G

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ARTICLE IN PRESS Model

HROMA-353252; No. of Pages 21

Journal of Chromatography A, xxx (2012) xxx– xxx

Contents lists available at SciVerse ScienceDirect

Journal of Chromatography A

jou rn al h om epage: www.elsev ier .com/ locat e/chroma

dentifying orthogonal and similar reversed phase liquid chromatographytationary phases using the system selectivity cube and the hydrophobicubtraction model

ndrew R. Johnsona, Carrie M. Johnsonb, Dwight R. Stollb, Mark F. Vithac,∗

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

r t i c l e i n f o

rticle history:eceived 25 August 2011eceived in revised form 9 May 2012ccepted 14 May 2012vailable online xxx

a b s t r a c t

We have compared over 500 RPLC columns characterized by the hydrophobic subtraction model using thesystem selectivity cube (SSC). We have shown numerous differences in column selectivity even amongcolumns in the same class (e.g., alkyl-silica, cyano, or embedded polar groups). We also illustrate the utilityof our method for selecting alternative columns with different selectivities for problematic separationsand for selecting orthogonal columns for use in two-dimensional separations. The system selectivity cubeoffers a visual way to easily compare many columns simultaneously and select those columns offering

eywords:ystem selectivity cubeydrophobic subtraction modelolumn selectivityeversed phaserthogonal separation

the desired selectivity.© 2012 Elsevier B.V. All rights reserved.

nyder–Dolan model

. Introduction

The abundance of commercially available columns for use ineversed phase liquid chromatography (RPLC) makes a wide rangef selectivities available, but it can also make column selection

daunting task. In selecting a replacement column with simi-ar selectivity, columns with seemingly identical characteristicse.g., silica type, chain length, carbon load, end-capping, pore size,tc.) often produce significantly different separations. Given allf the options, it is also difficult to systematically select alterna-ive columns for problematic separations and to choose orthogonalolumns for two-dimensional separations. One can fall back onlass designations (e.g., C 18, polar embedded), but these providenly broad brushstrokes and columns within the same class canisplay different selectivities as has been shown in a number oftudies [1–7].

To help facilitate column selection, we have developed the

Please cite this article in press as: A.R. Johnson, et al., J. Chromatogr. A (201

ystem selectivity cube (SSC) [8,9], a software program which,n conjunction with linear models of retention, is capable ofllustrating the chemical similarities and differences between

∗ Corresponding author. Tel.: +1 515 271 2596; fax: +1 515 271 1928.E-mail address: mark.vitha@drake.edu (M.F. Vitha).

021-9673/$ – see front matter © 2012 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.chroma.2012.05.049

chromatographic systems. We view the SSC as a complement tothe other methods of column comparison that have already beendescribed in the literature, which we summarize below. In this arti-cle we use the SSC, combined with the hydrophobic subtractionmodel (HSM) [3–6,10–14], to provide a powerful tool for identifyingsimilar and different RPLC columns.

This work is divided into three main sections. First, the HSM isexplained briefly. Second, the theoretical background of the SSC, aswell as practical details on operating the program, are described.Because these first two topics have already been explained ingreater detail elsewhere [3–6,8–14], this paper ultimately focuseson the third section, which involves a number of case studies com-paring and contrasting RPLC columns using the SSC program.

1.1. Other column comparison methods

There have been a number of proposed schemes for both charac-terizing and comparing RPLC columns. Early comparison methodswere based on retention factors. Horvath et al. measured the reten-tion factors of an identical solute set on two columns and usedthe correlation to determine how similar the two columns were

2), http://dx.doi.org/10.1016/j.chroma.2012.05.049

[15]. As reported by Snyder et al., Neue expanded this scheme bycorrelating the retention factors of an identical solute set on twoseparate columns as well as under different operating conditions(i.e., pH or mobile phase composition) in order to gain a complete

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2 A.R. Johnson et al. / J. Chromatogr. A xxx (2012) xxx– xxx

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

Solute number Solute �′ � ′ ˇ′ ˛′ �′ pKa

1 N,N-dimethylacetamide −1.903 0.001 0.994 −0.012 0.001 −0.28b

2 N,N-diethylacetamide −1.390 0.214 0.369 −0.215 0.0473 Berberine 2.47f

4 Nortriptyline −1.163 −0.018 −0.024 0.289 0.845 9.7e

5 4-Nitrophenol −0.968 0.040 0.009 0.098 −0.021 7.15d

6 Amitriptyline −1.094 0.163 −0.041 0.300 0.817 9.45e

7 5,5-Diphenylhydantoin −0.940 0.026 0.003 0.568 0.007 8.3a

8 Acetophenone −0.744 0.133 0.059 −0.152 −0.0099 Benzonitrile −0.703 0.317 0.003 0.080 −0.030

10 5-Phenylpentanol −0.495 0.136 0.030 0.610 0.01311 Anisole −0.467 0.062 0.006 −0.156 −0.00912 4-n-Butylbenzoic acid −0.266 −0.223 0.013 0.838 0.045 4.36c

13 Toluene −0.205 −0.095 0.011 −0.214 0.00514 Cis-chalcone −0.048 0.821 −0.030 0.466 −0.04515 Ethylbenzene 0 0 0 0 016 Trans-chalcone 0.029 0.918 −0.021 −0.292 −0.01717 Mefenamic acid 0.049 0.333 −0.049 1.123 −0.008 4.2d

a Ref. [31].b Ref. [32].c Ref. [33].

pashwcw

meccmL

l

w(mauvabuAwfiasaas

mhclaci

d Ref. [34].e Ref. [35].f Ref. [36].

icture of similarities between two columns under a range of oper-ting conditions [16,17]. Tanaka et al. developed a specific soluteet to probe particular interactions, such as shape selectivity andydrogen bond ability [18]. Euerby and Petersson expanded on thisork, adding additional probes and analyzing the results via prin-

iple component analysis [2,19,20]. The two preceding methods, asell as others, have been reviewed elsewhere [21,22].

In order to make comparisons more universal, many modernethods use retention models, such as the HSM or linear solvation

nergy relationships (LSERs) [23] in place of retention of a spe-ific solute set. LSERs have been used extensively to characterizehromatography systems, which we define as the combination ofobile phase, stationary phase, and support material of a column.

SERs are of the form:

og k = aA + bB + eE + sS + vV + c (1)

here each term signifies the contribution of solute characteristicsA, B, E, S, V) and the coefficients reflect differences in corresponding

obile and stationary phase characteristics (a, b, e, s, v). Ishihamand Asakawa constructed five-dimensional vectors using the col-mn coefficients (a, b, e, s, and v) and used the angle between twoectors to compare two systems [24]. Abraham and Martins used

similar approach, but made comparisons based on the distanceetween two vectors instead of the angle [25]. Lazaro et al. similarlysed distance between two vectors, but normalized them first [26].nother method of system comparison is the selectivity triangle, inhich either normalized retention factors or retention model coef-cients are plotted on a triangular plot, such that similar systemsre plotted close to one another. Triangle schemes related to linearolvation energy relationship studies of GC stationary phases [27]nd to HSM studies of RPLC systems have been published [1] andre summarized in a review article [28]. We note that the trianglechemes allow for facile, visual comparisons between columns.

Here, we present the use of the HSM and the comparisonethod of Horvath et al., combined with the SSC, to illustrate

ow our approach also offers a simple visualization scheme toompare many systems simultaneously and easily select simi-

Please cite this article in press as: A.R. Johnson, et al., J. Chromatogr. A (201

ar and different columns. While fundamentally related to thebove approaches, the SSC uses a different methodology to makeomparisons between columns. In this way, the SSC approachs complementary to the existing column comparison methods.

We address similarities and differences between the approachestoward 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 let-ters represent column characteristics. All values of the columnparameters are relative to a theoretical, ‘average,’ column in whichH = 1.0 and S, A, B, and C are identically 0.0 [13].

The �′H term quantifies the influence of hydrophobic/lipophilicinteractions on log ˛. Although there is contention over the mecha-nism by which hydrophobic species are retained [29], it is generallyregarded as the dominant influence on retention in reversed phaseliquid chromatography, especially in alkyl-silica columns [10]. The� ′S* term accounts for the influence of steric interactions betweenthe solute and the stationary phase on log (e.g., the resistanceof the stationary phase to penetration by bulky molecules). Theˇ′A term represents the influence of solute hydrogen bond accept-ing ability on log ˛. Non-ionized silanols on the silica surface areassumed to be the primary source of the hydrogen bond donat-ing ability of most columns. The ˛′B term represents the influenceof solute hydrogen bond donating ability on log ˛. Snyder et al.hypothesize that for many columns, especially high purity (typeB) alkyl-silica columns, the hydrogen bond accepting ability of thecolumn is due to sorbed water on the stationary phase [14]. The �′Cterm will be referred to as the cation exchange term throughoutthis work to comply with the history and convention of the HSMmodel. However, it appears this term also includes contributionsfrom ionic interactions not due to cation exchange. While not fullyunderstood, the interactions likely result from negatively and pos-itively charged sites present simultaneously in many columns atlow pH [30]. The solutes used to measure the HSM coefficients arelisted in Table 1 along with their solute parameters and pKa values.For a full discussion of how the HSM coefficients are determined for

2), http://dx.doi.org/10.1016/j.chroma.2012.05.049

a column, the reader is directed to a series of articles and reviewsby the authors of the HSM [3–6,10–14].

The column parameters are designed to be independentof the separation conditions. This means that mobile phase

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ARTICLEHROMA-353252; No. of Pages 21

A.R. Johnson et al. / J. Chr

omposition, pH, and temperature should not alter the HSM col-mn parameters [13]. The one exception is the C term. Becausehe C term is related to ionized silanols, it is pH dependent. Val-es of C for a column are generally reported at both pH 2.8 and.0 to cover a range of useful operating conditions and can be esti-ated for other pHs on the United States Pharmacopeia website

http://www.usp.org/USPNF/columns.html).

.1. The Fs metric

In order to select equivalent columns using the HSM, or to selectn alternative column with different selectivity in order to improve

problematic separation, a single metric has been proposed, Fs,iven by [13]

s =√

(12.5(H2 − H1))2 + (100(S2 − S1))2 + (30(A2 − A1))2 + (143(

s is the Euclidean distance in five-dimensional space between thewo systems. The weighting factors (12.5, 100, etc.) are included toormalize the varying contributions of the column parameters for

typical solute set [13]. It has been proposed that any two columnsith Fs ≤ 3.0 will behave ‘similarly,’ that is, they will provide essen-

ially equivalent separations [37]. For selecting different columns,wo columns yielding Fs > 65 if ionic solutes are present or Fs > 100f no ionic solutes are present, would be chosen [38]. Comparisonsielding 3 < Fs < 65 may yield similar or different results dependingn the solute set and other operating conditions.

. The system selectivity cube

.1. �–� plots

Horvath and co-workers developed a method for comparinghe retention characteristics of two chromatographic systems [15].heir method is based on plotting the logarithm of retention factors,, for a varied solute set on two different chromatography systemsgainst one another. Such a plot is called a �–� plot. Three dif-erent energetic relationships exist for any two systems based onhe correlation of the retention factors. When the retention factorsre well correlated (Horvath et al. specified r > 0.95), the two sys-ems are said to have a homeoenergetic relationship. This meanshat the two systems separate the solutes based on a similar blendf retention mechanisms. These two systems may provide differ-nt retention values, but there is little chance of differential bandpacing or elution order differences. If large changes to selectivityre required, a homeoenergetic system would be unlikely to pro-ide them. The special case in which the retention factors of thewo systems are well correlated (r > 0.95) and the slope of that cor-elation is equal to 1.0 (at the 95% confidence interval) is called aomoenergetic relationship (the intercept is inconsequential to thenterpretation of energy relationships). Systems with this relation-hip operate on an identical blend of retention energetics. Theseystems would provide nearly identical separations. They may dif-er slightly because the magnitudes of the retention factors for

given solute may differ, but the relative position of all solutesould remain identical on the two systems. The final relationship,

alled a heteroenergetic relationship, is present when the retentionactors are poorly correlated. It implies that the energetics gov-rning retention on the two systems are different. Switching fromne column to the other would be more likely to produce changes

Please cite this article in press as: A.R. Johnson, et al., J. Chromatogr. A (201

n selectivity for a problematic separation than would switchingetween homo- or homeoenergetic columns. Identifying heteroen-rgetic systems is also useful when selecting orthogonal columnsor use in two dimensional separations.

PRESSgr. A xxx (2012) xxx– xxx 3

B1))2 + (83(C2 − C1))2 (3)

3.2. Comparisons based on HSM parameters

We and others [1,8,15–17,24–26,28] have shown that instead ofusing retention factors for identical solute sets to compare systemselectivity, it is possible to determine the same energetic relation-ships of Horvath et al. using retention models such as LSERs. Herewe expand our approach to include the HSM.

For two columns, designated 1 and 2, we can write:

log ˛1 = �′H1 − � ′S∗1 + ˇ′A1 + ˛′B1 + �′C1 and, (4)

log ˛2 = �′H2 − � ′S∗2 + ˇ′A2 + ˛′B2 + �′C2 (5)

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

log k1

H1= log k2

H2− � ′

(S∗

1

H1− S∗

2

H2

)+ ˇ′

(A1

H1− A2

H2

)+ ˛′

(B1

H1− B2

H2

)

+ �′(

C1

H1− C2

H2

)+ log keb1

H1− log keb2

H2(6)

When the two systems are related such that

S∗1

H1= S∗

2H2

&A1

H1= A2

H2&

B1

H1= B2

H2&

C1

H1= C2

H2(7)

Eq. (6) simplifies to

log k1 = H1

H2log k2 + log keb1 − H1

H2log keb2 = H1

H2log k2 − constant (8)

where retention on system 1 is linearly related to retention on sys-tem 2 by a slope equal to H1/H2. The necessity of this relationshipand its consequences when the conditions in (7) are met has beendiscussed by Zhao and Carr [39] and Zhang and Carr [1].

In Eq. (8), the retention of ethylbenzene would be a constantvalue for both systems (although not necessarily the same value),and would therefore only modify the intercept. There are no soluteparameters present in Eq. (8), indicating that the �–� plot would beperfectly correlated and the two columns would exhibit a home-oenergetic relationship. The more specific case of a homoenergeticrelationship results when the ratio H1/H2 is equal to 1.0, such thatthe hydrophobicities of the two columns are equal. A heteroener-getic relationship exists when the equalities in (7) are not present.The choice of selecting the hydrophobicity, H, as the denominatorfor all ratios complies with the convention of selecting the domi-nant contributor to retention [1,39–43].

3.3. Visualization of system relationships – the system selectivitycube

The previous section makes it clear that it is necessary to checkif the relationships in (7) are satisfied by two columns in order todetermine their energetic relationship. This may be done graphi-cally 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 canbe characterized by three statistics; slope, intercept, and squareof 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 indicatesa heteroenergetic relationship. A homoenergetic relationship is a

2), http://dx.doi.org/10.1016/j.chroma.2012.05.049

special case where a homeoenergetic relationship exists and thehydrophobicities of the two columns are equal (i.e., H1/H2 = 1.0).

In order to visualize these regression statistics along with theH1/H2-ratios in a manner that makes it easy to compare many

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4 A.R. Johnson et al. / J. Chromato

Fig. 1. (A) A thermal heat map. Ratios of 1.00 are colored black, while subsequentlyhigher values get increasingly lighter. The colors are scaled to each data set such thatthe greatest H/H ratio is always white, and a ratio of 1.00 is always black. The colorsof the remaining points are interpolated between the two extremes. (B) An examplect

suscdtbittotcgpti(

iopvcawwob

atstcpScswocucepcot

tific), Hypersil Prism C18 RP (100 A, Thermo Scientific), Zorbax

olor scale legend. (For interpretation of the references to color in this figure legend,he reader is referred to the web version of the article.)

ystems simultaneously, we use the slope, intercept, and r2 val-es as axes to create a three dimensional plot called the systemelectivity cube (SSC) [8]. The correlation between two differenthromatography columns thus produces a single point in threeimensional space within the cube. The ideal homeoenergetic rela-ionship (slope = 1.0, intercept = 0.0, r2 = 1.0) is depicted on the SSCy a large light green glyph (a graphical object representing a point

n three dimensional space). [Note: Here, the word ‘ideal’ describeshe 1,0,1 point (i.e., perfect correlation) – it is not a comment abouthe ideality of the columns. In fact, in the case of trying to findrthogonal columns, having two columns with HSM parametershat are perfectly correlated would be anything but ideal.] Theloser a comparison point is plotted to this ideally homeoenergeticlyph, the more similar the two systems are. The further a point islotted from the homeoenergetic point, the more heteroenergetiche two compared systems are. In order to eliminate redundantnformation, the SSC shows only one comparison of two systemsi.e., the comparison of system 1 to 2, but not 2 to 1).

As noted above, a homoenergetic relationship is a special casenvolving both a homeoenergetic relationship and H1/H2 = 1.0. Inrder to display this information on the SSC, we use color map-ing. The color mapping replaces the ‘spikes’ we used in a previousersion of the SSC [8] as a simpler and more computationally effi-ient mode of display [9]. A heated color map, as shown in Fig. 1a ispplied across the range of H/H ratios, where 1.00 is colored black,ith subsequently higher values increasing in brightness towardhite. Therefore, a point in close proximity to the ideally home-

energetic point and colored black indicates that the two columnseing compared are homoenergetic.

The SSC program is highly interactive. The cube can be rotatednd zoomed in to view comparisons at any angle. One difficultyhat many comparison methods face is overplotting. That is, witho many columns available, it is difficult to look at them all simul-aneously. In fact, as we noted earlier, over 500 columns have beenharacterized by the HSM, allowing for over 125,000 possible com-arisons – clearly far too many to visualize and comprehend. TheSC provides tools for culling the data in order to display onlyolumns of interest. For example, a reference column can be cho-en in the user interface and only comparisons against that columnould be plotted. The use of this feature is demonstrated through-

ut the article. It is useful in method development for selecting aolumn which is similar or different in relation to the current col-mn that an analyst is using. The SSC can also compare systemsategorized by other retention models, such as linear solvationnergy relationships (LSERs). The SSC program will perform a com-arison regardless of the number of input parameters for each

Please cite this article in press as: A.R. Johnson, et al., J. Chromatogr. A (201

olumn. This feature may be useful to customize the comparisonf columns to a particular separation. For example, in a separa-ion of neutral solutes, the C term of the column is unlikely to

PRESSgr. A xxx (2012) xxx– xxx

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 characteristicsof the columns. The source code for the SSC is freely avail-able online at http://artsci.drake.edu/urness/download/ssc.htmland the authors encourage anyone wishing to use or modifythe program to do so. The HSM data are freely available athttp://www.usp.org/USPNF/columns.html [44].

The SSC is capable of displaying additional information abouta column with the ‘group’ feature. In addition to the HSM columnparameters, the user may also input a text field describing the col-umn. For example, if the text column lists the phase chemistry(C18, CN, F, etc.) for each column, the SSC is capable of illustrat-ing which comparisons involve two C18 phases, which involve aC18 compared to a fluorinated column, a cyano to a C18 column,etc. using color. A key for the color map is shown in a separatewindow, as shown in Fig. 1b. By default, the H/H ratio is shown asdescribed above, but through the user interface, the ‘group’ colorcan be shown instead. Other examples of possible ‘group’ assign-ments 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 aMillipore (Billerica, MA) Milli-Q water purification system. Ammo-nium acetate was purchased from Sigma–Aldrich and used asreceived. A 10 mM ammonium acetate buffer with pH of 3.5 wasprepared by first adding 0.77 g of ammonium acetate salt to about800 mL of water. The pH was then adjusted by adding 50% formicacid (Sigma–Aldrich) in water to bring the pH to 3.5. Finally,the volume of the buffer was brought to 1 L. A mobile phaseof 20/80 acetonitrile/buffer (v/v) was prepared online using theeluent mixing capabilities of the instrument following online vac-uum degassing. Solutes used in this study were obtained fromSigma–Aldrich: amphetamine, salicylic acid, trans-cinnamic acid,phenypropanolamine, hippuric acid, caffeine, 4-iodophenol, 2,4-dichlorophenoxyacetic acid, phenobarbital, lidocaine, bupropion,amitriptyline, diazepam, and oxazepam were obtained. A stocksolution of each solute was prepared in either acetonitrile ormethanol at 10 mg/mL. Following determination of MS/MS detec-tion parameters for each individual solute (see below), a singlemixture of all 14 solutes at 50 �g/mL of each was then preparedin 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 mmi.d., packed with 5 �m particles and generously provided by themanufacturers; particle pore diameters and manufacturers areindicated in parentheses: Discovery C18 (180 A, Sigma–Aldrich),ProntoSIL 200 C18 H (200 A, Bischoff Chromatography), Devel-osil C30-UG-5 (140 A, Nomura Chemical Co.), Zorbax 300SB-C18(300 A, Agilent Technologies), Alltima C18 (100 A, Alltech Asso-ciates), Hypersil BDS C18 (130 A, Thermo Scientific), ChromegabondWR C18 (120 A, ES Industries), Genesis C18 300A (300 A, JonesChromatography), Hypersil Biobasic C18 (300 A, Thermo Scien-

2), http://dx.doi.org/10.1016/j.chroma.2012.05.049

Bonus-RP (80 A, Agilent Technologies), Hypurity Advance (190 A,Thermo Scientific), Polaris C8-A (180 A, Agilent Technologies),Symmetry C18 (100 A, Waters Corporation), XTerra RP8 (125 A,

ARTICLE IN PRESSG Model

CHROMA-353252; No. of Pages 21

A.R. Johnson et al. / J. Chromatogr. A xxx (2012) xxx– xxx 5

Table 2HSM coefficients and Fs values for columns discussed in this article.

Name H S* A B C (2.8) C (7.0) Retention Type Source Phase Fs (pH 2.8)

Type-B alkyl-silica columnsDiscovery C18 0.984 0.027 −0.128 0.004 0.176 0.153 4.815 B Supelco C18 ReferenceProntoSIL 200 C18 H 0.955 −0.001 −0.121 0.016 0.163 0.218 4.774 B Bischoff C18 3.56Develosil C30-UG-5 0.976 −0.036 −0.196 0.011 0.158 0.176 7.792 B Nomura C30 6.87Zorbax StableBond 300 C18 0.905 −0.050 0.045 0.043 0.254 0.701 2.210 B Agilent C18 12.6Alltima C18 0.993 −0.014 0.035 −0.013 0.092 0.391 11.532 B Grace-Alltech C18 9.75Similar type-A and -B columnsHypersil BDS C18 0.993 0.016 −0.095 −0.009 0.337 0.281 5.564 A Thermo/Hypersil C18 ReferenceChromegabond WR C18 0.979 0.026 −0.159 −0.003 0.320 0.283 5.391 B ES Industries C18 2.74Genesis C18 300A 0.974 0.005 −0.086 0.013 0.266 0.270 3.489 B Grace-Jones C18 6.76Hypersil Bio Basic-18 0.974 0.025 −0.100 0.007 0.253 0.217 3.249 B Thermo/Hypersil C18 7.43EPG columnsHypersil Prism C18 RP 0.645 0.089 −0.459 0.301 −2.817 −0.716 4.819 EP Thermo/Hypersil EP ReferenceZorbax Bonus RP 0.654 0.107 −1.046 0.373 −2.971 −1.103 4.457 EP Agilent EP 24.1Hypurity Advance 0.412 −0.056 −0.095 0.249 −1.332 0.785 1.622 EP Thermo/Hypersil EP 124Polaris C8-A 0.601 −0.007 −0.609 0.104 −0.074 0.208 2.160 EP Varian C8 229Cyanopropyl columnsDiscovery CN 0.397 −0.11 −0.615 −0.002 −0.035 0.513 0.634 CN Supelco CN ReferenceZorbax SB-CN 0.502 −0.108 −0.224 0.042 −0.146 1.047 1.729 CN Agilent CN 16.2Luna CN 0.452 −0.112 −0.323 −0.024 0.439 1.321 1.271 CN Phenomenex CN 40.4Inertsil CN-3 0.369 0.049 −0.808 0.083 −2.607 −1.297 1.122 CN GL Science CN 214Orthogonal columnsSymmetry C18 1.052 0.063 0.018 −0.021 −0.302 0.123 9.815 B Waters C18 ReferenceXterra C8 RP 0.657 −0.049 −0.604 0.099 −0.187 −0.198 3.062 EP Waters EP 29.7Thermo CN 0.404 −0.111 −0.709 −0.009 −0.029 0.491 0.817 CN Thermo/Hypersil CN 36.9

10

89

78

WI

4

saaat3a(M

At1dueDcM

actrDt

5

a

Discovery HS F5 0.652 −0.125 −0.305 0.016 0.8ZirChrom-EZ 1.040 0.117 −0.999 −0.001 2.0Bondclone C18 0.824 −0.056 −0.125 0.044 0.0

aters Corporation), ZirChrom-EZ (300 A, ZirChrom Separations,nc.), Bondclone C18 (150 A, Phenomenex).

.3. Instrumentation and chromatographic conditions

Chromatographic data unique to this article (as opposed to thoseimulated from data that were used to construct the HSM andre thus detailed in the references provided) were obtained using

system composed of a quaternary pump (Model HP1050), anutosampler (Model HP1050), and a triple quadrupole mass spec-rometer equipped with an electrospray ionization source (Model20), all from Agilent Technologies (Palo Alto, CA). The pump andutosampler were controlled using Agilent Chemstation softwarev. A.08.03), and the mass spectrometer was controlled using Varian

S Workstation (v. 6.9.3).Columns were equilibrated for about one hour in the 20/80

CN/buffer mobile phase prepared as described above prior tohe separation of the 14 component mixture. The flow rate was.0 mL/min. and the column temperature was 35 ◦C. Solutes wereetected by the mass spectrometer operated in MS/MS mode andsing either positive (5000 V needle voltage) or negative (−4500 V)lectrospray ionization. Argon was used as the CID gas at 2 mTorr.etailed information including parent and fragment masses, andapillary and collision cell voltages are provided as Supplementaryaterial.Because of the excessively long analysis times (up to four hours)

ssociated with this diverse set of solutes and columns, mostolumns were run just once, but three columns were run two orhree times to evaluate the reproducibility of the data. The medianelative standard deviation of retention factors for the Alltima C18,iscovery C18, and Hypersil BDS C18 were 3.2, 3.5, and 1.8% respec-

ively.

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. Results – column comparisons using the SSC

The HSM has been used to characterize over 500 commerciallyvailable RPLC columns, covering a variety of manufacturers and

1.185 4.048 F Supelco F 95.02.089 1.147 Other ZirChrom C18 2000.347 4.488 B Phenomenex C18 35.3

column types, allowing for a very large number of possible com-parisons. In the analyses presented in this section, we have eitherstudied subsections of the data (e.g., just cyano phases comparedto each other), or we have used the ability to select a referencecolumn against which other, specifically selected columns are com-pared. We have chosen to use the same shorthand names for eachcolumn that were used in the work of Snyder et al. in order to facili-tate comparisons between that work and the work we present here.However, the shorthand names are not fully descriptive and readersare 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 impu-rities, which reduces the activity of acidic and ionized silanols onthe silica surface, thus reducing unanticipated interactions, bandbroadening, and peak tailing as well as increasing reproducibility[45]. In this section, we compare type-B silica columns derivatizedwith alkyl functionalities. Carr et al. [46] identified the DiscoveryC18 column as representative of the ‘average’ C18 column, thus, weuse it as a ‘reference’ column to which we compare other type-Balkyl silica phases. Furthermore, while the HSM has been used tocharacterize over 350 alkyl phases, we have selected a sample ofthese columns to illustrate comparisons within this class.

The SSC generated by comparing the Discovery C18 column tothe four other type-B alkyl-silica columns listed in Table 2 is shownin Fig. 2. The Fs values calculated according to Eq. (3) are also shownin Table 2. In the SSC, two of the comparisons fall close to the home-oenergetic green marker on the SSC (specific threshold values usedto classify columns as homo-, homeo-, or heteroenergetic based onthe statistics generated by the correlations between column param-eter ratios are discussed later in Section 6.3). The two columns inthis region are the Prontosil 200 C18-H and the Develosil C30 UG-

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5. The glyphs in Fig. 2 are colored according to the H/H ratio, witha ratio equal to 1.00 colored black. The comparison of the Discov-ery 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. 2. The SSC of several type-B alkyl silica columns at pH 2.8. Each point representsthe comparison of the Discovery C18 column to the labeled column. The H/H ratiofs

tcmchibtwcsti

Fr

or relevant column comparisons is shown under the column label. Note the r2 axispans from 0.00 on the left to 1.00 on the right and is not labeled for clarity.

hat, according to the designation system of Horvath et al., the twoolumns are homoenergetic. However, the more rigorous require-ent of Fs ≤ 3 does not qualify them as ‘equivalent’ columns. The

omparison of the Discovery C18 and Develosil C30 UG-5 columnsas an r2 of 0.95, slope of 0.829, intercept of 0.3, and hydrophobic-

ty ratio of 1.008. Given these statistics, these two columns woulde termed homeoenergetic according to Horvath et al. Accordingo the more rigorous demands of the Fs metric, the two columnsould not be identified as equivalent. Comparisons of the column

haracteristics can also be made using a radar plot [18,47–51] as

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hown in Fig. 3. When the ratios of S, A, B, and C to the H parame-er are plotted together, the columns appear to be similar but notdentical.

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

Fig. 4. A radar plot illustrating the similarities and differences in individual HSMratios for three type-B alkyl silica columns at pH 2.8.

The comparisons of the Alltima C18 column and the ZorbaxStableBond 300 C18 columns to the Discovery C18 column resultin glyphs in the heteroenergetic region of the SSC according tothe Horvath designation, indicating that the energetics governingretention on these two columns are different from that of the Dis-covery C18 column. This is consistent with the larger Fs values inTable 2. The radar plot in Fig. 4 shows that the major differencebetween the Alltima C18 and the Discovery C18 is the acidity ratio(A/H) of the two columns. The Zorbax StableBond 300 C18 col-umn exhibits differences in the acidity (A/H), basicity (B/H), cationexchange (C/H), and steric interaction (S*/H) ratios.

The practical differences in the performance of these fivecolumns can be illustrated with simulated chromatograms asshown in Fig. 5. Retention factors of the 17 solutes used to char-acterize the columns were generously provided by the developersof the HSM [3–6,10–14]. The retention factors were used to cre-ate simulated chromatograms assuming Gaussian peak shapes forall solutes and an arbitrarily selected dead time of 74 seconds. Theretention of 16 of the 17 solutes was only measured at pH 2.8. Assuch, our column comparisons will largely focus on this pH so thatwe may illustrate the comparisons with simulated chromatograms.It is important to note that we have no information regarding bandbroadening or peak tailing, and any such effects in any of the sim-ulated chromatograms are only included to add some realism tothe figures. Also, using the same solutes used to characterize thecolumns by the HSM for these chromatograms is not the most rig-orous test of the ability of the SSC to identify similar and differentcolumns. A comparison of these columns using an independentsolute set is discussed below.

Again regarding the Discovery C18 as the reference column, itis clear in Fig. 5B that the Prontosil column, which appeared to behomoenergetic on the SSC according to the Horvath requirements,produces generally comparable separation of the solutes. There areno differences in elution order and very little difference in bandspacing except 5-phenylpentanol (10) and anisole (11) and ethyl-benzene (15) and trans-4-chalcone (16). The Develosil C30 UG-5column exhibited a homeoenergetic relationship to the DiscoveryC18 column. It produces a similar but not equivalent separation

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(Fig. 5C), which is consistent with an Fs value of 6.87. The DevelosilC30 column does not provide a substantial change in the order ofelution, 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) DiscoveryC18, (B) Prontosil 200 C18-H, (C) Develosil C30 UG-5, (D) Zorbax StableBond 300 A C18, (E) Alltima C18.

IN PRESSG Model

C

8 omatogr. A xxx (2012) xxx– xxx

scfetaorLeEso(epsdco

tshntac(t

csstcaciadssco

cfi

5

s–ctdct

b2tbp

Fig. 6. A SSC showing the comparison of several type-B alkyl silica columns to the

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The Zorbax StableBond 300 C18 column, which the SSC indicatedhould have a heteroenergetic relationship with the Discovery C18olumn under the Horvath classification scheme, does exhibit dif-erent selectivity compared to the Discovery phase (Fig. 5D). Forxample, several elution order changes can be noted on thesewo phases. Specifically, nortriptyline (4) and p-nitrophenol (5)nd amitriptyline (6) and 5,5-diphenylhydantoin (7) switch elutionrder. Anisole (11) and 5-phenylpentanol (10), which are partiallyesolved on the Discovery phase, coelute on the Zorbax phase.astly, significant changes in selectivity are seen with compoundsthylbenzene (15), trans-chalcone (16), and mefenamic acid (17).thylbenzene (15) and trans-chalcone (16) coelute and are welleparated from mefenamic acid (17) on the Discovery phase, whilen the Zorbax phase, trans-chalcone (16) and mefenamic acid17) coelute and are well separated from ethylbenzene (15). Thus,ven though both columns are nominally type-B C18 phases, theyrovide different selectivities for the solute set employed here, con-istent with the designation of ‘heteroenergetic’ using Horvath’sesignations and an Fs > 3. However, the two columns would not beategorized as ‘orthogonal’ because they do not meet the criterionf Fs > 65.

The Alltima C18 column also appeared to be heteroenergetic onhe SSC, but the chromatogram shown in Fig. 5E shows a similareparation to the Discovery C18 column. In fact, only two solutesave changed their relative position, amitriptyline (6) and mefe-amic acid (17). Out of the set of 17 solutes used to characterizehese columns, these two solutes have the lowest ˇ′ values, −0.041nd −0.049, respectively. Because the difference between these twoolumns, as shown in Fig. 4, is due largely to the column acidity ratioA/H) it makes sense that those solutes would change position inhe separation.

This comparison also illustrates a fundamental difficulty in anyolumn comparison technique. Column characterization methodsuch as the HSM or LSERs are derived assuming a varied soluteet. For an individual separation, differences in selectivity betweenwo columns will always depend on the solute set. In the aboveomparison of the Discovery C18 and Alltima C18 columns, the A/Hnd C/H ratios are responsible for the difference between the twoolumns as shown in Figs. 3 and 4. However, because the solute setn Fig. 5 does not contain many ionized species, and most columnsre of similar basicity (see Table 2), the simulated chromatogramso not show the differential separation predicted by the SSC. Theample dimensionality, or range of interaction ability of the soluteet, must be complimentary to a chemical difference in any twoolumns for those two columns to provide differential separationf that solute set [52].

An SSC using the C value at pH 7.0 instead of pH 2.8 for the sameolumns analyzed in Fig. 3 is shown in Fig. 6. The conclusions drawnrom this SSC are essentially identical as above despite the changen pH.

.1.1. Independent solute set analysisTo assess the predictions based on the SSC and Fs values pre-

ented above, we have examined a solute set of 14 compounds selected to include acids, bases, and pharmaceutically relevantompounds – that is independent of the solutes used to measurehe HSM parameters (see Section 4). To examine similarities andifferences in selectivity, in Fig. 7 we plot log k on the referenceolumn (Discovery C18) vs. log k on the other columns discussed inhis section above.

It can be seen in Fig. 7A that in general, there is strong correlationetween retention on the Discovery C18 column and the ProntoSIL

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00 C18 H, consistent with the positioning of this comparison inhe SSC and their Fs value. There are some differences in selectivity,ut no elution order changes, between the two columns. For exam-le, the selectivity of Discovery C18 for salicyclic acid and lidocaine

Discovery C18 column at pH 7.0. The H/H ratio for relevant column comparisons isshown under the column label. Note the r2 axis spans from 0.00 on the left to 1.00on the right and is not labeled for clarity.

is 1.07 whereas on ProntoSIL the selectivity is 1.28. Similarly, theselectivity of Discovery C18 between caffeine and amphetamineis 1.02 whereas on Prontosil it is 1.06. Such differences may notbe acceptable if searching for identical replacement columns, butclearly, peaks that are overlapping or nearly so on one phase willlikely be so on the other. An analysis of the Develosil C30 columncompared to the Discovery column (Fig. 7C) yields essentially iden-tical results to that of the ProntoSIL comparison to Discovery (withthe exception that caffeine elutes slightly before amphetamine onthe Discovery phase and slightly after amphetamine on the Pron-toSIL phase, but by less than ten seconds in both cases).

As predicted by the SSC and Fs metric, the correlation betweenretention on the Discovery column and on the Zorbax SB 300A C18column is poor, as seen in Fig. 7B. For example, hippuric acid elutesearly on the Discovery column but is much more retained on theZorbax column. Furthermore, buproprion and trans-cinnamic acidelute before phenobarbital on the Zorbax column. On the Discoverycolumn, however, buproprion and trans-cinnamic acid are betterseparated and elute after phenobarbital.

Lastly, even though the SSC predicts that the Discovery C18 andAlltima C18 columns should yield heteroenergetic retention, and Fs

for these columns is 9.75, the retention of the solutes is generallywell correlated (Fig. 7D). Some subtle differences can be observed,however. For example, while caffeine and amphetamine nearlyco-elute on both phases, their elution order reverses on the twocolumns. Lidocaine and salicylic acid also switch elution order onthe two phases, and 2,4-dichlorophenoxyacetic and trans-cinnamicacid are better separated on the Discovery phase than on the Alltimaphase.

5.2. Type A compared to type B columns

Older, type-A silica columns often have more metal impuritiesin the silica, as well as less ligand coverage than newer, type-Bcolumns [6]. These packing properties may lead to undesirable peak

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shapes and faster column degeneration. As such, it may be bene-ficial to switch from a type-A column to a newer type-B column.However, because of the high variability in interaction abilities oftype-A columns, it is difficult to find type-B silica columns that

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F lute seC ons as

acfiaswlth(HrbpTc

scabituthiictt

tt

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

ig. 7. Comparison of selectivity on alkylsilica phases. Log k for the independent so30 UG-5, Alltima C18, and Zorbax StableBond 300 A C18. Chromatographic conditi

re equivalent to type-A columns. In a study of 43 type A silicaolumns and 87 type B columns, Gilroy et al. were only able tond one comparison which provided adequate similarity between

type-A and type-B column using the Fs metric [6]. The compari-on of the Hypersil BDS C18 column, a type-A alkyl silica column,ith the Chromegabond WR C18 was found to have a Fs value

ess than three, indicating equivalent selectivity. Using the SSC,wo other type-B columns were also found to have at least aomeoenergetic relationship with the Hypersil BDS C18 columnagain using the Horvath classification); the Genesis C18 300 A andypersil BioBasic-18 columns. Both exhibit high correlations (all

2 > 0.98) and H-ratios of 1.02, suggesting not just homeoenergetic,ut homoenergetic relationships. These columns, along with HSMarameters and Fs values for their comparisons, are listed in Table 2.he SSC of these three columns compared to the Hypersil BDS C18olumn at pH 2.8 is shown in Fig. 8.

We note here that a reviewer indicated that while the Hyper-il BDS column is not classified as type-B, it is not truly a type-Aolumn, either, due to pre-treatment of the silica to remove met-ls. Furthermore, the reviewer suggested that the BioBasic phase,eing from the same manufacturer, may be made with the same sil-

ca as the Hypersil BDS column. In general, the reviewer also notedhat the columns used in this section generally fall near the cut-offsed in the HSM to differentiate type-A phases (C(2.8) > 0.3) fromype-B phases (≤0.3). The columns considered in this section allave 0.25 < C(2.8) < 0.34. That these inter-type column similarities

dentified within the SSC can be rationalized based on manufactur-ng processes is a testament to the ability of the SSC to compareolumns over many phase types that might otherwise be thoughto be different because of the labels assigned to them (e.g., type-A,

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ype-B, etc.).Simulated chromatograms for the four columns considered in

his section are shown in Fig. 9. While retention is decreased onhe Genesis (Fig. 9C) and BioBasic columns (Fig. 9D), the elution

t on the reference Discovery C18 phase vs. log k on ProntoSIL 200 C18-H, Develosil described in Section 4.

order and band spacing is similar, but not equivalent, on all four ofthese columns. For example, some peaks that are resolved on the

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Fig. 8. The SSC of several type-B columns to the type-A column; Hypersil BDS C18 atpH 2.8. The H/H ratio for relevant column comparisons is shown under the columnlabel. Note the r2 axis spans from 0.00 on the left to 1.00 on the right and is notlabeled for clarity.

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F ype-AC

aWspm

ig. 9. Simulated chromatograms illustrating homeoenergetic columns among thromegabond WR C18, (C) Genesis 300 A C18, (D) Hypersil BioBasic-18.

re resolved on the Genesis column but not on the BioBasic column.

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hile these columns are not strictly equivalent for this particularolute set, despite satisfying the criteria for homoenergetics, theyrovide good leads for replacement columns if slight changes inobile phase composition can achieve the desired separation.

and type-B alkyl silica columns at pH 2.8. Columns: (A) Hypersil BDS C18, (B)

As we did with the alkylsilica columns, we have analyzed an

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independent set of solutes and here compare them to the resultsobtained with the solutes used to establish the HSM parameters.Plots of log k for the solutes on the reference column (HypersilBDS C18) vs. those on the other columns are shown in Fig. 10.

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F phasev hroma

Amao(tsme

5

utahlcsgucaaunpiP

ct1cg

tionship, providing near equivalent separation. The larger H-ratio,illustrated by the orange color of the comparison of the Hypu-rity Advance and the Hypersil Prism C18 RP columns indicates a

ig. 10. Comparison of selectivity on a type A silica phase compared to type-B silicas. log k on Chromegabond WR C18, Genesis C18 300 A, and Hypersil BioBasic-18. C

s can be seen, the correlations are all quite strong, with someinor variations in selectivity observed. For example, salicylic

cid (log k = 0.21) is better separated from lidocaine (log k = 0.31)n the Hypersil BDS phase than on the Hypersil Biobasic phaselog k = −0.029 and −0.017 for salicylic acid and lidocaine, respec-ively, Fig. 10C). The generally strong correlations across the soluteet seen in these figures are consistent with the simulated chro-atograms shown above that are based on the solutes used to

stablish the HSM.

.3. Embedded or endcapped polar groups

Columns with polar groups either embedded in an alkyl chain orsed to endcap a column often offer unique selectivity comparedo traditional, alkyl-silica columns. However, the variety of link-ge and endcapping groups, including amides, ureas, carbamates,ydroxyls, and ethers, among others, makes predictions of simi-

arities and differences in column selectivity difficult. Even amongolumns with varying polar groups, the SSC is capable of identifyingystems with similar and different overall blends of retention ener-etics. For example, the Hypersil Prism C18 RP column, which has area linkage embedded bonded phase, is compared to three otherolumns listed in Table 2. The first is the Zorbax Bonus RP column,n amide embedded column. The second is the Hypurity Advance,nother amide embedded column. The last is the Polaris C8-A col-mn, which has an embedded “polar group”, the nature of which isot specified. Even with varying bonded phase chemistries, com-arisons of each to the Hypersil Prism C18 RP column are all plotted

n the homeoenergetic region of the SSC (Fig. 11) except for one, theolaris C8-A column.

The color of the glyphs in Fig. 11, as well as the numbers adja-ent to each point for those viewing in black and white, illustrates

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he ratio of the hydrophobicities of the columns where a ratio of.00 is black and increasing ratios are given progressively brighterolors as shown in the color map in Fig. 1A. The dark coloredlyph in the homeoenergetic region is the comparison of the Zorbax

s. Log k’ for the independent solute set on Hypersil BDS C18 (as a reference column)tographic conditions as described in Section 4.

Bonus RP to the reference Hypersil Prism C18 RP column. Becausethe comparison is both in the homeoenergetic region of the SSCand illustrates a hydrophobicity ratio close to 1.00 (actually 1.01),these columns would be expected to have a homoenergetic rela-

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

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F rsil Pre thiour

hlrid(BttiNeto(e

cfNH(

ig. 12. Simulated chromatograms of several EPG type columns at pH 2.8. (A) Hypexclusion of solute 3, berberine, because it eluted prior to the dead time estimator,

omeoenergetic relationship between these columns, suggestingittle to no change in elution order on the Hypurity Advance columnelative to the Hypersil Prism column would occur, but systematicncreases or decreases to solute selectivities may occur. These pre-icted relationships are observed in the simulated chromatogramsFig. 12). Retention on the reference column (A) and the Zorbaxonus RP column (Fig. 12B) is quite similar. While overall reten-ion is greatly reduced on the Hypurity Advance column (Fig. 12C),he elution order is largely unchanged, although many changesn selectivity are observed. Note that N,N-dimethylacetamide (1),,N-diethylacetamide (2), notriptyline (4), and amitriptyline (6) alllute earliest in (A), (B), and (C). 5,5-Diphenylhydantoin (7), ace-ophenone (8), and benzonitrile (9) elute next (but in differentrders), followed closely by 4-nitrophenol (5), 5-phenylpentanol10), and anisole (11), and the remaining solutes follow identicallution order.

The position of the Polaris C8-A column comparison indi-ates a heteroenergetic relationship. This is exemplified by the

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act that nortriptyline (4) and amitriptyline (6) elute before,N-dimethylacetamide (1) and N,N-diethylacetamide (2) on theypersil Prism C18 RP (Fig. 12A) but after them on the Polaris C8-A

Fig. 12D). Additionally, 5-phenylpentanol (10) and anisole (11) are

ism C18 RP, (B) Zorbax Bonus RP, (C) Hypurity Advance, (D) Polaris C8-A. Note theea on many of the EPG type columns.

resolved on the Hypersil Prism C18 RP but coelute on the PolarisC8-A. The elution of ethylbenzene (15) and cis-chalcone (14) rela-tive to trans-chalcone (16) and n-butylbenzoic acid (12) also exhibitelution order changes. The primary reason for the poor correlationof the HSM parameters, and thus the heteroenergetic characteri-zation, is the C/H value of the columns. The average C/H ratio ofcolumns (A), (B), and (C) is −4.04 ± 0.58. The C/H value of the PolarisC8-A column is −0.12. The large difference dominates the compar-ison, but as Dolan and Snyder have pointed out [53], the C termonly provides significant impact on a separation when the solutesinclude ionized compounds. Nortriptyline (4) and amitriptyline (6),have the largest magnitude �′ values of any solutes, and the result-ing increased retention relative to N,N-dimethylacetamide (1) andN,N-diethylacetamide (2) in the other three columns is evident onthe chromatogram of the Polaris C8-A column (D).

Here again we have analyzed a separate solute set to check thepredictions made based on the SSC and created �–� plots sum-marizing solute retention shown in Fig. 13. Retention of these

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solutes on the Hypersil Prism C18 RP phase is generally well corre-lated with that on the Zorbax Bonus RP phase as seen in Fig. 13A,however, there are some selectivity differences observed withthis solute set that were not observed with the HSM solutes. For

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F roup pc tograp

edHcase

aatbAcPeptr

5

stttsfChrc6fm

values of the comparisons, are listed in Table 2. Fig. 15 shows theSSC using the Discovery CN column as the reference column againstwhich the other three are compared. It is clear that the Discovery CNcolumn has a heteroenergetic relationships to the Luna CN, Zorbax

ig. 13. Comparison of selectivity on embedded polar group or endcapped polar golumn) vs. log k on Zorbax Bonus RP, Hypurity Advance, and Polaris C8-A. Chroma

xample, salicylic acid elutes before trans-cinnamic acid, and 2,4-ichlorophenoxyacetic acid elutes just before diazepam on theypersil Prism phase, but trans-cinnamic acid elutes before sali-ylic acid and diazepam elutes before 2,4-dichlorophenoxylaceticcid on the Zorbax Bonus RP phase. Thus, these columns offer someimilarities in their retention energetics, but cannot be consideredquivalent, as suggested by their Fs value of 24.1.

There is little correlation between the Hypersil Prism C18 RPnd either the Hypurity Advance or Polaris C8-A phases (Fig. 13Bnd C, respectively). This is consistent with the predictions ofhe SSC for the Polaris phase, and with Fs values associated withoth comparisons, but somewhat unexpected for the Hypuritydvance which was predicted to have homeoenergetic retentionharacteristics according to the SSC. The �–� plots for both theolaris and Hypurity Advance phases show many differences inlution order. It should also be noted that on the Hypurity Advancehase, amphetamine, phenylpropanolamine, and lidocaine essen-ially elute with or slightly before the dead time marker, uracil,esulting in negative k values and are thus not shown in the plots.

.4. Cyanopropyl columns

Cyanopropyl columns are not as widely used as traditional alkylilica columns, but are valuable for the different retention charac-eristics they provide [54]. Cyano columns are generally more polarhan traditional alkyl silica columns. Snyder et al. have suggestedhat the functional groups are also highly ordered, leading to lessteric hindrance for the solute [3]. The cation exchange activity, C,or cyano columns varies among manufacturers. The difference in

terms for this class of columns also varies greatly with pH, withigher cation exchange activity at neutral pH than in acidic envi-onments. Fig. 14 shows an SSC plot comparing 12 different cyano

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olumns to one another, (e.g., 1 vs. 2, 3, 4. . .; 2 vs. 3, 4, 5. . .; 3 vs. 4, 5,. . .) for a total of 65 comparisons. Almost half of the comparisonsall within the homeoenergetic region of the SSC, indicating that

any of the 12 columns would provide similar retention. Since the

hases. Log k for the independent solute set on Hypersil Prism C18 (as a referencehic conditions as described in Section 4.

functional groups of these columns are identical it is not surprisingthat many of the columns are similar.

Equally evident from the figure, however, is that many of thecyano columns are different from one another. As an example, theDiscovery CN column is compared to the Inertsil CN, Zorbax SB-CN, and the Luna CN. The column characteristics, as well as the Fs

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Fig. 14. The SSC showing the comparison of 12 cyano columns (65 different com-parisons) to one another at pH 2.8. Note the r2 axis spans from 0.00 on the left to1.00 on the right and is not labeled for clarity.

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FCo

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

tableBond-CN, and Inertsil CN-3 columns. The origins of the het-roenergetic relationships are made clear by the radar plot shownn Fig. 16. In the case of the Inertsil column, the difference in selec-ivity compared to the Discovery column is due almost exclusivelyo the cation exchange (C-term in the HSM model) ability of thewo columns. The differences in selectivity between the Discoveryolumn and the Luna CN and Zorbax SB-CN columns are due to aixture of column acidity and cation exchange ability.As noted previously, the cation exchange term does not greatly

ffect the results of a separation with no ionizable solutes. Sinceost cyano columns have similar B and S* values, and generally vary

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lightly in A values, comparisons may be misleading if the intendedeparation mixture does not contain ionized solutes. Fig. 17 showshe simulated chromatograms of these four columns. The dramaticffect of the C-term on separations on these columns is illustrated

ig. 16. A radar plot showing the similarities and differences in the HSM ratios ofeveral cyanopropyl columns at pH 2.8.

PRESSgr. A xxx (2012) xxx– xxx

well by comparing the Discovery and Inertsil columns, Fig. 17Aand D, respectively. Ionizable solutes such as nortriptyline (4),berberine (3), mefenamic acid (17), and amitriptyline (6) change inelution order relative to the other solutes. Some differences in theelution order of other solutes are also observed. For example, 5,5-diphenylhydantoin (7) and anisole (11), 5-phenylpentanol (10) andtoluene (13), and ethylbenzene (15) and n-butylbenzoic acid (12)coelute on the Discovery CN column but are resolved on the InertsilCN. Thus, while the C-term may be responsible for the largest differ-ence in these columns, other characteristics are also contributingto the selectivity differences.

The Luna and Zorbax columns also appear in the heteroenergeticregion of the SSC, as compared to the Discovery column, but notexclusively due to the C/H term. These two columns differ fromthe Discovery in acidity, which affects more solutes than cationexchange. This is illustrated in Fig. 17. The elution order of mostof the solutes varies between the Discovery column (Fig. 17A) andthe Zorbax (Fig. 17B) and Luna (Fig. 17C) columns. Coeluting peakson the Discovery column, such as 5,5-diphenylhydantoin (7) andanisole (11) are resolved on the Zorbax and Luna columns but inreverse order on Inertsil CN (Fig. 17D). Acetophenone (8), which hasa large basicity term, ˇ′, in relation to most of the other test solutes,has a very different elution position in these cyano columns sincethey differ in their acidity terms.

5.5. Selection of orthogonal columns

The previous examples have focused largely on selecting similarcolumns within a particular class of stationary phase to emphasizethe abilities of the SSC program. However, the need for an orthog-onal column is more common, whether to improve a separation orto select a second column for a two-dimensional separation. Herewe show how the SSC may be practically used to select orthogonalcolumns. Because a C18 phase is often used as a starting point, theSymmetry C18 column is chosen as a reference. The simulated chro-matogram for this column is shown in Fig. 18A. Whether the desiredresult of this separation is complete resolution of all the compoundsor an orthogonal column for a two dimensional separation, thesolute pair N,N-dimethylacetamide (1) and berberine (3) must befurther separated, as well as the solutes N,N-dimethylacetamide(2), nortriptyline (4), and amitriptyline (6). In order to use the SSCto identify possible orthogonal columns, the Symmetry C18 col-umn is compared to a variety of other columns. In this example,the Symmetry C18 column is compared to the Thermo CN, Discov-ery HS-F5 (a fluorinated column), Xterra C8 RP (an EPG column),Bondclone C18 (a type-A silica ODS column), and ZirChrom EZ (azirconia based column) columns.

The SSC generated by these comparisons is shown in Fig. 19. Allof these columns appear to offer heteroenergetic relationships tothe Symmetry C18 column for the solute set used to establish theHSM, and would therefore likely offer the desired differential selec-tivity. Simulated chromatograms for these columns are shown inFig. 18. As predicted, these columns all offer substantially differ-ent selectivity to the Symmetry C18 column. The coeluting solutesN,N-dimethylacetamide (1) and berberine (3) are resolved on allthe other columns. The coeluting solutes N,N-diethylacetamide (2),nortriptyline (4) and amitriptyline (6) are at least partially resolvedon all of the alternative columns and show very high resolution ontwo of the five columns; the Discovery HS-F5 (Fig. 18C) and theZirChrom EZ (Fig. 18F). In addition, there are elution order changesto many solutes, such as N-butylbenzoic acid (12) and toluene (13),for which the elution order is reversed on all of the alternative

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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 Bond-clone C18 phases are more highly correlated with retention on the

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F ry CNc

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ig. 17. Simulated chromatograms of CN columns at pH 2.8. Columns: (A) Discoveolumns (C) and (D), due to large differences in increased retention.

ymmetry C18 phase (Fig. 20A and B, respectively) than might benticipated from the chromatograms discussed above. This illus-rates that the solutes must take advantage of the characteristicshat distinguish one phase from another in order to maximize theolumns’ potentials to offer different selectivities. That does noteem to be the case with the solutes and these two columns. There

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re some elution order changes observed on both phases relative tohe Symmetry C18 phase, but not the dramatic changes that woulde desired when searching for a truly ‘orthogonal’ phase. Botholumns have an Fs metric of approximately 30 when compared to

, (B) Zorbax SB-CN, (C) Luna CN, (D) Inertsil CN. Note the scale change in time for

the Symmetry phase, and thus do not satisfy the criteria for ‘orthog-onality.’ In this regard, the results of comparisons between thesephases using this alternative test solutes are consistent with theinterpretation of Fs values. The comparison between the ZirchromEZ phase to the Symmetry C18 phase (Fig. 20C), however, does illus-trate two phases that have very different retention characteristics

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(consistent with the Fs value of 201). Clearly, there is little corre-lation between retention on the two phases. This is evident bothfrom the solutes used to establish the HSM and our independentsolute 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 retentionon the symmetry column. Also, a different mobile phase composition is used for the Thermo CN column as discussed herein.

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F nary pr

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ig. 19. Two views of the SSC comparing the Symmetry C18 column to other statioight and is not labeled for clarity.

. Discussion

As illustrated above, the combination of the SSC and HSMields a tool that chromatographers can use to efficiently iden-ify similar and orthogonal columns. We have demonstrated thatithin column categories (e.g. cyano, fluoro, EPG, etc.) many

olumns are similar, but that significant differences in selectivity

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an arise and that the SSC makes it easy to find these differences.e have also illustrated the utility in using the SSC to choose

n orthogonal column among several different column types toelect the one offering the most different selectivity. Thus, the

ig. 20. Comparison of selectivity on a variety of phases. Log k for the independent solute18, and Zirchrom EZ. Chromatographic conditions as described in Section 4.

hase types as described. Note the r2 axis spans from 0.00 on the left to 1.00 on the

SSC can provide rapid and beneficial guidance when selectingcolumns.

As we noted in Section 1, there have been several methods pro-posed for column selection. The Fs parameter and the selectivitytriangles of Zhang and Carr are most closely related to our approachbecause they are also based on HSM coefficients. In the followingsection, we comment on how the SSC compares to and comple-

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ments both approaches. Before doing so, we note that the HSMis explicitly concerned with comparing stationary phases relativeto one another with regards to their influence on the selectivityof separations. Most fundamentally, all columns are compared to

set on Symmetry C18 (as a reference column) vs. log k on Xterra C8 RP, Bondclone

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reference ‘average’ C18 phase. Naturally, on any single phase, ahange in separation conditions (e.g., temperature, mobile phaseodifier type and amount, pH) can also influence selectivity. In

ractice, it is a logical first step to adjust these conditions in anffort to improve separations. The HSM and comparison schemesased on it such as the Fs metric, Zhang and Carr’s triangles, and theSC are useful in at least three situations: (1) when alterations to theobile phase do not provide the desired selectivity and therefore

lternative phases must be sought, (2) when ‘orthogonal’ phasesre sought for multidimensional separations, and (3) when an ana-yst must find a replacement column for a separation that had been

orking satisfactorily but for whatever reason (discontinuation,ot available in the laboratory, etc.) the column is no longer avail-ble. In the first two situations, it is clear that little is gained bywitching to stationary phases that are similar in their retentionharacteristics or using similar columns in multidimensional chro-atography. The HSM, and metrics such as Fs, triangles, and the

SC provide guidance regarding columns that will likely producehanges in selectivity. In the third situation, these methodologiesrovide guidance in identifying columns that are likely to be equiv-lent and therefore preserve the selectivity of an already successfuleparation, but do so on another column. In both situations, withver 500 commercially available columns, such guidance can saveonsiderable time, effort, and money.

Thus, while solvent effects on selectivity are clearly importantithin any single separation, the HSM is focused on the contri-

ution to selectivity of one stationary phase relative to another.urthermore, while the HSM parameters are measured for allolumns using only a single mobile phase composition at two dif-erent pH values, the originators of the HSM have studied the effectsf mobile phase composition and pH on the HSM parameters. Theyonclude that the relative selectivity of the phases does not changeignificantly with mobile phase variations [11]. Some caveats muste offered here. Changes in the relative selectivity of the phasesill not occur if a given change in mobile phase conditions alters

he selectivity of a separation in the same way on two columnshat are being compared. The authors of the above cited study actu-lly quantify the relative contribution of changes in mobile phaseonditions to column selectivity. They find that changes in percentodifier are least influential in affecting relative column selectiv-

ty, followed by temperature, followed by changes in mobile phaseodifier type. Furthermore, they acknowledge that the conclusions

re based on a study of C18 phases only and that larger changes inolumn parameters, and hence relative selectivity, can be expectedor comparisons made between C18 and other types of columnse.g., cyanos, fluoros, etc.). For columns of a given type, however,hey suggest that little change in the HSM parameters will be foundith variations in separation conditions.

While temperature and mobile phase modifier type and concen-ration were found to make relatively small contributions to theelative selectivity of different columns, changes in pH can influ-nce the HSM parameters – specifically the C-term. For this reason,

is measured at two pHs (2.8 and 7.0) and can be interpolated inhis range [11].

The take-home message for all of the above is that the HSMarameters are measured relative to an average C18 phase. Thus,omparisons between phases are made relative to one another.hanges in mobile phase conditions can and do alter selectivity,ut it has generally been found that they do so in similar waysn different columns, especially within the C18 class of columns.herefore, the HSM parameters generally do not change signifi-antly with changes in the mobile phase conditions (except pH asoted). Thus, analyses identifying equivalent, similar, and differentolumns that are made using a single mobile phase composition

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ill lead to generally the same conclusions under different compo-itions.

PRESSgr. A xxx (2012) xxx– xxx

6.1. Relationship between the SSC and the Fs metric

The SSC and the Fs metric both use HSM column parameters tomake comparisons between columns. The Fs metric, shown in Eq.(3), provides a convenient (albeit single-valued) method for com-paring any two systems characterized by the HSM. In this way, thegoals of the SSC and the Fs metric are similar. While Fs is easierto use, the SSC provides additional information about the relation-ships between two columns (r2, slope, and intercept).

A potential source of discrepancies between Fs and the SSCrelates to the fact that Fs compares two columns based on the abso-lute magnitudes of their HSM parameters, whereas the SSC usescoefficient ratios. Zhao and Carr [39] showed that in order to com-pare two systems characterized by retention models (LSERs, HSM,etc.) the ratios of two or more parameters are more important thanthe magnitudes of individual parameters. To demonstrate, considertwo hypothetical systems, designated 1 and 2. The HSM parametersof our two imaginary systems are shown below.

log ˛1 = �′1.0 − � ′1.0 + ˇ′1.0 + ˛′1.0 + �′1.0 and, (9)

log ˛2 = �′2.0 − � ′2.0 + ˇ′2.0 + ˛′2.0 + �′2.0 (10)

These two columns, when compared by the Fs metric, wouldhave an Fs value of 196, leading to the conclusion that the twocolumns would provide distinct selectivities. However, on the SSC,they would appear to be homeoenergetic because the ratios of eachparameter (all relative to H) are identical for both columns. Thechromatograms of these two columns would be very similar to theEPG column comparison discussed above (see Figs. 11 and 12 andaccompanying discussion). The second column would offer greaterretention of the solutes, but no difference in selectivity. Zhang andCarr performed a comparable analysis and reached an identical con-clusion, stating “differences in phase selectivity only exist when theratios of the phase coefficients differ, not when their absolute val-ues differ.” [1] Nevertheless, it should be noted that the range inH-values is not exceptionally wide (0.3–1.3) for the commerciallyavailable columns that have been characterized. This is perhapswhy cases like the imaginary one described above are generallynot observed, contributing to the general success of the Fs metric.

6.2. Threshold values for equivalent and orthogonal phases basedon the SSC

In this article we have noted multiple instances in which twocolumns that would be identified as homoenergetic or homeoen-ergetic by Horvath et al.’s classification do not produce equivalentselectivities. Snyder et al. have offered the most stringent criteriafor identifying equivalent columns (Fs ≤ 3) and orthogonal columns(Fs > 65 or 100 depending on the presence or absence of ionicspecies, respectively). It is reasonable to compare the statistical val-ues upon which the SSC is based to column characterizations basedon Fs. Before doing so, however, it should be noted that the Fs cut-offs cited above are deliberately stringent so as to virtually assurecolumn equivalence or orthogonality (i.e., eliminate the potentialfor false positives while accepting the potential for false negatives).This is exceptionally useful where such stringency is absolutelyrequired – particularly for regulatory compliance purposes. In sit-uations where such stringency is not required, however, (e.g., inearly exploratory stages of separation development), less strin-gent guidelines and more general guidance regarding equivalentand orthogonal columns can be useful. For example, if a particu-lar column is not resolving all of the compounds in a mixture, one

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potentially different selectivities. In this case, absolute orthogo-nality may not be required and column comparisons that yield Fs

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alues between 3 and 65 (or 100) may achieve the desired sep-ration. In these cases, ‘similar’ and ‘different’ may be just as, orore useful than, equivalent or orthogonal columns, particularly if

riteria for equivalency and orthogonality too rapidly winnow theumber of columns that one can explore or columns that satisfyhese criteria are not immediately available to the analyst.

With such situations in mind, in an effort to provide guidancend greater clarity regarding threshold values for ‘similar’ and

different’ columns – terms which are admittedly poorly definednd which we have therefore tried to avoid in this manuscript

we have compared the statistical values that we obtain usinghe SSC methodology with the Fs values obtained for the sameolumn comparisons. We did not find clear, absolute correlationsetween Fs and any of the SSC metrics. In other words, withegards to ‘equivalent’ columns, there is no value of r2 abovehich all comparisons have Fs ≤ 3.0. This is not surprising as theathematics underlying the two methodologies is different. For

urposes of suggesting some threshold values, however, based ononsiderations of numerous correlations and the examination ofeveral subsets of columns, we consider comparisons that have2 > 0.97, slope = 1.0 ± 0.3, intercept = 0.00 ± 0.03, and H/H < 1.1 (allour criteria met simultaneously) as columns that demonstrateomoenergetic behavior under the Horvath classification. Moreenerally, we suggest that columns that fit these criteria will ateast yield similar, if not identical, separations. Thus, in situations

here equivalence is not rigorously required, they will provideood alternatives which, with some manipulation of other operat-ng parameters, may yield comparable separations if a replacementolumn is needed. These threshold values are summarized in theext box below.

Homoenergetic columns Heteroenergetic columns

r2 < 0.97 r2 < 0.20Slope = 1.0 ± 0.3 Slope < 0 or >2Intercept = 0.00 ± 0.03 Intercept < −0.3 or >0.3H/H < 1.1 H/H � 1

Having defined these thresholds, we can compare them to Fs

alues. Considering 301 alkylsilica columns that have been char-cterized by the HSM – which makes possible 45,150 uniqueomparisons – 398 comparisons qualify as homoenergetic usingur threshold values. Using Fs ≤ 3 yields 234 comparisons that qual-fy as equivalent. A subset of 140 of these comparisons satisfy bothhe SSC and Fs thresholds. These results indicate that our thresholdsdentify a broader range of potentially similar columns, bringing

ith it an associated risk of higher false positive rates (acceptings ≤ 3 as the absolute standard for equivalence). Of the 258 com-arisons that satisfy our criteria but which have Fs > 3.0, 98 have.0 < Fs < 4.0. This indicates that many of our “false positives” (againsing Fs as the absolute standard for equivalence) have very lows values, although they are outside of the rigorous equivalenceindow defined by Snyder et al.

With regards to ‘different,’ or more rigorously, ‘orthogonal’olumns, clearly, comparisons yielding the poorest r2 values, slopesost deviated from 1.00, intercepts different than 0.00, and H/H

atios greater than 1.0 are most likely to produce different sepa-ations. As a general threshold, for orthogonality we recommend2 < 0.20, slope < 0 or >2, intercept < −0.3 or >0.3, and H/H � 1.hese values are summarized in the text box above. Homeoener-etic columns have the same threshold values as homoenergetic

Please cite this article in press as: A.R. Johnson, et al., J. Chromatogr. A (201

olumns except for the H/H ratio which can be greater than 1.1.e reiterate, however, that these guidelines have not been tested

n the ways that the Fs metric guidelines have and are there-ore suggestions meant to provide general guidance rather than

PRESSgr. A xxx (2012) xxx– xxx 19

rigorous instruction. Furthermore, like the Fs thresholds, thesevalues generally require that the solutes being separated takeadvantage of the HSM parameter(s) that is(are) giving rise to thepoor correlation. This consideration of solutes is relevant to allcolumn comparisons. HSM parameters are measured using 16 care-fully selected solutes identified from painstaking consideration ofhundreds of compounds. They were selected to represent a broadrange of interaction types and strengths. However, in any individualanalyte mixture, all interactions may not be equally represented.For example, if none of the solutes are hydrogen bond donors, thendifferences in the B-parameters between columns are not impor-tant. Thus, while Fs and the SSC provide general predictions, thosepredictions may be incorrect for extreme solute sets that are notwell represented by the solutes used to measure the HSM param-eters. In these situations, it is useful to weight the parametersdifferently before determining Fs and the SSC statistics. This hasbeen considered elsewhere for Fs [53] and can be easily achievedfor both Fs and the SSC.

Carr et al. tested predictions of Fs using 18 cationic drug solutesunder isocratic conditions [46]. They also used the 16 HSM testsolutes to re-measure the HSM parameters for the 14 columnsthey considered in their studies. Interestingly, they found somesignificant differences between their measured values and valuesobtained from Snyder et al., particularly for the A and C parame-ters. It was suggested that some of the changes arise from storageof the columns in acetonitrile/water mixtures. Changes in the HSMparameters over time naturally lead to changes in the predictedFs values. This suggests that some caution should be used whenusing Fs or the SSC to select alternative columns. Nevertheless, Carret al. conclude that for the columns and solutes they studied, theSnyder–Dolan (S–D) HSM “does a reasonably good job of predictingthe 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 goodjob, in general, of representing the behavior of drugs despite thefact that the S–D data set contains only two bases.” It should benoted that while only two bases are in the final 16 solutes, manymore were tested and contributed to the development of the HSMoverall.

Important to our considerations here, the work demonstratesthat for limited data sets, an Fs ≤ 3 is not required to obtain equiv-alent selectivities on two different columns. In fact, in Carr et al.’sarticle, two columns with Fs = 9.7 are shown to yield virtually iden-tical chromatograms for eight selected drugs. This shows that forgeneral guidance purposes, the cut-off of Fs ≤ 3, while having avery high probability of leading to equivalent columns, can berelaxed under the right conditions (i.e., depending on the com-plexity of the solute set, the requirements for absolutely identicalvs. similar separations, etc.). Carr et al. suggest that columns withFs ≤ 16 are ‘very similar’, Fs ≤ 35 are ‘similar’, 35 ≤ Fs ≤ 55 are ‘rea-sonably different’ and Fs ≥ 55 are ‘rather different’ – leaving thereader to translate the meaning of these characterizations into theselectivity 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 correla-tions of HSM parameters as identifying columns that one wouldexpect to provide quite similar chromatographic behavior (perhapsequivalent, perhaps not). Increasing deviations from these valuessuggest increasing differences in selectivities, again with the provi-sion that the solutes are exploring all of the potential interactions.

6.3. Relationship between the SSC and selectivity triangles

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Zhang and Carr used the HSM parameters to establish the apicesof triangles to make comparisons between columns [1]. Each phaseis represented by a dot in the triangle, the location being based onthe specific values of the HSM parameters for a particular column.

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n this way, columns that have similar HSM characteristics appearlose to one another in the triangle, and those that are chemicallyistinct from one another appear further apart on one or more axesf the set of four triangles. One advantage of this approach is thathe axes themselves reflect chemical information in that they relateo the actual HSM values, albeit in a somewhat complicated mannerue to normalization processes that are required to plot the data.his makes interpreting the exact location of the dots difficult inerms of absolute column characteristics. Nevertheless, the axes ofhe triangle reflect chemical information as opposed to the axesf the cube that only contain statistics related to the correlationf HSM parameters between two columns. Thus, in the cube, allnformation about the magnitudes of the HSM parameters is lost.he user has to refer to the actual HSM values after using the SSCo identify columns of interest.

Related to this issue, as the authors point out in their paper,he triangles make it clear that there is a great deal of ‘chemicalpace’ that is not explored by current RPLC columns, meaning thatesearchers have much room to develop novel rather than redun-ant phases. This is not evident from SSC or Fs analyses.

One disadvantage to the triangle approach is that only threearameters can be considered at a time (in some sense, four,ecause the parameters are divided by H). This means that forhe five-parameter HSM model, four different triangles are neces-ary to represent all the data. In contrast, the SSC considers all thearameters simultaneously in the regressions that dictate whereoints appear in the cube. Furthermore, two columns for whichour out of the five parameters are the same will appear as offer-ng similar selectivities on three of the graphs, but may appear aseing different on the fourth graph. Thus, different triangles can

ead to different conclusions regarding the similarity or differenceetween two columns. In some instances, only considering threearameters could be valuable. For example, for solute sets that doot contain ionic species, an analysis of selectivity differences thatmits the C-parameter of the HSM might be more appropriate thanne which considers it. In that case, one would consider the tri-ngle created without the C-parameter. An analysis without the-parameter can also be done with the SSC simply by feeding it aata set without the C-values.

More generally, if more complex models of retention or selec-ivity that contain more parameters are introduced, the SSC woulde able to accommodate them as there is no limit to the num-er of parameters that can be correlated with one another withhe resulting statistics plotted in an SSC. With triangles, however,he number of triangles needed to represent the data set wouldncrease, making it more complicated to analyze all of the differentolumn comparisons.

.4. Potential drawbacks to the SSC approach

We hope that the preceding examples have illustrated the ben-fits of using the SSC program for column selection in a varietyf situations. That is not to suggest, however, that there are notrawbacks with the approach. The SSC program relies on modelsf column characterization; in this case the HSM. Thus, any disad-antage in the model will carry over to the SSC. This is also trueor the Fs metric and selectivity triangles based on the HSM model.or example, as discussed above, the HSM also does not accountor changes in the column condition over time. As such, any con-lusions drawn from the SSC may be inaccurate when compared topecific columns that have been used in a laboratory for extendederiods of time.

Please cite this article in press as: A.R. Johnson, et al., J. Chromatogr. A (201

Another drawback to the SSC, of which most column comparisonethods suffer, is information reduction. The position of a point in

he SSC can only indicate the energetic relationship of two columns.ny specific chemical information leading to similarities or

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PRESSgr. A xxx (2012) xxx– xxx

differences is lost in the process of simplifying the comparison. Thisis also true of the Fs metric.

A third drawback, which has been discussed throughout thiswork, is that the conclusions drawn from the SSC are based onsolute sets spanning a large range of interaction abilities. If a sepa-ration involves only neutral solutes, columns which differ in theirC-terms will do little to improve a separation. However, the SSCcan alleviate this problem if the user inputs a more limited data setthat does not include the parameter that is not relevant to a givenseparation. This, however, assumes that the characteristics of thesolutes are generally known, which is not always the case.

7. Conclusion

We have used the system selectivity cube, a visualization toolfor comparing chromatographic systems, to find similarities anddifferences in RPLC columns characterized by the hydrophobic sub-traction model. We have shown, through a series of case studies,that the SSC is capable of efficiently identifying those columnswhich are similar to one another, and those which should offer dif-ferent selectivity, both among columns in the same class and acrossall column classes. Our methodology was juxtaposed with the Fs

function of column comparison and selectivity triangles. The singlevalue produced by the Fs function is simpler, but the SSC offers morestatistical information related to the two columns being compared.Furthermore, the SSC can distinguish between homo-, homeo-, andheteroenergetic systems, albeit at the cost of not explicitly display-ing the chemical characteristics of the systems being compared,which is an advantage of selectivity triangles. Both the HSM col-umn parameters and the SSC program are freely available, and wehope that chromatographers find the approach presented hereinuseful in method development.

Acknowledgements

We thank Dr. Lloyd Snyder and the contributors to the HSM forgenerously sharing data for the columns presented in this work andProfessor Peter Carr for his helpful suggestions. Acknowledgmentis made to the Donors of the American Chemical Society PetroleumResearch Fund for partial support of this research. Support was alsoprovided by the Drake University Science Collaborative Institute.Support for the experimental work was provided by a Camille andHenry Dreyfus Faculty Start-Up Award.

Appendix A. Supplementary data

Supplementary data associated with this article can befound, in the online version, at http://dx.doi.org/10.1016/j.chroma.2012.05.049.

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