16 INTRODUCTION 13. L. S. Ettre, LCGC, 25 (2007) 640. 14. L. S. Ettre, LCGC, 19 (2001) 506. 15. L. S. Ettre, LCGC, 243 (2006) 390. 16. L. S. Ettre, LCGC, 23 (2005) 752. 17. J. G. Kirchner, Thin-layer Chromatography, Wiley-Interscience, New York, 1978, pp. 5–8. 18. J. C. Moore, J. Polymer Sci. Part A, 2 (1964) 835. 19. L. S. Ettre and A. Zlatkis, eds., 75 years of Chromatography—A Historical Dialog, Elsevier, Amsterdam, 1979. 20. L. S. Ettre, LCGC, 23 (2005) 486. 21. J. F. K. Huber and J. A. R. Hulsman, J. Anal. Chim. Acta, 38 (1967) 305. 22. J. J. Kirkland, Anal. Chem., 40 (1968) 218. 23. L. R. Snyder, Anal. Chem., 39 (1967) 698, 705. 24. R. P. W. Scott, W. J. Blackburn, and T. J. Wilkens, J. Gas Chrommatogr., 5 (1967) 183. 25. J. J. Kirkland, ed., Modern Practice of Liquid Chromatography, Wiley-Interscience, New York, 1971. 26. T. Braumann, G. Weber, and L. H. Grimme, J. Chromatogr., 261 (1983) 329. 27. A. J. P. Martin and R. L. M. Synge, Biochem. J., 35 (1941) 1358. 28. A. T. James and A. J. P. Martin, Biochem. J., 50 (1952) 679. 29. L. S. Ettre, LCGC, 19 (2001) 120. 30. J. C. Giddings, Dynamics of Chromatography. Principles and Theory, Dekker, New York, 1965. 31. L. R. Snyder, J. Chem. Ed., 74 (1997) 37. 32. L. S. Ettre, LCGC Europe, 1 (2001) 314. 33. L. R. Snyder, Anal. Chem., 72 (2000) 412A. 34. C. W. Gehrke, ed., Chromatography—A Century of Discovery 1900–2000, Elsevier, Amsterdam, 2001. 35. R. L. Grob and E. F. Barry, Modern Practice of Gas Chromatography,4thed., Wiley-Interscience, NewYork, 2004. 36. B. Fried and J. Sherma, Thin-Layer Chromatography (Chromatographic Science, Vol. 81), Dekker, New York, 1999. 37. R. M. Smith and S. M. Hawthorne, eds., Supercritical Fluids in Chromatography and Extraction, Elsevier, Amsterdam, 1997. 38. T. Bamba, E. Fukusaki, Y. Nakazawa, H. Sato, K. Ute, T. Kitayama, and A. Kobayashi, J. Chromatogr. A, 995 (2003) 203. 39. K. D. Altria and D. Elder, J. Chromatogr. A , 1023 (2004) 1. 40. A. Berthod and C. G ´ arcia-Alvarez-Coque, Micellar Liquid Chromatography, Dekker, New York, 2000. 41. Y. Ito and W. D. Conway, eds., High-Speed Countercurrent Chromatography, Wiley, New York, 1996. 42. J M. Menet and D. Thiebaut, eds., Countercurrent Chromatography , Dekker, New York, 1999. 43. E. Gavioli, N. M. Maier, C. Minguill ´ on, and W. Lindner, Anal. Chem., 76 (2004) 5837. 44. K. D. Bartle and P. Meyers, Capillary Electrochromatography (Chromatography Mono- graphs), 2001. 45. F. Svec, ed., J. Chromatogr. A, 1044 (2004). REFERENCES 17 46. H. Yin and K. Killeen, J. Sep. Sci., 30 (2007) 1427. 47. J. S. Fritz and D. T. Gjerde, Ion Chromatography, 3rd ed., Wiley-VCH, Weinheim, 2000. 48. J. Weiss, Handbook of Ion Chromatography, 3rd ed., Wiley, 2005. 49. A. Berthod and M. C. G ´ arcia-Alvarez-Coque, Micellar Liquid Chromatography, Dekker, New York, 2000. CHAPTER TW O BASIC CONCEPTS AND THE CONTROL OF SEPARATION 2.1 INTRODUCTION, 20 2.2 THE CHROMATOGRAPHIC PROCESS, 20 2.3 RETENTION, 24 2.3.1 Retention Factor k and Column Dead-Time t 0 ,25 2.3.2 Role of Separation Conditions and Sample Composition, 28 2.4 PEAK WIDTH AND THE COLUMN PLATE NUMBER N ,35 2.4.1 Dependence of N on Separation Conditions, 37 2.4.2 Peak Shape, 50 2.5 RESOLUTION AND METHOD DEVELOPMENT, 54 2.5.1 Optimizing the Retention Factor k,57 2.5.2 Optimizing Selectivity α,59 2.5.3 Optimizing the Column Plate Number N,61 2.5.4 Method Development, 65 2.6 SAMPLE SIZE EFFECTS, 69 2.6.1 Volume Overload: Effect of Sample Volume on Separation, 70 2.6.2 Mass Overload: Effect of Sample Weight on Separation, 71 2.6.3 Avoiding Problems due to Too Large a Sample, 73 2.7 RELATED TOPICS, 74 2.7.1 Column Equilibration, 74 2.7.2 Gradient Elution, 75 2.7.3 Peak Capacity and Two-dimensional Separation, 76 2.7.4 Peak Tracking, 77 2.7.5 Secondary Equilibria, 78 2.7.6 Column Switching, 79 2.7.7 Retention Predictions Based on Solute Structure, 80 Introduction to Modern Liquid Chromatography, Third Edition, by Lloyd R. Snyder, Joseph J. Kirkland, and John W. Dolan Copyright © 2010 John Wiley & Sons, Inc. 19 20 BASIC CONCEPTS AND THE CONTROL OF SEPARATION 2.1 INTRODUCTION The successful use of HPLC requires an understanding of how separation is affected by experimental conditions: the column, solvent, temperature, flow rate and so forth. In this chapter we review some general features of HPLC for use in the laboratory, in order to develop an adequate separation (method development), to carry out a routine HPLC procedure for sample analysis, or to solve problems as they arise. A descriptive or qualitative approach is usually best suited for understanding both method development and the routine application of HPLC. For this reason the reader may wish to skim or skip any of the following derivations—at least initially. Important equations that are useful in practice are enclosed within a box; for example, Equation (2.5). 2.2 THE CHROMATOGRAPHIC PROCESS A schematic of an HPLC system is shown in Figure 2.1, with emphasis on the flow path of the solvent (solid arrows) as it proceeds from the solvent reservoir to the detector (the solvent is usually referred to as the mobile phase or eluent). A detailed discussion of each part of the system (HPLC equipment) is given in Chapter 3. After injection of the sample, a separation takes place within the column, and separated sample components leave (are eluted or washed from) the column—with detection in most cases by either ultraviolet absorption (UV) or mass spectrometry (MS); see Chapter 4 for details on the use of these and other HPLC detectors. The fundamental nature or ‘‘mode’’ of the separation is determined mainly by the choice of column, as summarized in Table 2.1. For sample analysis, the predominant HPLC mode in use today is reversed-phase chromatography (RPC), which features a nonpolar column in combination with a (polar) mixture of water plus an organic solvent as mobile phase. Unless noted otherwise, RPC separation will be assumed in this book. Other HPLC modes are described in later sections of the book, as noted in Table 2.1. In Chapters 2 through 8 we will assume that the composition of the solvent remains the same throughout separation, which is called isocratic elution, as opposed to Samples Column Detecto r Pump Injection valve Solvent reservoir Figure 2.1 Schematic of an HPLC system. 2.2 THE CHROMATOGRAPHIC PROCESS 21 gradient elution where the solvent composition is deliberately changed during the separation (Section 2.7.2, Chapter 9). The column consists of a cylindrical tube that is typically filled with small (usually 1.5- to 5-μm diameter) spherical particles (Fig. 2.2a). These particles are in most cases porous silica, with an individual pore portrayed in Figure 2.2b as a cylinder of some specified diameter (typically about 10 nm for use with ‘‘small-molecule’’ samples i.e., molecular weights <1000 Da). The inside of each pore is covered with the stationary phase—in this example, C 18 groups that are attached to the silica particle. Figure 2.2c shows a more realistic representation of present-day porous particles for HPLC. The particle is formed by aggregating small, spherical, subparticles as shown. The actual pores are formed by the spaces between the subparticles. Because almost all of the surface of the particle is contained within these pores, most sample molecules are held inside the particle rather than on the surface of the particle. That is, the internal surfaces of the pores account for 99% of the total surface area of the particle; the external surface area (and its effect on separation) is in most cases negligible. The mobile phase surrounds each particle as (a) (b) (c) Column, showing mobile-phase flow inlet outlet mobile phase pore Particle and surrounding mobile phase stationary phase C 18 C 18 C 18 C 18 C 18 C 18 mobile phase × 10 Porous particle (detail) particle Figure 2.2 The HPLC column. (a) Column packed with spherical particles; (b) schematic of an individual particle, showing an idealized pore with attached C 18 groups; (c) more realistic picture of a spherical, porous particle, showing detail (10× expansion). 22 BASIC CONCEPTS AND THE CONTROL OF SEPARATION Table 2.1 HPLC Separation Modes Chromatographic Mode Comment Details In Reversed-phase chromatography (RPC) The column is nonpolar (e.g., C 18 ), and the mobile phase is a polar mixture of water plus organic solvent (e.g., acetonitrile); RPC is the most widely used mode, especially for water-soluble samples. Chapter 6, Section 7.3 Normal-phase chromatography (NPC) The column is polar (e.g., unbonded silica), and the mobile phase is a mixture of less-polar organic solvents (e.g., hexane plus methylene chloride); NPC is used mainly for water-insoluble samples, preparative HPLC, and the separation of isomers. Chapter 8 Non-aqueous reversed-phase chromatography (NARP) The column is nonpolar (e.g., C 18 ), and the mobile phase is a mixture of organic solvents (e.g., acetonitrile plus methylene chloride); NARP is used for very hydrophobic, water-insoluble samples. Section 6.5 Hydrophilic interaction chromatography (HILIC) The column is polar (e.g., silica or amide-bonded phase), and the mobile phase is a mixture of water plus organic (e.g., acetonitrile); HILIC is useful for samples that are highly polar and therefore poorly retained in RPC. Section 8.6 Ion-exchange chromatography (IEC) The column contains charged groups that can bind sample ions of opposite charge, and the mobile phase is usually an aqueous solution of a salt plus buffer; IEC is useful for separating ionizable samples such as acids or bases, and especially for the separation of large biomolecules (e.g., proteins and nucleic acids). Sections 7.5, 13.4.2 Ion-pair chromatography (IPC) RPC conditions are used, except that an ion-pair reagent is added to the mobile phase for interaction with sample ions of opposite charge; IPC is useful for the separation of acids or bases that are weakly retained in RPC. Section 7.4 Size-exclusion chromatography (SEC) An inert column is used with either an aqueous or organic mobile phase; SEC provides separation on the basis of molecular weight and is used mainly for large biomolecules or synthetic polymers. Section 13.8 2.2 THE CHROMATOGRAPHIC PROCESS 23 it flows through the column, and sample molecules can enter the particle pores by diffusion (there is normally no significant flow of mobile phase through the particle). Figure 2.3 illustrates a hypothetical separation of a sample that contains three sample compounds (or solutes), with individual sample molecules represented by • for solute X,  for solute Y,and for solute Z. For clarity, molecules of the mobile phase are not shown, and molecules of the solvent that the sample is dissolved in are portrayed by +. The sample is applied to the column in (Fig. 2.3a) is carried through the column by the flowing mobile phase in successive stages (Fig. 2.3b–d), and eventually the sample leaves the column (Fig. 2.3e)toprovidea plot of detector response versus time (a chromatogram, or record of the separation). As the separation proceeds in Figure 2.3a–d, molecules of sample components X, Y, and Z exhibit two characteristic behaviors: differential migration and molecular spreading. By Figure 2.3d, solutes X, Y,andZ have become separated from each other within the column. (e) (f ) (a)(b)(c)(d ) flow X Y Z + + + + + + + + 0 1 2 3 4 5 (min) + solvent peak t 0 t 0 t R (X) k = 01234 5 inlet outlet Z Y X + + + + + + + + sample solvent column Figure 2.3 Illustration of the separation process in HPLC. (a–d) Sequential separation within the column (i.e., as a function of time); (e) the final chromatogram; (f ) estimating values of k from the chromatogram (e). Solute molecules X, Y,andZ are represented by • , ,and, respectively; sample solvent molecules are shown by +. 24 BASIC CONCEPTS AND THE CONTROL OF SEPARATION Differential migration (different average speeds at which solute molecules of X, Y,andZ move, or migrate, through the column) forms the basis of chromato- graphic separation. Without a difference in migration rates for two compounds, their separation cannot occur. In this example molecules of X ( • ) move fastest, and molecules of Z () move slowest; molecules of the sample solvent or mobile phase are not retained by the column-packing, pass through the column quickest of all, and leave the column first. Solvent molecules that form part of the injected sample are represented in Figure 2.3b–e by +. As a given solute moves through the column, its molecules become increasingly spread out, so as to occupy a larger volume within the column. The volume that encompasses the molecules of a given solute within the column defines what is called a band. The width of this solute-volume is measured in the direction of flow, and is defined as the band width, as indicated in Figure 2.3a–d for solute X by the arrow and bracket alongside molecules of X ( • ). When a band leaves the column and is recorded in the chromatogram (Fig. 2.3e), it is then referred to as a peak. The identity of each peak can be determined from the time at which it leaves the column (the retention time t R ), while the concentration of each solute in the sample is proportional to peak size (measured either as area or height; see Section 11.2.3). For sufficiently small samples (low-ng to μg injections, as typically used in HPLC assay procedures), peak retention times do not change as sample concentration (and resulting peak size) is varied. In the rest of this chapter we will examine separation further as a function of experimental conditions. 2.3 RETENTION The retention time t R for each solute is the time from sample injection to the appearance of the top of the peak in the chromatogram; in Figure 2.3e the retention times for solutes X, Y,andZ are, respectively, 2, 3, and 5 minutes. The retention time of the solvent peak at one minute is referred to as the column dead-time t 0 (Section 2.3.1) (sometimes t m is used instead of t 0 to represent column dead-time). The migration rate or velocity u x at which solute X moves through the column is determined by the fraction R of its molecules that are present in the flowing mobile phase at any time. On average, u x will be equal to R times the migration rate or velocity u of solvent molecules: u x = Ru (2.1) For example, if half of the molecules of X are in the mobile phase (R = 0.5) and half are in the stationary phase, only half of the molecules are moving at any given time, so the average migration rate of X will be one half as fast as that of the solvent. As illustrated in Figure 2.4, the fraction R of molecules X in the mobile (moving) phase is determined by an equilibrium process: X (mobile phase) ⇔ X (stationary phase) (2.2) Molecules of X in Figure 2.4 are found equally in the mobile and stationary phase at any time, while molecules of Z predominate in the stationary phase; that is, Z 2.3 RETENTION 25 mobile phase stationary phase particl e XZ pore mobile phase X Z Figure 2.4 Equilibrium distribution of solvent and sample molecules between the mobile and stationary phases, and the resulting effect on solute migration rate. The values of k for solutes X and Z are 1 and 4, respectively. Equal amounts of X and Z in the sample are assumed. is more retained than X and therefore migrates more slowly (indicated at the base of Fig. 2.4 by arrows, whose lengths denote migration rate). This equilibrium and the migration rate of a given solute are affected by the molecular structure of the solute, the chemical composition of the mobile and stationary phases (the solvent and column), and the temperature. The average pressure within the column can have a small effect on sample retention [1] (see also Section 2.5.3.1), but usually this can be ignored for moderate pressures (e.g., <5000 psi). 2.3.1 Retention Factor k and Column Dead-Time t 0 For a given solute, the retention factor k (this is still sometimes referred to as the capacity factor k  ) is defined as the quantity of solute in the stationary phase (s), divided by the quantity in the mobile phase (m). The quantity of solute in each phase is equal to its concentration (C s or C m , resp.) times the volume of the phase (V s or V m , resp.), which then gives k = C s V s C m V m = C s /C m V s /V m = K (2.3) . 74 2 .7. 2 Gradient Elution, 75 2 .7. 3 Peak Capacity and Two-dimensional Separation, 76 2 .7. 4 Peak Tracking, 77 2 .7. 5 Secondary Equilibria, 78 2 .7. 6 Column Switching, 79 2 .7. 7 Retention Predictions. Separation, 70 2.6.2 Mass Overload: Effect of Sample Weight on Separation, 71 2.6.3 Avoiding Problems due to Too Large a Sample, 73 2 .7 RELATED TOPICS, 74 2 .7. 1 Column Equilibration, 74 2 .7. 2 Gradient. Anal. Chem., 39 (19 67) 698, 70 5. 24. R. P. W. Scott, W. J. Blackburn, and T. J. Wilkens, J. Gas Chrommatogr., 5 (19 67) 183. 25. J. J. Kirkland, ed., Modern Practice of Liquid Chromatography, Wiley-Interscience,