ABSTRACT MOLECULAR MODELING of IONIC LIQUIDS for POTENTIAL APPLICATIONS in the DESULFURIZATION of DIESEL FUEL by Miranda R. Caud
ABSTRACT
MOLECULAR MODELING OF IONIC LIQUIDS FOR POTENTIAL APPLICATIONS IN THE DESULFURIZATION OF DIESEL FUEL
by Miranda R. Caudle
The sulfur compounds in diesel fuel produce harmful environmental pollutants during combustion. Hydrodesulfurization (HDS) is the most common technique to reduce the sulfur content of diesel fuel but cannot effectively remove the aromatic sulfur compounds to produce ultra-low-sulfur diesel. Ionic liquids (ILs) show potential as alternative solvents for extractive desulfurization to be implemented after a conventional HDS process, but the mechanism is not well understood. This work focuses on using a combination of free energy calculations and detailed structural analysis to better understand the molecular-level interactions between dibenzothiophene and seven common imidazolium-based ILs. The free energy calculations suggest that the ILs interact differently with thiophene and dibenzothiophene. No specific interactions were observed between the anion and dibenzothiophene; varying the anion showed no remarkable differences in the observed interactions. It was determined that interactions between dibenzothiophene and the cation were more significant; π-π stacking between the imidazole ring and thiophene ring plus electrostatic interactions between the alkyl chain and benzene rings were observed. The primary goal of this work was to use molecular dynamic simulations to complement current experimental research to find a suitable IL for potential desulfurization applications.
A Thesis
Submitted to the
Faculty of Miami University
in partial fulfillment of the requirements for the degree of
Master of Science
by
Miranda R. Caudle
Miami University
Oxford, Ohio
2018
Advisor: Dr. Andrew Paluch
Reader: Dr. Catherine Almquist
Reader: Dr. Justin Saul
©2018 Miranda R. Caudle
This Thesis titled
MOLECULAR MODELING OF IONIC LIQUIDS FOR POTENTIAL APPLICATIONS IN THE DESULFURIZATION OF DIESEL FUEL
by
Miranda R. Caudle
has been approved for publication by
The College of Engineering and Computing
and
Department of Chemical Engineering
______
Dr. Andrew Paluch
______
Dr. Catherine Almquist
______
Dr. Justin Saul
Table of Contents
Background and Introduction ...... 1
Methodology ...... 7
Computational Details ...... 9
Force Fields ...... 9
Molecular Dynamics ...... 10
Free Energy Calculations ...... 12
Structural Analysis ...... 14
Results and Discussion ...... 17
Free Energy Calculations ...... 17
Structural Analysis ...... 19
Conclusions ...... 25
References ...... 26
Appendix I: Additional Simulation Details ...... 33
Appendix II: Additional Structural Analysis ...... 37
iii
List of Tables
Table 1. Summary of the computed dimensionless chemical potential of dibenzothiophene and thiophene in the studied ILs with 0.8 charge scaling along with the computed IL/n-decane partition coefficient ...... 17
iv
List of Figures
Figure 1. The chemical structure of the solutes – thiophene and dibenzothiophene ...... 8
Figure 2. The chemical structure of the selected anions and imidazolium cation that constitute the seven ionic liquids of interest in this work ...... 8
Figure 3. Atom numbering scheme generated by TRAVIS for anion, cation, and solute molecules ...... 15
Figure 4. RDFs of cation-anion interactions for studied ILs with 0.1 mol frac solute ..... 19
+ - Figure 5a. RDFs of solute-anion interactions for [BMIM] [CH3SO4] ...... 21
+ - Figure 5b. RDFs of solute-cation interactions for [BMIM] [CH3SO4] ...... 21
+ - Figure 6. CDFs of solute-cation interactions for [BMIM] [CH3SO4] ...... 23
- + Figure 7. SDF for dibenzothiophene (red) and [CH3SO4] (blue) around [BMIM] ...... 24
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MOLECULAR MODELING OF IONIC LIQUIDS FOR POTENTIAL APPLICATIONS IN THE DESULFURIZATION OF DIESEL FUEL
Background and Introduction
Crude oil products contain sulfur compounds as impurities that are directly related to the emission of sulfur dioxide and sulfur particulate matter when the fuel is burned, which endangers public health and reduces the life of the engine. Research for more efficient and more effective processes to remove these sulfur compounds to reduce sulfur emissions has increased as regulations on the sulfur content of crude oil products have become more stringent [1,2]. Diesel fuel contained as much as 5,000 ppm before the Environmental Protection Agency (EPA) began regulating sulfur content in 1993. In the United States, the allowed sulfur content of diesel fuel has recently been reduced from 500 to 15 ppm and is expected to continue to decrease [3].
Although the percentage of energy obtained from fossil fuels (crude oil, natural gas, and coal) has decreased over recent years, fossil fuels still accounted for 80% of total energy consumption in 2017, and the total energy consumption in the United States continues to increase [4]. Energy obtained from crude oil products has also increased over the last few years and is the source of almost half (46.3%) of fossil fuel consumption in the United States.
Crude oil is a complex mixture of organic liquids that is refined to be used mostly as transportation fuels such as gasoline, diesel, and jet fuels. The amount of naturally occurring sulfur compounds present in crude oil depends on the source, but sulfur compounds are generally undesirable in the refining process because they can cause corrosion in the pipelines and refining equipment [1]. Any sulfur compounds left in fuel after processing tend to decrease the effectiveness of catalytic converters over time, resulting in increased emission levels from the vehicle [5]. During the combustion process, these sulfur compounds are oxidized and emitted as sulfur oxide gases (SOx), which react with water in the atmosphere to form sulfates and acid rain.
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The combustion process also produces sulfate PM that can cause lung cancer and aggravate existing respiratory and cardiovascular diseases. Furthermore, sulfate PM can accumulate on the surface of the catalysts in the exhaust emission control system, reducing the effectiveness of the reactions that remove carbon monoxide (CO), nitrogen oxide gases (NOx), and volatile organic compounds (VOCs). Sulfur-containing fuels generate harmful pollutants during the combustion process that lead to environmental concerns such as smog, global warming, and air and water pollution, even if the sulfur content is below acceptable levels.
The naturally occurring sulfur compounds present in diesel fuel are generally categorized into four groups: thiols (R – SH), sulfides (R – S – R’), disulfides (R – S – S – R’), and thiophenes [6,7]. Hydrodesulfurization (HDS) is one of the most common methods used to remove these sulfur compounds and reduce the sulfur content of diesel fuel. Conventional HDS techniques can effectively remove thiols and sulfides but are limited by the aromatic sulfur compounds that remain such as thiophene, benzothiophene, dibenzothiophene, and their alkylated derivatives (especially 4,6-dimethyl dibenzothiophene) [8-10]. During the HDS process, the sulfur compounds are reacted with hydrogen gas (3-5 MPa) at high temperatures (300-450 °C) in the presence of specific catalysts to form hydrogen sulfide gas (H2S), which can be captured and converted into elemental sulfur [1,11]. Operating at higher temperatures and pressures, using more active catalysts, or employing longer residence times can increase the effectiveness of HDS in the removal of aromatic sulfur compounds but are costly to refineries in terms of capital investment and operating costs [2,12,13].
Conventional HDS techniques are not able to produce ultra-low-sulfur diesel (ULSD) while maintaining other fuel requirements [7]. With the ultimate goal of zero-sulfur fuels in mind, there is some research looking at developing new catalysts for HDS or changing the operating conditions for use with existing catalysts; other research has been directed toward developing new processes for more effective desulfurization [1,2]. Alternative methods that can be used to remove sulfur compounds from diesel fuel include oxidative desulfurization, adsorption desulfurization, biodesulfurization, and solvent extraction, but these are not completely effective either [14,15].
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Nevertheless, HDS is still the primary method for removing sulfur compounds from diesel fuel, and there are two-stage processes that are very effective in reducing the sulfur content [16]. The first stage reactor utilizes conventional HDS techniques and is followed by an intermediate stage stripper to remove H2S and NH3. The second stage reactor operates at a higher temperature and pressure with a different catalyst to target aromatic sulfur compounds and is followed by a final stage stripper. This suggests that a conventional HDS process could be used to significantly reduce the sulfur content of diesel fuel before entering a selective extraction process to remove the remaining aromatic sulfur compounds to comply with more stringent environmental regulations and potentially produce zero-sulfur fuel more cost effectively.
Solvent extraction is applied to many industrial processes because it is often economically advantageous with simple and mild operating conditions, but the efficiency of this method relies on careful selection of the solvent [2,11]. Conventional solvents have a relatively narrow range of temperatures in which they are in the liquid state despite having a wide range of other physical properties [6,18]. Consequently, most processes have evolved under these limitations. Furthermore, conventional solvents are relatively volatile at normal operating conditions, which may lead to solvent loss and emission concerns. In the United States, one-third of all VOC emissions are attributed to the conventional solvents used in industrial applications [18].
The study of the use of ionic liquids (ILs) as potential replacements solvents for a variety of industrial applications has drawn considerable attention and research for a number of reasons [19]. ILs are organic salts made up of large, asymmetrical ions, which prevents them from crystallizing under normal operating conditions [14,18]. They are essentially nonvolatile and have high thermal stability, allowing them to be used as solvents under unique operating conditions, potentially from temperatures below ambient to above 400 °C, without risk of fugitive emissions. ILs usually consist of a bulky nitrogen- or phosphorus-containing organic cation with an associated organic or inorganic anion, often described using the notation [cation]+[anion]-. The physical properties of an IL can easily be modified for a particular application by changing the cation, anion, and substituents [6].
Although ILs have been known since 1914, they have only been thoroughly investigated as
3 replacement solvents for the past 20 years [20,21]. As more stringent environmental regulations are introduced in the United States and throughout the world, there is an increasing demand for new economical and environmentally friendly technologies in all industries [2]. With a wide variety of structures, ILs have the potential to be used as replacement solvents in a variety of applications, but the industrialization of IL technologies is rather slow. ILs are still in the research phase with only a few known industrial applications because designing an IL for a specific process can become time consuming and expensive if the mechanism of extraction is not well understood [22].
Selective extraction of sulfur compounds from diesel fuel with ILs was first described by Bösmann et al. in 2001 [23]. This study presented a new approach for more effective desulfurization of diesel fuel by targeting dibenzothiophene and potentially its alkylated derivatives, which are particularly difficult to convert to H2S through HDS due to steric hinderance at the surface of the catalyst. Bösmann et al. looked at the extraction of dibenzothiophene from n-dodecane, a liquid alkane hydrocarbon, which is often used as a model fuel for research purposes. The study compared common imidazolium-based ILs by the extent of desulfurization, which was defined as the remaining sulfur content (ppm). It was found that the selection of the anion had a relatively small impact on the extent of desulfurization compared to alkyl chain length of the imidazolium cation, and that desulfurization increased with increasing alkyl chain length. This suggested that the size of the ions is important and that the selection of the anion and cation will determine the success of ILs in this application. More importantly, this study demonstrated the potential of ILs in effective desulfurization of diesel fuel. Many experimental and theoretical studies have been conducted since to determine the most appropriate type of IL to extract the aromatic sulfur compounds that cannot be removed by conventional HDS techniques.
Zhang & Zhang [24] showed that ILs can have remarkable selectivity for thiophene over toluene and other hydrocarbons found in diesel fuel. They also found that the presence of a methyl group on the thiophene molecule (i.e. 2-methylthiophene) significantly reduced the absorption capacity of the IL. They compared the absorption capacity of three imidazolium-based ILs, where
4 absorption capacity was defined as mol solute absorbed per mol IL. It was determined that 1- + - butyl-3-methylimidazolium tetrafluoroborate ([BMIM] [BF4] ) had a higher absorption capacity + - than 1-ethyl-3-methylimidazolium tetrafluoroborate ([EMIM] [BF4] ), suggesting that a longer alkyl chain is also ideal in this system. It was also determined that 1-butyl-3-methylimidazolium + - + - hexafluorophosphate ([BMIM] [PF6] ) had a higher absorption capacity than [BMIM] [BF4] , suggesting that the selection of the anion is still important in this application. In this study, Zhang & Zhang also demonstrated that these ILs could easily be regenerated for reuse and the absorbed thiophene could be completely recovered.
Asumana et al. [11] compared imidazolium-based and sulfur-based ILs by looking at sulfur- extraction efficiency, defined as 푆표−푆푓 where 푆 and 푆 are the initial and final sulfur content 푆표 표 푓 (ppm), respectively. These ILs showed more efficient extraction of dibenzothiophene from a model diesel (n-hexane) than of thiophene from a model gasoline (n-hexane, toluene). This study + - also found that 1-butyl-3-methylimidazolium dicyanamide ([BMIM] [N(CN)2] ) had the highest extraction efficiency and that the sulfur-extraction efficiency of the IL is not significantly affected after six regeneration cycles. Asumana et al. showed that ILs have great potential for the desulfurization of diesel fuels, especially for the aromatic sulfur compounds that are most difficult to remove by conventional HDS techniques.
Kędra-Królik et al. [2] looked at extracting various sulfur and nitrogen compounds from aliphatic hydrocarbons by obtaining liquid-liquid equilibrium (LLE) data for five ternary systems. With this information, it was determined that 1-ethyl-3-methylimidazolium thiocyanate ([EMIM]+[SCN]-) and 1-butyl-3-methylimidazolium thiocyanate ([BMIM]+[SCN]-) have a good capacity for desulfurization of model diesel fuel (a mixture of hydrocarbons) with 88% reduction in thiophene content and complete extraction of dibenzothiophene after three process stages. Kędra-Królik et al. showed that these imidazolium-based ILs interact very little with the alkanes and cycloalkanes that make up diesel fuel but have very high selectivity for thiophene and dibenzothiophene, which is important to the success of ILs in this application.
A similar study was conducted by Mokhtarani et al. [25] in which ternary LLE data for the
5 extraction of thiophene from alkane compounds (hexane, heptane, and octane) was investigated + - with 1-butyl-3-methylimidazolium nitrate ([BMIM] [NO3] ) and 1-methyl-3-octylimidazolium + - + - nitrate ([OMIM] [NO3] ). Mokhtarani et al. found that [BMIM] [NO3] was more suitable for desulfurization due to higher selectivity for thiophene over alkane compounds, where selectivity was defined as the ratio of the activity coefficients of thiophene and alkanes in the ILs.
A follow-up study was published by Safa et al. [26] to compare the effect of cation type and alkyl chain length on the extraction efficiency of dibenzothiophene from model diesel (n- decane). The imidazolium-based ILs showed higher extraction efficieny of dibenzothiophene than the pyridinium-based ILs with the same cation alkyl chain length. The results also suggested that the longer cation alkyl chain was more appropriate for this system. Safa et al. showed that + - [OMIM] [NO3] could extract 94.8% of the dibenzothiophene in model diesel and be regenerated for reuse six times without significant reduction in sulfur-extraction efficiency.
These studies, along with countless others, demonstrate the remarkable potential ILs have in desulfurization applications but also the lack of understanding of the mechanism of extraction. It appears that the range of sulfur compounds present in diesel fuel interact differently with common ILs, however, many of these studies are limited by the number of ILs or aromatic sulfur compounds investigated. For example, Safa et al. suggested that increasing the alkyl chain length on imidazolium-based ILs would increase extraction of dibenzothiophene but Mokhtarani et al. did not observed the same results with thiophene in the same ILs. At the present time, there is no study conclusive enough to support the industrialization of a particular IL for the extractive desulfurization of diesel fuel.
Understanding the interactions between solute and solvent is essential to designing the best IL for any application and experimental data has failed to reach a consensus in this case. The hydrogen-bond basicity scale developed by Cláudio et al. [27] for imidazolium-based ILs has been shown to trend well with predicted solubility for multifunctional compounds like pharmaceuticals [19,28]. The aromatic sulfur compounds present in diesel fuel, however, do not contain functional groups capable of hydrogen bonding with the anion. Furthermore, Rai et al. suggest that the relatively weak intermolecular interactions associated with aromatic compounds
6 are often difficult to quantify experimentally [29,30]. Consequently, molecular simulations can provide valuable information about the molecular driving force for the extraction of aromatic sulfur compounds using ILs to complement experiment-based research.
Oliveira et al. [14] used molecular simulations to gain insight into the mechanism for the + - selective extraction of thiophene from model diesel (n-dodecane) with [BMIM] [BF4] . Using a combination of structural analysis and free energy calculations allowed the authors to better understand the molecular driving force behind the extraction process with a particular IL. The results indicate that the mechanism of desulfurization could be attributed mainly to π-π interactions between the imidazole and thiophene rings rather than interactions with the cation alkyl chain as previously suggested.
The present work will use molecular dynamic simulations to expand upon the work of Oliveira et al. [14] using the methods of Caudle et al. [19] to gain new insights into the interactions between common imidazolium-based ILs of the general type [BMIM]+[anion]- and thiophene or dibenzothiophene.
Methodology
The primary interest of this work was to study molecular-level interactions between seven common imidazolium-based ionic liquids (ILs) of the general type [BMIM]+[anion]- and dibenzothiophene for potential extractive desulfurization applications. Dibenzothiophene was chosen for this work because it is one of the more difficult sulfur compounds to remove from diesel fuel by conventional hydrodesulfurization (HDS) but easier to model than its alkylated derivatives. Thiophene was also studied to provide a better understanding of the effect of the aromatic rings in dibenzothiophene.
7
The chemical structures of thiophene and dibenzothiophene are shown in Figure 1. There are existing force fields that have been optimized for phase-equilibria calculations that can be used to model these aromatic sulfur compounds [14].
Figure 1. The chemical structure of the solutes – thiophene and dibenzothiophene
The seven ILs shown in Figure 2 can be modeled using the united atom force fields, proposed by Zhong et al., which have been optimized to reproduce a range of thermodynamic and transport properties [22]. Diesel fuel can be modeled by n-decane, which was used as the reference solvent in this work.
Figure 2. The chemical structure of the selected anions and imidazolium cation that constitute the seven ionic liquids of interest in this work
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Molecular dynamic simulations for the neat (pure) IL systems were performed as a baseline to understand how the anion and cation interact with each other and if the addition of the solute (thiophene or dibenzothiophene) changes these interactions. Simulations corresponding to the infinite dilution limit were used to predict IL/n-decane partition coefficients for thiophene and dibenzothiophene. Finally, to understand how these aromatic sulfur compounds interact with the anion and cation that constitute these IL systems, simulations for each IL with 0.1 mole fraction solute were analyzed.
This work used molecular dynamic simulations to address some of the limitations of many experimental studies by looking at both thiophene and dibenzothiophene in seven common imidazolium-based ILs. Detailed structural analysis of these simulations can provide a better understanding of the intermolecular interactions involved in the extraction of these aromatic sulfur compounds from diesel fuel using ILs to parallel recent experimental studies. With so much speculation around the most effective IL for extractive desulfurization applications, the molecular-level insights from this work may be able to provide better guidance for future research.
Computational Details
This work closely follows the methodology and computational details previously presented by Caudle et al. [19]
Force Fields
Interactions were modeled using a “class I” potential energy function where all non-bonded intermolecular interactions (푈푛푏) were accounted for using a combined Lennard-Jones (LJ) plus fixed point charge model of the form [31,32]
12 6 휎푖푗 휎푖푗 1 푞푖푞푗 푈푛푏(푟푖푗) = 4휀푖푗 [( ) − ( ) ] + (Equation 1) 푟푖푗 푟푖푗 4휋휀0 푟푖푗
9 where 푟푖푗 is the separation distance between sites 푖 and 푗, 휀푖푗 is the well depth of the LJ potential,
휎푖푗 is the distance at which the LJ potential is zero, and 푞푖 and 푞푗 are the partial charges of sites 푖 and 푗, respectively.
The ionic liquids (ILs) were modeled using the classical united atom force fields for imidazolium-based ILs proposed by Zhong et al. [22] Extensive molecular dynamics simulations were performed by Zhong et al. to validate that these force fields with scaled partial charges showed good agreement with experimental thermodynamic and transport property data.
N-decane, thiophene, and dibenzothiophene were modeled with Transferable Potentials for Phase Equilibria (TraPPE) force fields developed by the Siepmann Group [33]. The force field for n- decane was constructed based on TraPPE-United Atom (UA), where the hydrogen atoms are modeled implicitly with the carbon atoms they are bonded to in a single psuedoatom type. The force fields for thiophene and dibenzothiophene were constructed based on TraPPE-Explicit Hydrogen (EH), where the hydrogen atoms are modeled explicitly to capture interactions with aromatics. [28-30,34-37]. Charges for thiophene were obtained from Rai et al. [29]; charges for dibenzothiophene were obtained from Phifer et al. [38]
The intramolecular parameters for the solutes were taken from the General AMBER Force Field (GAFF), which has been shown to accurately predict thermodynamic and transport properties of many ILs [39-42]. The employed IL force field scales intramolecular 1-4 LJ and electrostatic interactions by a factor of ½ [22]; to be consistent with the IL force field, a scaling factor of ½ was additionally used for the intramolecular 1-4 LJ and electrostatic interactions of the solute. Bonds involving hydrogens were held fixed throughout this work.
Molecular Dynamics
As a result of their sluggish dynamics, extensive simulations were performed to equilibrate the IL systems. Simulations were performed for neat (pure) ILs, ILs plus a single solute molecule (thiophene or dibenzothiophene), which corresponds to the infinite dilution limit, and ILs plus approximately 0.1 mol frac solute. Simulations were also performed for neat n-decane, ILs plus a
10 single n-decane molecule, and n-decane plus a single solute molecule, which corresponds to the infinite dilution limit. All of these simulations were carried out following the same procedure.
First, Packmol was used to generate initial structures [43,44]. The number of IL pairs for the neat IL simulations were chosen to give a cubic box length of approximately 4.5 nm at 298.15 K (see Table A1). The number of IL pairs remained the same for systems containing solutes. This was followed by 3000 steepest descent minimization steps to remove any bad contacts that might have resulted from the packing.
The next two steps involved dynamics with the equations of motion integrated using the Verlet leap-frog algorithm [31,32,45,46]. The system was first equilibrated in an NVT ensemble at 738.15 K for 1 ns using stochastic velocity rescaling [45,47-49]. Next, the system was brought from 738.15 K to 298.15 K and 1 bar using simulated annealing stochastic velocity rescaling and the Berendsen barostat [45,46,50]. The system was initially carried out for 1 ns at 738.15 K and 1 bar. Over the next 8.8 ns, the temperature was decreased linearly at a rate of 50 K/ns to reach the final temperature of 298.15 K and was then held at 298.15 K for 1 ns.
Lastly, a 13 ns NpT simulation was performed at 298.15 K and 1 bar with the equations of motion integrated using the velocity Verlet algorithm [31,32,45,46]. The simulation used the Nosé-Hoover chain thermostat (with a chain length of 10) and the Martyna-Tuckerman-Tobias- Klein (MTTK) barostat [32,45,51,52]. To ensure accurate statistics when performing the structural analyses, the final NpT simulation for neat ILs and ILs plus approximately 0.1 mol frac solute were carried out for 13 ns, where the first 1 ns was discarded from analysis as equilibration. For all three steps involving dynamics, the equations of motion were integrated with a timestep of 2 fs, the time constant for the thermostat was 1 ps, and the time constant for the barostat was 4 ps.
Simulation volume was determined, and density was calculated using the number of IL pairs and corresponding molecular weights. The simulation densities were compared to simulation values from Zhong et al. [22] and experimental values (see Table A1). Agreement between simulation and experimental density values was verified that the simulation boxes were set up correctly.
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Free Energy Calculations
Free energy calculations in the NpT ensemble were conducted for systems with a single solute molecule in the IL and a single solute molecule in n-decane.
The free energy calculations were performed at 298.15 K and 1 bar. The infinite dilution residual 푟푒푠,∞ chemical potential, 휇1,푖 , of the solute in the ILs and n-decane was calculated using a multistate free energy perturbation method [53-57] with the multi-state Bennett’s acceptance ratio method (MBAR) [58-61]. A ‘soft-core’ potential was used to decouple the solute-solvent intermolecular
퐿퐽 푒푙푒푐 LJ interactions. Stage (푚)-dependent decoupling parameters 휆푚 = 휆푚 = 1, the solute is fully 퐿퐽 푒푙푒푐 coupled to the system. When 휆푚 = 휆푚 = 0, the solute is decoupled from the system. The ‘soft-core’ potential had the form [62-64]
6 6 푆퐶 퐿퐽 휎푖푗 휎푖푗 푈퐿퐽 (푟푖푗; 푚) = 4휆푚 휀푖푗 { 2 − 퐿퐽 } (Equation 2) 퐿퐽 6 6 [(1−휆 )훼 휎6 +푟6 ] [(1−휆푚 )훼퐿퐽휎푖푗+푟푖푗] 푚 퐿퐽 푖푗 푖푗
where 훼퐿퐽 is a constant, which has a value of ½. The advantage of using a ‘soft-core’ potential to decouple the LJ interactions is that while it yields the correct limiting value of the potential 퐿퐽 (when 휆푚 = 0 and 1), it additionally allows nearly decoupled molecules to overlap with a finite energy (and hence finite probability). The electrostatic term in the intermolecular potential was decoupled linearly as
푒푙푒푐 1 푞푖푞푗 푈푒푙푒푐(푟푖푗; 푚) = 휆푚 (Equation 3) 4휋휀0 푟푖푗
At each stage 푚, an independent MD simulation was performed. The simulation time for each stage was 20.5 ns, where the first 0.5 ns was discarded from analysis as equilibration. The simulation was originally run for 10.5 ns, but ILs have long correlation times. At 10.5 ns, the number of independent samples was less than recommended, so the simulation time was doubled and the issues were resolved. The initial structure for these simulations was taken as the final structure from the NpT simulation of a single solute in solution (either IL or n-decane). The
12 change in the Hamiltonian with the current configuration between stage 푚 and all other stages is computed every 0.20 ps. This is saved for subsequent post-simulation analysis with MBAR [61] 푟푒푠,∞ to determine 휇1,푖 . This analysis was performed using the Python implementation of MBAR (PyMBAR) and the GROMACS analysis script distributed with it [65-67].
A total of 15 different stages were used for the free energy calculations where 푚 = 0 corresponds to a non-interacting (ideal gas) state and 푚 = 14 is a fully interacting system. From 푚 = 1-10, the 퐿퐽 LJ interactions were increased from 휆푚 = 0.1 to 1.0. From 푚 = 11-14, the electrostatic 푒푙푒푐 interactions were increased in a square root fashion following 휆푚 = {0.50,0.71,0.87,1.00}.
The only difference for the n-decane simulations is that a total of 11 different stages were used. For this case, 푚 = 0 corresponds to a non-interacting (ideal gas) state and 푚 = 10 is a fully 퐿퐽 interacting system. From 푚 = 1-10, the LJ interactions were increased from 휆푚 = 0.1 to 1.0. There are no electrostatic interactions for n-decane so 푚 = 11-14 were not necessary.
The simulation parameters for the free energy calculations were the same as the last step of equilibration (i.e. using velocity Verlet with a Nosé-Hoover chain thermostat and MTTK barostat) except the LJ interactions were switched off smoothly between 1.15 and 1.2 nm, and the real space part of the electrostatic interactions were switched off smoothly between 1.18 and 1.2 nm. Long range corrections were applied as described previously.
Assuming the solute concentration is sufficiently small so as to be considered infinitely dilute, the relative solubility (or partition coefficient) may be computed using molecular simulation free energy calculations as [68,69]
i⁄ref c1,i res,∞ res,∞ ln K1 = ln = −[βμ1,i (T, p, N1 = 1, Ni) − βμ1,ref (T, p, N1 = 1, Nref)] c1,ref i/ref = −∆βμ1 (Equation 4)
푖/푟푒푓 where 퐾1 is the partition coefficient of the solute between solvent 푖 and n-decane; 푐1,푖 and
푐1,푟푒푓 are the molar or mass concentrations of the solute in solvent 푖 and n-decane at equilibrium,
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푟푒푠,∞ 푟푒푠,∞ respectively; 훽휇1,푖 and 훽휇1,푟푒푓 are the dimensionless residual chemical potential of the solute −1 infinitely dilute in solvent 푖 and n-decane, respectively, where 훽 = 푘퐵푇 and 푘퐵 is the
Boltzmann constant, 푇 is the temperature, 푝 is the pressure, and 푁1, 푁푖, 푁푟푒푓 are the number of solute, solvent 푖, and n-decane molecules in the simulation. The infinite dilution limit is achieved in a simulation by having a single solute molecule in a system with a large number of solvent 푖/푟푒푓 molecules. While the value of 퐾1 might not show excellent quantitative agreement with experiment, it can be used to compare the solute-solvent intermolecular interactions and rank the affinity of the solute in the ILs relative to n-decane. The partition coefficient was calculated using Equation 4 for thiophene and dibenzothiophene in the seven ILs of the general form [BMIM]+[anion]- shown in Figure 2.
Structural Analysis
Detailed structural analysis was performed for thiophene and dibenzothiophene in each of the ILs. To facilitate this analysis, the solute (thiophene or dibenzothiophene) concentration was increased from the infinite dilution limit (single solute molecule) to approximately 0.1 mol frac in the IL (see Table A2).
TRAVIS (“TRajectory Analyzer and VISualizer”) was used to generate various distribution functions explained in this section and presented later in this work [70].
A radial distribution function (RDF) provides insight into the system structure by plotting the probability of finding an observed particle as a function of distance from a reference particle relative to bulk [70]. This means that values larger than one indicate that finding an observed particle at this distance is more probable than it should be on average, and the value of the function approaches one at large distances.
Shown in Figure 3 are the atom assignments made by TRAVIS and referenced throughout this work. TRAVIS also defines virtual atoms at the center of geometry (COG), center of mass (COM), and center of ring (COR), where applicable.
14
Figure 3. Atom numbering scheme generated by TRAVIS for anion, cation, and solute molecules
+ - The [BMIM] molecule is labeled (cation). The anion molecules are labeled (a) [BF4] (b) ------[CF3CO2] (c) [CF3SO3] (d) [CH3CO2] (e) [CH3SO4] (f) [NTF2] (g) [PF6] . An ionic liquid (IL) is simulated using an equal number of anion and cation molecules. The solute molecules are labeled (thiophene) and (dibenzothiophene) accordingly.
The united atom force fields are also reflected in these structures. Cf is used for trifluoromethyl groups (CF3). Ct is used to for methyl groups (CH3) and to distinguish alkyl chain carbons from ring carbons. Oo is used to distinguish the oxygen connected to the methyl group from the three - equivalent oxygens double bonded to sulfur that carry the negative charge for the [CH3SO4] anion. The united atom groups were chosen by Zhong et al. to capture correct/important physics while improving computational efficiency [22].
The center of the imidazole ring for [BMIM]+ is defined as the geometric center of C1-N1-C2- C3-C4. The alkyl chain in [BMIM]+ is defined as Ct1/2/3. The center of the thiophene ring for thiophene and dibenzothiophene is defined as the geometric center of C1-S1-C2-C3-C4 (ref
15 thiophene in RDFs). The center of the benzene ring for dibenzothiophene is defined as the geometric center of C1-C3-C7-C12-C10 or C2-C4-C8-C11-C9 (ref benzene in RDFs).
Any combination of atoms or virtual atoms may be chosen to be analyzed. If multiple atoms are chosen, TRAVIS averages the RDFs for those atoms. This is advantageous when there are equivalent atoms defined in the molecule.
The interactions between the solute (thiophene or dibenzothiophene) and the ILs were of particular interest in this work. RDFs were computed compare the neat IL and IL plus 0.1 mol frac solute systems, where the cation was used was the reference molecule and the anion was used as the observed molecule (shown in Figure 4). RDFs were computed compare the strength of the solute-cation and solute-anion interactions, where the solute was used as the reference molecule and the cation or anion was the observed molecule (shown in Figure 5).
A combined distribution function (CDF) uses the radial distribution function (RDF) defined between two points and the angular distribution function (ADF) defined between two vectors (specified by two points) to create a surface plot of the occurrence as a function of distance and angle [70]. For the CDFs presented in this work, the distance is defined between the center of the thiophene ring and the center of the imidazole ring. The angle is defined between the S1-COR vector in the thiophene ring and C1-COR vector in the imidazole ring, which correspond to the planes of the rings. The color indicates the occurrence at a given distance and angle according to the legend produced with the surface plot.
A spatial distribution function (SDF) shows the probability of finding a particle at a certain position in space around a fixed reference system of other particles [70]. SDFs are similar to RDFs but are plotted in three dimensions and can involve more than two molecules.
16
Results and Discussion
Free Energy Calculations
Free energy calculations were performed for dibenzothiophene and thiophene at their infinite dilution limit in seven common imidazolium-based ionic liquids (ILs). The ILs studied in this work consisted of a [BMIM]+ cation paired with one of seven anions (shown in Figure 2). The 푟푒푠,∞ dimensionless chemical potentials of the solutes at infinite dilution in the ILs 훽휇1,푖 are reported in Table 1 (also see Table A3). The dimensionless chemical potentials of the solutes at 푟푒푠,∞ infinite dilution in n-decane were determined to be 훽휇1,푟푒푓 = -17.906 for dibenzothiophene and 푟푒푠,∞ 훽휇1,푟푒푓 = -6.940 for thiophene. The IL/n-decane partition coefficients for dibenzothiophene and thiophene were calculated using Equation 4 and are also included in Table 1.
푟푒푠,∞ Table 1. Summary of the computed dimensionless chemical potentials (훽휇1,푖 ) of dibenzothiophene and thiophene in the studied ILs with 0.8 charge scaling along with the 푖⁄푟푒푓 computed IL/n-decane partition coefficients (퐾1 )
Dibenzothiophene Thiophene
훽휇푟푒푠,∞ 푖⁄푟푒푓 훽휇푟푒푠,∞ 푖⁄푟푒푓 Ionic Liquid 1,푖 ln 퐾1 1,푖 ln 퐾1
+ - [BMIM] [CH3CO2] -15.3 -2.6 -4.9 -2.0
+ - [BMIM] [BF4] -15.4 -2.5 -5.3 -1.7
+ - [BMIM] [CH3SO4] -15.3 -2.6 -5.6 -1.3
+ - [BMIM] [CF3CO2] -16.0 -1.9 -5.6 -1.3
+ - [BMIM] [PF6] -16.4 -1.5 -5.0 -1.9
+ - [BMIM] [CF3SO3] -16.1 -1.8 -5.7 -1.2
+ - [BMIM] [NTF2] -17.1 -0.8 -6.0 -1.0
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The trends in the computed dimensionless chemical potential for dibenzothiophene with charge scaling agree reasonably well with values calculated from available reference data [71-73] (see Table A4). The absolute values differ slightly, but the trends are consistent, which suggests that the use of charge scaling is appropriate. The dimensionless chemical potentials are significantly different between the solutes, which suggests that the ILs and n-decane interact differently with thiophene and dibenzothiophene. This supports the differences observed in experiments by Mokhtarani et al. [25] and Safa et al. [26] as discussed earlier.
In Table 1, the ILs are listed in order of increasing molar volume. The computed partition coefficients for dibenzothiophene trend reasonably well with the molar volume, as suggested by Wilfred et al., [6] but the same trend is not observed for thiophene. Additionally, the computed partition coefficients do not trend well with hydrogen-bond basicity [27]. This suggests that the selection of the anion does not largely impact the affinity of the solute for the ILs and there are other important intermolecular interactions present between the solute and the cation. Detailed structural analysis was used to better understand these differences by looking at specific solvent- cation and solvent-anion interaction sites and will be discussed in the next section.
푖⁄푟푒푓 Looking at the computed partition coefficients, it is worth noting that values of ln 퐾1 < 0 푖⁄푟푒푓 (and therefore 퐾1 < 1) would indicate that dibenzothiophene and thiophene favor n-decane over the ILs. The use of charge scaling to model ILs has been shown to give good thermodynamic properties, which are important for the structural analysis but may cause the dimensionless chemical potential at infinite dilution to be less negative than expected [28].
Free energy calculations performed for dibenzothiophene and thiophene at their infinite dilution limit with full charges (no charge scaling) did not show good agreement with values calculated from available reference data [71-73] (see Table A5). This confirms that the 0.8 charge scaling suggested by Zhong et al. [22] is appropriate for modeling these IL systems.
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Structural Analysis
To better understand the underlying molecular driving forces, detailed structural analysis was performed for neat ILs and for systems of ILs with approximately 0.1 mol frac thiophene or dibenzothiophene. The figures in this section were generated using TRAVIS.
Ionic Liquids
The radial distribution functions (RDFs) describing the cation-anion interactions for each IL pair are shown in Figure 4 for the neat IL and IL plus 0.1 mol frac thiophene and dibenzothiophene. In Figure 4, the interaction distance is measured with respect to the center of ring (COR) of [BMIM]+ and the anion atom(s) that carry the negative charge (reference Figure 2).
Figure 4. RDFs of cation-anion interactions for studied ILs with 0.1 mol frac solute
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Comparing the RDFs of the neat ILs (shown by the solid black line in each graph), the distance to the first peak and the height of the first peak are different for each of the ILs, which suggests that the cation interacts differently with each of the anions. Looking at the sets of RDFs (neat IL, IL plus thiophene, and IL plus dibenzothiophene) computed for each IL, they are essentially unchanged with the addition of 0.1 mol frac solute, indicating that the IL structure is essentially unchanged. With the addition of the solute molecules, the height of the first peak is slightly higher, as expected, due to tighter packing.
In all cases, the IL structure appears to change little with a solute concentration of 0.1 mol frac, consistent with Oliveira et al. [14] This suggests that the affinity of the solutes for the ILs results from the ability of the ILs to accommodate the solute with little change to the IL structure while contributing favorable intermolecular interactions. It is now worth looking at specific interaction sites between the solute and the anion or cation to better understand the extraction mechanism.
Thiophene and Dibenzothiophene
+ - The interactions between 1-butyl-3-methylimidazolium methylsulfate ([BMIM] [CH3SO4] ) and thiophene or dibenzothiophene are discussed in this section. The free energy calculations suggested that thiophene and dibenzothiophene would interact differently with the ILs but that the selection of the anion should not significantly change the type or strength of these + - interactions. The interactions observed between the solutes and [BMIM] [CH3SO4] are similarly observed with the other studied ILs, except where noted. Detailed structural analysis for all studied ILs are available in Appendix II but are not included here because there were no remarkable differences between them and discussion of the results would be repetitive.
Since the IL structure does not appear to change with the addition of the solute (shown in Figure 4), specific interactions between the solute and the anion and the cation were analyzed to better understand the mechanism of extraction (reference atom numbering in Figure 3). Figure 5 shows the partial RDFs between the thiophene or benzene rings of the solute (COR) and methyl group - (Ct1) of the [CH3SO4] anion. The interaction distance is defined between the center of (thiophene or benzene) ring of the solute and specific atom(s) of the anion. Figure 5b shows the
20 partial RDFs between the thiophene or benzene rings of the solute (COR) and the imidazole ring (COR) or alkyl chain (Ct1/2/3) of the [BMIM]+ cation. The interaction distance is defined between the center of (thiophene or benzene) ring of the solute and the center of (imidazole) ring of the cation or averaged over the carbon atoms in the alkyl chain. A number of other partial RDFs were computed for solute-cation and solute-anion interactions but did not show anything particularly interesting in the context of this work, so they are not included here.
+ - Figure 5a. RDFs of solute-anion interactions for [BMIM] [CH3SO4]
+ - Figure 5b. RDFs of solute-cation interactions for [BMIM] [CH3SO4]
The RDFs shown in Figure 5a and Figure 5b suggest that there are no strong interactions observed between the solute and the IL indicated by the low intensity of the first peak, g(r) < 2.5.
Comparing Figure 5a and Figure 5b, it appears that thiophene slightly favors the anion over the cation by weak electrostatic interactions. The presence of the sulfur atom in thiophene could produce a slightly partial positive charge on the ring hydrogens, which could interact with the
21 negative charge of the anion. This is not observed with the thiophene ring in dibenzothiophene because the ring hydrogens are on the benzene rings. There are more ring hydrogens in dibenzothiophene, so the peak height is smaller but occurs at the same distance suggesting the same weak electrostatic interactions between the ring hydrogens and the anion.
Figure 5b shows that thiophene interacts more readily with the cation than dibenzothiophene likely due to the smaller size of the solute but the peaks are not very sharp, which indicates the interactions are not very specific. The computed partition coefficients, however, suggest that the ILs favor dibenzothiophene, likely due to more interaction sites. Since there are no specific interactions, simply having more interaction sites could explain the higher solubility corresponding to higher extraction efficiency as previously suggested.
The thiophene ring in dibenzothiophene favors the imidazole ring and the benzene rings favor the alkyl chain. The thiophene ring in dibenzothiophene likely interacts with the imidazole ring via π-π interactions suggested by the small peak around 440 nm. This peak is not observed for + - [BMIM] [CH3CO2] , which has the smallest molar volume of the studied ILs (see Appendix II). This suggests that dibenzothiophene is unable to fit nicely between the anion and cation, and there may be some minimum molar volume necessary to accommodate the dibenzothiophene.
Detailed structural analysis was also performed with full charges (no charge scaling) for + - [BMIM] [CH3SO4] , and the observed interactions did not change (also see Figure A1).
Combined distribution functions (CDFs) can be used to confirm the presence of π-π interactions. If π-π stacking is present, the occurrence would be significantly higher around 380 pm at angles less than 20° [74]. Figure 6 shows the CDFs between the imidazole ring and the thiophene ring where occurrence is plotted as a function of the distance and angle defined between the rings (red indicates a high occurrence region).
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+ - Figure 6. CDFs of solute-cation interactions for [BMIM] [CH3SO4]
The CDFs in Figure 6 confirm the presence of π-π stacking between the imidazole ring of the cation and the thiophene ring of dibenzothiophene but not for thiophene itself. This supports the idea that thiophene favors interactions with the anion via ring hydrogens and dibenzothiophene favors interactions with the cation. If the thiophene ring is planar with the imidazole ring, the benzene rings are near the alkyl chain by geometry. The benzene rings in dibenzothiophene could also interact with the alkyl chain via CH-π interactions, a type of weak electrostatic interaction [75,76].
+ - The CDF between dibenzothiophene and [BMIM] [CH3CO2] shows the occurrence is approximately half of the other studied ILs (see Appendix II). This suggests that π-π stacking is still observed, but due to the small molar volume of the IL, the thiophene ring in dibenzothiophene is likely only able to interact outside of the IL structure; it is not able to fit nicely between the anion and cation, which supports the computed RDFs.
It is likely that the combination of favorable intermolecular interactions between the thiophene ring and the imidazole ring coupled with favorable interactions between the benzene ring and the alkyl chain plus the interactions between the ring hydrogens and the anion that contribute to the higher affinity of dibenzothiophene for the ILs.
23
Spatial distribution functions (SDFs) can be used to better visualize these observations. For the + - SDF shown in Figure 7, [BMIM] is used as the reference molecule, COM [CH3CO2] is shown in blue (isovalue 20), COR dibenzothiophene is shown in red (isovalue 1.1).
- + Figure 7. SDF for dibenzothiophene (red) and [CH3SO4] (blue) around [BMIM] .
The SDF in Figure 7 confirms the suggested interactions between the imidazole and thiophene rings of dibenzothiophene, shown by the red isosurface (dibenzothiophene) concentrated above and below the ring. Interactions between the cation and anion are shown by the blue isosurface - ([CH3SO4] ) concentrated at the ring hydrogens. If the thiophene ring is likely to be found planar to the imidazole ring, then the benzene rings are still able to interact with the alkyl chain and the anion as previously suggested.
+ - [BMIM] [CH3SO4] was chosen for this discussion to explain the interactions observed between dibenzothiophene and all the studied ILs while considering the potential industrialization of this process. Free energy calculations and detailed structural analysis did not show remarkable differences between the studied ILs, and the decomposition of fluorinated anions has been shown to produce corrosive hydrogen fluoride (HF), which would be undesirable in industrial applications for no significant advantage in terms of extraction capacity [11]. + - [BMIM] [CH3CO2] was not chosen for the discussion because it did not show the same intensity of π-π stacking as the other studied ILs, which may be attributed to its small molar volume.
24
Conclusions
This work examined the molecular-level interactions between two aromatic sulfur compounds and seven common imidazolium-based ionic liquids (ILs). Dibenzothiophene was the primary interest of this work because it is more difficult to remove from diesel fuel via conventional HDS techniques. Thiophene was also studied to help explain how the addition of the benzene rings change the observed intermolecular interactions.
Solvation free energy calculations for the solutes at infinite dilution in the studied ILs and n- decane (model diesel) were used to predict partition coefficients. The IL/n-decane partition coefficients for dibenzothiophene trended reasonably well with molar volume but no significant differences were observed between the studied ILs.
Detailed structural analysis was performed to better understand the specific interactions between the solutes and studied ILs. The IL structures appeared to be essentially unchanged with the addition of 0.1 mol frac solute. Analysis of thiophene suggested that the ring hydrogens interact with the anion, but there were no strong, specific interactions with the cation. Analysis of dibenzothiophene suggested that the ring hydrogens interact less with the anion, but there is a combination of π-π stacking of the thiophene ring and the imidazole ring plus CH-π interactions between the benzene ring and alkyl chain that contribute to interactions with the cation. These interactions were observed for all the studied ILs.
The use of molecular dynamic simulations allowed this work to address some limitations of experimental studies and to support future simulation-based studies. Detailed structural analysis suggested that thiophene and dibenzothiophene interact very differently with ILs, so it will be important for future studies to expand the range of aromatic sulfur compounds examined or to focus on specific compounds that are more difficult to remove through conventional desulfurization processes. Since the observed intermolecular interactions were not significantly different varying the anion, future studies should also consider the impact of the industrialization of ILs for extractive desulfurization and focus their efforts on ILs with nonfluorinated anions. Hopefully, this work will serve as a good foundation for future simulation-based research.
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Appendix I: Additional Simulation Details
Table A1. Comparison of simulation densities to literature densities for pure ILs
Simulation Zhong et Experimental # IL Percent Percent Ionic Liquid Density al. Density Density pairs Error Error (g/cm3) (g/cm3) (g/cm3) + - [BMIM] [BF4] 271 1.164 1.196 2.68% 1.201 3.08% + - [BMIM] [CF3CO2] 247 1.186 1.212 2.15% 1.213 2.23% + - [BMIM] [CF3SO3] 235 1.289 1.320 2.35% 1.304 1.15% + - [BMIM] [CH3CO2] 273 1.027 1.0d5 2.65% 1.053 2.47% + - [BMIM] [CH3SO4] 253 1.206 1.235 2.35% 1.208 0.17% + - [BMIM] [NTF2] 177 1.415 1.445 2.08% 1.437 1.53% + - [BMIM] [PF6] 247 1.325 1.370 3.28% 1.368 3.14% n-decane 281 0.737 0.730 0.96%
The small differences between the simulation density values for this work and the Zhong et al. density values can be attributed to differences in computational details. Zhong et al. used different simulation times to equilibrate the system and collect property data.
Table A2. Simulation box set up for structural analysis of ILs with approx 0.1 mol frac solute
Ionic Liquid # IL pairs # solute molecules
+ - [BMIM] [BF4] 271 60 + - [BMIM] [CF3CO2] 247 55 + - [BMIM] [CF3SO3] 235 52 + - [BMIM] [CH3CO2] 273 61 + - [BMIM] [CH3SO4] 253 56 + - [BMIM] [NTF2] 177 39 + - [BMIM] [PF6] 247 55
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Table A3. Summary of solvation free energy with 0.8 charge scaling from simulation
dibenzothiophene thiophene n-decane 푟푒푠,∞ 푟푒푠,∞ 푟푒푠,∞ Solvent 훽휇1,푖 훽휇1,푖 훽휇1,푖 + - [BMIM] [BF4] -15.423 ± 0.208 -5.282 ± 0.087 -4.207 ± 0.179 + - [BMIM] [CF3CO2] -16.023 ± 0.111 -5.612 ± 0.050 -4.637 ± 0.117 + - [BMIM] [CF3SO3] -16.066 ± 0.214 -5.714 ± 0.078 -5.548 ± 0.192 + - [BMIM] [CH3CO2] -15.305 ± 0.245 -4.909 ± 0.120 -4.741 ± 0.100 + - [BMIM] [CH3SO4] -15.335 ± 0.297 -5.619 ± 0.147 -3.317 ± 0.297 + - [BMIM] [NTF2] -17.096 ± 0.156 -5.978 ± 0.063 -5.873 ± 0.116 + - [BMIM] [PF6] -16.433 ± 0.227 -5.000 ± 0.111 -4.004 ± 0.224 n-decane -17.906 ± 0.032 -6.940 ± 0.021
Table A4. Summary of solvation free energy calculated from reference predictions [71-73]
dibenzothiophene thiophene n-decane 푟푒푠,∞ 푟푒푠,∞ 푟푒푠,∞ Solvent 훽휇1,푖 훽휇1,푖 훽휇1,푖 + - [BMIM] [BF4] -10.893 -6.741 -5.058 + - [BMIM] [CF3CO2] -9.157 -6.346 -5.305 + - [BMIM] [CF3SO3] -9.504 -6.751 -5.591 + - [BMIM] [CH3CO2] -10.868 -6.772 -5.609 + - [BMIM] [CH3SO4] -9.674 -5.597 -4.279 + - [BMIM] [NTF2] -12.808 -6.977 -6.410 + - [BMIM] [PF6] -13.088 -6.626 -5.204
Limiting activity coefficients were calcualted using the LSSVM method proposed by Paduszynski [71], which were used to calculate the reference solvation free energies following Dhakal et al. [72] with vapor pressure data from Yaws [73].
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Table A5. Summary of solvation free energy with no charge scaling from simulation
dibenzothiophene thiophene n-decane 푟푒푠,∞ 푟푒푠,∞ 푟푒푠,∞ Solvent 훽휇1,푖 훽휇1,푖 훽휇1,푖 + - [BMIM] [BF4] -17.657 ± 0.161 -4.657 ± 0.052 -3.391 ± 0.332 + - [BMIM] [CF3CO2] -12.433 ± 0.247 -5.978 ± 0.143 -3.283 ± 0.277 + - [BMIM] [CF3SO3] -17.456 ± 0.300 -5.383 ± 0.077 -6.925 ± 0.326 + - [BMIM] [CH3CO2] -19.701 ± 0.241 -7.773 ± 0.079 -7.173 ± 0.257 + - [BMIM] [CH3SO4] -18.970 ± 0.036 -6.152 ± 0.068 -1.865 ± 0.376 + - [BMIM] [NTF2] -20.119 ± 0.184 -5.196 ± 0.147 -6.129 ± 0.305 + - [BMIM] [PF6] -21.113 ± 0.070 -4.629 ± 0.034 -7.645 ± 0.227
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+ - Figure A1a. RDFs of solute-anion interactions for [BMIM] [CH3SO4] with no charge scaling (shown in red) compared to 0.8 charge scaling (shown in black, also shown in Figure 5a)
+ - Figure A1b. RDFs of solute-cation interactions for [BMIM] [CH3SO4] with no charge scaling (shown in red) compared to 0.8 charge scaling (shown in black, also shown in Figure 5b)
The use of charge scaling shows very little difference in the structural analysis, and the peak heights are so small that it is not significant.
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Appendix II: Additional Structural Analysis
+ - 1-butyl-3-methylimidazolium tetrafluoroborate: [BMIM] [BF4]
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+ - 1-butyl-3-methylimidazolium trifluoroacetate: [BMIM] [CF3CO2]
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+ - 1-butyl-3-methylimidazolium trifluoromethanesulfonate: [BMIM] [CF3SO3]
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+ - 1-butyl-3-methylimidazolium acetate: [BMIM] [CH3CO2]
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+ - 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide: [BMIM] [NTF2]
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+ - 1-butyl-3-methylimidazolium hexafluorophosphate: [BMIM] [PF6]
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