This drop is significant as it does not appear in BEA_beta, showing that sites with the same DoC can have drastically different contributions to capacitance. The source of this low-CCpC region becomes clear when examining representative configurations of the most highly confined anions of BEA and BEA_beta in Figure 5.8. In BEA, the anion islocated in a cylindrical, nanotube-like structure, with a coordination shell of electrode atoms encircling the anion on all sides, while the anion in BEA_beta is only confined on two out of four sides by the electrode. The cylindrical pore of BEA is too small to fit another anion or even solvent molecule, but too large to snugly fit BF4 – , causing it to be stuck in the middle of the pore where it is not close enough to induce a strong compensating charge on any of the atoms within its coordination shell. As a result, the coordination shell atoms in BEA have a total charge of −0.026 e, while the coordination shell in BEA_beta has a total charge of 0.223 e. This effect has also been observed in the literature; for example, Kondrat et al. showed a local minimum in capacitance when the pore-to-ion-diameter ratio L/d was around 1.5, and increased capacitance when L/d was near 1 and 2.The charge storage efficiency also depends on the ion size in relation to the pore size: In the electrolyte studied here the cation is larger than the anion and its charge is distributed on three sites. As such, when a cation is at the center of the nanotube-like pore, the partial charges of its coarse-grained sites are able to approach more closely to the electrode surface, making the equivalent pore in the cathode more efficient at storing charge. This explains why there is no drop in h CCpCi DoC in the BEA cathode . These observations highlight one important role of pore geometry in determining charge storage efficiency, by influencing local ion density and electrolyte coordination environment. We show in Figure 5.11 the structures of the materials with highest and lowest Csim − Cf it,vertical garden grow system indicating the average charge of each crystallographically unique electrode carbon atom during the equilibrated constant potential run, along with the probability density isosurfaces of counterion locations within the electrodes.
Isosurfaces for adsorption sites with more than 0.1 e total charge compensation are shown in purple, while sites with less than 0.1 e charge compensation are shown in green. This allows us to visually associate geometry with average contribution to capacitance for an individual pore. We observe that the adsorption site iso surfaces which have more than 0.1 e coordination shell charge compensation are close to the surface of the frameworks, while the isosurfaces associated with less than 0.1 e charge compensation tend to be in the middle of the pores. Inspecting the average atomic charges, we observe that BEC and h91 have more individual carbon atoms with high charge, corresponding to high CCpC. As seen in Figure 5.9, BEC and h91 are also the two materials with the highest enhancement in capacitance compared to materials of similar A/h dsepi . In contrast, h18, h49, and ISV, which have A/h dsepi similar or greater than that of BEC, but lower capacitance, have fewer highly charged atoms. Figure 5.11f provides further quantitative evidence of the correlation between the probability of highly-charged atoms and Csim −Cf it: structures with a higher probability density of average atomic charge greater than 0.1 e tend to have a higher Csim − Cf it. In order to rationalize the differences in charge storage between these materials, we focus on the local radius of curvature of the materials, as this roughly determines the distribution of ion-electrode distances at a particular adsorption site. In BEC, which has square-shaped windows with right-angle “corners,” we see electrode atoms with large average partial charges at two locations for each adsorption isosurface, corresponding the positions at which an adsorbed ion can be in close proximity with two “walls” of the framework simultaneously. In h91, cynlindrical pores adjoining with rounded beams create small-radius of curvature sites where ions can again approach the electrode surface closely at multiple sites, leading to more electrode atoms with large partial charges. In contrast, adsorption sites which are near large radius of curvature sites, such as in h18, h49, and ISV, , tend to be associated with materials with lower capacitances relative to their respective A/h dsepi . In adsorption sites with a large radius of curvature, an ion is not able to induce as many favorable Coulombic interactions with the electrode surface, leading to lower charge compensation for ions within those materials.
ISV merits particular mention, as it does contain some adsorption sites with low radius of curvature and high charge compensation , but because it also has high radius of curvature/low charge compensation sites , ISV still has a relatively low capacitance considering its high A/h dsepi . Overall, our results demonstrate that pore geometries which are capacitance-enhancing tend to faciliate the close approach of counterions to multiple carbons within the electrode via low radius of curvature adsorption sites, so that the compensating charge from the electrodes can be localized and large in magnitude to most efficiently screen counter charges and allow for higher counterion loading in the pores. Conversely, capacitance-diminishing properties include pores with high radius of curvature and cylindrical and ill-fitting pores, as these types of sites have inefficient charge storage and therefore decrease the overall capacitance of the material.For a preliminary assessment of the ability of the different models, method and protocols to describe the adsorption of THC in microporous materials and MOFs, we investigated the well-studied Mg-MOF-74. This MOF was chosen because of its large channel diameter, which can host the bulky THC molecule, and because of the presence of strongly charged Mg open metal sites, which have a partial charge of 1.59 e as computed with the DDEC protocol.190 This allows us to asses the contribution of Coulombic interactions in the adsorption of THC, a weakly charged molecule within frameworks having strongly charged binding sites. The THC-head model was used for a preliminary simulations. Since the alkyl tail is charge-neutral, the THC-head portion of the molecule is also neutral and therefore it can be used to assess the contribution of Coulombic interactions. We ran NVT Monte Carlo simulations at 309 K, the human body temperature, and at infinite dilution, i.e., with one THC-head particle per simulation box, for a total of 2 · 106 Monte Carlo steps . To equilibrate the system before the production, 10 000 cycles were added, i.e., one tenth of the total number of steps. Each move was chosen from translation, rotation, and random insertion with equal probability. From the output of these calculations we observed that, while the acceptance ratios of translation and rotation moves are close to the 50%, the regrow acceptance ratio is only 4.8%. This means that it is particularly difficult for the THC molecule to find a new position in the pore volume that is not overlapping with the framework.
Nonetheless, we determined that this move is reasonably explored in our 2 · 106 steps of simulation. The average adsorption energy of THC in Mg-MOF-74 from the NVT simulation is kJ mol−1 , where the contribution from the Coulombic interaction is less than 0.5%, while most of the adsorption energy comes from dispersion interactions. Indeed, a new calculation with the charges turned off resulted in an adsorption energy of kJ mol−1 , and very similar acceptance ratios for the MC moves. It was therefore reasonable to neglect in the protocol Coulombic interactions even when strongly charged open metals site are present, as in the test case. This assumption has the twofold benefit of speeding up the MC simulations and avoiding the need to compute partial charges for the frameworks. We next compared the rigid THC-head rigid model with the flexible THC-full model that includes four coarse-grained sites to represent the alkyl tail. For this models we added the “reinsertion in place” step, where the algorithm attempts to regrow the alkyl tail from while keeping the aromatic head of the THC molecule fixed,vertical greenhouse growing occurring with the same probability as the other MC steps. The NVT calculation, with Coulomb interactions turned off, gave a resulting adsorption energy of kJ mol−1 , i.e., ca. 26 kJ mol−1 more favourable than using the THC-head model. This difference is due to the additional dispersion interactions of the four beads of the tail with the framework. However, we can not assume a priori that the same difference would be found for all the frameworks. Indeed, even in MOFs with similar chemistries, where we might assume that the dispersion interactions are similar, there is the possibility that in some frameworks, the THC-head model is confined in a small pore in such a way that there would be no room to grow the tail. The advantage, however, of using the rigid THC-head particle is a speedup of ca. 2X times for the non-charged model. Moreover, one has to consider that the reinsertion moves are accepted more rarely using the full model: the acceptance ratios lower to 1.8% for reinsertion and 2.2% for reinsertion in place. Finally, we compared the results from NVT simulations with Widom insertions: both methods are supposed to converge to the same adsorption energy, albeit faster in the first case, but the Widom insertion allows us to compute the Henry coefficient as well. This value quantifies the adsorption free energy at infinite dilution, including the entropy of adsorption which is expected to be largely influenced by the topology of the framework. As before, we tested the THC-head and THC-full particles in the charged MOF-74, for 2 and 20 million Widom insertions. Results are summarized in Table B.1. The electrode charging exhibits multiple timescales which are not captured by the single exponential charging of an ideal RC circuit. Modeling the system with additional RC elements, as in a transmission line model, would better capture charging dynamics, especially since we observe that the electrodes charge progressively, starting from the electrode-bulk interface and moving inward . This spatially progressive charging is a key characteristic of the transmission line model, and is more marked in the materials with smaller pores since slower ion diffusion creates a bigger difference between charging times for the outer and inner regions of the electrode. We observe that in many of the structures, particularly in the outer slice, the total ion occupancy exhibits a maximum value during charging which is higher than the equilibrated value, suggesting that the electrolyte molecules may encounter kinetic trapping as counter-ions enter the pores .
The increase of counter-ions in the pores allows for faster-than exponential charging upon initial application of a potential difference, but then the local density increase makes it more difficult for co-ions to diffuse out of the electrode, slowing further charging. This phenomenon is similar to the “overfilling” observed by Kondrat et al., in which the total number of ions inside the pore during the course of charging reaches values higher than the steady-state value.If the initial charging period after the constant potential is characterized by kinetic trapping, then we should see that the charging profile in this initial period differs between independent charging cycles of the same EDLC. When fit to an exponential, independent runs may have different τ as this is determined by dynamic processes during charging, but they should have similar Qinf . In order to test this we generated independent configurations of the 19 ZTCs from zero-charge runs, and repeated constant-potential simulations to compare the charging curves of the independent runs. These results, shown in Figure C.10, demonstrate that there is indeed more reproducibility in the maximum charge than in the charging rate between independent runs. While all but four of the maximum charges are within 10% of each other in independent runs, two-thirds of the materials have time constants that are more than 10% different from each other. Cancer is the leading cause of overall dog deaths with up to 27% of dog deaths attributed to this disease.This risk is highest for large breed dogs and those over 10 years of age.Cancer and its treatments cause disruptions in nutritional status, such as loss of appetite and cachexia in many species.In humans undergoing or surviving beyond treatment, evidence for the effectiveness of dietary strategies is inconsistent, which might reflect the complexity of the relationships among various nutritional factors, cancer biology, and both general and cancer-specific outcomes.