Systematic investigations of peak distortions due to additives in supercritical fluid chromatography

Journal of Chromatography A 1621 (2020) 461048

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

Systematic investigations of peak distortions due to additives in
supercritical fluid chromatography
Emelie Glenne a, Jörgen Samuelsson a,∗, Hanna Leek b, Patrik Forssén a, Magnus Klarqvist c,
Torgny Fornstedt a,∗
a
b
c

Department of Engineering and Chemical Sciences, Karlstad University, SE-651 88 Karlstad, Sweden
Early Chemical Development, Pharmaceutical Sciences, BioPharmaceuticals R&D, AstraZeneca, Gothenburg, Sweden
Early Product Development, Pharmaceutical Sciences, BioPharmaceuticals R&D, AstraZeneca, Gothenburg, Sweden

a r t i c l e

i n f o

Article history:
Received 10 January 2020
Revised 12 March 2020
Accepted 14 March 2020
Available online 16 March 2020
Keywords:
Supercritical fluid chromatography
Peak performance

Peak distortions
Additives
Basic components
Overloaded peaks

a b s t r a c t
The impact of eluent components added to improve separation performance in supercritical fluid chromatography was systematically, and fundamentally, investigated. The model system comprised basic pharmaceuticals as solutes and eluents containing an amine (i.e., triethylamine, diethylamine, or isopropylamine) as additive with MeOH as the co-solvent. First, an analytical-scale study was performed, systematically investigating the impact of the additives/co-solvent on solute peak shapes and retentions, using
a design of experiments approach; here, the total additive concentration in the eluent ranged between
0.021 and 0.105 % (v/v) and the MeOH fraction in the eluent between 16 and 26 % (v/v). The co-solvent
fraction was found to be the most efficient tool for adjusting retentions, whereas the additive fraction was
the prime tool for improving column efficiency and peak analytical performance. Next, the impacts of the
amine additives on the shapes of the so-called overloaded solute elution profiles were investigated. Two
principal types of preparative peak deformations appeared and were investigated in depth, analyzed using computer simulation with mechanistic modeling. The first type of deformation was due to the solute
eluting too close to the additive perturbation peak, resulting in severe peak deformation caused by coelution. The second type of deformation was also due to additive–solute interactions, but here the amine
additives acted as kosmotropic agents, promoting the multilayer adsorption to the stationary phase of
solutes with bulkier aryl groups.
© 2020 The Authors. Published by Elsevier B.V.
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1. Introduction
Preparative supercritical fluid chromatography (SFC) is an important technique in the pharmaceutical industry and of increasing
interest in the scientific community. In SFC, the mobile phase usually contains highly pressurized carbon dioxide (CO2 ) as the main
weak solvent, with a polar co-solvent added to control retention.
Many active pharmaceutical ingredients contain amine functional
groups [1]; therefore, an amine additive must be added to the eluent to obtain acceptable separation performance, reproducibility,
and productivity [2–4]. The addition of an amine additive will generally decrease the retention and improve the peak shapes for basic solutes in SFC [5,6], as was demonstrated in the early 1980s
in reversed-phase liquid chromatography (RPLC) [7]. In SFC it is

∗

Corresponding authors.

E-mail
addresses:

(T. Fornstedt).

(J.

Samuelsson),

common to use 0.1–1% amine additive in the co-solvent [8]. The
selection of the amine additive is based on several considerations,
such as the effect on the chromatographic performance, the detector used in controlling the fractioning, post-purification removal,
and reactivity. In preparative industrial applications, diethylamine
(DEA) is often used when the fraction collection is based on ultraviolet (UV) detection and ammonia when the fractions are analyzed by mass spectrometry detection. Recently, the component
ammonium hydroxide has been introduced as a water rich additive for improved chromatographic separation and purification of
highly polar pharmaceuticals and peptides [9].
Both modifiers and additives are used to modulate the retentions and shapes of the eluted peaks of the injected solutes, but
they operate in different ways. A modifier is defined as an added
compound that operates by modifying the solvent strength of the
mobile phase, whereas an additive is defined as a compound that
operates by competing with the solutes for the limited adsorption
sites on the stationary phase surface [10,11].

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2

E. Glenne, J. Samuelsson and H. Leek et al. / Journal of Chromatography A 1621 (2020) 461048

When modeled, the effect of a modifier on retention should

therefore be described using linear solvent strength theory [12];
here the logarithm of the retention factor (k) versus fraction cosolvent in the eluent should have a linear relationship [11,12],
whereas the effect of an additive is better described by a competitive adsorption isotherm [10]. If we have a competitive mechanism, the logarithm of the retention factor (k) versus fraction cosolvent will not show a non-linear relationship, instead the relationship will be non-linear [,13]. In a recent study we showed that,
in SFC using a diol silica adsorbent, the organic co-solvent MeOH,
considered a modifier, acts as an additive at low concentrations in
the eluent and as a modifier at higher MeOH concentrations [13].
Here, the MeOH fraction 13% (v/v) was the turning point since,
since the excess isotherm reached its maximum using a diol column at a backpressure of 120 bar and a column temperature of
40 °C [13]; this value might differ for other polar phase systems
in SFC since the methanol adsorption to the stationary phase depend strongly on the column chemistry as well as the temperature
and pressure. In later studies, we demonstrated that in the regions
where MeOH is acting as an additive, the shape of the so-called
overloaded elution profiles of the solutes changed in a most unusual way [14,16], depending on the level of the co-solvent fractions, such as observed before in RPLC systems having strongly adsorbed additives [15].
A more complete census and understanding of all interactions between the solute and the surface of the stationary phase
in analytical separation systems requires analyzing the shapes of
the overloaded solute bands under so-called nonlinear conditions
[10,11]. The reason why nonlinear studies of solute adsorption are
also important in analytical chromatography is that the different
adsorption sites operate to different degrees in different concentration ranges since they have different saturation capacities, so one
can distinguish the sites from one another by using a broad concentration range from low to high. In addition, the shapes of the
overloaded elution zone are related to the curvature of the adsorption isotherm, classified as of five main types [10]. The most common Type I adsorption isotherm is the Langmuir isotherm, which
is shaped convex upwards and reaches a limiting surface capacity.
The corresponding overloaded elution profile has a sharp front and
diffuse rear—the classical overloaded Langmuirian peak shape [10].
However, adsorption studies were we combine analytical-scale and
overloaded, non-linear, experiments for obtaining a deeper understanding of solutes underlying retention mechanism, requires welldesigned selections of model compounds accounting for many aspects among others purity, availability and solubility, due to the
large amounts used [10].
Systematic investigations of the remarkable peak deformations
in SFC have revealed that the overloaded solute bands have
the common Langmuirian shape at low co-solvent concentrations,

whereas at higher co-solvent concentrations (i.e., levels at which
the co-solvent acts as an additive), the overloaded solute band profiles have unusual anti-Langmuirian shapes (i.e., with diffuse fronts
and sharp rears) [14,16]. Between these characteristic shapes, the
bands appear generally deformed and almost round, with a hump
at the front or rear. These remarkable perturbation-peak–generated
deformations, were explained on a firm theoretical basis by Fornstedt and Guiochon for LC [11,15] and do occur in unusual LC/RPLC
systems especially designed to produce the deformation effects. It
was recently demonstrated that perturbation-peak–generated deformations appear in most general SFC systems under certain conditions, far more seriously than in RPLC, where the deformations
appear in more unusual systems and/or in systems especially designed to generate the effects by, for example, adding a more hydrophobic ion-pair reagent in RPLC than is necessary. The requirements for the effects to take place in SFC due to the co-solvent
are summarized in the following rule of thumb [14,16]. First, the

co-solvent in the SFC system should be operated using co-solvent
levels at which it acts as an additive (see above). Second, the cosolvent should adsorb more strongly (or at an equal strength) to
the stationary phase than does the solute in eluent without cosolvent. Third, the co-solvent perturbation peak should elute earlier than the solute in the actual eluent co-solvent concentration
plateau.
As discussed above, peak deformations can occur in most common SFC systems due to strong co-solvent adsorption to the stationary phase, i.e., under conditions in which the co-solvent acts
as an additive [14,16]. West et al. recently showed that ammonium
acetate used as an additive adsorbs even more strongly than MeOH
to a hybrid silica phase (BEH; Waters Corporation, Milford, MA,
USA) [8]. Therefore, it can be assumed that amine additives should
generate deformations similar to the way polar organic co-solvents
do [14].
The aim of this study is to systematically investigate the effects that amine additives have on analytical and preparative retentions and band shapes, as well as to better understand the
underlying mechanisms by which the additive affects the band
shapes. Three common basic pharmaceutical compounds were selected as model solutes, i.e., alprenolol, metoprolol, and propranolol, fulfilling the combined requirements for analytical-scale and
overloaded adsorption studies. As model additives three amines
were selected: triethylamine (TEA), diethylamine (DEA), and isopropylamine (iPrNH2 ). To understand how the co-solvents and additives affect retention and efficiency under analytical conditions,
design of experiments (DoE) modeling was used. The underlying
thermodynamics of the separation systems were further investigated by making overloaded injections of the solutes and then analyzing the corresponding preparative elution zones using mechanistic numerical modeling. We also intended to use the deeper
understanding thus attained to offer guidelines for designing these

more complicated SFC systems intended for separating basic solute
components, to give high performance and minimum risk of peak
distortion.
2. Theory
An adsorption isotherm describes the equilibrium distribution
of a solute between the stationary and mobile phases at a specific and constant temperature. When the mobile phase contains
an additive, which competes with the solute for the available stationary phase, a multi-component adsorption isotherm is required
[10,16]. In this study, we will use the multi-component competitive bi-Langmuir adsorption isotherm that, for the ith component
in the mixture, can be written [10]:

qi (C ) =

aI,iCi
1+

n
j=1

bI,jC j

+

1+

aII,iCi
,
n
j=1 bII,jC j

(1)

where a and b are the adsorption isotherm parameters and C and
q are the concentrations in the mobile and stationary phases, respectively. Here, we have two different adsorption sites, denoted I
and II in Eq. (1).
To describe the multilayer adsorption, the extended liquid–solid
bi-BET adsorption isotherm can be used [17]:

q(C ) =

aI C

(1 − bL,IC )(1 − bL,IC + bIC )

+

aIIC

(1 − bL,IIC )(1 − bL,IIC + bIIC )
(2)

where a, b, and bL are positive adsorption isotherm parameters.
The parameter b is related to the adsorption to the stationary
phase surface and the parameter bL to adsorption to a layer of previously adsorbed solute [10].
The inverse method [18] was used to estimate the adsorption
isotherm parameters by fitting calculated chromatograms using the

,


E. Glenne, J. Samuelsson and H. Leek et al. / Journal of Chromatography A 1621 (2020) 461048

equilibrium dispersive column model [10] to experimental chromatograms; see Section 3.4 for more details.
3. Experimental section
3.1. Chemicals and material
Carbon dioxide (CO2 , 99.99%) was obtained from AGA Gas AB
(Lidingö, Sweden), while HPLC-grade methanol (MeOH) (>99.9%),
diethylamine (DEA) (≥99.5%), triethylamine (TEA) (99%), and isopropylamine (iPrNH2 ) (≥99.5%) were obtained from Sigma-Aldrich
(St. Louis, MO, USA). As solutes, alprenolol HCL (≥99%), metoprolol tartrate (≥98%), and propranolol HCL (≥99%) were used after
transforming delivered form into free-base form, see Section 3.2 .
All solutes were obtained from Sigma-Aldrich.
A Kromasil Diol (150 × 4.6 mm) column with 5-μm particles
and a pore size of 60 A˚ (Nouryon, Bohus, Sweden) was used. Nitrous oxide (99.998%; Sigma-Aldrich) was used to determine the
˚
“dead volume” of the columns to be 1.69 mL, according to Asberg
et al. [19].
The SFC system was an ACQUITY UPC2 (Waters Corporation,
Milford, MA, USA) in its default configuration with a diode-array
detector and a column oven. A 10-μL loop was used for all injections. The mass flows of both the co-solvent and total eluent were
measured simultaneously using two mini CORI-FLOW M12 Coriolis mass flow meters (Bronkhorst High-Tech B.V., Ruurlo, Netherlands), as described by Glenne et al. [16]. The pressure was measured at the inlet and outlet of the column using two EJX530A absolute pressure transmitters (Yokogawa Electric Corporation, Tokyo,
Japan) [16]. The temperature was measured at the middle of the
column using a PT-100 four-wire resistance temperature detector with an accuracy of ±0.2°C (Pentronic AB, Gunnebo, Sweden)
permanently attached to the column surface using a silver-based
epoxy adhesive (Arctic Silver, CA, USA).
3.2. Procedures
In this study, the free-base forms of the solutes were always used. The solutes in salt form were transformed into freebase form by shaking a 1% solution of the solute salt dissolved
in 100 mM NaOH aqueous solution with an equal volume of
dichloromethane. The dichloromethane phase was then collected
and evaporated.
In all experiments, the backpressure regulator was adjusted to
give an average pressure over the column of 150 bar and the column oven was set to 40 °C. The flow rate was set to 1 mL min–1

in all experiments. The solutes were detected at 220 nm in the
analytical analysis; in the overloaded study, the solute zones were
recorded at 248 nm for alprenolol and metoprolol, at 325 nm for
propranolol, and at 205 nm for the additive zones. All samples
were filtered through a 0.45-μm PTFE filter prior to injection. The
retention volumes were calculated from the peak apex of the elution profiles and the column efficiencies were based on measuring
the peak width at half height.
In the procedure described in Section 4.1, “Analytical-scale analysis”, 1-μL samples of solute were injected; the concentrations
were 0.77 mM for propranolol, 0.75 mM for metoprolol, and
0.80 mM for alprenolol, all dissolved in neat MeOH. The additive
sample contained 0.1 M additive in MeOH, and 2-μL samples of
DEA or TEA or 5-μL samples of iPrNH2 were injected. The retention times of the additives were estimated using the first statistical moment due to the severe degree of peak tailing. For more
information about the DoE study, see Section 3.3.
In Section 4.2, “Overloaded analysis using DEA additive”, 2–8μL volumes of 99.90 mM alprenolol or metoprolol or of 99.95 mM
propranolol were injected using MeOH with 5 mM DEA as the

3

sample diluent. The MeOH content was calculated as the actual
MeOH fraction of 16, 21, or 26% (v/v), according to Section 3.4. DEA
was added to the co-solvent to achieve the overall (total) eluent
concentrations of 0.021, 0.063, and 0.105% (v/v) corresponding to
total eluent concentrations of 2.1, 6.3, and 10.2 mM, respectively.
The experiments described in Section 4.3, “Overloaded analysis
using different amine additives,” also including the additives TEA
and iPrNH2 , were conducted in a similar fashion as for DEA. However, in these experiments, the MeOH content in the mobile phase
was not varied, but was instead fixed at 16% (v/v), and MeOH
was used as the diluent with the different additive amines: either
5 mM TEA or 5 mM iPrNH2 , depending on the additive used. For
comparison purposes, the concentrations of iPrNH2 in the eluent

were 2.5, 7.5, and 12.4 mM and of TEA were 1.5, 4.6, and 7.6 mM,
corresponding to 0.021, 0.063, and 0.105% (v/v) additive in the eluent, respectively.
The additive concentration is often expressed as the additive
fraction added to the co-solvent. This practice, however, results in
a varied amount of additive in the total eluent depending on the
co-solvent fraction. To avoid this variation, we instead express the
additive concentration as the fraction of the total eluent. The additive concentrations used in this study correspond to additive fractions of 0.1, 0.3, and 0.5% (v/v) added to a MeOH fraction of 21%
(v/v) in the eluent. In this context, it should be noted that when
we selected the ranges of co-solvent (MeOH) and additive concentrations, we had in mind that, as well as covering interesting and
practically useful experimental concentration ranges, the analytes
selected should have sufficient solubility.
3.3. Design of experiments
A three-level, two-factor, full-factorial design with three center
points was used to study the variation in the retention factor and
efficiency (number of theoretical plates, N) with the two operational parameters: MeOH fraction and DEA concentration. The actual MeOH fractions were 16, 21, and 26% (v/v) and the DEA concentrations in the eluent were 0.021, 0.063, and 0.105% (v/v). Models were fitted using multiple linear regression implemented in
MODDE 11 (Umetrics AB, Sweden). Statistically insignificant (95%
confidence level) parameters were removed to refine the models.
All regression models had excellent R2 and Q2 values (see Table S.1
in the Supplementary Material). In this study a full factorial three
level design with two factors (CMeOH and CDEA ) was used. For the
regression model, constructed after removing insignificant coefficients at a 95% confidence level, give:
2
2
k = c0 + cCMeOH C MeOH + cCDEA C DEA + cC2 MeOH CMeOH
+ cC2 DEA CDEA
,

(3)

where ci are regression coefficients.

The column efficiency was estimated using the half-height
method and the retention factor was calculated from the retention
volume and column void volume; the latter was determined using
N2 O as non-retained marker [19].
3.4. Calculations
The measured mass flows (total and co-solvent), pressures, and
temperatures were used to estimate the actual average volumetric
flow rates and the actual average volumetric co-solvent fractions,
as described by Glenne et al. [13]. The partial molar volume was
calculated according to Kato et al. [20] and the density was estimated using the Kunz and Wagner [21] equation of state implemented in REFPROP v. 9.1 from the National Institute of Standards
and Technologies (NIST) [22].
The inverse method [18] was used to estimate the adsorption
isotherm parameters in this study (see Section 2). For the alprenolol using DEA as the additive (Fig. 4) and metoprolol with


4

E. Glenne, J. Samuelsson and H. Leek et al. / Journal of Chromatography A 1621 (2020) 461048

iPrNH2 as the additive (Fig. 9), simulated elution profiles were calculated using orthogonal collocation on finite elements [23], and
the bi-Langmuir model was used as the adsorption model, see
Eq. (1). The column efficiency was set to 80 0 0 and the total porosity to 0.678 (calculated from the column dimensions and the ‘dead
time’ t0 measured using an unretained substance); the flow rate
was 1.08 mL min–1 when using DEA and 1.09 mL min–1 when using iPrNH2 as the additive. The isotherm parameters for Fig. 9 were
estimated by fitting simultaneously to the three different additive
(iPrNH2 ) concentration levels in the eluent which makes the fitting
task somewhat more challenging than that in Fig. 4, comprising
only one level of the additive (DEA). For more experimental information regarding the inverse calculations, see Figs. 4 and 9; for the
isotherm parameters, see Table S.3 in the Supplementary Material.
For the propranolol case shown in Fig. 5, the simulated elution

profiles were calculated using a finite volume algorithm [24] and
the bi-BET adsorption model, see Eq. (2), where the total porosity
was 0.69 (calculated from the column dimensions and the ‘dead
time’ t0 measured using an unretained substance) and the flow
rate 1.094 mL min–1 . For the experimental data used for the inverse calculations, see Fig. 5. In addition to estimating the adsorption isotherms in Eq. (2), the inverse method was also used to estimate the number of theoretical plates, N, and time adjustment
factors, t, for the elution profiles, i.e., the elution time is adjusted
by adding the factor t (here we set t = 0 for the largest injection volume). This was done to account for possible delays between injections, flow rate variations inside the column, etc. For
more experimental information regarding the inverse calculations,
see Fig. 5; for the isotherm parameters, see Table S.4 in the Supplementary Material.
4. Results and discussion
Previously, we have shown how different co-solvents can generate peak deformations when they adsorb more strongly to the
stationary phase than does the solute [14,16]. Here, we will systematically investigate the impact on retention and peak/band
shapes of both co-solvent and amine additives in the more
complicated separation systems required for analysis of basic
components.
In a previous study, we learned that with large co-solvent (i.e.,
MeOH) fractions using diol silica as adsorbent, beyond the maximum point of co-solvent excess, MeOH acts more as a modifier
than as an additive (see. Fig. 7 in that study, where that point is
13% (v/v) [13]). To distinguish the effects of the amine as an additive from the co-solvent additive effects, in this study we selected
co-solvent levels of MeOH in the eluent at which the MeOH level
is at least 16% (v/v), well inside the region where the co-solvent
function of MeOH dominates [13,16].
In Section 4.1, “Analytical-scale analysis,” we investigate how
the retentions and peak shapes (efficiency) of analytical-size injections of the three model solutes depend on varying both the
co-solvent fraction and additive composition of the eluent additive
diethylamine (DEA), respectively.
In Section 4.2, we investigate how the shapes of the overloaded
eluted solute bands depend on varying the amount of the DEA additive in the eluent as well as varying the co-solvent (i.e., MeOH)
fraction. Adsorption studies over a broad range of solute concentrations give a complete census of all interactions between the solute
and stationary phases and are required for a deeper understanding of the underlying retention mechanisms of separation systems

[10]. The results were interesting and unexpected, and it was relevant to expand the study with additional overloaded experiments
confirming the generality of the results. Thus, in Section 4.3, we
investigate overloaded elution profiles also using the additives triethylamine (TEA) and isopropylamine (iPrNH2 ), keeping the co-

Fig. 1. Retention factors of the three basic model solutes used in the study, i.e., propranolol, metoprolol, and alprenolol, and the three additives used, i.e., diethylamine
(DEA), triethylamine (TEA), and isopropylamine (iPrNH2 ), versus the MeOH fraction
(v/v) in eluent lacking an amine additive.

solvent MeOH fraction in the eluent constant at 16% (v/v). We
used numerical tools for adsorption isotherm determinations and
mechanistic modeling to analyze the overloaded data generated in
Sections 4.2 and 4.3.
4.1. Analytical-scale analysis
First, we investigated the relative retention of the three basic β receptor antagonist model solutes and the DEA additive with different fractions of MeOH in the eluent without having any DEA additive in the eluent. The model solutes are β -receptor antagonists
with similar structures but different hydrophilicities. The experimental log KD values for metoprolol, alprenolol, and propranolol
are 1.88, 3.10, and 3.56, respectively [25]. Thus, the bulky propranolol containing a naphthyl group, instead of a benzyl group, is
the most hydrophobic of the model solutes (see solute structures
in Fig. S.1 in the Supplementary Material).
Fig. 1 shows the resulting retention factors of all solutes and
amine additives, injected using eluent lacking additive, versus the
MeOH fraction in the eluent. The retention factors of the β receptor antagonists decrease with increasing MeOH content (cf.
Fig. 1); see Table S.2 in the Supplementary Material for the corresponding numerical values. The most hydrophobic solute, propranolol, has much higher retention factors than do the less hydrophobic metoprolol and alprenolol. We can also see that all the
solutes are more retained than is DEA and that the retentions of
the solutes relative to the additive decrease with increasing MeOH
fraction; this observation regarding the relative retentions is in line
with West et al. [8]. With the high MeOH content of 26% (v/v), the
two less retained solutes alprenolol and metoprolol have almost a
combined elution with DEA.
To better investigate the impacts of the co-solvent and additive on retention and efficiency, we employed a DoE approach (see
Section 3.3 for details). In the DoE, the variation of all factors

are simultaneously evaluated in a minimal number of experiments
[26]. In this study a full factorial three-level design with two factors (CMeOH and CDEA ) was used, see Section 3.3 for details. Fig. 2a
presents the centered and normalized coefficients of the model fit
for the retention factors of the solutes, showing that the retentions
decrease with both increasing MeOH fraction and increasing DEA
concentration in the eluent, and that the MeOH fraction has a fivetimes-larger impact on the retention than does the DEA fraction.


E. Glenne, J. Samuelsson and H. Leek et al. / Journal of Chromatography A 1621 (2020) 461048

5

Fig. 2. Centered and normalized coefficients from the DoE model fit for (a) the retention factor and (b) the column efficiency of the analytical-size peaks resulting from
injections of the three β -receptor antagonists using eluents with varying MeOH fractions and DEA concentrations. The error bars represent the 95% confidence intervals of
the coefficients. CMeOH and CDEA are the eluent concentrations of MeOH and DEA, respectively, C2 MeOH and C2 DEA are the corresponding quadratic terms. Fig. S.2 and Table S.1
in the Supplementary Material contain the corresponding response surfaces and regression coefficients, respectively.

Therefore, it is much more effective to use the co-solvent to adjust the solute retention than it is to modulate the additive fraction level. The effect is largest for propranolol, followed by metoprolol and alprenolol; note that this is the same order as the relative retention order shown in Fig. 1. The model contains significant quadratic MeOH and DEA terms visualized as curves in the
response surfaces (see Fig. S.2 in the Supplementary Material).
Starting from zero additive concentration in the eluent and going to the lowest additive level, the solute retention factors decrease strongly with the added additive (see Table S.2 in the Supplementary Material). As soon as normal operative DEA levels have
been reached in the eluent contents, the solute retention factors
decrease only slightly with further increased DEA levels (cf. Table
S.2), in line with SFC studies using ammonium acetate as an additive [4,8,27].
Fig. 2b shows that the impacts of the additive and co-solvent
on column efficiency are comparable in size and that eluents having low MeOH and high DEA contents produce the highest possible column efficiencies. This model contains significant quadratic
DEA factors, visualized as some skewness in the response surfaces in Fig. S.2 (see also Table S.1 in the Supplementary Material,
containing the regression coefficients for the data used in Fig. 2a
and b).
To summarize, the co-solvent fraction is the most important
factor controlling the retention of the basic solutes, whereas both

the co-solvent and additive have an impact on the solutes’ column efficiencies. For the highest possible column efficiencies, separations using eluents with a combined small MeOH fraction
and high DEA content are recommended. Here, one also need to
consider the solutes solubility in the actual eluent composition.
More particularly for this system, the lowest allowed MeOH fraction in the eluent should be selected so that the solutes have
good enough solubility to avoid precipitations in te separation
system.

4.2. Overloaded analysis using DEA additive
The analytical investigation showed that adding the co-solvent
MeOH and the additive DEA to the eluent clearly affects both retention and efficiency. For a deeper investigation aiming at understanding the physico-chemical mechanisms, we have to make
a complete census of all possible sources of interactions between
the solutes and the stationary phase, and thus study the interactions over broad concentration ranges of the solutes—the nonlinear
operational conditions described by Guiochon et al. [10]. We complemented our analytical results with studies of overloaded elution
profiles resulting from the injections of high-concentration samples of the model solutes.
In the analytical section, we can see that alprenolol has the
lowest retention factors of the three model solutes (cf. Fig. 1).
Fig. 3 shows the overloaded elution profiles resulting from injections of four different injection volumes (2–8 μL) of 100 mM alprenolol. In Fig. 3 we see, in agreement with the experimental
design described in Section 4.1, shorter retentions of alprenolol
with increasing MeOH fractions, going from top to bottom, and a
sharpened overloaded elution profile with increasing DEA concentrations, going from left to right. In Fig. 3a we see some sign of
peak deformation at low DEA concentrations, becoming more severe with increasing MeOH fractions in the eluent, going first to
21% (Fig. 3d) and then to 26% (Fig. 3g). This trend to more severe
peak deformation is because, as mentioned in the introduction
(see Section 1), the second of three requirements for perturbationpeak–generated deformation to appear [14,16] is better approached
with a higher MeOH content in the eluent. The first requirement
for perturbation-peak–generated deformation is fulfilled in all cases in
this study, since we use amine additives, not a co-solvent that can
have a dual function, as in the earlier SFC studies of this deformation in which we defined the requirements [14,16]. The second
requirement was that the additive should adsorb more strongly (or

6

E. Glenne, J. Samuelsson and H. Leek et al. / Journal of Chromatography A 1621 (2020) 461048

Fig. 3. Overloaded alprenolol profiles resulting after 2-, 4-, 6-, and 8-μL injections of 100 mM alprenolol eluted with a mobile phase containing increasing DEA contents (left
to right, 0.021, 0.063, and 0.105%) and increasing MeOH fractions (top to bottom, 16, 21, and 26%). The arrows mark the positions of the DEA perturbation peaks.

at an equal strength) to the stationary phase than does the solute
in eluent without co-solvent. From Fig. 1 we can see that it is only
in Fig. 3d and g that the second requirement is approached, using combined low DEA/high MeOH eluent contents, conditions in
which the peak alprenolol and DEA retentions approach, in eluent
lacking DEA (cf. Fig. 1). The third requirement was that the additive
perturbation peak should elute earlier than the solute in the actual eluent co-solvent concentration plateau, which is fulfilled for
all chromatographic conditions in Fig. 3, as indicated by the arrows that mark the perturbation peak positions in the actual chromatographic runs. Thus, and in line with the rule of thumb for
co-solvent acting as the additive in SFC [14,16], the deformations
become more pronounced as the MeOH content increases, while
keeping the DEA content low (cf. Fig. 3d and g).
However, some degree of the perturbation-peak–generated type
of deformation should also be expected for metoprolol at this
MeOH level, which can be seen in the overloaded metoprolol experiments with the highest eluent MeOH 26% (v/v) content (see
Fig. S.3g, in the Supplementary Material). In the analytical section, we could see that the metoprolol has the next shortest retention of the three model solutes and also elutes close to DEA at
the highest MeOH content, i.e., 26% (v/v), in eluents lacking DEA
(cf. Fig. 1). However, the deformations are less pronounced than
those for alprenolol, appearing for metoprolol only at the highest MeOH/lowest DEA contents (cf. Fig. 3g), because the second requirement is not fulfilled at MeOH contents below 26%, unlike for
alprenolol and DEA (cf. Fig. 1).
The perturbation-peak–generated deformations are due to complex competitive interactions between the additive perturbation
zone and the solute zones as they resolve while traveling along
the column, forming internal gradients for each other, as previously
observed for 1-phenyl-1-propanol when the co-solvent MeOH was

acting as the additive [16]. If we can simulate the characteristic deformations using an established column model, such as the equilibrium dispersive column model [10], combined with a mechanistic competitive adsorption model, such as Eq. (1) in Section 2,

this will provide valid confirmation that a competitive mechanism
is the underlying reason for the observed deformations described
above.
The fitting of valid mechanistic models to experimental data is
important, and one always starts with the simplest model, thereafter, if it is needed, select a more complex model. Therefore, the
simple one-site Langmuir competitive model was first tested for
the adsorption of alprenolol and DEA, however, this model failed
to fit the data well. Next, the bi-Langmuir competitive adsorption
isotherm equation, Eq. (1), was used, this two-site model fitted the
data very well (for model coefficients, see Table S.3 in the Supplementary Material). Fig. 4a shows the agreement between experimental (solid lines) and simulated (dotted lines) overloaded alprenolol elution profiles using the competitive bi-Langmuir model,
and Fig. 4b shows the corresponding simulated perturbation signal of the DEA concentration plateau. We can see that the fits are
very good, especially bearing in mind that these deformations have
very unusual and characteristic shapes. Interestingly, the sharp rear
of the negative perturbation zone of DEA has a combined elution
with the rear of the alprenolol zone. Since the mechanistic simulations fit the experimental profiles so well, we can conclude that
the sharp rear part of the eluted alprenolol band is the result of
a complex competitive interplay with the rear of the DEA zone as
the zones travel along the column (cf. Fig. 4a and b).
Propranolol is the most hydrophobic and bulky of the three
model solutes (cf. Fig. S.1); it has much higher analytical retention factors that are always well resolved from the DEA peak, as
seen in the analytical section (cf. Fig. 1 and Table S.2). The important second requirement for perturbation-peak–generated deformations is far from being fulfilled. Therefore, when overloaded injections of propranolol are made, we cannot expect a similar tendency
for deformations of a competitive nature as discussed above for alprenolol and metoprolol. The overloaded experimental propranolol
profiles can be seen as the solid lines in the subplots in Fig. 5 with
varying MeOH and DEA contents in the eluent. Surprisingly, there
are also deformations for propranolol, but these deformations in-


E. Glenne, J. Samuelsson and H. Leek et al. / Journal of Chromatography A 1621 (2020) 461048

Fig. 4. (a) Comparison between simulated (dotted lines) and experimental (solid
lines) overloaded solute elution profiles resulting after 2-, 4-, 6-, and 8-μL injections of 100 mM alprenolol. (b) The corresponding simulated DEA concentration
plateau perturbations (dashed lines). The mobile phase contained 21% (v/v) MeOH
and 0.021% DEA. The simulations are based on the binary competitive bi-Langmuir
adsorption isotherm model, i.e., Eq. (1) in Section 2; for the best bi-Langmuir model
coefficients, see Table S.3 in the Supplementary Material.

7

stead become more pronounced with decreasing MeOH fractions
in the eluent (bottom to top in Fig. 5) and with increasing amine
additive contents in the eluent (left to right in Fig. 5), finally resulting in clearly overloaded anti-Langmuirian profiles (cf. Fig. 5c).
Thus, the deformations of the overloaded propranolol bands
display a completely opposite pattern to those of the earliereluting model solutes alprenolol and metoprolol. For these two latter solutes, which fulfill the requirements for perturbation-peak–
generated deformations, the overloaded deformations are most pronounced at high MeOH/low DEA contents in the eluent (for alprenolol see Fig. 3g and for metoprolol see Fig. S.3g). For propranolol, however, under these conditions the deformations do not
appear at all; in contrast, at the highest MeOH/lowest DEA contents, the overloaded propranolol displays a “normal” overloaded
Langmuirian band shape (see Fig. 5g). If we now, starting from this
position, decrease the MeOH content in the eluent while keeping
the DEA content constant, i.e., moving upwards in the left column
from Fig. 5g to 5a using 26% MeOH, we can see how the Langmuir profiles become successively deformed, developing a hump at
the front at the lowest MeOH content (16%), as shown in Fig. 5a.
Now, moving from this position and increasing the DEA content
while keeping the lowest MeOH content of 16%, i.e., moving from
Fig. 5a to c, we see how the overloaded propranolol is transformed,
in a fascinating way, from being a deformed band with a hump in
front (Fig. 5a) to a nice classical anti-Langmuirian profile (Fig. 5c).
This pattern is completely opposite to that displayed by the more
hydrophilic solutes alprenolol (cf. Fig. 3) and metoprolol (cf. Fig.
S.3), strongly indicating a completely different underlying mechanism for the deformation of the bulkier, hydrophobic model solute,

propranolol.
We more closely inspected the overloaded propranolol elution
profiles for the largest load at 16% (v/v) MeOH and the lowest DEA
concentration in the eluent in Fig. 5. The propranolol elution profile initially has a relatively sharp front at the lower concentra-

Fig. 5. Overloaded experimental (solid lines) and simulated (dotted lines) elution profiles for 2-, 4-, 6-, and 8-μL injections of 100 mM propranolol eluted with increasing
DEA contents in the eluent (left to right, 0.021, 0.063, and 0.105%) and with increasing MeOH contents (top to bottom, 16, 21, and 26%). The arrows mark the position of the
DEA perturbation peaks. The simulations (dotted lines) are based on the single-component bi-BET adsorption isotherm model, i.e., Eq. (2) in Section 2; for model coefficients
and model agreement, see Table S.4 in the Supplementary Material.


8

E. Glenne, J. Samuelsson and H. Leek et al. / Journal of Chromatography A 1621 (2020) 461048

Fig. 6. Adsorption isotherms of propranolol at different eluent compositions. (a) Constant MeoH fraction of 16% (v/v) and varying DEA contents of 0.021, 0.063, and 0.105%
(v/v). (b) Constant DEA content of 0.063% (v/v) and varying MeOH fractions of 16, 21, and 26% (v/v). The adsorption isotherm of propranolol eluted with 16% (v/v) MeOH
and 0.021% (v/v) DEA has an inflection point, indicated by the green circle in (a).

tions, which becomes dispersed at higher concentrations, whereas
the tail is sharp at higher concentrations and becomes dispersed at
lower concentrations (cf. Fig. 5a). Thus, the overloaded band shape
cannot be described by a Type I isotherm (Langmuirian), which
has a convex upwards curvature that flattens out. The profiles in
Fig. 5a instead indicate that the adsorption isotherm is of Type II
[28,29], with an initial convex upwards curvature (as in Type I)
that, instead of flattening out, becomes a concave (upwards) curvature. With higher additive concentrations (Fig. 5b to c), the overloaded solute profile instead becomes anti-Langmuirian, indicating that the adsorption isotherm is of Type III [28,29], with only
a concave (upwards) curvature, i.e., the isotherm does not flatten
out. Both Type II and III adsorption models are multilayer models
[10] and could be described using the BET adsorption model.

The adsorption isotherm parameters for the elution profiles
for propranolol were estimated using the inverse method (see
Section 3.4). Several adsorption isotherm models that could describe multilayer or solute–solute interactions (i.e., the Moreau,
bi-Moreau, and BET models) were evaluated, but only the bi-BET
model agreed well with all the experimental data. In Fig. 5, the
dotted lines show the simulated overloaded elution profiles of propranolol using the estimated bi-BET adsorption isotherm. We can
see how perfectly the bi-BET model (dotted lines) bands agree with
the corresponding experimental (solid lines) bands. For model coefficients and model agreement terms, see Table S.4 in the Supplementary Material.
Fig. 6 shows the propranolol adsorption isotherms for (a) varying DEA contents but a constant MeOH fraction of 16% (v/v) and
for (b) varying MeOH fractions but a constant DEA content of
0.063%. The adsorption isotherm for propranolol eluted with 16%
(v/v) MeOH and 0.021% DEA is of Type II, with an inflection
point marked by the circle in Fig. 6a (green line). With increasing DEA concentrations but a constant MeOH fraction, the adsorption isotherm becomes concave (upwards), indicating transformation from a Type II to Type III isotherm (red line in Fig. 6a) in
which adsorbed solute–solute interactions become dominant. With
a constant DEA concentration but increasing MeOH fractions in
the eluent, the isotherm is transformed from Type III to Type I
(Fig. 6b). There is an enhanced tendency for multilayer formation
with increasing DEA concentrations and decreasing MeOH fractions
with propranolol as the solute, as indicated by the overloaded elution shapes in Fig. 5b and c.
A possible underlying explanation for the layer formation is
the kosmotrope effect, in which hydrophobic interactions are favored. Kosmotropic ions usually have a large charge density and

Fig. 7. Retention factors of the β -receptor antagonists and the additive perturbation
peaks investigated in this study with 16% (v/v) MeOH in the eluent with different
amine additives: (a) iPrNH2 , (b) DEA, and (c) TEA.

interact strongly with water, tending to increase the order of the
water structure [30]. These so-called structure makers are commonly used for “salting-out” proteins by aggregating them. The
ions compete for the water molecules originally associated with
the protein surface, and in that way promote hydrophobic interactions between proteins that result in protein precipitation. The

order of the kosmotropic effect can be related to the Hofmeister series, in which ions are arranged according to their ability to
precipitate proteins [31]. In the Hofmeister series, the ammonium
salts are classified as kosmotropic agents [32]. Consequently, amine
additives may promote hydrophobic interactions that enhance the
solute–solute interactions, especially in the hydrophobic parts of a
molecule, for example, the naphthyl group in propranolol.


E. Glenne, J. Samuelsson and H. Leek et al. / Journal of Chromatography A 1621 (2020) 461048

9

Fig. 8. Overloaded metoprolol elution profiles for 2-, 4-, 6-, and 8-μL injections of 100 mM metoprolol eluted with 16% (v/v) MeOH and increasing additive contents (left
to right, 0.021, 0.063, and 0.105%) in the eluent, with different additives in the eluent: (a–c) iPrNH2 , (d–f) DEA, and (g–i) TEA. The arrows mark the position of the additive
perturbation peak.

4.3. Overloaded analysis using different amine additives
To confirm the generality of our conclusions, we expanded the
model separation system by using two other common SFC amine
additives: isopropylamine (iPrNH2 ) and triethylamine (TEA). These
additives were selected to cover the difference between primary,
secondary, and tertiary amines as well as because they are commonly used for separating amines in SFC [3,33,34].
First, we investigated the relative retentions of the solutes and
these additives with different fractions of MeOH in the eluent
without having the additive in the eluent. In Fig. 1 we can see
the retention factors of these additives together with the analytical size retention factors of the three β -receptor antagonists and
of DEA, versus the MeOH fraction in eluent lacking additive. As a
reminder, in this plot the amine additives are also injected as if they
were solutes. Fig. 1 shows that all model solutes are more retained
than are the amine additives used in this study and that iPrNH2

adsorbs somewhat more strongly to the stationary phase than does
DEA (already studied above), whereas TEA adsorbs somewhat more
weakly than does DEA (cf. Fig. 1 and Table S.2). The adsorption
strength of the amines to the stationary phase is in line with their
order concerning increasing capability for forming hydrogen bonding: primary amine > secondary amine > tertiary amine.
In Fig. 7, the retention factors of all solutes and the perturbation
peaks of all amine additives are plotted versus different amounts
of additive in the eluent using 16% (v/v) MeOH in the eluent. As in
the case with DEA as the additive, adding even small amounts of
additive to the eluent, compared with no additive, drastically affects the retention (cf. Table S.2 in the Supplementary Material).
The amine additive iPrNH2 is more potent at reducing the retention factors of the solutes, followed by DEA and finally by TEA (cf.
Fig. 7); this is the same order as the additives’ relative adsorption
to the stationary phase when injected into eluent lacking additive
(cf. Fig. 1). Inspecting the retentions of the perturbation peaks using 16% (v/v) MeOH in the eluent, one can observe that the iPrNH2

perturbation peak has higher retention factors than does alprenolol
but co-elutes more or less with metoprolol (cf. Fig. 7a and Table S.2). The DEA perturbation peak (Fig. 7b) always elutes earlier
than do the solutes, but metoprolol and especially alprenolol elute
very close to the perturbation peak, especially with high MeOH
contents, which is why it displays the perturbation-peak–generated
competitive type of deformation (cf. Fig. 3d and g; and Fig. S.3g).
The TEA perturbation peak always elutes earlier than the solutes
even with high MeOH contents (Fig. 7c), so we should not expect
any competitive deformations of any of the three model solutes
when using TEA as the additive in this separation system. Now let
us investigate what happens when we perform overloaded studies
using the amine additives iPrNH2 and TEA, respectively, and compare this with what we have already seen regarding how DEA affected the solute peak shapes.
Fig. 8 shows the overloaded solute elution profiles resulting
from 2 to 8-μL injections of 100 mM metoprolol with a constant 16% (v/v) MeOH content in the eluent and increasing concentrations of different additives. Inspecting the elution profiles in
the top row using iPrNH2 (Fig. 8a–c), severely deformed elution

profiles can be observed, and the metoprolol band deformation
changes strongly with the increasing amount of iPrNH2 in the eluent, from left (Fig. 8a) to right (Fig. 8c). On the other hand, no peak
deformations appear under the same operational conditions in the
middle row using the DEA additive (see Fig. 8d–f) or in the bottom row using the TEA additive (see Fig. 8g–i). This observation is
in line with Fig. 7, that one could expect solute peak deformation
due to co-elution or elution close to the perturbation peak to be
more severe for metoprolol using iPrNH2 than using DEA or TEA.
By visually comparing the overloaded metoprolol elution profiles
formed when using the less retained TEA in the eluent (Fig. 8g–i),
it is evident that TEA as the additive does not sharpen and concentrate the preparative peaks as efficiently as does using DEA as
the additive (Fig. 8d–f). This was confirmed using alprenolol as the
solute (see Fig. S.4 in the Supplementary Material). The last obser-


10

E. Glenne, J. Samuelsson and H. Leek et al. / Journal of Chromatography A 1621 (2020) 461048

Fig. 9. (a–c) Overloaded experimental (solid lines) and simulated (dotted lines) elution profiles for 8-μL injections of 100 mM metoprolol with different amounts of iPrNH2
in the eluent. (d–e) Corresponding simulated concentration plateau perturbations of iPrNH2 (dashed lines); here d corresponds to a, e to b, and f to c. The eluent contained
16% (v/v) MeOH with 0.021% (a, d), 0.063% (b, e), and 0.105% (c, f) iPrNH2 . The simulations are based on the binary competitive bi-Langmuir adsorption isotherm model, i.e.,
Eq. (1) in Section 2; for the model coefficients, see Table S.3 in the Supplementary Material.

Fig. 10. Overloaded elution profiles for 2-, 4-, 6-, and 8-μL injections of 100 mM propranolol eluted with 16% (v/v) MeOH and increasing additive contents (left to right,
0.021, 0.063, and 0.105%) in the eluent, and different additives in the eluent: (a–c) isopropylamine (iPrNH2 ), (d–f) diethylamine (DEA), and (g–i) trietylamine (TEA). The
arrows mark the amine additive perturbation peak position.

vation is very interesting because the purpose of using an amine
additive is to improve the separation performance.
The transformation of the deformed elution profiles when overloaded metoprolol is eluted with increasing iPrNH2 levels in the

eluent, as described above (cf. Fig. 8a–c), should be most interesting to understand mechanistically. Therefore, adsorption parameters assuming a competitive bi-Langmuir model describing the ad-

sorption competition between metoprolol and iPrNH2 were estimated using the inverse method, and the parameters were used
to simulate the elution profiles. In Fig. 9a–c, the most overloaded
experimental elution profiles (following 8-μL injections) are compared with the corresponding simulated profiles using different
amounts of iPrNH2 in the eluent. The model fits very nicely to the
characteristic and unusual solute band shapes at medium and high


E. Glenne, J. Samuelsson and H. Leek et al. / Journal of Chromatography A 1621 (2020) 461048

additive levels (cf. Fig. 9b and c) but less accurately to the more
withdrawn solute band shape at the low additive case (cf. Fig. 9a);
the reason for the latter can be that the isotherm parameter estimation for the data in the figure were estimated by fitting simultaneously to the three different additive (iPrNH2 ) concentration levels resulting in lower relative weight on the low additive concentration data of Fig 9a. In the bottom row of the Figure (Fig. 9d–f),
the corresponding simulated concentration plateaus of the additive
are shown; here it is remarkable how well these simulated additive perturbations reflects the unusual experimental top row solute
shapes, i.e. the experimental and simulated profiles in Fig 9a–c, in
this case even the weird profile region of Fig 9a was well captured.
Thus, acceptable model agreement was found using the same adsorption parameters for all iPrNH2 concentrations. This confirms
that the cause of these deformations is competition between the
additive and the solute, as also observed for alprenolol using DEA
as the additive (cf. Fig. 4).
We can also confirm the other type of deformation mechanism
observed for propranolol when the elution profile moves from a
Langmuirian towards an anti-Langmuirian shape when using DEA as
the additive (cf. Fig. 5). Fig. 10 presents the overloaded shapes of
propranolol with use of the three different additives. In line with
our hypothesis, the effect is clearly more pronounced with iPrNH2
(Fig. 10a–c) in the eluent, and the profile turns towards an antiLangmuirian shape with a lower additive content than when using
DEA as the additive (Fig. 10d–f). This suggests that the multilayer

tendency is stronger for propranolol separated using iPrNH2 rather
than DEA in the eluent. TEA seems to be the weakest additive, and
the elution profile for propranolol eluted with a small fraction of
TEA is Langmuirian, and multilayer characteristics are first observed
with higher amounts of additive in the eluent. Many primary, secondary, tertiary, and quaternary amines have a positive Jones−Dole
viscosity B coefficient [35] and therefore are kosmotropic agents
[36]. This result indicates that if a certain volume fraction of amine
additive is added to the co-solvent, iPrNH2 will promote multilayer
formation the strongest, followed by DEA and then TEA.
5. Conclusions and practical implications
For compounds containing amine functional groups there is often a need, except having a co-solvent in the eluent, to also add an
additive to the eluent to achieve acceptable peak shapes for both
analytical and preparative purposes. To understand the impact that
different compounds in the mobile phase have on retention and
peak shape, we undertook an analytical and overloaded investigation combined with design of experiments modeling and fundamental numerical modeling, respectively. The model system comprised three β -receptor antagonists as model solutes, a Diol column as the stationary phase, and CO2 with varied MeOH fractions
and additive concentrations in the eluent.
Using design of experiments, the co-solvent fraction and the additive concentration were investigated. It was shown that (i) the
co-solvent fraction is the most important factor controlling the retention and that (ii) the highest analytical peak efficiency is obtained by using eluents containing small fractions of MeOH and
high amine additive contents. In the model system used in this
study the solubility of the model solutes was good enough, but
if that should not be the case, it is not recommended using such
small MeOH fractions.
In the overloaded analysis, it could be concluded that more compact elution zones are generally observed when using a larger fraction of amine additives in the eluent. Also, two different types of
peak deformations were observed. The first type of deformation
probably results from the tag-along effect as the solute elutes close
to the additive perturbation peak. For the second type of deformation concerning a later-eluting solute, the adsorption study re-

11

vealed that the deformation was caused by multilayer adsorption.

In this case, the amine additive probably acts as a kosmotropic
agent promoting the multilayer adsorption of solutes to the stationary phase. Multilayer formation is strongly dependent on the
type of amine additive used, with the additive iPrNH2 promoting
multilayer formation the strongest, followed by the additives DEA
and then TEA.
A related topic is “stacked injections” [37], an approach often
used to increase the productivity of preparative separation. In this
approach, the next injection is made before the complete elution of
the current cycle. The cycle time of an injection is defined as the
difference between the time when the first-eluting component exceeds a certain threshold concentration and when the elution profile of the last-eluting component drops below this concentration.
The goal when conducting stacked injections is to have these cycles as close together as possible: if they are too far apart productivity will decrease, and if they are too close together, the new cycle might be affected by the previous injection, possibly deforming
the elution profiles. It should be noted that here we have an “invisible” additive, and it might be necessary to take this into account
when setting the cycle time. In previous LC studies we have shown
that in certain cases the additive must be taken into account [38],
while in others it can be ignored [39]. The conditions when the
additive must be taken into account, and when it can safely be ignored, remain to be systematically investigated. In the meantime,
we recommend studying the peak shapes when using the stacked
injection mode; if deformations occur that degrade separation performance, the most practical action is to increase the cycle time.
Declaration of Competing Interest
The authors declare that they have no conflict of interest.
CRediT authorship contribution statement
Emelie Glenne: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing - original draft, Writing - review & editing, Visualization. Jörgen Samuelsson: Conceptualization, Methodology, Software, Validation, Formal analysis,
Data curation, Writing - original draft, Writing - review & editing, Supervision. Hanna Leek: Conceptualization, Resources, Writing - original draft, Writing - review & editing. Patrik Forssén:
Software, Formal analysis, Writing - original draft, Visualization.
Magnus Klarqvist: Conceptualization, Resources, Writing - original
draft, Writing - review & editing. Torgny Fornstedt: Conceptualization, Methodology, Data curation, Writing - original draft, Writing
- review & editing, Supervision, Project administration, Funding acquisition.
Acknowledgements
This work was supported by the Swedish Knowledge Foundation via the KKS SYNERGY project “BIO-QC: Quality Control and Purification for New Biological Drugs” (grant number 20170059) and
by the Swedish Research Council (VR) via the project “Fundamental

Studies on Molecular Interactions aimed at Preparative Separations
and Biospecific Measurements” (grant number 2015–04627).
Supplementary materials
Supplementary material associated with this article can be
found, in the online version, at doi:10.1016/j.chroma.2020.461048.
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