Comments on the paper “Characterization of stationary phases by a linear solvation energy relationship utilizing supercritical fluid chromatography” by C. R. Mitchell, N. J. Benz,

Research Article

Comments on the paper ‘‘Characterizationof stationary phases by a linear solvationenergy relationship utilizing supercriticalfluid chromatography’’ by C. R. Mitchell,N. J. Benz, S. Zhang

In a recent paper published by Mitchell et al. in this journal, some results obtained in

supercritical fluid chromatography and interpreted with the solvation parameter model to

characterize interactions for ‘‘novel stationary phases’’ were surprising to us. Indeed, we

had already published results for most of the stationary phases reported, but, except for

polar phases, our results were not in agreement with those, despite the use of identical

mobile phases in both studies. These data were disturbing because they suggest that

supercritical fluid chromatography is always a normal-phase mode, while we have shown

that it is a reversed-phase mode when working with non-polar stationary phases. In the

process of establishing the reason for the differences between our works, we examined

several different factors. This paper deals with practice of linear solvation energy rela-

tionships: choice of dead-volume marker, choice of test-solutes to adequately probe the

possible interactions and appropriate column length for characterization of chromato-

graphic systems with highly eluting mobile phases are discussed. The importance of

control experiments to validate retention models and confirm their accordance with the

chromatographer’s experience is evidenced. Recommendations for good linear solvation

energy relationship practice are suggested in order to avoid the publication of results

leading to erroneous conclusions.

Keywords: Dead volume / Normal-phase mode / Reversed-phase mode /Solvation parameter model / Supercritical fluid chromatographyDOI 10.1002/jssc.201100278

1 Introduction

Supercritical fluid chromatography (SFC) is a versatile,

efficient and rapid separation method having several

interesting features. First of all, CO2 is non-toxic and cheap,

and can be used both in analytical and preparative scale.

Unfortunately, because CO2 is rather non-polar, most

chromatographers use it only as a replacement for hexane

in the normal-phase mode, thus with polar stationary

phases. The addition of polar organic modifier as methanol

(typically 10%) increases the solvating power of the CO2-

based mobile phase. However, separations can also be

performed in SFC with non-polar stationary phases such as

octadecylsiloxane-bonded silica (ODS) or phenyl-bonded

silica. In this case, the chromatographic behavior is a

reversed-phase mode [1, 2].

In the past years, we have used a linear solvation energy

relationship (LSER), the solvation parameter model based

on Abraham descriptors, to describe SFC systems [3–16]. It

is based on the following equation:

log k ¼ c1eE1sS1aA1bB1vV ð1Þ

where capital letters represent solute descriptors, while

lower case letters represent the system constants, related to

the interactions of the phases with the solutes. c is the

intercept term. E is the excess molar refraction and models

polarizability contributions from n and p electrons; S is the

solute dipolarity/polarizability; A and B are the overall

hydrogen-bond acidity and basicity; V is McGowan’s char-

acteristic volume. The system constants (e, s, a, b and v) are

obtained through a multilinear regression of the retention

data for a number of solutes with known descriptors. They

reflect the magnitude of difference for that particular

interaction between the mobile and stationary phases. Thus,

if a particular coefficient is numerically large, then any

Caroline WestEric Lesellier

Institut de Chimie Organique etAnalytique (ICOA), Universited’Orleans, CNRS UMR 6005,Orleans, France

Received March 30, 2011Revised May 5, 2011Accepted May 6, 2011

Abbreviations: LSER, linear solvation energy relationship;

NPLC, normal-phase HPLC; ODS, octadecylsiloxane-bondedsilica; PFP, penta-fluoro-phenyl; SFC, supercritical fluidchromatography; TTBB, 1,3,5-tri-tert-butylbenzene

Correspondence: Dr. Caroline West, Institut de Chimie Organi-que et Analytique (ICOA), Universite d’Orleans, CNRS UMR6005, B.P. 6759, 2 rue de Chartres, 45067 Orleans cedex 2, FranceE-mail: [email protected]: 133-23-8417281

& 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.jss-journal.com

J. Sep. Sci. 2011, 34, 1917–1924 1917

solute having the complementary property will interact

strongly with either the mobile phase (if the coefficient

is negative) or the stationary phase (if the coefficient is

positive).

We demonstrated the reliability of the LSER model to

SFC. In particular, we described the building of a set of

compounds resulting in accurate and relevant coefficients,

whatever the nature of the stationary phase [3, 6, 10, 16]. We

applied this model to numerous stationary phases such as

porous graphitic carbon [3–5]; alkyl-bonded phases (C4 to C18),

with or without endcapping treatments, with polar endcapping

or polar-embedded groups, or with C-type silica [6, 10–12, 14,

16]; polar phases as silica, cyano, amino or diol [8, 11, 14, 16];

and a large variety of aromatic phases [9, 11, 14, 16].

Based on these studies, it appears that polar and non-

polar phases have opposite behavior when used in identical

SFC conditions:

(i) On polar phases as silica, the v coefficient is negative,

indicating that increased hydrocarbon volume causes

decreased retention. All other coefficients are positive,

indicating that increased polarity causes increased

retention. This is in accordance with normal-phase

behavior [8].

(ii) On non-polar phases as ODS, the v coefficient is

positive, showing that increased hydrocarbon volume

causes increased retention. s, a and b are negative,

showing that increased polarity causes decreased

retention. This is in accordance with reversed-phase

behavior [6].

Moreover, these observations are in accordance with

chemical sense and the experimental knowledge of SFC

chromatographers.

Besides, aromatic phases were shown to provide

different behavior depending on the aromatic group [9].

They can be polar and provide normal-phase behavior (like

ethylpyridine-bonded silica); non-polar and provide

reversed-phase behavior (like phenylhexyl-bonded silica); or

establish both polar and non-polar interactions, thus

providing an intermediate behavior that finds no equivalent

in HPLC [14].

Besides, from these data, a dedicated representation

called a spider diagram was designed [7] and used to classify

over 80 different stationary phases [10, 12, 14, 16]. A simple

projection of the five-dimension solvation vectors on a plane

allows the comparison of all tested phases (Fig. 1A). The

relative location of the stationary phases indicates the

differences between them while bubble size is related to

the strength of interactions. The latter is evaluated with u,

the length of the solvation vector associated to the chro-

matographic system, calculated as follows:

ui ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffie2

i 1s2i 1a2

i 1b2i 1v2

i

qð2Þ

u was shown to be a valuable tool to compare the interaction

strength between different phases.

From this diagram, it appears that silica and ODS

phases display opposite SFC behavior as they are located at

extreme positions of the plot. The silica stationary phase is

located at the bottom right of the figure, in the ‘‘polar zone’’;

this is where all polar stationary phases are located in our

classification (amino, diol, etc). ODS phases on the contrary

are located at the top left, in the ‘‘non-polar zone’’. Aromatic

phases (in the example figure: propylphenyl, diphenyl,

penta-fluoro-phenyl (PFP) and naphtyl phases), and non-

polar phases displaying some polar character (ODS bonded

on C-type silica or Cholesterol phases) are located in the

intermediate region, indicating that they provide both polar

and non-polar interactions.

However, Mitchell et al. [17] have recently published

results that are different from ours. The differences can be

clearly visualized by comparison of Fig. 1A (our results) and

Fig. 1B (based on [17]). A closer look at system constants

shows that the v and b terms are the most different. In

particular, their conclusions are identical to ours for polar

phases (the silica stationary phase is in the same area of the

figure), but they are opposite for non-polar phases (ODS and

Cholesterol phases are closer to the ‘‘polar zone’’) and quite

different for some aromatic phases we had also tested,

although the SFC analytical conditions they used were very

close to ours. Observation of their results leads to the

following conclusions: (i) the Cholesterol and ODS phases

behave like polar stationary phases; (ii) the aromatic

stationary phases are more hydrophobic than ODS phases.

These are very surprising conclusions and do not seem in

accord with chemical sense. Besides, there is no mention

about the opposite results we published, while a quick

review of the literature makes it impossible that our work

should have escaped their attention.

The purpose of the present article is to offer some

comments regarding the paper ‘‘Characterization of

stationary phases by a linear solvation energy relationship

utilizing supercritical fluid chromatography’’ by C. R.

Mitchell, N. J. Benz and S. Zhang [17]. Judging from the

differences between their results and ours, we have

concerns regarding the experiments performed and the

conclusions drawn. As SFC is currently facing a regain in

popularity, it is particularly important that the information

provided to potential users is as clear as possible. SFC has

suffered for long of confusion and poor understanding, and

it is thus particularly important to avoid producing contra-

dictory conclusions without any discussion. Consequently,

we closely investigated the data published in [17] and carried

out additional experiments and calculation from our data in

order to understand the reported differences.

2 Materials and methods

2.1 Chemicals

Methanol (MeOH) and acetonitrile were purchased from J.

T. Baker (Noisy-le-Sec, France); 1,3,5-tri-tert-butylbenzene

J. Sep. Sci. 2011, 34, 1917–19241918 C. West and E. Lesellier


(TTBB) and alkylbenzenes from Sigma-Aldrich (L’ile

d’Abeau, France). Solutions were prepared in a methanol/

acetonitrile mixture.

2.2 Chromatographic system and conditions

A Jasco instrument (Tokyo, Japan) was used as described in

[16], except for a Gilson UV 151 detector (from Waters,

Milford, MA) equipped with a pressure-resistant cell.

Most data were collected from our previous publications

[3–16] with the following conditions: CO2-MeOH 90:10 v/v

251C, 15 MPa outlet pressure, 3 mL/min. Additional analy-

ses of TTBB and alkylbenzenes were carried out at 351C,

and 10 MPa. Injected volume was 2 mL and detection

wavelength 210 nm.

2.3 Stationary phases

The columns were all 250� 4.6 mm, 5 mm: Zorbax C18

Eclipse plus (Varian, Les Ulis, France), Cosmosil Cholester

and Cosmosil pi-NAP (Nacalai Tesque, Kyoto, Japan),

Cogent Bidentate C18 (Disruptive technologies, Ville-

cresnes, France).

2.4 Data analysis

Multiple linear regression analyses were performed using

XLStat 7.5 software (Addinsoft, New York, NY).

3 Results and discussion

3.1 The v coefficient

We focused out attention on the v coefficient. Although

other differences exist between the two studies, particularly

for the b coefficient, experience tells us that the factors

affecting one coefficient often have significant side-effects

on the others, depending on the interdependence level

between descriptor values among the solute set. For

instance, if one coefficient is lower than it should, other

coefficients are larger to compensate for the theoretical

‘‘loss’’ in retention.

Mitchell et al. obtained negative v coefficients for most

stationary phases they investigated, and in particular for the

Cholesterol (Cogent UDC Cholesterol, Microsolv), C18

(Zorbax Eclipse XDB C18, Agilent) and Bidentate C18

(Cogent Bidentate C18, Microsolv). However, the v coeffi-

cient was positive on aromatic phases, and in particular the

Naphtyl phase (Cosmosil pi-NAP, Nacalai Tesque). They

judge this positive coefficient as ‘‘surprising’’, while the

negative v coefficients obtained on all other phases are

considered normal.

In our works we have obtained positive v values on all

C18 and most aromatic stationary phases [6, 9, 10, 12, 16],

while only polar phases (bare or polar-bonded silica)

displayed negative v values.

While flow rate and mobile phase composition were

identical in both studies, the different temperature and

outlet pressure used in their and our studies could be partly

responsible for the differences in the calculated coefficients:

temperature was 351C against 251C, while pressure was

10 MPa against 15 MPa. Indeed, density of the supercritical

fluid participates in its elution strength.

When producing a retention model, the values obtained

must be in accordance with chemical sense. With a cleverly

designed solute set, this can be easily achieved by compar-

ing the coefficient values with the separation of well-chosen

compounds.

Negative v values mean that increased hydrocarbon

volume of the compound, for instance by increased chain

length, causes decreased retention. In such conditions,

separations of non-polar homologous series can generally

not be achieved. On the contrary, positive v values mean that

increased hydrocarbon volume causes increased retention

and separation of homologous series can be achieved.

Moreover, we have shown that methylene selectivity and

hydrophobic retention are correlated to the v coefficient

[4, 7, 12, 16]; thus hydrophobic stationary phases provide

DP

C3P

PFP

SI

C18

C18-C

DP-X

NAP Chol

e

s

ab

v

C3P PFP

SI

C18

C18-C

BIphenNAP

Chol

e

s

ab

v

A B Figure 1. Spider diagram based on two setsof data. (A) West and Lesellier [3–16].Operating conditions: CO2-MeOH 90:10 v/v,251C, 15 MPa, 3 mL/min. C18 (Kromasil C18100); C18-C (Cogent Bidentate C18); Chol(Cosmosil Cholester), NAP (Cosmosil pi-NAP); PFP (Discovery HSF5); C3P (Upti-sphere PH); DP (Pursuit Diphenyl); DP-X(Pursuit XRs Diphenyl); SI (Kromasil SIL100). (B) Mitchell et al. [17]. Operatingconditions: CO2-MeOH 90:10 v/v, 351C,10 MPa, 3 mL/min. C18 (Zorbax Eclipse XDBC18); C18-C (Cogent Bidentate C18); Chol(Cogent UDC Cholesterol), NAP (Cosmosilpi-NAP); PFP (Discovery HSF5); C3P(Ascentis phenyl); Biphen (Ultra II biphenyl);SI (Ascentis silica).

J. Sep. Sci. 2011, 34, 1917–1924 Other Techniques 1919


positive v values while hydrophilic stationary phases provide

negative v values. Looking at the separation of a homologous

series is sufficient to validate the positive or negative v value.

Figure 2 shows the separation of an alkylbenzene homo-

logous series (with alkyl chains of 7–10 carbon atoms)

analyzed in the same chromatographic conditions as those

used in [17] (351C, 10 MPa). It appears that the four

compounds, differing only of methylene units, are well

separated on the C18 (Zorbax C18 Eclipse plus, Varian),

Bidentate C18, Cholesterol and Naphtyl phases and eluted

according to increasing chain length. This is in accordance

with a positive v value. Thus, the different operating

conditions used in both studies cannot be incriminated for

the different v values, and there must be something wrong

in [17].

The surprising v values reported in [17] could have

been assessed by observing the separation between

(i) ethylbenzene, propylbenzene, butylbenzene; (ii) ethyl-4-

hydroxybenzoate, propyl-4-hydroxybenzoate, butyl-4-hydro-

xybenzoate or (iii) hexanophenone and heptanophenone,

which were all present in their data set. No chromatogram is

provided and there is no comment regarding the consis-

tency of v values with observed elution order among

homologous series. However, due to the strongly solvating

CO2/MeOH mixtures and the small column length used,

retention of these compounds should be low, which could

explain why the authors did not notice elution orders. There

is no reason why they should have observed different elution

orders from the ones we report here. Otherwise, it would be

the first report of normal-phase behavior on non-polar

phases in SFC.

In the light of the above, the system constants reported

by Mitchell et al. are highly questionable, thus deserved

deeper inquisition.

3.2 Choice of dead volume marker

As operating conditions cannot be blamed for the differ-

ences observed, we have looked for another suspect and

turned to dead time (t0) measurement. Unretained marker

injection is the most widely used method to determine t0,

with the obvious difficulty of selecting an unretained

compound.

Mitchell et al. use TTBB as a t0 marker. This is common

practice in normal-phase HPLC (NPLC), and as the authors

A B

C D

-100

0

100

200

300

400

500

0 0.5 1 1.5 2time (min)

UV

det

ecto

r re

spo

nse

(m

V)

0.94

dilu

tion

solv

ent 1.

60 C

71.

70 C

81.

82 C

9

1.95

C10

1.51

TT

BB

-100

0

100

200

300

400

500

0 0.5 1 1.5 2time (min)

0.96

dilu

tion

solv

ent

1.34

TT

BB

1.50

C7

1.58

C8

1.66

C9

1.75

C10

-50

50

150

250

350

450

550

0 0.5 1 1.5 2 2.5

time (min)

UV

det

ecto

r re

spo

nse

(m

V)

UV

det

ecto

r re

spo

nse

(m

V)

UV

det

ecto

r re

spo

nse

(m

V)

1.01

dilu

tion

solv

ent

1.43

TT

BB

1.70

C7

1.83

C8

1.98

C9

2.15

C10

-50

50

150

250

0 0.5 1 1.5 2

time (min)

1.13

dilu

tion

solv

ent

1.55

TT

BB

1.71

C7

1.77

C8

1.84

C9

1.92

C10

Figure 2. Superimposed chro-matograms of alkylbenzenes(from C7 to C10) and TTBB.Operating conditions: CO2-MeOH 90:10 v/v, 351C, 10 MPa,3 mL/min. (A) Zorbax EclipsePlus C18; (B) Cogent BidentateC18; (C) Cholesterol; (D) Naphtyl.



assume that SFC is normal-phase, it made sense to them.

The use of TTBB was reported with chiral stationary phases

operated in NPLC mode [18], where the authors mention

that TTBB was slightly retained on silica and alumina [19],

mainly in pure hexane.

In RPLC, uracil is frequently used as t0 marker because,

as a small polar compound, it is supposedly unretained.

However, a recent publication showed that its use with

polar-embedded or polar-endcapped phases in RPLC leads

to overestimation of t0 because it interacts with the polar

functions of the stationary phases [20].

In SFC, dead volume varies not only with the column

but also with the operating conditions because the fluid is

compressible, and because mobile phase adsorption on the

stationary phase varies with the operating conditions.

Among varied proposed methods, organic solvents

were tested for t0 measurement in SFC. In numerous

conditions, the marker injection leads to overestimation

of t0 [21]. For instance, methylene chloride appeared to be

retained on ODS phases [22]. In past studies, we

have suggested the use of the UV baseline disturbance

caused by the polar dilution solvent as t0 marker on ODS

phases [23], as this takes account of the changes in operating

conditions.

Figure 2 also shows the chromatograms of TTBB on

several non-polar stationary phases, obtained in the condi-

tions of [17]. As expected, this compound is retained on non-

polar stationary phases. It appears that the first baseline

disturbance, used to measure t0 in all our studies, appears

20–30 s before TTBB. The overlaid chromatograms obtained

for identical conditions show the significant retention

difference between the two t0 markers. This prompts several

remarks:

(i) Overestimation of t0 leads to underestimation of

retention factors.

(ii) The retention of most compounds used in [17] must

be below 5 min. A 30 s difference on the measurement

of t0 is thus highly significant.

(iii) A large proportion of compounds in their data set

must have eluted before TTBB on non-polar stationary

phases. Considering the definition of t0, no compound

should be eluted before it, unless it is excluded from

some pores. No such anomalous behavior is

mentioned in [17]. No retention factor can be

calculated for the compounds eluted before TTBB,

which must have been excluded from the model

calculation. This is not necessarily a problem with a

sufficiently large and diverse solute set. However, the

least retained compounds in a particular chromato-

graphic system generally share some common proper-

ties (for instance, they are polar on non-polar

stationary phases), thus correct evaluation of this

property is impaired.

Other arguments indicate that TTBB is inappropriate.

In RPLC, there is a linear relationship between log(k) and

the number of carbon atoms nc for homologous series. This

linear relationship is used to determine t0 value by extra-

polating the linear tendency curve [24]. Figure 3 shows the

relationship between log(k) of the C7- to C10-alkylbenzenes

plotted against nc for the C18 phase. log(k) was calculated

based on t0 determined with 1/TTBB retention (red squares)

and 2/dilution solvent (blue diamonds). TTBB provides a

curve best fitted with a polynomial regression, while the

dilution solvent provides a straight line. This again indicates

that TTBB is not relevant as t0 marker on non-polar

stationary phases. Moreover, the log(k) values obtained with

TTBB are much lower than those obtained with the dilution

solvent.

To further question the sign and magnitude of the

system constants in [17], we decided to re-calculate the

coefficients based on our data and using 1/the dilution

solvent and 2/TTBB as t0 markers. The solute set we used

for model calculation can be found in [16]. Table 1 gathers

the LSER models on Cholesterol, Bidentate C18 and

Naphtyl phases. Four equations are provided for each

column (the fourth is discussed later). Equation (1) was

calculated using the dilution solvent as t0 marker and all

compounds injected apart from experimental outliers.

Equation (2) is again calculated using the dilution solvent

for t0 but retaining only the compounds eluting later than

TTBB. Equation (3) is calculated using TTBB for t0, thus

obviously eliminating all compounds eluted before TTBB.

Several remarks can be made:

(i) Our initial data set comprises between 110 and 131

compounds. The number of solutes excluded between

Eqs. (1) and (2) is more or less significant, depending

on retention of TTBB. For the Cholesterol phase, it

represents more than 20% of the data. Thanks to

diversity among our solute set, it appears that the

system constants are not significantly affected by the

y = 0.060x - 0.554

R 2 = 0.9999

y = 0.228x - 2.775

R2 = 0.9717

y = 0.008x3 - 0.262x2 + 2.800x - 10.946

R2 = 1

-1.5

-1.0

-0.5

0.0

0.5

6 7 8 9 10 11nC

log

k

Figure 3. Variation of the retention in a homologous series(C7 to C10 alkylbenzenes) on Zorbax Eclipse Plus C18 column.Retention factors are calculated using either the UV baselinedeviation due to dilution solvent (diamonds) or TTBB retention(squares) as t0 marker. Operating conditions as in Fig. 2.



removal of the less retained compounds, when

the dilution solvent is used as t0 marker. As a result,

the differences observed between the two studies may

not be due to solute sets.

(ii) When using TTBB, all system constants vary signifi-

cantly on all three stationary phases (Eqs. (2) and (3)).

However, the v coefficient is seen to increase; thus this

cannot be the reason for the low v values reported in

[17].

(iii) When using TTBB, the statistics strongly deteriorate.

This could explain the fact that, in [17], the correlation

coefficient for the C18 phase, where the overestima-

tion of t0 is bound to be one of the largest, is

particularly low. The reduction in data set cannot be

incriminated for the poor statistics, as comparison

of Eqs. (1) and (2) shows that the statistics are

not significantly affected upon removal of test

compounds. The compounds exhibiting the smallest

retention are the most affected by an overestimation of

t0, possibly explaining deterioration of the statistics.

As the least retained compounds act as levers on the

regression equation (just as the most retained

compounds do), they significantly affect the quality

of the regression and the coefficient values. In this

case, good statistics can only be restored by removal of

the deviating compounds, which are then treated as

outliers.

This fact is evidenced in Fig. 4, showing the experi-

mental retention factors plotted against retention factors

calculated by the models for Bidentate C18. It appears that

retention of the least retained compounds is poorly predic-

ted when t0 is overestimated (Fig. 4B). On the contrary,

fitting of the least retained compounds is good when t0 is

estimated with the dilution solvent (Fig. 4A). This point

could have been easily checked by observation of the resi-

dual plot, an important control for multiple linear regres-

sion analysis. A residual graph was only provided for the

bare silica column, where overestimation of t0 is bound to be

the smallest. Indeed, TTBB elutes close to the dilution

solvent; thus the deviation of less retained compounds is

only marginal on this column.

On polar columns, when TTBB elutes close to the

dilution solvent, using one or the other as t0 marker does

not change the results significantly (results not shown),

explaining why the results in [17] on polar phases are

essentially comparable to ours.

3.3 Choice of testing compounds

As the dead volume marker chosen by Mitchell et al.,

although a serious flaw in their experiments, cannot be

incriminated for the negative v values obtained on non-polar

phases, we looked for yet another culprit. We then turned to

Table 1. System constants and model fit statisticsa)

Stationary phase Dead volume marker c e s a b v n R2adj SE

Cholesterol (1) Dilution solvent �1.12 0.59 �0.18 0.32 �0.62 0.47 110 0.974 0.05

0.03 0.02 0.03 0.02 0.03 0.01

(2) Dilution solvent �1.12 0.59 �0.17 0.32 �0.65 0.47 86 0.963 0.06

0.03 0.02 0.03 0.03 0.04 0.02

(3) TTBB �2.70 1.17 �0.37 1.01 �1.66 1.06 86 0.873 0.23

0.14 0.08 0.13 0.10 0.18 0.07


0.03 0.02 0.03 0.02 0.03 0.03

Bidentate C18 (1) Dilution solvent �0.85 0.61 �0.30 0.21 �0.20 0.23 123 0.957 0.08

0.03 0.02 0.04 0.03 0.05 0.02


0.04 0.02 0.04 0.03 0.05 0.02

(3) TTBB �1.95 0.96 �0.63 0.45 �0.30 0.65 108 0.822 0.27

0.12 0.08 0.15 0.10 0.19 0.08


0.03 0.02 0.04 0.03 0.05 0.04

Naphtyl (1) Dilution solvent �1.25 0.32 0.16 0.07 0.09 0.29 131 0.932 0.08

0.03 0.02 0.04 0.03 0.04 0.02

(2) Dilution solvent �1.21 0.32 0.14 0.06 0.08 0.28 127 0.933 0.08

0.03 0.02 0.04 0.02 0.04 0.02

(3) TTBB �2.10 0.41 0.34 0.15 0.15 0.45 127 0.819 0.20

0.09 0.05 0.09 0.06 0.11 0.05

(4) Dilution solvent �1.16 0.36 0.22 0.01 0.16 0.10 121 0.950 0.07

0.03 0.02 0.03 0.02 0.04 0.03

a) n is the number of solutes considered in the regression: (1) all injected solutes, (2) and (3) without the solutes eluting before TTBB, (4)

all injected solutes apart from alkylbenzenes with carbon chain 44. R2adj is the adjusted correlation coefficient. SE is the standard error

in the estimate and the numbers in italics represent 95% confidence limits.



the solute set. Other authors [25–27] have discussed the

importance of solute set to obtain chemically sound LSER

models.

The diversity of Mitchell’s solute set is appropriate. This

can be simply checked by plotting frequency histograms for

each descriptor value. Correlation is also generally absent

from this solute set. They provided a correlation table, but

correlation coefficients are generally not sufficient to ensure

the absence of correlation among a data set, as they are

strongly affected by lever compounds. Plotting each

descriptor against every other ensures the absence of

correlation. Having plotted frequency histograms and

correlation plots for the solute set used in [17], we confirm

the diversity and absence of correlation, when the whole

data set is considered. Naturally, these control operations

must be done again when a significant number of solutes

are removed from the data set, as is the case in [17] for the

Cholesterol and PFP-FC columns. The poor statistics

obtained on the PFP-FC column (R2 5 0.51) might result

from an unbalanced solute set after removal of 16 out of 41

compounds.

However, we found two defects in this data set. The first

one is in retention of the solutes. Based on our experience,

the retention of most compounds in Mitchell’s set must be

very low on aromatic and non-polar phases. Judging from

the fact that all columns used were only 15 cm (or even

10 cm), accuracy of the retention times is seriously ques-

tioned. The authors recognized that extra-column effects

may be more significant for the shorter column. Using a

wrong t0 is thus even more problematic in this case.

Retention factors on the silica stationary phase are the only

ones provided; thus this hypothesis is difficult to check.

We generally work with 25 cm columns to ensure

accuracy of the retention measurement. Besides, our solute

set comprises naphthalenic species, along with benzenic

species. This way, when polar benzenic species are not

sufficiently retained to ensure accuracy of retention

measurement and must be eliminated from the data set,

there always remains a sufficient number of polar naph-

thalenic species to probe polar interactions.

The second important defect in their data set is the

absence of large homologous series. As pointed out above,

there are three small homologous series in their solute set.

This may not be sufficient for a correct assessment of the

effect of volume on retention. Indeed, among small polar

compounds, shape of the whole molecule and polarity of the

parent structure are significantly affected by an increase of a

short alkyl chain; thus the alkylbenzene and paraben species

may not be sufficient.

To check this point, we calculated another multiple

linear regression, this time removing all large alkylbenzene

species from our data set. Indeed, our data set comprises

alkylbenzenes with nc varying from 1 to 14. To have a data

set closer to that of Mitchell et al., we removed all

compounds with nc larger than 4. The results for Choles-

terol, Bidentate C18 and Naphtyl phases are presented in

Table 1 where Eq. (1) with all solutes can be compared to

Eq. (4) without large alkylbenzenes.

While statistics are slightly improved or unchanged, the

v coefficient decreases significantly when large alkylben-

zenes are removed from the data set. In some cases, it

becomes of little significance. As a result, we believe that the

data set could be considered guilty for the incorrect v values

in [17], because the influence of molecular volume on

retention is not adequately probed.

3.4 Validating an LSER model

Other authors [25, 26] provided recommendations to assess

the validity of a LSER model. However, as appears in the

above discussion, good statistics are not sufficient to validate

a model. Thus, the controls suggested before should be

considered as minimum operations.

First of all, it is important that the system constants

must be in accordance with good chemical sense. Consid-

ering the present knowledge in SFC, one should be very

surprised about a normal-phase behavior observed with

non-polar stationary phases and control experiments should

be provided to support such an assertion.

-1

0

1

2

-1 0 1 2

log k calc

log

ke

xp

-2.5

-1.5

-0.5

0.5

1.5

-2.5 -1.5 -0.5 0.5 1.5

log k calc

log

ke

xp

A B

Figure 4. Experimental reten-tion factors compared to reten-tion factors calculated by theLSER models on Cogent Biden-tate C18, using (A) the UVbaseline deviation due to dilu-tion solvent (diamonds) or (B)the TTBB retention (squares) ast0 marker. Operating conditionsas in Fig. 1A.



Secondly, the simple observation of elution orders of

well-selected groups of solutes should confirm the sign and

magnitude of the system constants. We have already pointed

out above that the v coefficient is related to separation of

homologous series. Other groups of compounds can be

used to assess other coefficients. For instance, we have

shown that separation of species differing in hydroxyl

groups is related to the a coefficient [4, 5]. In a paper devoted

to quick estimation of system constants [11], we have

suggested compounds that are useful in assessing the sign

and magnitude of all five coefficients.

4 Concluding remarks

Most of the columns studied in [17] had already been

characterized in previous publications, with a method

producing accurate and relevant coefficients for all types

of stationary phases in SFC conditions. Unfortunately, close

inspection of the paper raises serious doubts about the

validity of the results and the conclusions drawn.

The author’s choice of t0 marker, based on erroneous

comparison between SFC and NPLC, is questionable for

SFC. This leads to irrelevant LSER models for non-polar and

aromatic phases. The use of the solvent disturbance peak,

when working with a UV detector at low wavelength ensures

avoiding these dramatic mistakes.

The solute set is also lacking some compounds to

adequately probe the effect of molecular volume on reten-

tion. Moreover, due to the high eluting power reached in

SFC, we recommend the use of sufficient column length

(25 cm) and sufficiently retained compounds, polar and

non-polar, i.e. large homologous series, and naphthalenic

species in addition to benzenic species.

The lack of important control experiments makes us

believe that the results published by Mitchell et al. are not

correct, particularly for non-polar and aromatic phases. It

appears that the critical review of this paper prior to publi-

cation did not provide appropriate feedback to the authors.

Finally, as reported in numerous publications, SFC can

work as a normal-phase mode with polar stationary phases but

as a reversed-phase mode with non-polar stationary phases.

The authors have declared no conflict of interest.

5 References

[1] Lesellier, E., J. Chromatogr. A 2009, 1216, 1881–1890.

[2] Lesellier, E., J. Sep. Sci. 2008, 31, 1238–1251.

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[4] West, C., Lesellier, E., J. Chromatogr. A 2005, 1087,64–76.








[12] West, C., Fougere, L., Lesellier, E., J. Chromatogr. A2008, 1189, 227–244.



[15] West, C., Ogden, J., Lesellier, E., J. Chromatogr. A 2009,1216, 5600–5607.

[16] West, C., Lesellier, E., in: Advances in Chromato-graphy, Grushka, E., Gringerg, N. (Eds.), Chapter 5, Vol.48, CRC Press, Boca Raton, FL 2010, pp. 195–254.

[17] Mitchell, C. R., Benz, N. J., Zhang, S., J. Sep. Sci. 2010,33, 3060–3067.

[18] Pirkle, W. H., Welsh, C., J. Liq. Chromatogr. 1991, 14,1–8.

[19] Rekker, R., De Vries, G., Bijloo, G., J. Chromatogr. 1986,370, 355–376.

[20] Perry, R. P., Coym, J. W., J. Sep. Sci. 2010, 33,2310–2315.

[21] Springston, S. R., David, P., Steger, J., Novotny, M.,Anal. Chem. 1986, 58, 997–1002.

[22] Shoenmakers, P. J., Uunk, L. G. M., Janssen, H.-G.,J. Chromatogr. 1990, 506, 563–578.

[23] Gurdale, K., Lesellier, E., Tchapla, A., J. Chromatogr. A2000, 866, 241–251.

[24] Lesellier, E., Gurdale, K., Tchapla, A., Chromatographia2002, 55, 555–563.

[25] Vitha, M., Carr, P. W., J. Chromatogr. A 2006, 1126,143–194.

[26] Trone, M. D., Khaledi, M. G., J. Chromatogr. A 2000,886, 245–257.

[27] Poole, C. F., Poole, S. K., Abraham, M. H., J. Chroma-togr. A 1998, 798, 207–222.



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Comments on the paper “Characterization of stationary phases by a linear solvation energy relationship utilizing supercritical fluid chromatography” by C. R. Mitchell, N. J. Benz,