Anal. Chem. 1982, 54, 2593-2596
131
LE!
-2
11 I /
spectra of a test sample (H20/D,0 doped with CuSO,) using pulse angle and T / T , values of: (A) go', 4.61; (B) 70°, 4.19; (C) 50°, 3.59; (D) 30°, 2.66; (E) IO', 0.92. These values are predicted from eq 1 and 4 to yield c = 1 %. Relative peak heights (proportlonalto S I N ) are closely comparable to the theoretical values shown in Figure 2, for E = 1%. Flgure 3. 'H NMR
Table I. Conditions for Obtaining an Acceptable Maximum Error Range ( E ) with Near-Optimal Efficiency required T/T,ratiosa for 6 = 70"
= 1.0% = 2.5% E = 5.0% E
E
f
a
= 10.0%
4.19 3.28 2.60 1.93
s
= 90"
4.61 3.69 3.00 2.30
From eq 1 and 4, T/T1 = ln[(100 - 100 cos 6 t
E
cos
)/El.
6. (T1)1/2(S/N) is indicaiive of SIN for a given Tl value and is plotted against T / T I for various 6 values in Figure 2. Sets of isoaccurate points (6, TIT,) deduced from Figure 1 are marked in Figure 2. These points occur to the right of the maxima in the figure. Thus, for a given longest T I value, an increase in T from that defined by the coordinates of any isoaccurate point results in a decrease in SIN. If on the other hand Tis decreased, the maximal acceptable error is exceeded (Figure 1). Consequently, the isoaccurate points in Figure 2 represent the maximal 9 / N attainable consistent with the chosen 6 value and desired error range. Clearly, for high accuracy, optimal SIN is always achieved by using large pulse angles of 70-90°, rather than small pulse angles. This is illustrated experimentally in Figure 3. The Tl value for the sample (H20/D20doped with CuS04)was determined by the inversion-recovery (12) procedure. Spectra were obtained by using 6 values of between 10' and 90°,and T values deduced from Figure 1Correspondingto E = 1%. In each case the same total experimental time was used to collect free induction decays, and the spectra were normalized to the same noise level by scaling by the square root of the number of
2593
scans. The relative peak heights (and therefore SIN) observed are close to the values for c = 1% shown in Figure 2. In this case use of 6 = 10' reduces SIN by a factor of 2.6 compared with the 6 = 90' result. This is equivalent to a factor of 6.8 in terms of the time required to obtain the same S I N ratio using 6 = 10' rather than 6 = 90'. The use of large pulse angles differs from the usual practice when routine lH NMR spectra are sought. It has been shown (6) that for a particular resonance characterized by a single T I value, optimal SIN may be achieved by setting the pulse to pulse time equal to the chosen acquisition time, and setting the pulse angle to the so-called Ernst angle (1,2) defined by
cos 6 = e-TIT1 (6) Acquisition times are usually chosen on the basis of the expected transverse relaxation rates (6) or may be simply limited by available computer memory. Most often these considerations lead to TITl < 1and hence small optimal pulse angles may be indicated. However, in general the Ernst angle approach for a sample characterized by a range of T1values will not yield quantitative data (6). Suitable conditions for obtaining near-optimal S I N ratios within the constraints imposed by the need for quantitativity are summarized in Table I. LITERATURE CITED (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)
(13)
Ernst, R. R. Adw. Magn. Reson. 1966, 2 , 1-135. Ernst, R. R.; Anderson, W. A. Rev. Sci. Insfrum. 1966, 3 7 , 93-102. Waugh, J. S. J . Mol. Spectrosc. 1970, 35, 298-305. Jones, D. E.; Sternlicht, H. J . Magn. Reson. 1972, 6 , 167-182. Ernst, R. R.; Morgan, R. E. Mol. fhys. 1973, 26, 49-74. Becker, E. D.; Ferretti, J. A.; Gambhlr, P. N. Anal. Chem. 1979, 51, 1413-1420. Solomon, I. Phys. Rev. 1955, 99, 559-565. Glllett, S.;Delpeuch, J.J. J . Magn. Reson. 1960, 38, 433-445. Cookson, D. J.; Smlth, B. E., unpublished results. Kalk, A.; Berendsen, H. J. C. J . Magn. Reson. 1976, 2 4 , 343-366. Lublanez, R. P.; Jones, A. A. J . Magn. Reson. 1980, 38, 331-341. Farrar, T. C.; Becker, E. D. "Pulse and Fourier Transform NMR"; Academic Press: New York, 1971. Llndon, J. C.; Ferrige, A. 0. frog. NMR Spectrosc. 1980, 14, 27-66.
David J. Cookson Brian E. Smith* The Broken Hill Proprietary Co. Ltd. Melbourne Research Laboratories 245 Wellington Road Clayton, 3168 Victoria, Australia RECEIVED for review May 14,1982. Accepted September 2, 1982. This work has been supported by the National Energy Research Development and Demonstration Programme administered by the Australian Commonwealth Department of National Development and Energy.
Classification of Multisolvent Mobile Phase Systems in Liquid Chromatography Sir: Interest in mobile ]phasestrength and selectivity effects in liquid chromatograph>r(LC) has increased recently (1-4), especially with regards to optimizing separations by statistical approaches (5-9). In addition to commonly used binary solvents, ternary and quaternary systems have been described for superior isocratic separations ( I , 7, 10-12),and certain ternary solvent gradients have demonstrated better separations than corresponding binary solvent mobile phases (13, 14). Despite the expanded use of multisolvent systems, no attempt has been made to describe all the possible mobile phase classifications systematically, especially as they relate
to both solvent strength and selectivity. A comprehensive description containing these factors is currently available only for the simplest case-that of binary solvent mobile phases (15, 16). We propose here a general description of multisolvent LC mobile phases that greatly expands the opportunity for optimized solvent strength and selectivity effects. The proposed classification should enhance a more systematic investigation of these important effects on LC solute retention and facilitate current efforts in LC optimization. Although the solvent classifications discussed below are largely qualitative, more
0003-2700/82/0354-2593$01.25/0 0 1982 American Chemlcal Society
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ANALYTICAL CHEMISTRY, VOL. 54, NO. 14, DECEMBER 1982
Table I name A
simple isocratic (SI)
B C
isocratic multisolvent programming (IMP) isoselective multisolvent gradient elution (IMGE)
D
selective multisolvent gradient elution (SMGE)
detailed and quantitative aspects of the effects of solvent strength and selectivity on LC retention behavior are currently being investigated and will be described shortly (17). Historically, there have been two major types of solvent systems available in LC, isocratic and gradient elution. Isocratic refers to a mobile phase of constant eluting strength, while gradient elution involves a change in the eluting strength during a separation (18). In the case of binary solvents, an isocratic condition occurs when the relative proportions of each solvent are fixed during the separation. A gradient elution effect occurs when the proportions of the solvents change during the separation, since no two solvents have exactly the same strength. Traditional definitions of isocratic and gradient elution solvent systems do not recognize the possibility of a change in solvent selectivity instead of, or with, a change in solvent strength. Dolan, Gant, and Snyder (16) have noted that solvent selectivity a values in LC may change slightly in a particular mobile phase system with a change in the slope of the gradient elution solvent profile, caused by an increase in the concentration of the modifying solvent (e.g., percent methanol in reverse-phase LC). However, this is a minor effect, relative to selectivity changes due to the deliberate introduction of modifying solvents of different chemical types. More important, the possibility of changing solvent selectivity during a separation, while keeping solvent strength constant, has not been suggested, as far as we are aware. We propose that solvent systems in LC can be rationally divided into four major types, based upon changes in solvent strength and selectivity. These four categories are listed in Table I. The first two cases are those where solvent strength remains constant during a separation, while in the latter two, solvent strength is varied. T o facilitate discussion of these mobile phase categories, we provide two models to represent possible changes in solvent selectivity and/or solvent strength. The solvent selectivity triangle in Figure l a represents possible selectivity effects for reverse-phase LC, according to Snyder (19). Any position in this triangle represents a unique solvent composition of methanol (MeOH), acetonitrile (ACN), and tetrahydrofuran (THF) with water carrier. The corners of this triangle represent binary solvent mixtures of MeOH/water, ACN/water, and THF/water, all of which have the same solvent strength or eluting power. Since the solvent strength (S) of each modifier is different (SMaH = 2.6, SA,, = 3.1, S= 4.4;S, defined as O.O),the volume percent of each organic modifier in water is different at each corner of the triangle. For example, in reverse-phase LC, if the top corner of the solvent triangle is 60% MeOH/40% water, one may be calculate that the equivalent solvent strength of the other corners would be 50.3% ACN/49.7% water and 35.5% THF/64.5% water (20). Total solvent strength, ST, can also be defied for n solvents as n
ST = c4isi i=l
where
is the volume fraction of the ith solvent and Si is the
condition during separation solvent strength, solvent selectivity, and solvent composition remain constant solvent strength remains constant; solvent selectivity and composition change solvent strength and solvent composition change; solvent selectivity, due to ratio of modifying solvents, remains constant solvent strength, solvent selectivity, and solvent composition all change a
SOLVENT TRIANGLE FOR REVERSE-PHASE LC CONSTANT SOLVENT STRENGTH
MeOH/H20
0.0
Figure 1. (a) Solvent Selectivity triangle for lsocratic reverse-phase LC. (b) Solvent selectivity prism for gradlent elution reverse-phase LC with water as carrier solvent. S represents the solvent strength pa-
rameter (see text).
strength value for that solvent. In the illustration just cited, ST = 1.56 for any of the corners of the solvent triangle. This S value would also be identical for any other solvent composition represented in this triangle. It is important to note that quaternary solvent mixtures are required for the total range of selectivity effects in LC. In reverse- or normal bonded-phase LC, mixtures of proton acceptor, proton donor, and dipole solvents may be required in the mobile phase carrier to form the mobile phase that exhibits the best resolution for all the peaks in a mixture (7). In adsorption LC, mixtures of nonlocalizing, localizing dipole, and localizing base solvents in the carrier provide the optimum opportunity for resolving all components in a sample (11,12). The model in Figure l b represents the generalized form of solvent selectivity for different solvent strengths. This solvent prism can be used to represent not only the relative proportions of three modifying solvents to each other but also the total solvent strength, ST,for the solvent system. The solvent selectivity triangle is inscribed in the left face of this solvent prism. However, two additional facets of the prism can be noted. First, the front face (left) of Figure l b represents a solvent strength ST = 0.0; any point on this triangle represents 100% water. Second, since the Sivalue for MeOH is 2.6, the back face corresponds to a solvent strength ST = 2.6, which is the maximum strength attainable in pure MeOH. The value of 4ACN for the back corner is 0.84 and + T m for the back-right corner is 0.59. Although it is possible to achieve a stronger
ANALYTICAL CHEMISTRY, VOL. 54, NO. 14, DECEMBER 1982 ISOCRATIC MULTISOLVENT PROGRAMMING
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\ ACN
C
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d
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' \
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i
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