Fundamental Investigations of Adsorption in SFC …1371010/FULLTEXT02.pdfIn supercritical fluid...

Fundamental Investigations of Adsorption in SFC

Emelie Glenne


In supercritical fluid chromatography (SFC), the eluent is composed by carbon dioxide, often with additional components, in a condition between gas and liquid. This thesis aims to reach a deeper understanding of SFC by revealing the function of the additional eluent components through systematic adsorption studies.

In Paper I, investigation of surface excess adsorption isotherms of methanol revealed that a monolayer of methanol was formed. In Paper II, severe peak deformation effects due to this adsorption were shown. The findings in these papers revealed that a competitive additive model best predicts the solute retention at low methanol fractions whereas at higher fractions, methanol acts just as a modifier. In Paper III, the generality of the effects was proven by investigation of several co-solvent and stationary phase combinations. In Paper IV it was investigated how the robustness of SFC separations depend on the co-solvent adsorption, pressure, and temperature. In Paper V, the impact of the addition of amine additives was investigated. Two different mechanisms for solute peak deformations were observed.

The knowledge achieved about SFC in this theses provides guidelines for development of more robust SFC methods where peak deformations/distortions can be avoided.

DOCTORAL THESIS | Karlstad University Studies | 2020:3

Faculty of Health, Science and Technology

Chemistry


ISSN 1403-8099

ISBN 978-91-7867-080-2 (pdf)

ISBN 978-91-7867-070-3 (print)



Emelie Glenne



Emelie Glenne

Print: Universitetstryckeriet, Karlstad 2020

Distribution:Karlstad University Faculty of Health, Science and TechnologyDepartment of Engineering and Chemical SciencesSE-651 88 Karlstad, Sweden+46 54 700 10 00

© The author

ISSN 1403-8099

urn:nbn:se:kau:diva-75766

Karlstad University Studies | 2020:3

DOCTORAL THESIS

Emelie Glenne


WWW.KAU.SE

ISBN 978-91-7867-080-2 (pdf)

ISBN 978-91-7867-070-3 (print)

Print: Universitetstryckeriet, Karlstad 2020

Distribution:Karlstad University Faculty of Health, Science and TechnologyDepartment of Engineering and Chemical SciencesSE-651 88 Karlstad, Sweden+46 54 700 10 00

© The author

ISSN 1403-8099

urn:nbn:se:kau:diva-75766

Karlstad University Studies | 2020:3

DOCTORAL THESIS

Emelie Glenne


WWW.KAU.SE

ISBN 978-91-7867-080-2 (pdf)

ISBN 978-91-7867-070-3 (print)

1

Abstract

In supercritical fluid chromatography (SFC) the mobile phase is com-posed by carbon dioxide as the main weak solvent, in a condition be-tween a gas and a liquid. The interest in SFC has recently increased due to several advantages compared to traditional liquid chromatography (LC) such as faster sample throughput and lower environmental im-pact. However, there is still a lack of fundamental knowledge about SFC, among others, due to the compressible mobile phase. This thesis work aims at a deeper understanding of the functions of the mobile phase components used in SFC through systematic adsorption studies. In Paper I, surface excess adsorption isotherms of the co-solvent methanol on a diol silica adsorbent was investigated. It was revealed that a monolayer of methanol was formed. In Paper II, severe peak deformation effects due to this adsorption were revealed, and it was demonstrated under which conditions these deformations appear and how the co-solvent fraction can tune the shape of the eluted peak. The findings in these papers revealed that a competitive additive model best predicts the solute retention at low methanol fractions whereas at higher fractions, when a solvent layer has formed, methanol acts just as a modifier. In Paper III, the generality of the effects was proven by investigations of other co-solvent/stationary phase combinations. In Paper IV it was investigated how the robustness of SFC separations depend on the co-solvent adsorption, pressure, and temperature. In Paper V, the impact of the addition of amine additives on separation performance was investigated. Two different underlying mechanisms for solute peak distortions were revealed: (i) deformations generated by the perturbation peak and (ii) deformation due to multilayer for-mation promoted by the additive. The deeper knowledge about SFC obtained in this thesis provides guidelines for development of more robust SFC methods for analysis and preparative separations where peak distortions can be avoided.

1

Abstract

In supercritical fluid chromatography (SFC) the mobile phase is com-posed by carbon dioxide as the main weak solvent, in a condition be-tween a gas and a liquid. The interest in SFC has recently increased due to several advantages compared to traditional liquid chromatography (LC) such as faster sample throughput and lower environmental im-pact. However, there is still a lack of fundamental knowledge about SFC, among others, due to the compressible mobile phase. This thesis work aims at a deeper understanding of the functions of the mobile phase components used in SFC through systematic adsorption studies. In Paper I, surface excess adsorption isotherms of the co-solvent methanol on a diol silica adsorbent was investigated. It was revealed that a monolayer of methanol was formed. In Paper II, severe peak deformation effects due to this adsorption were revealed, and it was demonstrated under which conditions these deformations appear and how the co-solvent fraction can tune the shape of the eluted peak. The findings in these papers revealed that a competitive additive model best predicts the solute retention at low methanol fractions whereas at higher fractions, when a solvent layer has formed, methanol acts just as a modifier. In Paper III, the generality of the effects was proven by investigations of other co-solvent/stationary phase combinations. In Paper IV it was investigated how the robustness of SFC separations depend on the co-solvent adsorption, pressure, and temperature. In Paper V, the impact of the addition of amine additives on separation performance was investigated. Two different underlying mechanisms for solute peak distortions were revealed: (i) deformations generated by the perturbation peak and (ii) deformation due to multilayer for-mation promoted by the additive. The deeper knowledge about SFC obtained in this thesis provides guidelines for development of more robust SFC methods for analysis and preparative separations where peak distortions can be avoided.

2

Contents

Abstract ...................................................................................................... 1

Contents ..................................................................................................... 2

List of Papers ............................................................................................. 3

Abbreviations ............................................................................................. 5

1 Introduction .................................................................................... 6

1.1 Supercritical fluid chromatography ............................................... 8 1.2 Aim ............................................................................................. 16

2 Theory and methodology ............................................................. 17

2.1 Determination of density, volumetric flow and volume fraction in SFC mobile phases ................................................................................ 17 2.2 Simulation of chromatographic separations ................................ 20 2.3 Adsorption isotherms .................................................................. 21 2.4 Peak deformations ...................................................................... 31

3 Discussion of papers ................................................................... 36

3.1 Paper I ........................................................................................ 36 3.2 Paper II ....................................................................................... 38 3.3 Paper III ...................................................................................... 40 3.4 Paper IV ..................................................................................... 43 3.5 Paper V ...................................................................................... 47

4 Conclusion and guidelines .......................................................... 52

Summary in Swedish ............................................................................... 54

Acknowledgment ..................................................................................... 57

References ................................................................................................ 58

2

Contents

Abstract ...................................................................................................... 1

Contents ..................................................................................................... 2

List of Papers ............................................................................................. 3

Abbreviations ............................................................................................. 5

1 Introduction .................................................................................... 6

1.1 Supercritical fluid chromatography ............................................... 8 1.2 Aim ............................................................................................. 16

2 Theory and methodology ............................................................. 17

2.1 Determination of density, volumetric flow and volume fraction in SFC mobile phases ................................................................................ 17 2.2 Simulation of chromatographic separations ................................ 20 2.3 Adsorption isotherms .................................................................. 21 2.4 Peak deformations ...................................................................... 31

3 Discussion of papers ................................................................... 36

3.1 Paper I ........................................................................................ 36 3.2 Paper II ....................................................................................... 38 3.3 Paper III ...................................................................................... 40 3.4 Paper IV ..................................................................................... 43 3.5 Paper V ...................................................................................... 47

4 Conclusion and guidelines .......................................................... 52

Summary in Swedish ............................................................................... 54

Acknowledgment ..................................................................................... 57

References ................................................................................................ 58

3

List of Papers

This thesis is based on the following papers, from here on referred to by their Roman numerals. Reprints are appended at the end of this the-sis with permission from the publisher.

I A closer study of methanol adsorption and its impact on solute retentions in supercritical fluid chromatog-raphy. Emelie Glenne, Kristina Öhlén, Hanna Leek, Magnus Klarqvist, Jörgen Samuelsson, Torgny Fornstedt. Journal of Chromatography A, 1442, 129-139 (2016), http://dx.doi.org/10.1016/j.chroma.2016.03.006

II Peak deformations in preparative supercritical fluid

chromatography due to co-solvent adsorption. Emelie Glenne, Hanna Leek, Magnus Klarqvist, Jörgen Samuelsson, Torgny Fornstedt. Journal of Chromatography A, 1468, 200-208 (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.019

III Systematic investigations of peak deformations due to

co-solvent adsorption in preparative supercritical fluid chromatography. Emelie Glenne, Hanna Leek, Magnus Klarqvist, Jörgen Samuelsson, Torgny Fornstedt. Journal of Chromatography A, 1496, 141-149 (2017), http://dx.doi.org/10.1016/j.chroma.2017.03.053

IV Unexpected impact of methanol adsorption on the ro-bustness of analytical supercritical fluid chromatog-raphy. Emelie Glenne, Marek Le ko, Jörgen Samuelsson and Torgny Fornstedt. Manuscript

V Systematic investigations of peak distortions due to ad-ditives in supercritical fluid chromatography. Emelie Glenne, Jörgen Samuelsson, Hanna Leek, Magnus Klarqvist, Torgny Fornstedt. Submitted to Journal of Chromatography A, January 2020.

3

List of Papers

This thesis is based on the following papers, from here on referred to by their Roman numerals. Reprints are appended at the end of this the-sis with permission from the publisher.

I A closer study of methanol adsorption and its impact on solute retentions in supercritical fluid chromatog-raphy. Emelie Glenne, Kristina Öhlén, Hanna Leek, Magnus Klarqvist, Jörgen Samuelsson, Torgny Fornstedt. Journal of Chromatography A, 1442, 129-139 (2016), http://dx.doi.org/10.1016/j.chroma.2016.03.006

II Peak deformations in preparative supercritical fluid

chromatography due to co-solvent adsorption. Emelie Glenne, Hanna Leek, Magnus Klarqvist, Jörgen Samuelsson, Torgny Fornstedt. Journal of Chromatography A, 1468, 200-208 (2016), http://dx.doi.org/10.1016/j.chroma.2016.09.019

III Systematic investigations of peak deformations due to

co-solvent adsorption in preparative supercritical fluid chromatography. Emelie Glenne, Hanna Leek, Magnus Klarqvist, Jörgen Samuelsson, Torgny Fornstedt. Journal of Chromatography A, 1496, 141-149 (2017), http://dx.doi.org/10.1016/j.chroma.2017.03.053

IV Unexpected impact of methanol adsorption on the ro-bustness of analytical supercritical fluid chromatog-raphy. Emelie Glenne, Marek Le ko, Jörgen Samuelsson and Torgny Fornstedt. Manuscript

V Systematic investigations of peak distortions due to ad-ditives in supercritical fluid chromatography. Emelie Glenne, Jörgen Samuelsson, Hanna Leek, Magnus Klarqvist, Torgny Fornstedt. Submitted to Journal of Chromatography A, January 2020.

4

My contribution to the papers included in the thesis were: Paper I: I did most of the planning, performed all the experiments and calculations, and wrote the manuscript together with my co-au-thors. Paper II: I did most of the planning, performed all the experiments, did some of the calculations, and wrote most of the manuscript to-gether with my co-authors. Paper III: I did most of the planning, performed all the experiments, did calculations, and wrote most of the manuscript together with my co-authors. Paper IV: I did the planning, the experiments and most of the calcu-lations, except the heat calculations, and wrote the manuscript with my co-authors. Paper V: I did most of the planning, performed all the experiments, did all calculations, except the estimation of the adsorption isotherm with the inverse method for propranolol, and wrote most of the man-uscript together with my co-authors. Paper not Included in the Thesis

VI Investigation of robustness for supercritical fluid chro-

matography separation of peptides: Isocratic vs gradi-ent mode. Martin Enmarknika Langborg Weinmann, Tomas Leek, Krzysztof Kaczmarski, Magnus Klarqvist, Jörgen Samuelsson, and Torgny Fornstedt, Journal of Chromatography A, 1568, (2018) 177-187. https://doi.org/10.1016/j.chroma.2018.07.029

4

My contribution to the papers included in the thesis were: Paper I: I did most of the planning, performed all the experiments and calculations, and wrote the manuscript together with my co-au-thors. Paper II: I did most of the planning, performed all the experiments, did some of the calculations, and wrote most of the manuscript to-gether with my co-authors. Paper III: I did most of the planning, performed all the experiments, did calculations, and wrote most of the manuscript together with my co-authors. Paper IV: I did the planning, the experiments and most of the calcu-lations, except the heat calculations, and wrote the manuscript with my co-authors. Paper V: I did most of the planning, performed all the experiments, did all calculations, except the estimation of the adsorption isotherm with the inverse method for propranolol, and wrote most of the man-uscript together with my co-authors. Paper not Included in the Thesis

VI Investigation of robustness for supercritical fluid chro-

matography separation of peptides: Isocratic vs gradi-ent mode. Martin Enmarknika Langborg Weinmann, Tomas Leek, Krzysztof Kaczmarski, Magnus Klarqvist, Jörgen Samuelsson, and Torgny Fornstedt, Journal of Chromatography A, 1568, (2018) 177-187. https://doi.org/10.1016/j.chroma.2018.07.029

5

Abbreviations

2-EP 2-Ethylpyridine-bonded silica BET Brunauer, Emmett, and Teller BPR Back pressure regulator

Diethylamine DoE Design of experiments ECP Elution by characteristic point ED Equilibrium-Dispersive EoS Equation of State GC Gas chromatography HPLC High-performance LC iPrNH2 Isopropyl amine LC Liquid chromatography LSS Linear solvent strength OCFE Orthogonal collocation on finite elements PP Perturbation peak REFPROP Reference fluid thermodynamic and transport

properties database SFC Supercritical fluid chromatography

Triethylamine TP Tracer pulse UHPLC Ultra-high-performance LC UHPSFC Ultra-high-performance SFC

5

Abbreviations

2-EP 2-Ethylpyridine-bonded silica BET Brunauer, Emmett, and Teller BPR Back pressure regulator

Diethylamine DoE Design of experiments ECP Elution by characteristic point ED Equilibrium-Dispersive EoS Equation of State GC Gas chromatography HPLC High-performance LC iPrNH2 Isopropyl amine LC Liquid chromatography LSS Linear solvent strength OCFE Orthogonal collocation on finite elements PP Perturbation peak REFPROP Reference fluid thermodynamic and transport

properties database SFC Supercritical fluid chromatography

Triethylamine TP Tracer pulse UHPLC Ultra-high-performance LC UHPSFC Ultra-high-performance SFC

6

1 Introduction

Chromatography is defined as a separation method in which the com-ponents to be separated are distributed between a stationary and a mo-bile phase [1]. The major different forms of chromatography are gas chromatography (GC), liquid chromatography (LC), and supercritical chromatography (SFC). Depending on the purpose, chromatography can be applied in either analytical or preparative mode. Analytical chromatography aims at obtaining quantitative and quali-tative information about components in a sample. Here, small sample amounts are injected, and the required information is obtained from the heights or areas of the eluted solute peaks. The concentration of solutes adsorbed on the stationary phase is proportional to the concen-tration of the solutes in the mobile phase and a further increased solute concentration, C, results in a proportional increase of the stationary phase concentration, q, (see the initial slope, blue line, in Figure 1). The column is, thus, operated under linear conditions, and the detector re-sponse will result in symmetrical Gaussian peaks (see inset in Figure 1). For reliable quantitative information, the peaks need to be well-re-solved and, preferably, more or less symmetrical. Preparative chromatography aims at isolating large amounts of de-sired target components from a complex sample mixture. The column is often operated under overloaded conditions, and a further increase of the sample load will result in a lower fraction being adsorbed because of the limited surface capacity of the stationary phase. The adsorption isotherm in preparative chromatography is therefore often nonlinear (see gray line in Figure 1b). The most common liquid-solid adsorption isotherm is the Langmuir adsorption [2]

S( )1

bCq C qbC

(1)

where qS is the monolayer saturation capacity, and b is the equilibrium constant.

6

1 Introduction

Chromatography is defined as a separation method in which the com-ponents to be separated are distributed between a stationary and a mo-bile phase [1]. The major different forms of chromatography are gas chromatography (GC), liquid chromatography (LC), and supercritical chromatography (SFC). Depending on the purpose, chromatography can be applied in either analytical or preparative mode. Analytical chromatography aims at obtaining quantitative and quali-tative information about components in a sample. Here, small sample amounts are injected, and the required information is obtained from the heights or areas of the eluted solute peaks. The concentration of solutes adsorbed on the stationary phase is proportional to the concen-tration of the solutes in the mobile phase and a further increased solute concentration, C, results in a proportional increase of the stationary phase concentration, q, (see the initial slope, blue line, in Figure 1). The column is, thus, operated under linear conditions, and the detector re-sponse will result in symmetrical Gaussian peaks (see inset in Figure 1). For reliable quantitative information, the peaks need to be well-re-solved and, preferably, more or less symmetrical. Preparative chromatography aims at isolating large amounts of de-sired target components from a complex sample mixture. The column is often operated under overloaded conditions, and a further increase of the sample load will result in a lower fraction being adsorbed because of the limited surface capacity of the stationary phase. The adsorption isotherm in preparative chromatography is therefore often nonlinear (see gray line in Figure 1b). The most common liquid-solid adsorption isotherm is the Langmuir adsorption [2]

S( )1

bCq C qbC

(1)

where qS is the monolayer saturation capacity, and b is the equilibrium constant.

7

Figure 1. a) Analytical (blue lines) and preparative (gray lines) elution profiles corresponding to the linear (blue line) and the non-linear part (gray line) of the Langmuirian adsorption isotherm in b), respectively. The insert in a) shows an enlargement of the analytical peaks. The horizontal line in b) shows the monolayer saturation capacity, qS.

Even though the focus often is on the adsorption of the sample solute, it is also likely that the components of the mobile phase adsorb on the stationary phase. mobile phase components can compete with the solute for adsorption sites, hence affecting the separation pro-cess. Such competitive effects have previously mainly been studied in LC systems before [2–5]. This thesis will, by careful measurements, in-vestigate the adsorption of mobile phase components and its impact on the separation process in SFC.

7

Figure 1. a) Analytical (blue lines) and preparative (gray lines) elution profiles corresponding to the linear (blue line) and the non-linear part (gray line) of the Langmuirian adsorption isotherm in b), respectively. The insert in a) shows an enlargement of the analytical peaks. The horizontal line in b) shows the monolayer saturation capacity, qS.

Even though the focus often is on the adsorption of the sample solute, it is also likely that the components of the mobile phase adsorb on the stationary phase. mobile phase components can compete with the solute for adsorption sites, hence affecting the separation pro-cess. Such competitive effects have previously mainly been studied in LC systems before [2–5]. This thesis will, by careful measurements, in-vestigate the adsorption of mobile phase components and its impact on the separation process in SFC.

8

1.1 Supercritical fluid chromatography

1.1.1 SFC - Background and applications SFC is a separation technique that has evolved from its original use with neat supercritical fluids and separations of low to moderate mo-lecular weight molecules towards a technique with a wide application range with the inclusion of co-solvents and additives in the mobile phase. The use of SFC was first reported in 1962 by Klesper et al., which employed high pressure to be able to extend the use of GC for thermally unstable compounds [6,7]. It was, however, first in the 1990s that SFC gain broader attention since commercial instruments became available [8]. In early days, capillary SFC with open tubular columns, typically with an inner diameter of 50 μm and coated with a polymer, dominated [9,10]. fter some years, applications with SFC using columns packed with porous particles grow more popular as limitations in application range became evident for capillary SFC [11].

is a phase condition between gas and liq-uid, achieved at a higher tem-perature, T, and pressure, P, than the components critical point (see Figure 2) [9]. Carbon dioxide, which is the component mainly used as the main weak solvent in SFC, has a critical temperature of 31 °C and a criti-cal pressure of 73.8 bar.

Figure 2. Phase diagram for carbon dioxide

8

1.1 Supercritical fluid chromatography

1.1.1 SFC - Background and applications SFC is a separation technique that has evolved from its original use with neat supercritical fluids and separations of low to moderate mo-lecular weight molecules towards a technique with a wide application range with the inclusion of co-solvents and additives in the mobile phase. The use of SFC was first reported in 1962 by Klesper et al., which employed high pressure to be able to extend the use of GC for thermally unstable compounds [6,7]. It was, however, first in the 1990s that SFC gain broader attention since commercial instruments became available [8]. In early days, capillary SFC with open tubular columns, typically with an inner diameter of 50 μm and coated with a polymer, dominated [9,10]. fter some years, applications with SFC using columns packed with porous particles grow more popular as limitations in application range became evident for capillary SFC [11].

is a phase condition between gas and liq-uid, achieved at a higher tem-perature, T, and pressure, P, than the components critical point (see Figure 2) [9]. Carbon dioxide, which is the component mainly used as the main weak solvent in SFC, has a critical temperature of 31 °C and a criti-cal pressure of 73.8 bar.

Figure 2. Phase diagram for carbon dioxide

9

SFC is used for a wide range of applications. Based on the number of papers published in recent years, it appears that the major application areas are natural products, bioanalysis, pharmaceutics, and food sci-ence [12]. Today, packed column SFC dominates strongly over capil-lary SFC, and a wide range of stationary phases are available, which makes SFC a versatile technique. Commonly used stationary phases are polar phases such as 2-ethylpyridine-bonded silica (2-EP), bare silica, and diol-bonded silica [12]. For polar stationary phases, the retention mode is similar to normal-phase HPLC, with hydrophobic species elut-ing first and the more polar ones are retained more [13,14]. It is also possible to use non-polar stationary phases such as octadecyl-bonded silica (C18). On these phases, polar compounds are less retained and the separation patterns can be compared to those of reverse-phase HPLC [15–17]. In the last 10-15 years, an evolution has been seen in HPLC as smaller stationary phase particles have been introduced in so-called ultra-high-performance liquid chromatography (UHPLC). similar trend is now seen in SFC with an increasing use of sub-2 μm particle size, referred to as ultra-high-performance SFC (UHPSFC) [12]. The smaller particle size is used to achieve higher efficiency, to reduce the analysis time and increase the throughput [18,19]. Compared to UHPLC, a much smaller pressure drop is generated in UHPSFC [19]. SFC is considered a “green” technique due to the avoidance of harmful solvents and reduced runtimes [20]. In SFC, the mobile phase is usu-ally comprised of carbon dioxide and a simple alcohol, such as metha-nol, which can be considered less environmentally harmful than many of the solvents used use in HPLC, particularly those used in normal

n additional aspect is that the primary car-bon dioxide supply is a byproduct in many industrial processes [21]. There are additional advantages of preparative SFC as compared to preparative LC. the avoidance of harmful solvents and the reduced solvent consumption is even more important due to the much larger volumes consumed. Moreover, the evaporation of collected fractions is much easier because the main part of the sol-vent is a gas in the eluate [22,23]. Even though scale-up from analytical

9

SFC is used for a wide range of applications. Based on the number of papers published in recent years, it appears that the major application areas are natural products, bioanalysis, pharmaceutics, and food sci-ence [12]. Today, packed column SFC dominates strongly over capil-lary SFC, and a wide range of stationary phases are available, which makes SFC a versatile technique. Commonly used stationary phases are polar phases such as 2-ethylpyridine-bonded silica (2-EP), bare silica, and diol-bonded silica [12]. For polar stationary phases, the retention mode is similar to normal-phase HPLC, with hydrophobic species elut-ing first and the more polar ones are retained more [13,14]. It is also possible to use non-polar stationary phases such as octadecyl-bonded silica (C18). On these phases, polar compounds are less retained and the separation patterns can be compared to those of reverse-phase HPLC [15–17]. In the last 10-15 years, an evolution has been seen in HPLC as smaller stationary phase particles have been introduced in so-called ultra-high-performance liquid chromatography (UHPLC). similar trend is now seen in SFC with an increasing use of sub-2 μm particle size, referred to as ultra-high-performance SFC (UHPSFC) [12]. The smaller particle size is used to achieve higher efficiency, to reduce the analysis time and increase the throughput [18,19]. Compared to UHPLC, a much smaller pressure drop is generated in UHPSFC [19]. SFC is considered a “green” technique due to the avoidance of harmful solvents and reduced runtimes [20]. In SFC, the mobile phase is usu-ally comprised of carbon dioxide and a simple alcohol, such as metha-nol, which can be considered less environmentally harmful than many of the solvents used use in HPLC, particularly those used in normal

n additional aspect is that the primary car-bon dioxide supply is a byproduct in many industrial processes [21]. There are additional advantages of preparative SFC as compared to preparative LC. the avoidance of harmful solvents and the reduced solvent consumption is even more important due to the much larger volumes consumed. Moreover, the evaporation of collected fractions is much easier because the main part of the sol-vent is a gas in the eluate [22,23]. Even though scale-up from analytical

10

to preparative scale is more complex in SFC than in LC, this can be done successfully, as shown by Enmark et al. [24]. Preparative SFC is, due to the reasons mentioned, very suitable for pharmaceutical purification.

ery is at , with whom most studies in this thesis are written in collaboration with. Here, SFC is currently the pri-mary technique used for purifications of small molecules [24–26], other techniques are considered first when SFC is unsuccessful, mainly when limited by solubility in the supercritical mobile phase. When choosing methods for chiral separations, SFC is considered as the first choice [15,27–29]. The proportions between chiral and achiral SFC have, however, shifted in favor of achiral separation. While chiral sep-arations still make up about 60% of publications about preparative scale applications, for analytical applications achiral separations are dominating with about 80 % of the publications [12].

Figure 3. Isopycnic plot of neat carbon dioxide at working temperatures and pressures commonly used in SFC. The resulting density is given by numbers in the lines. The plot was generated using REFPROP [30]

10

to preparative scale is more complex in SFC than in LC, this can be done successfully, as shown by Enmark et al. [24]. Preparative SFC is, due to the reasons mentioned, very suitable for pharmaceutical purification.

ery is at , with whom most studies in this thesis are written in collaboration with. Here, SFC is currently the pri-mary technique used for purifications of small molecules [24–26], other techniques are considered first when SFC is unsuccessful, mainly when limited by solubility in the supercritical mobile phase. When choosing methods for chiral separations, SFC is considered as the first choice [15,27–29]. The proportions between chiral and achiral SFC have, however, shifted in favor of achiral separation. While chiral sep-arations still make up about 60% of publications about preparative scale applications, for analytical applications achiral separations are dominating with about 80 % of the publications [12].

Figure 3. Isopycnic plot of neat carbon dioxide at working temperatures and pressures commonly used in SFC. The resulting density is given by numbers in the lines. The plot was generated using REFPROP [30]

11

supercritical fluid has a lower viscosity and a higher diffusion coeffi-cient as compared to most solvents used in HPLC [27]. an example, at typical conditions used in SFC, the diffusion coefficient for carbon dioxide varies between 10-4 and 10-3 cm2 s-1, compared to liquids that typically have diffusivities of 10-5 or lower [9]. Similarly, the viscosities are a factor of 10 to 100 times lower than for liquids, which enables operation at higher flow rates in SFC compared to in LC, and it is also possible to use longer columns to obtain higher separation efficiencies.

. The den-sity of the fluid can, therefore, be altered by changing the pressure and temperature, as is shown for pure carbon dioxide in Figure 3. quence of the compressibility is, however, that pressure drops and tem-perature deviations inside the SFC instrument, both along the tubing and in the column, will lead to that set instrumental conditions deliv-ered at the pump will differ from the actual conditions inside the col-umn [31,32]. It is, therefore, essential to determine the actual condi-tions inside the column, which is highlighted in Paper I and will be further discussed in Section 2.1.

11

supercritical fluid has a lower viscosity and a higher diffusion coeffi-cient as compared to most solvents used in HPLC [27]. an example, at typical conditions used in SFC, the diffusion coefficient for carbon dioxide varies between 10-4 and 10-3 cm2 s-1, compared to liquids that typically have diffusivities of 10-5 or lower [9]. Similarly, the viscosities are a factor of 10 to 100 times lower than for liquids, which enables operation at higher flow rates in SFC compared to in LC, and it is also possible to use longer columns to obtain higher separation efficiencies.

. The den-sity of the fluid can, therefore, be altered by changing the pressure and temperature, as is shown for pure carbon dioxide in Figure 3. quence of the compressibility is, however, that pressure drops and tem-perature deviations inside the SFC instrument, both along the tubing and in the column, will lead to that set instrumental conditions deliv-ered at the pump will differ from the actual conditions inside the col-umn [31,32]. It is, therefore, essential to determine the actual condi-tions inside the column, which is highlighted in Paper I and will be further discussed in Section 2.1.

12

1.1.2 Mobile phase composition in SFC In the early days of SFC, several solvents were used as the main solvent, such as hydrocarbons, nitrous oxide, ammonia gas, haloalkanes, sulfur hexafluoride, and water [33–38]. Today, carbon dioxide, is almost ex-clusively used for several reasons: (i) it has a moderate critical point (see table 1) ii) it is relatively inert (iii) it is not flammable (iv) it has low toxicity and (iv) it is inexpensive [15].

Table 1. Critical properties of some mobile phase components used in SFC [39,40]

Solvent TC [°C]

PC [bar]

Discussed in paper

Carbon dioxide 31.3 73.9 I-V Water 374 230 VI

132.5 114 - Nitrous oxide 36.5 73.5 - Butane 152 38 - Sulfur hexafluoride 45.5 37.6 - Trifluoromethane 25.9 47.5 - Methanol 239.5 81.0 I-V Ethanol 240.8 61.5 III 2-Propanol 235.2 47.6 III

271.9 48.7 III Diethylamine 223.5 37.1 IV Triethylamine 261.9 30.0 IV Isopropylamine 198.7 45.4 IV

12

1.1.2 Mobile phase composition in SFC In the early days of SFC, several solvents were used as the main solvent, such as hydrocarbons, nitrous oxide, ammonia gas, haloalkanes, sulfur hexafluoride, and water [33–38]. Today, carbon dioxide, is almost ex-clusively used for several reasons: (i) it has a moderate critical point (see table 1) ii) it is relatively inert (iii) it is not flammable (iv) it has low toxicity and (iv) it is inexpensive [15].

Table 1. Critical properties of some mobile phase components used in SFC [39,40]

Solvent TC [°C]

PC [bar]

Discussed in paper

Carbon dioxide 31.3 73.9 I-V Water 374 230 VI

132.5 114 - Nitrous oxide 36.5 73.5 - Butane 152 38 - Sulfur hexafluoride 45.5 37.6 - Trifluoromethane 25.9 47.5 - Methanol 239.5 81.0 I-V Ethanol 240.8 61.5 III 2-Propanol 235.2 47.6 III

271.9 48.7 III Diethylamine 223.5 37.1 IV Triethylamine 261.9 30.0 IV Isopropylamine 198.7 45.4 IV

13

Figure 4, the use of neat carbon dioxide in the mobile phase has limited applicability for packed column SFC, due to its non-polarity. To be able to use SFC for compounds with high polarity, a po-lar organic co-solvent must be added to the mobile phase. In achiral separations the most commonly used co-solvent is methanol [12] alt-hough other co-solvents such as ethanol and acetonitrile are also used. In chiral separations the co-solvent 2-propanol is often used [25,41]. The co-solvent is often called a modifier since it modifies the solvent strength of the mobile phase [2]. Thus, when modeled, retention times obtained in such SFC systems should be described using the linear sol-vent strength (LSS) theory (Eq. (19) discussed in Section 2.3.4) [42].

Figure 4. Overview of the application range of SFC with co-solvents and addi-tives. Adapted from A. Tarafder, TrAC, 81, 3-10, Copyright (2016), with permission from Elsevier [7]

-solvent is that the critical point will

change as the critical temperature of the co-solvents is substantially higher than for carbon dioxide (see Table 1). The critical point of the mixed fluid may, therefore, be higher than the operational conditions, and the supercritical phase maybe not reached. If the pressure is main-tained above the critical pressure a subcritical fluid is achieved and phase separation can be avoided [15,43]

13

Figure 4, the use of neat carbon dioxide in the mobile phase has limited applicability for packed column SFC, due to its non-polarity. To be able to use SFC for compounds with high polarity, a po-lar organic co-solvent must be added to the mobile phase. In achiral separations the most commonly used co-solvent is methanol [12] alt-hough other co-solvents such as ethanol and acetonitrile are also used. In chiral separations the co-solvent 2-propanol is often used [25,41]. The co-solvent is often called a modifier since it modifies the solvent strength of the mobile phase [2]. Thus, when modeled, retention times obtained in such SFC systems should be described using the linear sol-vent strength (LSS) theory (Eq. (19) discussed in Section 2.3.4) [42].

Figure 4. Overview of the application range of SFC with co-solvents and addi-tives. Adapted from A. Tarafder, TrAC, 81, 3-10, Copyright (2016), with permission from Elsevier [7]

-solvent is that the critical point will

change as the critical temperature of the co-solvents is substantially higher than for carbon dioxide (see Table 1). The critical point of the mixed fluid may, therefore, be higher than the operational conditions, and the supercritical phase maybe not reached. If the pressure is main-tained above the critical pressure a subcritical fluid is achieved and phase separation can be avoided [15,43]

14

The co-solvent fraction has a large impact on retention and is an im-portant factor in controlling selectivity and productivity [31,44]. The main factor attributed to control the retention in SFC is the solvent strength [45,46]. The solvent strength is proportional to the density and Figure 5 shows how the addition of a co-solvent affects the density of the mobile phase. However, the solvent strength alone cannot ex-plain the retention mechanisms, as interactions with the stationary phase also need to be considered. In SFC, the co-solvents adsorb to the stationary under normal operational conditions, as shown in Papers I-IV. peak distortion, where the shape of the overloaded elution profile will change with co-solvent fractions. These deformations, previously only studied in LC [5], were investigated in and Papers II and III and will be further discussed in Section 2.4.1. In Papers I-IV, it is shown that the co-solvent can adsorb to the stationary phase and compete with the solute for active sites, thus affecting the retention, as will be discussed in Section 2.3.4.

Figure 5. Isopycnic plot of mixtures of carbon dioxide in presence of various methanol fractions at common operational pressures in SFC. The data shown was calculated for a constant temperature of 40 °C. The plot was generated in the same way as figure 2a and b in Paper IV

14

The co-solvent fraction has a large impact on retention and is an im-portant factor in controlling selectivity and productivity [31,44]. The main factor attributed to control the retention in SFC is the solvent strength [45,46]. The solvent strength is proportional to the density and Figure 5 shows how the addition of a co-solvent affects the density of the mobile phase. However, the solvent strength alone cannot ex-plain the retention mechanisms, as interactions with the stationary phase also need to be considered. In SFC, the co-solvents adsorb to the stationary under normal operational conditions, as shown in Papers I-IV. peak distortion, where the shape of the overloaded elution profile will change with co-solvent fractions. These deformations, previously only studied in LC [5], were investigated in and Papers II and III and will be further discussed in Section 2.4.1. In Papers I-IV, it is shown that the co-solvent can adsorb to the stationary phase and compete with the solute for active sites, thus affecting the retention, as will be discussed in Section 2.3.4.

Figure 5. Isopycnic plot of mixtures of carbon dioxide in presence of various methanol fractions at common operational pressures in SFC. The data shown was calculated for a constant temperature of 40 °C. The plot was generated in the same way as figure 2a and b in Paper IV

15

Figure 6 Elution profiles of 5 μL injections of 100 mM of alprenolol, metoprolol, and propranolol eluted with a methanol fraction of 21 %. a) No additive is added, b) DEA added as an additive to a concentration of 0.105 v% of the total eluent.

For challenging solute separations, a co-solvent may not be sufficient to achieve acceptable peak shapes (see Figure 6 a). Then a third com-ponent may be added to the mobile phase, a so-called additive. The ad-dition of the additive has been proven both in LC [47,48] and SFC [49] to improve the peak shape and decrease the retention. op-erates by competing with the solutes for the limited number of adsorp-tion sites on the stationary phase surface. The retention is described by a competitive adsorption isotherm [2,3]. There are many different pro-posed explanations for the effects of additive such as changing the ap-parent pH [50], forming ion-pairs with the solute [51], suppression of ionization of the solute [52] and covering of free silanols to suppress unwanted interactions [53]. The adsorption of the additive and its ef-fect is discussed in Paper V.

15

Figure 6 Elution profiles of 5 μL injections of 100 mM of alprenolol, metoprolol, and propranolol eluted with a methanol fraction of 21 %. a) No additive is added, b) DEA added as an additive to a concentration of 0.105 v% of the total eluent.

For challenging solute separations, a co-solvent may not be sufficient to achieve acceptable peak shapes (see Figure 6 a). Then a third com-ponent may be added to the mobile phase, a so-called additive. The ad-dition of the additive has been proven both in LC [47,48] and SFC [49] to improve the peak shape and decrease the retention. op-erates by competing with the solutes for the limited number of adsorp-tion sites on the stationary phase surface. The retention is described by a competitive adsorption isotherm [2,3]. There are many different pro-posed explanations for the effects of additive such as changing the ap-parent pH [50], forming ion-pairs with the solute [51], suppression of ionization of the solute [52] and covering of free silanols to suppress unwanted interactions [53]. The adsorption of the additive and its ef-fect is discussed in Paper V.

16

1.2 Aim The interest for SFC is increasing and is now used in a wide variety of applications [12]. However, as SFC is more complex than LC, it is not sufficient to rely on LC theory, and more fundamental knowledge is needed to understand the separation mechanisms in SFC better. This thesis aims at a deeper understanding of the function of the mobile phase components by systematically studying these components ad-sorption and how that adsorption affects the separation performance in both analytical and preparative SFC separations nalytical as well as overloaded (preparative) experiments are performed. In the latter case, a broad concentration range is covered (see Figure 1), which is important in order to obtain a complete understanding of all interac-tions, both for preparative and analytical separations. The work in this thesis addresses accurate measurements of the adsorption isotherm. Moreover, modeling and simulations are used to clarifying the impact that the adsorbing mobile phase components have on solute retention time and elution profiles. Finally, acquired information is utilized to address the impact of the most important operational parameters on the robustness of separation methods.

16

1.2 Aim The interest for SFC is increasing and is now used in a wide variety of applications [12]. However, as SFC is more complex than LC, it is not sufficient to rely on LC theory, and more fundamental knowledge is needed to understand the separation mechanisms in SFC better. This thesis aims at a deeper understanding of the function of the mobile phase components by systematically studying these components ad-sorption and how that adsorption affects the separation performance in both analytical and preparative SFC separations nalytical as well as overloaded (preparative) experiments are performed. In the latter case, a broad concentration range is covered (see Figure 1), which is important in order to obtain a complete understanding of all interac-tions, both for preparative and analytical separations. The work in this thesis addresses accurate measurements of the adsorption isotherm. Moreover, modeling and simulations are used to clarifying the impact that the adsorbing mobile phase components have on solute retention time and elution profiles. Finally, acquired information is utilized to address the impact of the most important operational parameters on the robustness of separation methods.

17

2 Theory and methodology

2.1 Determination of density, volumetric flow and volume frac-tion in SFC mobile phases

The volumetric flow rate and the co-solvent fraction are two essential parameters for measurements of co-solvent adsorption [31]. cation in SFC is that these parameters, are not constant with changing pressure and temperature due to the compressibility of carbon dioxide. The flow rate and co-solvent fractions delivered at the pump may, therefore, differ from the actual conditions inside the column [24]. In Figure 7a, it is shown that the actual flow rate inside the column can be almost double that of the flow rate set at the pump. Even more severe, the actual volumetric co-solvent fraction can differ up to 50 % from the set conditions, as is evident from the data shown in Figure 7b. From earlier Design of experiments (DoE) studies it is known that the co-solvent fraction is the single most important factor to control the solute retention [31,44]. The differences are especially prominent at low co-solvent fractions, high temperature, and low pressure and declines with increasing co-solvent fractions as the mobile phase becomes less com-pressible. Similar results were also presented in Paper I. Determina-tion of actual conditions is therefore vital for correct adsorption meas-urements. Moreover, insensibility to the actual conditions may also have a negative effect on scale-up from analytical to preparative sys-tems [24] and with method transfer between laboratories [54].

17

2 Theory and methodology

2.1 Determination of density, volumetric flow and volume frac-tion in SFC mobile phases

The volumetric flow rate and the co-solvent fraction are two essential parameters for measurements of co-solvent adsorption [31]. cation in SFC is that these parameters, are not constant with changing pressure and temperature due to the compressibility of carbon dioxide. The flow rate and co-solvent fractions delivered at the pump may, therefore, differ from the actual conditions inside the column [24]. In Figure 7a, it is shown that the actual flow rate inside the column can be almost double that of the flow rate set at the pump. Even more severe, the actual volumetric co-solvent fraction can differ up to 50 % from the set conditions, as is evident from the data shown in Figure 7b. From earlier Design of experiments (DoE) studies it is known that the co-solvent fraction is the single most important factor to control the solute retention [31,44]. The differences are especially prominent at low co-solvent fractions, high temperature, and low pressure and declines with increasing co-solvent fractions as the mobile phase becomes less com-pressible. Similar results were also presented in Paper I. Determina-tion of actual conditions is therefore vital for correct adsorption meas-urements. Moreover, insensibility to the actual conditions may also have a negative effect on scale-up from analytical to preparative sys-tems [24] and with method transfer between laboratories [54].

18

Figure 7. Relative error between set and actual conditions of a) flow rate and b) co-solvent fractions. The flow rate was set to 1 mL min-1 in all experiments. In a) the flow rate was measured with the back pressure regulator (BPR) set to 110 bar and the temperature to 55 °C and in b) the co-solvent fractions were set to 1-30 v% and measured with the BPR set to 140 bar and temperature to 40 °C.

The importance of using external devices to measure the actual condi-tions in the column has been shown by several studies [31,44,55–58]. In contrast to the volumetric flow rate and the volume fraction, the mass flow and the mass ratio is considered constant [56]. It is, there-fore, suitable to use measurements of the mass flow in combination with measurements of pressure and temperature to calculate the volu-metric flow and volume fractions in SFC. In large scale preparative sys-tems, it is common that the flow is mass controlled whereas in analyti-cal systems the standard is to use volume-controlled flow rate. To measure the mass flow in analytical systems there is a need to use ex-ternal sensors. In this work, mass flow meters working on the principle of the Coriolis effect were used [31,44,55–57,59]. The pressure was measured using two absolute pressure transducers connected to the in-let and the outlet of the column. The temperature was monitored with external resistance temperature detectors attached at the surface of the column.

18

Figure 7. Relative error between set and actual conditions of a) flow rate and b) co-solvent fractions. The flow rate was set to 1 mL min-1 in all experiments. In a) the flow rate was measured with the back pressure regulator (BPR) set to 110 bar and the temperature to 55 °C and in b) the co-solvent fractions were set to 1-30 v% and measured with the BPR set to 140 bar and temperature to 40 °C.

The importance of using external devices to measure the actual condi-tions in the column has been shown by several studies [31,44,55–58]. In contrast to the volumetric flow rate and the volume fraction, the mass flow and the mass ratio is considered constant [56]. It is, there-fore, suitable to use measurements of the mass flow in combination with measurements of pressure and temperature to calculate the volu-metric flow and volume fractions in SFC. In large scale preparative sys-tems, it is common that the flow is mass controlled whereas in analyti-cal systems the standard is to use volume-controlled flow rate. To measure the mass flow in analytical systems there is a need to use ex-ternal sensors. In this work, mass flow meters working on the principle of the Coriolis effect were used [31,44,55–57,59]. The pressure was measured using two absolute pressure transducers connected to the in-let and the outlet of the column. The temperature was monitored with external resistance temperature detectors attached at the surface of the column.

19

The average flow rate in the column was calculated from the average density based on the pressure and temperature at the inlet and the out-let of the column. In Papers I, II, IV, and V, the density was calcu-lated using the Reference Fluid Thermodynamic and Transport Prop-erties Database (REFPROP) program from the National Institute of Standards and Technologies [30]. In this program, the equation of state (EoS) of Span and Wagner is used [60] with the mixing rule of Kunz et al. [61] to calculate the density of the mixture of carbon dioxide and methanol. The accuracy in the calculated density and flow rate is affected by errors in measurements and the used EoS. Tarafder et al. [62] showed that, in general, the error is below 3.5 % when calculations with REFPROP were compared with experimental data. The volume fraction of methanol can be calculated using the method of Kato et al. [63]. Initially, the molar volume of the fluid (V) is calculated using

2 2CO CO MeOH MeOH

MV

M x M x M (2)

where M is the molecular weight of the fluid, is the mass density of the fluid, and x is the mole fraction. The partial molar volumes (Vi) are calculated according to

MeOHCO2CO2

VV V xx

(3)

and

MeOH CO2CO2

VV V xx

(4)

The partial derivative V x is estimated numerically. Thereafter, the volumetric fraction of methanol can be calculated from the molar vol-ume and measured mass flows m of carbon dioxide and methanol

2

2

2

MeOHMeOH

MeOHMeOH

COMeOHMeOH C0

MeOH CO

v% 100

m VM

mm V VM M

(5)

19

The average flow rate in the column was calculated from the average density based on the pressure and temperature at the inlet and the out-let of the column. In Papers I, II, IV, and V, the density was calcu-lated using the Reference Fluid Thermodynamic and Transport Prop-erties Database (REFPROP) program from the National Institute of Standards and Technologies [30]. In this program, the equation of state (EoS) of Span and Wagner is used [60] with the mixing rule of Kunz et al. [61] to calculate the density of the mixture of carbon dioxide and methanol. The accuracy in the calculated density and flow rate is affected by errors in measurements and the used EoS. Tarafder et al. [62] showed that, in general, the error is below 3.5 % when calculations with REFPROP were compared with experimental data. The volume fraction of methanol can be calculated using the method of Kato et al. [63]. Initially, the molar volume of the fluid (V) is calculated using

2 2CO CO MeOH MeOH

MV

M x M x M (2)

where M is the molecular weight of the fluid, is the mass density of the fluid, and x is the mole fraction. The partial molar volumes (Vi) are calculated according to

MeOHCO2CO2

VV V xx

(3)

and

MeOH CO2CO2

VV V xx

(4)

The partial derivative V x is estimated numerically. Thereafter, the volumetric fraction of methanol can be calculated from the molar vol-ume and measured mass flows m of carbon dioxide and methanol

2

2

2

MeOHMeOH

MeOHMeOH

COMeOHMeOH C0

MeOH CO

v% 100

m VM

mm V VM M

(5)

20

2.2 Simulation of chromatographic separations Simulations can be used to obtain a better understanding of the sepa-ration processes. commonly used to describe how the solute migrate along the column is the Equilibrium-Dispersive (ED) model [2]. This model is a good choice for small molecule separation systems with sufficiently high column efficiency. When the mass transfer kinetics is fast, the ED model can be written as

2

2aC q C CF u Dt t z z

(6)

where C and q are the concentration of the solute in the mobile phase and the stationary phase, respectively. z is the length coordinate, t is the time coordinate, and u is the linear velocity of the mobile phase. In the ED model the mass transfer and apparent dispersion coefficient are lumped together in an apparent axial dispersion coefficient, Da, that is calculated by

2aLuDN

(7)

where L is the length of the column, and N is the column efficiency (number of theoretical plates). Different approaches can be used to obtain a solution for the model equation [64–67]. In this thesis (Papers II, III, and V), the ED model was solved using the orthogonal collocation on finite elements (OCFE) method [52], and in Paper V the finite volume method was also used [64,68].

20

2.2 Simulation of chromatographic separations Simulations can be used to obtain a better understanding of the sepa-ration processes. commonly used to describe how the solute migrate along the column is the Equilibrium-Dispersive (ED) model [2]. This model is a good choice for small molecule separation systems with sufficiently high column efficiency. When the mass transfer kinetics is fast, the ED model can be written as

2

2aC q C CF u Dt t z z

(6)

where C and q are the concentration of the solute in the mobile phase and the stationary phase, respectively. z is the length coordinate, t is the time coordinate, and u is the linear velocity of the mobile phase. In the ED model the mass transfer and apparent dispersion coefficient are lumped together in an apparent axial dispersion coefficient, Da, that is calculated by

2aLuDN

(7)

where L is the length of the column, and N is the column efficiency (number of theoretical plates). Different approaches can be used to obtain a solution for the model equation [64–67]. In this thesis (Papers II, III, and V), the ED model was solved using the orthogonal collocation on finite elements (OCFE) method [52], and in Paper V the finite volume method was also used [64,68].

21

2.3 Adsorption isotherms (see. Figure 1c) contain important information

for modeling in SFC. In this section, a closer presentation of the ad-sorption isotherm models and the methods used in this work to deter-mine the adsorption isotherms will be given.

2.3.1 Adsorption isotherms and their relation to elution profiles In chromatography, an adsorption isotherm describes the relation be-tween the concentration of adsorbed components on the surface of the stationary phase (q) and the concentration in the bulk mobile phase (C) [2] dsorption isotherms can be classified as different types depend-ing on the adsorption pattern, type I-III are shown in Figure 8 [69]. type I adsorption isotherm, such as the simple Langmuir isotherm in Figure 1, has a convex upwards shape (Figure 8 aI). The corresponding overloaded elution profile has a “Langmuirian”-shape, i.e., a steep front and a diffuse rear (Figure 8 bI). The type I adsorption isotherms, assumes that a limited amount of a single type of adsorption sites exists and that the solute only adsorbs to these sites at the surface. Hence, it can only describe monolayer saturation. If solute-solute interactions are present between the adsorbed solutes, more complex models such as type II and III (Figure 8 aII and aIII) must be used to describe the isotherm. In type II, the interaction to the stationary phase is dominant while the solute-solute interaction is dominant in type III. With a Type II isotherm model, a second layer is formed after the initial monolayer has been completed (Figure 8 cII). In the corresponding overloaded elu-tion profile the inflection point is reflected as a reversal from sharp to disperse in both the front and the rear. The front is sharp at low con-centrations and then turns disperse closer to the top of the profile and the rear is sharp at high concentrations and disperse near the base. In contrast, with type III, incomplete layers will be formed (Figure 8 cIII), resulting in an overloaded elution profile showing “anti-Langmuirian”-shape, with a diffuse front and a sharp rear, see Figure 8 bIII.

21

2.3 Adsorption isotherms (see. Figure 1c) contain important information

for modeling in SFC. In this section, a closer presentation of the ad-sorption isotherm models and the methods used in this work to deter-mine the adsorption isotherms will be given.

2.3.1 Adsorption isotherms and their relation to elution profiles In chromatography, an adsorption isotherm describes the relation be-tween the concentration of adsorbed components on the surface of the stationary phase (q) and the concentration in the bulk mobile phase (C) [2] dsorption isotherms can be classified as different types depend-ing on the adsorption pattern, type I-III are shown in Figure 8 [69]. type I adsorption isotherm, such as the simple Langmuir isotherm in Figure 1, has a convex upwards shape (Figure 8 aI). The corresponding overloaded elution profile has a “Langmuirian”-shape, i.e., a steep front and a diffuse rear (Figure 8 bI). The type I adsorption isotherms, assumes that a limited amount of a single type of adsorption sites exists and that the solute only adsorbs to these sites at the surface. Hence, it can only describe monolayer saturation. If solute-solute interactions are present between the adsorbed solutes, more complex models such as type II and III (Figure 8 aII and aIII) must be used to describe the isotherm. In type II, the interaction to the stationary phase is dominant while the solute-solute interaction is dominant in type III. With a Type II isotherm model, a second layer is formed after the initial monolayer has been completed (Figure 8 cII). In the corresponding overloaded elu-tion profile the inflection point is reflected as a reversal from sharp to disperse in both the front and the rear. The front is sharp at low con-centrations and then turns disperse closer to the top of the profile and the rear is sharp at high concentrations and disperse near the base. In contrast, with type III, incomplete layers will be formed (Figure 8 cIII), resulting in an overloaded elution profile showing “anti-Langmuirian”-shape, with a diffuse front and a sharp rear, see Figure 8 bIII.

22

Figure 8. Top row: Characteristic adsorption isotherms of types I and II, and III. Middle row: The corresponding overloaded elution profiles. Bottom row: Illustra-tion of the formation of adsorbed solutes layers with increasing solute concentra-tion.

The Langmuir adsorption isotherm in Eq. (1) (see Figure 1) assumes a limited amount (qS) of identical interaction sites. If the stationary phase contains two different types of adsorption sites, the Langmuir isotherm can be extended to the bi-Langmuir isotherm [2]:

I IIS,I S,II

I II

( )1 1

b C b Cq C q qb C b C

(8)

where qS is the monolayer saturation capacity, b is the association equi-librium constant between the solute and the stationary phase, and the indices I and II refer to site I and II, respectively. The mobile phase usually contains several components that compete for the available sta-tionary phase surface, and a multi-component adsorption isotherm is then required. In the case where the mobile phase contains an additive

22

Figure 8. Top row: Characteristic adsorption isotherms of types I and II, and III. Middle row: The corresponding overloaded elution profiles. Bottom row: Illustra-tion of the formation of adsorbed solutes layers with increasing solute concentra-tion.

The Langmuir adsorption isotherm in Eq. (1) (see Figure 1) assumes a limited amount (qS) of identical interaction sites. If the stationary phase contains two different types of adsorption sites, the Langmuir isotherm can be extended to the bi-Langmuir isotherm [2]:

I IIS,I S,II

I II

( )1 1

b C b Cq C q qb C b C

(8)

where qS is the monolayer saturation capacity, b is the association equi-librium constant between the solute and the stationary phase, and the indices I and II refer to site I and II, respectively. The mobile phase usually contains several components that compete for the available sta-tionary phase surface, and a multi-component adsorption isotherm is then required. In the case where the mobile phase contains an additive

23

that competes with a solute, the additive must be treated as a compo-nent, in addition to the solute in the model. The competitive version of the Langmuir adsorption isotherm can then be described by [2]

I,solute solutesolute S,I,solute

I,solute solute I,additive additive

( )1

b Cq C q

b C b C (9)

where the indices solute and additive refer to the solute and the addi-tive, respectively. -competitive Langmuir isotherm can also Eq. (9) be extended to the competitive bi-Langmuir adsorption iso-therm, which was used in Papers II, III, IV, and V (see Eq. (2) in Paper II) The Langmuir adsorption isotherm only assumes adsorption to the sta-tionary phase. For type II and III mechanisms, where there is solute-solute interaction between the adsorbed solutes, the liquid-solid Brunauer, Emmett, and Teller (BET) model may be used [70]:

L L

( )1 1S

bCq C qb C b C bC

(10)

where bL is the association equilibrium constant between the solute and the layer of the previously adsorbed solutes.

2.3.2 Excess adsorption determination The adsorption isotherms in Section 2.3.1 describes the absolute ad-sorption to the surface or stationary phase concentrations (q) of a com-pound. co-solvent adsorp-tion is, however, not possible in a liquid-solid system. Instead, Gibbs proposed an alternate method derived from a mass balance equation [71]. describes the difference between the amount of component actually present in the system, and the amount that would be present in a reference system without adsorp-tion, for a particular bulk concentration, in the adjoining liquid phase at the surface [72]. The excess amount adsorbed ( ) can be expressed as M

i i 0n C V (11)

23

that competes with a solute, the additive must be treated as a compo-nent, in addition to the solute in the model. The competitive version of the Langmuir adsorption isotherm can then be described by [2]

I,solute solutesolute S,I,solute

I,solute solute I,additive additive

( )1

b Cq C q

b C b C (9)

where the indices solute and additive refer to the solute and the addi-tive, respectively. -competitive Langmuir isotherm can also Eq. (9) be extended to the competitive bi-Langmuir adsorption iso-therm, which was used in Papers II, III, IV, and V (see Eq. (2) in Paper II) The Langmuir adsorption isotherm only assumes adsorption to the sta-tionary phase. For type II and III mechanisms, where there is solute-solute interaction between the adsorbed solutes, the liquid-solid Brunauer, Emmett, and Teller (BET) model may be used [70]:

L L

( )1 1S

bCq C qb C b C bC

(10)

where bL is the association equilibrium constant between the solute and the layer of the previously adsorbed solutes.

2.3.2 Excess adsorption determination The adsorption isotherms in Section 2.3.1 describes the absolute ad-sorption to the surface or stationary phase concentrations (q) of a com-pound. co-solvent adsorp-tion is, however, not possible in a liquid-solid system. Instead, Gibbs proposed an alternate method derived from a mass balance equation [71]. describes the difference between the amount of component actually present in the system, and the amount that would be present in a reference system without adsorp-tion, for a particular bulk concentration, in the adjoining liquid phase at the surface [72]. The excess amount adsorbed ( ) can be expressed as M

i i 0n C V (11)

24

where ni is the total molar amount of component i in the column, CiM is the molar concentration in the mobile phase, and V0 the thermody-namic void volume. Determination of the excess adsorption can be made with the minor disturbance method, also called the perturbation peak (PP) method, and with the tracer pulse (TP) method [73,74]. These methods will be further discussed in Section 2.3.3. In the TP method, a labeled mole-cule is needed to distinguish the injected tracer from the mobile phase. In Papers I, II, and III, the tracers were isotopically labeled with deu-terium. Using the TP method, the relationship between the retention volume of an isotopically labeled tracer ( *

RV ( )) and the excess adsorp-

tion ( ( )) is given by

*

R 0( ( ) )( )

V VS

(12)

where V0 is the void volume of the column and S the total surface area of the stationary phase and is the volume fraction of the co-solvent. In the PP method, retention volumes of the perturbation peaks (VR, pert) are used instead of tracer peaks. The expression used is similar to Eq. (12) but requires the integration of the retention data with respect to eluent composition [75]:

R,pert 0

0

( ( ) )( )

V V dS

(13)

The typical appearance of an excess adsorption isotherm includes an initially increased accumulation of adsorbed solutes up to the maxi-mum of the excess (see I and II in Figure 9, respectivelymum, the increase in surface concentration is equal to the increase in the bulk concentrationleads to a decrease in the excessive adsorbed quantity (III in Figure 9). When the bulk concentration reaches 100 v%, the excess reaches a zero value (IV in Figure 9).

24

where ni is the total molar amount of component i in the column, CiM is the molar concentration in the mobile phase, and V0 the thermody-namic void volume. Determination of the excess adsorption can be made with the minor disturbance method, also called the perturbation peak (PP) method, and with the tracer pulse (TP) method [73,74]. These methods will be further discussed in Section 2.3.3. In the TP method, a labeled mole-cule is needed to distinguish the injected tracer from the mobile phase. In Papers I, II, and III, the tracers were isotopically labeled with deu-terium. Using the TP method, the relationship between the retention volume of an isotopically labeled tracer ( *

RV ( )) and the excess adsorp-

tion ( ( )) is given by

*

R 0( ( ) )( )

V VS

(12)

where V0 is the void volume of the column and S the total surface area of the stationary phase and is the volume fraction of the co-solvent. In the PP method, retention volumes of the perturbation peaks (VR, pert) are used instead of tracer peaks. The expression used is similar to Eq. (12) but requires the integration of the retention data with respect to eluent composition [75]:

R,pert 0

0

( ( ) )( )

V V dS

(13)

The typical appearance of an excess adsorption isotherm includes an initially increased accumulation of adsorbed solutes up to the maxi-mum of the excess (see I and II in Figure 9, respectivelymum, the increase in surface concentration is equal to the increase in the bulk concentrationleads to a decrease in the excessive adsorbed quantity (III in Figure 9). When the bulk concentration reaches 100 v%, the excess reaches a zero value (IV in Figure 9).

25

Figure 9. At top, schematic illustrations of the surface excess, , (red line) and the corresponding surface concentration, q, (blue line) versus the co-solvent fraction in the eluent ( ). The vertical lines denote the maximum of the excess (dashed line) and the inflection point of the linear decrease (dotted line). At bottom, schematic illustration of solute adsorption at a molecular level at the surface, corresponding to the different modifier fraction regions I–IV. Circles below the dashed line (Gibbs dividing plane) are adsorbed molecules. Red circles indicate the excess amount compared to the amount in the bulk (blue). See Paper I for more details.

To determine the absolute adsorption isotherm from the excess iso-therm a hypothetical plane (Gibbs dividing plane) that separates the bulk phase from the adsorbed layer needs to be defined [73,75,76]. The layer thickness of the adsorbed layer can be estimated from the maxi-mal linear decrease, around the inflection point of the excess adsorp-tion isotherm. The decrease of the excess in this region is essentially due to the saturation of the stationary surface. Since there is no sites available for additional adsorption, a further increase of the bulk con-centration will lead to a decrease in the difference between the concen-tration in bulk and the adsorbed phase. The linear region can be de-scribed by [73,76]

max max ads( )

( )dq q V

d (14)

25

Figure 9. At top, schematic illustrations of the surface excess, , (red line) and the corresponding surface concentration, q, (blue line) versus the co-solvent fraction in the eluent ( ). The vertical lines denote the maximum of the excess (dashed line) and the inflection point of the linear decrease (dotted line). At bottom, schematic illustration of solute adsorption at a molecular level at the surface, corresponding to the different modifier fraction regions I–IV. Circles below the dashed line (Gibbs dividing plane) are adsorbed molecules. Red circles indicate the excess amount compared to the amount in the bulk (blue). See Paper I for more details.

To determine the absolute adsorption isotherm from the excess iso-therm a hypothetical plane (Gibbs dividing plane) that separates the bulk phase from the adsorbed layer needs to be defined [73,75,76]. The layer thickness of the adsorbed layer can be estimated from the maxi-mal linear decrease, around the inflection point of the excess adsorp-tion isotherm. The decrease of the excess in this region is essentially due to the saturation of the stationary surface. Since there is no sites available for additional adsorption, a further increase of the bulk con-centration will lead to a decrease in the difference between the concen-tration in bulk and the adsorbed phase. The linear region can be de-scribed by [73,76]

max max ads( )

( )dq q V

d (14)

26

where qmax is the maximum amount of modifier that can be adsorbed per square meter of the stationary phase, and Vads is the surface-specific volume of the adsorbed phase. This expression is only valid in the re-gion of linear decrease, and here the surface-specific layer volume is equal to the slope of the excess adsorption in this region (gray dash-dotted line in Figure 8). With the values determined with the slope, the absolute adsorption (q(C)) can be calculated by ads( ) ( )q V (15)

Eq.(14) and (15) is essentially the same, however, in the linear region, the values of qmax and Vads can be determined from the intercept and the slope as they here can be considered as constant.

2.3.3 Determination of adsorption isotherms dsorption isotherm can be determined using several methods [2]. In

this thesis, the TP method (Papers I, II, and III), the PP method (Pa-per IV), the slope-ECP method (Papers II, III, and IV), and the in-verse method (Paper V) have been used. The TP and PP methods belong to the so-called pulse methods [77]. Here, the column is equilibrated with an eluent containing a continu-ous stream of the molecules whose isotherm is to be determined. When a small excess of identical molecules are injected this perturbs the es-tablished equilibria generating a displacement zone of concentration plateau molecules, called a perturbation peak (PP) when detected as a peak (red peak in Figure 10a). The PP consist of displaced molecules already adsorbed to the stationary phase, (gray positive concentration plateau perturbation in Figure 9b). The injected molecules, on the other hand, are eluted in a more retained positive perturbation zone called the tracer zone if detected (blue peak in Figure 9b). In order to re-establish the plateau concentration equilibria, the displaced amount of molecules is adsorbed from incoming bulk eluent, leaving a deficiency zone of the plateau level (gray negative zone in Figure 9b). This negative plateau zone is eluting simultaneously with the positive tracer zone. The latter zone will, therefore, be canceled out and any ordinary detection principle cannot detect the tracer molecules.

26

where qmax is the maximum amount of modifier that can be adsorbed per square meter of the stationary phase, and Vads is the surface-specific volume of the adsorbed phase. This expression is only valid in the re-gion of linear decrease, and here the surface-specific layer volume is equal to the slope of the excess adsorption in this region (gray dash-dotted line in Figure 8). With the values determined with the slope, the absolute adsorption (q(C)) can be calculated by ads( ) ( )q V (15)

Eq.(14) and (15) is essentially the same, however, in the linear region, the values of qmax and Vads can be determined from the intercept and the slope as they here can be considered as constant.

2.3.3 Determination of adsorption isotherms dsorption isotherm can be determined using several methods [2]. In

this thesis, the TP method (Papers I, II, and III), the PP method (Pa-per IV), the slope-ECP method (Papers II, III, and IV), and the in-verse method (Paper V) have been used. The TP and PP methods belong to the so-called pulse methods [77]. Here, the column is equilibrated with an eluent containing a continu-ous stream of the molecules whose isotherm is to be determined. When a small excess of identical molecules are injected this perturbs the es-tablished equilibria generating a displacement zone of concentration plateau molecules, called a perturbation peak (PP) when detected as a peak (red peak in Figure 10a). The PP consist of displaced molecules already adsorbed to the stationary phase, (gray positive concentration plateau perturbation in Figure 9b). The injected molecules, on the other hand, are eluted in a more retained positive perturbation zone called the tracer zone if detected (blue peak in Figure 9b). In order to re-establish the plateau concentration equilibria, the displaced amount of molecules is adsorbed from incoming bulk eluent, leaving a deficiency zone of the plateau level (gray negative zone in Figure 9b). This negative plateau zone is eluting simultaneously with the positive tracer zone. The latter zone will, therefore, be canceled out and any ordinary detection principle cannot detect the tracer molecules.

27

Figure 10. Schematic chromatograms of the detected PP (red) (a) and the three zones actually present in the system, where the TP (blue) travels with the deficiency peak (gray negative peak) and the gray positive peak is the PP. Modified from J. Samuelsson, Anal. Chem. 76, 953. Copyright (2004) with permission from Ameri-can Chemical Society.

lthough only one peak is visible there are in reality, in the single-component case, three zones traveling through the column for the pulse methods (see Figure 10) [78,79]. To be able to detect the TP molecules they must be labeled in some way. One approach, used in Paper I, is to use stable isotopes that can be distinguished with a mass spectrometer [80]. Other less practical methods are to use radioactive tracers detected with a radiation detector [78] or to use enantiomers in an achiral column followed by analysis of the ratio of the enantiomers on a chiral column [78,81].

27

Figure 10. Schematic chromatograms of the detected PP (red) (a) and the three zones actually present in the system, where the TP (blue) travels with the deficiency peak (gray negative peak) and the gray positive peak is the PP. Modified from J. Samuelsson, Anal. Chem. 76, 953. Copyright (2004) with permission from Ameri-can Chemical Society.

lthough only one peak is visible there are in reality, in the single-component case, three zones traveling through the column for the pulse methods (see Figure 10) [78,79]. To be able to detect the TP molecules they must be labeled in some way. One approach, used in Paper I, is to use stable isotopes that can be distinguished with a mass spectrometer [80]. Other less practical methods are to use radioactive tracers detected with a radiation detector [78] or to use enantiomers in an achiral column followed by analysis of the ratio of the enantiomers on a chiral column [78,81].

28

Figure 11. Illustration of the relationship of the PPs and TPs to the adsorption isotherm. a) A type I adsorption isotherm where the perturbation peak is associ-ated with the tangential (solid red line) and the tracer peak to the chord (dashed blue line). b) The corresponding retention volumes of the PPs (red lines) and TPs (blue lines)

The velocity of the PPs and TPs are, respectively, related to the tangen-tial slope and the chord of the adsorption isotherm (Figure 11a). PPs and TPs have different retention volumes at different concentra-tion plateau levels (see Figure 10b) they can be used for adsorption iso-therm determinations. In the one-component case, the retention vol-ume of the PP can be obtained by

0R, pert 0

0

1dq C

V V FdC

(16)

and the retention volume of the TP by

0R, tracer 0

0

1q C

V V FC

(17)

where F is the phase ratio (i.e., the ratio of the volumes of stationary and mobile phases in the column), C0 is the concentration at the estab-lished concentration plateau, and VR is the retention volume of the PP or the TP.

28

Figure 11. Illustration of the relationship of the PPs and TPs to the adsorption isotherm. a) A type I adsorption isotherm where the perturbation peak is associ-ated with the tangential (solid red line) and the tracer peak to the chord (dashed blue line). b) The corresponding retention volumes of the PPs (red lines) and TPs (blue lines)

The velocity of the PPs and TPs are, respectively, related to the tangen-tial slope and the chord of the adsorption isotherm (Figure 11a). PPs and TPs have different retention volumes at different concentra-tion plateau levels (see Figure 10b) they can be used for adsorption iso-therm determinations. In the one-component case, the retention vol-ume of the PP can be obtained by

0R, pert 0

0

1dq C

V V FdC

(16)

and the retention volume of the TP by

0R, tracer 0

0

1q C

V V FC

(17)

where F is the phase ratio (i.e., the ratio of the volumes of stationary and mobile phases in the column), C0 is the concentration at the estab-lished concentration plateau, and VR is the retention volume of the PP or the TP.

29

-consuming and tedious since each required data point of the isotherm requires one experiment. One method to determine an adsorption isotherm that re-quires few experiments is the elution by characteristic point (ECP) method [82], in which the adsorption isotherm data is determined from the diffuse part of an overloaded elution profile. In Papers II, III and IV, the slope version of the ECP method was used [83,84]. In this method the raw slope data of the adsorption isotherm is deter-mined using

R 0 inj

a

V C V Vdq CdC V

(18)

where VR(C) is the retention volume corresponding to the mobile phase concentration C, V0 is the holdup volume, Vinj is the injection volume, and Va is the volume of the stationary phase.

requiring only a few experiments for obtaining an ad-sorption isotherm is the inverse method [66,85]. Here the adsorption isotherm is determined by iteratively solving the mass balance equa-tion. In this method, assumed isotherm models are used to minimize the difference between profiles calculated for a compound and the ex-perimental band profiles [66,85].

2.3.4 Solvents effects on retention dded to the mobile phase to modify

the solvent strength of the mobile phase, whereas the additive is added to the mobile phase to influence solute retention by competing for sta-tionary phase adsorption sites. In Papers I, II, and III it was shown that the co-solvent can act as both a modifier and an additive depend-ing on the co-solvent fraction. With a modifier, the retention factor of the solute (ksolute) will depend on the change in solvent strength and can be described with the LSS theory [86]: solute 0,solutelog logk k S (19)

29

-consuming and tedious since each required data point of the isotherm requires one experiment. One method to determine an adsorption isotherm that re-quires few experiments is the elution by characteristic point (ECP) method [82], in which the adsorption isotherm data is determined from the diffuse part of an overloaded elution profile. In Papers II, III and IV, the slope version of the ECP method was used [83,84]. In this method the raw slope data of the adsorption isotherm is deter-mined using

R 0 inj

a

V C V Vdq CdC V

(18)

where VR(C) is the retention volume corresponding to the mobile phase concentration C, V0 is the holdup volume, Vinj is the injection volume, and Va is the volume of the stationary phase.

requiring only a few experiments for obtaining an ad-sorption isotherm is the inverse method [66,85]. Here the adsorption isotherm is determined by iteratively solving the mass balance equa-tion. In this method, assumed isotherm models are used to minimize the difference between profiles calculated for a compound and the ex-perimental band profiles [66,85].

2.3.4 Solvents effects on retention dded to the mobile phase to modify

the solvent strength of the mobile phase, whereas the additive is added to the mobile phase to influence solute retention by competing for sta-tionary phase adsorption sites. In Papers I, II, and III it was shown that the co-solvent can act as both a modifier and an additive depend-ing on the co-solvent fraction. With a modifier, the retention factor of the solute (ksolute) will depend on the change in solvent strength and can be described with the LSS theory [86]: solute 0,solutelog logk k S (19)

30

where k0,solute is the retention factor of the solute in a weak eluent with no co-solvent (in the case of SFC, neat carbon dioxide), S is a com-pound-specific constant, and is the modifier fraction in the eluent. When an additive is present in the eluent, a competitive model is needed to describe the retention. The retention volume of the solute can, theoretically, be calculated using the theory of indirect detection [87]. This is done by first describing the adsorption using a competitive adsorption isotherm and then calculate the retention using

soluteR 0

solute

1q

V V FC

(20)

low and that a bi-Lang-muir adsorption model describes the adsorption of both solute and co-solvent, the retention can be expressed as

I, solute II, solutesolute S,I,solute S,II,solute

I,additive additive II, additive additive1 1b b

k Fq Fqb C b C

(21)

using parameters from the bi-Langmuir adsorption of the solute and the additive.

30

where k0,solute is the retention factor of the solute in a weak eluent with no co-solvent (in the case of SFC, neat carbon dioxide), S is a com-pound-specific constant, and is the modifier fraction in the eluent. When an additive is present in the eluent, a competitive model is needed to describe the retention. The retention volume of the solute can, theoretically, be calculated using the theory of indirect detection [87]. This is done by first describing the adsorption using a competitive adsorption isotherm and then calculate the retention using

soluteR 0

solute

1q

V V FC

(20)

low and that a bi-Lang-muir adsorption model describes the adsorption of both solute and co-solvent, the retention can be expressed as

I, solute II, solutesolute S,I,solute S,II,solute

I,additive additive II, additive additive1 1b b

k Fq Fqb C b C

(21)

using parameters from the bi-Langmuir adsorption of the solute and the additive.

31

2.4 Peak deformations Peak deformations occur in chromatographic systems for several dif-ferent reasons. The more complex the chromatographic system, the larger is common reason for peak de-formations in SFC is a sample diluent and eluent mismatch [88–90].

In SFC, the samples cannot be dissolved in the mobile phase, which can generate distortions based on the contrast between the eluent and the diluent and/or viscous fingering effects [89]. The deformations often decrease with modifier stream injections, where the sample is injected in the co-solvent stream before the mixer. Most analytical systems are, however, built with mixed stream injections, where the sample is in-jected after the co-solvent and carbon dioxide have already been mixed [88,89,91]. Below follows a discussion of the peak deformations that were treated in Papers II, III and V and which are connected to the competition with the solute for active sites on the stationary phase. De-formations may also appear when the solute interacts with other so-lutes that have already adsorbed on the stationary phase and multilayer are formed, as discussed in Section 2.3.1. This deformation will further be discussed in the discussion of Paper V.

2.4.1 Perturbation-peak-generated deformations One type of competitive peak distortion, observed in Papers II, III, and V, is caused by the system peak (i.e., the perturbation peak). Sys-tem peaks can be generated in systems where components from the mobile phase, other than the main solvent adsorb to the stationary phase [4]. This phenomenon has previously only been studied in LC systems with strongly adsorbing additives [3,5,92,93]. In the presence of an additive, the elution profile of a solute that has a Langmuirian shape (sharp front and diffuse tail) in an eluent containing only weak solvent, could turn into an anti-Langmuirian shape (diffuse front and sharp rear) with an increasing amount of the additive in the eluent. To predict if this distortion might appear, Fornstedt and Guiochon devel-oped the “rule of thumb” illustrated in Figure 12 [3,4,94]. This rule identifies two cases, , the retention factor of the solute (k0,solute) is larger than the retention factor of the additive (k0,additive) when eluted with a neat weak solvent, i.e. as carbon dioxide in SFC. In

31

2.4 Peak deformations Peak deformations occur in chromatographic systems for several dif-ferent reasons. The more complex the chromatographic system, the larger is common reason for peak de-formations in SFC is a sample diluent and eluent mismatch [88–90].

In SFC, the samples cannot be dissolved in the mobile phase, which can generate distortions based on the contrast between the eluent and the diluent and/or viscous fingering effects [89]. The deformations often decrease with modifier stream injections, where the sample is injected in the co-solvent stream before the mixer. Most analytical systems are, however, built with mixed stream injections, where the sample is in-jected after the co-solvent and carbon dioxide have already been mixed [88,89,91]. Below follows a discussion of the peak deformations that were treated in Papers II, III and V and which are connected to the competition with the solute for active sites on the stationary phase. De-formations may also appear when the solute interacts with other so-lutes that have already adsorbed on the stationary phase and multilayer are formed, as discussed in Section 2.3.1. This deformation will further be discussed in the discussion of Paper V.

2.4.1 Perturbation-peak-generated deformations One type of competitive peak distortion, observed in Papers II, III, and V, is caused by the system peak (i.e., the perturbation peak). Sys-tem peaks can be generated in systems where components from the mobile phase, other than the main solvent adsorb to the stationary phase [4]. This phenomenon has previously only been studied in LC systems with strongly adsorbing additives [3,5,92,93]. In the presence of an additive, the elution profile of a solute that has a Langmuirian shape (sharp front and diffuse tail) in an eluent containing only weak solvent, could turn into an anti-Langmuirian shape (diffuse front and sharp rear) with an increasing amount of the additive in the eluent. To predict if this distortion might appear, Fornstedt and Guiochon devel-oped the “rule of thumb” illustrated in Figure 12 [3,4,94]. This rule identifies two cases, , the retention factor of the solute (k0,solute) is larger than the retention factor of the additive (k0,additive) when eluted with a neat weak solvent, i.e. as carbon dioxide in SFC. In

32

case , the elution profile will remain Langmuirian independent of ad-ditive concentration in the eluent. In case B, when k0,additive k0,solute, three different situations are possible at different additive concentra-tions depending on the relative retention factors of the perturbation peak (kadditive) and the solute peak (ksolute):

Case BI: when kadditive > ksolute, the elution profile has a Lang-muirian shape.

Case BII: when kadditive ksolute, the elution profile has a rounded shape.

Case BIII: when kadditive < ksolute, the elution profile has an anti-Langmuirian shape.

Visualization of the additive signal (red line in Figure 12) reveals that the shape of the elution profile of the solute depends on the additive zone. The additive zone creates a local concentration gradient. In all cases presented here, the additive first appears as a positive peak and then a negative peak. Rajendran showed, based on a local equilibrium theory, that it actually exists ten different cases with different combi-nations of the additive peaks [95]. The four cases presented here are representative for these cases, and include all outcomes for the shape of the solute peak.

In case BI, the solute has a combined elution with the positive zone of the awhere the additive concentration rapidly increases. The increased ad-ditive concentration increases the velocity of the solute, and the elution profile for the solute will be Langmuirian. In case BIII, the solute in-stead co-elutes with a negative additive zone. In this zone, the additive concentration gradually decreases, causing a local gradient where the velocity of the solute molecules slows down. This decreased velocity will result in an anti-Langmuirian elution profile with a diffuse front. The rear will be sharp where the additive concentration drastically in-creases. In case BII, the rounded peak can be seen as an intermediate with an elution profile that consists of the anti-Langmuirian front merged with the Langmuirian rear.

32

case , the elution profile will remain Langmuirian independent of ad-ditive concentration in the eluent. In case B, when k0,additive k0,solute, three different situations are possible at different additive concentra-tions depending on the relative retention factors of the perturbation peak (kadditive) and the solute peak (ksolute):

Case BI: when kadditive > ksolute, the elution profile has a Lang-muirian shape.

Case BII: when kadditive ksolute, the elution profile has a rounded shape.

Case BIII: when kadditive < ksolute, the elution profile has an anti-Langmuirian shape.

Visualization of the additive signal (red line in Figure 12) reveals that the shape of the elution profile of the solute depends on the additive zone. The additive zone creates a local concentration gradient. In all cases presented here, the additive first appears as a positive peak and then a negative peak. Rajendran showed, based on a local equilibrium theory, that it actually exists ten different cases with different combi-nations of the additive peaks [95]. The four cases presented here are representative for these cases, and include all outcomes for the shape of the solute peak.

In case BI, the solute has a combined elution with the positive zone of the awhere the additive concentration rapidly increases. The increased ad-ditive concentration increases the velocity of the solute, and the elution profile for the solute will be Langmuirian. In case BIII, the solute in-stead co-elutes with a negative additive zone. In this zone, the additive concentration gradually decreases, causing a local gradient where the velocity of the solute molecules slows down. This decreased velocity will result in an anti-Langmuirian elution profile with a diffuse front. The rear will be sharp where the additive concentration drastically in-creases. In case BII, the rounded peak can be seen as an intermediate with an elution profile that consists of the anti-Langmuirian front merged with the Langmuirian rear.

33

Figure 12. Schematic flowchart of the rule of thumb proposed by Fornstedt and Guiochon [3,4]. Black lines represent the solute and red the additive. Modified from E. Glenne, et al., J. Chromatogr. A, 1468, 200-208, Copyright (2016), with permis-sion from Elsevier.

33

Figure 12. Schematic flowchart of the rule of thumb proposed by Fornstedt and Guiochon [3,4]. Black lines represent the solute and red the additive. Modified from E. Glenne, et al., J. Chromatogr. A, 1468, 200-208, Copyright (2016), with permis-sion from Elsevier.

34

2.4.2 Displacement and tag-along When a solute is competing with another simultaneously injected com-ponent peak deformations can occur due to so-called displacement or tag-along effects [2,3,58]. Which of the effects that will influence the peak shape is depending on the relative retention and concentration ratio between the solute and the competing component. The competing component can be another closely eluting solute in the sample, but also a solvent used to dilute the sample, i.e., the diluent. In Paper II and III, the co-solvent used as diluent was the cause for this kind of defor-mations. With the displacement effect is the first eluting solute displaced by the second, more strongly adsorbed, component. For small injection vol-umes, the displacement will only lead to decreased retention. s larger volumes are injected, the elution profile will also be deformed in such a way that it will be more compressed (see Figure 13 c). The tag-along effect can occur if the component that elutes first is in much larger concentration than the second more strongly adsorbing component. Figure 13d, this effect is expressed as a dragged out elution profile of the later eluting solute, with a front that is eluting earlier with increasing concentration of the competing com-ponent [58]. Inspecting the competitive Langmuir adsorption isotherm (Eq. (9)), it can be seen that if the concentration of a competing com-ponent increases, it will decrease the adsorption (q) of the other com-ponent [96]. With increasing sample size the front of the second solute approaches the rear of the first solute. Molecules in the front of the sec-ond solute zone that is expelled by the competition with the first solute will move with the zone of the first solute and have a higher velocity. This increased velocity will result in a hump on the front of the elution profile.

34

2.4.2 Displacement and tag-along When a solute is competing with another simultaneously injected com-ponent peak deformations can occur due to so-called displacement or tag-along effects [2,3,58]. Which of the effects that will influence the peak shape is depending on the relative retention and concentration ratio between the solute and the competing component. The competing component can be another closely eluting solute in the sample, but also a solvent used to dilute the sample, i.e., the diluent. In Paper II and III, the co-solvent used as diluent was the cause for this kind of defor-mations. With the displacement effect is the first eluting solute displaced by the second, more strongly adsorbed, component. For small injection vol-umes, the displacement will only lead to decreased retention. s larger volumes are injected, the elution profile will also be deformed in such a way that it will be more compressed (see Figure 13 c). The tag-along effect can occur if the component that elutes first is in much larger concentration than the second more strongly adsorbing component. Figure 13d, this effect is expressed as a dragged out elution profile of the later eluting solute, with a front that is eluting earlier with increasing concentration of the competing com-ponent [58]. Inspecting the competitive Langmuir adsorption isotherm (Eq. (9)), it can be seen that if the concentration of a competing com-ponent increases, it will decrease the adsorption (q) of the other com-ponent [96]. With increasing sample size the front of the second solute approaches the rear of the first solute. Molecules in the front of the sec-ond solute zone that is expelled by the competition with the first solute will move with the zone of the first solute and have a higher velocity. This increased velocity will result in a hump on the front of the elution profile.

35

Figure 13. Illustration of displacement (a, c) and tag-along effects (b, d). In a) and b), the simulations of elution profiles of solute and diluent assume no compe-tition. In c) and d) it is assumed that competition occurs. Reprinted from E. Glenne, et al., J. Chromatogr. A, 1496, 141-149, Copyright (2017), with permission from Elsevier.

35

Figure 13. Illustration of displacement (a, c) and tag-along effects (b, d). In a) and b), the simulations of elution profiles of solute and diluent assume no compe-tition. In c) and d) it is assumed that competition occurs. Reprinted from E. Glenne, et al., J. Chromatogr. A, 1496, 141-149, Copyright (2017), with permission from Elsevier.

36

3 Discussion of papers

The focus in this work has been to investigate the adsorption of co-sol-vents (Papers I-IV) and additives (Paper V) to stationary phases, and the effect these adsorptions have on the separation performance. The following section is intended to summarize the results from Pa-pers I-V.

3.1 Paper I Even though the understanding of SFC is increasing, the fundamental knowledge of SFC is still limited compared to HPLC. The co-solvent fraction is of high importance in SFC [31,44], and even though the den-sity and the solvent strength are shown to play important roles for the separation, also the adsorption of co-solvents has been indicated to af-fect the separation process [97,98]. The aim of Paper I was, therefore, to study the adsorption of the co-solvent methanol and to investigate how retention of solutes is related to this co-solvent adsorption. The adsorption isotherm of methanol has, in earlier studies, been de-termined for low co-solvent fractions [99,100] or with the PP method [76,101]. In Paper I, the surface excess adsorption isotherm of meth-anol was determined on a diol silica surface using the TP method. In the separation system studied in Paper I, the detected signals of the PPs were very noisy and contained several peaks at some concentration plateaus. The TPs generated one clear peak at all concentrations plat-eaus. Moreover, the TP method provides a more straightforward calcu-lation of the adsorption data compared to the PP method (cf. Eq. (12) and Eq. (13) in Section 2.3.2). The TP-method is, therefore, preferred over the PP method if adsorption isotherms are to be determined over the whole methanol fraction range. To detect the TPs, deuterium-labeled methanol (methanol-d4) was in-jected and monitored using a mass spectrometer. This labeling was de-termined suitable as it showed minimal labeling effect, i.e., the reten-tion of the labeled molecule showed the same retention behavior as un-labeled methanol.

36

3 Discussion of papers

The focus in this work has been to investigate the adsorption of co-sol-vents (Papers I-IV) and additives (Paper V) to stationary phases, and the effect these adsorptions have on the separation performance. The following section is intended to summarize the results from Pa-pers I-V.

3.1 Paper I Even though the understanding of SFC is increasing, the fundamental knowledge of SFC is still limited compared to HPLC. The co-solvent fraction is of high importance in SFC [31,44], and even though the den-sity and the solvent strength are shown to play important roles for the separation, also the adsorption of co-solvents has been indicated to af-fect the separation process [97,98]. The aim of Paper I was, therefore, to study the adsorption of the co-solvent methanol and to investigate how retention of solutes is related to this co-solvent adsorption. The adsorption isotherm of methanol has, in earlier studies, been de-termined for low co-solvent fractions [99,100] or with the PP method [76,101]. In Paper I, the surface excess adsorption isotherm of meth-anol was determined on a diol silica surface using the TP method. In the separation system studied in Paper I, the detected signals of the PPs were very noisy and contained several peaks at some concentration plateaus. The TPs generated one clear peak at all concentrations plat-eaus. Moreover, the TP method provides a more straightforward calcu-lation of the adsorption data compared to the PP method (cf. Eq. (12) and Eq. (13) in Section 2.3.2). The TP-method is, therefore, preferred over the PP method if adsorption isotherms are to be determined over the whole methanol fraction range. To detect the TPs, deuterium-labeled methanol (methanol-d4) was in-jected and monitored using a mass spectrometer. This labeling was de-termined suitable as it showed minimal labeling effect, i.e., the reten-tion of the labeled molecule showed the same retention behavior as un-labeled methanol.

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Figure 14. Surface excess adsorption determined using 1) set flow rate and meth-anol fraction (gray dashed line), 2) actual flow rate and set methanol fraction (gray dash-dotted line) or 3) both actual flow and methanol fraction (red line). The blue line shows estimated surface concentration determined with the measured flow and actual volume fractions. Modified from E. Glenne, et al., J. Chromatogr. A, 1442, 129-139, Copyright (2016), with permission from Elsevier.

Section 2.1, the actual conditions inside the column can

differ substantially from the conditions set in the instrument, due to the compressibility of carbon dioxide. , the ex-cess adsorption isotherm will differ if actual or set conditions are used. Figure 14 illustrates the difference for the excess adsorption deter-mined in three ways: 1) with set conditions, 2) with the measured flow rate but set volume fractions, and 3) with measured flow rate and actual volume fraction. In this case, the slope in the excess adsorption curve was much steeper when calculated with set conditions compared to ac-

thickness was estimated to be 60-90 % thicker when calculated with set conditions compared to actual conditions. Using actual conditions the thickness of the adsorption layer of meth-anol was determined to be 4Å, which corresponds to a monolayer. The

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Figure 14. Surface excess adsorption determined using 1) set flow rate and meth-anol fraction (gray dashed line), 2) actual flow rate and set methanol fraction (gray dash-dotted line) or 3) both actual flow and methanol fraction (red line). The blue line shows estimated surface concentration determined with the measured flow and actual volume fractions. Modified from E. Glenne, et al., J. Chromatogr. A, 1442, 129-139, Copyright (2016), with permission from Elsevier.

Section 2.1, the actual conditions inside the column can

differ substantially from the conditions set in the instrument, due to the compressibility of carbon dioxide. , the ex-cess adsorption isotherm will differ if actual or set conditions are used. Figure 14 illustrates the difference for the excess adsorption deter-mined in three ways: 1) with set conditions, 2) with the measured flow rate but set volume fractions, and 3) with measured flow rate and actual volume fraction. In this case, the slope in the excess adsorption curve was much steeper when calculated with set conditions compared to ac-

thickness was estimated to be 60-90 % thicker when calculated with set conditions compared to actual conditions. Using actual conditions the thickness of the adsorption layer of meth-anol was determined to be 4Å, which corresponds to a monolayer. The

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maximum of the excess was reached at a methanol fraction of 13 v% (vertical dashed line in Figure 14). The inflection point on the negative slope of the excess adsorption isotherm, used to determine the volume of the adsorbed layer, was determined at 28 v% (vertical dotted line in Figure 14). When the measured adsorption isotherm was compared with the re-tention fractions, the relationship between the logarithms of the retention fac-tor of the solutes and the methanol fraction shows a curvature. This curvature correlates well with the first part of the methanol adsorption isotherm before the formation of a monolayer. The curvature indicates that in this region, the methanol might be competing with the solute for the available surface, which is further investigated in Paper II. higher fractions, when the methanol layer on the phase has formed, the logarithm of the retention factor reaches a more or less linear relation-ship with the methanol fraction.

3.2 Paper II In Paper I, it was shown that the co-solvent methanol adsorbs to the stationary phase. Further, it was indicated that the co-solvent might compete with the solutes for available sites on the stationary phase sur-face, hence functioning as an additive. In Paper II the effect of this competition on retention was investigated by fitting the different mechanistic models described in Section 2.3.4 to experimental data. Measurement of the retention resulted in the same pattern as in Paper I with a clear curvature at fractions below the excess of the adsorption isotherm (dashed vertical line in Figure 15). The curvature then gradu-ally declines. t fractions above the inflection point, where a methanol monolayer has been obtained (dotted vertical line in Figure 15), the re-lationship is more or less linear. The LSS-theory, discussed in Section 2.3.4, could only be used to describe the retention in the linear region where the methanol layer had been formed. t lower methanol frac-tions, the competitive model (Eq.(21)) was needed to describe the re-tention. This demonstrates that in SFC, the co-solvent has a dual func-tion and can act both as a modifier and an additive.

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maximum of the excess was reached at a methanol fraction of 13 v% (vertical dashed line in Figure 14). The inflection point on the negative slope of the excess adsorption isotherm, used to determine the volume of the adsorbed layer, was determined at 28 v% (vertical dotted line in Figure 14). When the measured adsorption isotherm was compared with the re-tention fractions, the relationship between the logarithms of the retention fac-tor of the solutes and the methanol fraction shows a curvature. This curvature correlates well with the first part of the methanol adsorption isotherm before the formation of a monolayer. The curvature indicates that in this region, the methanol might be competing with the solute for the available surface, which is further investigated in Paper II. higher fractions, when the methanol layer on the phase has formed, the logarithm of the retention factor reaches a more or less linear relation-ship with the methanol fraction.

3.2 Paper II In Paper I, it was shown that the co-solvent methanol adsorbs to the stationary phase. Further, it was indicated that the co-solvent might compete with the solutes for available sites on the stationary phase sur-face, hence functioning as an additive. In Paper II the effect of this competition on retention was investigated by fitting the different mechanistic models described in Section 2.3.4 to experimental data. Measurement of the retention resulted in the same pattern as in Paper I with a clear curvature at fractions below the excess of the adsorption isotherm (dashed vertical line in Figure 15). The curvature then gradu-ally declines. t fractions above the inflection point, where a methanol monolayer has been obtained (dotted vertical line in Figure 15), the re-lationship is more or less linear. The LSS-theory, discussed in Section 2.3.4, could only be used to describe the retention in the linear region where the methanol layer had been formed. t lower methanol frac-tions, the competitive model (Eq.(21)) was needed to describe the re-tention. This demonstrates that in SFC, the co-solvent has a dual func-tion and can act both as a modifier and an additive.

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Figure 15. Relationship between the logarithms of the retention factor for solutes to different methanol fractions on a diol silica surface.

When the co-solvent is acting as an additive, it might, in addition to the effects on retention, also affect the shape of the solutes elution profiles.

additive that is adsorbing more strongly than the solute can cause severe deformations, as discussed in Section 2.4.1. To investigate if these perturbation-peak-generated deformations, previously only ob-served in LC, occur in SFC, elution profiles from overload injections of phenol, 1-phenyl-1-propanol, and valerophenone were investigated. When eluted with neat carbon dioxide, these solutes showed different relative retention compared to methanol under the same conditions (see Figure 14). Injections of phenol, that eluted much later than meth-anol, always resulted in elution profiles with a Langmuirian shape, in-dependent of the methanol fraction in the eluent. Using the rule of thumb, discussed in Section 2.4.1, phenol Valerophenone eluted earlier than methanol using neat carbon dioxide as eluent (see Figure 16a), and, as expected according to the rule of thumb, the elution profiles became distorted with increasing methanol fraction in the eluent. In neat carbon dioxide, the elution profile has a Langmuirian shape, but with increasing methanol fractions, the profile first becomes rounded and then anti-Langmuirian (see Figure 16b). The rounded shape is observed at a methanol fraction of approximately 6 v%, where valerophenone co-elutes with the perturbation peak of methanol (kadditive solute), as in case BII. For higher methanol fractions valerophenone elutes later than the perturbation peak (kadditive < ksolute), and the elution profile becomes anti-Langmuirian, as in case BIII.

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Figure 15. Relationship between the logarithms of the retention factor for solutes to different methanol fractions on a diol silica surface.

When the co-solvent is acting as an additive, it might, in addition to the effects on retention, also affect the shape of the solutes elution profiles.

additive that is adsorbing more strongly than the solute can cause severe deformations, as discussed in Section 2.4.1. To investigate if these perturbation-peak-generated deformations, previously only ob-served in LC, occur in SFC, elution profiles from overload injections of phenol, 1-phenyl-1-propanol, and valerophenone were investigated. When eluted with neat carbon dioxide, these solutes showed different relative retention compared to methanol under the same conditions (see Figure 14). Injections of phenol, that eluted much later than meth-anol, always resulted in elution profiles with a Langmuirian shape, in-dependent of the methanol fraction in the eluent. Using the rule of thumb, discussed in Section 2.4.1, phenol Valerophenone eluted earlier than methanol using neat carbon dioxide as eluent (see Figure 16a), and, as expected according to the rule of thumb, the elution profiles became distorted with increasing methanol fraction in the eluent. In neat carbon dioxide, the elution profile has a Langmuirian shape, but with increasing methanol fractions, the profile first becomes rounded and then anti-Langmuirian (see Figure 16b). The rounded shape is observed at a methanol fraction of approximately 6 v%, where valerophenone co-elutes with the perturbation peak of methanol (kadditive solute), as in case BII. For higher methanol fractions valerophenone elutes later than the perturbation peak (kadditive < ksolute), and the elution profile becomes anti-Langmuirian, as in case BIII.

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Figure 16. a) Retention factor of perturbation peaks of methanol (gray) and vale-rophenone (blue) b) Elution profiles for injections of valerophenone. Reprinted from E. Glenne, et al., J. Chromatogr. A, 1468, 200-208 Copyright (2016), with permission from Elsevier.

1-phenyl-1-propanol eluted closely, but slightly later, than methanol in neat carbon dioxide. 0,methanol k0, solute the requirement for the per-turbation-peak-generated deformation is approached, and the elution profile gets slightly rounded with methanol present in the eluent (see Fig. 6 in Paper II). This roundness has previously been noted for so-lutes that have identical adsorption strength as the co-solvent [102]. The adsorption of methanol is, however, not strong enough to turn the elution profile into the anti-Langmuirian shape.

3.3 Paper III Even if methanol is the most frequently used co-solvent in SFC, other alcohols are also used. Method development in SFC often includes a screening of a variety of column chemistries and co-solvents to find the optimal separation condition. To investigate the generality of an ad-sorbing co-solvent and the peak deformations seen in Paper I-II the investigations were extended with the co-solvents 2-propanol, ethanol, and acetonitrile and with a 2-EP and a silica stationary phase. Compared to mixtures of carbon dioxide and methanol, EoS for mix-tures with other co-solvents are not as well investigated. Prior to the study in Paper III, it was attempted to find suitable EoS also for other

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Figure 16. a) Retention factor of perturbation peaks of methanol (gray) and vale-rophenone (blue) b) Elution profiles for injections of valerophenone. Reprinted from E. Glenne, et al., J. Chromatogr. A, 1468, 200-208 Copyright (2016), with permission from Elsevier.

1-phenyl-1-propanol eluted closely, but slightly later, than methanol in neat carbon dioxide. 0,methanol k0, solute the requirement for the per-turbation-peak-generated deformation is approached, and the elution profile gets slightly rounded with methanol present in the eluent (see Fig. 6 in Paper II). This roundness has previously been noted for so-lutes that have identical adsorption strength as the co-solvent [102]. The adsorption of methanol is, however, not strong enough to turn the elution profile into the anti-Langmuirian shape.

3.3 Paper III Even if methanol is the most frequently used co-solvent in SFC, other alcohols are also used. Method development in SFC often includes a screening of a variety of column chemistries and co-solvents to find the optimal separation condition. To investigate the generality of an ad-sorbing co-solvent and the peak deformations seen in Paper I-II the investigations were extended with the co-solvents 2-propanol, ethanol, and acetonitrile and with a 2-EP and a silica stationary phase. Compared to mixtures of carbon dioxide and methanol, EoS for mix-tures with other co-solvents are not as well investigated. Prior to the study in Paper III, it was attempted to find suitable EoS also for other

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mixtures by comparing calculated density with experimental data in the literature. For mixtures with ethanol, a few reported measurements at suitable pressures and temperatures are available [103–105] and cal-culations with the PC [106] showed good agreement with the experimental data. On the other hand, no experimental data at appro-priate conditions were found for mixtures with acetonitrile. To make accurate calculations of the density of the solvents used in SFC more experimental measurements are needed. One approach that later was shown to be successful was the use of a Coriolis mass flowmeter to measure the density [VI]. consequence of the lack of suitable EoS, the volumetric flow and co-solvent fraction set on the instrument were used together with a void volume marker to normalize the results. The aim of the paper was, therefore, to give a relative comparison between the different conditions and not to determine the exact adsorption iso-therm.

Figure 17. Adsorption isotherm of methanol, ethanol, 2-propanol, and acetoni-trile. For experimental conditions, see Paper III. Reprinted from E. Glenne, et al., J. Chromatogr. A, 1496, 141-149, Copyright (2017), with permission from Elsevier.

When the adsorption of different common co-solvents to the diol sta-tionary phase was compared it was evident that methanol has the strongest adsorption, followed by ethanol, 2-propanol, and acetonitrile (see Figure 17). Overloaded elution profiles for the same solutes as in Paper II were investigated. an all the

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mixtures by comparing calculated density with experimental data in the literature. For mixtures with ethanol, a few reported measurements at suitable pressures and temperatures are available [103–105] and cal-culations with the PC [106] showed good agreement with the experimental data. On the other hand, no experimental data at appro-priate conditions were found for mixtures with acetonitrile. To make accurate calculations of the density of the solvents used in SFC more experimental measurements are needed. One approach that later was shown to be successful was the use of a Coriolis mass flowmeter to measure the density [VI]. consequence of the lack of suitable EoS, the volumetric flow and co-solvent fraction set on the instrument were used together with a void volume marker to normalize the results. The aim of the paper was, therefore, to give a relative comparison between the different conditions and not to determine the exact adsorption iso-therm.

Figure 17. Adsorption isotherm of methanol, ethanol, 2-propanol, and acetoni-trile. For experimental conditions, see Paper III. Reprinted from E. Glenne, et al., J. Chromatogr. A, 1496, 141-149, Copyright (2017), with permission from Elsevier.

When the adsorption of different common co-solvents to the diol sta-tionary phase was compared it was evident that methanol has the strongest adsorption, followed by ethanol, 2-propanol, and acetonitrile (see Figure 17). Overloaded elution profiles for the same solutes as in Paper II were investigated. an all the

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solutes, while the other co-solvents adsorbed stronger than valerophe-none but weaker than 1-phenyl-1-propanol and phenol. Both phenol and 1-phenyl-1-propanol eluted with Langmuirian elution profiles. The roundness observed for 1-phenyl-1-propanol when eluted with metha-nol was also found when it was eluted with ethanol. The roundness de-creased with decreased adsorption strength of the co-solvent, and for acetonitrile, the elution profile was sharply Langmuirian. For vale-rophenone, the perturbation-peak-generated distortion observed in Paper II was present with all co-solvents except the weakest adsorbing acetonitrile. With decreasing adsorption strength of the co-solvents, the shift from the Langmuirian shape to the anti-Langmuirian shape occurred at lower co-solvent fractions. Since acetonitrile adsorbed weaker than valerophenone, the roundness seen for 1-phenyl-1-propa-nol was also observed for this solute.

Figure 18. Elution profiles for injections of methanol eluted with neat carbon di-oxide on three stationary phases: diol, 2-EP, and silica.

The adsorption of methanol was strongest to the silica phase, followed by 2-EP and was weakest to the diol stationary phase (see Figure 18). In the column study, it was demonstrated that a simple way to test the risk for the perturbation-peak-generated deformation is to elute the so-

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solutes, while the other co-solvents adsorbed stronger than valerophe-none but weaker than 1-phenyl-1-propanol and phenol. Both phenol and 1-phenyl-1-propanol eluted with Langmuirian elution profiles. The roundness observed for 1-phenyl-1-propanol when eluted with metha-nol was also found when it was eluted with ethanol. The roundness de-creased with decreased adsorption strength of the co-solvent, and for acetonitrile, the elution profile was sharply Langmuirian. For vale-rophenone, the perturbation-peak-generated distortion observed in Paper II was present with all co-solvents except the weakest adsorbing acetonitrile. With decreasing adsorption strength of the co-solvents, the shift from the Langmuirian shape to the anti-Langmuirian shape occurred at lower co-solvent fractions. Since acetonitrile adsorbed weaker than valerophenone, the roundness seen for 1-phenyl-1-propa-nol was also observed for this solute.

Figure 18. Elution profiles for injections of methanol eluted with neat carbon di-oxide on three stationary phases: diol, 2-EP, and silica.

The adsorption of methanol was strongest to the silica phase, followed by 2-EP and was weakest to the diol stationary phase (see Figure 18). In the column study, it was demonstrated that a simple way to test the risk for the perturbation-peak-generated deformation is to elute the so-

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lute and the co-solvent with neat carbon dioxide and compare the re-tention. If the solute elutes earlier than the co-solvent, which was the case for valerophenone on all columns, the deformation is likely to ap-pear. The strong adsorption of methanol to the silica column caused some degree of the perturbation-peak-generated deformations for all the so-lutes. In addition, other competitive effects such as tag-along and dis-placement effects were also enhanced on this column. These effects were also observed in Paper II, where the rear of the elution profile of valerophenone (profile I in Figure 16b) and the front of the elution pro-file of 1-phenyl-1-propanol were displaced. On the silica column the peaks were more severely deformed. These deformations were ob-served when the solutes were eluted with neat carbon and they are not caused by methanol present in the eluent. The cause of these defor-mations is, instead, a competition with the methanol used as diluent. Injections of the solutes in heptane confirmed this solute-diluent com-petition. Heptane adsorbs much weaker than methanol and caused no deformations.

3.4 Paper IV The density is traditionally mentioned as the main factor regulating the retention in SFC, where an increasing density will decrease the reten-tion [15,107–110]. The results reported in Papers I, II, and III have, however, shown that the adsorption of the co-solvent also influences the retention. In Papers I, II, and III, the adsorption was investigated with a set temperature of 40 °C, and the BPR set to 120 or 140 bar. the density of the mobile phase is sensitive to pressure and tempera-ture, it was of interest to investigate how the co-solvent adsorption is affected by pressure and temperature and how this adsorption affects the robustness of the separation. In addition to measuring the metha-nol adsorption, the retention for several solutes was measured at sev-eral different pressures, temperatures, and co-solvent fractions.

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lute and the co-solvent with neat carbon dioxide and compare the re-tention. If the solute elutes earlier than the co-solvent, which was the case for valerophenone on all columns, the deformation is likely to ap-pear. The strong adsorption of methanol to the silica column caused some degree of the perturbation-peak-generated deformations for all the so-lutes. In addition, other competitive effects such as tag-along and dis-placement effects were also enhanced on this column. These effects were also observed in Paper II, where the rear of the elution profile of valerophenone (profile I in Figure 16b) and the front of the elution pro-file of 1-phenyl-1-propanol were displaced. On the silica column the peaks were more severely deformed. These deformations were ob-served when the solutes were eluted with neat carbon and they are not caused by methanol present in the eluent. The cause of these defor-mations is, instead, a competition with the methanol used as diluent. Injections of the solutes in heptane confirmed this solute-diluent com-petition. Heptane adsorbs much weaker than methanol and caused no deformations.

3.4 Paper IV The density is traditionally mentioned as the main factor regulating the retention in SFC, where an increasing density will decrease the reten-tion [15,107–110]. The results reported in Papers I, II, and III have, however, shown that the adsorption of the co-solvent also influences the retention. In Papers I, II, and III, the adsorption was investigated with a set temperature of 40 °C, and the BPR set to 120 or 140 bar. the density of the mobile phase is sensitive to pressure and tempera-ture, it was of interest to investigate how the co-solvent adsorption is affected by pressure and temperature and how this adsorption affects the robustness of the separation. In addition to measuring the metha-nol adsorption, the retention for several solutes was measured at sev-eral different pressures, temperatures, and co-solvent fractions.

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Figure 19. Isopycnic plots showing the density at varying pressure and co-solvent fractions at a) 25 and b) 55 °C. Red horizontal lines represent the experimental con-ditions used in Paper IV.

The horizontal lines in the isopycnic plots in Figure 19 show the exper-imental conditions used in Paper IV. The plot shows that the density can be the same at different conditions. For example, the density is more or less unchanged with increasing methanol fraction at a temper-ature of 25 °creasing with increasing co-density is not suitable to be used as a descriptor for retention, as the retention is decreasing with increasing co-solvent fractions, as shown in Figure 20.

Figure 20. a) Retention factor for carbazole and b) adsorption isotherm for meth-anol measured with a set BPR of 110, 210, and 310 bar and a set temperature of 25 or 55 °C. Lines in a) show fit to Eq. (21). Reproduced from Paper IV.

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Figure 19. Isopycnic plots showing the density at varying pressure and co-solvent fractions at a) 25 and b) 55 °C. Red horizontal lines represent the experimental con-ditions used in Paper IV.

The horizontal lines in the isopycnic plots in Figure 19 show the exper-imental conditions used in Paper IV. The plot shows that the density can be the same at different conditions. For example, the density is more or less unchanged with increasing methanol fraction at a temper-ature of 25 °creasing with increasing co-density is not suitable to be used as a descriptor for retention, as the retention is decreasing with increasing co-solvent fractions, as shown in Figure 20.

Figure 20. a) Retention factor for carbazole and b) adsorption isotherm for meth-anol measured with a set BPR of 110, 210, and 310 bar and a set temperature of 25 or 55 °C. Lines in a) show fit to Eq. (21). Reproduced from Paper IV.

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The retention factor was measured for several solutes, all showing sim-ilar results to those of carbazole in Figure 20a, with decreasing reten-tion at increasing co-solvent fraction and increasing pressure. Most no-ticeable is the drastic decrease in retention with increasing co-solvent at high temperature and low pressure. The sensitivity of the separation system decreases with increasing pressure and decreasing tempera-ture. variation of the retention factor with the density

sity drastically decreases at high temperature, low pressure and low co-solvent fraction. The increased retention at low co-solvent fractions at other conditions is, on the other hand, not well explained by the den-sity. When the adsorption of methanol was measured at the same conditions as the solutes, a drastic increase at low co-solvent fractions was noted (see Figure 20b). The increase declines around 4 w%, which was con-sistent with the pattern in the retention of the solutes. The adsorption was strongly dependent on pressure and temperature, and methanol adsorption was strongest at low pressure and high temperature. The adsorption did decrease with increasing pressure but had no clear re-lation to the temperature. . (21) showed that there is a strong relationship between the co-solvent ad-sorption and solvent retention (Figure 20a).

approach was used to further investigate how temperature, pressure, and amount of modifier affects the retention factors for the solutes. -solvent fraction is non-linear two designs, one with low methanol frac-tions and one with high fractions, were used. The design showed that co-solvent fraction and pressure, more or less, have the same effect on the retention. The temperature, however, had a smaller effect on reten-tion as compared to pressure and co-solvent fractions.

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The retention factor was measured for several solutes, all showing sim-ilar results to those of carbazole in Figure 20a, with decreasing reten-tion at increasing co-solvent fraction and increasing pressure. Most no-ticeable is the drastic decrease in retention with increasing co-solvent at high temperature and low pressure. The sensitivity of the separation system decreases with increasing pressure and decreasing tempera-ture. variation of the retention factor with the density

sity drastically decreases at high temperature, low pressure and low co-solvent fraction. The increased retention at low co-solvent fractions at other conditions is, on the other hand, not well explained by the den-sity. When the adsorption of methanol was measured at the same conditions as the solutes, a drastic increase at low co-solvent fractions was noted (see Figure 20b). The increase declines around 4 w%, which was con-sistent with the pattern in the retention of the solutes. The adsorption was strongly dependent on pressure and temperature, and methanol adsorption was strongest at low pressure and high temperature. The adsorption did decrease with increasing pressure but had no clear re-lation to the temperature. . (21) showed that there is a strong relationship between the co-solvent ad-sorption and solvent retention (Figure 20a).

approach was used to further investigate how temperature, pressure, and amount of modifier affects the retention factors for the solutes. -solvent fraction is non-linear two designs, one with low methanol frac-tions and one with high fractions, were used. The design showed that co-solvent fraction and pressure, more or less, have the same effect on the retention. The temperature, however, had a smaller effect on reten-tion as compared to pressure and co-solvent fractions.

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Figure 21. The standard deviation of the retention factor of carbazole at a con-trolled perturbation at different temperatures and pressures at a methanol frac-tion of a) 2.5 w% or b) 13 w%. Reproduced from Paper IV

The robustness of a system can be seen as the ability of a system to stay unaffected with small perturbations of the system. To estimate the ro-bustness the retention models from the DoE were used to simulate how perturbations in temperature, pressure, and co-solvent affect the re-tention. The standard deviations of retention factors calculated for a large number of experiments, where perturbations in pressure, tem-perature and amount of co-solvents were randomly generated, are pre-sented in Figure 21 shows. The standard deviation decreases with in-creasing pressure and decreasing temperature with both retention models. Using the model based on low methanol fractions the varia-tions in retention are, however, much larger. This indicates that the system becomes more robust with high methanol fractions, higher pressure and lower temperature.

-called UHPSFC. the use of smaller particles is that the pressure drop over the column is drastically increased. To avoid ex-ceeding the maximum pressure allowed it may be needed to use low backpressure. This lower backpressure may lead to a less robust sys-tem, as shown for the SFC column. ducted on a UHPSFC column and an SFC column revealed that the UHPSFC system is generally less robust since the UHPSFC system is

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Figure 21. The standard deviation of the retention factor of carbazole at a con-trolled perturbation at different temperatures and pressures at a methanol frac-tion of a) 2.5 w% or b) 13 w%. Reproduced from Paper IV

The robustness of a system can be seen as the ability of a system to stay unaffected with small perturbations of the system. To estimate the ro-bustness the retention models from the DoE were used to simulate how perturbations in temperature, pressure, and co-solvent affect the re-tention. The standard deviations of retention factors calculated for a large number of experiments, where perturbations in pressure, tem-perature and amount of co-solvents were randomly generated, are pre-sented in Figure 21 shows. The standard deviation decreases with in-creasing pressure and decreasing temperature with both retention models. Using the model based on low methanol fractions the varia-tions in retention are, however, much larger. This indicates that the system becomes more robust with high methanol fractions, higher pressure and lower temperature.

-called UHPSFC. the use of smaller particles is that the pressure drop over the column is drastically increased. To avoid ex-ceeding the maximum pressure allowed it may be needed to use low backpressure. This lower backpressure may lead to a less robust sys-tem, as shown for the SFC column. ducted on a UHPSFC column and an SFC column revealed that the UHPSFC system is generally less robust since the UHPSFC system is

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more sensitive to flow rate changes. From calculations of temperature and density profiles for the columns, it was also clear that these gradi-ents are much larger in the UHPSFC column than in the SFC column. In the UHPSFC column the temperature drop was approximately 6 °C larger than the SFC column. In the UHPSFC column the density dropped nearly 20% compared to only 3% in the SFC column.

3.5 Paper V Pharmaceutical compounds often contain amine functional groups. To obtain acceptable peak shapes for these types of compounds it is often needed to use a basic additive in addition to the co-solvent (see Figure 6). These additives can adsorb even stronger to the stationary phase than the co-solvent, and the study in Paper V aimed at investigating in more detail how these additives affect the separation performances of basic pharmaceuticals. lprenolol, metoprolol, and propranolol were used as model solutes. The eluent consisted of methanol as co-solvent and diethylamine , triethylamine , or isopropyla-mine (iPrNH2) were used as additives at variating concentrations. Since the mobile phase consisted of both the co-solvent and an addi-tive, there was a need to distinguish the effects of the two components. To reduce the additive effects from the co-solvent higher fractions than the maximum point of the excess adsorption of methanol was used. In this region, methanol functions mainly as a co-solvent, according to the findings in Paper I and II. DoE approach was used to separate the effects of the co-solvent from the effects of the additive. In the DoE, the concentrations of and methanol were used as factors, and the re-tention time and peak efficiency for analytical injections of the solutes were used as responses. The results show that the co-solvent had a more substantial effect on retention, whereas both the co-solvent and the additive affected the peak shapes. To conclude, it is best to use the co-solvent to tune the retention and an additive can be used to improve the peak shape. The analytical study was complemented with studies of overloaded elu-tion profiles to get a more complete understanding of the interactions. For alprenolol, in agreement with the DoE, the elution profile was

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more sensitive to flow rate changes. From calculations of temperature and density profiles for the columns, it was also clear that these gradi-ents are much larger in the UHPSFC column than in the SFC column. In the UHPSFC column the temperature drop was approximately 6 °C larger than the SFC column. In the UHPSFC column the density dropped nearly 20% compared to only 3% in the SFC column.

3.5 Paper V Pharmaceutical compounds often contain amine functional groups. To obtain acceptable peak shapes for these types of compounds it is often needed to use a basic additive in addition to the co-solvent (see Figure 6). These additives can adsorb even stronger to the stationary phase than the co-solvent, and the study in Paper V aimed at investigating in more detail how these additives affect the separation performances of basic pharmaceuticals. lprenolol, metoprolol, and propranolol were used as model solutes. The eluent consisted of methanol as co-solvent and diethylamine , triethylamine , or isopropyla-mine (iPrNH2) were used as additives at variating concentrations. Since the mobile phase consisted of both the co-solvent and an addi-tive, there was a need to distinguish the effects of the two components. To reduce the additive effects from the co-solvent higher fractions than the maximum point of the excess adsorption of methanol was used. In this region, methanol functions mainly as a co-solvent, according to the findings in Paper I and II. DoE approach was used to separate the effects of the co-solvent from the effects of the additive. In the DoE, the concentrations of and methanol were used as factors, and the re-tention time and peak efficiency for analytical injections of the solutes were used as responses. The results show that the co-solvent had a more substantial effect on retention, whereas both the co-solvent and the additive affected the peak shapes. To conclude, it is best to use the co-solvent to tune the retention and an additive can be used to improve the peak shape. The analytical study was complemented with studies of overloaded elu-tion profiles to get a more complete understanding of the interactions. For alprenolol, in agreement with the DoE, the elution profile was

48

sharpened with increasing concentration (Figure 22a-c). additive concentrations, some signs of deformations that were en-hanced with increasing methanol fraction were observed (Figure 22d-f). Without the additive in the eluent, alprenolol eluted later, but close

s for perturbation-peak-generated distor-tion were approached.

Figure 22. Overloaded elution profiles for injections of alprenolol eluted with in-creasing DEA concentration, and increasing MeOH concentration. The arrows show the elution volume of the DEA perturbation peak. For experimental details see Paper V.

The shape of the distorted elution profiles obtained for valerophenone shows similarities to the tag-along effect seen in Papers II and III (Figure 23). In this case, the perturbation peak and not the diluent is the cause of the distortion. Simulations of the distortion showed that the solute zone travels with both the positive perturbation zone and the negative deficiency zone (Figure 23). The perturbation zone forms an internal gradient for the solute, where the molecules in the front of the solute zone experience an increased velocity due to the increased addi-tive concentration. The molecules in the rear of the solute zone travel

48

sharpened with increasing concentration (Figure 22a-c). additive concentrations, some signs of deformations that were en-hanced with increasing methanol fraction were observed (Figure 22d-f). Without the additive in the eluent, alprenolol eluted later, but close

s for perturbation-peak-generated distor-tion were approached.

Figure 22. Overloaded elution profiles for injections of alprenolol eluted with in-creasing DEA concentration, and increasing MeOH concentration. The arrows show the elution volume of the DEA perturbation peak. For experimental details see Paper V.

The shape of the distorted elution profiles obtained for valerophenone shows similarities to the tag-along effect seen in Papers II and III (Figure 23). In this case, the perturbation peak and not the diluent is the cause of the distortion. Simulations of the distortion showed that the solute zone travels with both the positive perturbation zone and the negative deficiency zone (Figure 23). The perturbation zone forms an internal gradient for the solute, where the molecules in the front of the solute zone experience an increased velocity due to the increased addi-tive concentration. The molecules in the rear of the solute zone travel

49

with the negative deficiency zone of the additive. In the rear of the neg-ative zone the ly increases, causing a rapid in-crease of the rear of elution profile of the solute is sharp.

Figure 23. a) Simulated (red line) and experimental (black line) alprenolol signal following injections of 2-, 4-, 6- and 8-μL of 100 mM alprenolol and b) the corre-sponding simulated DEA additive signal. The mobile phase contained 21 v% MeOH and 0.021 v% DEA. Reproduced from Paper V

Deformations were also noted for propranolol, even though this solute was eluting much later and was well resolved from the additive. This deformation could not be explained by competition for active sites on the stationary phase. Inspecting the shape of the elution profiles of the solute eluted with 16 v% methanol and varying content in Figure 24, that becomes dispersed at higher concentration whereas the tail is sharp at high concentrations and then disperse at low concentrations.

ed in Section 2.3.1, this profile can be related to an adsorp-, the profile gets

an anti-Langmuirian shape indicating a type III isotherm.

49

with the negative deficiency zone of the additive. In the rear of the neg-ative zone the ly increases, causing a rapid in-crease of the rear of elution profile of the solute is sharp.

Figure 23. a) Simulated (red line) and experimental (black line) alprenolol signal following injections of 2-, 4-, 6- and 8-μL of 100 mM alprenolol and b) the corre-sponding simulated DEA additive signal. The mobile phase contained 21 v% MeOH and 0.021 v% DEA. Reproduced from Paper V

Deformations were also noted for propranolol, even though this solute was eluting much later and was well resolved from the additive. This deformation could not be explained by competition for active sites on the stationary phase. Inspecting the shape of the elution profiles of the solute eluted with 16 v% methanol and varying content in Figure 24, that becomes dispersed at higher concentration whereas the tail is sharp at high concentrations and then disperse at low concentrations.

ed in Section 2.3.1, this profile can be related to an adsorp-, the profile gets

an anti-Langmuirian shape indicating a type III isotherm.

50

Figure 24. Overloaded elution profiles for propranolol eluted with a constant methanol fraction and increasing DEA content in eluent from. Red lines are calcu-lated elution profiles. For experimental details see Paper V. Reproduced from Pa-per V

tion profiles indicated multilayer formations a

BET adsorption model was used to estimate the adsorption isotherm data with the inverse method. This model provided a very good fit to the experimental data (red dotted line in Figure 24). The modeling con-firmed that at low concentration propranolol has a type II adsorp-tion isotherm with an inflection point (see Figure 25a), indicating that there are solute-solute interactions that causes layer formations. With increasing content, the adsorption isotherm turns into type III in-dicating that the solute-solute interactions increase and that incom-plete layers are formed.

Figure 25. a) Adsorption isotherms for propranolol at different eluent composi-tions corresponding to Figure 24. b) Illustration of layer formations correspond-ing to the isotherms in a). Reproduced from Paper V

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Figure 24. Overloaded elution profiles for propranolol eluted with a constant methanol fraction and increasing DEA content in eluent from. Red lines are calcu-lated elution profiles. For experimental details see Paper V. Reproduced from Pa-per V

tion profiles indicated multilayer formations a

BET adsorption model was used to estimate the adsorption isotherm data with the inverse method. This model provided a very good fit to the experimental data (red dotted line in Figure 24). The modeling con-firmed that at low concentration propranolol has a type II adsorp-tion isotherm with an inflection point (see Figure 25a), indicating that there are solute-solute interactions that causes layer formations. With increasing content, the adsorption isotherm turns into type III in-dicating that the solute-solute interactions increase and that incom-plete layers are formed.

Figure 25. a) Adsorption isotherms for propranolol at different eluent composi-tions corresponding to Figure 24. b) Illustration of layer formations correspond-ing to the isotherms in a). Reproduced from Paper V

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If the methanol concentration instead was increased at constant concentration, the adsorption isotherm of propranolol turned from type III to type I and at the elution profile had the classic Langmuirian shape. Propranolol, contains a naphthyl group, which is hydrophobic.

proposed explanation for the layer formation is that the amine addi-tive acts as a kosmotropic agent, which enhances the hydrophobic in-teractions with increasing concentration. n increase in methanol con-centration will increase the polarity of the mobile phase which will counteract this effect.

Figure 26. Illustration of possible adsorption of propranolol to a diol surface. To the right, a propranolol molecule interacting with the hydrophobic part of an al-ready adsorbed propranolol molecule, causing a multilayer formation.

The multilayer formation was strongly dependent on the type of amine additive used. Of the studied additives, iPrNH2 promotes multilayer formation strongest, followed by and then . order of a primary, a secondary, and a tertiary amine, this indicates that an additive with a more accessible amine group will promote this effect.

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If the methanol concentration instead was increased at constant concentration, the adsorption isotherm of propranolol turned from type III to type I and at the elution profile had the classic Langmuirian shape. Propranolol, contains a naphthyl group, which is hydrophobic.

proposed explanation for the layer formation is that the amine addi-tive acts as a kosmotropic agent, which enhances the hydrophobic in-teractions with increasing concentration. n increase in methanol con-centration will increase the polarity of the mobile phase which will counteract this effect.

Figure 26. Illustration of possible adsorption of propranolol to a diol surface. To the right, a propranolol molecule interacting with the hydrophobic part of an al-ready adsorbed propranolol molecule, causing a multilayer formation.

The multilayer formation was strongly dependent on the type of amine additive used. Of the studied additives, iPrNH2 promotes multilayer formation strongest, followed by and then . order of a primary, a secondary, and a tertiary amine, this indicates that an additive with a more accessible amine group will promote this effect.

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4 Conclusion and guidelines

The work in this thesis has shown that several commonly used mobile phase components adsorb to different types of stationary phases and this adsorption strongly affects the separation in terms of retention, peak deformations and robustness. Improved understanding of the de-tailed adsorption of mobile phase components is essential for SFC method development. Furthermore, such knowledge can provide key information for accurate predictions of preparative SFC separations. From the present work, a few guidelines can be drawn:

Competitive models are necessary for accurate predictions of so-lute retention at low co-solvent fractions, i.e., lower than when a complete solvent layer has formed. Here one needs to consider the co-solvent as a competing component.

The simpler linear solvent strength theory is sufficient for accu-rate predictions of solute retentions at higher co-solvent frac-tions, i.e., when the co-solvent layer is saturated. Here the mod-ifier function of the co-solvent is dominant.

Peak deformation can appear if an additive adsorbs more

strongly than the solute, in neat weak solvent. To test the possi-bility for these deformations in SFC one can measure the reten-tion of the solute and the additive in neat carbon dioxide. If the additive has stronger retention than the solute the deformation may appear.

o To avoid this deformation, one can change the co-solvent

to one that adsorbs more weakly. On a diol stationary phase, methanol adsorbs strongest, followed by ethanol, 2-propanol and acetonitrile.

o ationary phase. In this thesis, it was shown that methanol adsorbs strongest to a bare silica phase followed by 2-EP and the diol phase.

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4 Conclusion and guidelines

The work in this thesis has shown that several commonly used mobile phase components adsorb to different types of stationary phases and this adsorption strongly affects the separation in terms of retention, peak deformations and robustness. Improved understanding of the de-tailed adsorption of mobile phase components is essential for SFC method development. Furthermore, such knowledge can provide key information for accurate predictions of preparative SFC separations. From the present work, a few guidelines can be drawn:

Competitive models are necessary for accurate predictions of so-lute retention at low co-solvent fractions, i.e., lower than when a complete solvent layer has formed. Here one needs to consider the co-solvent as a competing component.

The simpler linear solvent strength theory is sufficient for accu-rate predictions of solute retentions at higher co-solvent frac-tions, i.e., when the co-solvent layer is saturated. Here the mod-ifier function of the co-solvent is dominant.

Peak deformation can appear if an additive adsorbs more

strongly than the solute, in neat weak solvent. To test the possi-bility for these deformations in SFC one can measure the reten-tion of the solute and the additive in neat carbon dioxide. If the additive has stronger retention than the solute the deformation may appear.

o To avoid this deformation, one can change the co-solvent

to one that adsorbs more weakly. On a diol stationary phase, methanol adsorbs strongest, followed by ethanol, 2-propanol and acetonitrile.

o ationary phase. In this thesis, it was shown that methanol adsorbs strongest to a bare silica phase followed by 2-EP and the diol phase.

53

It is possible to tune the elution profile with the co-solvent frac-tion if a deformation appears. the flowchart in Fig-ure 12 the elution profile will have a Langmuirian shape at low fractions, and with increasing co-solvent fraction, the profile will first become rounded and finally obtain an anti-Langmuirian shape.

Other deformations can appear when an adsorbing additive/co-

solvent is used as diluent. If the solute elutes close to the pertur-bation peak created by the additive, it can either be displaced or dragged out. Therefore a sample solvent with weak adsorption is preferable.

The robustness in solute retention can be increased by decreas-

ing the temperature, increasing the co-solvent fraction or in-creasing the pressure. For the separation system investigated in Paper IV, it is preferable to use a pressure above 150 bar, or a temperature below 40 °C to achieve a robust system.

In this thesis, the effect of several co-solvents has been investigated. One component that has not been mentioned is water. In the studies in this thesis, inclusion of water has been avoided, as it is assumed to ad-sorb more strongly than other additives. However, water has an in-creasing interest in being used as additive or in addition to an additive. In the increasing number of investigations of peptide separations, wa-ter appears to be essential to achieve acceptable performance [VI]. Wa-ter is, therefore, a strong candidate for future investigations.

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It is possible to tune the elution profile with the co-solvent frac-tion if a deformation appears. the flowchart in Fig-ure 12 the elution profile will have a Langmuirian shape at low fractions, and with increasing co-solvent fraction, the profile will first become rounded and finally obtain an anti-Langmuirian shape.

Other deformations can appear when an adsorbing additive/co-

solvent is used as diluent. If the solute elutes close to the pertur-bation peak created by the additive, it can either be displaced or dragged out. Therefore a sample solvent with weak adsorption is preferable.

The robustness in solute retention can be increased by decreas-

ing the temperature, increasing the co-solvent fraction or in-creasing the pressure. For the separation system investigated in Paper IV, it is preferable to use a pressure above 150 bar, or a temperature below 40 °C to achieve a robust system.

In this thesis, the effect of several co-solvents has been investigated. One component that has not been mentioned is water. In the studies in this thesis, inclusion of water has been avoided, as it is assumed to ad-sorb more strongly than other additives. However, water has an in-creasing interest in being used as additive or in addition to an additive. In the increasing number of investigations of peptide separations, wa-ter appears to be essential to achieve acceptable performance [VI]. Wa-ter is, therefore, a strong candidate for future investigations.

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Summary in Swedish

Kromatografi är en separationsteknik som bygger på att de ämnen som skall separeras fördelar sig i olika grad mellan en stillastående (stat-ionär) och en rörlig (mobil) fas. Kromatografi kan användas både ana-lytiskt, för att se vilka ämnen som ett prov innehåller och preparativt, för att rena prover, exempelvis läkemedel, från oönskade ämnen. Det finns många varianter av kromatografi där huvudtyperna är gaskro-matografi och vätskekromatografi, vid vilka gas respektive vätska an-vänds som mobil fas. Fokus i avhandlingen har varit på tekniken su-perkritisk kromatografi, som förkortas SFC. I SFC utgörs den mobila fasen av ett ämne (oftast koldioxid) i ett tillstånd mitt emellan gas och vätska, ett så kallat superkritiskt tillstånd. Detta tillstånd kan uppnås när ett ämne utsätts för vissa speciella tryck- och temperaturförhållan-den (se Figur 2). I SFC har man den stationära fasen packad i ett stålrör, som kallas ko-lonn. Ämnena i provet injiceras med vätskan i den mobila fasen som man låter passera över den stationära ytan i kolonnen. När lösningen passerar genom kolonnen kommer ämnena att binda (adsorbera) olika starkt på den stationära ytan, och därmed vandra olika fort genom ko-lonnen och kommer därmed att separeras. Ämnen som adsorberas minst kommer ut först. När molekylerna kommer ut ur kolonnen de-tekteras de och resultatet visas i ett kromatogram, där man ser toppar som motsvarar de separerade ämnena. Om den injicerade mängden är väldigt liten kommer de resulterande topparna ha ett symmetriskt klockformat utseende medan stora provmängder kan medföra skeva toppar. För att nå en bra separation och för att kunna göra korrekta kvantitativa bedömningar är det önskvärt att formen på den detekte-rade toppen är symmetrisk (klockformad).

54

Summary in Swedish

Kromatografi är en separationsteknik som bygger på att de ämnen som skall separeras fördelar sig i olika grad mellan en stillastående (stat-ionär) och en rörlig (mobil) fas. Kromatografi kan användas både ana-lytiskt, för att se vilka ämnen som ett prov innehåller och preparativt, för att rena prover, exempelvis läkemedel, från oönskade ämnen. Det finns många varianter av kromatografi där huvudtyperna är gaskro-matografi och vätskekromatografi, vid vilka gas respektive vätska an-vänds som mobil fas. Fokus i avhandlingen har varit på tekniken su-perkritisk kromatografi, som förkortas SFC. I SFC utgörs den mobila fasen av ett ämne (oftast koldioxid) i ett tillstånd mitt emellan gas och vätska, ett så kallat superkritiskt tillstånd. Detta tillstånd kan uppnås när ett ämne utsätts för vissa speciella tryck- och temperaturförhållan-den (se Figur 2). I SFC har man den stationära fasen packad i ett stålrör, som kallas ko-lonn. Ämnena i provet injiceras med vätskan i den mobila fasen som man låter passera över den stationära ytan i kolonnen. När lösningen passerar genom kolonnen kommer ämnena att binda (adsorbera) olika starkt på den stationära ytan, och därmed vandra olika fort genom ko-lonnen och kommer därmed att separeras. Ämnen som adsorberas minst kommer ut först. När molekylerna kommer ut ur kolonnen de-tekteras de och resultatet visas i ett kromatogram, där man ser toppar som motsvarar de separerade ämnena. Om den injicerade mängden är väldigt liten kommer de resulterande topparna ha ett symmetriskt klockformat utseende medan stora provmängder kan medföra skeva toppar. För att nå en bra separation och för att kunna göra korrekta kvantitativa bedömningar är det önskvärt att formen på den detekte-rade toppen är symmetrisk (klockformad).

55

Figure 27 Schematisk bild av ett SFC system

En fördel med SFC jämfört med traditionell vätskekromatografi är att den superkritiska vätskan är mer lättflytande än en vanlig vätska. Där-med kan ett högre flöde användas vilket ger en snabbare och mer effek-tiv separation. Vidare är metoden bättre för miljön då mindre mängd miljöfarliga lösningsmedel behöver användas eftersom dessa kan er-sättas med koldioxid och den koldioxid som används är i huvudsak en biprodukt från andra industriella processer. En nackdel med SFC är att metoden är mycket mer komplex, bland annat för att den mobila fasen är komprimerbar, vilket gör att den kommer bete sig olika beroende på vilket tryck och vilken temperatur den utsätts för. Jämfört med väts-kekromatografi är metoden mycket mindre undersökt. Det räcker oftast inte att endast ha koldioxid i den mobila fasen i SFC, då det är ett dåligt lösningsmedel för polära ämnen, vilket exempelvis är typiskt för läkemedel. Därför tillsätts ofta polära ämnen, ofta i form av alkoholer. Dessa brukar kallas modifierare. I vissa fall kan även till-satser i form av syror och baser, kallade additiver, förekomma. Syftet med mitt avhandlingsarbete har varit att visa hur dessa tillsatta ämnen adsorberar på den stationära fasen och vilka följder det får för separat-ionen.

initialt visa hur den vanligast före-kommande modifieraren metanol adsorberar till en typisk stationär fas (Artikel I). Detta utökades sedan med fler modifierare och stationära faser i Artikel III. När modifieraren adsorberar på den stationära fa-sen kommer den att konkurrera med komponenterna i provet om den

55

Figure 27 Schematisk bild av ett SFC system

En fördel med SFC jämfört med traditionell vätskekromatografi är att den superkritiska vätskan är mer lättflytande än en vanlig vätska. Där-med kan ett högre flöde användas vilket ger en snabbare och mer effek-tiv separation. Vidare är metoden bättre för miljön då mindre mängd miljöfarliga lösningsmedel behöver användas eftersom dessa kan er-sättas med koldioxid och den koldioxid som används är i huvudsak en biprodukt från andra industriella processer. En nackdel med SFC är att metoden är mycket mer komplex, bland annat för att den mobila fasen är komprimerbar, vilket gör att den kommer bete sig olika beroende på vilket tryck och vilken temperatur den utsätts för. Jämfört med väts-kekromatografi är metoden mycket mindre undersökt. Det räcker oftast inte att endast ha koldioxid i den mobila fasen i SFC, då det är ett dåligt lösningsmedel för polära ämnen, vilket exempelvis är typiskt för läkemedel. Därför tillsätts ofta polära ämnen, ofta i form av alkoholer. Dessa brukar kallas modifierare. I vissa fall kan även till-satser i form av syror och baser, kallade additiver, förekomma. Syftet med mitt avhandlingsarbete har varit att visa hur dessa tillsatta ämnen adsorberar på den stationära fasen och vilka följder det får för separat-ionen.

initialt visa hur den vanligast före-kommande modifieraren metanol adsorberar till en typisk stationär fas (Artikel I). Detta utökades sedan med fler modifierare och stationära faser i Artikel III. När modifieraren adsorberar på den stationära fa-sen kommer den att konkurrera med komponenterna i provet om den

56

tillgängliga ytan och därmed påverkas separationen. Bland annat kom-mer retentionstiden, d.v.s. tiden det tar för ett ämne att färdas igenom kolonnen, att förändras. För att förutsäga retentionstiden kan då inte de enkla modeller som ofta används i vätskekromatografi användas, utan istället behövs en modell där adsorptionsmekanismen inklude-rats, vilket jag visat i Artiklarna II-IV. En annan följd av att modifi-eraren konkurrerar med provkomponenterna är att denna då inte bara fungerar som en klassisk modifierare, som bara påverkar den mobila fasen, utan även som ett adsorberande additiv. Förutom att retentionstiden förändras av en modifierare som adsorbe-rar kan även utseendet på de toppar som detekteras förändras. Vid pre-parativa separationer är toppformen viktigt för att få ut ämnet i så kon-

topparnas form kan även bidra till bättre optimering av separationsmetoder. I Ar-tiklarna II och III visas att om modifieraren fastnar hårdare på ko-lonnen än provkomponenten kan den orsaka att toppformen för prov-komponenten går från att ha en form med en skarp framsida och en svansande baksida till att istället ha en oskarp framsida, då mängden modifierare förändras i den mobila fasen. Denna deformation följer en tumregel som presenteras i Artikel II. I arbetet beskrivet i Artikel V tillsätts förutom modifieraren även ett additiv till den mobila fasen. Även denna komponent visas kunna orsaka deformation. Dessa defor-meringar följer dock inte tumregeln men beror även de på att additivet konkurrerar med provkomponenterna. Denna avhandling visar att det är viktigt att ta hänsyn till hur kompo-nenterna i den mobila fasen adsorberar på den stationära fasen, då detta har stor effekt både på hur snabbt ämnen färdas genom kolonnen och på utseendet av de detekterade topparna. Med bättre kunskap om hur separationssystemet fungerar, kan man bättre förutsäga hur ett op-timalt system ska designas. Vidare kan svåra deformationer av toppar undvikas med bättre kunskap om när och hur dessa uppstår.

56

tillgängliga ytan och därmed påverkas separationen. Bland annat kom-mer retentionstiden, d.v.s. tiden det tar för ett ämne att färdas igenom kolonnen, att förändras. För att förutsäga retentionstiden kan då inte de enkla modeller som ofta används i vätskekromatografi användas, utan istället behövs en modell där adsorptionsmekanismen inklude-rats, vilket jag visat i Artiklarna II-IV. En annan följd av att modifi-eraren konkurrerar med provkomponenterna är att denna då inte bara fungerar som en klassisk modifierare, som bara påverkar den mobila fasen, utan även som ett adsorberande additiv. Förutom att retentionstiden förändras av en modifierare som adsorbe-rar kan även utseendet på de toppar som detekteras förändras. Vid pre-parativa separationer är toppformen viktigt för att få ut ämnet i så kon-

topparnas form kan även bidra till bättre optimering av separationsmetoder. I Ar-tiklarna II och III visas att om modifieraren fastnar hårdare på ko-lonnen än provkomponenten kan den orsaka att toppformen för prov-komponenten går från att ha en form med en skarp framsida och en svansande baksida till att istället ha en oskarp framsida, då mängden modifierare förändras i den mobila fasen. Denna deformation följer en tumregel som presenteras i Artikel II. I arbetet beskrivet i Artikel V tillsätts förutom modifieraren även ett additiv till den mobila fasen. Även denna komponent visas kunna orsaka deformation. Dessa defor-meringar följer dock inte tumregeln men beror även de på att additivet konkurrerar med provkomponenterna. Denna avhandling visar att det är viktigt att ta hänsyn till hur kompo-nenterna i den mobila fasen adsorberar på den stationära fasen, då detta har stor effekt både på hur snabbt ämnen färdas genom kolonnen och på utseendet av de detekterade topparna. Med bättre kunskap om hur separationssystemet fungerar, kan man bättre förutsäga hur ett op-timalt system ska designas. Vidare kan svåra deformationer av toppar undvikas med bättre kunskap om när och hur dessa uppstår.

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Acknowledgment

Many people have supported me throughout my work with this thesis, and I am very grateful to my supervisor Professor Torgny Fornstedt that you have given me the opportunity to participate in this project. Thank you for sharing your knowledge and experience in chromatography and all that is “bizarre”. My assistant supervisor Dr. Jörgen Samuelsson, for sharing your prac-tical and theoretical knowledge in chromatography, but also for your support and patience in my struggle to learn Python. Hanna Leek, Kristina Öhlén, and Magnus Klarqvist with coworkers at

st eneca for your accommodation at the beginning of my journey. Thank you for all your practical guidance around how to run SFC and for all fruitful discussions and support through my research. My co-workers Dr. Martin Enmark, Dr. Dennis Åsberg and Dr. Marek Le ko for nice collaborations. Thank you for your support in all from calculations to more practical issues in the lab.

colleagues at Karlstad University for interesting conversations. Thanks to fellow Ph.D. students (present and former) Miriam, Sara,

-Sofia and Ishita for your support. thanks dersén, for invaluable help in the lab, and for your pleasant company. Jag vill också tacka några utanför universitetet, vänner och familj. Utan ert stöd hade denna avhandling inte varit möjlig: Min familj, tack mamma och pappa för att ni alltid har stöttat mig i alla mina vägval, i allt från teater till forskning. Till min syster för att du alltid finns där och är min vän. Och Inger och Lars för allt stöd med William under denna intensiva tid Slutligen tack Erik för allt ditt stöd, jag hade inte tagit mig igenom detta utan dig. Och till min söta älskade lille Wille. Ni är mitt allt!

57

Acknowledgment

Many people have supported me throughout my work with this thesis, and I am very grateful to my supervisor Professor Torgny Fornstedt that you have given me the opportunity to participate in this project. Thank you for sharing your knowledge and experience in chromatography and all that is “bizarre”. My assistant supervisor Dr. Jörgen Samuelsson, for sharing your prac-tical and theoretical knowledge in chromatography, but also for your support and patience in my struggle to learn Python. Hanna Leek, Kristina Öhlén, and Magnus Klarqvist with coworkers at

st eneca for your accommodation at the beginning of my journey. Thank you for all your practical guidance around how to run SFC and for all fruitful discussions and support through my research. My co-workers Dr. Martin Enmark, Dr. Dennis Åsberg and Dr. Marek Le ko for nice collaborations. Thank you for your support in all from calculations to more practical issues in the lab.

colleagues at Karlstad University for interesting conversations. Thanks to fellow Ph.D. students (present and former) Miriam, Sara,

-Sofia and Ishita for your support. thanks dersén, for invaluable help in the lab, and for your pleasant company. Jag vill också tacka några utanför universitetet, vänner och familj. Utan ert stöd hade denna avhandling inte varit möjlig: Min familj, tack mamma och pappa för att ni alltid har stöttat mig i alla mina vägval, i allt från teater till forskning. Till min syster för att du alltid finns där och är min vän. Och Inger och Lars för allt stöd med William under denna intensiva tid Slutligen tack Erik för allt ditt stöd, jag hade inte tagit mig igenom detta utan dig. Och till min söta älskade lille Wille. Ni är mitt allt!

58

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In supercritical fluid chromatography (SFC), the eluent is composed by carbon dioxide, often with additional components, in a condition between gas and liquid. This thesis aims to reach a deeper understanding of SFC by revealing the function of the additional eluent components through systematic adsorption studies.

In Paper I, investigation of surface excess adsorption isotherms of methanol revealed that a monolayer of methanol was formed. In Paper II, severe peak deformation effects due to this adsorption were shown. The findings in these papers revealed that a competitive additive model best predicts the solute retention at low methanol fractions whereas at higher fractions, methanol acts just as a modifier. In Paper III, the generality of the effects was proven by investigation of several co-solvent and stationary phase combinations. In Paper IV it was investigated how the robustness of SFC separations depend on the co-solvent adsorption, pressure, and temperature. In Paper V, the impact of the addition of amine additives was investigated. Two different mechanisms for solute peak deformations were observed.

The knowledge achieved about SFC in this theses provides guidelines for development of more robust SFC methods where peak deformations/distortions can be avoided.


Faculty of Health, Science and Technology

Chemistry


ISSN 1403-8099

ISBN 978-91-7867-080-2 (pdf)

ISBN 978-91-7867-070-3 (print)

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