Combined Computational and Experimental Study on the Influence of

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C: Energy Conversion and Storage; Energy and Charge Transport

Combined Computational and Experimental Study on the Influence of Surface Chemistry of Carbon-Based Electrodes on Electrode-Electrolyte Interactions in Supercapacitors Sabine Schweizer, Johannes Landwehr, Bastian J.M. Etzold, Robert Horst Meissner, Marc Amkreutz, Peter Schiffels, and Jörg-Rüdiger Hill J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b07617 • Publication Date (Web): 11 Jan 2019 Downloaded from http://pubs.acs.org on January 13, 2019

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The Journal of Physical Chemistry

Combined Computational and Experimental Study on the Influence of Surface Chemistry of Carbon-Based Electrodes on Electrode-Electrolyte Interactions in Supercapacitors Sabine Schweizer,† Johannes Landwehr,‡ Bastian J. M. Etzold,‡ Robert Horst Meißner,¶,§ Marc Amkreutz,k Peter Schiffels,k and Jörg-Rüdiger Hill∗,† †Scienomics GmbH, B¨ urgermeister-Wegele-Straße 12, 86167 Augsburg, Germany ‡Ernst-Berl-Institut f¨ ur Technische und Makromolekulare Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 8, 64287 Darmstadt, Germany ¶Institute of Polymer and Composites, Hamburg University of Technology, Denickestraße 15, 21073 Hamburg, Germany §MagIC Magnesium Innovation Centre, Helmholtz-Zentrum Geesthacht, Max-Planck Straße 1, 21502 Geesthacht, Germany kFraunhofer-Institut f¨ ur Fertigungstechnik und Angewandte Materialforschung IFAM Klebtechnik und Oberflächen -, Wiener Straße 12, 28359 Bremen, Germany E-mail: [email protected] Phone: + 49 (0) 821 450 165 60. Fax: + 49 (0) 821 450 165 62

Abstract

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Supercapacitors are regarded as promising technology for novel powerful energy storage systems. The mechanism of energy storage in these capacitors is not fully understood yet because of the complex molecular mechanisms at the atomistic scale. Exploring the processes at the nanoscale provides necessary fundamental and thorough insights for improving the performance of such devices. In this work, we present a combined computational and experimental study on electrode-electrolyte interactions in electric double layer capacitors. The influence of pore size and surface chemistry of carbon-based electrode material on interactions with the electrolyte has been investigated for an organic and inorganic electrolyte using density functional theory calculations. In addition, solvent effects on the interaction strength have been systematically explored. We found that experimentally determined effects of pore confinement can be linked with calculated interaction energies providing a suitable descriptor for virtual pre-screening approaches. Our results show that the pore size significantly affects the interaction quality with the electrolyte. This effect and the influence of chemical functionalization has a stronger impact on the interaction with anions than with cations. Moreover, our studies indicate that solvent effects are especially important for surface functional groups that allow for hydrogen bonding. Overall, our results provide relevant information how structural and electronic effects affect confinement, wettability and mobility of electrolyte molecules which is important for boosting and tuning the performance of supercapacitors.

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Introduction

In order to escape from the dependency on fossil energy sources, alternative economical ways for energy supply need to be developed to cover the increasing energy demand. Energy storage systems play a crucial role in the context of sustainable energy supply. Different concepts can be applied to store energy. Batteries, for example, convert chemical energy into electricity, while in capacitors energy is directly stored statically as electrical energy. Each technology has, however, its own strengths and weaknesses. 2


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Supercapacitors represent a promising technique between batteries and capacitors and combine advantages of both technologies. 1–3 They have the excellent charging characteristics of conventional capacitors, but offer considerably higher capacitances through a combination of double-layer and pseudocapacity. 1,4 The great advantage of supercapacitors over batteries is the high power density which ensures remarkably faster charging and discharging. 1,5,6 At the same time, supercapacitors tolerate significantly more recharging cycles compared to conventional batteries and thus provide a long lifetime without any need for replacement. 7,8 Moreover, the operating temperature of supercapacitors covers a much broader range and they can be designed environmentally friendly. 7–9 Supercapacitors are capable to shield devices from voltage fluctuations and are used in various areas ranging from renewable energy over large scale backup power up to automotive applications, for example for recapturing braking energy. 7 The family of supercapacitors can be divided into three groups depending on the design of the device: electric double-layer capacitors (EDLC), electrochemical pseudocapacitors, and hybrid capacitors. 1,10 EDLCs usually consist of two or more electrodes and are ionically connected through an aqueous or organic electrolyte. Commercially, organic electrolytes containing tetraethylammonium (TEA) tetrafluoroborate (BF4 ) salts are used, which allow operating voltages up to 2.7 V. 11–13 High capacitances can be achieved using porous carbon electrodes which possess a large surface area. 1,4,14 When an electric field is applied the ions in the electrolyte diffuse into the pores and charge accumulates at the electrode/electrolyte interface. Despite many benefits, supercapacitors offer only a low energy density, are limited to low cell voltages, and suffer from high self-discharging. 7 For overcoming limitations and improving the performance of theses capacitors, it is essential to understand processes at the molecular level. Although much work has been dedicated to broaden the understanding of the energy storage mechanism of these systems, see e.g. Refs. 3,15–21 and references therein, there are ongoing efforts to explore the relevant processes and to elucidate the complex interplay of parameters such as pore confinement, wettability, mobility or variations in the

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local composition that govern the performance of the capacitors. A better wettability, i. e. how much of the porous electrode surface is accessible for the electrolyte, increases the capacity. At the same time, confining ions in the pores is important for charge accumulation, while the interaction of ions with the electrode surface affects their mobility and thus the charging and discharging process. An optimal tuning of the individual parameters, especially confinement effects and mobility, imposes conflicting requirements to a certain degree. A strong interaction of ions is advantageous for charge accumulation, but if ions adhere too tightly to the electrode surface the mobility suffers. It is therefore important, to have a fundamental understanding how these effects correlate and how they can be modulated for finding and adjusting an optimal balance. In the last decades, molecular modeling has been established as valuable technique for revealing fundamental insights into problems at the atomistic level. While the application of force field-based methods traditionally focuses on dynamic processes, ab initio methods are most suited to address questions with respect to reactivity and electronic effects. Molecular dynamics (MD) simulations have been used, for instance, for creating model structures of porous materials, such as activated carbon used in EDLCs 18,22–25 and for investigating various model systems of EDLCs, e.g. Refs. 3,15,17–19,21,26–29 In this type of studies, electronic effects are usually not taken into account, although they can play an important role and significantly govern molecular properties and their behavior. Activated porous carbon exhibits a rather large ratio of sp2 hybridized carbon indicating the graphitic nature of the porous carbon. Hence, it can be expected that electronic effects play a role regarding electrodeelectrolyte interactions. For this reason, ab initio simulations can be leveraged to study if and how interactions between carbon electrodes and electrolyte ions can be correlated with the performance of EDLCs and how surface functionalization can affect the interaction. Due to the computational demand of ab initio calculations, the size of the system which can be treated is limited. In order to study complex and large systems at this level of theory, commonly smaller model systems mimicking the essential characteristics of the actual

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environment are used for the computational studies. By systematically increasing the system size, the influence of a larger environment can be assessed. Using smaller model systems also allows to screen efficiently the effect of functionalization. Moreover, pure hypothetical or experimentally not practical states can be investigated virtually to gain a better understanding and more background information on the molecular systems of interest. Computational methods can be leveraged, for instance, to consider interfering effects separately which is experimentally not always feasible. In this way, critical information about the importance of different effects that govern the performance of a system can be obtained. This information can then be used to guide product development and tune properties and performance in the desired direction. A fruitful interplay of simulation and experimentation allows ultimately to save time and cost. The present work aims to provide detailed insights into the electrolyte-electrode interface of porous carbon electrode-based devices to gain a better understanding of the energy storage mechanism in EDLC supercapacitors for improving the performance of such devices. In this context, it is necessary to know how properties of the electrode material and electrolyte can be modulated, for example, how surface functional groups affect mobility and wettability or how the pore size affects confinement. In a recently published study, Ruzanov et al. 30 discuss the adsorption behavior of ionic pairs on a coronene-based carbon system based on ab initio calculations. Ruzanov et al. 30 focused on imidazolium based ion pairs on circumcoronene. They observed that dispersion plays a critical role with respect to the interaction between carbon model and ion pair. Moreover, they analyzed the interaction as a function of the anion and found different interaction strengths depending on the ion type. Here, we present a study that analyzes the correlation between electrode-electrolyte interaction and capacitance as a function of the chemical environment and surface functionalization in a systematic way. In a combined computational and experimental study, we have therefore investigated how the interaction between electrode and electrolyte affects the capacity and which factors have critical influence on this interaction. Density functional theory (DFT) calculations on

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various model structures based on aromatic hydrocarbons and carbon nanotubes (CNT) in the presence of electrolyte ions have been performed. The model systems have been varied systematically with respect to size, shape and chemical functionalization in order to identify and characterize the relevant influences and parameters that affect the performance. In particular, the influence of surface functional groups, pore size and solvent will be shown. Calculated interaction energies will be analyzed to obtain information how tightly electrolyte ions can adhere to the electrode surface which has consequences on how easily ions can travel and be accumulated. The results will be related to experimental measurements of the capacitance and implications on confinement, mobility and wettability in EDLCs will be discussed.

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Computational Details

Structures of the model systems were generated using Scienomics MAPS platform. 31 For studying the carbon electrode-electrolyte interaction, several sets of models were considered: (a) Aromatic hydrocarbons together with (i) an electrolyte ion pair of a commonly used organic electrolyte and (ii) with the individual ions, i. e. either cation or anion, respectively. (b) Naphthalene and indole derivatives together with (i) an electrolyte ion pair, (ii) with the individual ions, and (iii) the electrolyte ion pair together with an acetonitrile (ACN) molecule representing the solvent. (c) Carbon nanotubes together with either the cation or the anion of the ion pair. The model systems of set (a) and (b) are summarized in Fig. 1. The structures of set (a) and (b) were fully geometry optimized using the density functional PBE0 32 with the basis set def2-SVPD 33 and applying the dispersion correction (D3) developed by Grimme et al. 34,35 The choice of the method and basis set can be a delicate question as discussed, e.g. by 6


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Michaelides and co-workers. 36 In the present work, density functional and basis set have been chosen as compromise between computational effort and accuracy. Mardirossian and HeadGordon performed a comprehensive density functional benchmark study 37 and found that the widely used density functional PBE0 performs reasonably well compared to other local and hybrid density functionals. With respect to the basis set quality, we have compared the interaction energy between an ion pair at PBE0-D3/def2-SVPD level and PBE0-D3/def2-TZVPP. A difference in the interaction energy of about 4 kJ/mol was found which is commonly regarded as chemical accuracy. It should be stressed that even at lower computational level, general trends are usually reflected quite well, which is of main importance for the aim of our work. An ion pair consisting of TEA (tetraethylammonium) and BF4 (tetrafluoroborate) was placed above the ring plane of the aromatic compound (see Fig. 2 for illustration). The geometry optimization has been performed in two steps: First, the ion pair has been kept fixed during optimization and then the whole system has been allowed to relax. Interaction energies between the ion pair and the aromatic compound were calculated at PBE0-D3/def2SVPD level based on the geometry optimized structures. The basis set superposition error (BSSE) was corrected applying the counterpoise correction. 38 Interaction energies with individual ions were calculated using the geometry optimized structures of the whole complex, if not otherwise stated. Either the cation (TEA) or the anion (BF4) was removed before calculating the interaction energies at PBE0-D3/def2-SVPD level. In addition, solvent effects were evaluated using implicit and explicit models. The COSMO approach 39 was used for implicitly treating the solvent in the electrolyte layer. A dielectric constant of = 37.5 was applied to mimic the acetonitrile solvent environment. For the explicit treatment, an acetonitrile molecule was added to ion pair model systems of set (b). The structures were geometry optimized stepwise at the same level of theory as described above: After keeping the ion pair and acetonitrile fixed, the whole system was relaxed. Interaction energies were calculated in a two fragment approach between the electrolyte and the carbon model, i. e. ion pair and ACN together were considered as one fragment and the carbon model as the second

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fragment. The interaction energy was calculated as Eint = Etotal − Efragment1 − Efragment2 . For the naphthalene derivatives, interaction energies based on a three fragment approach were also calculated. Here, the ion pair and the ACN molecule were treated as separate fragments. The interaction energy is given as Eint = Etotal − Efragment1 − Efragment2 − Efragment3 with Efragment1 as energy of the ion pair, Efragment2 as energy of the ACN, and Efragment3 as energy of the naphthalene derivative. In addition to the organic electrolyte represented through a TEA/BF4 ion pair, a hydrated sulfuric acid dimer was used as an example for an aqueous, inorganic electrolyte. The initial structure of the sulfuric acid dimer was taken from literature. 40 For a subset of carbon models, which were used for studying the interaction with the organic electrolyte, corresponding models with the inorganic electrolyte were built. The sulfuric acid dimer was placed above the ring plane in a similar way as done for the organic electrolyte. The structures were fully geometry optimized at the PBE0-D3/def2-SVPD level and interaction energies between the hydrated acid dimer and the carbon model were calculated at the same level of theory. For set (c), the carbon nanotubes were created using the Nanotube builder tool implemented in MAPS. The number of cells for building the nanotube was chosen to be five. Five differently sized CNTs were generated setting the vectors n = m = 5, 6, 7, 8, 10, which will be denoted in the following as CNT (5,5), CNT (6,6), etc. For the five CNT systems, two sets of calculations were performed: (i) with TEA inside the tube and (ii) with BF4 inside the tube. The geometries of set (c) were optimized at slightly lower level (RI-PBE-D3-MJ/def2SVP 41,42 ) due to the fairly large system size. Interaction energies for the CNT-based systems were calculated at PBE0-D3/def2-SVPD level. For introducing substituents into the CNTs, an arbitrarily selected 6-membered ring was deleted in the middle of the CNT (8,8) and the respective functional group has been inserted oriented towards the inner of the tube. Hydrogen atoms were then added at the remaining five unbound carbon atoms to avoid dangling bonds. We have chosen a position in the middle of the CNT to provide a kind of

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carbon cavity around functional group and ion. As functional groups −SO3 H and −COOH have been considered. These two groups served as representatives for sulfur- and oxygen containing functional groups. At the same time both groups have in principle the ability to form hydrogen bonds which is an important aspect with respect to the interaction with electrolyte ions. Due to the fairly large system size, we have restricted the number of different substituents to these two groups. Screening of other functional groups and incorporation of more than two functional groups at once is beyond the scope of the present study. One set of model structures was built with only −SO3 H. A second set of model structures contained two substituents, i. e. −SO3 H and −COOH which were placed on opposite sides of the CNT. Either TEA or BF4 were placed in the middle of the tube similar to the unsubstituted CNT systems. The structures were geometry optimized at RI-PBE-D3-MJ/def2-SVP level and interaction energies have been calculated at PBE0-D3/def2-SVPD level. Cartesian coordinates of the final structures are provided in the supporting information.

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Experimental Details

The experimental study was performed on carbide derived carbons (CDC) based on titanium carbide (1-5 µm). This type of porous carbon material was chosen for the model study due to the high chemical purity, narrow pore size distribution and tunable pore size in the microporous region. The carbons were synthesized by selective etching of titanium carbide with chlorine at temperatures ranging from 500 ◦ C to 1200 ◦ C. Depending on the etching temperature the process yielded microporous carbons with specific surface areas (SSA) ranging from 1165 m2 g−1 to 1740 m2 g−1 and pore volumes V of 0.55 cm3 g−1 to 0.77 cm3 g−1 , respectively. The data is based on high resolution nitrogen sorption analysis at 77 K using the instrument Autosorb-1P by Quantachrome Instruments. Data evaluation was based on the quenched solid density functional theory (QSDFT) method assuming equilibrium condition and slit

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pores. The average pore diameter d of the synthesized carbons was calculated from the ratio 2 · V/SSA. According to this method, CDC was synthesized that exhibited an average pore diameter of 0.65 nm, 0.72 nm, 0.83 nm or 1.32 nm. In all cases, the carbon texture is predominantly amorphous 43 as shown in previous work of one of the authors of the present study. The post synthetic surface functionalization of CDC was realized by sulfuric acid treatment at different concentrations. Therefore, sulfuric acid at concentrations of 50%, 98% and oleum at a concentration of 65% was used. The different functionalization agents are abbreviated in the following as “SO50”, “SO98” and “OL65”, respectively. The functionalized samples were dried at 50 ◦ C and analyzed by thermogravimetry (TG) in helium up to 1000 ◦ C at 5 K/min, while the off-gas was analyzed by mass spectrometry (MS). The electrochemical characterization was realized by cyclovoltammetry with a standard three electrode setup, with the carbon material being the active electrode material on the working electrode. Details on the textural properties of the synthesized CDC, the surface functionalization, TG-MS analysis and the electrochemical characterization are provided in the supporting information. More details on the post synthetic surface functionalization of CDC is provided elsewhere. 44

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Results and Discussion

Advanced porous electrode materials consist of carbide-derived carbon (CDC) with which high capacitances can be achieved due to their high surface area. 1,1,12,14,45,46 These materials exhibit a high degree of sp2 -hybridization and their pore volume can be controlled precisely. 22,47 Aromatic hydrocarbons and carbon nanotubes seem to be thus a suitable choice for emulating the carbon electrode environment. Since organic electrolytes typically offer higher operating voltages, we have used a tetraethylammonium tetrafluoroborate (TEA/BF4 ) ion pair for our studies. 11–13 Particular emphasis has been put on studying the influence of

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functional groups and on estimating the impact of the pore size on the carbon-electrolyte interaction. Using hydrocarbon-based models allows to analyze the influence of functional groups detached from confinement effects, while the latter can be explored using carbon nanotube-based model systems. An overview over the tested aromatic compounds is given in Fig. 1. By systematically varying the surrounding of the ions, size effects were addressed and it was examined how functionalization affects the interaction between electrode and electrolyte.

4.1

Aromatic hydrocarbons based systems

First, we have investigated the interaction between the ion pair and pure hydrocarbons. In this context, it has been also evaluated how the interaction depends on the size of the hydrocarbon compound in order to study the influence of a larger surrounding. For this purpose, the system size has been systematically increased starting from benzene over naphthalene, phenanthrene, pyrene, chrysene, up to coronene. In addition, the number of surrounding benzene molecules has been increased up to three for investigating how the spatial arrangement of the benzene rings compares to single molecules with the same number of aromatic rings, i. e. two benzenes versus naphthalene and three benzenes versus phenanthrene. After having performed a full geometry optimization, counterpoise-corrected interaction energies have been calculated (for details see section 2). As representative example, the geometry optimized structure of pyrene and the ion pair is illustrated in Fig. 2 and the results of the interaction energy calculations are listed in Tab. 1 (entries (1) to (6)). The results reveal a strong interaction between ion pair and the respective hydrocarbon system with interaction energies ranging between -40 and -114 kJ/mol (A negative value means attractive interactions, while a positive value indicates repulsive interactions. A more negative value means thus an increase in the interaction energy, i. e. an increase of the strength of interactions). The strengh of interactions between hydrocarbon and ion pair increases with the number of rings in the hydrocarbon. The strongest interaction within this set is found with coronene. 11



Although pyrene and chrysene are both four-ring systems, the interaction with pyrene is stronger compared to chrysene indicating that a stretched geometry is less favorable for the interaction with the electrolyte. Based on the geometry optimized structures, the interaction energy with the cation and the anion were calculated separately by removing the respective counterion from the system. The results are listed in Tab. 1 (entries (1) to (6) last two columns) and indicate a significantly stronger interaction with the cation than with the anion. This observation can be explained by non-covalent interactions between the positively charged cation and the electron-rich π-system of the aromatic compound (cation-π interaction). Since the interaction energies with the individual ions were calculated based on the geometry optimized structure of the whole ion pair-hydrocarbon complex, we have analyzed if and how the geometry affects the interaction energies with the individual ions. For that reason, the structures of pyrene + TEA and pyrene + BF4 were fully relaxed at PBE0-D3/def2-SVPD level to investigate how the geometry and the interaction energy changes after re-optimization of the ion-hydrocarbon systems. While the magnitude of the interaction energy with TEA increases only slightly from -74.2 kJ/mol to -75.9 kJ/mol, the effect is distinctly higher in the anionic system and the interaction strength increases from -26.2 kJ/mol to -44.6 kJ/mol. In the ion pair complex, the anion is located near the edge of the hydrocarbon, but above the ring plane. During re-optimization of the pyrene + BF4 model, the anion moves beside the ring plane presumably triggered through the electrostatic repulsion between the anion and the electronrich π-system of pyrene. Nevertheless, the interaction with the cation is still considerably stronger. Thus, we assume that the observed trends will be the same also for other reoptimized structures. For further evaluating the influence of the surrounding, we have applied a continuum model to mimic the carbon environment implicitly. 39 Again, the same model, i. e. ion pair + pyrene, has been used for probing the influence of the carbon surrounding. The structure has been geometry optimized at PBE0-D3/def2-SVPD level using a dielectric constant of =

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12.5 to simulate the carbon environment implicitly. The structures obtained in the vacuum and in the carbon environment (mimicked by the continuum model) differ only slightly. A superposition of both structures gives a root mean square deviation (RMSD) of 0.13 ˚ A. The geometry optimized structure was then used for calculating the interaction energy between the ion pair and pyrene and between the individual ions (TEA, BF4 ) and pyrene, respectively. As it can be expected, the interaction is weakened in the medium compared to the vacuum and the interaction energy reduces from -75.3 kJ/mol (vacuum) to -52.8 kJ/mol (medium) for the ion pair. Likewise, the interaction with the cation becomes smaller by 25 kJ/mol and the interaction with the anion decreases to -7.0 kJ/mol. Hence, the same trend is predicted in the vacuum and the medium. Next, we compare the interaction of the ion pair with a number of molecules spatially arranged around the ion pair. The idea is to systematically increase the environment in a three dimensional way. Up to three benzene molecules have been placed around the TEA/BF4 ion pair and the corresponding structures have been fully geometry optimized. The magnitude of the interaction energy increases significantly with the number of surrounding molecules. With the two benzene rings, an interaction energy of -86.5 kJ/mol was obtained and with three benzene rings the strength of the interaction energy increases to -114.3 kJ/mol. In addition, we have calculated the individual interaction energies between the cation with the three benzene rings and between the anion with the three benzene rings based on the geometry optimized structure of the whole system (i. e. ion pair + three benzene molecules). In this conformation, the interaction of the cation with its surrounding is -108.1 kJ/mol and of the anion -43.1 kJ/mol. It is revealing to compare the strength of interaction obtained for the two ring system naphthalene with the interaction found for two benzene rings which are spatially arranged around the ion pair. In the latter system, the interaction is more than twice as strong compared to naphthalene. The effect is even more pronounced when adding a third benzene molecule and compared to the interaction energy with the three-ring system phenanthrene. These results suggest that an aromatic, cavity-like environment as found in

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nanoporous carbons induces stronger interactions with the electrolyte and hence facilitates charge accumulation as the ions are retained. In order to investigate this further, we have studied carbon nanotubes systems which will be discussed below.

4.2

Naphthalene and indole derivative based systems

In addition to the system size of pure aromatic hydrocarbons and their spatial arrangement, we have studied how functional groups affect the interaction with the electrolyte ions. For testing functional groups, we have focused on two-ring systems and introduced various functional groups to naphthalene. In this context, indole-like systems have been considered, too. The functional groups have been selected based on experimental data. As for the previous set, the structures have been fully geometry optimized before calculating interaction energies. The results are listed in Tab. 1 (entries (6) to (18)). The interaction energies range between -48 and -159 kJ/mol. Most compounds of the test set show a stronger interaction compared to naphthalene. Only for 1,4-naphthoquinone and 2-oxindole, slightly weaker interaction energies are found. The strongest interaction is predicted for a sulfonyl substituent, followed by acid and hydroxyl substituents. This finding can be rationalized by the fact that these systems allow for the formation of a hydrogen bond between the functional group and BF4 and exhibit therefore stronger interactions. To assess how the relative orientation of the ion pair and the functional group affects the strength of the interaction energy, additional calculations have been performed for the hydrogen bonding systems 1-OH-naphthalene and 1-COOH-naphthalene. In case of 1-COOHnaphthalene, the starting geometry was manipulated and an initial conformation less prone to the formation of a hydrogen bond was created. The hydrogen atom of the −COOH group was turned away from BF4 and the geometry optimized structure showed indeed no hydrogen bond. Consequently, a significantly smaller interaction energy of -70.1 kJ/mol was obtained. Despite the missing stabilizing hydrogen bond, the interaction is rather strong compared to the other tested compounds. A similar test was carried out for 1-OH-naphthalene. Here, 14


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1-OH-naphthalene was flipped vertically to the ring plane so that the hydroxyl group was placed below the cation instead of the anion. After geometry optimization, the ion pair moved in such a way that again a hydrogen bond was formed between BF4 and the hydroxyl group, but with the anion being no longer above the ring plane. For this geometry, a reduced interaction energy of -85.2 kJ/mol was obtained, which is still a comparably large value. The results show that the formation of a hydrogen bond is a strong driving force with respect to structural aspects. However, even if hydrogen bonding is not accomplished for some reason, the corresponding functional group induces still a rather strong interaction with the ion pair. For this test set, we have also calculated the interaction energies between the individual ions and the functionalized compound based on the geometry optimized structures of the whole complex. The results are shown in Tab. 1 (entries (6) to (18), last two columns). The interaction energies with the cation (TEA) range between -40 to -65 kJ/mol, while the interaction energies with the anion (BF4 ) are between -21 kJ/mol and -123 kJ/mol. These results suggest that the cation is less influenced through the functional group than the anion. The strikingly strong interaction obtained for the anion in the case of 1-sulfonyl-naphthalene, 1-COOH-naphthalene, 1-OH-naphthalene, and indole can be attributed to the presence of a hydrogen bond. In addition to single substituted systems, the interaction was evaluated for double substituted naphthalenes, too. For this purpose, a SO3 H- and a COOH-group were introduced in naphthalene in 1,5-position and in 1,8-position in order to study whether an opposite position or a neighboring position of functional groups intensifies the interaction with the ion pair. The structures are schematically illustrated in Fig. 3. The structures of the disubstituted naphthalenes have been pre-optimized at RI-PBE-D3-MJ/def2-SVP level. The systems including the ion pair have been fully geometry optimized at PBE0-D3/def2-SVPD level and interaction energy energies have been calculated at the same level of theory. Two different relative orientations of ion pair and disubstituted naphthalene have been tested for both the 1,5- and 1,8-substituted system: The ion pair was placed in such a way that

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the anion was either closer to the SO3 H-group (denoted as orientation (I)) or closer to the COOH-group (denoted as orientation (II)). The absolute energies indicate that the systems with 1,5-substitution are energetically more favorable compared to 1,8-substitution. Regarding the relative orientation, we found that orientation (II), i. e. with the anion being located closer to the COOH-group, is slightly preferred by 0.6 kJ/mol in case of the 1,5-substituted systems. Likewise, orientation (II) is favored by 2.4 kJ/mol in the 1,8-substituted systems. The 1,8-substituted systems are 14.6 and 17.1 kJ/mol higher in energy compared to the energetically lowest 1,5-substituted system. Interaction energies are listed in Tab. 2. In contrast to the absolute energies, significantly stronger interactions are predicted for the 1,8-substituted systems: Interaction energies of -153.5 kJ/mol and -146.7 kJ/mol are obtained for orientation (I) and (II), respectively, for the 1,8-substituted systems, while for the 1,5-substituted systems, interaction energies of -129.7 and -109.1 kJ/mol are found for orientation (I) and (II), respectively. Thus, stronger interactions are found for disubstituted systems with adjacent neighboring groups compared to systems with opposite lying groups. In addition to the gas phase simulations, solvent effects were taken into account for structure set (b). Solvent models have been applied in three ways to assess how the solvent affects the interaction between electrode and conducting salt: (I) Implicit solvent simulations 39 were performed using a dielectric constant of = 37.5 to mimic the acetonitrile (ACN) environment. Interaction energies were calculated at the PBE0-D3/def2-SVPD level for the gas phase structures. In this way, we gain information about the influence of the solvent for a given geometry. (II) In order to explore how the solvent affects the relative orientation between ions and carbon model, the structures have been fully geometry optimized while applying the continuum model with a dielectric constant of = 37.5. Starting structures were the same as for the gas phase simulations. This allows to examine how the solvent affects the relative orientation compared to pure gas phase simulations. (III) The solvent was taken explicitly into account by adding an ACN molecule and geometry optimizing the structures. In case of the implicit solvent calculations (I) and (II), interaction energies have been calculated

16


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between the ion pair and the carbon model, i. e. the ion pair has been considered as one fragment and the carbon model as the other fragment. In the case of explicit solvent simulations (III), the interaction energy was again calculated in a two fragment approach, i. e. ion pair + ACN were treated as one fragment and the carbon compound as second fragment. The results are listed in Tab. 3. A comparison of the interaction energies of the gas phase structure with and without implicit solvent (set-up (I), i. e. without further geometry optimization) (Tab. 1, first column versus Tab. 3, first column) shows that the general trend is basically the same. The interaction strength is reduced compared to the pure gas phase calculations, because the solvent screens the interaction. This effect is more pronounced for functional groups that allow for hydrogen bonding, i. e. 1-sulfonyl-naphthalene, 1-COOH-naphthalene, 1-OH-naphthalene, and indole. The strongest interaction is found for 1-sulfonyl-naphthalene with -87 kJ/mol and the weakest for 1,4-naphthoquinone with roughly -32 kJ/mol. After applying the implicit solvent during geometry optimization (set-up (II)), the interaction energies range between -55 and -22 kJ/mol. The solvent has the strongest impact on structures that had formed a hydrogen bond in the gas phase (compounds (8) - (10) and (16)) which is similar to the results obtained for set-up (I). Interestingly, the hydrogen bond that has been observed in the gas phase structure of (compounds (8) - (10)) has not been created during geometry optimization when applying the continuum model. This observation can be attributed to the solvation effect which weakens electrostatic interactions. However, it can be expected that if the starting conformation already contains a hydrogen bond, it is kept during the geometry optimization and the interaction strength will just be damped by the solvent as shown above for the gas phase structures. Future studies are planned to investigate the conformational influence on energetics and properties further, but this is beyond the scope of the present work. In order to probe how solvent molecules change the interaction between ion pair and surrounding, we created simple model systems containing a solvent molecule. To each model structure of the test set, an ACN molecule was added arbitrarily near the functional group.

17



The geometry optimization was carried out in two steps: First, the position of the carbon molecule was optimized, while keeping the ion pair and ACN molecule fixed. Afterwards, the whole structure was relaxed. The resulting interaction energies are listed in Tab. 3 (column 3). The interaction strength ranges between -101 kJ/mol and -25 kJ/mol. The strongest interaction is found for 1-OH-naphthalene, whereas the weakest interaction is observed for unsubstituted naphthalene. Visual inspection of the geometry optimized structures reveals that a close contact (hydrogen bond) has been formed between the nitrogen of ACN and the hydrogen atom of the functional group in the respective carbon models. This interaction seems to be even more favorable than the interaction observed in the gas phase and implicit solvent calculations, where a hydrogen bond between anion and carbon was found. Hydrogen bonds have occurred in the systems with 1-sulfonyl-naphthalene, 1-OH-naphthalene, naphthylamine, and indole. In the system with 1-COOH-naphthalene, a hydrogen bond has not been formed which may be attributed to an unfavorable starting conformation. As mentioned above, additional studies on how properties and relative energies are affected by a specific starting geometry will be subject to future work. As explained above, interaction energies have been calculated using a two fragment approach with ion pair and ACN as one fragment and the carbon compound as another fragment, since we wanted to estimate how ACN affects the interaction between carbon and electrolyte. There exist also other options for analyzing the interaction in these systems: Apart from the presented approach, the interaction between all three partners or the interaction between ion pair and carbon together with ACN can be evaluated. For unsubstituted naphthalene, we evaluated also the other types of interactions. The interaction energy using a three fragment approach with ion pair as one fragment, the ACN molecule as another fragment, and naphthalene as third fragment is -85.5 kJ/mol indicating a strong interaction between all partners. When regarding the ion pair as one fragment and ACN together with naphthalene as second fragment, the interaction energy is -78.0 kJ/mol demonstrating that there is a strong attraction between ion pair and its local surrounding.

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Overall, the analysis of solvent effects suggests that the interaction between ion pair and carbon model is screened by the presence of the solvent. Implicit solvent simulations indicate an equalizing influence in the interaction strength between ion pair and carbon. Explicit solvent simulations show that the solvent can compete with the ions for hydrogen bonding, while interactions between ion pair and surrounding remain attractive. In this context, we would like to mention that ions have to desolvate before they adsorb on the electrode surface. The process of desolvation has not been taken into account explicitly in the present work, whose focus is on analyzing how surface-electrolyte interactions depend on chemical functionalization. Considering the desolvation will be subject to future studies. In addition to the organic electrolyte, we have performed simulations on model systems with an inorganic electrolyte to address the role of the kind of electrolyte. For this purpose, a hydrated sulfuric acid dimer was chosen as model for the electrolyte. Interaction energies were calculated for a representative subset comprising benzene, naphthalene, 1Cl-naphthalene, 1-OH-naphthalene, 1-COOH-naphthalene, and 1-SO3 H-naphthalene. The results are listed in Tab. 4. A comparison with the interaction energies obtained for the organic electrolyte is most instructive. While for TEA/BF4 a higher interaction energy was obtained when increasing the system size from benzene to naphthalene, the interaction energy is almost the same when using the sulfuric acid dimer. When considering the interaction with the naphthalene derivatives, a similar trend is observed as for the organic electrolyte, but the interaction is found to be less strong. In summary, surface functional groups can affect the interaction with the electrolyte significantly. The strength of the interaction depends on the combination of electrolyte ion and functional group. Specific surface functionalization can thus be used to tune the interaction strength and influence therefore the retention of the electrolyte in the pores.

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4.3

Pore size dependency

The results obtained so far suggest that a cavity-like environment with functional groups allowing for the formation of hydrogen bonds is favorable for a strong interaction with the electrolyte ions. To mimic a cavity, we have chosen carbon nanotubes (CNT) as additional model systems. This type of systems allows also to study systematically the influence of the pore size of carbon nanopores on the interaction. CNTs with different diameters ranging from 6.7 to 13.5 ˚ A were created. Either the cation or the anion was placed inside the CNT. For the smallest CNT (5,5), only the anionic system was considered, because the cation is already too large for placing it conveniently into the tube. After full geometry optimization, interaction energies have been calculated. The interaction energies are listed in Tab. 5 and the geometry optimized structure are illustrated in Fig. 4. For the cationic systems, interaction energies between -34 and -229 kJ/mol are obtained. The strongest interaction with TEA was found for CNT(7,7) with a diameter of 9.5 ˚ A. The geometry optimized structure of this model is shown in Fig. 4a. The interaction energies of the cationic systems agree very nicely with experimental measurements of the capacitance in EDLCs of different pore size which is illustrated in Fig. 5. In Fig. 5, the SSA-normalized capacitance is plotted over the average pore size. The highest capacitance is found for an average pore size of around 8.3 ˚ A. The calculated interaction energy in dependence of the initial CNT diameter shows an overall similar behavior, but with an offset towards larger values. The calculations predict a diameter of 9.5 ˚ A for the optimal pore size. Taking into account that the CNT is a simplified model with two open ends and a very regular structure compared to the real cavities in the electrode, the agreement between experimental and calculated data is acceptable. The interaction energies of the anionic CNT systems are smaller and cover a range between +13 and -97 kJ/mol. The CNT (6,6) based system shows the strongest interaction, which is shown in Fig. 4b, while for CNT (5,5) a repulsive interaction was found. Due to the absence of functional groups, the interaction is dominated by electronic effects. The interactions are stronger the better the pore size fits the size of the ion. Our findings on CNT systems 20


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demonstrate that this type of interaction can be considerable and contribute to retention effects. The results indicate that there is an optimal pore size for confining ions. In addition, we have added functional groups and evaluated the impact on the interaction when introducing −SO3 H alone and −SO3 H together with −COOH. The geometry optimized structures for the disubstituted CNTs are illustrated in Fig. 4c and Fig. 4d, respectively. During the geometry optimization, we observed in both anionic systems that the anion is drifting towards one of the ends of the CNT tube. The effect is less pronounced if both groups are present, because BF4 forms a hydrogen bond to both substituents and is thus kept back inside the CNT. In contrast to this, the cation is more or less staying in the middle of the CNT where it was initially placed. The interaction energies are listed in Tab. 5. Compared to the unsubstituted CNT, the magnitude of the interaction energies become larger throughout. Due to the hydrogen bonds formed between BF4 and the functional groups in the CNT, i. e. −SO3 H and −COOH, (for illustration, see Fig. 4d), the increase is remarkably larger in the anionic systems. This finding is in line with the results presented above. The quantum chemical simulations revealed that the introduction of the functional groups −SO3 H and −COOH yield the most pronounced changes in intermolecular interactions of the electrolytes with the carbon backbone. In order to verify these results, the functionalization of carbon by sulfuric acid was applied for an experimental approach, because this functionalization is known to introduce the functional groups −SO3 H and −COOH, respectively. 48 Experimental measurements of the specific capacitance of functionalized CDCs are shown in Fig. 6. The surface functionalization of CDC was quantified by TG-MS. It was found that the following functional groups are found on the carbon surface: carboxylic acid (−COOH), sulfonic acid (−SO3 H), hydroxyl (−OH) and various carbon monoxide releasing groups (e.g. carbonyls, lactones, anhydrides). The composition depends on the CDC synthesis temperature and the sulfuric acid concentration. In general, two effects of CDC functionalization can be summarized. First, with increasing graphitic character of the car-

21



bon the amount of carbonyl releasing surface groups decreases, while the amount of sulfonic and carboxylic acid groups increases. The graphitic character of CDCs itself, increases with increasing synthesis temperature. Second, the amount of carbonyl releasing groups is higher when concentrated oleum is used for functionalization instead of sulfuric acid. More details on the compositions and the high textural stability of the carbon upon functionalization, revealed by nitrogen sorption measurements, are provided in the supporting information. The results are summarized in Table S3. The effect on the specific capacitance by the functionalization of CDC with concentrated oleum (65 %) is shown in Figure 6a. The figure summarizes the performance of pristine CDC, as a function of increasing graphitic character and average pores size (CDC-800 < CDC-1000 < CDC-1200), and the effect of surface functionalization. The results of pristine CDC materials exemplify the effects of confinement and charge mobility. The results were already discussed in Figure 5, which shows the surface normalized capacitance. Here, the specific capacitance is discussed. The materials CDC-800 and CDC-1000 exhibit an average pore size of 0.72 nm and 0.83 nm and, therefore, a strong confinement effect on the electrolyte ion TEA. They show an exceptionally high specific capacitance of 102.2 F/g and 94.3 F/g. The material CDC-1200 exhibits a significantly bigger average pore size of 1.32 nm and shows a much lower specific capacitance of 31.2 F/g. One must notice, that the specific surface area decreases with increasing CDC synthesis temperature, as well. The mobility of charge carriers is affected in the opposite way. The capacity retention, from a low scanning rate of 5 mVs−1 to a high scanning rate of 100 mVs−1 , is higher when pristine CDC exhibits a bigger average pore size. The retention increases from 88% (CDC-800), over 94% (CDC-1000) to 98 % (CDC1200). The functionalization by concentrated oleum (65%) affects the performance of pristine CDC materials according to their confinement properties, as well. Upon functionalization, the specific capacitance at a low scanning rate of 5 mVs−1 increases from 102.2 F/g to 113.6 F/g for CDC-800 and decreases from 94.3 F/g to 88.0 F/g for CDC-1000. In case of CDC-1200, no significant change is observed, with a specific capacitance of 31.5 F/g after

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functionalization. The retention of oleum functionalized CDC-800 and CDC-1000 (74 %) is significantly lower than the retention of the pristine materials CDC-800 (88 %) and CDC1000 (94 %). In contrast, the retention of oleum functionalized CDC-1200 (96 %) is similar to the retention of the pristine material CDC-1200 (98 %). These preliminary results suggest that for materials with a strong confinement effect, a functionalization with coordinating surface groups can increase the specific capacitance, if a higher surface wettability of the effectively interacting carbon surface used for charge accumulation (CDC-800). At the same time, the retention at higher scanning rates decreases, due to the lower mobility of the charge carriers within the electrolyte. A more detailed view on the effect of functionalization on the specific capacitance of the confined materials CDC-800 and CDC-1000 is provided in Figure 6b. The highly amorphous material CDC-800 is sensitive to mild oxidation agents like diluted sulfuric acid (50%) and concentrated sulfuric acid (98%). This was used to vary the composition of surface functional groups in comparison to CDC-800 and CDC-1000 which was functionalized by concentrated oleum (65%). The results are summarized in Table 6. It was found that the specific capacitance is positively influenced by carbon monoxide (CO) releasing surface groups (e.g. carbonyls, lactones, anhydrides) and negatively influenced by the carbon dioxide (CO2 ) releasing surface group carboxylic acid and the sulfur dioxide (SO2 ) releasing surface group sulfonic acid, which both decompose at low temperatures (< 300 ◦ C). Thus, an increase of the specific capacitance can be observed with increasing ratio [CO/(CO2 +SO2 )]. Experimental measurements reflect the charging and discharging process, while the quantum chemical simulations describe a static scenario in the discharged state based on suitable model systems. Nevertheless, the simulations provide fundamental information on how intermolecular interactions are influenced by the chemical environment which is important to gain a more detailed understanding of the processes in supercapacitors at the molecular level. Analyzing the correlation between interaction strength and measured capacity provides a first important step towards deriving molecular descriptors for large-scale virtual screening

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of possible surface modifications. In future work, we will extend our studies and include other types of electrolytes, additional carbon models such as charged electrode models and multiple substituted carbon models for analyzing the correlation of interaction energies and other properties with experimentally observed capacitance. Intermolecular interactions are one important aspect amongst others that determine the performance of supercapacitors. On-going studies of the authors address other features that are important for characterizing the performance of such devices. Our ultimate goal is to determine a set of critical descriptors that can be leveraged for QSPR modeling for predicting capacitance of EDLCs. Correlating the experimental findings with calculated interactions energies suggests indeed that the latter can serve as descriptor for predicting changes in the capacitance of porous carbon-based electrodes. Modulating effects of surface functional groups can be assessed based on the interaction energy. Comparing experimental and calculated data shows that a too strong interaction has negative influence on the capacitance, while medium interactions increase the capacitance in the confined pore size regime. This can be rationalized by the fact that ion mobility and retention need to be balanced. Our results are in line with previous studies 15 where the authors studied oxidized pores which had a positive effect on the capacitance. Moreover, by analyzing the interaction as a function of the pore size diameter, the optimal confined pore size regime can be estimated for the individual electrolyte ions.

5

Conclusion

In this work, we have presented a combined experimental and computational study on electrode-electrolyte interactions in supercapacitors. DFT calculations have been performed for a variety of model systems comprising pure hydrocarbons, naphthalene and indole derivatives, as well as carbon nanotubes. Based on theses systems we have systematically evaluated the effect of system size, functionalization, and pore size on the electrode-electrolyte interaction. Our strategy allowed us to separate the different influences on the interaction

24


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and thus to gain a fundamental understanding of effects that drive the electrode-electrolyte interaction. Experimental data for the capacitance have been compared with the simulated interaction energies. For pristine CDCs, we found a correlation of the pore size dependence of the capacitance and the calculated interaction energies. The latter can thus serve for predicting the optimal pore size regime for electrolyte ions. For surface functionalized systems, the strength of the interaction energies cannot be directly correlated with the capacitance, but can be used to assess the mobility and retention in the pores which influence the capacitance. We have found that medium interaction energies translate into an increased capacitance. This means that polar groups such as carbonyl groups lead to an increase of the capacitance. Though the formation of hydrogen bonds leads to stronger interactions between electrolyte and electrode surface, this effect is less advantageous with respect to the capacitance, since then the mobility of the electrolyte is too restricted. Based on our studies, we believe that calculated interaction energies can serve as descriptor for assessing and predicting the effect of functionalization and pore size on the capacitance which can ultimately help to improve the performance of EDLC systems. Our results are important to understand how electronic and structural effects influence electrode-electrolyte interactions which affect pore confinement, ion mobility, and wettability that govern the capacitive properties of EDLCs.

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6

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Tables

Table 1: Interaction energies between carbon models and TEA/BF4 calculated at PBE0D3/def2-SVPD level. The model structures with the ion pair were fully geometry optimized at the same level of theory. Interaction energies with the individual ions refer to the geometry optimized structure of the ion pair complex. Interaction energy Ion pair TEA (1), benzene -40.0 -32.7 (2), phenanthrene -56.9 -67.1 (3), pyrene -75.3 -74.2 (4), chrysene -70.6 -74.9 (5), coronene -84.1 -86.3 (6), naphthalene -56.6 -56.7 (7), 1-Cl-naphthalene -61.6 -56.2 (8), 1-OH-naphthalene -103.0 -41.6 (9), 1-COOH-naphthalene -104.3 -53.1 (10), 1-SO3 H-naphthalene -158.5 -57.4 (11), naphthylamine -81.1 -65.4 (12), 1-nitronaphthalene -67.0 -51.9 (13), 1,4-naphthoquinone -53.0 -39.9 (14), quinoline -58.6 -54.1 (15), quinoline-N-oxide -72.7 -60.3 (16), indole -96.7 -53.4 (17), N-methyl-indole -73.8 -40.2 (18), 2-oxindole -48.3 -60.3 Compound

/ kJ/mol BF4 -24.2 -12.7 -26.2 -25.1 -29.1 -20.8 -29.5 -94.1 -76.1 -123.3 -40.0 -41.0 -34.7 -26.7 -37.9 -67.4 -28.5 -39.1

Table 2: Interaction energies between double substituted naphthalene and TEA/BF4 calculated at PBE0-D3/def2-SVPD level. The model structures were fully geometry optimized at the same level of theory. Compound 1-SO3 H,5-COOH-naphthalene 1-SO3 H,8-COOH-naphthalene

Interaction energy / kJ/mol Configuration (I) Configuration (II) -129.7 -109.1 -153.5 -146.7

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Table 3: Interaction energies between carbon models and TEA/BF4 calculated at PBE0D3/def2-SVPD level using implicit and explicit solvent models: (I) An implicit solvent model was applied on geometry optimized gas phase structures without further structural refinement, (II) full geometry optimizations were performed using an implicit solvent model approach, and (III) structures containing an explicit acetonitrile molecule were fully geometry optimized. The dielectric constant for calculations using the implicit solvent model was set to 37.5. Interaction energy / kJ/mol (I) (II) (III) (6), naphthalene -36.5 -40.0 -24.7 (7), 1-Cl-naphthalene -37.8 -40.6 -48.6 (8), 1-OH-naphthalene -60.7 -40.5 -101.0 (9), 1-COOH-naphthalene -67.6 -46.7 -51.3 (10), 1-SO3 H-naphthalene -87.3 -43.5 -78.4 (11), naphthylamine -47.1 -43.4 -73.2 (12), 1-nitronaphthalene -38.0 -42.0 -52.9 (13), 1,4-naphthoquinone -31.5 -22.4 -44.3 (14), quinoline -34.7 -38.1 -39.9 (15), quinoline-N-oxide -36.7 -34.7 -48.8 (16), indole -54.7 -54.8 -85.1 (17), N-methyl-indole -44.1 -38.4 -74.7 (18), 2-oxindole -35.7 -41.3 -51.6 Compound

Table 4: Interaction energies between carbon models and a hydrated sulfuric acid dimer calculated at PBE0-D3/def2-SVPD level. The model structures were fully geometry optimized at the same level of theory. Compound Interaction energy / kJ/mol (1), benzene -40.2 (6), naphthalene -39.8 (7), 1-Cl-naphthalene -37.3 (8), 1-OH-naphthalene -43.5 (9), 1-COOH-naphthalene -42.9 (10), 1-SO3 H-naphthalene -82.6

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Table 5: Interaction energies between CNTs and electrolyte ions (TEA, BF4 ) at PBE0D3/def2-SVPD level. The structures have been optimized at the same level of theory. Interaction energy / kJ/mol TEA BF4 (5,5) n.d. 12.6 (6,6) -33.5 -96.5 (7,7) -228.7 -72.1 (8,8) -212.3 -59.1 (8,8) with −SO3 H -247.1 -156.8 (8,8) with −SO3 H and −COOH -258.8 -203.7 (10,10) -175.2 -51.8 CNT

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2 1.7 2.5 4.9 1.8 1 0.8

8.3 8 8.2 10.1 1.6 6.6 0.7 5.5

CDC-800 CDC-800-SO50 CDC-800-SO98 CDC-800-OL65 CDC-1000 CDC-1000OL65 CDC-1200 CDC-1200OL65


29 31.2 31.5

102.2 91.4 97.4 113.6 94.3 88

Ratio Cspec @ [CO/(CO2 +SO2 )] 5mVs−1 [F/g]

Mass-loss [%]

Material

30.6 30.2

Cspec @ 100mVs−1 [F/g] 89.9 62.4 68.9 84.4 88.3 65.2

98 96

88 68 71 74 94 74

Retention [%]

1043 978

1662 1575 1606 1600

SSA(QSDFT) [m2 g−1 ]

Table 6: Experimental data of various pristine and functionalized CDC. TG-MS results for heating to 1000 ◦ C (5 K/min) in helium. Specific capacitance (Cspec ) for 1.5 M TEA in AN. Specific surface area (SSA) determined by nitrogen sorption at 77 K (Quadrasorb, Quantachrome Instruments), degassing at 120 ◦ C for 4 h.

Page 29 of 41 The Journal of Physical Chemistry


7

Figures

Figure 1: Model structures of hydrocarbons, naphthalene, and indole derivatives for calculating interaction energies with electrolyte ions. (1) – benzene, (2) – phenanthrene, (3) – pyrene, (4) – chrysene, (5) – coronene, R1 = -H: (6) – naphthalene, R1 = -Cl: (7) – 1-Cl-naphthalene, R1 = -OH: (8) – 1-OH-naphthalene, R1 = -COOH: (9) – 1-COOHnaphthalene, R1 = -SO3 H: (10) – 1-SO3 H-naphthalene, R1 = -NH2 : (11) – naphthylamine, R1 = -NO2 : (12) – 1-nitronaphthalene, (13) – 1,4-naphthoquinone, (14) – quinoline, (15) – quinoline-N-oxide, R2 = -H (16): – indole, R2 = -CH3 : (17) – N-methyl-indole, (18) – 2-oxindole.

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Figure 2: Geometry optimized structure of pyrene with a TEA/BF4 ion pair. Color code: C - gray, H - white, N - blue, B - green, F - lime.

Figure 3: Model structures of 1,5- and 1,8-disubstituted naphthalene derivatives with R1=SO3 H and R2=-COOH

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(a) CNT (6,6) with TEA.

(b) CNT (5,5) with BF4 .

(c) Disubstituted CNT (8,8) with TEA.

(d) Disubstituted CNT (8,8) with BF4 .

Figure 4: Geometry optimized structures of carbon nanotubes with electrolyte ions. Color code: CNT - blue, ion - red, −COOH - green, −SO3 H - yellow.

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Figure 5: Comparison of measured SSA-normalized capacitance for TEA as a function of the average pore size (blue, straight line) and calculated interaction energy between TEA and CNT model as a function of the CNT diameter (red, dashed line).

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(a) Influence of functionalization with oleum (65%) on the performance of the pristine CDC at low (5 mVs−1 ) and high (100 mVs−1 ) scanning rates.

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(b) Electrochemical performance as a function of the ratio of CO-releasing surface groups (TG-MS) to CO2 and SO2 releasing groups at 5 mVs−1

Figure 6: Specific capacitance (Cspec ) of various pristine and functionalized CDCs for 1.5M TEA in ACN.

Supporting Information Available Supporting information: Cartesian coordinates of geometry optimized substituted CNT structures, textural properties of the carbons (CDC), functionalization of CDC, TG-MS analysis of functional surface groups, electrochemical characterization.

This material is

available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement The authors gratefully acknowledge financial support by the German Ministry of Education and Research in the AktivCAPs project (grant no. 02E2-ESP077).

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Combined Computational and Experimental Study on the Influence of

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