Introduction to Modern Liquid Chromatography, Third Edition part 8 doc

26 BASIC CONCEPTS AND THE CONTROL OF SEPARATION where K = (C s /C m ) is the equilibrium constant for Equation (2.2), and  = (V s /V m ) is the phase ratio—the ratio of stationary and mobile-phase volumes within the column. We will see that k is a very important property of each peak in the chromatogram; values of k can help us interpret and improve the quality of a separation. A solute molecule must be present in either the mobile or stationary phase so that, if the fraction of molecules in the mobile phase is R, the fraction in the stationary phase must be 1 − R; therefore from Equation (2.3) we have k = 1 − R R (2.3a) or R = 1 1 + k (2.3b) The retention time (t R )ofX can be defined as distance divided by speed (or band velocity), where the distance is the column length L and the band velocity is u x : t R = L u x (2.4) Similarly the retention time of the solvent peak is t 0 = L u (2.4a) where u is the average mobile-phase velocity. Eliminating L between Equations (2.4) and (2.4a)gives t R = t 0 u u x (2.4b) which, with R = u x /u 0 (Eq. 2.1) and Equation (2.3b), then gives t R = t 0 (1 + k) (2.5) Equation (2.5) can also be expressed in terms of retention volume V R = t R F,where F is the mobile-phase flow rate (mL/min): V R = V m (1 + k) (2.5a) Here V m is the column dead-volume, equal to t 0 F (see the further discussion of V m and Eq. 2.5a below). Equation (2.5) can be rearranged to give k = t R − t 0 t 0 (2.6) 2.3 RETENTION 27 which allows the calculation of values of k for each peak in the chromatogram. Visual estimates of k from the chromatogram (based on Eq. 2.6) are often used in practice, because exact values of k are seldom needed for developing a separation (method development) or during routine analysis. Thus k is equal to the corrected retention time (t R − t 0 ), measured in units of t 0 ,or k =  t R t 0  − 1 (2.6a) As illustrated in Figure 2.3f (which corresponds to the chromatogram of Fig. 2.3e), the distance t 0 can be used to mark off approximate values of k, beginning at time t 0 ; thus k equals 1, 2, and 4, respectively, for compounds X, Y,andZ. We will see in Section 2.4.1 that values of k between about 1 and 10 are preferred for various reasons. Therefore it is important to be able to estimate (or calculate) values of k for the different peaks in a chromatogram, which in turn requires a value of the column dead-time t 0 . A value of t 0 can often be obtained from a visual inspection of the initial portion of the chromatogram, as illustrated in Figure 2.5a–b. Sometimes the first baseline disturbance assumes the characteristic shape illustrated in Figure 2.5a, which is a clear indication of the unretained solvent peak. This t 0 -disturbance is usually the result of a change in refractive index (RI) of the mobile phase (due to differences in RI for the sample solvent vs. the mobile phase), which in turn affects the amount of light that passes through the flow cell of the detector. If the sample is dissolved in the mobile phase (usually the preferred choice), a t 0 peak as in Figure 2.5a may not be observed. At other times, especially for the injection of a reaction product, environmental sample, or plant or animal extract, a very large (‘‘excipient’’ or ‘‘junk’’) peak may be observed at the beginning of the chromatogram (Fig. 2.5b). In this case t 0 corresponds to the initial rise of the peak. Sometimes no obvious solvent peak is observed (Fig. 2.5c), in which case a value of t 0 can either be measured or estimated. (a)(b) t 0 t 0 t 0 t 0 ?? (c)(d) 00 00 thiourea Figure 2.5 Determining the column dead-time t 0 . 28 BASIC CONCEPTS AND THE CONTROL OF SEPARATION The most direct procedure for determining t 0 is to inject a solute (dissolved in water or the mobile phase) that is unretained (k = 0) and readily detected, as in Figure 2.5d. When UV detection below 220 nm is used, thiourea as test solute fulfills both requirements, and is therefore a good choice for the measurement of t 0 .Other test solutes have also been used for measuring t 0 , for example, uracil or concentrated solutions of a UV-absorbing salt such as sodium nitrate [2–4]. Observed values of t 0 for a given column can vary with mobile-phase composition by as much as ±10–15% for 0–100% B (%B refers to the percent by volume of organic solvent in the mobile phase), but usually t 0 varies by <5% for 20–80% B [5]. For approximate estimates of k as in Figure 2.3e, a value of t 0 measured for one value of %B can be assumed to be the same for all values of %B (when only %B is changed). Alternatively, a value of t 0 can be estimated from the column dimensions and flow rate (for columns packed with fully porous particles): t 0 ≈ 5 × 10 −4 Ld 2 c F (2.7) Here L is the column length in mm, d c is the column inner diameter in mm, F is the flow rate in mL/min, and t 0 is in minutes. For several hundred different RPC columns, it was found that Equation (2.7) agrees with experimental values of t 0 with an average error of only ±10% (1 SD) [6], which again is accurate enough for practical purposes. The column dead-volume V m is related to t 0 as V m = t 0 F ≈ 5 × 10 −4 Ld 2 c (2.7a) with L and d c in mm. The dead-volume V m represents the total volume of mobile phase inside the column, both inside and outside of the column particles. For example, if V m = 2mL,andF = 0.5mL/min,thent 0 = V m /F = 2/0.5 = 4min;t 0 can be regarded as the time required to empty the column of the mobile phase that was originally present in the column. For the common case where the column inner diameter ≈ 4.6 mm, we can conveniently estimate values of V m (by combining Eqs. 2.7 and 2.7a): V m (mL) ≈ 0.01L (for 4 to 5 mm i.d. columns, with L in mm) (2.7b) Values of t 0 can then be obtained from Equation (2.7b), with t 0 = V m /F.For a further discussion of the measurement, accuracy and significance of column dead-time or dead-volume, see [2–4]. 2.3.2 Role of Separation Conditions and Sample Composition The relative effect of different separation conditions on sample retention k is summa- rized in the second column of Table 2.2. Table 2.2 is applicable for different HPLC modes, but the following discussion will assume reversed-phase chromatography (RPC). The mobile phase for RPC is usually a mixture of water or aqueous buffer (A-solvent) and an organic solvent (B-solvent) such as acetonitrile or methanol. As the volume-percent of organic solvent (%B) is increased, the retention of all sample compounds decreases. A mobile phase that provides smaller values of k is referred to as a ‘‘stronger’’ mobile phase; similarly water is referred to as a ‘‘weak’’ solvent, and 2.3 RETENTION 29 Table 2.2 Effect of Different Separation Conditions on Retention (k), Selectivity (α), and Plate Number (N) Condition k α N %B ++ + − B-solvent (acetonitrile, methanol, etc.) + ++ − Temperature + + + Column type (C 18 , phenyl, cyano, etc.) + ++ − Mobile phase pH a ++ ++ + Buffer concentration a ++− Ion-pair-reagent concentration a ++ ++ + Column length 0 0 ++ Particle size 0 0 ++ Flow rate 0 0 + Pressure −−+ b Note: ++,majoreffect;+, minor effect; -, relatively small effect; 0, no effect; bolded quantities denote conditions that are primarily used (and recommended) to control k, α,orN, respectively (e.g., %B is varied to control korα, column length is varied to control N). a For ionizable solutes (acids or bases). b Higher pressures allow larger values of N by a proper choice of other conditions; pressure per se, how- ever, has little direct effect on N (see Sections 2.4.1.1 and 2.5.3.1). organic solvents are ‘‘strong.’’ Typically values of k decrease by a factor of 2 to 3 for a change of +10% B; an example of the effect of %B on sample retention is shown in Figure 2.6, for the separation of a mixture of five herbicides. A mobile phase of 80% B in Figure 2.6a results in rapid elution of the sample, with small values of k (0.3–0.8) and poor separation. When %B is decreased (50% B, Fig. 2.6b), separa- tion improves, separation or ‘‘run time’’ increases (16 min vs. 1.5 min in Fig. 2.6a), and peak heights are reduced because the peaks are wider. Retention normally is controlled within a desired range of k by the choice of %B. The conditions of Table 2.2 can also be varied in order to control separation selectivity (α) or column efficiency (N); see Section 2.5 for details. Reversed-phase chromatography involves a nonpolar stationary phase or col- umn (e.g., C 18 ) and a polar, water-containing mobile phase. Polar solutes will prefer the polar mobile phase (‘‘like attracts like’’) and be less retained (larger R, smaller k), while nonpolar solutes will interact preferentially with the nonpolar stationary phase and be more retained (smaller R, larger k). The preferential interaction of a nonpolar solute (n-hexane) with the nonpolar stationary phase is illustrated in Figure 2.7a, while Figure 2.7b shows the preferential interaction of a polar solute (1,3-propanediol) with the polar mobile phase. Figure 2.7c is a chromatogram of several mono-substituted benzenes that vary in polarity or ‘‘hydrophobicity’’ because of the nature of the substituent group. Polar (less hydrophobic) groups such as –NHCHO, –CH 2 OH, or –OH reduce retention relative to the unsubstituted solute benzene (shaded peak), while less polar (more hydrophobic) groups such as chloro, methyl, bromo, iodo, and ethyl increase retention. 30 BASIC CONCEPTS AND THE CONTROL OF SEPARATION 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Time (min) 80% methanol (0.3 ≤ k ≤ 0.8) 50% methanol (4 ≤ k ≤ 19) (a) (b) 1 2 3 4 5 t 0 51015 1 2 3 4 5 0 Time ( min ) Figure 2.6 Separation as a function of mobile phase %B (%v methanol). Herbicide sample: 1, monolinuron; 2, metobromuron; 3, diuron; 4, propazine; 5, chloroxuron. Conditions, 150 × 4.6-mm, 5-μmC 18 column; methanol/water mixtures as mobile phase; 2.0 mL/min; ambient temperature. Recreated chromatograms from data of [7]. Ionized acids and bases are much more ‘‘polar’’ and therefore less retained than their neutral counterparts. A change in mobile phase pH that results in increased solute ionization will therefore lead to a decrease in retention time (Section 7.2). 2.3.2.1 Intermolecular Interactions This section provides additional insight into sample retention as a function of the solute, column, and mobile phase; it also represents more information than is usually required in practice. The reader may therefore prefer to skip to following Section 2.3.2.2, and return to this section as needed. The attraction between adjacent molecules of a solute and solvent is the result of several different intermolecular interactions, as illustrated in Figure 2.8. In principle, a quantitative understanding of these interactions should allow estimates—or even predictions—of retention as a function of molecular structure. While this is usually not possible at the present time (see Section 2.7.7), an understanding of these interactions can prove useful in other ways; for example, when selecting a different column for a change in separation (Section 5.4). Dispersion interactions (Fig. 2.8a) result from the random, instantaneous positions of electrons around adjacent atoms of either the solvent (S)orthesolute (X). Typically the arrangement of electrons around the nucleus of atom S will be unsymmetrical at any instant of time (as in Fig 2.8a), and this will cause the electrons in adjacent atom X to move as shown (due to coulombic repulsion). The result is an instantaneous dipole moment for both S and X that favors electrostatic attraction. The strength of dispersion interactions increases with the polarizability 2.3 RETENTION 31 (a)(b) sample molecule H O H Nonpolar (hydrophobic) interaction with the nonpolar stationary phase Polar(hydrogen bonding) interaction with the polar mobile phase C 18 C 18 C 18 C 18 C 18 C 18 C 18 CH 3 −CH 2 −CH 2 −CH 2 −CH 2 −CH 3 HO− CH 2 −CH 2 −CH 2 −OH H O H 0246 Time (min) −OCH 3 (anisole) benzene −NH−CHO (benzylformamide) −CH 2 OH (benzyl alcohol) −OH (phenol) −CHO (benzaldehyde) −COCH 3 (acetophenone) −CN (benzonitrile) −NO2 −COOCH 3 (methylbenzoate) −Cl+ −CH 3 (chlorobenzene + toluene) −I −CH 2 CH 3 −Br (c) Figure 2.7 Sample polarity and retention. Illustration of the interaction of a nonpolar sam- ple solute with the stationary phase (a) and of a polar solute with the mobile phase (b); (c) effect of different substituents on the retention of monosubstituted benzenes; 150 × 4.6-mm Hypersil C 18 column, 50% acetonitrile/water as mobile phase, 25 ◦ C, 2 mL/min; recreated chromatogram from data of [8]. of each of the two adjacent atoms. Solute polarizability increases with the size of the molecule (number of atoms or molecular weight) and with refractive index [9]; dispersion interactions are therefore stronger for aromatic compounds and for molecules substituted by atoms of higher atomic weight (sulfur, chlorine, bromine, etc.)—provided that molecules are of similar size. Dispersion interactions exist between every adjacent pair of atoms, and this interaction largely accounts for the physical attraction between molecules of all kinds (especially for less polar molecules). Because of the nonspecific and universal nature of dispersion interactions, they are significant in both the mobile and stationary phases. Dispersion interactions therefore tend to cancel, and they generally play only a minor role in determining selective interactions of the kind that result in changes in relative retention when the mobile phase or column is changed. Dispersion interactions contribute to hydrophobic interactions, so called because 32 BASIC CONCEPTS AND THE CONTROL OF SEPARATION Dispersion Dipole-dipole S X . . . NO 2 NO 2 Charge transfer (π−π) (a)(b) (c)(d) (e) CH 3 −C≡N NO 2 + − + − R N(CH 3 ) 2 CH 3 O−H Hydrogen bonding Ionic . . . . . . O H−O + − − + +− − + X + Figure 2.8 Intermolecular interactions that can contribute to sample retention and selectivity. of the attraction of less polar solutes to nonpolar RPC stationary phases (or their ‘‘water-fearing’’ rejection from the polar aqueous phase). As the strength of dispersion interactions increases (for larger, less polar solute molecules), the solute is increasingly retained. Dipole–dipole interaction is illustrated in Figure 2.8b for the case of dipolar molecules of solvent (acetonitrile, CH 3 C≡N) and solute (a nitroalkane, R–NO 2 ). The functional groups (–C≡Nand–NO 2 ) in these two molecules each have a large, permanent, dipole moment, causing the two molecules to align for maximum electrostatic interaction (positive end of one molecule adjacent to the negative end of the other). The strength of dipole interaction is proportional to the dipole moments of each of the two interacting groups (not the dipole moment of an entire, multi-substituted molecule), because dipole interactions are only effective at very close range (i.e., adjacent atoms or groups). Hydrogen bonding interactions are shown in Figure 2.8c,fortwocases: an acidic (or proton-donor) solvent (methanol) interacting with a basic (proton- acceptor) solute (N,N-dimethylaniline), or an acidic solute (phenol) interacting with a basic solvent tetrahydrofuran (THF). The strength of hydrogen bonding increases with increasing hydrogen-bond acidity and basicity of the two interacting species (Table 2.3). Ionic (coulombic) interaction is illustrated in Figure 2.8d for a positively charged sample ion (X + ) interacting with surrounding molecules of a polarizable 2.3 RETENTION 33 Table 2.3 Solvent Selectivity Characteristics Normalized Selectivity a Solvent H-B Acidity α/ H-B B asicity β/ Dipolarity π ∗ / P b ε c Acetic acid 0.54 0.15 0.31 6.0 6.2 Acetonitrile 0.15 0.25 0.60 5.8 37.5 Alkanes 0.00 0.00 0.00 0.1 1.9 Chloroform 0.43 0.00 0.57 4.1 4.8 Dimethylsulfoxide 0.00 0.43 0.57 7.2 4.7 Ethanol 0.39 0.36 0.25 4.3 24.6 Ethylacetate 0.00 0.45 0.55 4.4 6.0 Ethylene chloride 0.00 0.00 1.00 3.5 10.4 Methanol 0.43 0.29 0.28 5.1 32.7 Methylene chloride 0.27 0.00 0.73 3.1 8.9 Methyl-t-butylether 0.00 ≈0.6 ≈0.4 ≈2.4 ≈4 Nitromethane 0.17 0.19 0.64 6.0 35.9 Propanol (n-oriso) 0.36 0.40 0.24 3.9 6.0 Tetrahydrofuran 0.00 0.49 0.51 4.0 7.6 Triethylamine 0.00 0.84 0.16 1.9 2.4 Water 0.43 0.18 0.45 10.2 80 Note: see Appendix I (Table I.4) for additional solvent information. a Values from [11], where  refers to the sum of values of α, β,andπ ∗ for each solvent. b Polarity index; values from [12]. c Dielectric constant; values from [13]. solvent. The positive charge on the solute ion causes a displacement of charge in the solvent molecules, for maximum electrostatic interaction. The strength of ionic interaction increases for solvents with a larger dielectric constant ε (Table 2.3). Ionic interaction can also occur between a charged sample ion and ions in either the mobile or stationary phases; see the discussion of ion-pair chromatography (Section 7.4.1) and ion-exchange chromatography (Section 7.5.1). Charge transfer or π –π interaction is illustrated in Figure 2.8e for the π -acid (electron-poor) solute 1,3-dinitrobenzene and the π-base (electron-rich) solvent benzene. Interactions of this kind can occur between any two aromatic (or unsat- urated) species, with the strength of the interaction increasing for stronger π-bases such as polycyclic aromatics (e.g., naphthalene and anthracene), and for stronger π-acids (e.g., aromatics substituted by electron withdrawing nitro groups). The solvent acetonitrile (a π-acid) can also interact with aromatic solutes by π –π interaction [10]. The polar interactions of various nonionic aliphatic solvents used in HPLC can be described by the solvent-selectivity triangle (Fig. 2.9, [11]). The position of each solvent in this plot indicates its relative hydrogen-bond acidity α/, hydrogen-bond basicity β/, and dipolarity π */. Thus amines are relatively strong hydrogen-bond bases, as indicated by their position near the top of the triangle (large β). Similarly 34 BASIC CONCEPTS AND THE CONTROL OF SEPARATION H-B Basic (β/∑) H−B acidic (α/∑) Dipolar (π∗/∑ ) amines ethers THF DMSO esters N,N-dialkyl amides ketones nitriles nitro compounds H 2 O glycols formamide alcohols R-COOH CH 2 Cl 2 CHCl 3 perfluoroalcohols basic solvents dipolar solvents acidic solvents Figure 2.9 Solvent-selectivity triangle for aliphatic solvents of various kinds. See Table 2.3 for values of the solvent properties plotted. Adapted from [11]. nitroalkanes, aliphatic nitriles, and CH 2 Cl 2 all have groups with large dipole moments, and they are situated near the lower right-hand side of the triangle. Perfluoroalcohols are especially strong hydrogen-bond donors (and simultaneously very weak acceptors); they and carboxylic acids (R–COOH) are found near the lower left of the triangle (large α). Table 2.3 lists (1) relative contributions to solvent polarity from dipolarity and hydrogen-bond acidity or basicity, (2) a measure of overall solvent polarity (P  ), and (3) values of the dielectric constant ε. Larger values of ε for the mobile phase indicate increasing ionic interaction with solute molecules as in Figure 2.8d, increasing solubility in the mobile phase for ionic solutes, and smaller values of k for ionic solutes. For a comprehensive review of intermolecular interactions in chromatography, see [14]. More will be said about the solvent-selectivity triangle of Figure 2.9 and solvent selectivity in Chapters 6 and 8. Section 5.4 on column selectivity provides a similar treatment of interactions between the solute and the stationary phase. 2.3.2.2 Temperature Temperature is an important variable in HPLC, as it has a significant effect on values of k. For most solute molecules and customary separation conditions, solute retention varies with temperature according to the Van’t Hoff equation, which can be expressed in HPLC as log k = A + B T K (2.8) 2.4 Peak Width and the Column Plate Number N 35 For a given solute and other conditions unchanged, A and B are temperature- independent constants, and T K is the temperature (K). Values of k usually decrease with increasing temperature (positive value of B)by1–2%per ◦ C; thus a 50 ◦ C increase will cause about a 2-fold decrease in k. As temperature increases, separation often worsens, while peak heights increase (similar to an increase in %B, as in Fig. 2.6). It should be noted that deviations from Equation (2.8) are not uncommon, sometimes resulting in curved plots of log k against 1/T K . In a few cases, retention is observed to increase with an increase in temperature. These exceptions to Equation (2.8) can arise for various reasons, including changes with temperature of (1) the ionization of a solute [15, 16], (2) solute molecular conformation [17], and (3) the stationary phase [18]. Temperature also affects the column plate number N and pressure drop (see Section 2.4). The practical use of most current HPLC equipment is limited to temperatures of <80 ◦ C (Section 3.7.2), and HPLC column lifetimes often are shorter at temperatures > 60 ◦ C (Section 5.8). For a further discussion of the role of temperature in HPLC, see Section 2.5.3.1 and [19–20a]. 2.4 PEAK WIDTH AND THE COLUMN PLATE NUMBER N As illustrated in Figure 2.3, solute molecules spread out to enclose a larger volume (or form a wider band) during their migration through the column. When the band leaves the column to become a peak in the chromatogram, it will have a width that can be defined in various ways. The baseline peak width W is illustrated for the first peak i of Figure 2.10a. Tangents are drawn to each side of the peak (through the inflection points), and their intersection with the baseline determines the value of W. When referring to peak width in this book, we will assume values of baseline peak width W. The relative ability of a column to furnish narrow peaks is described as column efficiency, and is defined by the plate number N: N = 16  t R W  2 (2.9) For example, W for peak i in Figure 2.10a is equal to (4.00 − 3.85) = 0.15 min, and t R = 3.93 min. Therefore N = 16 × (3.93/0.15) 2 = 10, 980. Values of N can vary for different samples, separation conditions, and columns (Section 2.4.1). The larger the value of N, the narrower are the peaks in the chromatogram, and the better is the separation. Peak width can be measured more conveniently (and precisely) by the half-height peak width W 1/2 , as illustrated for peak j in Figure 2.10a; values of W 1/2 ≡ 0.588W are reported by many data systems. When the peak width at half height is used to calculate N, N = 5.54  t R W 1/2  2 (2.9a) . stationary phase Polar(hydrogen bonding) interaction with the polar mobile phase C 18 C 18 C 18 C 18 C 18 C 18 C 18 CH 3 −CH 2 −CH 2 −CH 2 −CH 2 −CH 3 HO− CH 2 −CH 2 −CH 2 −OH H O H 0246 Time (min) −OCH 3 (anisole) benzene −NH−CHO. around the nucleus of atom S will be unsymmetrical at any instant of time (as in Fig 2.8a), and this will cause the electrons in adjacent atom X to move as shown (due to coulombic repulsion) benzenes; 150 × 4.6-mm Hypersil C 18 column, 50% acetonitrile/water as mobile phase, 25 ◦ C, 2 mL/min; recreated chromatogram from data of [8] . of each of the two adjacent atoms. Solute polarizability