Search Results (13)

An accurate description of short-range interactions among atoms is crucial for simulating irradiation effects in applications related to ion modification techniques. A smooth integration of the Ziegler–Biersack–Littmark (ZBL) potential with the adaptive intermolecular reactive empirical bond-order (AIREBO) potential was achieved to accurately describe the short-range interactions for carbon-based materials. The influence of the ZBL connection on potential energy, force, and various AIREBO components, including reactive empirical bond-order (REBO), Lennard–Jones (LJ), and the torsional component, was examined with configurations of the dimer structure, tetrahedron structure, and monolayer graphene. The REBO component is primarily responsible for the repulsive force, while the LJ component is mainly active in long-range interactions. It is shown that under certain conditions, the torsional energy can lead to a strong repulsive force at short range. Molecular dynamics simulations were performed to study the collision process in configurations of the C-C dimer and bulk graphite. Cascade collisions in graphite with kinetic energies of 1 keV and 10 keV for primary knock-on atoms showed that the short-range description can greatly impact the number of generated defects and their morphology. Full article

Complex networks is a growing discipline aimed at understanding large interacting systems. One of its goals is to establish a relation between the interactions of a system and the networks structure that emerges. Taking a Lennard-Jones particle system as an example, we show that when interactions are governed by a potential, the notion of structure given by the physical arrangement of the interacting particles can be interpreted as a binary approximation to the interaction potential. This approximation simplifies the calculation of the partition function of the system and allows to study the stability of the interaction structure. We compare simulated results with those from the approximated partition function and show how the network and system perspective complement each other. With this, we draw a direct connection between the interactions of a molecular system and the network structure it forms and assess the degree to which it describes the system. We conclude by discussing the advantages and limitations of this method for weighted networks, as well as how this concept might be extended to more general systems. Full article

Umbrella Sampling Molecular Dynamics has been used to determine transition energies for different guest molecules through hydroquinone $\beta$-clathrate nanochannels, as well as their temperature trend. This clathrate has been shown to successfully enclathrate different types of small gases with remarkable selectivity, and thus it has been proposed as a potential gas separation and storage medium. Most of these potential guest gases can be successfully modeled as single Lennard–Jones spheres. Then, to obtain a general view of diffusion probabilities for different potential guest molecules, a comparative study for different virtual guest molecules described by different Lennard–Jones parameters has been performed. A regular temperature trend has been obtained for the transition energies for the molecular model characteristic parameter range explored. Finally, to locate the transition energy values of real gases within the space of phases explored, calculations have been repeated for molecular models of different noble gases and H${}_2$. The correlation results presented allow a wide interpolation ability for determining the transition energies of potential guest molecules stored or diffusing through the nanochannels of the studied clathrate structure. Full article

We present a numerical study of the asymmetric dumbbell model consisting of “molecules” constructed as two different-sized Lennard-Jones spheres connected by a rigid bond. In terms of the largest (A) particle radius, we report data for the structure and dynamics of the liquid phase for the bond lengths 0.05, 0.1, 0.2, and 0.5, and analogous data for the plastic-crystal phase for the bond lengths 0.05, 0.1, 0.2, and 0.3. Structure is probed by means of the AA, AB, and BB radial distribution functions. Dynamics is probed via the A and B particle mean-square displacement as functions of time and via the rotational time-autocorrelation function. Consistent with the systems’ strong virial potential-energy correlations, the structure and dynamics are found to be isomorph invariant to a good approximation in reduced units, while they generally vary considerably along isotherms of the same (20%) density variation. Even the rotational time-autocorrelation function, which due to the constant bond length is not predicted to be isomorph invariant, varies more along isotherms than along isomorphs. Our findings provide the first validation of isomorph-theory predictions for plastic crystals for which isomorph invariance, in fact, is found to apply better than in the liquid phase of asymmetric-dumbbell models. Full article

Physical aging deals with slow property changes over time caused by molecular rearrangements. This is relevant for non-crystalline materials such as polymers and inorganic glasses, both in production and during subsequent use. The Narayanaswamy theory from 1971 describes physical aging—an inherently nonlinear phenomenon—in terms of a linear convolution integral over the so-called material time $\xi$. The resulting “Tool–Narayanaswamy (TN) formalism” is generally recognized to provide an excellent description of physical aging for small, but still highly nonlinear, temperature variations. The simplest version of the TN formalism is single-parameter aging according to which the clock rate $d\xi /dt$ is an exponential function of the property monitored. For temperature jumps starting from thermal equilibrium, this leads to a first-order differential equation for property monitored, involving a system-specific function. The present paper shows analytically that the solution to this equation to first order in the temperature variation has a universal expression in terms of the zeroth-order solution, $R_0\left(t\right)$. Numerical data for a binary Lennard–Jones glass former probing the potential energy confirm that, in the weakly nonlinear limit, the theory predicts aging correctly from $R_0\left(t\right)$ (which by the fluctuation–dissipation theorem is the normalized equilibrium potential-energy time-autocorrelation function). Full article

The objective of this paper is to investigate the convergence of coupling-parameter expansion-based solutions to the Ornstein–Zernike equation in liquid state theory. The analytically solved Baxter’s adhesive hard sphere model is analyzed first by using coupling-parameter expansion. It was found that the expansion provides accurate approximations to solutions—including the liquid-vapor phase diagram—in most parts of the phase plane. However, it fails to converge in the region where the model has only complex solutions. Similar analysis and results are obtained using analytical solutions within the mean spherical approximation for the hardcore Yukawa potential. However, numerical results indicate that the expansion converges in all regions in this model. Next, the convergence of the expansion is analyzed for the Lennard-Jones potential by using an accurate density-dependent bridge function in the closure relation. Numerical results are presented which show convergence of correlation functions, compressibility versus density profiles, etc., in the single as well as two-phase regions. Computed liquid-vapor phase diagrams, using two independent schemes employing the converged profiles, compare excellently with simulation data. The results obtained for the generalized Lennard-Jones potential, with varying repulsive exponent, also compare well with the simulation data. Solution-spaces and the bifurcation of the solutions of the Ornstein–Zernike equation that are relevant to coupling-parameter expansion are also briefly discussed. All of these results taken together establish the coupling-parameter expansion as a practical tool for studying single component fluid phases modeled via general pair-potentials. Full article

Molecular dynamic simulations of polyacrylic acid polyelectrolyte (PAA) analyzed its interaction with the main minerals that make up characteristic tailings of the mining industry, in this case, quartz, kaolinite, and montmorillonite. The simulations were carried out with the package Gromacs 2020.3. The interaction potentials used were General AMBER Force Field (GAFF) for PAA and CLAYFF-MOH for mineral surfaces. The SPC/E model described water molecules and Lennard-Jones 12-6 parameters adjusted for SPC/E model were used for Na⁺ and Cl⁻ ions. The studied systems were carried out at pH 7, obtaining stable adsorption between the PAA and the studied surfaces. Interestingly, the strongest adsorptions were for montmorillonite at both low and high salt concentrations. The effect of salinity differs according to the system, finding that it impairs the absorption of the polymer on montmorillonite surfaces. However, a saline medium favors the interaction with quartz and kaolinite. This is explained because montmorillonite has a lower surface charge density and a greater capacity to adsorb ions. This facilitated the adsorption of PAA. It was possible to identify that the main interaction by which the polymer is adsorbed is through the hydroxyl of the mineral surface and the COO⁻Na⁺ complexes. Molecular dynamics allows us to advance in the understanding of interactions that define the behavior of this promising reagent as an alternative for sustainable treatment of complex tailings in highly saline environments. Full article

We present a combined experimental and theoretical investigation on Ca${}^{+}$ ions in helium droplets, He${}_N$Ca${}^{+}$. The clusters have been formed in the laboratory by means of electron-impact ionization of Ca-doped helium nanodroplets. Energies and structures of such complexes have been computed using various approaches such as path integral Monte Carlo, diffusion Monte Carlo and basin-hopping methods. The potential energy functions employed in these calculations consist of analytical expressions following an improved Lennard-Jones formula whose parameters are fine-tuned by exploiting ab initio estimations. Ion yields of He${}_N$Ca${}^{+}$ -obtained via high-resolution mass spectrometry- generally decrease with N with a more pronounced drop between $N=17$ and $N=25$, the computed quantum He${}_N$Ca${}^{+}$ evaporation energies resembling this behavior. The analysis of the energies and structures reveals that covering Ca${}^{+}$ with 17 He atoms leads to a cluster with one of the smallest energies per atom. As new atoms are added, they continue to fill the first shell at the expense of reducing its stability, until $N=25$, which corresponds to the maximum number of atoms in that shell. Behavior of the evaporation energies and radial densities suggests liquid-like cluster structures. Full article

Understanding of CO₂ hydrate–liquid water two-phase equilibrium is very important for CO₂ storage in deep sea and in submarine sediments. This study proposed an accurate thermodynamic model to calculate CO₂ solubility in pure water and in seawater at hydrate–liquid water equilibrium (HL_WE). The van der Waals–Platteeuw model coupling with angle-dependent ab initio intermolecular potentials was used to calculate the chemical potential of hydrate phase. Two methods were used to describe the aqueous phase. One is using the Pitzer model to calculate the activity of water and using the Poynting correction to calculate the fugacity of CO₂ dissolved in water. Another is using the Lennard–Jones-referenced Statistical Associating Fluid Theory (SAFT-LJ) equation of state (EOS) to calculate the activity of water and the fugacity of dissolved CO₂. There are no parameters evaluated from experimental data of HL_WE in this model. Comparison with experimental data indicates that this model can calculate CO₂ solubility in pure water and in seawater at HL_WE with high accuracy. This model predicts that CO₂ solubility at HL_WE increases with the increasing temperature, which agrees well with available experimental data. In regards to the pressure and salinity dependences of CO₂ solubility at HL_WE, there are some discrepancies among experimental data. This model predicts that CO₂ solubility at HL_WE decreases with the increasing pressure and salinity, which is consistent with most of experimental data sets. Compared to previous models, this model covers a wider range of pressure (up to 1000 bar) and is generally more accurate in CO₂ solubility in aqueous solutions and in composition of hydrate phase. A computer program for the calculation of CO₂ solubility in pure water and in seawater at hydrate–liquid water equilibrium can be obtained from the corresponding author via email. Full article

In a recent paper [S. Khrapak, Molecules 25, 3498 (2020)], the longitudinal and transverse sound velocities of a conventional Lennard–Jones system at the liquid–solid coexistence were calculated. It was shown that the sound velocities remain almost invariant along the liquid–solid coexistence boundary lines and that their magnitudes are comparable with those of repulsive soft-sphere and hard-sphere models at the fluid–solid phase transition. This implies that attraction does not considerably affect the magnitude of the sound velocities at the fluid–solid phase transition. This paper provides further evidence to this by examining the generalized Lennard–Jones (n − 6) fluids with n ranging from 12 to 7 and demonstrating that the steepness of the repulsive term has only a minor effect on the magnitude of the sound velocities. Nevertheless, these minor trends are identified and discussed. Full article

In this paper, we consider the problem of characterizing the minimum energy configurations of a finite system of particles interacting between them due to attractive or repulsive forces given by a certain intermolecular potential. We limit ourselves to the cases of three particles arranged in a triangular array and that of four particles in a tetrahedral array. The minimization is constrained to a fixed area in the case of the triangular array, and to a fixed volume in the tetrahedral case. For a general class of intermolecular potentials we give conditions for the homogeneous configuration (either an equilateral triangle or a regular tetrahedron) of the array to be stable that is, a minimizer of the potential energy of the system. To determine whether or not there exist other stable states, the system of first-order necessary conditions for a minimum is treated as a bifurcation problem with the area or volume variable as the bifurcation parameter. Because of the symmetries present in our problem, we can apply the techniques of equivariant bifurcation theory to show that there exist branches of non-homogeneous solutions bifurcating from the trivial branch of homogeneous solutions at precisely the values of the parameter of area or volume for which the homogeneous configuration changes stability. For the triangular array, we construct numerically the bifurcation diagrams for both a Lennard–Jones and Buckingham potentials. The numerics show that there exist non-homogeneous stable states, multiple stable states for intervals of values of the area parameter, and secondary bifurcations as well. Full article

The formation of crystals and symmetry on the atomic scale has persistently attracted scientists through the ages. The structure itself and its subtle dependence on boundary conditions is a reflection of three principles: atomic attraction, repulsion, and the limitations in 3D space. This involves a competition between simplicity and high symmetry on the one hand and necessary structural complexity on the other. This work presents a simple atomistic crystal growth model derived for equivalent atoms and a pair potential. It highlights fundamental concepts, most prominently provided by a maximum number of equilibrium distances in the atom’s local vicinity, to obtain high symmetric structural motifs, among them the Platonic Solids. In this respect, the harmonically balanced interaction during the atomistic nucleation process may be regarded as origin of symmetry. The minimization of total energy is generalized for 3D periodic structures constituting these motifs. In dependence on the pair potential’s short- and long-range characteristics the, by symmetry, rigid lattices relax isotropically within the potential well. The first few coordination shells with lattice-specific fixed distances do not necessarily determine which equilibrium symmetry prevails. A phase diagram calculated on the basis of these few assumptions summarizes stable regions of close-packed fcc and hcp, next to bcc symmetry for predominantly soft short-range and hard long-range interaction. This lattice symmetry, which is evident for alkali metals as well as transition metals of the vanadium and chromium group, cannot be obtained from classical Morse or Lennard-Jones type potentials, but needs the range flexibility within the pair potential. Full article

Nanoporous “Raney gold” sponge was prepared by de-alloying an Au-Al precursor alloy. Catalytic tests using a micro-reactor confirmed that Raney gold can serve as an active heterogeneous catalyst for CO oxidation, reduction of NO to N₂, and oxidation of NO to NO₂. In general, the specific surface area of a heterogeneous catalyst has an influence on its catalytic efficacy. Unfortunately, gold sponges coarsen readily, leading to sintering of their structure and reduction in surface area. This potentially places constraints on their upper operating temperature in catalytic reactors. Here we analyzed the behavior of Raney gold when the temperature was raised. We examined the kinetics and mechanism of coarsening of the sponge using a combination of in situ optical measurements and Metropolis Monte Carlo modeling with a Lennard-Jones interatomic potential. Modeling showed that the sponges started with an isotropic “foamy” morphology with negative average “mean curvature” but that subsequent thermally activated coarsening will drive the morphology through a bi-continuous fibrous state and on, eventually, to a sponge consisting of sintered blobs of predominantly positive “mean curvature”. Full article