“Orthogonal” separations for reversed-phase liquid chromatography

Journal of Chromatography A, 1101 (2006) 122–135

“Orthogonal” separations for reversed-phase liquid chromatography Jackson Pellett a , Patrick Lukulay a , Yun Mao b , William Bowen b , Robert Reed b , M. Ma c , R.C. Munger c , J.W. Dolan d , Loren Wrisley e , K. Medwid e , N.P. Toltl f , C.C. Chan f , M. Skibic g , Kallol Biswas g , Kevin A. Wells g , L.R. Snyder h,∗ a b

Pfizer Global Research & Development, Pharmaceutical Sciences, Analytical R&D, Michigan Laboratories, Ann Arbor, MI, USA Merck & Co., Inc., Pharmaceutical Research & Development, Pharmaceutical Analysis and Control, West Point, PA 19486, USA c Amgen Inc., Analytical Sciences, One Amgen Center Drive, Thousand Oaks, CA 91320, USA d BASi Northwest Laboratory, McMinnville, OR 97128, USA e Wyeth Research, Pearl River, NY 10965, USA f Eli Lilly Canada, Toronto, Canada g Eli Lilly, Indianapolis, IN, USA h LC Resources, 26 Silverwood Ct., Orinda, CA 94563, USA Received 11 July 2005; received in revised form 27 September 2005; accepted 27 September 2005 Available online 19 October 2005

Abstract A general procedure is proposed for the rapid development of a reversed-phase liquid chromatographic (RP-LC) separation that is “orthogonal” to a pre-existing (“primary”) method for the RP-LC separation of a given sample. The procedure involves a change of the mobile-phase organic solvent (B-solvent), the replacement of the primary column by one of very different selectivity, and (only if necessary) a change in mobile phase pH or the use of a third column. Following the selection of the “orthogonal” B-solvent, column and mobile phase pH, further optimization of peak spacing and resolution can be achieved by varying separation temperature and either isocratic %B or gradient time. The relative “orthogonality” of the primary and “orthogonal” RP-LC methods is then evaluated from plots of retention for one method versus the other. The present procedure was used to develop “orthogonal” methods for nine routine RP-LC methods from six pharmaceutical analysis laboratories. The relative success of this approach can be judged from the results reported here. © 2005 Elsevier B.V. All rights reserved. Keywords: Reversed-phase liquid chromatography; Orthogonal method; Pharmaceutical analysis

1. Introduction When pharmaceutical samples are to be separated by reversed-phase liquid chromatography (RP-LC), a common concern is that an impurity or sample degradation peak may be overlooked—due to its being overlapped by a second (possibly larger) peak in the chromatogram. This has led to a need for so-called “orthogonal” separations; i.e., two separations of quite different selectivity, with marked changes in relative retention so that two peaks which are unresolved in one chromatogram will likely be separated in the second chromatogram. Note that the term “orthogonal” is presently used in the literature [1–4] and within the pharmaceutical industry to denote separations, which

∗

Corresponding author.

0021-9673/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2005.09.080

simply provide differing relative retention. Other workers prefer to limit the use of “orthogonal” to systems where elution times can be treated as statistically independent [5]—a much more restrictive definition than is used by us. In the present paper, which deals with separations that are not statistically independent, we distinguish our use of “orthogonal” by enclosing the word in quotation marks. A hypothetical example of separation “orthogonality” is shown in Fig. 1. Assuming an original (primary) RP-LC method: (a) in which such a peak overlap occurs (peaks 6, 6a), an “orthogonal” separation (b) should have a high probability of disengaging the two peaks. The degree of “orthogonality” for two such separations is commonly characterized by the scatter of plots of retention for one separation versus the other (Fig. 1c). Isocratic elution is assumed in Fig. 1, but gradient separations are more common for measurements of sample impurities.

J. Pellett et al. / J. Chromatogr. A 1101 (2006) 122–135

Prior attempts [1–4] at developing pairs of RP-LC “orthogonal” procedures as in Fig. 1a and b have started with the selection of a representative set of test compounds (e.g., pharmaceutical compounds of varying molecular weight and functionality), followed by collecting retention data for these compounds with different mobile phase-column combinations. Different sets of data (same compounds, different conditions) can then be compared as in Fig. 1c in order to determine which “orthogonal”-method pairs have retention times which are least correlated (minimum r2 , corresponding to maximally “orthogonal” separation). The separation of a particular sample can then be carried out by means of two or more such mutually “orthogonal” methods, which should minimize the likelihood that a sample component might be overlooked because it was overlapped by a larger peak in one of the two separations. This approach is facilitated by the use of mass-spectrometric (LC–MS) detection, which does not require the baseline separation of every peak in either the primary or “orthogonal” procedure. A final (primary) procedure for the routine measurement of sample purity, on the other hand, usually involves UV detection and requires the separation of all known sample components of

123

Fig. 2. Recommended procedure for the development of a “orthogonal” method.

interest. It is also desirable to have available a corresponding “orthogonal” procedure based on UV detection which also separates all known sample components of interest. In the present study, we have examined a somewhat different approach for the development of “orthogonal” RP-LC methods, one that may be more applicable for routine application. Rather than using two previously identified “orthogonal” procedures at the start of method development for purposes of finding all impurity peaks present in the sample, we assume that an original or “primary” method already exists. This will often be the case, as many workers have a preference for columns and other separation conditions that may differ from the recommendations of published procedures [1–4] that emphasize method “orthogonality”. Once the primary method has been developed, an “orthogonal” procedure can be used to either: (a) check for possible overlapping (and therefore overlooked) sample components in the primary method or (b) test that no new overlapped impurities appear in later samples. For two such routine, sampleanalysis procedures, we assume UV detection and a preference for the separation of all known sample components by each method. Starting with an existing primary method, an efficient procedure for the development of an “orthogonal” RP-LC method is proposed (Fig. 2). This procedure was evaluated in six different pharmaceutical laboratories as described below. For the samples and separations discussed here, mobile phase pH was not varied as a means of increasing separation “orthogonality”. 2. Background and theory

Fig. 1. Hypothetical illustration of: (a) an original (primary) and (b) an “orthogonal” separation; (c) plot of log k for the separation of (b) vs. (a). The shaded peak #6a was originally hidden under peak #6. See text for details.

The success of an “orthogonal” separation as illustrated in Fig. 1 rests on two requirements. First, changes in selectivity for the “orthogonal” method must be large (and verifiable) so as to likely move any “new” peak from its original position under the overlapping peak. Second, the final “orthogonal” separation

124

J. Pellett et al. / J. Chromatogr. A 1101 (2006) 122–135

should separate all of the peaks in the original sample (preferably with baseline resolution, Rs > 1.5). A standardized, proven procedure for the development of an “orthogonal” method (as in Fig. 2) is also desirable, preferably one requiring a minimum of effort. The required change in selectivity for an observable separation of two previously overlapped peaks (as in Fig. 1a) by an “orthogonal” separation (Fig. 1b) corresponds to an increase in Rs of at least 1 unit. Resolution for two adjacent peaks can be described [6] by a well-known relationship 
  k 1 Rs = (α − 1) N 1/2 (1) 4 (1 + k) where α is the separation factor for the two peaks, N is the column plate number, and k is the retention factor of the first peak. For representative conditions (N = 10,000, k > 1), Eq. (1) requires a corresponding value of (α − 1) ≥ 0.08 for Rs = 1. However, a change in α can move an overlapped band either toward or away from the center of the overlapping band, so a safer requirement is a change in Rs by at least 1.5 units. The latter requires a change in (α − 1) = 0.12, which can be expressed as a change in the absolute value of log α (|δlog α|) of ≥ 0.05 units. An average value of |δlog α| ≡ |δlog α|avg > 0.10 for all peak-pairs in the “orthogonal” separation therefore seems likely to result in an adequate separation of any overlapped peak-pairs in the primary method. Larger values of |δlog α|avg further increase the probability of separating any overlapped peaks from the primary method, and further application of the procedure of Fig. 2 may suggest a larger minimum allowable value of |δlog α|avg . The latter criterion (|δlog α|avg > 0.10) is somewhat arbitrary, but it does have the advantage of providing an objective, quantitative measure of how well an “orthogonal” separation is likely to achieve its intended purpose. It also has the advantage of being determined for compounds known to be present in the sample; likely impurities are usually structurally related to these sample compounds, and are correspondingly more likely to exhibit similar changes in

relative retention for the changed conditions of the “orthogonal” method. The development of an “orthogonal” separation (starting with the primary method) requires attention to three questions: • What separation conditions are best changed in order to achieve |δlog α|avg ≥ 0.10? • How is the average value of |δlog α|avg for an “orthogonal” separation best measured? • Following some change in conditions that results in a large enough value of |δlog α|avg , what further change in conditions can best achieve an adequate separation of all previously known sample components by the “orthogonal” method (e.g., with Rs > 1.5)? 2.1. Choice of experimental conditions for an “orthogonal” separation Several experimental conditions can affect selectivity, as summarized in Table 1. Note that the first five variables (#1–5) are effective for any sample—neutral or ionized, whereas variables #6–9 primarily affect selectivity for samples that contain ionizable compounds (acids or bases). Because some samples may not contain ionizable compounds, or the composition of the sample may not be fully known, a general procedure for developing an “orthogonal” method should be applicable for any sample (therefore primarily based on one or more of variables #1–5). A very limited survey [7] has compared the relative effect on RP-LC selectivity for a change in variables #1–4 of Table 1, finding that changes in temperature (option #3 of Table 1) are less effective, and changes in solvent type (option #4; e.g., methanol replacing acetonitrile) are more effective. More recently, experimental data have become available which allow a more reliable and complete assessment of changes in selectivity for different conditions [8] or for a change in RP-LC columns [9,10]. Based on the latter data, resulting estimates of |δlog α|avg for different changes in conditions are derived in Appendix A and summa-

Table 1 Experimental conditions that affect selectivity in RP-LC Condition

Comment

1. Solvent strength (%B) 2. Gradient steepness, tG 3. Temperature T

Usually a maximum change in %B ≤10% Usually a maximum change in tG ≤10-fold Maximum change in T is limited by a need to maintain 1 ≤ k ≤ 10 and avoid temperature degradation of the column (allowed change in temperature ≤30 ◦ C)

4. Solvent type Acetonitrile Methanol Tetrahydrofuran 5. Column type 6. Mobile phase pH 7. Mobile phase buffer type concentration 8. Mobile phase amine additives 9. Ion-pair reagents

Preferred initial solvent Acceptable alternative, unless detection at <210 nm is required Less desirable alternative, avoided by many laboratories Very wide range of columns available [10]; change in selectivity cannot be varied continuously, unlike other selectivity variables Potentially large change in selectivity for ionizable compounds; no change for other compounds Moderate change in selectivity for ionized bases; little change for other compounds Moderate change in selectivity for protonated bases; little change for other compounds Potentially large change in selectivity for ionized compounds; little change for other compounds

J. Pellett et al. / J. Chromatogr. A 1101 (2006) 122–135

125

Table 2 Relative effect of different changes in RP-LC conditions on selectivity Value of |δlog α|avg for a change in each condition %B conditiona

Change in Maximum |δlog α|avg

10 0.08

tG

T

MeOH

10-fold 0.20

20 ◦ C

b

0.07

0.20

Column

pH

Buffer

0.19c

5 units  0.7

Two-fold 0.02

Values calculated from data of [8,10] as described in Appendix A. The values below are average values for a sample composed of 67 different components of quite varied molecular structure. Corresponding values for a specific sample may vary widely. a Proposed change in each condition. b Methanol replaces acetonitrile or vice versa. c Assumes F = 65, which is just 1/3 the average value of the “orthogonal” columns of Table 4; i.e., a value of |δlog α| s avg = 0.19 is very conservative.

rized in Table 2 for a mixture of 67 test compounds of widely varying molecular structure. The results of Table 2 are an average of data from Appendix A for: (a) neutral compounds and (b) ionizable compounds (see Table 5); values of |δlog α|avg are two- to four-times larger for ionizable compounds versus neutral species. Samples composed of compounds of similar functionality and molecular structure (e.g., homologs) can have much smaller values of |δlog α|avg than are shown in Table 2. Values of |δlog α|avg are seen to be fairly large for a change in solvent type (methanol replacing acetonitrile, or vice versa; 0.20) or the column (0.19). This suggests that an “orthogonal” method can be based on changes in just the last two separation conditions. Further adjustments in separation for the purpose of resolving all sample peaks to baseline (Rs ≥ 1.5) might employ changes in temperature and either %B or gradient time. Although changes in temperature and gradient time often yield smaller changes in selectivity, these variables are convenient to use and in combination have been shown capable of resolving typical samples to baseline [11–16]. If an adequate separation of all components by the “orthogonal” method cannot be achieved in the latter way, or if the resulting average value of |δlog α|avg is too small, further changes in conditions can be explored (e.g., a second replacement of the column, and/or a change in mobile phase pH (Fig. 2). 2.2. Measurement of |δlog α|avg for an “orthogonal” separation The data of Table 2 suggest that a change in both the column and B-solvent can yield a combined value of |δlog α|avg ≈ (0.202 + 0.192 )1/2 ≈ 0.28; the required value of |δlog α|avg ≥ 0.10 thus appears to be a generally attainable value. However, the actual value of |δlog α|avg will depend on the nature of the sample; e.g., smaller values of |δlog α|avg are likely for samples that do not contain acids or bases. Because of the uncertainty that the predicted values of |δlog α|avg in Table 2 will apply for a given sample, it is important to measure an actual value of |δlog α|avg for the final “orthogonal” separation of a given sample, compared to the primary method. For an isocratic method, values of log k for the “orthogonal” method can be plotted versus values for the primary method, and a value of δlog k determined by linear (least squares) regression (δlog k equals the standard error SE of the plot). Since a value of

α equals the ratio of two k-values, a corresponding value of δlog α for the latter plot ≈ (21/2 ) δlog k ≈ 1.4 SE. Fig. 1c illustrates this procedure for the hypothetical example of Fig. 1a and b, with |δlog α|avg ≈ 0.25. This is a large enough change in selectivity for this (hypothetical) sample to make it likely that any overlapped peaks in the primary method will be separated by the “orthogonal” procedure. For gradient methods, it can be shown [9] that if values of gradient retention time tR (in min) are plotted for the “orthogonal” (y) versus primary (x) methods, and a value of SE is determined, then
 b ∗ δ log k = SE (2) t0 where t0 is the column dead-time (min), and b = t0 φ

S F tG

(3)

here, φ is the change in volume-fraction of the B-solvent during the gradient, tG is gradient time (min), F is flow rate (mL/min), and S ≈ 4 (S is equal to d[log k]/dφ, where φ = 0.01%B is the volume-fraction of B-solvent in the mobile phase) for samples with molecular weights M < 500 [17]; a value of S can also be estimated from the sample molecular weight (equal to 0.25 M1/2 ), or measured by means of two experiments where only isocratic %B or gradient time is varied [18]. Eq. (2) can be used to obtain values of |δlog α|avg = 1.4 δlog k for gradient elution (comparable to values of |δlog α|avg for isocratic separation). The above discussion assumes approximately linear plots of retention for the “orthogonal” versus primary method. When this appears not to be the case, a quadratic fit of the data can be used instead (Section 4.1 below). For further details on the calculation of |δlog α|avg , see Appendix B. 2.3. Proposed approach for the development of an “orthogonal” separation It is assumed that the primary method has already been developed as discussed in [6], following which the procedure of Fig. 2 will be followed for the development of an “orthogonal” method. The B-solvent chosen for RP-LC is usually either methanol or acetonitrile, although tetrahydrofuran is sometimes used. The first step in selecting conditions for the “orthogonal” separation

J. Pellett et al. / J. Chromatogr. A 1101 (2006) 122–135

126

is to change the B-solvent to either methanol or acetonitrile; i.e., a different B-solvent from that used in the primary method. When a mixture of two solvents forms the B-solvent (e.g., mixtures of methanol and acetonitrile), select either a third solvent or the B-solvent that was present in lower concentration in the mobile phase for the primary method. Next select a column of very different selectivity as described in [10]. Column selectivity can be described by values of five, measurable column characteristics: H, hydrophobicity; S* , steric selectivity; A, column hydrogen-bond acidity; B, column hydrogen-bond basicity; C, column cation-exchange capacity (which increases with mobile phase pH and the related negative charge on the column). Values of H, S* , etc. have been reported for over 300 RP-LC columns [10]. Differences in the selectivity of two columns can be described by a function Fs∗ : Fs∗ = {[12.5 (H2 − H1 )]2 + [100(S∗2 − S∗1 )]2 + [30(A2 − A1 )]2 + [143xB (B2 − B1 )]2 1/2

+ [83xC (C2 − C1 )]2 }

(4)

here, values of H1 and H2 refer to values of H for columns 1 and 2, respectively (and similarly for values of S* , A, etc.), while values of xB and xC vary from 0 to 1 and depend on mobile phase pH and whether acids or bases are present in the sample (see discussion of [9,10]). In the present study, we assumed xB = xC = 1.0, which is equivalent to replacing the function Fs∗ by a related function Fs [10]. Commercial software is available (Column Match, see Section 3) which allows values of Fs to be predicted for any two columns contained in a database of 300+ columns. The selectivity of the “orthogonal” column should be chosen to be as different as possible from that of the primary column (largest possible value of Fs ), while avoiding columns with undesirable characteristics (e.g., older, type-A alkylsilica columns [6], or columns known to be unstable for the separation conditions to be used). Since the “orthogonal” procedure will normally be used much less frequently than the primary method, however, column stability becomes less of an issue. The use of mobile phase pH values which otherwise limit column lifetime may therefore be acceptable for an “orthogonal” procedure. Some workers may also prefer to restrict potential “orthogonal” columns to those columns for which they have prior experience. 3. Experimental Experiments described in Section 4 were carried out in six laboratories that are experienced in the RP-LC analysis of pharmaceutical products; it can be assumed that the equipment, materials and procedures used for these assays meet the usual regulatory requirements. In most cases, however, these routine RP-LC assay procedures are proprietary, which precludes our disclosure of sample composition and certain other experimental details. For similar reasons, the contributing laboratories for the individual separations (primary and “orthogonal” methods) summarized in Table 3 are not identified.

Nine different routine separations (examples A–I of Table 3) from the above laboratories were studied, for each of which one or more “orthogonal” methods was developed. Resulting chromatograms for the primary and corresponding “orthogonal” separations are presented and discussed in Section 4. 3.1. Software The column comparisons described in this paper (values of Fs ) were carried out with commercial software (Column Match® ; Rheodyne LLC; Rohnert Park, CA). The latter software uses a database which contains column selectivity parameters (H, S* , etc.) for more than 300 RP-LC columns. The original database described in [10] has since been expanded and upgraded [19]. In the present study, the choice of “orthogonal” column was not restricted to the column with a maximum value of Fs (many columns are always available with large values of Fs ). Optimized temperatures and values of either %B (isocratic) or gradient time were obtained by carrying out four separations at two different temperatures and gradient times, following which best conditions were selected by computer simulation software (DryLab® , Rheodyne LLC, Rohnert Park, CA). See [11–16,20], for examples, of this approach, as well as the example of Section 4.1 below. 4. Results and discussion The various participants in the present project were asked to follow the recommended procedure of Fig. 2 for the development of an “orthogonal” method. In each case, these workers started with a previously developed primary method that was in use in their laboratory. The first step (change of B-solvent and column) was followed (if needed) by four experiments where temperature and either isocratic %B or gradient time were varied. On the basis of the latter four runs, optimized conditions for the “orthogonal” method were selected for maximum sample resolution. The value of |δlog α|avg for the resulting “orthogonal” method was then measured; if |δlog α|avg ≥ 0.1, the relative “orthogonality” of the two methods was considered adequate. If an increase in “orthogonality” is necessary or desired, two options are possible. For samples that contain acids or bases, a change in mobile phase pH by 3–5 units is likely to result in a large increase in |δlog α|avg ([1–5] and see Table 2). For other samples, a further change in column is recommended. The replacement column should be selected to be as different as possible from the two previous columns (large value of Fs when compared to either previous column). For the most part, the participants in the present study followed the above recommendations; in some cases added improvisations were suggested by circumstances or a desire for a further evaluation of the present procedure. In each case, the selection of the “orthogonal” column was made on the basis of a large value of Fs compared to the primary column, but the column with the largest possible value of Fs was not necessarily selected. The results of each “orthogonal” method development are described below.

J. Pellett et al. / J. Chromatogr. A 1101 (2006) 122–135

127

Table 3 Experimental conditions for the primary and “orthogonal” separations of the present study (mobile phase pH and flow rate were maintained the same for corresponding primary and “orthogonal” methods) Experimentala

◦

Mobile phaseb

C

Gradient (or isocratic %B)

Columnc

Flow (mL/min)

A- and B-solvents

pH

A primary A “orthogonal”

0% ACN 10% ACN 0% MeOH 50% MeOH

2.5

30 23

0/0/100% B in 0/24.5/44.5 min 0/0/16/70% B in 0/10/23/25 min

15 × 0.46-cm Aquasil C18 15 × 0.46-cm Betamax Acid

1.0

B primary B “orthogonal”

5% ACN 95% ACN 0% MeOH 100% MeOH

2.0

30 33

20–100% B in 10 min 20–95% B in 12 min

15 × 0.46-cm Prontosil C18-EPS 15 × 0.46 cm Supelcosil LC-18

1.2

C primary C “orthogonal”

0% ACN 100% ACN 0% MeOH 100% MeOH

2.0

22 45

20/60/90% B in 0/20/25 min 30–90% B in 34 min

15 × 0.46-cm Atlantis dC18 15 × 0.46-cm Symmetry C8

1.0

D primary D “orthogonal”

0% MeOH 100% MeOH 0% ACN 100% ACN

6.6

40 40

70% B (isocratic) 75% B (isocratic)

15 × 0.46-cm Zorbax Bonus RP 15 × 0.46-cm Altima HP C18 High Load

1.0

E primary E orthogonal-i E orthogonal-ii

% ACN 100% CAN 0% MeOH 100% MeOH 0% MeOH 100% MeOH

30 30 30

5–90% B in 35 min 5–90% B in 35 min 5–90% B in 35 min

15 × 0.46-cm YMC ODS-AQ 15 × 0.46-cm EC Nucleosil 100-5 Protect 1 15 × 0.46-cm Agilent Bonus RP

1.0

2.0

F primary F “orthogonal”

5.5

30 50

32.3% MeOH 9.0% THF 58.7% buffer 27–56% in 50 min

7.5 × 0.46-cm ACE C8 (3-␮m) 15 × 0.46-cm Zorbax Bonus RP (3.5-␮m)

1.5

0% ACN 100% ACN

G primary G “orthogonal”

0% ACN 100% ACN 0% MeOH 100% MeOH

2.0

60 50

20–90% B in 30 min 10–90% B in 45 min

15 × 0.46-cm Zorbax SB-C18 15 × 0.46-cm Symmetry Shield C18

1.0

H primary H “orthogonal”

20% ACN 75% ACN 20% MeOH 75% MeOH

2.0

23 23

0–100% B in 60 min 0–100% B in 60 min

15 × 0.46-cm Symmetry C8 15 × 0.46-cm Bonus RP

1.0

I primary I orthogonal-i I orthogonal-ii

0% MeOH 100% MeOH 0% ACN 100% ACN 0% ACN 100% ACN

23 23 23

3/3/50 % B in 0/8/13 min 3/3/50% B in 0/8/13 min 3/3/50% B in 0/8/13 min

25 × 0.46-cm Zorbax SB-C8 15 × 0.46-cm Zorbax Bonus RP 15 × 0.46-cm Prism RP

1.2

2.5

a b c

“Primary” refers to conditions for the primary method, “orthogonal” refers to conditions for the orthogonal method. ACN, acetonitrile; MeOH, methanol; THF, tetrahydrofuran. For suppliers of each column, see Table 13 of [10].

4.1. Example A: separation of a drug product and four previously identified impurities or degradation products This first example is described here in some detail, as an illustration of the procedure outlined in Fig. 2. The original (primary) gradient separation is shown in Fig. 3a, where four known impu-

Fig. 3. Separation of a sample by primary and “orthogonal” methods: Example A of Table 3. Conditions for these two separations given in Table 3. The peaks marked by “*” are gradient artifacts.

rities and degradation products (#1, 2, 4, and 5) are separated from the drug product (#3); i.e., the sample was initially believed to contain only five compounds. The conditions for this separation are given in Table 3 (“Example A”). The B-solvent for the primary separation is acetonitrile (ACN), which was replaced by methanol (MeOH) in the“orthogonal” method. The column used in the primary method was Aquasil C18 (Thermo); the column for the “orthogonal” separation was selected using Column Match: Betamax Acid (Thermo) with Fs = 196. (note that the broad peaks marked “*” in Fig. 3 are gradient artifacts, not sample peaks) Four separations with the latter B-solvent (MeOH) and column (Betamax Acid) for the “orthogonal” method were carried out next, varying temperature and gradient time in order to separate the five compounds believed present in this sample. These separations (0–50% methanol/buffer gradients) are shown in Fig. 4 (reconstructed chromatograms from separations of partial samples). A surprising result was immediately apparent: the appearance of a previously unsuspected peak (#6). This unexpected finding represents a successful application of the “orthogonal” method for this assay procedure; i.e., the discovery of a sample component that was missed in the primary separation, because this impurity was present in only a few production lots (including the sample of Figs. 3 and 4). Apart from the presence of a new peak in the separations of Fig. 4, it is seen that peak-5 is only separated from peak-3 by gradient times >20 min.

128

J. Pellett et al. / J. Chromatogr. A 1101 (2006) 122–135

Fig. 4. Separation of the sample of example A using “orthogonal” conditions of Table 3 (new column and B-solvent) as a function of varying temperature and gradient time. Reconstructed (computer simulated) chromatograms as described in the text. Gradients of 0–50% methanol/buffer.

Computer simulation using DryLab® software was next used with data from Fig. 4 to optimize gradient conditions for the final “orthogonal” separation of Fig. 3b, where the separation of all six peaks is achieved within a run time of 33 min (the gradient is delayed by the equipment dwell time = 1.4 min plus the column dead-time of 1.5 min; i.e., the gradient ends at 28 min). For further details on the optimization of gradient time and temperature in this way, see the review of [20]. The final question is whether the “orthogonal” method is sufficiently different in selectivity to resolve other peak-pairs that might have been overlapped in the primary method. The actual discovery of a new peak using the “orthogonal” method might seem to answer this question, but a measurement of |δlog α|avg for the “orthogonal” method as in Fig. 1c is more reliable. Fig. 5 plots values of retention time for the “orthogonal” versus primary separations. (Gradient data should be compared as in Fig. 5 using retention times, whereas isocratic data should be plotted using log k, as in Fig. 1c.) The data of Fig. 5 yield a value of SE = 5.6 min and |δlog α|avg = 0.49 (quadratic fit). The latter value of |δlog α|avg is large enough (0.1) to inspire confidence in the ability of this “orthogonal” method to perform as hoped for in the analysis of future samples that might involve new impurities or degradation products. Table 4 summarizes values of |δlog α|avg and r2 for these two separations, assuming either a linear or quadratic fit to the data. For each of the examples of Table 4 it is presumed that the lower (usually quadratic-fit) value of |δlog α|avg rep-

resents a more conservative estimate of method “orthogonality”. 4.2. Example B: separation of a drug product and three previously identified impurities The primary gradient separation is shown in Fig. 6a, where three known impurities (#2–4) are separated from the drug

Fig. 5. Plot of values of retention time for the “orthogonal” separation (Fig. 3b) vs. values for the primary separation (Fig. 3a) as a measure of the change in separation selectivity. Regression data for quadratic fit of data. See text for details.

J. Pellett et al. / J. Chromatogr. A 1101 (2006) 122–135

129

Table 4 Differences in selectivity of primary and “orthogonal” methods for different examples of present study r2

|δlog α|avg b

Fs c

Linear Quadratic

0.802 0.954

0.88 0.49

196

Linear Quadratic

0.877 0.954

0.19 0.16

152

Linear Quadratic

0.692 0.757

0.30 0.29

45

Linear Quadratic

0.945 0.972

0.12 0.09

132

E-i Linear Quadratic

0.98 0.995

0.21 0.12

267

E-ii Linear Quadratic

0.966 0.994

0.27 0.13

231

Linear Quadratic

0.971 0.972

0.10 0.10

165

Linear Quadratic

0.962 0.967

0.22 0.23

72

Linear Quadratic

0.822 0.866

0.45 0.41

196

I-ia Linear Quadratic

0.904 0.962

0.24 0.18

238

I-ii Linear Quadratic

0.852 0.970

0.38 0.21

243

0.22 ± 0.14 (1 SD)

176

Example A

B

C

D

onal” separation, but this possible additional impurity was not investigated.

F

G

H

Averaged

Fig. 6. Separation of a sample by primary and “orthogonal” methods: Example B of Table 3. Conditions for these two separations given in Table 3.

See text for details. a Log k (“orthogonal”) plotted vs. t (primary); all peaks in two orthogonal R separations eluted isocratically in 3% MeOH. b For each sample, the lower (more conservative) value of |δlog α| avg is cited in the text. c Calculated from Eq. (4), assuming x = x = 1.0. B C d For the lower (more conservative) value of |δlog α| avg (usually the “quadratic” value.

product (#1). The conditions for this separation are given in Table 3 (Example B). The B-solvent for the primary separation is acetonitrile, which was replaced by methanol in the planned “orthogonal” method. The column used in the primary method was Prontosil C18-EPS (Bischoff); the column for the “orthogonal” separation was Supelcosil LC-18 (Supelco; a typeA column) with Fs = 152. The “orthogonal” method in Fig. 6b can be compared with that in Fig. 6a. Some re-ordering of the peaks in the chromatogram can be seen, and the value of |δlog α|avg = 0.16; this is acceptably large for an “orthogonal” method. A distinct shoulder can be seen on peak-1 in the “orthog-

4.3. Example C: separation of a drug product and eight impurities or degradants The gradient separation of this sample by the primary method is shown in Fig. 7a, using an Atlantis dC18 column (Waters) and acetonitrile as B-solvent (two different samples are separated, in order to show the various sample impurities and degradants). Other conditions are listed in Table 3. The first attempt at developing an “orthogonal” method, using methanol as B-solvent and a Zorbax Bonus RP column (Agilent, Fs = 239), resulted in the disappearance of peak-4 (a carboxylic acid), presumably due to its strong retention by this column. A further attempt with another column (Symmetry Shield RP18; Waters, Fs = 61) and methanol as B-solvent now resulted in the elution of peak-1 at the solvent front. A final choice of a Symmetry C8 column (Waters, Fs = 45) with methanol as B-solvent provided acceptable retention of all peaks after optimizing temperature and gradient time (Fig. 7b). Some re-ordering of peaks in the “orthogonal” separation of Fig. 7b is observed (especially peak4); the value of |δlog α|avg = 0.28, which meets the requirement of |δlog α|avg > 0.10. 4.4. Example D: separation of a drug product and five impurities or degradants The isocratic separation of this sample by the primary method is shown in Fig. 8a, using a Zorbax Bonus RP column (Agilent) and methanol as B-solvent. Other conditions are listed in Table 3. For the “orthogonal” method, an Altima HP C18 High Load column (Alltech, Fs = 132) with acetonitrile as Bsolvent was used. The final choice of temperature and %B for the “orthogonal” method was chosen for both baseline resolution and maximum changes in relative retention order (75%

J. Pellett et al. / J. Chromatogr. A 1101 (2006) 122–135

130

increase in “orthogonality”, but neither of these options was pursued. 4.5. Example E: separation of a drug product and five impurities or degradants The gradient separation of this sample by the primary method is shown in Fig. 9a, using a YMC ODS-AQ column (Waters) with acetonitrile as B-solvent. The column was changed to EC Nucleosil 100-5 Protect 1 (Machery Nagel, Fs = 267) and methanol as B-solvent. For the same temperature and gradient time (Fig. 9b), peak resolution was excellent and no further changes in the latter conditions were made. While relative retention does not appear to have changed much for the “orthogonal” separation of Fig. 9b, the value of |δlog α|avg = 0.12, which should be considered barely acceptable. We will refer to the latter separation as “orthogonal-i”. A further change in the orthogonal-i separation was made in a search for increased “orthogonality”, by replacing the column with a Zorbax Bonus RP column (Agilent; Fs = 231 versus the YMC column, Fs = 38 versus the Nucleosil column). The resulting value of |δlog α|avg = 0.13 for the latter separation (“orthogonal-ii”) represents a very marginal improvement in the “orthogonality” of this separation (Fig. 9c). Further changes in either the column or mobile phase pH would be appropriate, but were not carried out.

Fig. 7. Separation of a sample by primary and “orthogonal” methods: Example C of Table 3. Conditions for these two separations given in Table 3.

40 ◦ C);

ACN and see Fig. 8b. Despite a reversal of peaks #2 and 3, the value of |δlog α|avg = 0.09, which must be considered marginal. The contributing laboratory noted that the compounds in this sample consist of structurally related bases with similar pKa values. The relatively similar selectivity of the two separations is therefore not unexpected. Further changes in either the column or mobile phase pH might be considered for an

Fig. 8. Separation of a sample by primary and “orthogonal” methods: Example D of Table 3. Conditions for these two separations given in Table 3.

4.6. Example F: separation of a drug product from eight impurities and degradants The initial method for the isocratic separation of this sample gave the chromatogram of Fig. 10a. The choice of an isocratic procedure in this case reflects a desire for a simpler, more easily transferable method, despite the fact that a near maximum range in values of k is observed (1 < k < 16) [6]. However, the present

Fig. 9. Separation of a sample by primary and “orthogonal” methods: Example E of Table 3. Conditions for these two separations given in Table 3. Two different columns were used, resulting in “orthogonal” methods i and ii. Conditions for these three separations given in Table 3.

J. Pellett et al. / J. Chromatogr. A 1101 (2006) 122–135

Fig. 10. Separation of a sample by primary and “orthogonal” methods: Example F of Table 3. Conditions for these two separations given in Table 3.

approach for developing an “orthogonal” method is favored by either a narrower range in k or the use of gradient elution; the development of a gradient “orthogonal” method was therefore pursued. The “orthogonal” conditions included a change of column from ACE C8 to Zorbax Bonus RP (Agilent, Fs = 165), and replacement of the original methanol/tetrahydrofuran mobile phase with acetonitrile as B-solvent (Fig. 10b). For the final separation (27–56% ACN in 50 min, 50 ◦ C), a value of |δlog α|avg = 0.10 resulted based on plots of retention time for the gradient “orthogonal” method versus the isocratic primary method (Fig. 6b). The resolution of peak-pairs 4/5 and 8/9 in the “orthogonal” method is seen to be marginal, and the “orthogonal” separation is only slightly different in selectivity.

131

Fig. 11. Separation of a sample by primary and “orthogonal” methods: Example G of Table 3. Conditions for these two separations given in Table 3.

4.9. Example I: separation of a drug product from four impurities The gradient separation of this sample by the primary method is shown in Fig. 13a, using a Zorbax C8 column (Agilent) with methanol as B-solvent. The column was changed to Bonus RP (Agilent, Fs = 238) and acetonitrile as B-solvent (Fig. 12b), without further adjustment of temperature of gradient time. The resulting value of |δlog α|avg = 0.18 was acceptable. The results for this “orthogonal” separation in Tables 3 and 4 are referred to as “orthogonal-i”. A Prism RP column (Thermo, Fs = 243 versus Zorbax C8 and Fs = 20 versus Bonus RP) was also tried for the “orthogonal” method with acetonitrile as solvent (“orthogonal-ii” in Tables 3 and 4). The resulting value of |δlog α|avg = 0.21 was

4.7. Example G: separation of a drug product from five impurities and degradants The gradient separation of this sample by the primary method is shown in Fig. 11a, using a Zorbax SB-C18 column (Agilent) with acetonitrile as B-solvent. The column was changed to Symmetry Shield C18 (Waters, Fs = 72) and methanol as B-solvent (Fig. 11b); no further changes in conditions were attempted. The resulting value of |δlog α|avg = 0.22 (acceptable). 4.8. Example H: separation of a drug product from five impurities and degradants The gradient separation of this sample by the primary method is shown in Fig. 12a, using a Symmetry C8 column (Waters) with acetonitrile as B-solvent. The column was changed to Bonus RP (Agilent, Fs = 196) and methanol as B-solvent (Fig. 12b); no further changes in temperature or gradient time were attempted. The resulting value of |δlog α|avg = 0.41 (acceptable).

Fig. 12. Separation of a sample by primary and “orthogonal” methods: Example H of Table 3. Conditions for these two separations given in Table 3.

132

J. Pellett et al. / J. Chromatogr. A 1101 (2006) 122–135

Fig. 13. Separation of a sample by primary and “orthogonal” methods: Example I of Table 3. Two different columns were used, resulting in “orthogonal” methods i and ii. Conditions for these three separations given in Table 3.

acceptable, but only slightly improved versus the orthogonali separation. Both “orthogonal” methods for sample I have marginal retention (0.1 ≤ k < 4); since all compounds elute isocratically with 3% acetonitrile, little could be done to increase sample retention with either of the two “orthogonal” columns. A better approach for this sample would have been to select a potential “orthogonal” column with greater retention (greater value of kEB in [10]). 5. Conclusions “Orthogonal” methods for analysis are needed in order to increase the probability that a primary assay has provided the separation (and recognition) of all peaks of interest. A standardized procedure is described for the development of an “orthogonal” RP-LC separation (Fig. 2), assuming that a primary RP-LC method for a given sample already exists. An average change in resolution Rs > 3 for all adjacent peaks in the chromatogram seems likely (but not certain) to provide sufficient “orthogonality” to allow the recognition of any peaks in the “orthogonal” method that may have been overlapped and hidden in the primary method. Rs > 3 corresponds to twice the maximum change in resolution required to separate two overlapped peaks; it is equivalent to an average change in the separation factor α by a factor of about 1.25 (see below). Previous data for a large number of test compounds and columns were examined in order to establish changes in conditions that would likely result in a change

in resolution Rs > 3. It appears that a simultaneous change in the column and mobile-phase B-solvent (e.g., methanol replaces acetonitrile) should be sufficient for many samples. The choice of column for the “orthogonal” method is critically important, as the primary and “orthogonal” columns should be quite different in terms of selectivity. Relative RP-LC column selectivity can be compared by means of a function Fs that has been defined previously [10]. In the present study, the average value of Fs was 176 for the columns used in the present 11 “orthogonal” methods. Most laboratories today prefer the use of RP-LC columns made from less acidic, type-B silica [6], and more than 200 such columns can be compared in terms of their Fs -values [10]. Restricting our choice of column to those that use type-B silica does not significantly limit the maximum possible selectivity of an “orthogonal” procedure, as demonstrated by the present study. Similarly, there is probably little need to consider mobile phase solvents other than acetonitrile and methanol, especially when a change in mobile phase pH can be used for a further increase in separation “orthogonality”. However, pH was not varied in the present study. Following the development of an “orthogonal” method in this way, it is necessary to determine its relative “orthogonality” as measured by changes in relative retention versus the primary method. A criterion is proposed (|δlog α|avg ≥ 0.10, equivalent to an average change in α by a factor of 1.25, or Rs by 3 units) for the assessment of whether the resulting “orthogonal” method is likely to be adequate for the purpose of resolving peaks that were overlapped in the primary method; the measurement of values of |δlog α|avg is described in detail (Appendix B). Six pharmaceutical analysis laboratories have evaluated the procedure outlined in Fig. 2 as a means of developing “orthogonal” methods for nine different primary RP-LC methods. For eight of nine samples, |δlog α|avg ≥ 0.10, suggesting that the proposed procedure for developing an “orthogonal” separation is generally adequate; the average value of |δlog α|avg for the nine samples was 0.22. In one case (Example A), the “orthogonal” method separated a previously unsuspected impurity that was overlapped in the primary method (the ultimate goal of an “orthogonal” method). For remaining samples B-I it appears that all compounds in each sample are resolved by both the primary and “orthogonal” method. When a further change in separation “orthogonality” is required, a change in mobile phase pH and/or a second change in column selectivity is recommended. In some cases, changes in separation temperature and/or isocratic %B or gradient steepness may further enhance separation “orthogonality”, although the latter two separation conditions are normally less effective in influencing separation selectivity. Still another option is the use of a non-RP-LC procedure; recently an “orthogonal” separation based on hydrophilic interaction chromatography has been described [21]. When assessing the relative selectivity of an “orthogonal” versus primary RP-LC method by means of retention plots as in Fig. 1c, different groups use different criteria. We have chosen the standard error SE of such plots, in preference to correlation coefficients r2 , because values of SE can be used to calculate values of |δlog α|avg and are more directly related to peak sep-

J. Pellett et al. / J. Chromatogr. A 1101 (2006) 122–135

aration or resolution (Section 2). Table 4 compares values of both r2 and |δlog α|avg for Examples A–I, based on either a linear or a quadratic fit of the data. A quadratic fit for the determination of SE is recommended for samples that contain five or more analytes, as this usually results in a more conservative value of |δlog α|avg and separation “orthogonality”. Reversals in retention order are an additional indication of relative “orthogonality”; eight of the present 11 “orthogonal” methods resulted in one or more such peak reversals. It must be emphasized that the present criterion for adequate separation “orthogonality” (|δlog α|avg ≥ 0.10) is tentative, and the application of the present procedure to additional samples may eventually suggest a higher minimum value of |δlog α|avg . Also, the concept behind this measure of separation “orthogonality” presumes a Gaussian distribution of |δlog α|avg values for different compounds, which creates added uncertainty when only a small number (e.g., <10) of specific compounds are present in a given sample. Similarly, it is possible that changes in mobile phase pH may eventually be regarded as a requirement for adequately “orthogonal” separation, rather than an option that depends on the value of |δlog α|avg . Finally, it should be recalled that some extreme samples (e.g., enantiomers or compounds which vary only in the extent of isotope labeling) cannot be separated by “conventional” RP-LC, regardless of the value of |δlog α|avg for other compounds in the sample. Similarly, some structurally related compounds (other than enantiomers, etc.) may be quite difficult to separate by any choice of RP-LC separation conditions. As a result, none of the “orthogonal” separations developed in this study can guarantee that two peaks which overlap in the primary separation will be adequately resolved by the “orthogonal” method, regardless of the required value of |δlog α|avg . Similar uncertainty exists for any two “orthogonal” separations; i.e., we are dealing with probabilities, rather than certainties.

133

Fs∗ H

column selectivity comparison function; Eq. (4) column hydrophobicity (relative to an average type-B alkyl-silica column) H1 , H2 value of H for columns 1 and 2; Eq. (4) k retention factor, equal to (tR − t0 )/t0 MeOH methanol N column plate number r correlation coefficient RP-LC reversed-phase liquid chromatography Rs resolution of two adjacent bands S slope of plots of log k for a given solute when only %B is varied; S = d(log k)/dφ, where φ is the volume fraction of B-solvent in the mobile phase (φ = 0.01%B) S* steric resistance to insertion of bulky solute molecules into the stationary phase (relative to an average typeB alkyl-silica column); as S* increases, bulky solute molecules experience greater difficulty in penetrating the stationary phase and being retained previously S* 1 , S* 2 value of S* for columns 1 and 2; Eq. (4) SD standard deviation SE standard error t0 column dead time (min) tR retention time (min) THF tetrahydrofuran type-A column based on (impure) metal-containing silica type-B column based on (pure) metal-free silica α separation factor for two solutes δlog α change in log α for two bands when separation conditions are changed (as for an “orthogonal” versus primary separation) |δlog α|avg average value of δlog α for all band-pairs in the chromatogram (Eq. (B.1)) Appendix A. Choice of conditions for a maximum change in separation selectivity

6. Nomenclature

A

A1 , A2 ACN b B B B1 , B2 C

C1 , C2 Fs

column hydrogen-bond acidity (relative to an average type-B alkyl-silica column), related to number and accessibility of silanol groups in the stationary phase; also “type-A” column based on metal-containing silica value of A for columns 1 and 2; Eq. (4) acetonitrile gradient steepness parameter (Eq. (3)) “type-B” column based on pure silica; also, organic solvent in the mobile phase column hydrogen-bond basicity (relative to an average type-B alkyl-silica column) value of B for columns 1 and 2; Eq. (4) column cation exchange activity (relative to an average type-B alkyl-silica column); related to number and accessibility of ionized silanols in stationary phase value of C for columns 1 and 2; Eq. (4) column selectivity comparison function, based on differences in H, S* , A, B and C for two columns; Eq. (4) with xB = xC = 1.0

For 67 solutes of widely varied molecular structure, values of k were measured as a function of changes of 10% B, 10 ◦ C and solvent type (10% methanol or tetrahydrofuran replacing 10% acetonitrile in a mobile phase of 50% acetonitrile/buffer) [8]. The latter measurements were carried out on a single column (Symmetry C18 from Waters), but it was shown that similar changes in k are obtained for other columns. Using 16 test solutes and the same initial conditions (50% acetonitrile/pH 2.8 buffer at 35 ◦ C), changes in k for about 300 different RP-LC columns were also reported [10]. Changes in %B, ◦ C and solvent type were analyzed in the following way. First, the 67 test compounds were divided into neutral or ionizable groups and each group was arranged in order of increasing k; values of α were then calculated for every adjacent band-pair. For each of the above changes in either mobile phase or temperature, the change in α for each adjacent bandpair as a result of each change in condition can be determined. The latter change in α (δα) can be expressed as the absolute value of δlog α, and averaged for the entire set of band-pairs in each of the two groups (neutrals and ionizable). Resulting values of |δlog α|avg can then be identified with the average change in

J. Pellett et al. / J. Chromatogr. A 1101 (2006) 122–135

134

Table 6 Retention data for separations of example E-ii (orthogonal-2 method)

Table 5 Effect of a change in individual conditions on separation selectivity Value of |δlog α|avg for a change in each condition T Changea

10 ◦ C

Neutrals Ionics Average Allowedc Maximumd

0.014 0.055 0.034 20 0.068

%B 10% B 0.048 0.114 0.081 10 0.081

tG

MeOH

pH

Buffer

10-fold

10%b

0.2

Two-fold

0.20

0.025 0.059 0.042 100% ≈0.2e

0.682 0.682 5  0.7

0.016 0.016 Five-fold 0.040

Compound

1 2 3 4 5 6

Change in condition which results in indicated value of |δlog α|avg . For replacement of 10% of acetonitrile (ACN) by 10% methanol (MeOH); i.e., 50% ACN is replaced by 45% ACN + 5% MeOH. c Arbitrary values (see text for discussion). d For allowed change in conditions. e Conservative value, recognizing effect of %-MeOH may be nonlinear. a

Retention time (min) Primary method

Orthogonal method

5.808 8.445 11.117 18.654 22.723 25.003

5.043 11.454 16.268 23.788 27.448 29.069

See Table 3 for conditions.

b

selectivity due to that variable (Table 5). Next, maximum allowable changes in the value of each separation condition were assumed, based on practical considerations (next to last line of data in Table 5). Finally, maximum values of |δlog α|avg are shown in the last line of Table 5 for the allowable changes in the previous line. Values of |δlog α|avg for a change in column (compared to Symmetry C18 ) can be obtained in similar fashion for different columns, based on the same band-pairs as for the Symmetry C18 column [10]: |δ log α|avg ≈ 0.003Fs

(A-1)

Assuming an average value of Fs ≈ 65 for the replacement of the primary column by the orthogonal column, the estimated value of |δlog α|avg ≈ 0.19. Note that considerably larger values of Fs are possible for individual pairs of columns, as noted in most of the examples of Table 4. However, values of Fs∗ are often much smaller than values of Fs , and it is values of Fs∗ that are directly related to separation orthogonality. Appendix B. Measurement of values of |δlog α|avg for an orthogonal separation

for each method. Retention times for the primary and orthogonal methods are given in Table 6. Fig. 14 plots retention times for orthogonal versus primary methods; the solid line represents a quadratic fit of the data. A value of |δlog α|avg = 0.13 can be calculated from the standard error SE = 0.95 (Eq. (B.2)); the value of b for the orthogonal method (Eq. (3)) is equal to (1.5 × 0.85 × 4)/(35 × 1.0); note that: (a) Vm can be approximated by 0.1 times the column length (cm), for a column diameter of 0.46-cm, and (b) S is estimated equal to 4 for a sample with molecular weight <500. Vm can also be estimated from the column dead-time t0 and flow rate F: Vm = t0 /F. In most cases involving linear gradients, a simple linear fit is usually adequate. However, as can be seen from Fig. 14 for Example E-ii, as well as Fig. 5 for Example A, there is often an apparent curvature of the plot. In some cases, the use of a quadratic fit may over-fit the data, resulting in erroneously low values of SE and |δlog α|avg , but this results in a perhaps overly conservative value of |δlog α|avg . These two examples (Figs. 5 and 14) illustrate the somewhat subjective nature of derived values of |δlog α|avg , especially when plots as in Fig. 14 appear to be curved. Curved retention plots are more likely when segmented gradients are used (as for Example A and Fig. 5). A value of |δlog α|avg can also be obtained from plots of retention time for the primary method (y) versus the orthogonal method (x) (instead of the reverse as in Figs. 5 and 14), but in that case,

When both the primary and orthogonal methods are isocratic, a value of SE is determined for the correlation of values of log k for the orthogonal method versus log k for the primary method. A value of |δlog α|avg is then given by |δ log α|avg = 1.4 SE

(B.1)

When both the primary and orthogonal methods are carried out by gradient elution, values of retention time tR for the orthogonal method (y) are correlated with values of tR for the primary method (x), assuming either a linear or quadratic (y = a + b x + cx2 ) fit, and a value of SE is again determined. A value of |δlog α|avg is then given (see Eqs. (2) and (3)) as
 b ||δ log α|avg = 1.4 SE (B.2) t0 As example of the application of Eq. (B.2), consider Example E-ii of Tables 3 and 4, involving linear-gradient separations

Fig. 14. Plot of retention times for “orthogonal” vs. primary methods for Example E (orthogonal-ii) of Table 3.

J. Pellett et al. / J. Chromatogr. A 1101 (2006) 122–135

the value of b used in Eq. (B.2) must correspond to the value for the primary separation. References [1] E. Van Gyseghem, I. Crosiers, S. Gourvenec, D.L. Massart, Y. Vander Heyden, J. Chromatogr. A 1026 (2004) 117. [2] B.D. Karcher, M.L. Davies, J.J. Venit, E.J. Delaney, Am. Pharm. Rev. 7 (2004) 62. [3] G. Xue, A.D. Bendick, R. Chen, S.S. Sekulic, J. Chromatogr. A 1050 (2004) 159. [4] E. Van Gyseghem, M. Jimidar, R. Sneyers, D. Redlich, E. Verhoeven, D.L. Massart, Y. Vander Heyden, J. Chromatogr. A 1074 (2005) 117. [5] P.J. Schoenmakers et al., LC–GC Europe, June 2003, p. 1. [6] L.R. Snyder, J.J. Kirkland, J.L. Glajch, Practical HPLC Method Development, 2nd ed., Wiley-Interscience, New York, 1997. [7] L.R. Snyder, J. Chromatogr. B 689 (1997) 105. [8] N.S. Wilson, M.D. Nelson, J.W. Dolan, L.R. Snyder, P.W. Carr, J. Chromatogr. A 961 (2002) 195.

135

[9] J.W. Dolan, A. Maule, L. Wrisley, C.C. Chan, M. Angod, C. Lunte, R. Krisko, J. Winston, B. Homeier, D.V. McCalley, L.R. Snyder, J. Chromatogr. A 1057 (2004) 59. [10] L.R. Snyder, J.W. Dolan, P.W. Carr, J. Chromatogr. A 1060 (2004) 77. [11] P.L. Zhu, J.W. Dolan, L.R. Snyder, D.W. Hill, L. Van Heukelem, T.J. Waeghe, J. Chromatogr. A 756 (1996) 51. [12] P.L. Zhu, J.W. Dolan, L.R. Snyder, N.M. Djordjevic, D.W. Hill, J.-T. Lin, L.C. Sander, L. Van Heukelem, J. Chromatogr. A 756 (1996) 63. [13] J.W. Dolan, L.R. Snyder, D.L. Saunders, L. Van Heukelem, J. Chromatogr. A 803 (1998) 33. [14] J.W. Dolan, L.R. Snyder, N.M. Djordjevic, D.W. Hill, L. Van Heukelem, T.J. Waeghe, J. Chromatogr. A 857 (1999) 1. [15] L.R. Snyder, J.W. Dolan, J. Chromatogr. A 892 (2000) 107. [16] J.W. Dolan, L.R. Snyder, T. Blanc, L. Van Heukelem, J. Chromatogr. A. 897 (2000) 37. [17] L.R. Snyder, J.W. Dolan, J. Chromatogr. A 721 (1996) 3. [18] L.R. Snyder, J.W. Dolan, Adv. Chromatogr. 38 (1998) 115. [19] L.R. Snyder, J.W. Dolan, High-performance Gradient Elution, Wiley, New York, 2006. [20] I. Molnar, J. Chromatogr. A 965 (2002) 175. [21] X. Wang, W. Li, H.T. Rasmussen, J. Chromatogr. A 1083 (2005) 58.