466 GRADIENT ELUTION Table 9.6 Dependence of k on %B for Different Separation Modes (Eq. 9.1 or 9.26) Separation Mode Dependence of Definition of k w (Eq. 9.1) Dependence of S or k on %B or k B (Eq. 9.26) n on the solute Reversed-phase (RPC) Eq. (9.1) (k w ) value of isocratic k for A-solvent (water or buffer) as mobile phase S increases with solute molecular size (Eq. 9.21) Normal-phase (NPC, Chapter 7) Eq. (9.24) (k B ) value of isocratic k for B-solvent (more polar solvent) as mobile phase n increases with the number of polar groups in the solute molecule (Section 8.2) Ion-exchange (IPC, Chapter 7) Eq. (9.24) (k B ) value of isocratic k for mobile phase with salt concentration (φ) = 1.00 M n = number of charges on solute molecule (assumes mono-valent buffer) Hydrophobic interaction (HIC, Chapter 13) Eq. (9.1) (k w ) value of isocratic k for A-solvent as mobile phase (higher salt concentration) S ≈ 0.14M 0.37 [2] Hydrophilic interaction (HILIC, Chapter 8) Eq. (9.24) (k B ) value of isocratic k for A-solvent (organic) as mobile phase n increases with the number of polar groups in the solute molecule (Section 8.6) Here the value of n varies for different solutes and separation modes (as defined in Table 9.6); φ f and φ 0 refer to values of φ ≡ φ B at the beginning (0) and end (f)of the gradient, respectively. For small-molecule samples, values of n for different separation modes usually vary between 1 and 4; a value of n ≈ 2 can be used as a starting approximation, prior to method development. Thus, for a NPC separation with a 150 × 4.6-mm column, a flow rate of 2 mL/min, and gradient of 10–100% B in 10 minutes, the value of k ∗ would be approximately (10 × 2)/(1.5 × 2 × log 10) = 6.7, that is, not much different from the value of k ≈ 4 for similar RPC conditions. For an IEC separation with a 150 × 4.6-mm column, a flow rate of 2 mL/min, and gradient of 10–100 mM in 10 minutes, the same value of k ∗ results from Equation (9.26) (note also for IEC that the salt concentration φ is the sum of concentrations of salt plus buffer). For further details on the theory of gradient elution for separation modes other than RPC, see Chapter 13 of [2] and [75]. 9.5.2 Normal-Phase Chromatography (NPC) Section 8.5 summarized some disadvantages of isocratic normal-phase chromatog- raphy (NPC) with silica columns. With the exception of HILIC (Section 9.5.3), these same problems apply equally for corresponding gradient separations. When 9.5 OTHER SEPARATION MODES 467 the A- and B-solvents are quite different in polarity or strength, solvent demixing (Section 8.5.2) is a potentially serious problem [76] (very few gradient NPC sep- arations with silica columns have been reported in the past 30 years). The use of polar-bonded-phase columns (Section 8.3.4) largely avoids the problem of solvent demixing in gradient elution. 9.5.3 Hydrophilic-Interaction Chromatography (HILIC) Isocratic hydrophilic-interaction chromatography (HILIC) separations were reviewed in Section 8.6; most conclusions presented there apply equally for HILIC gradient elution. The use of HILIC gradient elution is as convenient and free from problems as are gradient separations by RPC—which in part accounts for the increasing popularity of HILIC. The applicability of HILIC for different kinds of samples can be visualized in the hypothetical separations of Figure 9.26a,b,where gradient separations by RPC and HILIC are compared. A series of solutes (1–29) of decreasing polarity (or increasing hydrophobicity) is visualized, where RPC retention increases in this order. The shaded peak 20 corresponds approximately to toluene, which provides a reference point for comparing these two separations. Compounds 1 to 6 are unretained by RPC (because of their greater polarity), while compounds 19 to 29 are unretained by HILIC because of their greater hydrophobicity. Compounds 26 to 29 are very hydrophobic, might not be eluted in RPC with this acetonitrile/buffer gradient, and therefore require the use of nonaqueous RPC (NARP; Section 6.5) for their effective separation. For the corresponding HILIC separation of Figure 9.26b, compounds 1 to 6 are strongly retained and well separated—in contrast to their poor retention by RPC. This ability of HILIC to separate polar compounds that are unretained or poorly retained by RPC represents its primary advantage. Compounds 7 to 17 (indicated by double-headed arrows in both chromatograms) are retained on both columns, so that these compounds of intermediate polarity or hydrophobicity can be separated by either RPC or HILIC. The gradient separations of such a sample by both RPC and HILIC are shown in Figure 9.27a,b for a mixture of peptides. 9.5.3.1 Applications The hypothetical gradient separations of Figure 9.26 suggest a reversal of relative retention for separations by RPC and HILIC, and an inverse correlation of solute retention (i.e., non-orthogonal separation). This is only roughly the case for actual separations, as shown by the examples of Figure 9.27a,b—and summarized in the plot of gradient retention times in Figure 9.27c (for which r 2 = 0.00; i.e., orthogonal separation). Whereas Figure 9.26 suggests that two compounds that are overlapped in a RPC separation will also be overlapped in a HILIC separation, this usually is not the case. Furthermore changes in other conditions (gradient steepness, temperature, column type, etc.) are known to further affect selectivity in both RPC and HILIC. The analysis of samples composed of compounds with widely varying polarity may require the use of both HILIC and RPC for adequate retention and sub- sequent separation. Using the example of compounds 1 to 25 in Figure 9.26, RPC could be used for the analysis of compounds 13 to 25, and HILIC could 468 GRADIENT ELUTION 02468 10 Time (min) 20 15 10 25 (a) (b) RPC 0-100% ACN/buffer HILIC 3-40% buffer/ACN 12 NARP #26-29 #7-17 0246810 Time (min) 10 5 1 15 20 19-29 #7-17 1-6 Figure 9.26 Hypothetical example of retention in RPC (a)andHILIC(b) as a function of solute polarity (solute polarity decreases from compound 1 to 29). Same sample assumed for (a)and(b). be used for the balance of the sample (compounds 1 to 12). An example is provided by the HILIC separation of Figure 9.28, which was applied to the unre- tained fraction from the separation of a wheat gluten hydrolysate by RPC gradient elution. 9.5.3.2 Separation Conditions Bare silica or bonded-amide columns are often used, with gradients that begin with 3–5% aqueous buffer (B)/acetonitrile (A) and end with 40–60% B, in a time of 20 to 60 minutes; other conditions are similar to those used for RPC (Table 9.3). Gradient HILIC separations are often employed for the same reasons cited in Section 13 for isocratic HILIC (usually for polar samples that are poorly retained in RPC, and especially for use with LC-MS). In addition, for samples that are retained by both RPC and HILIC, the two separation modes are often assumed to be orthogonal—allowing their use for 2D separation (Section 9.3.10). However, fractions from a first- dimension RPC separation will be in a strong solvent for the second-dimension HILIC separation, and vice versa (see Section 9.3.10.4) 9.5 OTHER SEPARATION MODES 469 1 5 + 8 46 3 2 7 1 2 3 4 5 6 78 RP-LC HILIC (a) (b) 40 010203040 30 20 10 0 0 5 10 15 20 (min) t R (HILIC) t R (RPC) y = 42 − 2x r 2 = 0.00 1 7 (c) Figure 9.27 Selectivity in RPC versus HILIC for a mixture of peptides. Conditions: (a)C 18 column; 5–55% acetonitrile–aqueous buffer (pH-2) in 83 minutes; (b) TSKgel Amide-80 col- umn; 3–45% aqueous buffer (pH-2)–acetonitrile in 70 minutes; (c) comparison of retention times from separation of (b) versus (a). Adapted from [77]. 0 20 30 40 80 100 (min) Figure 9.28 Separation by HILIC of a polar, unretained fraction from RPC of a wheat gluten hydrolysate. Conditions: 250 × 1.5-mm TSK Gel Amide 80 column; 10–40% buffer (pH-7.0)–acetonitrile in 50 minutes; 100 μL/min. Reproduced from [78] with permission. 470 GRADIENT ELUTION 9.5.4 Ion-Exchange Chromatography (IEC) As noted in Section 7.5, ion-exchange chromatography (IEC) is rarely used today for small-molecule separations, with the exception of carbohydrates, carboxylic acids, and ion chromatography for inorganic ions. IEC in a gradient mode is much more popular for the separation of large biomolecules such as polysaccharides, proteins, nucleic acids, and viruses (Chapter 13). 9.6 PROBLEMS Various problems can be encountered with gradient elution that are either less common or nonexistent for isocratic elution. These include: • solvent demixing • ghost peaks • baseline drift 9.6.1 Solvent Demixing In gradient elution, demixing refers to the preferential uptake by the stationary phase of the B-solvent, because of its greater affinity for the stationary phase. In most cases solvent demixing is not sufficiently pronounced in RPC to compromise separation. Its effects are to slightly increase retention for initial peaks in the chromatogram. Solvent demixing is especially a problem in separations by normal-phase chromatography [79] with base silica as column packing. This can result in complete retention of the B-solvent during the early part of the gradient, followed by a sudden breakthrough of B-solvent in the column effluent. The result is to elute all early peaks together as a single peak, with a major loss in sample resolution. For a further discussion of solvent demixing in gradient elution, see [2]. 9.6.2 Ghost Peaks These refer to extraneous peaks in the chromatogram that do not correspond to sample components. These can be the result of impurities in the mobile-phase solvents, buffers, or other additives. Ghost peaks can also arise from carryover of sample from one injection to the next, or as a result of adsorption of sample in the autosampler or on the column inlet frit. For a general discussion of ghost peaks, see [80] and [81]. Means for the elimination of ghost peaks are discussed in Section 17.4.5.2. 9.6.3 Baseline Drift This is common in gradient elution, as a result of differences in the detector response for the A- and B-solvent. As a result the baseline can drift during the gradient. Baseline drift is common in RPC with UV detection because organic solvents (the B-solvent) generally absorb more strongly than water, especially at low wavelengths. For a further discussion of baseline drift, see Section 17.4.5.1. REFERENCES 471 REFERENCES 1. P. L. Zhu, L. R. Snyder, J. W. Dolan, N. M. Djordjevic, D. W. Hill, L. C. Sander, and T. J. Waeghe, J. Chromatogr. A, 756 (1996) 21. 2. L. R. Snyder and J. W. Dolan, High-Performance Gradient Elution, Wiley-Interscience, New York, 2007. 3. F. Leroy, B. Presle, F. Verillon, and E. Verette, J. Chromatogr. Sci., 39 (2001) 487. 4. S. R. Needham and T. Wehr, LCGC Europe, 14 (2001) 244. 5. J.Ayrton,G.J.Dear,W.J.Leavens,D.N.Mallet,andR.S.Plumb,J. Chromatogr. B, 709 (1998) 243. 6. L. R. Snyder, J. J. Kirkland, and J. L. Glajch, Practical HPLC Method Development, 2nd ed., Wiley-Interscience, New York, 1997. 7. L. Hagdahl, R. J. P. Williams, and A. Tiselius, Arkiv. Kemi, 4 (1952) 193. 8. T. Braumann, G. Weber, and L. H. Grimme, J. Chromatogr., 261 (1983) 329. 9. P. L. Zhu, L. R. Snyder, J. W. Dolan, N. M. Djordjevic, D. W. Hill, L. C. Sander, and T. J. Waeghe, J. Chromatogr. A, 756 (1996) 21. 10. P. Jandera and M. ˇ Spa ˇ cek, J. Chromatogr., 366 (1986) 107. 11. L. R. Snyder and J. W. Dolan, J. Chromatogr. A, 799 (1998) 21. 12. A. P. Schellinger and P. W. Carr, J. Chromatogr. A, 1077 (2005) 110. 13. W. Hancock, R. C. Chloupek, J. J. Kirkland, and L. R. Snyder, J. Chromatogr. A, 686 (1994) 31. 14. T. Jupille, L. Snyder, and I. Molnar, LCGC Europe, 15 (2002) 596. 15. B. F. D. Ghrist, B. S. Cooperman, and L. R. Snyder, J. Chromatogr., 459 (1989) 1. 16. B. F. D. Ghrist and L. R. Snyder, J. Chromatogr., 459 (1989) 63. 17. B. F. D. Ghrist and L. R. Snyder, J. Chromatogr., 459 (1989) 25. 18. V. Concha-Herrera, G. Viv ´ o-Truyols, J. R. Torres-Lapasi ´ oandM.C.Garci ´ a- Alvarez-Coque, J. Chromatogr. A, 1063 (2005) 79 19. S. V. Galushko and A. A. Kamenchuk, LCGC Intern., 8 (1995) 581. 20. H. Xiao, X. Liang, and P. Lu, J. Sep. Sci., 24 (2001) 186. 21. W. Markowski and W. Golkiewicz, Chromatographia, 25 (1988) 339. 22. P. Jandera, Adv. Chromatogr., 43 (2004) 1. 23. L. R. Snyder and D. L. Saunders, J. Chromatogr. Sci., 7 (1969) 195. 24. U. D. Neue, D. H. Marchand, and L. R. Snyder, J. Chromatogr. A, 1111 (2006) 32. 25. H. Poppe, J. Paanakker, and M. Bronkhorst, J. Chromatogr., 204 (1981) 77. 26. L. R. Snyder and J. W. Dolan, Adv. Chromatogr., 38 (1998) 115. 27. J. Pellett, P. Lukulay, Y. Mao, W. Bowen, R. Reed, M. Ma, R. C. Munger, J. W. Dolan, L. Wrisley, K. Medwid, N. P. Toltl, C. C. Chan, M. Skibic, K. Biswas, K. A. Wells, and L. R. Snyder, J. Chromatogr. A, 1101 (2006) 122. 28. Z.Li,S.C.RutanandS.Dong, Anal. Chem., 68 (1996) 124. 29. R. Majors, LCGC, 20 (2002) 516. 30. L. R. Snyder and J. W. Dolan, J. Chromatogr. A, 721 (1996) 3. 31. P. J. Schoenmakers, H. A. H. Billiet, and L. De Galan, J. Chromatogr., 205 (1981) 13. 32. P. J. Schoenmakers, A. Bartha, and H. A. H. Billiet, J. Chromatogr., 550 (1991) 425. 33. P. Schoenmakers, in Handbook of HPLC, E. Katz, R. Eksteen, P. Schoemnakers, and N. Miller, eds., Dekker, New York, 1998, pp. 218–220. 472 GRADIENT ELUTION 34. A. P. Schellinger and P. W. Carr, J. Chromatogr. A, 1109 (2006) 253. 35. L. R. Snyder and J. W. Dolan, J. Chromatogr. A, 892 (2000) 107. 36. J. W. Dolan, L. R. Snyder, N, M. Djordjevic, D. W. Hill, L. Van Heukelem, and T. J. Waeghe, J. Chromatogr. A, 857 (1999) 41. 37. P. L. Zhu, J. W. Dolan and L. R. Snyder, D. W. Hill, L. Van Heukelem, and T. J. Waeghe, J. Chromatogr. A, 756 (1996) 51. 38. W. Hancock, R. C. Chloupek, J. J. Kirkland, and L. R. Snyder, J. Chromatogr. A, 686 (1994) 31, 45. 39. J. W. Dolan, L. R. Snyder, N. M. Djordjevic, D. W. Hill, L. Van Heukelem, and T. J. Waeghe, J. Chromatogr. A, 857 (1999) 1. 40. J. W. Dolan, L. R. Snyder, T. Blanc, and L. Van Heukelem, J. Chromatogr. A , 897 (2000) 37. 41. J. W. Dolan, J. Chromatogr. A, 965 (2002) 195. 42. J. W. Dolan, L. R. Snyder, N. M. Djordjevic, D. W. Hill, D. L. Saunders, L. Van Heukelem, and T. J. Waeghe, J. Chromatogr., 803 (1998) 1. 43. A. P. Schellinger, D. R. Stoll, and P. W. Carr, J. Chromatogr. A, 1064 (2005) 143. 44. A. P. Schellinger, D. R. Stoll, and P. W. Carr, J. Chromatogr. A, 1192 (2008) 41. 45. A. P. Schellinger, P. Adam, D. R. Stoll, and P. W. Carr, J. Chromatogr. A, 1192 (2008) 54. 46. J. Garc ´ ıa,J.A.Mart ´ ınez-Pontevedra, M. Lores, and R. Cela, J. Chromatogr. A, 1128 (2006) 17. 47. V. R. Meyer, J. Chromatogr. A, 1187 (2008) 138. 48. U. D. Neue and J. R. Mazzeo, J. Sep. Sci., 24 (2001) 921. 49. U. D. Neue, J. Chromatogr. A, 1079 (2005) 153. 50. D. R. Stoll, X. Wang, and P. W. Carr, Anal. Chem., 78 (2006) 3406. 51. S. E. G. Porter, D. R. Stoll, S. C. Rutan, P. W. Carr, and Cohen, Anal. Chem., 78 (2006) 5559. 52. X. Wang, W. E. Barber, and P. W. Carr J. Chromatogr. A, 1107 (2006) 139. 53. D. R. Stoll, X. Li, X. Wang, P. W. Carr, S. E. G. Porter, and S. C. Rutan, J. Chromatogr. A, 1168 (2007) 3. 54. M. Gilar and U. D. Neue, J. Chromatogr. A, 1169 (2007) 139. 55. U. D. Neue, J. Chromatogr. A, 1184 (2008) 107. 56. D. R. Stoll, X. Wang, and P. W. Carr, Anal. Chem., 80 (2008) 268. 57. J. M. Davis, D. R. Stoll, and P. W. Carr, Anal. Chem., 80 (2008) 461, 8122. 58. X.Li,D.R.Stoll,andP.W.Carr,Anal. Chem., 81 (2009) 845. 59. L. A. Romanyshyn and P. R. Tiller, J. Chromatogr. A, 928 (2001) 41. 60. K. D. Patel, A. D. Jerkovich, J. C. Link, and J. W. Jorgenson, Anal. Chem., 76 (2004) 5777. 61. H. Chen and C. Horv ´ ath, J. Chromatogr. A, 705 (1995) 3. 62. S. K. Paliwal, M. de Frutos, and F. E. Regnier, in Methods in Enzymology, Vol. 270. W. S. Hancock and B. L. Karger, eds., Academic Press, Orlando, 1996, p. 133. 63. J. J. Kirkland, F. A. Truszkowski, and R. D. Ricker, J. Chromatogr. A, 965 (2002) 25. 64. L. Xiong, R. Zhang, and F. E. Regnier, J. Chromatogr. A., 1030 (2004) 187. 65. P. Brown and E. Grushka, eds., Design of Rapid Gradient Methods for the Analysis of Combinatorial Chemistry Libraries and the Preparation of Pure Compounds, Dekker, New York, 2001. REFERENCES 473 66. P. J. Schoenmakers, P. Marriott, and J. Beans, LCGC Europe, 16 (2003) 335. 67. J. C. Giddings, Multidimensional Chromatography: Techniques and Applications; Dekker, New York, 1990. 68. R. E. Murphy, M. R. Schure, and J. P. Foley, Anal. Chem., 70 (1998) 1585. 69. K. Horie, H. Kimura, T. Ikegama, A. Iwatsuka, N. Saad, O. Fiehn, and N. Tanaka, Anal. Chem., 79 (2007) 3764. 70. D. R. Stoll, J. D. Cohen, and P. W. Carr, J. Chromatogr. A, 1122 (2006) 123. 71. S. Peters, G. Viv ´ o-Truyols, P. J. Marriott, and P. J. Schoenmakers, J. Chromatogr. A, 1156 (2007) 14. 72. J. W. Dolan and L. R. Snyder, J. Chromatogr. A, 1216 (2009) 3467. 73. M. Gilar, P. Olivova, A. E. Daly, and J. C. Gebler, Anal. Chem., 77 (2005) 6426. 74. K. Horie, H. Kimura, T. Ikegami, A. Iwatsuka, N. Saad, O. Fiehn, and N. Tanaka, Anal. Chem., 79 (2007) 3764. 75. P. J. Schoenmakers, G. Vivo-Truyols, and W. M. C. Decrop, J.Chromatogr. A, 1120 (2006) 282. 76. P. Jandera, J. Chromatogr. A, 965 (2002) 239. 77. P. Jandera, J. Chromatogr. A, 1126 (2006) 195. 78. T. Yoshida, J. Chromatogr. A, 60 (2004) 265. 79. H. Schlichtherle-Cerny, M. Affolter, and C. Cerny, Anal. Chem., 75 (2003) 2349. 80. P. Jandera, J. Chromatogr. A, 965 (2002) 239. 81. S. Williams, J. Chromatogr. A, 1052 (2004) 1. CHAPTER TEN COMPUTER-ASSISTED METHOD DEVELOPMENT 10.1 INTRODUCTION, 475 10.1.1 Basis and History of Computer Simulation, 478 10.1.2 When to Use Computer Simulation, 478 10.2 COMPUTER-SIMULATION SOFTWARE, 481 10.2.1 DryLab Operation, 481 10.2.2 Gradient Optimization, 483 10.2.3 Other Features, 485 10.2.4 Peak Tracking, 489 10.2.5 Sources of Computer-Simulation Software, 489 10.3 OTHER METHOD-DEVELOPMENT SOFTWARE, 491 10.3.1 Solute Retention and Molecular Structure, 491 10.3.2 Solute pK a Values and Molecular Structure, 491 10.3.3 Reversed-Phase Column Selectivity, 492 10.3.4 Expert Systems for Method Development, 492 10.4 COMPUTER SIMULATION AND METHOD DEVELOPMENT, 492 10.4.1 Example 1: Separation of a Pharmaceutical Mixture, 492 10.4.2 Example 2: Alternative Method Development Strategy, 494 10.4.3 Verifying Method Robustness, 496 10.4.4 Summary, 497 10.1 INTRODUCTION Computer-assisted method development is a broad term, one that might be applied to the use of any software that facilitates method development. In this chapter we will Introduction to Modern Liquid Chromatography, Third Edition, by Lloyd R. Snyder, Joseph J. Kirkland, and John W. Dolan Copyright © 2010 John Wiley & Sons, Inc. 475 . software that facilitates method development. In this chapter we will Introduction to Modern Liquid Chromatography, Third Edition, by Lloyd R. Snyder, Joseph J. Kirkland, and John W. Dolan Copyright. Jandera, J. Chromatogr. A, 965 (2002) 239. 81. S. Williams, J. Chromatogr. A, 1 052 (2004) 1. CHAPTER TEN COMPUTER-ASSISTED METHOD DEVELOPMENT 10.1 INTRODUCTION, 475 10.1.1 Basis and History of Computer. Waeghe, J. Chromatogr., 803 (1998) 1. 43. A. P. Schellinger, D. R. Stoll, and P. W. Carr, J. Chromatogr. A, 1064 (2005) 143. 44. A. P. Schellinger, D. R. Stoll, and P. W. Carr, J. Chromatogr. A, 1192