The mobility of the amine groups is an important property influencing CO2 adsorption, since CO2 molecules must insert into the metal-amine bond to adsorb at saturation. If the amine groups interchange more quickly, that might make it easier for CO2 to insert in the coordination bond. On the contrary, if there is little or no inter conversion, it might be because the amine groups are sterically hindered from “hopping.” This steric hindrance could also make the barrier for CO2 adsorption higher, and perhaps push the temperatures and pressures at which the CO2 adsorption step takes place to lower and higher values, respectively. In order to study the amine group dynamics for different amines, we made the structures in silico and relaxed with DFT as described. In addition to mmen, three additional amines were simulated: ethylenediamine, methylethylethylenediamine, and N,N’– diethylethylenediamine, shown in Table 4.1. The same simulation protocol was used as for mmen to measure the simulated rates of reaction at different temperatures and extract the enthalpies and entropies of activation. The computed energies of activation are provided in Table 4.2. The only amine for which an enthalpy and entropy of activation could not be calculated was ethylenediamine, the only primary-primary diamine . When the ethylenediamine-appended MOF was simulated, the ethylenediamine groups virtually all detached from the metal nodes. In NMR experiments carried out by collaborators, loss of diamine was also observed. In the remaining two amines, methylethylethylenediamine and N,N’-diethylethylenediamine , the methyl end groups of mmen were changed,one at a time, into ethyl groups, to increase the steric hindrance around the amine tails. As the steric hindrance increased, from mmen to methylethyl to diethyl, the enthalpy of conversion computed from simulation also increased from to to kJ mol−1 , respectively,vertical cannabis grow racks while the entropy of conversion decreased from to to J mol−1 K−1 , respectively.
The increasing activation enthalpy is due to the steric hindrance of the increasingly bulky alkyl end groups in the interconversion transition state. Since both amine groups need to be coordinated to the metal node during the transition state, the larger alkyl groups make this configuration more energetically unfavorable. The decreasing activation entropy could reflect the fact that in the reactant/product states , bulkier amines already have somewhat restricted mobility since the adjacent ethyl groups along the metal rod crowd each other. In the transition state, more sterically hindered molecules should also have lower entropy, but the loss of entropy in the non-transition states are larger than in the transition state, making the ∆Sa smaller. Molecular dynamics simulations were also used in conjunction with NMR experiments performed by a collaborator to verify that the local structure around the Mg centers in mmenMg2 is deformed with respect to the bare Mg2 MOF, in order to explain the distribution in 25Mg NMR parameters when mmen is coordinated to the MOF.Snapshots from molecular dynamics simulations were used to calculate the 25Mg NMR parameters as a function of time over 50 ps. These NMR parameters can be found in the Electronic Supporting Information of Xu et al.and vary between different Mg sites at a single point in time, and for individual Mg sites over time. The reason for this distribution in NMR parameters is thought to be the motion in the amine groups. Simulations show that at experimentally relevant temperatures, amine molecules are mobile within the MOF channels. These amine motions are thought to sterically stabilize more bending fluctuations in the linkers than is present in the bare MOF,and these dynamic motions of the linker result in a dynamic pore deformation and resulting distribution of NMR parameters. A movie of the dynamic framework deformation can be found online in the published work.For an idealized parallel plate capacitor consisting of metallic electrodes enclosing a dielectric medium of uniform dielectric constant, ε, the capacitance can be derived exactly as where A is the cross-sectional area of the capacitor and d is the separation distance between the electrodes.
If we transpose this expression to an EDLC, A would be the surface area of the electrode which is accessible to electrolyte ions, and d the characteristic thickness of the electrode-electrolyte interface. Equation 5.2 provides some intuition for why EDLCs have increased capacitance over their traditional counterparts: First, the charge separation distance is smaller in an EDLC than in a traditional capacitor, since ions can approach within less than 0.5 nm of the electrode surface, while in a traditional capacitor d is a few nanometers or higher.Second, the accessible surface area of an EDLC can be increased by several orders of magnitude using rough or porous electrode. Multiple theories have arisen to describe the electrochemical double layer, beginning with the classical theory of Helmoltz,which was subsequently improved by Gouy,Chapman,and Stern to consider discrete ions and complex double layer structures. These theories can accurately predict capacitances of EDLCs whose pores are macroscopic. However, when the pores become comparable in size to the electrolyte ions, so-called “anomalously” high capacitances have been observed that break with both existing theories and empirical trends.Reports of materials with such impressive capacitances have led to considerable growth in the field of microporous materials for EDLCs, to better understand the mechanisms behind capacitance in small pores.A popular choice of material for EDLC electrodes is porous carbon, due to its stability, ease of synthesis, and low cost. Porous carbons used in EDLCs include activated carbons,carbide-derived carbons, carbon onions and nanotubes,carbonized precursors such as metal-organic frameworks,and graphene-based composites.Experiments and simulations have shed some light on the charge-storage mechanisms in such materials; however, a major challenge is that most microporous carbon materials have neither a welldefined porosity nor long-range order, making it difficult to draw conclusions between structure and performance.
A new class of materials called zeolite-templated carbons , which are synthesized using a sacrificial zeolite scaffold,has been demonstrated as a promising EDLC material.Thus far ZTCs have been synthesized from just three zeolites of the 245 frameworks recognized by the IZA Structure Commission.Recently, Braun and coworkers reported a method to computationally synthesize ZTCs from a given zeolite structure.Their predicted ZTCs are composed of sp2 -hybridized carbons which tile a surface that is dual to the zeolite. Templating on a crystalline framework confers welldefined pore geometries which could yield insights into the structure-property relationships of electrode materials, motivating further study of ZTCs for energy storage applications. In this work we use molecular dynamics simulations to screen the ZTC materials of Braun et al. as electrode materials in EDLC cells. We show that the charging timescale of the ZTCs is negatively correlated with pore limiting diameter,vertical cannabis grow solution and that there is evidence of both progressive charge penetration and kinetic trapping within the ZTCs during charging. We then study the equilibrium capacitance of the ZTCs to investigate the correlation between geometric descriptors, local electrolyte configurations, and charge storage mechanisms within the electrode. Introducing the concept of charge compensation per carbon , We find that charge storage is more efficient at ion adsorption sites with high CCpC, which are more likely within pores with a lower radius of curvature. Conversely, charge storage is diminished at high-radius-of-curvature sites and within sites with a mismatch of local pore diameter and ion size. In our simulations we used an organic electrolyte composed of a mixture of 1-butyl-3- methylimidazolium tetrafluoroborate and acetonitrile with the concentration of ions equal to 1 m. We modeled the organic electrolyte using a coarse-grained description consisting of a three-site model for BMI+ and ACN, and a single-site model for BF4 – , as shown in Supplementary Figure C.1. Non-bonded interactions were described by a pairwise Lennard-Jones potential with Lorentz-Berthelot mixing rules, and electrostatic interactions by a Coulombic potential. For the non-bonded parameters of BMI+ we used those developed by Roy and Maroncelli.The non-bonded parameters for BF4 – and ACN were taken from Merlet et al.and from Edwards et al.respectively. Bonds and angles of BMI+ , and bonds of ACN, were kept rigid using the SHAKE algorithm. For the angles of ACN we used a harmonic potential with a stiff spring constant of 400 kcal2 rad−1 mol−1 to keep the molecule close to linear.
The carbon atoms of the electrodes were modeled as rigid. During the constant applied potential simulations, the charges of the electrode atoms were computed at each time step according to the constant-potential method.All force field parameters and further details regarding the constant-potential method are provided in the Supporting Information. ZTC materials were synthesized in silico as described in Braun, et al.Carbide-derived carbon materials, which are studied in depth computationally by Merlet and coworkers,are used here as a reference material. CDC structures were taken from Palmer et al., who generated them using Quench Molecular Dynamics. In this work, we consider 27 ZTC and 2 CDC materials for the constant-charge simulations and a subset of 19 of the ZTCs for constant-potential simulations. CDCs are named as in the original article by Palmer et al. ZTCs are referred to using the name of the templating zeolite. We indicate hypothetical zeolites using the prefix “h” and the last 2 digits of their 7-digit identifier . Complete names for all the zeolites referenced in the text can be found in the Supporting Information, along with information on framework properties . We used a semi-automated protocol to build two-electrode EDLC cells using the Zeo++ software suite and the VMD script interface with the TopoTools package.Further details are provided in the Supporting Information. This protocol was designed to fill the EDLC cell with an amount of electrolyte such that when the capacitor is equilibrated at either constant-charge or constant-voltage, the electrolyte density and composition in the bulk region matches the experimental values. We present these results in a later section. An example of the simulation setup for FAU_1 ZTC is provided in Figure 5.1. MD simulations were done using the LAMMPS simulation package with Velocity-Verlet time integration using a time step of 1 fs, and a Nosé-Hoover thermostat to maintain a temperature of 300 K. The initial EDLC cell was equilibrated with a constant charge of 0 e on each carbon atom for 4 ns. Final configurations from the zero-charge simulations were used to initialize all further simulation steps. Molecular simulation is a powerful tool to study EDLCs, as it allows for precise determination of the microscopic properties, such as the structure of the electrolyte within the pores, which can be difficult to access experimentally but which play an important role in determining the capacitance of the material.At the same time, simulation of EDLCs presents technical challenges due to long equilibration times and the need to compute the fluctuating charges in the electrode in response to a constant applied potential. The constant potential approach is more accurate but also much more computationally expensive than simulating an EDLC with constant charges on the electrode atoms.We tested multiple protocols for equilibrating the simulation cells, one with a constantcharge equilibration followed by a short constant-potential equilibration step,and the other with a long constant-potential equilibration. In the constant-charge equilibration method,partial charges of ±0.01 e were applied to all the electrode atoms, positive charges for anode atoms and negative charges for cathode atoms. The EDLC cell was equilibrated with these fixed charges for 8 ns. Then, the effective potential across the cell was calculated using either the 1-D Poisson equation or using the averaged local potentials at each electrode atom, and this potential was applied for the constant-potential equilibration and production runs. In the constant-potential equilibration, a constant potential difference of 1 V was applied across the EDLC cell , and the constant potential simulation was run for at least 10 ns. During the constant-potential run, the average absolute charge on the electrodes was monitored and fit to an exponential. The equilibration step was considered completed when the simulation was at least as long as 5τ , where τ is the time constant of the exponential. This equilibration process was found to be the best following a number of tests which are described in the next section, “Development of Computational Protocol”. Production runs for simulation of capacitance were carried out after equilibration at constant potential.