large-molecule separations because of a reduced contribution of the Cν term of Equation (2.17). Pellicular columns have a thin coating of porous packing material on a solid bead and are easily overloaded, which restricts their use to very small samples. Shell columns have a thicker coating of porous packing than pellicular columns and can be used with sample loadings that are almost as large as those for fully porous columns. Monolithic columns are much more permeable than particulate columns, which allows higher flow rates and faster separation, other factors being equal. The relative merits of these and various conventional columns can be evaluated by means of Poppe plots as in Figure 2.14b. 2.5.4 Method Development The preceding discussion of Sections 2.5.1–2.5.3 deals with the selection of experi- mental conditions for an acceptable HPLC separation, primarily one with baseline resolution and a reasonable run time. Adequate separation by itself, however, is not the complete story; other steps are often involved in method development [44]: • assessment of sample composition and separation goals • sample pretreatment • selection of chromatographic mode • detector selection • choice of separation conditions • anticipation, identification, and solution of potential problems • method validation and the determination of system suitability criteria Some of these steps may not be required, or they may need only minimal attention. ‘‘Difficult’’ samples and/or demanding assay procedures may involve more than simply following the steps outlined above and detailed in other chapters of this book. That is, special problems may arise during method development that require a logical response, based on the chromatographer’s prior experience and familiarity with or access to the literature. For some such examples of method development, see [62, 63]. 2.5.4.1 Assessment of Sample Composition and Separation Goals At the start of method development, available information about the chemical composition of the sample should be reviewed. If acidic or basic compounds are . laboratories have preferred columns packed with -5μm particles. Such columns are less demanding in terms of equipment (Section 3.9), and are less likely to be plugged by particulates. Today,. 2.20b.Wecan see from these two chromatograms that an intermediate value of %B is likely to improve resolution, by moving peaks 3 and 4 apart—before peak-pairs 1/2 or 5/6 come together. In fact a mobile. peak heights are normalized to 100% for tallest peak in each chromatogram. Simulated chro- matograms based on data of [50, 51]. changes in both %B and temperature, it is possible to achieve a maximum