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Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

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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*,† †

Scienomics GmbH, Bürgermeister-Wegele-Straße 12, 86167 Augsburg, Germany Ernst-Berl-Institut für 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 ⊥ Fraunhofer-Institut für Fertigungstechnik und Angewandte Materialforschung IFAMKlebtechnik und Oberflächen, Wiener Straße 12, 28359 Bremen, Germany

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‡

S Supporting Information *

ABSTRACT: Supercapacitors are regarded as a 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 prescreening approaches. Our results show that the pore size significantly affects the interaction quality with the electrolyte. This effect and the influence of chemical functionalization have 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 on how structural and electronic effects affect confinement, wettability, and mobility of electrolyte molecules, which is important for boosting and tuning the performance of supercapacitors.

1. INTRODUCTION 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. Energystorage systems play a crucial role in the context of sustainable energy supply. Different concepts can be applied to store energy. Batteries, e.g., 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. Supercapacitors represent a promising technique between batteries and capacitors and combine the advantages of both technologies.1−3 They have excellent charging characteristics of conventional capacitors, but offer considerably higher capacitances through a combination of double-layer capacitor and pseudocapacitor.1,4 The great advantage of supercapacitors © XXXX American Chemical Society

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 of shielding devices from voltage fluctuations and are used in various areas ranging from renewable energy over large-scale backup power up to automotive applications, e.g., for recapturing braking energy.7 Received: August 6, 2018 Revised: December 30, 2018 Published: January 11, 2019 A

DOI: 10.1021/acs.jpcc.8b07617 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

essential characteristics of the actual 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 electrodebased devices to gain a better understanding of the energystorage 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, e.g., how surface functional groups affect mobility and wettability or how the pore size affects confinement. In a recently published study, Ruzanov et al.30 discussed the adsorption behavior of ionic pairs on a coronenebased carbon system using 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 various model structures based on aromatic hydrocarbons and carbon nanotubes (CNTs) in the presence of electrolyte ions have been performed. The model systems have been varied systematically with respect to size, shape, and chemical functionalization 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 on 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 the experimental measurements of the capacitance, and implications on confinement, mobility, and wettability in EDLCs will be discussed.

The family of supercapacitors can be divided into three groups depending on the design of the device: electric doublelayer capacitors (EDLCs), 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 the 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 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 of 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 a valuable technique for revealing fundamental insights into problems at the atomistic level. While the application of forcefield-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 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 the 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 electrode−electrolyte 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. To study complex and large systems at this level of theory, commonly smaller model systems mimicking the

2. 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: B


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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-COOH-naphthalene, R1 = −SO3H: (10) 1-SO3H-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) Nmethyl-indole, (18) 2-oxindole.

(a) Aromatic hydrocarbons together with (i) an electrolyte ion pair of a commonly used organic electrolyte and (ii) individual ions, i.e., either cation or anion. (b) Naphthalene and indole derivatives together with (i) an electrolyte ion pair, (ii) individual ions, and (iii) electrolyte ion pair together with an acetonitrile (ACN) molecule representing the solvent. (c) Carbon nanotubes together with either the cation or anion of the ion pair. 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.

The model systems of sets (a) and (b) are summarized in Figure 1. The structures of sets (a) and (b) were fully geometry-optimized using the density functional PBE032 with the basis set def2-SVPD33 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 Michaelides and co-workers.36 In the present work, density functional and basis set have been chosen as a compromise between computational effort and accuracy. Mardirossian and Head-Gordon performed a comprehensive density functional benchmark study37 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 the PBE0-D3/def2SVPD 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 tetraethylammonium (TEA) and tetrafluoroborate (BF4) was placed above the ring plane of the aromatic compound (see Figure 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 the 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 the PBE0-D3/def2SVPD level. In addition, solvent effects were evaluated using

implicit and explicit models. The COSMO approach39 was used for implicitly treating the solvent in the electrolyte layer. A dielectric constant of ϵ = 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 by 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 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 the energy of the ion pair, Efragment2 as the energy of the ACN, and Efragment3 as the 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 the 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 to 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. C


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Therefore, sulfuric acid at concentrations of 50 and 98% and oleum at a concentration of 65% were used. The different functionalization agents are abbreviated 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, surface functionalization, TG-MS analysis, and the electrochemical characterization are provided in the Supporting Information. More details on the postsynthetic surface functionalization of CDC are provided elsewhere.44

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 = 5−8 and 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 a slightly lower level (RI-PBE-D3-MJ/ def2-SVP41,42) due to the fairly large system size. Interaction energies for the CNT-based systems were calculated at the PBE0-D3/def2-SVPD level. For introducing substituents into the CNTs, an arbitrarily selected six-membered ring was deleted in the middle of the CNT (8,8) and the respective functional group was inserted oriented toward the inner side 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 carbon cavity around functional group and ion. As functional groups, −SO3H and −COOH have been considered. These two groups served as representatives for sulfurand 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 −SO3H. A second set of model structures contained two substituents, i.e., −SO3H and −COOH, which were placed on opposite sides of the CNT. Either TEA or BF4 was placed in the middle of the tube similar to the unsubstituted CNT systems. The structures were geometry-optimized at the RI-PBE-D3-MJ/def2-SVP level, and interaction energies were calculated at the PBE0-D3/def2SVPD level. Cartesian coordinates of the final structures are provided in the Supporting Information.

4. 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.1,12,14,45,46 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 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 Figure 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 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, and 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 a representative example, the geometry-optimized structures of pyrene and the ion pair are illustrated in Figure 2, and the results of the interaction energy calculations are listed in Table 1 (entries 1−6). 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 strength of interactions between hydrocarbon and ion pair increases with

3. EXPERIMENTAL SECTION The experimental study was performed on carbide-derived carbons (CDCs) 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 to 1200 °C. Depending on the etching temperature, the process yielded microporous carbons with specific surface areas (SSAs) ranging from 1165 to 1740 m2/g and pore volumes V of 0.55−0.77 cm3/g. The data are 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 pores. The average pore diameter d of the synthesized carbons was calculated from the ratio 2V/SSA. According to this method, CDC was synthesized, which exhibited average pore diameters of 0.65, 0.72, 0.83, or 1.32 nm. In all cases, the carbon texture is predominantly amorphous43 as shown in previous work of one of the authors of the present study. The postsynthetic surface functionalization of CDC was realized by sulfuric acid treatment at different concentrations. D


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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 geometryoptimized at the PBE0-D3/def2-SVPD level using a dielectric constant of ϵ = 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 of 0.13 Å. The geometryoptimized structure was then used for calculating the interaction energy between the ion pair and pyrene and between the individual ions (TEA, BF4) and pyrene. 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 that of the anion with its surrounding is −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 nanoporous carbons induces stronger interactions with the electrolyte and hence facilitates charge accumulation as the ions are retained. 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

Table 1. Interaction Energies between Carbon Models and TEA/BF4 Calculated at the PBE0-D3/def2-SVPD Levela interaction energy (kJ/mol) compound

ion pair

TEA

BF4

(1), benzene (2), phenanthrene (3), pyrene (4), chrysene (5), coronene (6), naphthalene (7), 1-Cl-naphthalene (8), 1-OH-naphthalene (9), 1-COOH-naphthalene (10), 1-SO3H-naphthalene (11), naphthylamine (12), 1-nitronaphthalene (13), 1,4-naphthoquinone (14), quinoline (15), quinoline-N-oxide (16), indole (17), N-methyl-indole (18), 2-oxindole

−40.0 −56.9 −75.3 −70.6 −84.1 −56.6 −61.6 −103.0 −104.3 −158.5 −81.1 −67.0 −53.0 −58.6 −72.7 −96.7 −73.8 −48.3

−32.7 −67.1 −74.2 −74.9 −86.3 −56.7 −56.2 −41.6 −53.1 −57.4 −65.4 −51.9 −39.9 −54.1 −60.3 −53.4 −40.2 −60.3

−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

a

The model structures with the ion pair were fully geometryoptimized at the same level of theory. Interaction energies with the individual ions refer to the geometry-optimized structure of the ion pair complex.

the number of rings in the hydrocarbon. The strongest interaction within this set is found with coronene. Although both pyrene and chrysene are 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. On the basis of the geometry-optimized structures, the interaction energies with the cation and the anion were calculated separately by removing the respective counterion from the system. The results are listed in Table 1 (entries 1−6, last two columns) and indicate a significantly stronger interaction with the cation than with the anion. This observation can be explained by noncovalent interactions between the positively charged cation and the electron-rich πsystem 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 the PBE0-D3/ def2-SVPD level to investigate how the geometry and the interaction energy change after reoptimization of the ion− hydrocarbon systems. While the magnitude of the interaction energy with TEA increases only slightly from −74.2 to −75.9 kJ/mol, the effect is distinctly higher in the anionic system and the interaction strength increases from −26.2 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 reoptimization of the pyrene + BF4 model, the anion moves beside the ring plane presumably triggered through the electrostatic repulsion between the anion and the electron-rich π-system of pyrene. Nevertheless, the interaction with the cation is still considerably stronger. Thus, we assume that the E


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The Journal of Physical Chemistry C structures have been fully geometry-optimized before calculating interaction energies. The results are listed in Table 1 (entries 6−18). 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 1,4naphthoquinone and 2-oxindole, slightly lower 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 the case of 1-COOH-naphthalene, 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 lower 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, 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 Table 1 (entries 6− 18, last two columns). The interaction energies with the cation (TEA) range between −40 and −65 kJ/mol, while the interaction energies with the anion (BF4) are between −21 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 SO3H group and a COOH group were introduced in naphthalene in 1,5-position and in 1,8-position 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 Figure 3. The structures of the disubstituted naphthalenes have been preoptimized at the RI-PBE-D3-MJ/def2-SVP level. The systems including the ion pair have been fully geometryoptimized at the PBE0-D3/def2-SVPD level, and the interaction energies have been calculated at the same level of

Figure 3. Model structures of 1,5- and 1,8-disubstituted naphthalene derivatives with R1 = −SO3H and R2 = −COOH.

theory. Two different relative orientations of ion pair and disubstituted naphthalene have been tested for both the 1,5and 1,8-substituted systems: The ion pair was placed in such a way that the anion was closer to either the SO3H group (denoted as orientation (I)) or 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 the 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 1,5substituted system. The interaction energies are listed in Table 2. In contrast to the absolute energies, significantly Table 2. Interaction Energies between Double-Substituted Naphthalene and TEA/BF4 Calculated at the PBE0-D3/ def2-SVPD Levela interaction energy (kJ/mol) compound

configuration (I)

configuration (II)

1-SO3H,5-COOH-naphthalene 1-SO3H,8-COOH-naphthalene

−129.7 −153.5

−109.1 −146.7

a

The model structures were fully geometry-optimized at the same level of theory.

stronger interactions are predicted for the 1,8-substituted systems: Interaction energies of −153.5 and −146.7 kJ/mol are obtained for orientation (I) and (II), respectively, for the 1,8substituted 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 simulations39 were performed using a dielectric constant of ϵ = 37.5 to mimic the acetonitrile (ACN) environment. Interaction energies were calculated at the PBE0D3/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) 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 ϵ = 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 F


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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. 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. 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. Afterward, the whole structure was relaxed. The resulting interaction energies are listed in Table 3 (column 3). The interaction strength ranges between −101 and −25 kJ/mol. The strongest interaction is found for 1-OHnaphthalene, whereas the weakest interaction is observed for unsubstituted naphthalene. Visual inspection of the geometryoptimized 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-COOHnaphthalene, 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 the 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 the second fragment, the interaction energy is −78.0 kJ/mol, demonstrating that there is a strong attraction between ion pair and its local surrounding. 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 the 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

simulations. (III) The solvent was taken explicitly into account by adding an ACN molecule and geometry-optimizing the structures. In the case of the implicit solvent calculations (I) and (II), interaction energies have been calculated 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 and ACN were treated as one fragment and the carbon compound as the second fragment. The results are listed in Table 3. A comparison of the interaction energies Table 3. Interaction Energies between Carbon Models and TEA/BF4 Calculated at the PBE0-D3/def2-SVPD Level Using Implicit and Explicit Solvent Modelsa Interaction energy (kJ/mol) compound

(I)

(II)

(III)

(6), naphthalene (7), 1-Cl-naphthalene (8), 1-OH-naphthalene (9), 1-COOH-naphthalene (10), 1-SO3H-naphthalene (11), naphthylamine (12), 1-nitronaphthalene (13), 1,4-naphthoquinone (14), quinoline (15), quinoline-N-oxide (16), indole (17), N-methyl-indole (18), 2-oxindole

−36.5 −37.8 −60.7 −67.6 −87.3 −47.1 −38.0 −31.5 −34.7 −36.7 −54.7 −44.1 −35.7

−40.0 −40.6 −40.5 −46.7 −43.5 −43.4 −42.0 −22.4 −38.1 −34.7 −54.8 −38.4 −41.3

−24.7 −48.6 −101.0 −51.3 −78.4 −73.2 −52.9 −44.3 −39.9 −48.8 −85.1 −74.7 −51.6

a

(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.

of the gas-phase structure with and without implicit solvent (setup (I), i.e., without further geometry optimization) (Table 1 first column vs Table 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-COOHnaphthalene, 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 (setup (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 setup (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 G


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The Journal of Physical Chemistry C 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, 1-Clnaphthalene, 1-OH-naphthalene, 1-COOH-naphthalene, and 1-SO3H-naphthalene. The results are listed in Table 4. A

Table 5. Interaction Energies between CNTs and Electrolyte Ions (TEA, BF4) at the PBE0-D3/def2-SVPD Levela interaction energy (kJ/mol)

Table 4. Interaction Energies between Carbon Models and a Hydrated Sulfuric Acid Dimer Calculated at the PBE0-D3/ def2-SVPD Levela compound

interaction energy (kJ/mol)

(1), benzene (6), naphthalene (7), 1-Cl-naphthalene (8), 1-OH-naphthalene (9), 1-COOH-naphthalene (10), 1-SO3H-naphthalene

−40.2 −39.8 −37.3 −43.5 −42.9 −82.6

a

CNT

TEA

BF4

(5,5) (6,6) (7,7) (8,8) (8,8) with −SO3H (8,8) with −SO3H and −COOH (10,10)

n.d. −33.5 −228.7 −212.3 −247.1 −258.8 −175.2

12.6 −96.5 −72.1 −59.1 −156.8 −203.7 −51.8

The structures have been optimized at the same level of theory.

The highest capacitance is found for an average pore size of around 8.3 Å. The calculated interaction energy in dependence of the initial CNT diameter shows an overall similar behavior, but with an offset toward larger values. The calculations predict a diameter of 9.5 Å 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 lower and cover a range between +13 and −97 kJ/mol. The CNT (6,6)-based system shows the strongest interaction, which is shown in Figure 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 stronger the interactions, the better the pore size fits the size of the ion. Our findings on CNT systems 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 −SO3H alone and −SO3H together with −COOH. The geometry-optimized structures for the disubstituted CNTs are illustrated in Figure 4c and d, respectively. During the geometry optimization, we observed in both anionic systems that the anion is drifting toward 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 Table 5. Compared to the unsubstituted CNT, the magnitudes of the interaction energies become larger throughout. Due to the hydrogen bonds formed between BF4 and the functional groups in the CNT, i.e., −SO3H and −COOH (for illustration, see Figure 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 −SO3H and −COOH yield the most pronounced changes in intermolecular interactions of the electrolytes with the carbon backbone. 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 −SO3H and −COOH.48 Experimental measurements of the specific capacitance of functionalized CDCs are shown in Figure 6. The surface functionalization of CDC was quantified

a

The model structures were fully geometry-optimized at the same level of theory.

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. 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 (CNTs) 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 Å 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 Table 5, and the geometry-optimized structures are illustrated in Figure 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 Å. The geometry-optimized structure of this model is shown in Figure 4a. The interaction energies of the cationic systems agree very well with experimental measurements of the capacitance in EDLCs of different pore sizes, which is illustrated in Figure 5. In Figure 5, the SSAnormalized capacitance is plotted over the average pore size. H


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Figure 4. Geometry-optimized structures of carbon nanotubes with electrolyte ions. Color code: CNTblue, ionred, −COOHgreen, −SO3Hyellow.

sulfonic acid (−SO3H), 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 carbon, 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 carbonylreleasing 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 are already discussed in Figure 5, which shows the surface normalized capacitance. Here, the specific capacitance is discussed. The materials CDC-800 and CDC1000 exhibit average pore sizes of 0.72 and 0.83 nm,

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).

by TG-MS. It was found that the following functional groups are found on the carbon surface: carboxylic acid (−COOH), I


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

Table 6. Experimental Data of Various Pristine and Functionalized CDCa material

mass loss (%)

ratio (CO/(CO2 + SO2))

Cspec @ 5 mV/s (F/g)

Cspec @ 100 mV/s (F/g)

retention (%)

SSA (QSDFT) (m2/g)

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

8.3 8 8.2 10.1 1.6 6.6 0.7 5.5

2 1.7 2.5 4.9 1.8 1

102.2 91.4 97.4 113.6 94.3 88 31.2 31.5

89.9 62.4 68.9 84.4 88.3 65.2 30.6 30.2

88 68 71 74 94 74 98 96

1662

0.8

1575 1606 1600 1043 978

TG-MS results for heating to 1000 °C (5 K/min) in helium. Specific capacitance (Cspec) for 1.5 M TEA in ACN. Specific surface area (SSA) determined by nitrogen sorption at 77 K (Quadrasorb, Quantachrome Instruments), degassing at 120 °C for 4 h. a

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, both of which decompose at low temperatures (

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