Canonical Simulations Research Articles

Influence of electrical images and electrolyte concentration on capacitance of the electrode - molten salt interface

Results of Monte Carlo grand canonical ensemble simulations of electrical double layer (EDL), with and without electrical images on the electrode, are presented. Calculations were carried out for a wide range of electrode surface charge, σ from -0.7 to 0.7 Cm−2 and a wide range electrolyte concentrations, c = 1.00 – 8.67 M. The electrolyte concentration of 8.67 M corresponds to the density of molten salts. It is known from earlier studies that for low electrolyte concentrations and low electrode charges, the EDL capacitances obtained for electrical images included in the calculations are greater than those calculated excluding them. For high electrolyte concentrations, especially for those which correspond to the molten salt densities, the situation unexpectedly turns around, i.e. the EDL capacitances obtained for the case of excluded images are greater than those calculated including them. For the whole range of applied electrolyte concentrations and electrode charges greater than σ ≈ 0.4 Cm−2 and lower than σ ≈ -0.4 Cm−2 no visible influence of applying the electrical images is observed on the EDL capacitance values. The above observations are discussed, explained in terms of the relationship between EDL thickness and the capacitance value, and analysed in terms of the electrostatic interactions of ion charges with their images.

Dynamic Docking Using Multicanonical Molecular Dynamics: Simulating Complex Formation at the Atomistic Level.

Multicanonical molecular dynamics (McMD)-based dynamic docking has been applied to predict the native binding configurations for several protein receptors and their ligands. Due to the enhanced sampling capabilities of McMD, it can exhaustively sample bound and unbound ligand configurations, as well as receptor conformations, and thus enables efficient sampling of the conformational and configurational space, not possible using canonical MD simulations. As McMD samples a wide configurational space, extensive analysis is required to study the diverse ensemble consisting of bound and unbound structures. By projecting the reweighted ensemble onto the first two principal axes obtained via principal component analysis of the multicanonical ensemble, the free energy landscape (FEL) can be obtained. Further analysis produces representative structures positioned at the local minima of the FEL, where these structures are then ranked by their free energy. In this chapter, we describe our dynamic docking methodology, which has successfully reproduced the native binding configuration for small compounds, medium-sized compounds, and peptide molecules.

Finite temperature auxiliary field quantum Monte Carlo in the canonical ensemble.

Finite temperature auxiliary field-based quantum Monte Carlo methods, including determinant quantum Monte Carlo and Auxiliary Field Quantum Monte Carlo (AFQMC), have historically assumed pivotal roles in the investigation of the finite temperature phase diagrams of a wide variety of multidimensional lattice models and materials. Despite their utility, however, these techniques are typically formulated in the grand canonical ensemble, which makes them difficult to apply to condensates such as superfluids and difficult to benchmark against alternative methods that are formulated in the canonical ensemble. Working in the grand canonical ensemble is furthermore accompanied by the increased overhead associated with having to determine the chemical potentials that produce desired fillings. Given this backdrop, in this work, we present a new recursive approach for performing AFQMC simulations in the canonical ensemble that does not require knowledge of chemical potentials. To derive this approach, we exploit the convenient fact that AFQMC solves the many-body problem by decoupling many-body propagators into integrals over one-body problems to which non-interacting theories can be applied. We benchmark the accuracy of our technique on illustrative Bose and Fermi-Hubbard models and demonstrate that it can converge more quickly to the ground state than grand canonical AFQMC simulations. We believe that our novel use of HS-transformed operators to implement algorithms originally derived for non-interacting systems will motivate the development of a variety of other methods and anticipate that our technique will enable direct performance comparisons against other many-body approaches formulated in the canonical ensemble.

Crystalline-to-Amorphous Phase Transformations As a Key Ingredient to Enhanced Rate Performance and Cycle Life in Mg- and Na-Ion Battery Anodes: Operando x-Ray Scattering Studies

The increasing popularity of Li-ion batteries in new applications such as electric vehicles is expected to cause the key resources (Li, Ni and Co) used in these batteries to become scarce. Alternative battery technologies, including Mg-ion, Na-ion, and metal-air batteries are therefore desirable. In this talk, I will discuss the use of operando wide-angle X-ray scattering (WAXS) to study the crystalline to amorphous phase transformations that are key to the outstanding performance of state-of-the-art alloy-type Mg- and Na-ion anodes. The 1st part of the talk will be on the impact of the crystalline-to-amorphous transformation on batteries cycle life. Here I will discuss our novel self-healing Ga/Mg anode, which holds the current record for cycle performance and rate capability in alloy-type Mg-ion battery anodes, owing to a crystalline Mg2Ga5 to amorphous liquid Ga phase transformation occurring near room temperature, preventing the well-known pulverization issue in alloy-type anodes.[1] The 2nd part of the talk will detail the impact of the crystalline-to-amorphous transformation on the rate capabilities of batteries. Here, I will present our nanoporous Sb/Na system, which transforms from crystalline Na3Sb to crystalline Sb, going through an amorphous intermediate. It will be shown using a combination of WAXS, electrochemical characterization, and computational study based on ab initio grand canonical (aiGCMC) simulations that the amorphous intermediate phase favors high rate Na storage in Sb.[2] [1] Wang, L., Welborn, S. S., Kumar, H., Li, M., Wang, Z., Shenoy, V. B., Detsi, E.: High‐Rate and Long Cycle‐Life Alloy‐Type Magnesium‐Ion Battery Anode Enabled Through (De)magnesiation‐Induced Near‐Room‐Temperature Solid–Liquid Phase Transformation. Adv. Energy Mater. 2019, 1902086. https://doi.org/10.1002/aenm.201902086 [2] M. Li, T. Qiu, S. Welborn, A. Foucher, B. Lesel, E. Stach, A. M. Rappe, E. Detsi: Understanding the Fast Kinetics of Sodium Storage in Antimony (unpublished)

Monte-Carlo Simulation Combined with Density Functional Theory to Investigate the Equilibrium Thermodynamics of Electrode Materials: Lithium Titanate As Model Compounds

Thermodynamics of the electrode materials is of interest in understanding their mechanism of electrochemical reactions, which should in turn contribute to designing and developing a new material for rechargeable batteries. While the recent development in the computational power has remarkably advanced the highly accurate electronic structure simulations, such as density functional theory (DFT), it is not always straightforward to extract from those theoretical studies certain insights that are “understood” or “interpreted” in simple terms. One also occasionally comes across the situation where the thermodynamics at the finite temperature T > 0 is beyond the general DFT considerations. Monte-Carlo simulation, on the other hand, tries to describe the physical process at the finite temperature in a simple (or an abstract) manner of which the meaning is clear to understand, although one has to worry if the simple model represents the reality.Dealing with lithium titanate (LiTi2O4 and Li4/3Ti5/3O4, LTO) as a model electrode material, we propose a method to describe its equilibrium thermodynamics based on the Monte-Carlo simulation (MC), for which the energetic parameters are determined by the density functional theory (DFT). The electrochemical potential profile is simulated by a simple topological model which consists only of three parameters representing the Li site energies; namely, the binding energy of the 8a site (ε8a), the difference in the site energy between the 8a and 16c sites (∆ε) and the repulsion between two Li atoms situated at the adjacent 8a and 16c sites (J).Parameter physics by the MC revealed that the term ∆ε plays a decisive role, with a collateral effect from J, for characterizing the thermodynamics of the material whereas the term ε8a determines the electrochemical potential at which the reaction takes place. For instance, if ∆ exceeds the thermal energy at the temperature under consideration, i.e., if ∆ε > 3kT, the first order phase transition takes place during which two phases coexist, resulting in a plateau region in the potential profile. On the other hand, if ∆ε < 3kT, the lithiation of LTO is viewed as a phenomenon above the critical point, above which the material is in a homogeneous uniphasic state.A multiple regression analysis of a set of the total energy of LiTi2O4 calculated by DFT allows us to determine these energetic terms. The MC simulation with the determined parameters well reproduces the shape and position of the experimental potential profile of LTO. Since the determined value, ∆ε/eV ~ 0.4, far exceeds the thermal energy at ambient temperature, the potential plateau of LTO is explained by the first-order phase transition as long as the equilibrium state is concerned. Unlike for LiTi2O4, we were unsuccessful in determining the parameters for Li4/3Ti5/3O4, for which the reason we will briefly address on site.In the paper, the outline of the methodology will be presented, of which the details are available in our recent publication.[1] Reference [1] H. Ozaki, K. Tada and T. Kiyobayashi, Phys. Chem. Chem. Phys., 21, 15551 (2019). Figure Caption Potential profile of LTO. Exp: Li4/3Ti5/3O4 experimentally determined by the galvanostatic intermittent titration test (GITT) during the Li extraction process at T/K = 303. Sim: Result of the grand canonical Monte-Carlo simulation at T/K = 300, for which the energetic parameters were determined by the DFT calculations based on LiTi2O4. The error bar placed in the middle of the potential plateau for the simulated result indicates twice the standard deviation (±2σ) estimated from the multiple regression analysis of the DFT total energy data set. The abscissa is scaled so as to fit the experimental data. Figure 1

Shock compression of vanadium at extremes: Theory and experiment

The equation of state (EOS) and shock compression of bulk vanadium were investigated using canonical ab initio molecular dynamic simulations, with experimental validation to 865 GPa from shock data collected at Sandia's Z Pulsed Power Facility. In simulations the phase space was sampled along isotherms ranging from 3000 K to $50\phantom{\rule{0.16em}{0ex}}000$ K, for densities between $\ensuremath{\rho}=3$ and $15\phantom{\rule{0.16em}{0ex}}\mathrm{g}/{\mathrm{cm}}^{3}$, with a focus on the liquid regime and the body-centered-cubic phase in the vicinity of the melting limit. The principal Hugoniot predicted from first principles is overall consistent with shock data, while it showed that current multiphase SESAME-type EOS for vanadium needed revision in the liquid regime. A more accurate SESAME EOS was developed using constraints from experiments and simulations. This work emphasizes the need to use a combined theoretical and experimental approach to develop high-fidelity EOS models for extreme conditions.

Molecular Simulation Study on Adsorption and Diffusion Behaviors of CO2/N2 in Lignite.

Understanding the adsorption and diffusion of CO2 and N2 in lignite at high temperature is of great significance for fire prevention and control. Considering the influence of temperature on coal structure, molecular structure models of lignite at 298.15, 323.15, 423.15, and 523.15 K were constructed by molecular mechanics and dynamics, and grand canonical Monte Carlo molecular simulation was conducted for single-component and two-component systems under different temperatures, pressures, and gas ratios. The adsorption capacity was positively correlated with the pressure and molar ratio of CO2 but negatively correlated with the temperature. The adsorption amount of CO2 (1.060 mmol/g) was generally larger than that of N2 (0.069 mmol/g), showing a greater selectivity. However, CO2 was more sensitive to temperature, and the adsorption amount decreased faster with the increase in temperature. At high temperature, the adsorption amount of CO2 and N2 is basically equal, both of which are at a low level. The CO2 isosteric heat of adsorption (7.46–8.84 kcal/mol) varies significantly with temperature. The interaction energy is consistent with the change trend of adsorption quantity, and van der Waals energy plays a dominant role in adsorption. Injecting CO2 and N2 at the high temperature stage has a poor extinguishing effect, which can only dilute oxygen content and exchange heat, and the advantage of CO2 will be lost. It may be more effective using liquid nitrogen which has the properties of low temperature and high specific heat capacity. The results are of great significance to improve the efficiency of fire prevention and suppression in underground coal mines.

Titration of Adenine in a GA Mismatch with Grand Canonical Simulations

Computational prediction of the pKa of ionizable groups remains a central challenge in biomolecular modeling. Although all-atom fixed-charge force fields could be accurate to describe the interaction network within the biomolecules, proper sampling techniques are required to obtain the thermodynamic information in the (de)protonation event. Sufficient sampling requires an ensemble of structures from simulations with proper treatments of the acid-base equilibria, and the grand canonical simulation technique could be used to model the growth/annihilation of hydrogen atoms by merging Hamiltonians of different protonation states into one simulation ensemble. The electrostatic feature of nucleotide systems is especially difficult to model, and the situation becomes more challenging when the ionizable site is highly perturbed. Although there are many successful predictions obtained from the grand canonical constant pH simulations, few reports focus on highly perturbed nucleotide systems with unconventional base-pair features. In this work, with the discrete constant pH method, we investigate the titration thermodynamics of an adenine in the catalytic triad in a 35-nucleotide single-stranded RNA hairpin, featuring an unconventional GA mismatch and a substantially shifted pKa value. Validation tests are performed with two system setups, both of which provide pKa predictions in good agreement with the experimental value. A single-configuration-based technique is used to calculate the pKa for comparison. The current success indicates the predictive power of the current nucleotide modeling framework.

Dynamics of gold clusters on ceria during CO oxidation

Modeling the evolution of the active phase in terms of shape and composition in supported catalysts as function of the reaction conditions is an important challenge. Herein, we employ methods rooted in genetic algorithms and grand canonical Monte-Carlo simulations to determine relevant structures of a gold clusters placed on a ceria support in oxygen atmosphere. Based on optimized structures, microkinetics simulations identify relevant structures present under the out-of-equilibrium conditions of the ongoing CO oxidation reaction. The results emphasize the role of cationic gold atoms at the interface between gold and ceria, which bind oxygen atoms strongly. At low temperature and low CO/O2 ratio, the catalytic cycle for a 6-atom gold cluster mainly involves the Au6O3 and Au6O2 couple via the associative O2 mechanism of CO oxidation. At higher CO/O2 ratio and elevated temperature, the Au6O and Au6 couple are the dominant active species.

Understanding the Dehydrogenation Pathways of Ammonium Octahydrotriborate (NH4B3H8) by Molecular Dynamics Simulations with the Reactive Force Field (ReaxFF)

AbstractAmmonium octahydrotriborate (NH4B3H8) is a potential candidate for hydrogen storage, due to its chemical stability and high hydrogen content. To systematically investigate its initial decomposition and dehydrogenation pathways, molecular dynamics simulations with a reactive force field are conducted. Both temperature ramping and the canonical ensemble simulations are carried out. A compositional analysis for the simulated systems is also applied to monitor the possible intermediate products during its decomposition and dehydrogenation processes. At around 1000 K, the molecular hydrogen is released via inter‐molecular interaction between B‐H and N‐H. It is also noticed that the formed NH3 and BH3 can react to generate BN bonds; as the temperature further increases, the isomers with a skeleton of BNB are observed, and the corresponding dehydrogenation is also increased. The present work provides detailed pictures of the decomposition and dehydrogenation pathways for NH4B3H8.

Parallel Prefetching for Canonical Ensemble Monte Carlo Simulations.

In order to enable large-scale molecular simulations, algorithms must efficiently utilize multi-core processors that continue to increase in total core count over time with relatively stagnant clock speeds. Although parallelized molecular dynamics (MD) software has taken advantage of this trend in computer hardware, single-particle perturbations with Monte Carlo (MC) are more difficult to parallelize than system-wide updates in MD using domain decomposition. Instead, prefetching reconstructs the serial Markov chain after computing multiple MC trials in parallel. Canonical ensemble simulations of a Lennard-Jones fluid with prefetching resulted in up to a factor of 1.7 speedup using 2 threads, and a factor of 3 speedup using 4 threads. Strategies for maximizing efficiency of prefetching simulations are discussed, including the potentially counter-intuitive benefit of reduced acceptance probabilities. Determination of the optimal acceptance probability for a parallel simulation is simplified by theoretical prediction from serial simulation data. Finally, complete open-source code for parallel prefetch simulations was made available in the Free Energy and Advance Sampling Simulation Toolkit (FEASST).

Optimal excitation mechanism for combustion enhancement of supersonic shear layers with pulsed jets

Supersonic shear layers (convection Mach number = 0.6) with flow direction excitation are studied by a canonical Large Eddy Simulation (LES) method with quasi-laminar turbulent reaction model. By modulating velocity of central jet through ideal square wave under four excitation periods (τ = 20, 40, 60, and 80 μs), the present study aims to explore the optimal excitation mechanism for combustion enhancement. As the excitation period increases, combustion efficiency tends to increase and then decrease. The maximum combustion efficiency is achieved at τ=40μs, which is nearly four times that in the no excitation scenario. The analysis of mixing characteristics of the nonreacting cases reveals that mixing enhancement mainly explains combustion gain of different excitation modes. From the limiting formation of vortex, the size of the vortex core has fully developed to reach axial contact at τ=40μs. Any further increase in excitation intervals implies a larger vortex spacing, which leads to poor fluid mixing while lower excitation case forms continuous small vortices with less mixing region. The comparison of the circulation decomposition of the main vortex and trailing wakes indicates the pinch-off characteristic of the limiting formation of vortical structure. On the basis of these results, an optimal forcing criterion is proposed according to the limiting vortex formation with dimensionless excitation time scale τ∗≈1.64. This study provides a novel perspective for the optimal combustion enhancement of supersonic shear layers from the aspect of vorticity dynamics.

Exploring the Structure\u2013Activity Relationship on Platinum Nanoparticles

The design of active and stable Pt-based nanoscale electrocatalysts for the oxygen reduction reaction (ORR) plays the central role in ameliorating the efficiency of proton exchange membrane fuel-cells towards future energy applications. On that front, theoretical studies have contributed significantly to this research area by gaining deeper insights and understanding of the ongoing processes. In this work, we present an approach capable of characterizing differently-shaped platinum nanoparticles undergoing thermally- and adsorbate-induced restructuring of the surface. Further, by performing ReaxFF-Grand Canonical Molecular Dynamics simulations we explored the water formation on these roughened (“realistic”) nanoparticles in a H2/O2 environment. Taking into consideration the coverage of oxygen-containing intermediates and occurring surface roughening the nanoparticles’ activities were explored. Hereby, we succeeded in locally resolving the water formation on the nanoparticles’ surfaces, allowing an allocation of the active sites for H2O production. We observed that exposed, low-coordinated sites as well as pit-shaped sites originating from roughening of vertices and edges are most active towards H2O formation.

Fast and accurate determination of phase transition temperature via individual generalized canonical ensemble simulation**Project supported by the National Natural Science Foundation of China (Grant Nos. 11574310, 11674345, and 21733010) and Beijing National Laboratory for Molecular Sciences, China (Grant No. BNLMS201835).

It is very important to determine the phase transition temperature, such as the water/ice coexistence temperature in various water models, via molecular simulations. We show that a single individual direct simulation is sufficient to get the temperature with high accuracy and small computational cost based on the generalized canonical ensemble (GCE). Lennard–Jones fluids, the atomic water models, such as TIP4P/2005, TIP4P/ICE, and the mW water models are applied to illustrate the method. We start from the coexistent system of the two phases with a plane interface, then equilibrate the system under the GCE, which can stabilize the coexistence of the phases, to directly derive the phase transition temperature without sensitive dependence on the applied parameters of the GCE and the size of the simulation systems. The obtained result is in excellent agreement with that in literatures. These features make the GCE approach in determining the phase transition temperature of systems be robust, easy to use, and particularly good at working on computationally expensive systems.

Data-driven Classification and Modeling of Combustion Regimes in Detonation Waves

A data-driven approach to classify combustion regimes in detonation waves is implemented, and a procedure for domain-localized source term modeling based on these classifications is demonstrated. The models were generated from numerical datasets of canonical detonation simulations. In the first phase, delineations of combustion regimes within the detonation wave structure were analyzed through a clustering procedure. The clustering output usefully illuminated distinctions between detonation, deflagration, and intermediary regimes within the wave structure. In the second phase, the resulting delineated fields from the clustering step were used to guide localized source term modeling via artificial neural networks (ANNs), enabling a type of classification-based regression approach for source term estimation. A comparison of the estimations obtained from the local ANNs (trained for a subset of the domain given by a particular cluster) with the global ANN counterparts (trained agnostic to the clustering) showed general improvement of estimations provided by the domain-localized modeling in most cases. Ultimately, this work illuminates the useful role of data-driven classification and regression techniques for both physical analysis of the complex wave structure and for the development of new models which may serve as suitable pathways for long-time simulations of complex combustion systems (such as rotating detonation combustors).

Upgrading Wood Gas Using Bentonite Clay: A Multiscale Modeling and Simulation Study.

Wood gas is the producer gas resulting from gasification of wood biomass and is an important renewable fuel gas in rural areas. This study assessed the capacity of bentonite, a widely used clay mineral, to upgrade wood gas via pressure swing adsorption in order to improve its calorific value (i.e., the amount of energy released per kilogram of gas). Grand canonical Monte Carlo molecular simulations using a self-consistent force field were performed to generate adsorption isotherms for wood gas components—methane, carbon monoxide, carbon dioxide, hydrogen, nitrogen, and oxygen—in montmorillonite (the main crystalline constituent of bentonite) at conditions appropriate to downdraft gasification. The Langmuir adsorption isotherm model was successfully fitted to each component’s adsorption isotherm and was then coupled with a batch equilibrium approach to model a single-stage pressure swing adsorption system with a discharge stream at ambient pressure. A response surface was then computed in terms of the net change in the calorific value as a function of both adsorbent quantity and operating pressure. It was found that the system can improve the calorific value of the gas by over five percent.

Acetonitrile confined in carbon nanotubes, part I: Structure, dynamic and transport properties

In the first part of our study, here an all atom molecular dynamic study on the effect of confinement on structure, dynamic and transport properties of acetonitrile is presented. For this purpose, Single Walled Carbon Nanotubes (SWCNTs) were filled with the acetonitrile by employing isothermal-isobaric ensemble followed by canonical ensemble molecular dynamics simulations for investigating interactions between the acetonitrile and SWCNTs. Several interesting features of the acetonitrile were identified as the diameter of CNTs becomes smaller. First, two distinct regions were identified i.e., a core region along the longitudinal direction dominated by rarefaction effects and an interface shell with relatively high density of fluid. Volume of rarefied region decreases with larger values of tube diameters. Secondly, interfacial mobility in the vicinity fluid-CNT interface favors axial mean squared displacements of the acetonitrile molecules. Analyses also show that radial mobility of the molecules strongly depends on the size of the core region and diameter of the tube whereas the axial self-diffusion coefficient varies almost exponentially with the tube diameter. Thirdly, a preferred coordination between each pair of the C (methyl group carbon), C (nitrile group carbon) and N atoms, and an ordering in the vicinity of wall were observed contrary to those of larger tubes. Fourthly, we observed that the E2g mode frequencies of SWCNT dominates those of C1-C2-N bending and C1-C2 stretching modes. The frequencies of both SWCNTs and those of the fluid are the same in these modes. Lastly, the shear viscosity diminishes with the diameter of the tube.

Crystalline-to-Amorphous Phase Transformations As a Key Ingredient to Enhanced Rate Performance and Cycle Life in Mg- and Na-Ion Battery Anodes: Operando X-Ray Scattering Studies

The increasing popularity of Li-ion batteries in new applications such as electric vehicles is expected to cause the key resources (Li, Ni and Co) used in these batteries to become scarce. Alternative battery technologies, including Mg-ion, Na-ion, and metal-air batteries are therefore desirable. In this talk, I will discuss the use of operando wide-angle X-ray scattering (WAXS) to study the crystalline to amorphous phase transformations that are key to the outstanding performance of state-of-the-art alloy-type Mg- and Na-ion anodes. The 1st part of the talk will be on the impact of the crystalline-to-amorphous transformation on batteries cycle life. Here I will discuss our novel self-healing Ga/Mg anode, which holds the current record for cycle performance and rate capability in alloy-type Mg-ion battery anodes, owing to a crystalline Mg2Ga5 to amorphous liquid Ga phase transformation occurring near room temperature, preventing the well-known pulverization issue in alloy-type anodes.[1] The 2nd part of the talk will detail the impact of the crystalline-to-amorphous transformation on the rate capabilities of batteries. Here, I will present our nanoporous Sb/Na system, which transforms from crystalline Na3Sb to crystalline Sb, going through an amorphous intermediate. It will be shown using a combination of WAXS, electrochemical characterization, and computational study based on ab initio grand canonical (aiGCMC) simulations that the amorphous intermediate phase favors high rate Na storage in Sb.[2][1] Wang, L., Welborn, S. S., Kumar, H., Li, M., Wang, Z., Shenoy, V. B., Detsi, E.: High‐Rate and Long Cycle‐Life Alloy‐Type Magnesium‐Ion Battery Anode Enabled Through (De)magnesiation‐Induced Near‐Room‐Temperature Solid–Liquid Phase Transformation. Adv. Energy Mater. 2019, 1902086. https://doi.org/10.1002/aenm.201902086 [2] M. Li, T. Qiu, S. S. Welborn, A. Foucher, B. Lesel, E. Stach, A. M. Rappe, E. Detsi: Understanding the Fast Kinetics of Sodium Storage in Antimony (unpublished)

The Henry constant and isosteric heat at zero loading for adsorption on energetically heterogeneous solids absolute versus excess

We present a self-consistent analysis of adsorption of gases on energetically heterogeneous solids and derive expressions for the Henry constant and the isosteric heat at zero loading, qst(0), for both excess and absolute amounts of molecules; the latter being amenable to thermodynamic analysis. Results obtained by Monte Carlo integration are shown to depend on the system size for calculations using the total number of molecules in the adsorbed and gas phases of the system. In the limit when loading approaches zero, the thermodynamic variables obtained from the fluctuation theory in a grand canonical simulation are in agreement with the Henry constant and the isosteric heat at zero loading calculated from Monte Carlo integration, establishing the consistency of the analysis of isotherm and isosteric heat for the full range of loading. The equations for the isotherm (and the Henry constant), and the isosteric heat for a complex substrate, can be written in terms of the local isotherms and the local isosteric heats of the components comprising the substrate for all loadings. This results in a significant saving in computing time for the calculation of the thermodynamic variables of a complex substrate.

Steady state dynamic dependence between local mobility and non-affine fluctuations in two-dimensional aggregates

Motivated by qualitative experimental observations in collective behavior of self-propelled camphor particles at air-water interfaces, we study a generic aggregate forming system in two dimensions using canonical ensemble constant temperature molecular dynamics simulation. The aggregates form due to the competition between short-range attraction and long-range repulsion of pair-wise interactions as a generic proxy for the specific case of short-range capillary attraction competing with long-range Marangoni-assisted repulsion in camphor boat systems. Choosing the appropriate set of interaction parameters, we focus on characterising the local dynamics in two specific limiting morphologies, viz. compact and string-like aggregates. We focus on the temporal evolution of the mobility of an individual particle and the dynamic change in its nearest neighbourhood, measured in terms of the Debye–Waller factor () and the non-affine parameter (), respectively (both defined in the text), and their interrelation over several lengths of observation time . The distribution for both measures are found to follow the relation: for the measured quantity x. The exponent is equal to two and one respectively, for the compact and string-like morphologies following the respective ideal fractal dimension of these aggregates. A functional dependence between these two observables is determined from a detailed statistical analysis of their joint and conditional distributions. The results obtained can readily be used and verified by experiments on aggregate forming systems more generic than the specific camphor boat system that motivated us, such as globular proteins, nanoparticle self-assembly etc. Further, the insights gained from this study might be useful to understand the evolution of collective dynamics in diverse glass-forming systems.