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63f4de869da0bc6b334ea018 | 10 | At longer times, analysis of interfacial tension (IFT) data from pendant drop method at different asphaltene concentration was found to follow predictions from surface diffusion-mediated random sequential adsorption (RSA) theory , where the surface pressure is independent of viscosity. The surface coverage showed asymptotic behavior with a linear dependency of surface coverage with inverse of √t and the asymptotic limit close to 2D random close packing of disks around 85% (Pauchard et al. 2014). |
63f4de869da0bc6b334ea018 | 11 | When emulsions are left at rest or gently stirred, the coalescence process continues until the surface concentration reaches the critical value of around 3.5 mg/m 2 . This critical value of surface concentration is found to be independent of adsorption properties such as bulk concentration or nature of the solvent (Pauchard and Roy 2014; Rapid contractions and expansion of asphaltene-laden interfaces using the pendant drop as Langmuir trough experiment is performed to simulate the rapid increase and decrease in interfacial asphaltene concentration that occurs during coalescence events . In contraction experiments of droplets aged in asphaltene solutions, contraction curves follow the Langmuir EOS for surface pressure values up to 21 mN/m (Figure ). Beyond that, the contraction curves deviate from Langmuir EOS consistently at a surface pressure value ∼21 mN/m, which corresponds to a surface coverage of approximately 80%. At this stage the droplet does not follow the shape of the Laplace-Young equation, indicating solid-like surface behavior. On further contraction wrinkles appear. Wrinkles observed are, however, not stable and disappear after a few minutes. This behavior is interpreted to be due to a transition to a glassy interface on contraction past the packing limit (~85% as determined in previous study by , followed by slow desorption. Figure shows the surface pressure versus interfacial coverage for 4 loops of expansion and contraction hysteresis experiments. The results show that there does not appear to be aging /crosslinking /gelation at the interface as all the curves fall onto the same Langmuir EOS for surface pressure value ∼21 mN/m. |
63f4de869da0bc6b334ea018 | 12 | The two different radii of curvature in a pendent drop leads to the anisotropic stresses due to the interfacial deformation (Kotula and Anna 2016). Compression of aged asphaltenescovered water droplet in a region of low interfacial viscosity could result in no distortion is visible on the droplet while the interfacial tension is still reducing or result in wrinkles appearing on the droplet to relax the large compressional stresses . However, the droplet will return to the laplacian shape over stopping the compressional mode and compressional modulus decreases to reach the plateau ). This observation is in contrast with gel point rheology, where decreasing the modulus by increasing the concentration is unexpected . At high elasticity, strong birefringence is observed upon contracting the aged oil droplet containing asphaltenes using cross-polarized light microscopy which is an indication of particles ordering within the interface . It is also reported that at high concentration, the skin remains on the droplet even after the re-expansion . |
63f4de869da0bc6b334ea018 | 13 | The reversibility of asphaltene adsorption has been a subject of debate in the literature. Indirect observations that are used to support the argument in favor of irreversibility of adsorption include formation of wrinkles on the surface of water droplets aged in asphaltene solution upon compression similar to other irreversibly adsorbed particles , caused by layer collapse when the saturation surface coverage is reached with decrease in interfacial area. Some investigations of wrinkling and water/crude oil emulsion stability suggest that factors other than irreversible adsorption can cause the layer collapse . Moreover, observations from contraction experiments of droplet aged with asphaltenes left at rest indicate relaxation towards higher interfacial tensions till similar values to those before the compression are approached and the wrinkles formed on contraction also disappear after some time suggesting the partial desorption of asphaltenes from the interface . |
63f4de869da0bc6b334ea018 | 14 | The coarse-grained model coupled with DPD also shows that at high surface coverage, some of the asphaltenes molecules desorbed into the oil region due to the steric hindrance between adsorbed particles (Ruiz-Morales and Mullins 2015). Experiments involving desorption of adsorbed asphaltenes using rinsing procedures suggest that asphaltene adsorption at oil-water interface is irreversible ). The molecular composition and heteroatoms such as oxygen, nitrogen and sulfur in asphaltene molecules impacts the asphaltene adsorption Gibbs free energy at the oil-water interface . The charge of heteroatoms determines the strength of hydrogen bond with the water molecules and, thereby, the stability of asphaltene adsorption at the oil-water interface . |
63f4de869da0bc6b334ea018 | 15 | The current understanding of the mechanism of asphaltene adsorption and emulsion stability in the oil-water interface have been summarized in the paper. Although significant research has been accomplished in this area, consensus has not been found on several aspects, including the reversibility of asphaltene adsorption, coalescence mechanism and structure and orientation of the asphaltenes. One reason for discrepancies in results could be due the methodology employed currently, which require subjective interpretation of indirect results to some extent. The simultaneous analysis of the asphaltene structures at the interface using direct imaging methods combined with the corresponding IFT and rheological responses can be a way of reducing the subjectivity. |
63f4de869da0bc6b334ea018 | 16 | Moreover, the source of asphaltenes used in different studies can vary resulting in differences in the composition, heteroatoms and the surface-active fractions present in the samples. This could potentially lead to contrary observations. The nature of solvent also potentially impacts the results discussed in this paper. Some of the results are obtained with asphaltenes in poor solvents, while other experiment involves asphaltenes in good solvents. Thus, a systematic approach is needed, where the variability of solvent and surface activity of asphaltenes is minimized to ensure comparability of results. |
60c75678567dfe34eaec64ac | 0 | Precise manipulation capabilities at small scales are of increasing importance for a wide variety of research fields such as biomedicine or biology, e.g., for the investigation of morphogenesis through single-cell analysis or detailed 3D reconstruction of complex model organisms. Therefore, it is not surprising that a large number of techniques have been introduced to facilitate the controlled rotation of small particles based on mechanical, magnetic, electrical, hydrodynamic, and optical forces. Unfortunately, many of these techniques rely on specific properties of the specimen, which significantly reduces their applicability for biological samples. The controlled particle manipulation using acoustic forces, acoustophoresis, has been widely applied due to its advantages of being label-free, contactless, and flexible in design while exposing biocompatible behaviour. Recent publications have illustrated a large variety of microstructures suitable for the controlled manipulation of single cells and particles through acoustic forces. Solid features such as polydimethylsiloxane (PDMS) or silicon sharp-edges are acoustically excited via an external piezoelectric transducer, leading to the formation of acoustic streaming patterns in the nearby liquid. Unfortunately, the majority of these acoustofluidic setups require a high input power to generate acoustic fields that are strong enough to manipulate the specimens, which might damage biological samples. Additionally, depending on their design and arrangement, hydrophilic surface coatings are required to prevent the unintended formation of air bubbles which otherwise significantly alter the anticipated streaming patterns. Furthermore, most solid-feature-based designs are limited to the generation of in-plane vortices and are, therefore, unable to provide additional visual insights through the re-orientation of the specimen. |
60c75678567dfe34eaec64ac | 1 | To overcome these challenges, microstreaming induced by an oscillating microbubble can be utilized. The streaming patterns of the microbubble can be switched from in-plane to out-of-plane streaming via altering the excitation frequency, allowing for controlled threedimensional rotations of cells and organisms, as well as microfluidic applications including pumping or mixing. Due to its high compressibility and the corresponding strong oscillations, the microvortices produced by acoustically-activated microbubbles are significantly enhanced compared to the ones caused through the vibration of solid structures. However, the major drawback of microbubbles is their limited temporal stability. If acoustically excited, rectified diffusion leads to the bubble's growth, which alters its resonance frequency and by that the strength and shape of the vortices. This process can be decelerated using commercially available encapsulated bubbles; however, the instability of the thin polymer membrane of encapsulated bubbles complicates their application for longterm investigations. Lastly, as microbubbles are prone to be trapped in cavities due to hydrophilic/hydrophobic interactions, their dimensions show slight variations between multiple experiments, making it difficult to predict their precise response to acoustic excitation and preventing their use for clinical applications. |
60c75678567dfe34eaec64ac | 2 | In this work, we introduce the embedded microbubble, a novel PDMS-based microstructure combining the low power advantage of bubble-based acoustic streaming with the temporal stability of acoustically-excited solid features. We perform in-depth numerical investigations and quantify the influence of geometrical parameters, such as the PDMS wall thickness or the microbubble's length, on the acoustic streaming inside the fluid channel and utilise these findings to optimise our device design. The manipulation capabilities of our acoustofluidic lab-on-chip are analysed through experimental characterisations and the revealed insights are discussed in further detail with respect to the numerical results. Finally, we highlight our device through the controlled and reliable out-of-plane rotation of single HeLa cells; a task beneficial to improve our understanding of biological processes on the cellular and sub-cellular level, and demonstrate the relevance of our approach for additional microfluidic applications through its use for mixing; a key step required for a wide variety of biomedical as well as chemical research. |
60c75678567dfe34eaec64ac | 3 | where τ = 2π ω is the period of oscillation, with angular frequency ω. The Gor'kov potential is derived under the assumption that boundaries are far away from the region of interest, which is not the case here. However, experimental studies revealed, that the theory should be valid up to close proximity of the embedded microbubble. In acoustofluidics, the acoustic energy density is often used as a benchmark for the device's performance and, therefore, used in our numerical analysis. The average acoustic energy density E ac is given as 24 |
60c75678567dfe34eaec64ac | 4 | We built a 2D numerical model of the chip and evaluated it in COMSOL Multiphysics (version 5.4). We specifically studied the frequency response of the device. At resonance frequencies, we looked at the wall displacement as well as the Gor'kov potential and streaming velocity. First, a mesh study was conducted, to determine the converged mesh parameters (see Figure ). After the initial frequency domain study of the Thermoviscous Acoustics and Solid Mechanics interface, a stationary study of the Creeping Flow interface at the resonance frequency was carried out by taking the solutions from the first study into account. |
60c75678567dfe34eaec64ac | 5 | Preliminary experiments to find the best excitation frequencies via attraction forces were performed with 10.29 ± 1.01 µm fluorescence polystyrene particles (FSEG008, Bangs Laboratories). When strong resonances were found, yeast cells, i.e., Saccharomyces cerevisiae, bought from a local supermarket, were submerged in de-ionised water and injected into the microfluidic channel to be used as tracer particles for the acoustic streaming. Given the limited visual accessibility of the out-of-plane vortices, experimental evaluation relied on secondary in-plane streaming visualized by the yeast cell circulation near the embedded microbubbles. |
60c75678567dfe34eaec64ac | 6 | The piezoelectric transducer has been excited via an arbitrary function generator (AFG3011C, Tektronix ). The motion of the yeast cells has been captured at 12 -17 frames/s using an inverted microscope (IX81, Olympus). To account for the varying size of yeast cells, multiple frames of the recordings were averaged. All data required for individual qualitative evaluations of design or process parameters has been collected in single experimental sessions to ensure comparability and to prevent inter-device discrepancies such as in the distance between the transducer and the PDMS device. |
60c75678567dfe34eaec64ac | 7 | Our device's mixing capabilities have been evaluated using normalised grey-scale analysis, with a standard deviation threshold of 10 % denoting sufficient mixing. Mixing has been performed using a constant excitation frequency of 69 kHz. Steady volume flows of 0.3 µl min -1 and 0.66 µl min -1 for de-ionised water and black ink (4001, Pelikan) were achieved by syringe pumps (neMESYS, Cetoni ). |
60c75678567dfe34eaec64ac | 8 | In numerical simulations, the air chamber length L has been increased from 250 to 1000 µm with steps of 50 µm. Figure ) indicates that the strongest average streaming velocity can be expected for L = 500 µm. At this air chamber length, the surrounding PDMS seems to compress the embedded air in a way that supports the vibrational mode of the resonating thin wall. However, further investigations are needed to evaluate the influence of the air chamber length properly. Additionally, we cannot fully exclude other factors such as large scale deformations of the PDMS device due to overall changes in the stability of the features. |
60c75678567dfe34eaec64ac | 9 | While the experimentally obtained results expose a similar trend as predicted by the numerical simulations, the superiority regarding streaming size of L = 500 µm is less pronounced in experiments, therefore further investigations might be necessary to allow for the appropriate interpretation of these results. A non-negligible reason for the variation observed between the numerically determined results and the experimental quantifications might also be based on differences in the evaluated quantity. While the numerical simulations allow for a direct investigation of the streaming velocity of the produced out-of-plane streaming near the embedded microbubble, due to limited accessibility to this streaming during experimental evaluations, the latter has to rely on the generated in-plane vortices. Therefore, the comparison of the results obtained through the different techniques, i.e., numerical and experimental evaluations, might be restricted by the complex and possibly non-linear relationship between the out-of-plane and the in-plane streaming vortices. |
60c75678567dfe34eaec64ac | 10 | Based on the results presented in the device optimisation, we opted for a design with wall thickness T = 5 µm and air chamber length L = 500 µm and performed more specific numerical analyses to gain further insights regarding the underlying mechanisms and the acoustic phenomena. Figure a) shows the average wall displacement and the average acoustic energy density for frequencies from 40 to 90 kHz with 100 Hz steps. The maximal energy density correlates with the highest displacement of the wall and reveals two strong resonances (41.89 kHz and 69.03 kHz). Experimental investigations showed that frequencies around 69 kHz lead to much stronger particle attraction and streaming velocities than frequencies around 40 kHz. The deviation from observed and simulated resonance frequency can be attributed to idealised material parameters and the limited significance of the displacement boundary condition, e.g., through lower amplitudes of the piezoelectric element at this frequency range. However, the aim of the numerical investigations is not to attain exact amplitudes but to show trends and get insight into the physical phenomena of the device. |
60c75678567dfe34eaec64ac | 11 | However, the particle needs to be positioned close to the thin wall to be influenced by the streaming vortex, which can be achieved by the acoustic radiation force. For particle attraction towards the thin wall, the Gor'kov potential minimum needs to be close to the embedded microbubble (see Equation ). As can be seen in Figure ), at the resonance frequency of 69.03 kHz a Gor'kov potential minimum is generated at half of the height of the thin wall; thus, particles are attracted to the displacement node of the thin PDMS wall. It is important to highlight, that the generated node is not based on a standing wave formation inside the channel and, thereby, does not rely on the geometrical dimensions of the PDMS as a whole. The experimentally determined relationship between the excitation voltage and the out-of-plane rotational speed of a specimen (rotation around x-axis). While the excitation frequency is kept constant at 69.2 kHz, an increase of the input power leads to stronger streaming velocities (Eq. 6) and subsequently to faster rotations of the specimen. The dashed line denotes a fitted quadratic curve with a coefficient of determination R 2 = 0.98. |
60c75678567dfe34eaec64ac | 12 | speed follows the input voltage in a quadratic dependency (R 2 = 0.98), demonstrating our approach's high controllability of the specimens orientation which is crucial for biomedical applications such as single-cell analysis. It is important to note that the increasing error at high voltages might be induced through uncertainties based on frame rate limitations of the experimental setup. However, additional sources, including possible cell membrane instabilities or the motion of intracellular features during fast rotational manipulations, can not be excluded. |
60c75678567dfe34eaec64ac | 13 | We expand the investigation of our device by demonstrating its application for two diverse applications, i.e., single-cell manipulation as well as microfluidic mixing. HeLa cells are a prominent model organism for biomedical as well as genetic research and their controlled manipulation exposes great potential to allow for further insights on a single cell level. The image sequence in Figure a) presents the slow and stable out-of-plane rotation of a single HeLa cell near an embedded microbubble with a wall thickness T = 5 µm, while the piezoelectric transducer is excited with a constant frequency of 69.2 kHz and voltage of 5 V P P . |
60c75678567dfe34eaec64ac | 14 | The HeLa cell's motion is further presented in Supporting Information SV-2. Please note that, in contrast to many solid microstructures used for acoustic manipulation, 31 the demonstrated rotational motion has been achieved at a low excitation voltage of 6 V PP , thereby preventing possible damage to the sample due to high power pressure fields. The successful manipulation of the HeLa cell is based on the combination of the acoustic radiation force and acoustic streaming. As demonstrated through the numerical simulations, the Gor'kov potential (see Figure ) ) leads to a force which pushes biological specimens towards the embedded microbubble. Once trapped, the single cell is rotated via the viscosity-related acoustic streaming, which allows for the visual investigation of the specimens intracellular components as well as individual features of the cell membrane. Please note that the wall thickness appears larger in the image sequence due to the plane of focus being set on the specimen. |
60c75678567dfe34eaec64ac | 15 | Due to the flow limitations at the low Reynolds regime, reliable mixing is essential for a variety of lab-on-chip applications in chemical as well as biomedical analysis. Our acoustic-based mixer consists of a series of alternating embedded microbubbles with wall thickness T = 5 µm arranged along a single microchannel. The channel dimension D has been set to 150 µm based on numerical investigations to ensure strong and local streaming near the microstructures. Two liquids, i.e., de-ionised water and blue ink, are introduced through separated channels while their volume flow is controlled via a high-precision microfluidic pumping system to achieve an average flow velocity v avg . The inlet channels meet at an angle of 90°to minimise diffusion-based mixing while avoiding possible acoustic streaming near sharp-edge features. Figure 4 b) shows the PDMS device with the two laminar flows prior to acoustic excitation, i.e., the piezoelectric transducer is off, as well as during mixing of two fluids using an input voltage of 20 V PP (see Supporting Information SV-3). The average flow velocity inside the microchannel is v avg = 2.13 mm s -1 , which, despite requiring significantly lower input power and not relying on surface treatments, is comparable to results presented for solid-structure-based acoustic mixers. Additionally, as our design allows to prevent geometrical constrictions, unintended trapping of microbubbles inside the mixing channel can be avoided. While bubble-based acoustic mixers allow for increased handling of fluid volumes, our approach circumvents their limitations in temporal stability and re-usability. The graph in Figure ) demonstrates the experimentally determined relationship between the applied input power and the acoustic manipulation capabilities of our device. To allow for the evaluation of device performance, we calculated the mixing indices at different positions of the microchannel, starting with position 1 in front of the mixer (see red labels in Figure ) ). For each position, a mixing index has been derived as the standard deviation of the normalised grey-scale image (area highlighted with yellow lines). A threshold of 10 % has been defined as sufficient mixing based on previous literature. The graph demonstrates that, for our design with 20 alternating embedded microbubbles and for average flow velocities v avg = 2.13 mm s -1 , successful mixing can be achieved for excitation voltages as low as 16 V PP (blue squares) while, for 20 V PP (orange triangle), the threshold is already reached after 8 features. |
60c75678567dfe34eaec64ac | 16 | To allow for direct comparison between various designs and techniques applied in microfluidic mixing, the average mixing time can be derived as τ S = L mix /v avg ≈ 376 ms (7) where L mix = 800 µm is the mixing distance required to achieve sufficient mixing for an excitation voltage of 20 V P P . However, it is important to note that the device's efficiency might be further improved through design optimisations, such as by arranging the embedded bubbles in an opposite instead of an alternating manner. Additionally, as active streaming has only been observed directly in front of the embedded microbubbles, the distance between the features could be reduced without leading to unintended and possibly unfavorable interactions between the generated vortices. Furthermore, through the simple application of an external amplifier, the strength of the acoustic streaming could be further increased, which would allow to reduce the derived mixing distance. |
60c75678567dfe34eaec64ac | 17 | In this work, we introduced a novel acoustofluidic device combining the advantages of solid and bubble-based features and demonstrated its use for particle and single-cell manipulation as well as microfluidic applications. We numerically investigated different geometrical design parameters and derived their complex relationship to the acoustically generated streaming pattern. Then, following noticeable fabrication improvements, we successfully confirmed our observations through experimental characterisations. Optimum device performance with regards to its out-of-plane rotation capabilities has been numerically determined for a microbubble length of 500 µm, wall width of 5 µm, and fluid channel width of 150 µm. |
60c75678567dfe34eaec64ac | 18 | We explored the applicability of our device for biomedical research through the controlled out-of-plane rotation of single HeLa cells and quantified the near quadratic dependency between the applied voltage and the specimen's rotational speed, which allows for the high controllability necessary to achieve slow yet stable motions crucial for future biological investigations, e.g., through fluorescence imaging. Finally, we illustrated our lab-on-chip sub-second mixing performance and discussed potential design improvements for increased efficiency. Nevertheless, it is worth highlighting that the current achievements are comparable to previous publications while relying on significantly lower input power and maintaining the microbubble's temporal stability. |
678ceb1681d2151a02c1a235 | 0 | High-performance membranes have immense potential to improve carbon capture efficiency if they can be designed to yield a high CO2 selectivity and a high CO2 permeance. Nanoporous atomically thin membranes (NATM), particularly porous graphene, have attracted substantial attention. A single translocation event across the zero-dimensional pore determines selective transport. Attractive gas separation performance has been observed, with selectivity arising from relative mass, molecular size, and binding affinity differences. An accurate prediction of capture performance from graphene pores is needed to highlight the true potential of NATM. This will help design improved membranes for carbon capture. |
678ceb1681d2151a02c1a235 | 1 | Accurate and rapid computation of capture performance from realistic CO2-selective pores, mimicking those formed in experiments, is needed. Å-scale pores in graphene for CO2 separation are prepared by oxidation involving controlled lattice gasification. The resulting pore edges are passivated with O functional groups. These groups evolve from the chemisorption of a single epoxy followed by an organization of epoxies in a cluster (Supplementary Section 1). When the cluster size is sufficiently large, strain-mediated C-C bond cleavage followed by gasification yields a carbon vacancy defect (pore) with ether and semiquinones (C=O) decorated at the pore edge. Pores formed in this way have yielded attractive carbon capture performances, however, pores terminated with C=O have not been explored by computational studies. Extensive computational studies have been conducted to analyze gas transport from graphene pores since attractive gas separation from graphene pores was first predicted in the year 2009. For simplicity, early studies probed pore edges devoid of functional groups and assumed rigid apertures with a fixed pore-limiting diameter. Other studies probed pore edges passivated with atomic H, N, or O, however, gas transport was still investigated, assuming a rigid aperture with a fixed PLD. When lattice flexibility and vibrational dynamics were included, PLD modulation and enlargement were predicted, resulting in an increased gas permeance. Pores decorated with the C=O group have not been studied. One expects the pore edge C=O group to interact strongly with polar molecules such as CO2 and even flip-flop across the plane of the pore. This is expected to result in a unique occupancy-dependent guest environment, which could strongly control transport and the resulting separation performance. However, such guestmolecule-induced dynamics of C=O have not been studied. Small pores in graphene impose an energy barrier for the translocation of gas molecules. When the energy barrier becomes large, the transport event becomes a rare event in the MD simulations, which makes accurate measurement of gas separation performance challenging. TST, which estimates the transport rate based on a classical energy barrier event, is extremely useful in predicting transport rates and carbon capture performance in these cases. However, TST calculations have been mainly used to predict qualitative trends, and gas flux predicted by TST has not been validated, e.g., with predictions from MD simulations. |
678ceb1681d2151a02c1a235 | 2 | Herein, we report a unique transport behavior of gases in the presence of C=O at the pore edge. C=O bond exhibits a dynamic out-of-plane motion based on the extent of interaction with the gas molecule. The PLD, often assumed to be a constant, is found to have a large variance. Small pores with a strong molecular confinement exhibit a distinct open and closed state at a given temperature. |
678ceb1681d2151a02c1a235 | 3 | The dynamic motion makes small pores CO2 permeable, which would otherwise be impermeable with rigid PLD. The strong interaction of CO2 with C=O ensures adsorbed-phase transport even at elevated temperatures, resulting in a selective gating of CO2 over O2 and N2 even from large pores, which would otherwise be nonselective. Finally, a quantitative agreement is achieved between the flux predicted by the transition-state-theory (TST) calculations and the translocation rates from the MD simulations. This will allow one to avoid time-consuming and expensive simulations. These insights highlight the unprecedented high potential of porous graphene membranes for carbon capture and will inspire improved membrane design. |
678ceb1681d2151a02c1a235 | 4 | Carbon capture from flue gas emission requires the separation of CO2 from N2 and O2. CO2/O2 separation is more challenging than CO2/N2. O2 permeates faster than N2 because of its smaller kinetic diameter (3.30, 3.46, and 3.64 Å for CO2, O2, and N2, respectively). However, studies on CO2 transport across graphene pores primarily focus on CO2/N2 separations. CO2/O2 separation has received much less attention. For several critical emissions, such as from natural gas combined cycle and cement plant, O2 concentration in the flue gas can be as high as 10%, making this separation important. Therefore, we focus on CO2/O2 separation. CO2/N2 separation was also studied, and results confirmed that CO2/N2 selectivities are much higher than those of CO2/O2. |
678ceb1681d2151a02c1a235 | 5 | The MD simulation configuration used to analyze gas transport consists of graphene hosting 16 identical pores dividing feed and permeate chambers. The simulation box is enclosed in the zdirection by walls made of pristine graphene (Figure ) with potentials similar to the literature. At the start of the simulation, the feed side has an equimolar CO2/O2 mixture while the permeate side is under vacuum. ) O-functionalized graphene pores in this study. Pore-10, pore-13, and pore-16 are prepared by removing 10, 13, and 16 carbon atoms, respectively, from the graphene lattice, followed by pore edge termination with ether and C=O. |
678ceb1681d2151a02c1a235 | 6 | Three Å-scale pores, pore-10, pore-13, and pore-16 are investigated. The digits represent the number of missing carbon atoms for forming pores (Figure ). For a given number of missing carbon atoms, the pore skeleton is consistent with the most probable structure reported in the literature, validated by the observation under microscopy. Pore edges are functionalized with C=O (3-4 edge atoms) and ether groups (rest of the pore edge atoms). The assignment of the number of C=O is consistent with the experimental data based on the concentration of C=O per pore when pores are created by oxidation. The remaining pore edge atoms are passivated by ether because, upon oxidation, ether is formed at the center of the oxygen cluster. |
678ceb1681d2151a02c1a235 | 7 | The C=O group is observed to be dynamic, leading to modulation of the electron density gap in the pore. PLD, defined as the largest van der Waals sphere that can be accommodated inside the pore, (Figure ) was evaluated every 50 ps at 298 K in the presence of the CO2/O2 feed. A distinct PLD distribution is observed for all three pores (Figure ), indicating that the PLD is not a single value as often assumed. Strikingly, the corresponding variance (up to ~0.24 Å) is significant, considering that the difference in kinetic diameters of CO2 and O2 is only 0.16 Å. |
678ceb1681d2151a02c1a235 | 8 | At 298 K, pore-10 PLD has a distinct shoulder, indicating the presence of two states. One with a mean PLD of 2.4 Å and second with a mean PLD of 2.0 Å (Figure ). Snapshots of the pore corresponding to these two states reveal that the larger PLD is manifested when C=O swings out-ofplane of the pore (open state), while the smaller PLD occurs when they are in-plane (closed state, Figure ). |
678ceb1681d2151a02c1a235 | 9 | To test this hypothesis further, pore-10 is exposed to pure CO2, O2, and N2 gases and a vacuum (Figure ). A distinct preference for the open state is established only in the case of CO2. In contrast, a stronger preference for the closed state is observed for O2 and N2, which have weaker interactions with the pore. |
678ceb1681d2151a02c1a235 | 10 | For larger pores, the two distinct states were not observed (Figure ). For pore-13, PLD decreases slightly from 2.45 to 2.35 Å when temperature is reduced from 423 to 298 K, consistent with higher interaction with CO2 at lower temperatures. The largest pore (pore-16) has a single peak at 3.65 Å, indicating that the confinement is not strong enough to alter PLD (Figure ). These observations confirm that a strong interaction between C=O and CO2 results in the accommodation of CO2 in the pore-10. This takes place via the out-of-plane motion of C=O. A single state is observed for pore-16 because CO2 can be accommodated in the in-plane configuration. The above analysis reveals that C=O is dynamic and makes the pore environment dynamic. Dynamic transport from graphene pores has been experimentally observed from an ensemble of just of few pores, with transport characterized by quantized pore gating. The gas translocation rate, j, is evaluated from the cumulative number of molecules crossing the graphene pore as a function of time (Supplementary Section S2, Figure ). An interesting trend concerning temperature is observed. For smaller pores (pore-10 and pore-13), a two-fold increase in jCO2 occurs from 298 to 323 K. Above 323 K, a steady decrease in translocation rate is observed for jCO2. A key finding is negligible O2 translocation for pore-10 and pore-13 in the 30 ns simulations. These pores are highly selective to CO2. Similar trends are observed at pore-16, where the pores are selective to CO2 at lower temperatures; however, the O2 translocation rate increases at higher temperatures. We reconcile these different trends in translocation rate by examining the free energy for translocation through the pores. |
678ceb1681d2151a02c1a235 | 11 | The potential mean force (PMF) profiles for CO2 translocation through all three pores were computed to understand the underlying energetics that determine transport (Figure ). We quantify the free energy barrier for translocation (∆A) by calculating the differences in PMFs at the center of the pore (z = 0) and the position where the minima in the PMFs are observed on the feed side (adsorbed state; see methods section). We note that PMF computations in the literature are typically carried out for a single molecule translocating under vacuum conditions. In this study, PMF computations are carried out in the mixture to represent the free energy landscape under realistic mixture transport conditions. ∆A for CO2 is the highest for the smallest pore (pore-10), decreasing as the pore size increases (Figure ). Interestingly, ∆A values for pore-10 and pore-13 show a decrease when temperature increases from 298 to 323 K and increase monotonically for higher temperatures thereafter. For pore-16, where the confinement is the least, ∆A increases monotonically with temperature for CO2; however, the opposite is observed for O2, where a slight decrease occurs with increasing temperature (Figure ). |
678ceb1681d2151a02c1a235 | 12 | The unusual increase in jCO2 correlates well with the decrease in ∆A from 298-323 K, and the steady decrease from 323-423 K is consistent with the increasing free energy barrier for translocation (Figure ). The translocation trends for pore-16 follow the temperature dependence of free energy (Figure ). O2 is a larger molecule than CO2. Given that CO2 translocation follows an energy barrier, one expects O2 to experience an even more significant barrier. This is indeed observed from PMF calculation (Figure ). This translates into a slower translocation rate for O2 than CO2, leading to highly selective CO2 transport. |
678ceb1681d2151a02c1a235 | 13 | Simulations with rigid pores were carried out to understand the impact of the dynamic motion of C=O on gas transport. In the rigid case, pore-10 and pore-13 were found to be impermeable (Figure ). For pore-16, while the CO2 permeation event is observed from the rigid pores, the translocation rate is underestimated by an order of magnitude (Figure ). A similar flux underestimation was observed for the CO2/N2 case (Figure ). This demonstrates that neglecting functional group dynamics for graphene pores leads to highly erroneous results, making highly permeable and selective pores impermeable. , (e) pore-13, (f) pore-16, and O2 molecules from (g) pore-16. The porous graphene is located at z = 0, and the regions z > 0 and z < 0 depict the feed and permeate sides, respectively. Free energy barriers (∆AT) for the translocation of (h) CO2 through pore-10, pore-13, and pore-16 and (j) CO2 and O2 through pore-16. Translocation rates of CO2 as a function of temperature through porous graphene hosting dynamic and rigid (j) pore-10, (k) pore-13, and (l) pore-16. |
678ceb1681d2151a02c1a235 | 14 | The dynamics of the flexible pore functional group leading to dynamic PLD must be associated with a competitive uptake of CO2; otherwise, the selective gating of CO2 discussed above would not be feasible. To understand this, the density distributions of CO2 and O2 on the porous graphene lattice (pore-13) were analyzed (Figure ). It shows that CO2 adsorbs much more strongly than O2 in the entire temperature range (298-423 K). At 298 K, the CO2 population is 8-fold higher than that of O2 in the feed side of the pore, and a weak density peak on the permeate side is observed only for CO2. This competitive uptake is due to strong charge polarity in the C=O group, which attracts CO2 to electronegative O. As expected, the interaction weakens at higher temperatures, reducing the CO2/O2 occupancy ratio to 2.5 at 423 K. Similar trends are observed for pore-10 and pore-16 (Supplementary Figures and). |
678ceb1681d2151a02c1a235 | 15 | The surface density profiles provide crucial insights into the distribution of gases on the lattice near and away from the pore. CO2 populates the pore region to a significantly greater extent than the lattice region (Figure ). At 298 K, the CO2 population in the pore region is ∼ 1.9-2.5 times greater than the lattice region. At 423 K, the overall CO2 population decreases. Nevertheless, relatively higher adsorption on the pore is still observed compared to the lattice (Figure ). In contrast, a negligible population of O2 is observed in the pore region (Figure ). O2 adsorbs predominantly on the graphene lattice away from the pore. We infer that the high propensity of CO2 towards the pore region inhibits O2, contributing to the selective CO2 translocation. Similar observations have been made in crown-ether pores. However, pore dynamics and gating are not at play in these pore. Therefore, competitive adsorption of CO2 near the C=O group plays a crucial role in pore dynamics and selective gating. An adsorption peak in the density profiles is also observed on the permeate side (Figure ). This agrees well with the literature on transport dominated by surface or adsorbed-phase transport. In this case, after translocating through the pores, gases tend to first adsorb on the permeate side of graphene, and the final permeation event takes place when the gas desorbs from this adsorbed layer (Figure ,i, Figure ). PMF calculations confirm this, where a free energy valley on the permeate side was also observed (Figure ). |
678ceb1681d2151a02c1a235 | 16 | A competing transport mode to the surface transport is direct or effusive transport, where a gas molecule impinges on the pores directly from the gas phase (Figure , ii). For small pores, there is no consensus in the literature on the extent of direct versus surface transport. It is convenient to model CO2 transport by assuming direct transport, where the transport rate can be calculated by adding an energy barrier term to the effusive transport rates (modified effusion model). We show that CO2 primarily transports via the surface transport mechanism. For this, the contribution of direct and surface flux to the overall transport rate is quantified. Tracking the path of CO2 in the MD simulation, we find that surface flux overwhelmingly dominates CO2 transport, with 99% of translocation events taking place by surface pathway at room temperature. Even at elevated temperatures (e.g., 423 K), surface flux contributes 90% of the total translocation events. |
678ceb1681d2151a02c1a235 | 17 | Interestingly, the surface flux pathway is also dominant for O2, a gas with a relatively weak interaction with the pore (67 and 55% at 298 and 423K, respectively). The dominance of surface flux and the competitive adsorption of CO2 has an important ramification, i.e., selectivity can be achieved from pores with pore size larger than the size of the molecule, as observed in this study for pore-16. |
678ceb1681d2151a02c1a235 | 18 | TST-based calculation of gas flux through a zero-dimensional pore is promising for predicting the gas separation performance for NATM. It helps one bypass the lengthy MD simulations, especially when molecular transport is a rare event, e.g., for O2 in the current study. While TST calculations have been used in the past to estimate transport rates, the propagation for error is high mainly because of assumptions made for the estimation of energy barrier and pre-exponential coefficient. |
678ceb1681d2151a02c1a235 | 19 | where [𝐶𝑂 : ] is the concentration of gas molecules adsorbing onto the pore, P is the pressure on the feed side, and 𝐴 ;<"= is the pore area (Table -S5). Based on Eq. 5, TST significantly underpredicts the gas translocation rate (Figure ). To understand the reason for this underestimation, we compared 𝛥𝐸 and 𝐴 !"#$% &'& computed from MD simulations and TST (Figure b-c, Section S7). 𝛥𝐸 is similar for both TST and MD and thus, is not responsible for TST underpredictions. 𝐴 !"#$% &'& is found to be significantly lower than 𝐴 !"#$% >? |
678ceb1681d2151a02c1a235 | 20 | explaining underestimation of gas flux by TST. This can be explained by approximation of |𝑧(0)| using the Maxwell-Boltzmann distribution, where particles are considered free from interactions. However, in confined pores, molecules experience a strong interaction. This especially important for C=O terminated pores, as in this study. We introduce a correction factor, β such that |
678ceb1681d2151a02c1a235 | 21 | These calculations show that graphene pores are highly attractive for carbon capture. jO2 is extremely small for pore-10 and pore-13. However, we can confidently say that S is larger than 100 for these pores. For pore-16, S ranges from 42 and 10 at 298 and 323 K, respectively, dropping to 1 at 423 K. |
678ceb1681d2151a02c1a235 | 22 | Porous graphene membrane hosting C=O functionalized pore-16 outperforms state-of-the-art membranes (Figure ). In particular, a density ≥ 10 11 pores cm -2 , feasible in pore generation by oxidation, yields a very attractive CO2 permeance (>10000 gas permeation units or GPU, 1 GPU = 3.35 ´ 10 -10 mol m -2 s -1 Pa -1 ) accompanying large CO2/O2 and CO2/N2 selectivities. Such high performance is expected to reduce the energy input and cost of carbon capture, even from dilute point source emissions. |
678ceb1681d2151a02c1a235 | 23 | We report that Å-scale graphene pores decorated with C=O groups, generated from the oxidation of graphene, selectively gate CO2 largely driven by the dynamic behavior of pore edge C=O. The gas permeance and selectivity predicted from graphene pores are shown to be highly erroneous with the assumption of fixed PLD, indicating that fixed PLD calculation should be only considered for the cases with negligible molecule-pore interactions. Strong interactions between the pore edge functional group (C=O) with gas molecules control transport. These interactions open a seemingly impermeable pore or provides high selectivity from a seemingly nonselective pore. Therefore, capturing these interactions is extremely important for reliable gas flux and permeance predictions. TST-based rate calculation can be used to accurately predict gas flux and corresponding selectivity if the assumptions in the TST formulation are corrected to account for pore confinement effects. This allows one to rapidly predict gas permeance events even when the energy barrier for pore translocation is high, a scenario that greatly limits the applicability of MD simulations. These findings pave the way to understanding and predicting mass transport in realistic graphene pores and will guide the design of graphene membranes for molecular separation. |
678ceb1681d2151a02c1a235 | 24 | Quantum ESPRESSO package was used for performing density functional theory calculations to obtain the relaxed structures of oxygen-functionalized pores. The plane-wave basis sets were employed to carry out the electronic wave function expansion with the cutoffs of 50 Ry and 500 Ry employed for the wave function and charge density, respectively. Perdew-Bruke-Ernzerhof functional was used to describe the exchange-correlation, and ultrasoft pseudopotentials 72 were utilized to model the interactions between the ionic core and valence electrons. A vacuum of 2.0 nm was incorporated along the direction normal to the oxygen-functionalized pores' surface to avoid interactions between the periodic images. Owing to the large supercell, the Brillouin zone sampling was restricted to the Γ point, and the Broyden-Fletcher-Goldfar-Shanno scheme was employed to perform structural relaxation until the Hellmann-Feynman forces were less than 10 -3 Ry Bohr -1 . |
678ceb1681d2151a02c1a235 | 25 | Molecular dynamics simulations to examine the effectiveness of oxygen-functionalized graphene pores for CO2/O2 separation were performed using GROMACS 5.1.4 simulation package. simulation boxes were enclosed along the z direction by the porous graphene hosting 16 oxygenfunctionalized pores and a reflective wall made of a single-layer pristine graphene sheet. In order to generate the permeate side, another reflective wall was used such that the volume of the permeate side is the same as that of the reservoir. A similar simulation protocol has been employed previously to study gas separation and water evaporation from graphene nanopores. Owing to the hexagonal graphene lattice, a parallelepiped simulation box was used with a cross-sectional area of 142.18 nm 2 . |
678ceb1681d2151a02c1a235 | 26 | During the course of the simulation, all atoms of the porous graphene except the functional groups terminating the pores were fixed in their respective atomic positions. The Lennard-Jones interaction parameters and charges of the CO2 and O2 gas molecules were parameterized using the TraPPE model. On the other hand, all-atom optimized potentials for liquid simulation parameters were used for functional groups terminating graphene pores and parameters developed by Cheng and Steele, were used to simulate the pristine lattice. 11,79 van der Waals interactions were modeled using Lennard-Jones potential with a cutoff of 1.2 nm, and Lorentz-Berthelot mixing rules were applied for the cross-interaction parameters for the Lennard-Jones potential between other unlike pairs. Additionally, the Particle Mesh Ewald algorithm was used to compute the long-range electrostatic interactions with a cutoff of 1.2 nm for real space force calculations. All the simulations were performed in a canonical (NVT) ensemble, and the temperature was controlled using the v-rescale thermostat with a time constant of 0.2 ps. Each simulation was carried out for 30.5 ns, of which the first 2 ns were treated as the equilibration stage. |
678ceb1681d2151a02c1a235 | 27 | The umbrella sampling method is used to evaluate the potential of mean force (PMF) profiles for gas permeation through the oxygen-functionalized graphene pores at different temperatures. Force constants of 500-1000 kJ mol -1 nm -2 are used in the harmonic umbrella potential, and the zcoordinate of the probe gas molecule is varied from 2.0 to -2.0 nm in decrements of 0.05 nm, with the porous graphene located at z = 0. The probe gas molecule is free to move in the x-y plane bounded by the cylindrical region across the nanopore. This cylindrical region extends up to 2.0 nm into both the feed and permeate side of the nanoporous graphene and exhibits a diameter equal to the effective diameter of the nanopore (as determined in Figure ). This resulted in 81 windows along the z direction, and each window is sampled for at least 15 ns, where the first 1.0 ns is treated as the equilibration stage. The collected data is analyzed using a weighted histogram analysis method. |
628bf0ca59f0d6b8549b0bfb | 0 | The study of molten salt properties has seen a major resurgence in recent decades due to promising applications in clean energy technologies such as molten salt reactors and concentrated solar power storage. The diverse application of molten salts is primarily due to their usage in high-temperature heat-transfer media. Molten salts are excellent candidates in these systems due to their favorable physicochemical properties (e.g., thermal conductivity, heat capacity, viscosity, etc.) and relatively low cost of production. When designing and optimizing salt mixture compositions for various applications, however, exploration of a high-dimensional material space is required to select for candidates with optimal properties. In addition, it is important to understand corrosion at alloy/molten-salt interfaces and propertyevolution during reactor operation. This makes the experiments (such as X-ray and neutron diffraction and electrochemical mea-surements ) expensive and challenging under extreme conditions. |
628bf0ca59f0d6b8549b0bfb | 1 | Therefore molecular dynamics (MD) simulations have been exploited to calculate molten salt properties. Classical simulations are efficient for modelling systems over timescales on the order of nanoseconds in order to make viable predictions. Empirical force-field molecular dynamics (FFMD) simulations with classical potentials such as the Born-Mayer-Huggins-Tosi-Fumi (BMHTF) rigid-ion potential have been demonstrated to lack full predictive capabilities due to the lack of many-body interactions that influence local structure. Polarizable ion models (PIM) developed in conjunction with quantum mechanical calculations have led to significant improvements in modeling structure, thermodynamics, and dynamic properties. Ab initio molecular dynamics (AIMD) simulations have been shown to be capable of accurately capturing local structure and solute chemistry in comparison with experiments. AIMD is computationally expensive, however, and therefore it is difficult to access long time and large length scales to predict the dynamic and thermal properties. Recently, state-of-the-art artificial neural network-based interatomic potential molecular dynamics (NNIP-MD) has been demonstrated as a promising computational tool to explore the underlying physics of the high-dimensional molten salt compositions by simulating 10 4 atoms on the timescale of nanoseconds with an accuracy at the level of density functional theory (DFT). It has been demonstrated that the NNIP-MD studies are capable of accurately predicting molten salt struc-ture, heat capacity, self-diffusion coefficients, thermal conductivity, electrical conductivity, viscosity and the melting/freezing point in comparison with experimental measurements. |
628bf0ca59f0d6b8549b0bfb | 2 | Understanding phase behavior remains a great challenge at the forefront of molten salt research. In addition, during reactor operation, there is continuous evolution due to processes such as transmutations, fission/corrosion product generation, gas bubble formation, precipitation of insoluble species and other reactions. A challenge facing the molten salt research community is to directly model these properties starting from phase diagrams, but many of the phase diagrams have never been constructed. |
628bf0ca59f0d6b8549b0bfb | 3 | The CALPHAD method is a principal method for phase diagram and molten salt database development. Experimental thermodyanmic data (from phase equilibria measurements and activities of solution species) and/or AIMD simulations are used to empirically fit models and then predict stable phases at different temperatures or compositions. As mentioned above it would be difficult, expensive, and time-consuming to obtain data for highdimensional salt systems through either experiments or AIMD simulations. The chemical potential is central for understanding molten salt thermodynamic properties and predicting phase behavior. Studies of the chemical potential are limited due to the abovementioned difficulties, however. The classical PIM potential force field has been used to calculate the activity coefficient ratios for lanthanide cations (e.g. U +3 to Y +3 in the LiCl/KCl eutectic mixture ) and the free energy change for the reaction of the Eu +3 /Eu +2 redox couple in molten KCl. The Widom particle insertion method has been employed with AIMD simulations to calculate the chemical potential and the solubility of the sodium atom in molten NaCl. The cutting-edge NNIP-MD methods hold significant promise to play a vital role in exploring the thermodynamic properties since they provide quantum-level accuracy with efficiency similar to classical simulations. In the present work, molten NaCl is chosen as a prototype system to demonstrate the validity of the NNIPbased quasichemical theory (QCT) calculations, which is shown to be an efficient approach for directly calculating the solute ion solvation free energy via molecular dynamics simulations. To our knowledge, this is the first application of deep learning methods to the calculation of excess thermodynamic properties of molten salts. |
628bf0ca59f0d6b8549b0bfb | 4 | where the angled brackets denote the ensemble average and the subscript "0" indicates that the solute X is absent during the simulation. In the QCT, the excess free energy is partitioned into three physical parts by manipulations involving insertion and withdrawal of a hard particle that carves out a cavity in the liquid: µ ex X = -kT ln⟨e -M λ /kT ⟩ 0 + kT ln⟨e -M λ /kT ⟩ ε X -kT ln⟨e -ε X /kT ⟩ M λ (3) where M λ is a repulsive potential (half-harmonic potential in the current work) that pushes solvent ions away to the distance λ . The first term (packing, PK) is the free energy change to grow a cavity of radius λ in the liquid. The second term (inner-shell, IS) is minus the free energy change to grow the same cavity in the liquid around the solute X and the subscript ε X indicates that the solute X is present during the simulation. The third term (longranged, LR) is the free energy change for inserting the solute X into the cavity center and the subscript M λ indicates that the solute X is absent and there is a cavity generated by the repulsive potential M λ during the simulation (referred to as "uncoupled" below). |
628bf0ca59f0d6b8549b0bfb | 5 | where the subscript M λ + ε X indicates the solute X is present at the cavity center fully interacting with solvent ions during the simulation (referred to as "coupled" below). The PK and IS contributions are computed via thermodynamic integration (TI) by slowly growing in the repulsive potential M λ using the functional form |
628bf0ca59f0d6b8549b0bfb | 6 | The regularization due to the repulsive potential M λ (that pushes the solvent molecules/ions away from the solute) produces near-Gaussian statistics for ε X , and thus the two fluctuation terms of the uncoupled (Eq. 8) and the coupled (Eq. 9) samplings are of close magnitude. Consequently, the average of the two mean terms gives a relatively accurate approximation for the LR contribution. |
628bf0ca59f0d6b8549b0bfb | 7 | The initial configurations were generated during classical molecular dynamics simulations using the GROMACS 4.5.5 package, and the ions were modeled with the OPLS-AA forcefield. With 1 fs as the time step, all classical force-field based simulations were run for 1.5 ns in the NVT ensemble after 1 ns of equilibration in the NPT ensemble. The temperature was set at 1150 K for the classical simulations. For the AIMD simulations, we employed the dual basis sets of Gaussian-type orbitals (double zeta bases, DZVP-GTH) and plane waves with a 600 Ry cutoff. Atomic cores were modeled with the Goedecker-Teter-Hutter pseudopotentials (GTH). The Perdew-Burke-Ernzerhof (PBE) functionals were used for all atoms in the system, and the D2 dispersion corrections were utilized. |
628bf0ca59f0d6b8549b0bfb | 8 | The Ewald potential was applied for the electrostatic interactions under periodic boundary conditions (PBC), and a Nos é-Hoover thermostat chain of length 3 was coupled to each ion to maintain a temperature of 1150 K for all the NVT ensemble simulations. Due to the requirement of many simulations along the thermodynamic integration paths to grow the nano-scale cavities, we were not able to employ the path integral formalism for incorporating quantum effects. These corrections are expected to be small at such a high temperature, however. |
628bf0ca59f0d6b8549b0bfb | 9 | The time step was taken as 0.5 fs. For the LR contribution, two 25 ps simulations (50,000 configurations) (coupled and uncoupled) were implemented. This is found to be sufficient for calculating ensemble-average energies based on previous AIMD studies with molten salts. We performed 9-step integrations for the PK and IS calculations, and we ran simulations for 10 ps (20,000 configurations) for each step. |
628bf0ca59f0d6b8549b0bfb | 10 | In the DeePMD-kit framework, a local coordinate frame should be constructed to preserve translational, rotational, and permutational (same atom exchange) symmetry. We set up the axes with the first axis along the direction to the nearest atom of the same ion type and the second axis along the direction to the nearest atom of the other ion type. Within this local coordinate system, the descriptors were assembled for each atom, including the full radial information for 20 atoms and the angular information for 40 atoms within the cutoff distance of R c = 6.8 Å. |
628bf0ca59f0d6b8549b0bfb | 11 | The descriptors of each atom flowed into a DNN of 5 hidden layers with decreasing numbers of neurons, (512, 256, 128, 32, 8), which mapped the descriptors into the output layer, which produces the atomic energy E i . The non-linear activation function was taken to be the hyperbolic tangent. The forces on each atom were computed as negative derivatives with respect to position. The loss function was taken as |
628bf0ca59f0d6b8549b0bfb | 12 | where ∆E and ∆F i are the root mean square (RMS) errors of the energy of the system and the force F on atom i, N is the number of atoms, and p ε and p f are the adjustable pre-factors. As the training proceeded, p ε began at 0.02 and ended at 8, and p f changed from 1000 to 1. The initial learning rate was 0.0001 with a decay rate of 0.95 for 5,000 total decay steps. The loss function optimization was done using the Adam stochastic gradient descent method. The batch-size was 5 and the training process proceeded for 1,000,000 steps. The training data consisted of energies and forces from AIMD simulations. |
628bf0ca59f0d6b8549b0bfb | 13 | From the AIMD simulations, we generated 20,000 configurations for each of the first 9 steps of the thermodynamic integration. For the last step, where γ=1, 50,000 configurations were collected from the two coupled simulations (IS of Na + and Cl -) and one uncoupled simulation (PK), respectively. We trained a model for each step of the TI process (IS and PK, 10 models in total) and another 2 models for the interaction energy calculations over the uncoupled and coupled configurations of the LR simulations, respectively. We also tried to obtain a single NNIP model by using all of the collected AIMD data. This all-in-one model produced an error of magnitude about 3 kcal/mol for the solutesolvent interaction energy compared with the AIMD calculation, and a similar error in the free energy. Due to this relatively large error, we did not utilize the all-in-one method further. |
628bf0ca59f0d6b8549b0bfb | 14 | DeePMD-kit provides LAMMPS support through a third-party package in order to produce classical MD simulations using the NNIP to compute the atomic interactions. In this way, large timescale simulations are accessible with quantum accuracy. We ran NVT simulations using the LAMMPS code for systems of each ion in the molten salt liquid. Following the calculation for the Na + ion hydration free energy, a cavity of radius 4.0 Å was included at the periodic box center. The variations in each contribution due to the change of the cavity size are discussed in detail in our previous calculations. We applied a Nos é-Hoover thermostat chain of length 3 to maintain a temperature of 1150 K. The system sizes were calculated following the above method. The NNIP-MD simulations were run for 1000 ps with the first 250 ps for equilibration and the subsequent 750 ps for data production. A time step of 0.5 fs was utilized and the configurations were recorded every 0.01 ps (every 20 steps). |
628bf0ca59f0d6b8549b0bfb | 15 | We first present results related to the NNIP model validation. For the LR contributions, the solute-solvent ion interaction energies calculated via AIMD and NNIP-MD simulations are shown in panel a of Fig. . Averaging over 1,000 configurations drawn from NNIP-MD simulations for the systems of one solute ion and 64 solvent ion pairs, the interaction energy of the solute Na + calculated via NNIP exhibits a 1.4 kcal/mol deviation from AIMD for the uncoupled simulation and 1.3 kcal/mol deviation for the coupled case. The deviations for the solute Cl -are -0.4 kcal/mol (uncoupled) and 0.4 kcal/mol (coupled). These values are close to chemical accuracy (∼1 kcal/mol) and indicate sufficient accuracy of the NNIP model for the free energy calculations. |
628bf0ca59f0d6b8549b0bfb | 16 | Next, as shown in panels b and c of Fig. , the overlapping of radial distribution functions (RDF or g(r)) indicates that NNIP sufficiently reproduces the local structure predicted by the AIMD simulations and uncovers the oscillating structures at larger distances as well. Additionally, the RDF of the Na + -Cl -pair in panel b exhibits a first maximum position at 2.77 Å and a first minimum position at 4.27 Å, which are close to those reported recently using NNIP training employing a different protocol. This indicates that the presence of a cavity with a radius of 4.0 Å does not significantly affect the average liquid structure in the nearby bulk. |
628bf0ca59f0d6b8549b0bfb | 17 | Just outside of the cavity, it is observed that there is a slightly higher density of the Cl -ions than the Na + cations. Integrating to a distance of 5.5 Å the coordination number of Cl -is 0.7 higher than that of Na + . This leads to a dipole layer in the vicinity of a cavity of 4 Å size. When the solute ion is present at the center of the cavity as shown in panel c, however, both solvent ions exhibit charge-symmetrical behavior, as evidenced by the overlaps in the IS RDFs. |
628bf0ca59f0d6b8549b0bfb | 18 | The LR contribution is estimated from the two distributions of solute-solvent ion interaction energies, which are calculated over configurations from uncoupled and coupled simulations. As shown in panel a of Fig. for the solute Na + , the mean uncoupled interaction energy is -125.62 kcal/mol with a fluctuation contribution (Eq. 8) of 28.2 kcal/mol, while the mean coupled interaction energy is -180.81 kcal/mol with a fluctuation contribution of 21.3 kcal/mol. The difference between the two fluctuation terms leads to an error of 3.5 kcal/mol for the LR free energy contribution, indicating that the Gaussian approximation is inappropriate and a larger cavity is required to observe Gaussian behaviour as was previously seen in the calculation of the hydration free energy of the Na + ion in water. As discussed in the theoretical methods section above, however, the long-range contribution is equal to the interaction energy at the intersection point of the two distributions. Thus we estimate the long-ranged contribution for Na + as -156.0 kcal/mol. In panel b of Fig. , the distributions for the Cl -ion exhibit more closely Gaussian behavior since the fluctuation terms are closer: 25.2 kcal/mol for uncoupled simulation with a mean value of 84.05 kcal/mol and 27.6 kcal/mol for coupled simulation with mean value of 21.40 kcal/mol. |
628bf0ca59f0d6b8549b0bfb | 19 | Based on the estimation of the intersection point of the two energy distributions, we estimate the LR contribution for Cl -ion as 54.0 kcal/mol. The dramatic increase of the LR contribution (including the sign) for the anion is attributed to the electrostatic potential at the center of the cavity. Assuming that the electrostatic interaction dominates the interactions between the center solute ion and solvent ions outside the cavity of 4 Å , the average energies of both Na + and Cl -ions over the uncoupled configurations gives an estimate of the electrostatic potential at the center of the cavity as -4.55 Volt, relative to the average potential in the bulk region of molten salt liquids. |
628bf0ca59f0d6b8549b0bfb | 20 | Multipole electrostatic moment analysis of the cavity-water interfacial potential reveals that there is a potential shift of -3.96 Volt from the liquid water bulk phase to the cavity center, which is primarily attributed to the water molecular Bethe potential (quadrupole) contribution. Since the current work focuses on the excess free energy for the solute ion pair (in which case the interfacial potential contributions cancel exactly), the Bethe potential for liquid NaCl is not discussed further here. |
628bf0ca59f0d6b8549b0bfb | 21 | The numerical results for the IS and PK contributions are shown in panel c of Fig. by presenting the cumulative work computed during the NNIP-MD simulations. Both Na + and Cl -ions share the same PK contribution (24.2 kcal/mol), while the IS contribution to the Na + solvation free energy is -44.7 kcal/mol and that for the Cl -ion is -43.6 kcal/mol. |
628bf0ca59f0d6b8549b0bfb | 22 | The numerical results for both the Na + and Cl -ions are listed in Table , where the finite-size correction term is due to the artificial effect of the Ewald potential on the free energy. The summation of the excess free energy for both solute ions with 256 solvent ion pairs is -178.5 kcal/mol, which is converged to within the standard error of the mean (SEM) of ±1.1 kcal/mol as the system size increases to 512 ion pairs. The SEM in parentheses is calculated using the block-average method (10 blocks) over the production configurations. To the best of our knowledge, this is the first prediction of the absolute solvation free energy for ions LR coupled RDF (c) Fig. The process of excess chemical potential calculation for the systems of solute Na + and Cl -ions with 256 solvent ion pairs. Panel a and panel b are for the long-ranged (LR) contributions to the solvation free energy of the solute ions Na + and Cl -, respectively. The logarithms of the distribution of interaction energies from uncoupled (right, blue) and coupled (left, black) configurations are presented with the mean value ε and standard deviation σ . The right dashed curves and the left dash-dotted curves are the Gaussian fit to both distributions. Panel c is for the packing (PK) and minus the Inner-Shell (IS) cumulative contributions for both solute ions. Along with the expansion of the cavity with(IS)/without(PK) the solute ions at the center, the coupling parameter γ increases from 0 to 1. The IS and PK contributions are listed in Table . Panel d is the distributions of interaction energy corrections ε DFTε MP2 for the solute ion with 7 and 17 solvent ion pairs. The sampling is over 400 cluster configurations carved from DFT simulation trajectories. The DFT calculation is under Periodic Boundary Conditions (PBC) in a cell of size 25.4 Å. |
628bf0ca59f0d6b8549b0bfb | 23 | Table The excess chemical potentials (kcal/mol) for the Na + ion and the Cl -ion in molten NaCl at 1150 K. The second column is the packing contribution. The third column is the inner-shell contribution. The fourth column is the long-ranged contribution, and the fifth column is the finite-size correction (FS). The sixth column is the excess chemical potential of each solute ion and solute ion pair. The number of solvent ion pairs is given after "NaCl". In the parentheses is the standard error of the mean (SEM) over 10 blocks. The last two columns give an estimate of the computational cost (core-hour/atom/MD-step) for the PK contribution where γ=0.1. The calculations were performed on the OSC Pitzer cluster (Dual Intel Xeon 6148s Skylakes 2.4 GHz and 192 GB RAM). AIMD used 400 cores (4 nodes) and NNIP-MD used 40 cores (1 node) in a molten salt using deep learning techniques. |
628bf0ca59f0d6b8549b0bfb | 24 | The computational cost by AIMD and NNIP-MD are shown in the last columns of Table , where it is shown that the efficiency of the NNIP-MD simulation is about 3 orders greater than that of AIMD for all the molten salt systems and the SEMs are reduced by about 1 order of magnitude compared to the calculation reported. The AIMD cost for 128, 256 and 512 systems are estimated over 100 MD-steps. |
628bf0ca59f0d6b8549b0bfb | 25 | The experimental data are analyzed in terms of a Born-Haber cycle as illustrated in Fig. . Assuming that all the gas states are well-approximated by the ideal gas, the sum of the solvation free energies of both solute ions is calculated from thermochemical tables to be -163.5 kcal/mol. Consequently our QCT calculation at the DFT level over-estimates the excess Gibbs binding free energy by roughly -15 kcal/mol. |
628bf0ca59f0d6b8549b0bfb | 26 | In a previous study by Gray-Weale et al., it was noted that the DFT calculation over-estimates the Na atom solvation free energy in liquid Na by -19 kcal/mol and the total Gibbs free energy change for the redox reaction Na(l)+ 2 Cl 2 (g) ⇀ ↽ NaCl(l) by -15 kcal/mol. The molten salt density is over-estimated by up to 10% when using the PBE DFT functional with the D2 dispersion correction, while the system appears to be unstable without the D2 correction. These results indicate both the importance and the subtlety of dispersion forces in the molten salt liquids. It is not surprising that the over-estimation of the density correlates with the over-estimation of the magnitude of the excess free energy. Some over-binding is also observed in ion solvation for the aqueous solution. Herein to estimate the correction for the free energy based on the underlying DFT simulations, we implement higher-level density-fitted MP2 theory 68 calculations over 400 cluster configurations with the basis set aug-cc-pvdz in the Psi4 package. The cluster configurations with 7 and 17 solvent ion pairs are carved from a trajectory generated by the DFT simulation. |
628bf0ca59f0d6b8549b0bfb | 27 | where the first term is the interaction energy correction and the second term is the fluctuation correction. The subscript ε DFT indicates that the sampling is over configurations produced by the DFT simulation. As presented in Table , the results of DFT calculations (with the same basis set, pseudo-potential and functional as those in the above simulation) are close to the results of the MP2 calculations obtained with the Psi4 code for the sampled clusters. (Note that in Table the results are presented in reference to the MP2 data; thus, the sign of the energetic correction should be flipped when inserting the data into Eq. 12.) Inclusion of the D2 correction over-estimates the interaction energy by -6.4 kcal/mol on average. As mentioned above, the over-binding between ions is also indicated by the 7% overestimation of the molten NaCl density at 1150K. The PBC interactions (related to the Ewald potential ) for the simulation cell of size 16.0 Å contributes about 10.0 kcal/mol to the interaction energy correction for the solute ion pair, while in the cell of size 25.4 Å it contributes about 2.0 kcal/mol. The distributions of the interaction energy corrections under PBC in the cell of size 25.4 Å are presented in panel d of Fig. . |
628bf0ca59f0d6b8549b0bfb | 28 | To estimate the total free energy correction, including contributions from outside the clusters, we extrapolate the cluster interaction energy correction to 256 ion pairs. Considering the cancellation of Ewald potential contributions for the solute ion pair, we assume that it is convergent to 1.6 (1.4) kcal/mol. Assuming the dispersion interaction energy (∝ 1 r 6 ) is proportional to the solvent ion density (which is approximately a constant outside the first solvation shell), the spherical integration leads to the expression of dispersion energy correction as a + b/N, where N is the solvent ion pair number. Using the dispersion energy corrections presented in row number 2 of Fig. The Born-Haber cycle scheme for Na + and Cl -ion solvation. The ions are assumed to be solvated from the ideal gas state (g) to liquid state (l) with number density ρ o = 15.61(nm) -3 and T 1 = 1150 K (NVT ensemble). The ideal gas of ions are changed into the NPT ensemble with pressure p o = 1 bar and temperature of 1150 K. Then the temperature of the ideal gases is reduced to T 0 = 298.15 K isobarically. At room temperature the sodium ion is changed to the sodium atom and chloride ion to the chlorine radical. Both atoms are then changed into elements, respectively. The solid state (s) NaCl is formed from component elements at room temperature and 1 bar pressure. Then the solid salt are heated isobarically into the liquid phase (l) at T 1 = 1150 K. The change of free energy from the NVT ensemble (ρ o ,T1) to the NPT ensemble (p o ,T1) of the liquid molten NaCl(l) is neglected. All of the Gibbs free energy changes are from thermodynamic tables, and the total change of the solvation free energy is -163.5 kcal/mol. |
628bf0ca59f0d6b8549b0bfb | 29 | Cl -, which leads to the extrapolation for the dispersion energy correction as -11.5(1.1) kcal/mol for Na + and -8.8(0.8) kcal/mol for Cl -(in the MP2→DFT direction). The total dispersion energy correction for the solute ion pair is then -20.3(1.4) kcal/mol or +20.3 kcal/mol in the desired DFT→MP2 direction. The Ewald correction in this direction is -1.6 kcal/mol. |
628bf0ca59f0d6b8549b0bfb | 30 | Summing up the total correction (PBC/Ewald and dispersion) of the solute ions, we see that the correction from the cluster calculations with 17 solvent ion pairs dominates 89.3% of that with 256 solvent ion pairs. As a result, the fluctuation term in Eq. 12 is assumed to be primarily captured by the interaction energy correction of 17 solvent ion pair cluster. This leads to a -2.5(0.1) kcal/mol correction for each of the Na + and Cl -solute ions. Inserting these results into Eq.12, we obtain the total correction (in the DFT→MP2 direction) as +13.7(1.9) kcal/mol for the solute ions. Compared to the experimental reference value of -163.5 kcal/mol, the calculated total excess chemical potential of -164.8(2.2) kcal/mol provides strong initial validation of the methodology. |
628bf0ca59f0d6b8549b0bfb | 31 | Through investigation of the solvation thermodynamics of the Na + and Cl -ions in the molten NaCl liquid, we have presented and validated an efficient and general methodology to calculate the solvation free energy of ionic species in the molten salts. The methodology incorporates ab initio molecular dynamics simulations, interatomic potentials based on deep neural network models, and quasichemical theory. Efficient molecular dynamics sim-ulations with the NNIP model reduces the calculation uncertainty significantly to roughly 1 kcal/mol. Due to the over-estimation of the magnitude of the attractive interaction energy of the solute ion with the solvent ions at the DFT level (with D2 dispersion corrections), a high-level quantum chemical correction of roughly 15 kcal/mol to the free energy is required to make a quantifiable prediction of the excess free energy. These results highlight the importance of dispersion and polarization interactions in the molten salt liquids. |
628bf0ca59f0d6b8549b0bfb | 32 | The methodology sets the stage for larger-scale simulations of molten salt mixtures at a quantum mechanical level of accuracy, allowing for quantitative investigations of the activities, solubilities, and redox potentials of ionic species (including the corrosion and fission products) in the liquid phase. The methodology holds the potential to provide essential data for molten salt applications in both concentrated solar energy storage materials and molten salt reactors. |
67720c63fa469535b9343b2c | 0 | The impressive progress in experimental femtosecond spectroscopy stimulates rapid development of accurate (especially, ab initio) methods of simulations of spectroscopic signals, see, for example, the original works and recent reviews . The signals are usually calculated by using the nonlinear response-function (NRF) approach, in which interactions of molecules with laser fields are assumed to be weak and treated in the lowest order of perturbation theory. However, a direct computation of the NRFs is tedious, especially for complex multidimensional molecular systems. The doorway-window (DW) approximation provides a practical alternative which substantially alleviates the computational costs . The DW representation of TA PP signals hinges on two assumptions: (1) the pump and probe pulses are well separated in the time domain; |
67720c63fa469535b9343b2c | 1 | (2) durations of both pulses are much shorter than the time scale of the system evolution. Under the DW approximation, evaluation of the TA PP signal is decomposed into three steps: evaluation of the doorway operator which describes interaction of the system with the pump pulse, field-free propagation of the doorway wavepacket, convolution of the doorway wavepacket with the window operator which describes interaction of the system with the probe pulse. In other words, calculation of TA PP signals is reduced to the propagation of the electronic ground-state and excited-state wavepackets. |
67720c63fa469535b9343b2c | 2 | A variety of theoretical approaches of different complexity and accuracy are available for the nonadiabatic excited-state wavepacket propagation in complex molecular systems. On the one hand, a fully quantum evaluation of the Hamiltonian dynamics or the dissipative dynamics is certainly possible, but these methods are suitable only for the excitonic or linearvibronic-coupling Hamiltonians. On the other hand, great efforts have been devoted to development of mixed quantum-classical trajectory-based or Gaussian-wavepacket-based propagation schemes . In the commonly used trajectory surface hopping (TSH) method , for example, the nuclear propagation is governed by classical mechanics and the electronic evolution is described by quantum mechanics. These trajectory-based approaches are especially attractive: Firstly, they usually require only the local information on the potential energy surface along the trajectory. |
67720c63fa469535b9343b2c | 3 | Recently considerable efforts have been devoted to the implementation of these on-the-fly trajectory-based dynamics methods for the simulations of time-resolved spectroscopic signals of model and realistic systems by using the NRFs and DW formalisms, see the original papers and the reviews . For example, the ab initio TSH-DW methodology has been developed in Ref. However, it is well known that all mixed quantum-classical dynamics methods may suffer from a number of deficiencies and restrictions. For instance, the famous fewest-switches surfacehopping algorithm (FSSH) does not properly describe electronic decoherence . It is thus worthwhile to explore a possibility of using alternative quantum-classical methods for the onthe-fly evaluation of nonlinear spectroscopic responses, in the hope that these methods will better reproduce the effects related to electronic and vibrational coherences. |
67720c63fa469535b9343b2c | 4 | A promising and viable alternative to trajectory-based nonadiabatic simulations is provided by the mapping Hamiltonian framework. Instead of running the dynamics generated by the original electron-vibrational Hamiltonian, the mapping Hamiltonian is used in which electronic degrees of freedom (DoF) are transformed into coupled continuous classical degrees of freedom DoFs . This provides a starting point for a family of various trajectory-based dynamics approaches . |
67720c63fa469535b9343b2c | 5 | In the well-known Meyer-Miller (MM) mapping model (frequently, it is referred to as the Meyer-Miller-Stock-Thoss model ), the quantum Hamiltonian containing N coupled electronic states is mapped into the Hamiltonian containing N coupled harmonic oscillators. This mapping procedure is founded on Schwinger's theory of angular momentum . Among different MM mapping schemes, the symmetrical quasi-classical (SQC) variant provides an effective way to simulate nonadiabatic processes . Several benchmark calculations have shown that the SQC/MM method gives a reasonably accurate description at affordable computational costs . In the SQC/MM simulations, the triangle windowing protocol and the adjusted γ correction are always recommended . After convincing demonstrations of performing mapping dynamics in on-thefly , the SQC/MM and other mapping approaches have been successfully applied to realistic polyatomic systems . |
67720c63fa469535b9343b2c | 6 | Several decades ago, the mapping approach was used for the calculation of spectroscopic signals . Nowadays, the methodology has actively been used and advanced . Yet it is rather demanding to employ the mapping method for the calculation of three-time NRFs, owing to the necessity to do multiple forward and backward propagations on a three-dimensional time grid. Hence the methodology is usually applied to model systems, because its use for the onthe-fly spectroscopic simulations of realistic molecules is computationally costly. Spectroscopic signals can also be computed by combining the SQC/MM dynamics with the time-dependent nonperturbation approach . However, this implementation is highly demanding for on-the-fly simulations: It requires a direct inclusion of the laser field into the Hamiltonian, and each time delay between the pulses requires a separate calculation. |
67720c63fa469535b9343b2c | 7 | In the present work, we propose a protocol in which the on-the-fly SQC/MM dynamics is combined with the DW methodology, and apply it for the simulation of TA PP spectra. In our protocol, the windowing scheme employed for the assignment of quantum states in the SQC/MM framework is used to define the currently occupied electronic state and to specify the transition dipole moment (TDM) between this state and the target state. This simplified treatment permits a convenient and efficient evaluation of the DW functions and provides an efficient and effective way to simulate TA PP signals on-the-fly. |
67720c63fa469535b9343b2c | 8 | It should be noted that Miller, Stock and their coworkers used the mapping approach in combination with the DW methodology for the calculation of time-resolved spectra for several model systems described by linear-vibronic-coupling Hamiltonians 100,101,112 . As distinct from these works, we develop the on-the-fly DW-MM methodology: The SQC scheme employed in the present work transforms the mapping variables back to the occupation numbers, which allows us to obtain simple explicit expressions for the DW functions which are convenient for the on-the-fly simulations. This largely extends the applicability of the on-the-fly SQC/MM-DW methodology, which can be used for the description of photoinduced dynamics and spectroscopic responses in realistic molecular systems. In this work, we simulate TA PP spectra of two popular molecular systems 113 , azobenzene and cis-hepta-3,5,7-trieniminium cation (PSB4) . |
67720c63fa469535b9343b2c | 9 | The SQC/MM method was implemented in the on-the-fy nonadiabatic dynamics simulation because of its excellent balance between computational costs and accuracy. . In this method, a quantum Hamiltonian with N discrete states is transformed into a mapping Hamiltonian with N coupled harmonic oscillators . The replacement of quantum operators by the classical ones enables the implementation of the quasiclassical dynamics with the trajectory-adjusted zero point energy (ZPE) correction . The "bin" technique is employed in the initial sampling and in the final assignment of quantum states. As is usually recommended, the triangle window technique is employed in the present work. |
67720c63fa469535b9343b2c | 10 | where R and P are, respectively, coordinates and momenta of the nuclear DoFs. x i and p i are coordinates and momenta of the mapping electronic variables. i labels the electronic states, F is the total number of these states, V i (R) is the potential energy of i th electronic state, γ denotes the ZPE correction and d i j represents the first-order non-adiabatic coupling (NAC) vector. |
67720c63fa469535b9343b2c | 11 | Here τ is the time delay between the pulses, ε ε ε pu and ε ε ε pr are the unit vectors of the linear polarization of the pulses, A pu and A pr are the pulse amplitudes, E pu (t) and E pr (t) are the dimensionless envelope functions, k pu and k pr are the wave vectors and ω pu and ω pr are the pulse carrier frequencies. |
67720c63fa469535b9343b2c | 12 | Here Ĥ0 is the nuclear Hamiltonian in the electronic ground state 0, ĤI is the Hamiltonian governing the initial excitation and nonadiabatic dynamic in the lower-lying excited states, ĤII is the Hamiltonian describing vibronic dynamics in higher-lying states, while Ĥ0I and its Hermite conjugated ĤI0 describe the NACs. The molecular electronic states fall into three manifolds 0, I and II according to their energies: I consists of the excited states interrogated via the pump pulse from the electronic ground state as well as of those states which are nonadiabatically coupled to them, while II includes the excited states accessible to the probe pulse from I. |
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