Identifying orthogonal and similar reversed phase liquid chromatography stationary phases using the system selectivity cube and the hydrophobic subtraction model

Journal of Chromatography A, 1249 (2012) 62–82

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Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma

Identifying orthogonal and similar reversed phase liquid chromatography stationary phases using the system selectivity cube and the hydrophobic subtraction model Andrew R. Johnsona , Carrie M. Johnsonb , Dwight R. Stollb , Mark F. Vithac,∗ a

Indiana University, Department of Chemistry, 800 E. Kirkwood Ave., Bloomington, IN 47405, USA Department of Chemistry, Gustavus Adophus College, 800 West College Avenue, Saint Peter, MN 56082, USA c Department of Chemistry, Drake University, 2507 University Ave, Des Moines, IA 50311, USA b

a r t i c l e

i n f o

Article history: Received 25 August 2011 Received in revised form 9 May 2012 Accepted 14 May 2012 Available online 22 May 2012 Keywords: System selectivity cube Hydrophobic subtraction model Column selectivity Reversed phase Orthogonal separation Snyder–Dolan model

a b s t r a c t We have compared over 500 RPLC columns characterized by the hydrophobic subtraction model using the system selectivity cube (SSC). We have shown numerous differences in column selectivity even among columns in the same class (e.g., alkyl-silica, cyano, or embedded polar groups). We also illustrate the utility of our method for selecting alternative columns with different selectivities for problematic separations and for selecting orthogonal columns for use in two-dimensional separations. The system selectivity cube offers a visual way to easily compare many columns simultaneously and select those columns offering the desired selectivity. © 2012 Elsevier B.V. All rights reserved.

1. Introduction The abundance of commercially available columns for use in reversed phase liquid chromatography (RPLC) makes a wide range of selectivities available, but it can also make column selection a daunting task. In selecting a replacement column with similar selectivity, columns with seemingly identical characteristics (e.g., silica type, chain length, carbon load, end-capping, pore size, etc.) often produce significantly different separations. Given all of the options, it is also difficult to systematically select alternative columns for problematic separations and to choose orthogonal columns for two-dimensional separations. One can fall back on class designations (e.g., C 18, polar embedded), but these provide only broad brushstrokes and columns within the same class can display different selectivities as has been shown in a number of studies [1–7]. To help facilitate column selection, we have developed the system selectivity cube (SSC) [8,9], a software program which, in conjunction with linear models of retention, is capable of illustrating the chemical similarities and differences between

∗ Corresponding author. Tel.: +1 515 271 2596; fax: +1 515 271 1928. E-mail address: [email protected] (M.F. Vitha). 0021-9673/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.chroma.2012.05.049

chromatographic systems. We view the SSC as a complement to the other methods of column comparison that have already been described in the literature, which we summarize below. In this article we use the SSC, combined with the hydrophobic subtraction model (HSM) [3–6,10–14], to provide a powerful tool for identifying similar and different RPLC columns. This work is divided into three main sections. First, the HSM is explained briefly. Second, the theoretical background of the SSC, as well as practical details on operating the program, are described. Because these first two topics have already been explained in greater detail elsewhere [3–6,8–14], this paper ultimately focuses on the third section, which involves a number of case studies comparing and contrasting RPLC columns using the SSC program. 1.1. Other column comparison methods There have been a number of proposed schemes for both characterizing and comparing RPLC columns. Early comparison methods were based on retention factors. Horvath et al. measured the retention factors of an identical solute set on two columns and used the correlation to determine how similar the two columns were [15]. As reported by Snyder et al., Neue expanded this scheme by correlating the retention factors of an identical solute set on two separate columns as well as under different operating conditions (i.e., pH or mobile phase composition) in order to gain a complete

A.R. Johnson et al. / J. Chromatogr. A 1249 (2012) 62–82

63

Table 1 Solutes and their associated parameters used to measure HSM column coefficients [14]. Solute number

Solute



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

N,N-dimethylacetamide N,N-diethylacetamide Berberine Nortriptyline 4-Nitrophenol Amitriptyline 5,5-Diphenylhydantoin Acetophenone Benzonitrile 5-Phenylpentanol Anisole 4-n-Butylbenzoic acid Toluene Cis-chalcone Ethylbenzene Trans-chalcone Mefenamic acid

−1.903 −1.390

0.001 0.214

0.994 0.369

−0.012 −0.215

0.001 0.047

−1.163 −0.968 −1.094 −0.940 −0.744 −0.703 −0.495 −0.467 −0.266 −0.205 −0.048 0 0.029 0.049

−0.018 0.040 0.163 0.026 0.133 0.317 0.136 0.062 −0.223 −0.095 0.821 0 0.918 0.333

−0.024 0.009 −0.041 0.003 0.059 0.003 0.030 0.006 0.013 0.011 −0.030 0 −0.021 −0.049

0.289 0.098 0.300 0.568 −0.152 0.080 0.610 −0.156 0.838 −0.214 0.466 0 −0.292 1.123

0.845 −0.021 0.817 0.007 −0.009 −0.030 0.013 −0.009 0.045 0.005 −0.045 0 −0.017 −0.008

a b c d e f



ˇ

˛



pKa −0.28b 2.47f 9.7e 7.15d 9.45e 8.3a

4.36c

4.2d

Ref. [31]. Ref. [32]. Ref. [33]. Ref. [34]. Ref. [35]. Ref. [36].

picture of similarities between two columns under a range of operating conditions [16,17]. Tanaka et al. developed a specific solute set to probe particular interactions, such as shape selectivity and hydrogen bond ability [18]. Euerby and Petersson expanded on this work, adding additional probes and analyzing the results via principle component analysis [2,19,20]. The two preceding methods, as well as others, have been reviewed elsewhere [21,22]. In order to make comparisons more universal, many modern methods use retention models, such as the HSM or linear solvation energy relationships (LSERs) [23] in place of retention of a specific solute set. LSERs have been used extensively to characterize chromatography systems, which we define as the combination of mobile phase, stationary phase, and support material of a column. LSERs are of the form: log k = aA + bB + eE + sS + vV + c

(1)

where each term signifies the contribution of solute characteristics (A, B, E, S, V) and the coefficients reflect differences in corresponding mobile and stationary phase characteristics (a, b, e, s, v). Ishihama and Asakawa constructed five-dimensional vectors using the column coefficients (a, b, e, s, and v) and used the angle between two vectors to compare two systems [24]. Abraham and Martins used a similar approach, but made comparisons based on the distance between two vectors instead of the angle [25]. Lazaro et al. similarly used distance between two vectors, but normalized them first [26]. Another method of system comparison is the selectivity triangle, in which either normalized retention factors or retention model coefficients are plotted on a triangular plot, such that similar systems are plotted close to one another. Triangle schemes related to linear solvation energy relationship studies of GC stationary phases [27] and to HSM studies of RPLC systems have been published [1] and are summarized in a review article [28]. We note that the triangle schemes allow for facile, visual comparisons between columns. Here, we present the use of the HSM and the comparison method of Horvath et al., combined with the SSC, to illustrate how our approach also offers a simple visualization scheme to compare many systems simultaneously and easily select similar and different columns. While fundamentally related to the above approaches, the SSC uses a different methodology to make comparisons between columns. In this way, the SSC approach is complementary to the existing column comparison methods.

We address similarities and differences between the approaches toward the end of this article. 2. The hydrophobic subtraction model The HSM is a linear retention model of the form log ˛ =  H −   S ∗ + ˇ A + ˛ B +  C

(2)

where log ˛ = log(ksolute /kethylbenzene ) [3–6,10–14]. The lower case, Greek coefficients are solute descriptors, while the upper case letters represent column characteristics. All values of the column parameters are relative to a theoretical, ‘average,’ column in which H = 1.0 and S, A, B, and C are identically 0.0 [13]. The  H term quantifies the influence of hydrophobic/lipophilic interactions on log ˛. Although there is contention over the mechanism by which hydrophobic species are retained [29], it is generally regarded as the dominant influence on retention in reversed phase liquid chromatography, especially in alkyl-silica columns [10]. The   S* term accounts for the influence of steric interactions between the solute and the stationary phase on log ˛ (e.g., the resistance of the stationary phase to penetration by bulky molecules). The ˇ A term represents the influence of solute hydrogen bond accepting ability on log ˛. Non-ionized silanols on the silica surface are assumed to be the primary source of the hydrogen bond donating ability of most columns. The ˛ B term represents the influence of solute hydrogen bond donating ability on log ˛. Snyder et al. hypothesize that for many columns, especially high purity (type B) alkyl-silica columns, the hydrogen bond accepting ability of the column is due to sorbed water on the stationary phase [14]. The  C term will be referred to as the cation exchange term throughout this work to comply with the history and convention of the HSM model. However, it appears this term also includes contributions from ionic interactions not due to cation exchange. While not fully understood, the interactions likely result from negatively and positively charged sites present simultaneously in many columns at low pH [30]. The solutes used to measure the HSM coefficients are listed in Table 1 along with their solute parameters and pKa values. For a full discussion of how the HSM coefficients are determined for a column, the reader is directed to a series of articles and reviews by the authors of the HSM [3–6,10–14]. The column parameters are designed to be independent of the separation conditions. This means that mobile phase

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A.R. Johnson et al. / J. Chromatogr. A 1249 (2012) 62–82

composition, pH, and temperature should not alter the HSM column parameters [13]. The one exception is the C term. Because the C term is related to ionized silanols, it is pH dependent. Values of C for a column are generally reported at both pH 2.8 and 7.0 to cover a range of useful operating conditions and can be estimated for other pHs on the United States Pharmacopeia website (http://www.usp.org/USPNF/columns.html).

2.1. The Fs metric

3.2. Comparisons based on HSM parameters We and others [1,8,15–17,24–26,28] have shown that instead of using retention factors for identical solute sets to compare system selectivity, it is possible to determine the same energetic relationships of Horvath et al. using retention models such as LSERs. Here we expand our approach to include the HSM. For two columns, designated 1 and 2, we can write: log ˛1 =  H1 −   S1∗ + ˇ A1 + ˛ B1 +  C1 and, 

In order to select equivalent columns using the HSM, or to select an alternative column with different selectivity in order to improve a problematic separation, a single metric has been proposed, Fs , given by [13] Fs =

log ˛2 = 

H2 −   S2∗





(4)



+ ˇ A2 + ˛ B2 +  C2

(5)

where again, log ˛ = log(ksolute /kethylbenzene ). Similar to what we have shown with LSERs [8], we can relate retention on system 1 to system 2 such that



(12.5(H2 − H1 ))2 + (100(S2 − S1 ))2 + (30(A2 − A1 ))2 + (143(B2 − B1 ))2 + (83(C2 − C1 ))2

Fs is the Euclidean distance in five-dimensional space between the two systems. The weighting factors (12.5, 100, etc.) are included to normalize the varying contributions of the column parameters for a typical solute set [13]. It has been proposed that any two columns with Fs ≤ 3.0 will behave ‘similarly,’ that is, they will provide essentially equivalent separations [37]. For selecting different columns, two columns yielding Fs > 65 if ionic solutes are present or Fs > 100 if no ionic solutes are present, would be chosen [38]. Comparisons yielding 3 < Fs < 65 may yield similar or different results depending on the solute set and other operating conditions.

log k2 log k1 = −  H1 H2 + 



 S∗

1

H1

C2 C1 − H1 H2

(3)

−



S2∗



H2

+

+ ˇ



A2 A1 − H1 H2



+ ˛



B2 B1 − H1 H2



log keb1 log keb2 − H1 H2

(6)

When the two systems are related such that S1∗ H1

=

S2∗ H2

&

A1 A2 = H1 H2

&

B1 B2 = H1 H2

&

C1 C2 = H1 H2

(7)

Eq. (6) simplifies to 3. The system selectivity cube 3.1. – plots Horvath and co-workers developed a method for comparing the retention characteristics of two chromatographic systems [15]. Their method is based on plotting the logarithm of retention factors, k, for a varied solute set on two different chromatography systems against one another. Such a plot is called a ␬–␬ plot. Three different energetic relationships exist for any two systems based on the correlation of the retention factors. When the retention factors are well correlated (Horvath et al. specified r > 0.95), the two systems are said to have a homeoenergetic relationship. This means that the two systems separate the solutes based on a similar blend of retention mechanisms. These two systems may provide different retention values, but there is little chance of differential band spacing or elution order differences. If large changes to selectivity are required, a homeoenergetic system would be unlikely to provide them. The special case in which the retention factors of the two systems are well correlated (r > 0.95) and the slope of that correlation is equal to 1.0 (at the 95% confidence interval) is called a homoenergetic relationship (the intercept is inconsequential to the interpretation of energy relationships). Systems with this relationship operate on an identical blend of retention energetics. These systems would provide nearly identical separations. They may differ slightly because the magnitudes of the retention factors for a given solute may differ, but the relative position of all solutes would remain identical on the two systems. The final relationship, called a heteroenergetic relationship, is present when the retention factors are poorly correlated. It implies that the energetics governing retention on the two systems are different. Switching from one column to the other would be more likely to produce changes in selectivity for a problematic separation than would switching between homo- or homeoenergetic columns. Identifying heteroenergetic systems is also useful when selecting orthogonal columns for use in two dimensional separations.

log k1 =

H1 H1 H1 log k2 + log keb1 − log keb2 = log k2 − constant H2 H2 H2

(8)

where retention on system 1 is linearly related to retention on system 2 by a slope equal to H1 /H2 . The necessity of this relationship and its consequences when the conditions in (7) are met has been discussed by Zhao and Carr [39] and Zhang and Carr [1]. In Eq. (8), the retention of ethylbenzene would be a constant value for both systems (although not necessarily the same value), and would therefore only modify the intercept. There are no solute parameters present in Eq. (8), indicating that the ␬–␬ plot would be perfectly correlated and the two columns would exhibit a homeoenergetic relationship. The more specific case of a homoenergetic relationship results when the ratio H1 /H2 is equal to 1.0, such that the hydrophobicities of the two columns are equal. A heteroenergetic relationship exists when the equalities in (7) are not present. The choice of selecting the hydrophobicity, H, as the denominator for all ratios complies with the convention of selecting the dominant contributor to retention [1,39–43]. 3.3. Visualization of system relationships – the system selectivity cube The previous section makes it clear that it is necessary to check if the relationships in (7) are satisfied by two columns in order to determine their energetic relationship. This may be done graphically by plotting the i/H ratio for two systems against one another, where i = S, A, B, or C. The linear regression of such a plot can be characterized by three statistics; slope, intercept, and square of the correlation coefficient (r2 ). When the relationships in (7) exist, this plot will be perfectly correlated with r2 = 1.0, slope = 1.0, and intercept = 0.0. Significant deviation of these statistics indicates a heteroenergetic relationship. A homoenergetic relationship is a special case where a homeoenergetic relationship exists and the hydrophobicities of the two columns are equal (i.e., H1 /H2 = 1.0). In order to visualize these regression statistics along with the H1 /H2 -ratios in a manner that makes it easy to compare many

A.R. Johnson et al. / J. Chromatogr. A 1249 (2012) 62–82

Fig. 1. (A) A thermal heat map. Ratios of 1.00 are colored black, while subsequently higher values get increasingly lighter. The colors are scaled to each data set such that the greatest H/H ratio is always white, and a ratio of 1.00 is always black. The colors of the remaining points are interpolated between the two extremes. (B) An example color scale legend. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

systems simultaneously, we use the slope, intercept, and r2 values as axes to create a three dimensional plot called the system selectivity cube (SSC) [8]. The correlation between two different chromatography columns thus produces a single point in three dimensional space within the cube. The ideal homeoenergetic relationship (slope = 1.0, intercept = 0.0, r2 = 1.0) is depicted on the SSC by a large light green glyph (a graphical object representing a point in three dimensional space). [Note: Here, the word ‘ideal’ describes the 1,0,1 point (i.e., perfect correlation) – it is not a comment about the ideality of the columns. In fact, in the case of trying to find orthogonal columns, having two columns with HSM parameters that are perfectly correlated would be anything but ideal.] The closer a comparison point is plotted to this ideally homeoenergetic glyph, the more similar the two systems are. The further a point is plotted from the homeoenergetic point, the more heteroenergetic the two compared systems are. In order to eliminate redundant information, the SSC shows only one comparison of two systems (i.e., the comparison of system 1 to 2, but not 2 to 1). As noted above, a homoenergetic relationship is a special case involving both a homeoenergetic relationship and H1 /H2 = 1.0. In order to display this information on the SSC, we use color mapping. The color mapping replaces the ‘spikes’ we used in a previous version of the SSC [8] as a simpler and more computationally efficient mode of display [9]. A heated color map, as shown in Fig. 1a is applied across the range of H/H ratios, where 1.00 is colored black, with subsequently higher values increasing in brightness toward white. Therefore, a point in close proximity to the ideally homeoenergetic point and colored black indicates that the two columns being compared are homoenergetic. The SSC program is highly interactive. The cube can be rotated and zoomed in to view comparisons at any angle. One difficulty that many comparison methods face is overplotting. That is, with so many columns available, it is difficult to look at them all simultaneously. In fact, as we noted earlier, over 500 columns have been characterized by the HSM, allowing for over 125,000 possible comparisons – clearly far too many to visualize and comprehend. The SSC provides tools for culling the data in order to display only columns of interest. For example, a reference column can be chosen in the user interface and only comparisons against that column would be plotted. The use of this feature is demonstrated throughout the article. It is useful in method development for selecting a column which is similar or different in relation to the current column that an analyst is using. The SSC can also compare systems categorized by other retention models, such as linear solvation energy relationships (LSERs). The SSC program will perform a comparison regardless of the number of input parameters for each column. This feature may be useful to customize the comparison of columns to a particular separation. For example, in a separation of neutral solutes, the C term of the column is unlikely to

65

make any difference in the selectivity of the columns. In this case, only the A, B, S*, and H parameters could be input for each column, and the comparison would ignore the ion exchange characteristics of the columns. The source code for the SSC is freely available online at http://artsci.drake.edu/urness/download/ssc.html and the authors encourage anyone wishing to use or modify the program to do so. The HSM data are freely available at http://www.usp.org/USPNF/columns.html [44]. The SSC is capable of displaying additional information about a column with the ‘group’ feature. In addition to the HSM column parameters, the user may also input a text field describing the column. For example, if the text column lists the phase chemistry (C18, CN, F, etc.) for each column, the SSC is capable of illustrating which comparisons involve two C18 phases, which involve a C18 compared to a fluorinated column, a cyano to a C18 column, etc. using color. A key for the color map is shown in a separate window, as shown in Fig. 1b. By default, the H/H ratio is shown as described above, but through the user interface, the ‘group’ color can be shown instead. Other examples of possible ‘group’ assignments include, but are not limited to, manufacturer, silica type, cost, or pore size.

4. Experimental 4.1. Reagents HPLC/MS-grade acetonitrile was obtained from Sigma–Aldrich (St. Louis, MO). HPLC grade water was prepared in-house from a Millipore (Billerica, MA) Milli-Q water purification system. Ammonium acetate was purchased from Sigma–Aldrich and used as received. A 10 mM ammonium acetate buffer with pH of 3.5 was prepared by first adding 0.77 g of ammonium acetate salt to about 800 mL of water. The pH was then adjusted by adding 50% formic acid (Sigma–Aldrich) in water to bring the pH to 3.5. Finally, the volume of the buffer was brought to 1 L. A mobile phase of 20/80 acetonitrile/buffer (v/v) was prepared online using the eluent mixing capabilities of the instrument following online vacuum degassing. Solutes used in this study were obtained from Sigma–Aldrich: amphetamine, salicylic acid, trans-cinnamic acid, phenypropanolamine, hippuric acid, caffeine, 4-iodophenol, 2,4dichlorophenoxyacetic acid, phenobarbital, lidocaine, bupropion, amitriptyline, diazepam, and oxazepam were obtained. A stock solution of each solute was prepared in either acetonitrile or methanol at 10 mg/mL. Following determination of MS/MS detection parameters for each individual solute (see below), a single mixture of all 14 solutes at 50 ␮g/mL of each was then prepared in 50/50 acetonitrile/water (v/v) and a 5 ␮L injection was made.

4.2. Columns The columns used in this work were all 150 mm × 4.0 or 4.6 mm i.d., packed with 5 ␮m particles and generously provided by the manufacturers; particle pore diameters and manufacturers are ˚ Sigma–Aldrich), indicated in parentheses: Discovery C18 (180 A, ˚ Bischoff Chromatography), DevelProntoSIL 200 C18 H (200 A, ˚ Nomura Chemical Co.), Zorbax 300SB-C18 osil C30-UG-5 (140 A, ˚ Agilent Technologies), Alltima C18 (100 A, ˚ Alltech Asso(300 A, ˚ Thermo Scientific), Chromegabond ciates), Hypersil BDS C18 (130 A, ˚ ES Industries), Genesis C18 300A (300 A, ˚ Jones WR C18 (120 A, ˚ Thermo ScienChromatography), Hypersil Biobasic C18 (300 A, ˚ Thermo Scientific), Zorbax tific), Hypersil Prism C18 RP (100 A, ˚ Agilent Technologies), Hypurity Advance (190 A, ˚ Bonus-RP (80 A, ˚ Agilent Technologies), Thermo Scientific), Polaris C8-A (180 A, ˚ Waters Corporation), XTerra RP8 (125 A, ˚ Symmetry C18 (100 A,

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A.R. Johnson et al. / J. Chromatogr. A 1249 (2012) 62–82

Table 2 HSM coefficients and Fs values for columns discussed in this article. Name Type-B alkyl-silica columns Discovery C18 ProntoSIL 200 C18 H Develosil C30-UG-5 Zorbax StableBond 300 C18 Alltima C18 Similar type-A and -B columns Hypersil BDS C18 Chromegabond WR C18 Genesis C18 300A Hypersil Bio Basic-18 EPG columns Hypersil Prism C18 RP Zorbax Bonus RP Hypurity Advance Polaris C8-A Cyanopropyl columns Discovery CN Zorbax SB-CN Luna CN Inertsil CN-3 Orthogonal columns Symmetry C18 Xterra C8 RP Thermo CN Discovery HS F5 ZirChrom-EZ Bondclone C18

H

S*

A

B

C (2.8)

C (7.0)

Retention

Type

Source

Phase

Fs (pH 2.8)

0.984 0.955 0.976 0.905 0.993

0.027 −0.001 −0.036 −0.050 −0.014

−0.128 −0.121 −0.196 0.045 0.035

0.004 0.016 0.011 0.043 −0.013

0.176 0.163 0.158 0.254 0.092

0.153 0.218 0.176 0.701 0.391

4.815 4.774 7.792 2.210 11.532

B B B B B

Supelco Bischoff Nomura Agilent Grace-Alltech

C18 C18 C30 C18 C18

Reference 3.56 6.87 12.6 9.75

0.993 0.979 0.974 0.974

0.016 0.026 0.005 0.025

−0.095 −0.159 −0.086 −0.100

−0.009 −0.003 0.013 0.007

0.337 0.320 0.266 0.253

0.281 0.283 0.270 0.217

5.564 5.391 3.489 3.249

A B B B

Thermo/Hypersil ES Industries Grace-Jones Thermo/Hypersil

C18 C18 C18 C18

Reference 2.74 6.76 7.43

0.645 0.654 0.412 0.601

0.089 0.107 −0.056 −0.007

−0.459 −1.046 −0.095 −0.609

0.301 0.373 0.249 0.104

−2.817 −2.971 −1.332 −0.074

−0.716 −1.103 0.785 0.208

4.819 4.457 1.622 2.160

EP EP EP EP

Thermo/Hypersil Agilent Thermo/Hypersil Varian

EP EP EP C8

Reference 24.1 124 229

0.397 0.502 0.452 0.369

−0.11 −0.108 −0.112 0.049

−0.615 −0.224 −0.323 −0.808

−0.002 0.042 −0.024 0.083

−0.035 −0.146 0.439 −2.607

0.513 1.047 1.321 −1.297

0.634 1.729 1.271 1.122

CN CN CN CN

Supelco Agilent Phenomenex GL Science

CN CN CN CN

Reference 16.2 40.4 214

1.052 0.657 0.404 0.652 1.040 0.824

0.063 −0.049 −0.111 −0.125 0.117 −0.056

0.018 −0.604 −0.709 −0.305 −0.999 −0.125

−0.021 0.099 −0.009 0.016 −0.001 0.044

−0.302 −0.187 −0.029 0.810 2.089 0.078

0.123 −0.198 0.491 1.185 2.089 0.347

9.815 3.062 0.817 4.048 1.147 4.488

B EP CN F Other B

Waters Waters Thermo/Hypersil Supelco ZirChrom Phenomenex

C18 EP CN F C18 C18

Reference 29.7 36.9 95.0 200 35.3

˚ ZirChrom Separations, Waters Corporation), ZirChrom-EZ (300 A, ˚ Phenomenex). Inc.), Bondclone C18 (150 A, 4.3. Instrumentation and chromatographic conditions Chromatographic data unique to this article (as opposed to those simulated from data that were used to construct the HSM and are thus detailed in the references provided) were obtained using a system composed of a quaternary pump (Model HP1050), an autosampler (Model HP1050), and a triple quadrupole mass spectrometer equipped with an electrospray ionization source (Model 320), all from Agilent Technologies (Palo Alto, CA). The pump and autosampler were controlled using Agilent Chemstation software (v. A.08.03), and the mass spectrometer was controlled using Varian MS Workstation (v. 6.9.3). Columns were equilibrated for about one hour in the 20/80 ACN/buffer mobile phase prepared as described above prior to the separation of the 14 component mixture. The flow rate was 1.0 mL/min. and the column temperature was 35 ◦ C. Solutes were detected by the mass spectrometer operated in MS/MS mode and using either positive (5000 V needle voltage) or negative (−4500 V) electrospray ionization. Argon was used as the CID gas at 2 mTorr. Detailed information including parent and fragment masses, and capillary and collision cell voltages are provided as Supplementary Material. Because of the excessively long analysis times (up to four hours) associated with this diverse set of solutes and columns, most columns were run just once, but three columns were run two or three times to evaluate the reproducibility of the data. The median relative standard deviation of retention factors for the Alltima C18, Discovery C18, and Hypersil BDS C18 were 3.2, 3.5, and 1.8% respectively. 5. Results – column comparisons using the SSC The HSM has been used to characterize over 500 commercially available RPLC columns, covering a variety of manufacturers and

column types, allowing for a very large number of possible comparisons. In the analyses presented in this section, we have either studied subsections of the data (e.g., just cyano phases compared to each other), or we have used the ability to select a reference column against which other, specifically selected columns are compared. We have chosen to use the same shorthand names for each column that were used in the work of Snyder et al. in order to facilitate comparisons between that work and the work we present here. However, the shorthand names are not fully descriptive and readers are encouraged to consult prior papers for full details [3–6,10–14]. 5.1. Type-B alkyl-silica columns The majority of commercial columns are made using high purity (type-B) silica particles. Type-B silica contains fewer metal impurities, which reduces the activity of acidic and ionized silanols on the silica surface, thus reducing unanticipated interactions, band broadening, and peak tailing as well as increasing reproducibility [45]. In this section, we compare type-B silica columns derivatized with alkyl functionalities. Carr et al. [46] identified the Discovery C18 column as representative of the ‘average’ C18 column, thus, we use it as a ‘reference’ column to which we compare other type-B alkyl silica phases. Furthermore, while the HSM has been used to characterize over 350 alkyl phases, we have selected a sample of these columns to illustrate comparisons within this class. The SSC generated by comparing the Discovery C18 column to the four other type-B alkyl-silica columns listed in Table 2 is shown in Fig. 2. The Fs values calculated according to Eq. (3) are also shown in Table 2. In the SSC, two of the comparisons fall close to the homeoenergetic green marker on the SSC (specific threshold values used to classify columns as homo-, homeo-, or heteroenergetic based on the statistics generated by the correlations between column parameter ratios are discussed later in Section 6.3). The two columns in this region are the Prontosil 200 C18-H and the Develosil C30 UG5. The glyphs in Fig. 2 are colored according to the H/H ratio, with a ratio equal to 1.00 colored black. The comparison of the Discovery C18 and Prontosil 200 C18-H has an r2 of 0.98, slope of 1.03, intercept of 0.01, and hydrophobicity ratio (H/H) of 1.03, indicating

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Fig. 4. A radar plot illustrating the similarities and differences in individual HSM ratios for three type-B alkyl silica columns at pH 2.8. Fig. 2. The SSC of several type-B alkyl silica columns at pH 2.8. Each point represents the comparison of the Discovery C18 column to the labeled column. The H/H ratio for relevant column comparisons is shown under the column label. Note the r2 axis spans from 0.00 on the left to 1.00 on the right and is not labeled for clarity.

that, according to the designation system of Horvath et al., the two columns are homoenergetic. However, the more rigorous requirement of Fs ≤ 3 does not qualify them as ‘equivalent’ columns. The comparison of the Discovery C18 and Develosil C30 UG-5 columns has an r2 of 0.95, slope of 0.829, intercept of 0.3, and hydrophobicity ratio of 1.008. Given these statistics, these two columns would be termed homeoenergetic according to Horvath et al. According to the more rigorous demands of the Fs metric, the two columns would not be identified as equivalent. Comparisons of the column characteristics can also be made using a radar plot [18,47–51] as shown in Fig. 3. When the ratios of S, A, B, and C to the H parameter are plotted together, the columns appear to be similar but not identical.

Fig. 3. A radar plot illustrating the similarities and differences in individual HSM ratios for three type-B alkyl silica columns at pH 2.8.

The comparisons of the Alltima C18 column and the Zorbax StableBond 300 C18 columns to the Discovery C18 column result in glyphs in the heteroenergetic region of the SSC according to the Horvath designation, indicating that the energetics governing retention on these two columns are different from that of the Discovery C18 column. This is consistent with the larger Fs values in Table 2. The radar plot in Fig. 4 shows that the major difference between the Alltima C18 and the Discovery C18 is the acidity ratio (A/H) of the two columns. The Zorbax StableBond 300 C18 column exhibits differences in the acidity (A/H), basicity (B/H), cation exchange (C/H), and steric interaction (S*/H) ratios. The practical differences in the performance of these five columns can be illustrated with simulated chromatograms as shown in Fig. 5. Retention factors of the 17 solutes used to characterize the columns were generously provided by the developers of the HSM [3–6,10–14]. The retention factors were used to create simulated chromatograms assuming Gaussian peak shapes for all solutes and an arbitrarily selected dead time of 74 seconds. The retention of 16 of the 17 solutes was only measured at pH 2.8. As such, our column comparisons will largely focus on this pH so that we may illustrate the comparisons with simulated chromatograms. It is important to note that we have no information regarding band broadening or peak tailing, and any such effects in any of the simulated chromatograms are only included to add some realism to the figures. Also, using the same solutes used to characterize the columns by the HSM for these chromatograms is not the most rigorous test of the ability of the SSC to identify similar and different columns. A comparison of these columns using an independent solute set is discussed below. Again regarding the Discovery C18 as the reference column, it is clear in Fig. 5B that the Prontosil column, which appeared to be homoenergetic on the SSC according to the Horvath requirements, produces generally comparable separation of the solutes. There are no differences in elution order and very little difference in band spacing except 5-phenylpentanol (10) and anisole (11) and ethylbenzene (15) and trans-4-chalcone (16). The Develosil C30 UG-5 column exhibited a homeoenergetic relationship to the Discovery C18 column. It produces a similar but not equivalent separation (Fig. 5C), which is consistent with an Fs value of 6.87. The Develosil C30 column does not provide a substantial change in the order of elution, but does provide a general increase in retention.

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Fig. 5. Simulated chromatograms at pH 2.8 of several type-B alkyl silica columns. Note the scale change in (E) to allow for the increased retention. Columns: (A) Discovery C18, (B) Prontosil 200 C18-H, (C) Develosil C30 UG-5, (D) Zorbax StableBond 300 A˚ C18, (E) Alltima C18.

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The Zorbax StableBond 300 C18 column, which the SSC indicated should have a heteroenergetic relationship with the Discovery C18 column under the Horvath classification scheme, does exhibit different selectivity compared to the Discovery phase (Fig. 5D). For example, several elution order changes can be noted on these two phases. Specifically, nortriptyline (4) and p-nitrophenol (5) and amitriptyline (6) and 5,5-diphenylhydantoin (7) switch elution order. Anisole (11) and 5-phenylpentanol (10), which are partially resolved on the Discovery phase, coelute on the Zorbax phase. Lastly, significant changes in selectivity are seen with compounds ethylbenzene (15), trans-chalcone (16), and mefenamic acid (17). Ethylbenzene (15) and trans-chalcone (16) coelute and are well separated from mefenamic acid (17) on the Discovery phase, while on the Zorbax phase, trans-chalcone (16) and mefenamic acid (17) coelute and are well separated from ethylbenzene (15). Thus, even though both columns are nominally type-B C18 phases, they provide different selectivities for the solute set employed here, consistent with the designation of ‘heteroenergetic’ using Horvath’s designations and an Fs > 3. However, the two columns would not be categorized as ‘orthogonal’ because they do not meet the criterion of Fs > 65. The Alltima C18 column also appeared to be heteroenergetic on the SSC, but the chromatogram shown in Fig. 5E shows a similar separation to the Discovery C18 column. In fact, only two solutes have changed their relative position, amitriptyline (6) and mefenamic acid (17). Out of the set of 17 solutes used to characterize these columns, these two solutes have the lowest ˇ values, −0.041 and −0.049, respectively. Because the difference between these two columns, as shown in Fig. 4, is due largely to the column acidity ratio (A/H) it makes sense that those solutes would change position in the separation. This comparison also illustrates a fundamental difficulty in any column comparison technique. Column characterization methods such as the HSM or LSERs are derived assuming a varied solute set. For an individual separation, differences in selectivity between two columns will always depend on the solute set. In the above comparison of the Discovery C18 and Alltima C18 columns, the A/H and C/H ratios are responsible for the difference between the two columns as shown in Figs. 3 and 4. However, because the solute set in Fig. 5 does not contain many ionized species, and most columns are of similar basicity (see Table 2), the simulated chromatograms do not show the differential separation predicted by the SSC. The sample dimensionality, or range of interaction ability of the solute set, must be complimentary to a chemical difference in any two columns for those two columns to provide differential separation of that solute set [52]. An SSC using the C value at pH 7.0 instead of pH 2.8 for the same columns analyzed in Fig. 3 is shown in Fig. 6. The conclusions drawn from this SSC are essentially identical as above despite the change in pH. 5.1.1. Independent solute set analysis To assess the predictions based on the SSC and Fs values presented above, we have examined a solute set of 14 compounds – selected to include acids, bases, and pharmaceutically relevant compounds – that is independent of the solutes used to measure the HSM parameters (see Section 4). To examine similarities and differences in selectivity, in Fig. 7 we plot log k on the reference column (Discovery C18) vs. log k on the other columns discussed in this section above. It can be seen in Fig. 7A that in general, there is strong correlation between retention on the Discovery C18 column and the ProntoSIL 200 C18 H, consistent with the positioning of this comparison in the SSC and their Fs value. There are some differences in selectivity, but no elution order changes, between the two columns. For example, the selectivity of Discovery C18 for salicyclic acid and lidocaine

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Fig. 6. A SSC showing the comparison of several type-B alkyl silica columns to the Discovery C18 column at pH 7.0. The H/H ratio for relevant column comparisons is shown under the column label. Note the r2 axis spans from 0.00 on the left to 1.00 on the right and is not labeled for clarity.

is 1.07 whereas on ProntoSIL the selectivity is 1.28. Similarly, the selectivity of Discovery C18 between caffeine and amphetamine is 1.02 whereas on Prontosil it is 1.06. Such differences may not be acceptable if searching for identical replacement columns, but clearly, peaks that are overlapping or nearly so on one phase will likely be so on the other. An analysis of the Develosil C30 column compared to the Discovery column (Fig. 7C) yields essentially identical results to that of the ProntoSIL comparison to Discovery (with the exception that caffeine elutes slightly before amphetamine on the Discovery phase and slightly after amphetamine on the ProntoSIL phase, but by less than ten seconds in both cases). As predicted by the SSC and Fs metric, the correlation between retention on the Discovery column and on the Zorbax SB 300A C18 column is poor, as seen in Fig. 7B. For example, hippuric acid elutes early on the Discovery column but is much more retained on the Zorbax column. Furthermore, buproprion and trans-cinnamic acid elute before phenobarbital on the Zorbax column. On the Discovery column, however, buproprion and trans-cinnamic acid are better separated and elute after phenobarbital. Lastly, even though the SSC predicts that the Discovery C18 and Alltima C18 columns should yield heteroenergetic retention, and Fs for these columns is 9.75, the retention of the solutes is generally well correlated (Fig. 7D). Some subtle differences can be observed, however. For example, while caffeine and amphetamine nearly co-elute on both phases, their elution order reverses on the two columns. Lidocaine and salicylic acid also switch elution order on the two phases, and 2,4-dichlorophenoxyacetic and trans-cinnamic acid are better separated on the Discovery phase than on the Alltima phase. 5.2. Type A compared to type B columns Older, type-A silica columns often have more metal impurities in the silica, as well as less ligand coverage than newer, type-B columns [6]. These packing properties may lead to undesirable peak shapes and faster column degeneration. As such, it may be beneficial to switch from a type-A column to a newer type-B column. However, because of the high variability in interaction abilities of type-A columns, it is difficult to find type-B silica columns that

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Fig. 7. Comparison of selectivity on alkylsilica phases. Log k for the independent solute set on the reference Discovery C18 phase vs. log k on ProntoSIL 200 C18-H, Develosil C30 UG-5, Alltima C18, and Zorbax StableBond 300 A˚ C18. Chromatographic conditions as described in Section 4.

are equivalent to type-A columns. In a study of 43 type A silica columns and 87 type B columns, Gilroy et al. were only able to find one comparison which provided adequate similarity between a type-A and type-B column using the Fs metric [6]. The comparison of the Hypersil BDS C18 column, a type-A alkyl silica column, with the Chromegabond WR C18 was found to have a Fs value less than three, indicating equivalent selectivity. Using the SSC, two other type-B columns were also found to have at least a homeoenergetic relationship with the Hypersil BDS C18 column (again using the Horvath classification); the Genesis C18 300 A˚ and Hypersil BioBasic-18 columns. Both exhibit high correlations (all r2 > 0.98) and H-ratios of 1.02, suggesting not just homeoenergetic, but homoenergetic relationships. These columns, along with HSM parameters and Fs values for their comparisons, are listed in Table 2. The SSC of these three columns compared to the Hypersil BDS C18 column at pH 2.8 is shown in Fig. 8. We note here that a reviewer indicated that while the Hypersil BDS column is not classified as type-B, it is not truly a type-A column, either, due to pre-treatment of the silica to remove metals. Furthermore, the reviewer suggested that the BioBasic phase, being from the same manufacturer, may be made with the same silica as the Hypersil BDS column. In general, the reviewer also noted that the columns used in this section generally fall near the cut-off used in the HSM to differentiate type-A phases (C(2.8) > 0.3) from type-B phases (≤0.3). The columns considered in this section all have 0.25 < C(2.8) < 0.34. That these inter-type column similarities identified within the SSC can be rationalized based on manufacturing processes is a testament to the ability of the SSC to compare columns over many phase types that might otherwise be thought to be different because of the labels assigned to them (e.g., type-A, type-B, etc.). Simulated chromatograms for the four columns considered in this section are shown in Fig. 9. While retention is decreased on the Genesis (Fig. 9C) and BioBasic columns (Fig. 9D), the elution

order and band spacing is similar, but not equivalent, on all four of these columns. For example, some peaks that are resolved on the Hypersil BDS C18 (e.g., compounds 4 and 7 and 10 and 11 in Fig. 9A) are not resolved on the Genesis or BioBasic columns. Conversely, compounds 15 and 16 which coelute on the Hypersil BDS column

Fig. 8. The SSC of several type-B columns to the type-A column; Hypersil BDS C18 at pH 2.8. The H/H ratio for relevant column comparisons is shown under the column label. Note the r2 axis spans from 0.00 on the left to 1.00 on the right and is not labeled for clarity.

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Fig. 9. Simulated chromatograms illustrating homeoenergetic columns among type-A and type-B alkyl silica columns at pH 2.8. Columns: (A) Hypersil BDS C18, (B) Chromegabond WR C18, (C) Genesis 300 A˚ C18, (D) Hypersil BioBasic-18.

are resolved on the Genesis column but not on the BioBasic column. While these columns are not strictly equivalent for this particular solute set, despite satisfying the criteria for homoenergetics, they provide good leads for replacement columns if slight changes in mobile phase composition can achieve the desired separation.

As we did with the alkylsilica columns, we have analyzed an independent set of solutes and here compare them to the results obtained with the solutes used to establish the HSM parameters. Plots of log k for the solutes on the reference column (Hypersil BDS C18) vs. those on the other columns are shown in Fig. 10.

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Fig. 10. Comparison of selectivity on a type A silica phase compared to type-B silica phases. Log k’ for the independent solute set on Hypersil BDS C18 (as a reference column) ˚ and Hypersil BioBasic-18. Chromatographic conditions as described in Section 4. vs. log k on Chromegabond WR C18, Genesis C18 300 A,

As can be seen, the correlations are all quite strong, with some minor variations in selectivity observed. For example, salicylic acid (log k = 0.21) is better separated from lidocaine (log k = 0.31) on the Hypersil BDS phase than on the Hypersil Biobasic phase (log k = −0.029 and −0.017 for salicylic acid and lidocaine, respectively, Fig. 10C). The generally strong correlations across the solute set seen in these figures are consistent with the simulated chromatograms shown above that are based on the solutes used to establish the HSM.

Bonus RP to the reference Hypersil Prism C18 RP column. Because the comparison is both in the homeoenergetic region of the SSC and illustrates a hydrophobicity ratio close to 1.00 (actually 1.01), these columns would be expected to have a homoenergetic relationship, providing near equivalent separation. The larger H-ratio, illustrated by the orange color of the comparison of the Hypurity Advance and the Hypersil Prism C18 RP columns indicates a

5.3. Embedded or endcapped polar groups Columns with polar groups either embedded in an alkyl chain or used to endcap a column often offer unique selectivity compared to traditional, alkyl-silica columns. However, the variety of linkage and endcapping groups, including amides, ureas, carbamates, hydroxyls, and ethers, among others, makes predictions of similarities and differences in column selectivity difficult. Even among columns with varying polar groups, the SSC is capable of identifying systems with similar and different overall blends of retention energetics. For example, the Hypersil Prism C18 RP column, which has a urea linkage embedded bonded phase, is compared to three other columns listed in Table 2. The first is the Zorbax Bonus RP column, an amide embedded column. The second is the Hypurity Advance, another amide embedded column. The last is the Polaris C8-A column, which has an embedded “polar group”, the nature of which is not specified. Even with varying bonded phase chemistries, comparisons of each to the Hypersil Prism C18 RP column are all plotted in the homeoenergetic region of the SSC (Fig. 11) except for one, the Polaris C8-A column. The color of the glyphs in Fig. 11, as well as the numbers adjacent to each point for those viewing in black and white, illustrates the ratio of the hydrophobicities of the columns where a ratio of 1.00 is black and increasing ratios are given progressively brighter colors as shown in the color map in Fig. 1A. The dark colored glyph in the homeoenergetic region is the comparison of the Zorbax

Fig. 11. The SSC comparing the Hypersil Prism C18 RP, an EPG column to several others labeled in the figure. The H/H ratio for relevant column comparisons is shown under the column label. Note the r2 axis spans from 0.00 on the left to 1.00 on the right and is not labeled for clarity.

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Fig. 12. Simulated chromatograms of several EPG type columns at pH 2.8. (A) Hypersil Prism C18 RP, (B) Zorbax Bonus RP, (C) Hypurity Advance, (D) Polaris C8-A. Note the exclusion of solute 3, berberine, because it eluted prior to the dead time estimator, thiourea on many of the EPG type columns.

homeoenergetic relationship between these columns, suggesting little to no change in elution order on the Hypurity Advance column relative to the Hypersil Prism column would occur, but systematic increases or decreases to solute selectivities may occur. These predicted relationships are observed in the simulated chromatograms (Fig. 12). Retention on the reference column (A) and the Zorbax Bonus RP column (Fig. 12B) is quite similar. While overall retention is greatly reduced on the Hypurity Advance column (Fig. 12C), the elution order is largely unchanged, although many changes in selectivity are observed. Note that N,N-dimethylacetamide (1), N,N-diethylacetamide (2), notriptyline (4), and amitriptyline (6) all elute earliest in (A), (B), and (C). 5,5-Diphenylhydantoin (7), acetophenone (8), and benzonitrile (9) elute next (but in different orders), followed closely by 4-nitrophenol (5), 5-phenylpentanol (10), and anisole (11), and the remaining solutes follow identical elution order. The position of the Polaris C8-A column comparison indicates a heteroenergetic relationship. This is exemplified by the fact that nortriptyline (4) and amitriptyline (6) elute before N,N-dimethylacetamide (1) and N,N-diethylacetamide (2) on the Hypersil Prism C18 RP (Fig. 12A) but after them on the Polaris C8-A (Fig. 12D). Additionally, 5-phenylpentanol (10) and anisole (11) are

resolved on the Hypersil Prism C18 RP but coelute on the Polaris C8-A. The elution of ethylbenzene (15) and cis-chalcone (14) relative to trans-chalcone (16) and n-butylbenzoic acid (12) also exhibit elution order changes. The primary reason for the poor correlation of the HSM parameters, and thus the heteroenergetic characterization, is the C/H value of the columns. The average C/H ratio of columns (A), (B), and (C) is −4.04 ± 0.58. The C/H value of the Polaris C8-A column is −0.12. The large difference dominates the comparison, but as Dolan and Snyder have pointed out [53], the C term only provides significant impact on a separation when the solutes include ionized compounds. Nortriptyline (4) and amitriptyline (6), have the largest magnitude  values of any solutes, and the resulting increased retention relative to N,N-dimethylacetamide (1) and N,N-diethylacetamide (2) in the other three columns is evident on the chromatogram of the Polaris C8-A column (D). Here again we have analyzed a separate solute set to check the predictions made based on the SSC and created ␬–␬ plots summarizing solute retention shown in Fig. 13. Retention of these solutes on the Hypersil Prism C18 RP phase is generally well correlated with that on the Zorbax Bonus RP phase as seen in Fig. 13A, however, there are some selectivity differences observed with this solute set that were not observed with the HSM solutes. For

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Fig. 13. Comparison of selectivity on embedded polar group or endcapped polar group phases. Log k for the independent solute set on Hypersil Prism C18 (as a reference column) vs. log k on Zorbax Bonus RP, Hypurity Advance, and Polaris C8-A. Chromatographic conditions as described in Section 4.

example, salicylic acid elutes before trans-cinnamic acid, and 2,4dichlorophenoxyacetic acid elutes just before diazepam on the Hypersil Prism phase, but trans-cinnamic acid elutes before salicylic acid and diazepam elutes before 2,4-dichlorophenoxylacetic acid on the Zorbax Bonus RP phase. Thus, these columns offer some similarities in their retention energetics, but cannot be considered equivalent, as suggested by their Fs value of 24.1. There is little correlation between the Hypersil Prism C18 RP and either the Hypurity Advance or Polaris C8-A phases (Fig. 13B and C, respectively). This is consistent with the predictions of the SSC for the Polaris phase, and with Fs values associated with both comparisons, but somewhat unexpected for the Hypurity Advance which was predicted to have homeoenergetic retention characteristics according to the SSC. The ␬–␬ plots for both the Polaris and Hypurity Advance phases show many differences in elution order. It should also be noted that on the Hypurity Advance phase, amphetamine, phenylpropanolamine, and lidocaine essentially elute with or slightly before the dead time marker, uracil, resulting in negative k values and are thus not shown in the plots.

functional groups of these columns are identical it is not surprising that many of the columns are similar. Equally evident from the figure, however, is that many of the cyano columns are different from one another. As an example, the Discovery CN column is compared to the Inertsil CN, Zorbax SBCN, and the Luna CN. The column characteristics, as well as the Fs values of the comparisons, are listed in Table 2. Fig. 15 shows the SSC using the Discovery CN column as the reference column against which the other three are compared. It is clear that the Discovery CN column has a heteroenergetic relationships to the Luna CN, Zorbax

5.4. Cyanopropyl columns Cyanopropyl columns are not as widely used as traditional alkyl silica columns, but are valuable for the different retention characteristics they provide [54]. Cyano columns are generally more polar than traditional alkyl silica columns. Snyder et al. have suggested that the functional groups are also highly ordered, leading to less steric hindrance for the solute [3]. The cation exchange activity, C, for cyano columns varies among manufacturers. The difference in C terms for this class of columns also varies greatly with pH, with higher cation exchange activity at neutral pH than in acidic environments. Fig. 14 shows an SSC plot comparing 12 different cyano columns to one another, (e.g., 1 vs. 2, 3, 4. . .; 2 vs. 3, 4, 5. . .; 3 vs. 4, 5, 6. . .) for a total of 65 comparisons. Almost half of the comparisons fall within the homeoenergetic region of the SSC, indicating that many of the 12 columns would provide similar retention. Since the

Fig. 14. The SSC showing the comparison of 12 cyano columns (65 different comparisons) to one another at pH 2.8. Note the r2 axis spans from 0.00 on the left to 1.00 on the right and is not labeled for clarity.

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Fig. 15. The SSC showing the comparison of the Discovery CN column to the Inertsil CN, Zorbax SB-CN, and Luna CN columns at pH 2.8. Note the r2 axis spans from 0.00 on the left to 1.00 on the right and is not labeled for clarity.

StableBond-CN, and Inertsil CN-3 columns. The origins of the heteroenergetic relationships are made clear by the radar plot shown in Fig. 16. In the case of the Inertsil column, the difference in selectivity compared to the Discovery column is due almost exclusively to the cation exchange (C-term in the HSM model) ability of the two columns. The differences in selectivity between the Discovery column and the Luna CN and Zorbax SB-CN columns are due to a mixture of column acidity and cation exchange ability. As noted previously, the cation exchange term does not greatly affect the results of a separation with no ionizable solutes. Since most cyano columns have similar B and S* values, and generally vary slightly in A values, comparisons may be misleading if the intended separation mixture does not contain ionized solutes. Fig. 17 shows the simulated chromatograms of these four columns. The dramatic effect of the C-term on separations on these columns is illustrated

Fig. 16. A radar plot showing the similarities and differences in the HSM ratios of several cyanopropyl columns at pH 2.8.

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well by comparing the Discovery and Inertsil columns, Fig. 17A and D, respectively. Ionizable solutes such as nortriptyline (4), berberine (3), mefenamic acid (17), and amitriptyline (6) change in elution order relative to the other solutes. Some differences in the elution order of other solutes are also observed. For example, 5,5diphenylhydantoin (7) and anisole (11), 5-phenylpentanol (10) and toluene (13), and ethylbenzene (15) and n-butylbenzoic acid (12) coelute on the Discovery CN column but are resolved on the Inertsil CN. Thus, while the C-term may be responsible for the largest difference in these columns, other characteristics are also contributing to the selectivity differences. The Luna and Zorbax columns also appear in the heteroenergetic region of the SSC, as compared to the Discovery column, but not exclusively due to the C/H term. These two columns differ from the Discovery in acidity, which affects more solutes than cation exchange. This is illustrated in Fig. 17. The elution order of most of the solutes varies between the Discovery column (Fig. 17A) and the Zorbax (Fig. 17B) and Luna (Fig. 17C) columns. Coeluting peaks on the Discovery column, such as 5,5-diphenylhydantoin (7) and anisole (11) are resolved on the Zorbax and Luna columns but in reverse order on Inertsil CN (Fig. 17D). Acetophenone (8), which has a large basicity term, ˇ , in relation to most of the other test solutes, has a very different elution position in these cyano columns since they differ in their acidity terms. 5.5. Selection of orthogonal columns The previous examples have focused largely on selecting similar columns within a particular class of stationary phase to emphasize the abilities of the SSC program. However, the need for an orthogonal column is more common, whether to improve a separation or to select a second column for a two-dimensional separation. Here we show how the SSC may be practically used to select orthogonal columns. Because a C18 phase is often used as a starting point, the Symmetry C18 column is chosen as a reference. The simulated chromatogram for this column is shown in Fig. 18A. Whether the desired result of this separation is complete resolution of all the compounds or an orthogonal column for a two dimensional separation, the solute pair N,N-dimethylacetamide (1) and berberine (3) must be further separated, as well as the solutes N,N-dimethylacetamide (2), nortriptyline (4), and amitriptyline (6). In order to use the SSC to identify possible orthogonal columns, the Symmetry C18 column is compared to a variety of other columns. In this example, the Symmetry C18 column is compared to the Thermo CN, Discovery HS-F5 (a fluorinated column), Xterra C8 RP (an EPG column), Bondclone C18 (a type-A silica ODS column), and ZirChrom EZ (a zirconia based column) columns. The SSC generated by these comparisons is shown in Fig. 19. All of these columns appear to offer heteroenergetic relationships to the Symmetry C18 column for the solute set used to establish the HSM, and would therefore likely offer the desired differential selectivity. Simulated chromatograms for these columns are shown in Fig. 18. As predicted, these columns all offer substantially different selectivity to the Symmetry C18 column. The coeluting solutes N,N-dimethylacetamide (1) and berberine (3) are resolved on all the other columns. The coeluting solutes N,N-diethylacetamide (2), nortriptyline (4) and amitriptyline (6) are at least partially resolved on all of the alternative columns and show very high resolution on two of the five columns; the Discovery HS-F5 (Fig. 18C) and the ZirChrom EZ (Fig. 18F). In addition, there are elution order changes to many solutes, such as N-butylbenzoic acid (12) and toluene (13), for which the elution order is reversed on all of the alternative columns with the exception of the ZirChrom EZ column. Using our independent set of solutes yields some interesting results shown in Fig. 20. Retention on the Xterra C8 and Bondclone C18 phases are more highly correlated with retention on the

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Fig. 17. Simulated chromatograms of CN columns at pH 2.8. Columns: (A) Discovery CN, (B) Zorbax SB-CN, (C) Luna CN, (D) Inertsil CN. Note the scale change in time for columns (C) and (D), due to large differences in increased retention.

Symmetry C18 phase (Fig. 20A and B, respectively) than might be anticipated from the chromatograms discussed above. This illustrates that the solutes must take advantage of the characteristics that distinguish one phase from another in order to maximize the columns’ potentials to offer different selectivities. That does not seem to be the case with the solutes and these two columns. There are some elution order changes observed on both phases relative to the Symmetry C18 phase, but not the dramatic changes that would be desired when searching for a truly ‘orthogonal’ phase. Both columns have an Fs metric of approximately 30 when compared to

the Symmetry phase, and thus do not satisfy the criteria for ‘orthogonality.’ In this regard, the results of comparisons between these phases using this alternative test solutes are consistent with the interpretation of Fs values. The comparison between the Zirchrom EZ phase to the Symmetry C18 phase (Fig. 20C), however, does illustrate two phases that have very different retention characteristics (consistent with the Fs value of 201). Clearly, there is little correlation between retention on the two phases. This is evident both from the solutes used to establish the HSM and our independent solute set.

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Fig. 18. (A) Symmetry C18, (B) Thermo CN, (C) Discovery HS-F5, (D) Xterra C8 RP, (E) Bondclone C18, (F) Zirchrom EZ. Note the scale changes to account for increased retention on the symmetry column. Also, a different mobile phase composition is used for the Thermo CN column as discussed herein.

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Fig. 19. Two views of the SSC comparing the Symmetry C18 column to other stationary phase types as described. Note the r2 axis spans from 0.00 on the left to 1.00 on the right and is not labeled for clarity.

6. Discussion As illustrated above, the combination of the SSC and HSM yields a tool that chromatographers can use to efficiently identify similar and orthogonal columns. We have demonstrated that within column categories (e.g. cyano, fluoro, EPG, etc.) many columns are similar, but that significant differences in selectivity can arise and that the SSC makes it easy to find these differences. We have also illustrated the utility in using the SSC to choose an orthogonal column among several different column types to select the one offering the most different selectivity. Thus, the

SSC can provide rapid and beneficial guidance when selecting columns. As we noted in Section 1, there have been several methods proposed for column selection. The Fs parameter and the selectivity triangles of Zhang and Carr are most closely related to our approach because they are also based on HSM coefficients. In the following section, we comment on how the SSC compares to and complements both approaches. Before doing so, we note that the HSM is explicitly concerned with comparing stationary phases relative to one another with regards to their influence on the selectivity of separations. Most fundamentally, all columns are compared to

Fig. 20. Comparison of selectivity on a variety of phases. Log k for the independent solute set on Symmetry C18 (as a reference column) vs. log k on Xterra C8 RP, Bondclone C18, and Zirchrom EZ. Chromatographic conditions as described in Section 4.

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a reference ‘average’ C18 phase. Naturally, on any single phase, a change in separation conditions (e.g., temperature, mobile phase modifier type and amount, pH) can also influence selectivity. In practice, it is a logical first step to adjust these conditions in an effort to improve separations. The HSM and comparison schemes based on it such as the Fs metric, Zhang and Carr’s triangles, and the SSC are useful in at least three situations: (1) when alterations to the mobile phase do not provide the desired selectivity and therefore alternative phases must be sought, (2) when ‘orthogonal’ phases are sought for multidimensional separations, and (3) when an analyst must find a replacement column for a separation that had been working satisfactorily but for whatever reason (discontinuation, not available in the laboratory, etc.) the column is no longer available. In the first two situations, it is clear that little is gained by switching to stationary phases that are similar in their retention characteristics or using similar columns in multidimensional chromatography. The HSM, and metrics such as Fs , triangles, and the SSC provide guidance regarding columns that will likely produce changes in selectivity. In the third situation, these methodologies provide guidance in identifying columns that are likely to be equivalent and therefore preserve the selectivity of an already successful separation, but do so on another column. In both situations, with over 500 commercially available columns, such guidance can save considerable time, effort, and money. Thus, while solvent effects on selectivity are clearly important within any single separation, the HSM is focused on the contribution to selectivity of one stationary phase relative to another. Furthermore, while the HSM parameters are measured for all columns using only a single mobile phase composition at two different pH values, the originators of the HSM have studied the effects of mobile phase composition and pH on the HSM parameters. They conclude that the relative selectivity of the phases does not change significantly with mobile phase variations [11]. Some caveats must be offered here. Changes in the relative selectivity of the phases will not occur if a given change in mobile phase conditions alters the selectivity of a separation in the same way on two columns that are being compared. The authors of the above cited study actually quantify the relative contribution of changes in mobile phase conditions to column selectivity. They find that changes in percent modifier are least influential in affecting relative column selectivity, followed by temperature, followed by changes in mobile phase modifier type. Furthermore, they acknowledge that the conclusions are based on a study of C18 phases only and that larger changes in column parameters, and hence relative selectivity, can be expected for comparisons made between C18 and other types of columns (e.g., cyanos, fluoros, etc.). For columns of a given type, however, they suggest that little change in the HSM parameters will be found with variations in separation conditions. While temperature and mobile phase modifier type and concentration were found to make relatively small contributions to the relative selectivity of different columns, changes in pH can influence the HSM parameters – specifically the C-term. For this reason, C is measured at two pHs (2.8 and 7.0) and can be interpolated in this range [11]. The take-home message for all of the above is that the HSM parameters are measured relative to an average C18 phase. Thus, comparisons between phases are made relative to one another. Changes in mobile phase conditions can and do alter selectivity, but it has generally been found that they do so in similar ways on different columns, especially within the C18 class of columns. Therefore, the HSM parameters generally do not change significantly with changes in the mobile phase conditions (except pH as noted). Thus, analyses identifying equivalent, similar, and different columns that are made using a single mobile phase composition will lead to generally the same conclusions under different compositions.

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6.1. Relationship between the SSC and the Fs metric The SSC and the Fs metric both use HSM column parameters to make comparisons between columns. The Fs metric, shown in Eq. (3), provides a convenient (albeit single-valued) method for comparing any two systems characterized by the HSM. In this way, the goals of the SSC and the Fs metric are similar. While Fs is easier to use, the SSC provides additional information about the relationships between two columns (r2 , slope, and intercept). A potential source of discrepancies between Fs and the SSC relates to the fact that Fs compares two columns based on the absolute magnitudes of their HSM parameters, whereas the SSC uses coefficient ratios. Zhao and Carr [39] showed that in order to compare two systems characterized by retention models (LSERs, HSM, etc.) the ratios of two or more parameters are more important than the magnitudes of individual parameters. To demonstrate, consider two hypothetical systems, designated 1 and 2. The HSM parameters of our two imaginary systems are shown below. log ˛1 =  1.0 −   1.0 + ˇ 1.0 + ˛ 1.0 +  1.0 and, 









log ˛2 =  2.0 −  2.0 + ˇ 2.0 + ˛ 2.0 +  2.0

(9) (10)

These two columns, when compared by the Fs metric, would have an Fs value of 196, leading to the conclusion that the two columns would provide distinct selectivities. However, on the SSC, they would appear to be homeoenergetic because the ratios of each parameter (all relative to H) are identical for both columns. The chromatograms of these two columns would be very similar to the EPG column comparison discussed above (see Figs. 11 and 12 and accompanying discussion). The second column would offer greater retention of the solutes, but no difference in selectivity. Zhang and Carr performed a comparable analysis and reached an identical conclusion, stating “differences in phase selectivity only exist when the ratios of the phase coefficients differ, not when their absolute values differ.” [1] Nevertheless, it should be noted that the range in H-values is not exceptionally wide (0.3–1.3) for the commercially available columns that have been characterized. This is perhaps why cases like the imaginary one described above are generally not observed, contributing to the general success of the Fs metric. 6.2. Threshold values for equivalent and orthogonal phases based on the SSC In this article we have noted multiple instances in which two columns that would be identified as homoenergetic or homeoenergetic by Horvath et al.’s classification do not produce equivalent selectivities. Snyder et al. have offered the most stringent criteria for identifying equivalent columns (Fs ≤ 3) and orthogonal columns (Fs > 65 or 100 depending on the presence or absence of ionic species, respectively). It is reasonable to compare the statistical values upon which the SSC is based to column characterizations based on Fs . Before doing so, however, it should be noted that the Fs cutoffs cited above are deliberately stringent so as to virtually assure column equivalence or orthogonality (i.e., eliminate the potential for false positives while accepting the potential for false negatives). This is exceptionally useful where such stringency is absolutely required – particularly for regulatory compliance purposes. In situations where such stringency is not required, however, (e.g., in early exploratory stages of separation development), less stringent guidelines and more general guidance regarding equivalent and orthogonal columns can be useful. For example, if a particular column is not resolving all of the compounds in a mixture, one would want to avoid potentially similar columns (not just rigorously equivalent columns) and instead explore columns that offer potentially different selectivities. In this case, absolute orthogonality may not be required and column comparisons that yield Fs

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values between 3 and 65 (or 100) may achieve the desired separation. In these cases, ‘similar’ and ‘different’ may be just as, or more useful than, equivalent or orthogonal columns, particularly if criteria for equivalency and orthogonality too rapidly winnow the number of columns that one can explore or columns that satisfy these criteria are not immediately available to the analyst. With such situations in mind, in an effort to provide guidance and greater clarity regarding threshold values for ‘similar’ and ‘different’ columns – terms which are admittedly poorly defined and which we have therefore tried to avoid in this manuscript – we have compared the statistical values that we obtain using the SSC methodology with the Fs values obtained for the same column comparisons. We did not find clear, absolute correlations between Fs and any of the SSC metrics. In other words, with regards to ‘equivalent’ columns, there is no value of r2 above which all comparisons have Fs ≤ 3.0. This is not surprising as the mathematics underlying the two methodologies is different. For purposes of suggesting some threshold values, however, based on considerations of numerous correlations and the examination of several subsets of columns, we consider comparisons that have r2 > 0.97, slope = 1.0 ± 0.3, intercept = 0.00 ± 0.03, and H/H < 1.1 (all four criteria met simultaneously) as columns that demonstrate homoenergetic behavior under the Horvath classification. More generally, we suggest that columns that fit these criteria will at least yield similar, if not identical, separations. Thus, in situations where equivalence is not rigorously required, they will provide good alternatives which, with some manipulation of other operating parameters, may yield comparable separations if a replacement column is needed. These threshold values are summarized in the text box below.

Homoenergetic columns

Heteroenergetic columns

r2 < 0.97 Slope = 1.0 ± 0.3 Intercept = 0.00 ± 0.03 H/H < 1.1

r2 < 0.20 Slope < 0 or >2 Intercept < −0.3 or >0.3 H/H  1

Having defined these thresholds, we can compare them to Fs values. Considering 301 alkylsilica columns that have been characterized by the HSM – which makes possible 45,150 unique comparisons – 398 comparisons qualify as homoenergetic using our threshold values. Using Fs ≤ 3 yields 234 comparisons that qualify as equivalent. A subset of 140 of these comparisons satisfy both the SSC and Fs thresholds. These results indicate that our thresholds identify a broader range of potentially similar columns, bringing with it an associated risk of higher false positive rates (accepting Fs ≤ 3 as the absolute standard for equivalence). Of the 258 comparisons that satisfy our criteria but which have Fs > 3.0, 98 have 3.0 < Fs < 4.0. This indicates that many of our “false positives” (again using Fs as the absolute standard for equivalence) have very low Fs values, although they are outside of the rigorous equivalence window defined by Snyder et al. With regards to ‘different,’ or more rigorously, ‘orthogonal’ columns, clearly, comparisons yielding the poorest r2 values, slopes most deviated from 1.00, intercepts different than 0.00, and H/H ratios greater than 1.0 are most likely to produce different separations. As a general threshold, for orthogonality we recommend r2 < 0.20, slope < 0 or >2, intercept < −0.3 or >0.3, and H/H  1. These values are summarized in the text box above. Homeoenergetic columns have the same threshold values as homoenergetic columns except for the H/H ratio which can be greater than 1.1. We reiterate, however, that these guidelines have not been tested in the ways that the Fs metric guidelines have and are therefore suggestions meant to provide general guidance rather than

rigorous instruction. Furthermore, like the Fs thresholds, these values generally require that the solutes being separated take advantage of the HSM parameter(s) that is(are) giving rise to the poor correlation. This consideration of solutes is relevant to all column comparisons. HSM parameters are measured using 16 carefully selected solutes identified from painstaking consideration of hundreds of compounds. They were selected to represent a broad range of interaction types and strengths. However, in any individual analyte mixture, all interactions may not be equally represented. For example, if none of the solutes are hydrogen bond donors, then differences in the B-parameters between columns are not important. Thus, while Fs and the SSC provide general predictions, those predictions may be incorrect for extreme solute sets that are not well represented by the solutes used to measure the HSM parameters. In these situations, it is useful to weight the parameters differently before determining Fs and the SSC statistics. This has been considered elsewhere for Fs [53] and can be easily achieved for both Fs and the SSC. Carr et al. tested predictions of Fs using 18 cationic drug solutes under isocratic conditions [46]. They also used the 16 HSM test solutes to re-measure the HSM parameters for the 14 columns they considered in their studies. Interestingly, they found some significant differences between their measured values and values obtained from Snyder et al., particularly for the A and C parameters. It was suggested that some of the changes arise from storage of the columns in acetonitrile/water mixtures. Changes in the HSM parameters over time naturally lead to changes in the predicted Fs values. This suggests that some caution should be used when using Fs or the SSC to select alternative columns. Nevertheless, Carr et al. conclude that for the columns and solutes they studied, the Snyder–Dolan (S–D) HSM “does a reasonably good job of predicting the classification of these columns if we were to use drug solutes” and that “the original 16 solutes of the S–D method do a very good job, in general, of representing the behavior of drugs despite the fact that the S–D data set contains only two bases.” It should be noted that while only two bases are in the final 16 solutes, many more were tested and contributed to the development of the HSM overall. Important to our considerations here, the work demonstrates that for limited data sets, an Fs ≤ 3 is not required to obtain equivalent selectivities on two different columns. In fact, in Carr et al.’s article, two columns with Fs = 9.7 are shown to yield virtually identical chromatograms for eight selected drugs. This shows that for general guidance purposes, the cut-off of Fs ≤ 3, while having a very high probability of leading to equivalent columns, can be relaxed under the right conditions (i.e., depending on the complexity of the solute set, the requirements for absolutely identical vs. similar separations, etc.). Carr et al. suggest that columns with Fs ≤ 16 are ‘very similar’, Fs ≤ 35 are ‘similar’, 35 ≤ Fs ≤ 55 are ‘reasonably different’ and Fs ≥ 55 are ‘rather different’ – leaving the reader to translate the meaning of these characterizations into the selectivity differences one would expect to see between columns. Similarly, we have proposed the statistical thresholds of r2 > 0.97, slope = 1.0 ± 0.3, intercept = 0.00 ± 0.03, and H/H < 1.1 for correlations of HSM parameters as identifying columns that one would expect to provide quite similar chromatographic behavior (perhaps equivalent, perhaps not). Increasing deviations from these values suggest increasing differences in selectivities, again with the provision that the solutes are exploring all of the potential interactions. 6.3. Relationship between the SSC and selectivity triangles Zhang and Carr used the HSM parameters to establish the apices of triangles to make comparisons between columns [1]. Each phase is represented by a dot in the triangle, the location being based on the specific values of the HSM parameters for a particular column.

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In this way, columns that have similar HSM characteristics appear close to one another in the triangle, and those that are chemically distinct from one another appear further apart on one or more axes of the set of four triangles. One advantage of this approach is that the axes themselves reflect chemical information in that they relate to the actual HSM values, albeit in a somewhat complicated manner due to normalization processes that are required to plot the data. This makes interpreting the exact location of the dots difficult in terms of absolute column characteristics. Nevertheless, the axes of the triangle reflect chemical information as opposed to the axes of the cube that only contain statistics related to the correlation of HSM parameters between two columns. Thus, in the cube, all information about the magnitudes of the HSM parameters is lost. The user has to refer to the actual HSM values after using the SSC to identify columns of interest. Related to this issue, as the authors point out in their paper, the triangles make it clear that there is a great deal of ‘chemical space’ that is not explored by current RPLC columns, meaning that researchers have much room to develop novel rather than redundant phases. This is not evident from SSC or Fs analyses. One disadvantage to the triangle approach is that only three parameters can be considered at a time (in some sense, four, because the parameters are divided by H). This means that for the five-parameter HSM model, four different triangles are necessary to represent all the data. In contrast, the SSC considers all the parameters simultaneously in the regressions that dictate where points appear in the cube. Furthermore, two columns for which four out of the five parameters are the same will appear as offering similar selectivities on three of the graphs, but may appear as being different on the fourth graph. Thus, different triangles can lead to different conclusions regarding the similarity or difference between two columns. In some instances, only considering three parameters could be valuable. For example, for solute sets that do not contain ionic species, an analysis of selectivity differences that omits the C-parameter of the HSM might be more appropriate than one which considers it. In that case, one would consider the triangle created without the C-parameter. An analysis without the C-parameter can also be done with the SSC simply by feeding it a data set without the C-values. More generally, if more complex models of retention or selectivity that contain more parameters are introduced, the SSC would be able to accommodate them as there is no limit to the number of parameters that can be correlated with one another with the resulting statistics plotted in an SSC. With triangles, however, the number of triangles needed to represent the data set would increase, making it more complicated to analyze all of the different column comparisons. 6.4. Potential drawbacks to the SSC approach We hope that the preceding examples have illustrated the benefits of using the SSC program for column selection in a variety of situations. That is not to suggest, however, that there are not drawbacks with the approach. The SSC program relies on models of column characterization; in this case the HSM. Thus, any disadvantage in the model will carry over to the SSC. This is also true for the Fs metric and selectivity triangles based on the HSM model. For example, as discussed above, the HSM also does not account for changes in the column condition over time. As such, any conclusions drawn from the SSC may be inaccurate when compared to specific columns that have been used in a laboratory for extended periods of time. Another drawback to the SSC, of which most column comparison methods suffer, is information reduction. The position of a point in the SSC can only indicate the energetic relationship of two columns. Any specific chemical information leading to similarities or

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differences is lost in the process of simplifying the comparison. This is also true of the Fs metric. A third drawback, which has been discussed throughout this work, is that the conclusions drawn from the SSC are based on solute sets spanning a large range of interaction abilities. If a separation involves only neutral solutes, columns which differ in their C-terms will do little to improve a separation. However, the SSC can alleviate this problem if the user inputs a more limited data set that does not include the parameter that is not relevant to a given separation. This, however, assumes that the characteristics of the solutes are generally known, which is not always the case. 7. Conclusion We have used the system selectivity cube, a visualization tool for comparing chromatographic systems, to find similarities and differences in RPLC columns characterized by the hydrophobic subtraction model. We have shown, through a series of case studies, that the SSC is capable of efficiently identifying those columns which are similar to one another, and those which should offer different selectivity, both among columns in the same class and across all column classes. Our methodology was juxtaposed with the Fs function of column comparison and selectivity triangles. The single value produced by the Fs function is simpler, but the SSC offers more statistical information related to the two columns being compared. Furthermore, the SSC can distinguish between homo-, homeo-, and heteroenergetic systems, albeit at the cost of not explicitly displaying the chemical characteristics of the systems being compared, which is an advantage of selectivity triangles. Both the HSM column parameters and the SSC program are freely available, and we hope that chromatographers find the approach presented herein useful in method development. Acknowledgements We thank Dr. Lloyd Snyder and the contributors to the HSM for generously sharing data for the columns presented in this work and Professor Peter Carr for his helpful suggestions. Acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research. Support was also provided by the Drake University Science Collaborative Institute. Support for the experimental work was provided by a Camille and Henry Dreyfus Faculty Start-Up Award. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.chroma. 2012.05.049. References [1] Y. Zhang, P.W. Carr, J. Chromatogr. A 1216 (2009) 6685. [2] M.R. Euerby, P. Petersson, J. Chromatogr. A 994 (2003) 13. [3] D.H. Marchand, K. Croes, J.W. Dolan, L.R. Snyder, J. Chromatogr. A 1062 (2005) 57. [4] D.H. Marchand, K. Croes, J.W. Dolan, L.R. Snyder, R.A. Henry, K.M.R. Kallury, S. Waite, P.W. Carr, J. Chromatogr. A 1062 (2005) 65. [5] N.S. Wilson, J.J. Gilroy, J.W. Dolan, L.R. Snyder, J. Chromatogr. A 1026 (2004) 91. [6] J.J. Gilroy, J.W. Dolan, P.W. Carr, L.R. Snyder, J. Chromatogr. A 1026 (2004) 77. [7] U.D. Neue, K. VanTran, P.C. Iraneta, B.A. Alden, J. Sep. Sci. 26 (2003) 174. [8] A.R. Johnson, M.F. Vitha, T. Urness, T. Marrinan, Anal. Chem. 82 (2010) 6251. [9] T. Urness, T. Marrinan, A.R. Johnson, M.F. Vitha, Visualization and Data Analysis 2011: Proceedings of SPIE-IS&T Electronic Imaging, vol. 7868-11, 2011. [10] N.S. Wilson, M.D. Nelson, J.W. Dolan, L.R. Snyder, R.G. Wolcott, P.W. Carr, J. Chromatogr. A 961 (2002) 171. [11] N.S. Wilson, M.D. Nelson, J.W. Dolan, L.R. Snyder, P.W. Carr, J. Chromatogr. A 961 (2002) 195. [12] N.S. Wilson, J.W. Dolan, L.R. Snyder, P.W. Carr, L.C. Sander, J. Chromatogr. A 961 (2002) 217.

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