Isotropic Potential Research Articles

On the formation of structural states in dusty plasmas

The paper considers the basis of the approach used to study the response of dusty plasma clusters of various compositions in confining fields of various configurations. The problem statement and analysis are based on the concepts of physical mesomechanics. For an external confining field an electric field and gravity force combination is used. Calculations were performed in the framework of molecular dynamics. The interparticle interaction is described by the Debye-Hiickel pair isotropic potential. The charge of dust particles is calculated using the orbital motion limited theory. The parameters of the field configuration are determined with the use of experimental data. Calculations of both the structure of a formed dusty plasma cluster and the characteristic spacings of dust particles agree well with available experimental data. The emphasis in the paper is on the dependence of the structure and shape of dusty plasma clusters on the number of dust particles in confining fields of varying anisotropy. It is shown that in the crystalline state, dust particles form a Coulomb ball with a shell structure in an isotropic external field. It is pointed out that dusty plasma clusters can transform from the bulk to plane state. In the crystalline state, both plane and bulk dusty plasma clusters have a shell structure; however in the anisotropic state, their structure becomes more complex and split.

Softness dependence of the anomalies for the continuous shouldered well potential

By molecular dynamic simulations we study a system of particles interacting through a continuous isotropic pairwise core-softened potential consisting of a repulsive shoulder and an attractive well. The model displays a phase diagram with three fluid phases: a gas-liquid critical point, a liquid-liquid critical point, and anomalies in density, diffusion, and structure. The hierarchy of the anomalies is the same as for water. Here we study in a systematic way the effect on the anomalies of varying the softness of the potential. We find that, making the soft-core steeper and more penetrable, the regions of density and diffusion anomalies contract in the T-rho plane, while the region of structural anomaly is weakly affected. Therefore, a liquid can have anomalous structural behavior without having density or diffusion anomalies. We show that, by considering as effective distances those corresponding to the maxima of the first two peaks of the radial distribution function g(r) in the high-density liquid, we can generalize to continuous two-scale potentials a criterion for the occurrence of the anomalies of density and diffusion, originally proposed for discontinuous potentials. However, we observe that the knowledge of the structural behavior within the first two coordination shells of the liquid is not enough to establish, in general, the occurrence of the anomalies. By introducing the density derivative of the cumulative order integral of the excess entropy, measuring shell by shell the amount of order in the liquid, we show that the anomalous behavior is regulated by the structural order at distances as large as the fourth coordination shell. By comparing the results for different softness of the potential, we conclude that the disappearance of the density and diffusion anomalies for the steeper potentials is due to a more structured short-range order. All these results increase our understanding on how, knowing the interaction potential, we can evaluate the possible presence of anomalies for a liquid.

Isotropic soft-core potentials with two characteristic length scales and anomalous behaviour

Isotropic soft-core potentials with two characteristic length scales have been used since 40 years ago to describe systems with polymorphism. In the recent years intense research is showing that these potentials also display polyamorphism and several anomalies, including structural, diffusion and density anomaly. These anomalies occur in a hierarchy that resembles the anomalies of water. However, the absence of directional bonding in these isotropic potentials makes them different from water. Other systems, such as colloidal suspensions, protein solutions or liquid metals, can be well described by this family of potentials, opening the possibility of studying the mechanism generating the polyamorphism and anomalies in these complex liquids.

Energy Landscapes of Clusters Bound by Short‐Ranged Potentials

The study of atomic and molecular clusters has long been an active research field for both experimentalists and theoreticians. For atomic clusters bound by simple isotropic potentials detailed predictions of the structure, dynamics and thermodynamics are often available from calculations. [1–4] Many of these properties are unique to the finite size regime, including systems with melting points above the bulk value, [5] and negative microcanonical heat capacities. [6] Making detailed connections between theory and experiment can be problematic, but often leads to important new insights. For example, ingenious experiments to probe the thermodynamics of gas phase sodium clusters [7–10] have provided new benchmarks for comparison with calculations. [11, 12] Recent work by Meng et al. provides new data for the properties of clusters in the mesoscopic regime. [13, 14] Using colloidal particles of polystyrene microspheres as “pseudoatoms”, these authors have obtained direct structural information from optical microscopy. The ability to distinguish different geometries provides details for comparison with calculations based on model potentials. In particular, the probability distribution for alternative structures can be obtained from the occurrence frequencies based on thousands of isolated clusters contained in “microwells” that minimise the cluster–surface interaction. The prospect of comparisons with structural “phase diagrams” predicted from theory [15] is particularly exciting. The colloids studied by Meng et al. are bound by attractive forces that result from a depletion interaction with a range of about 1.05 times the particle diameter and a pair well depth of around 4kBT, [13] where T is the temperature and kB is Boltzmann’s constant. The effective range of the potential, compared to the pair equilibrium separation, is therefore very short. A similar effect occurs for clusters of C60 molecules due to the excluded volume of the fullerene cage. The properties of both clusters and bulk phase C60 can be understood by analysing how the strain energy caused by nearest-neighbour contacts that deviate from the optimal pair separation varies with the range of the potential. [16, 17] Unstrained, close-packed geometries are favoured for C60 clusters, rather than icosahedra and polytetrahedral arrangements. [18–22] Bulk liquid C60 is desta

On the local virial theorems for linear and isotropic harmonic oscillator potentials in d dimensions

For the system of noninteracting fermions in a one-body potential , the local virial theorems (LVT) are relations, at a given point in space, between this potential, kinetic energy and particle densities. It was recently shown (Brack et al 2010 J. Phys. A: Math. Theor. 43 255204) that for d-dimensional linear and also for isotropic harmonic oscillator potentials these LVTs are exactly satisfied. We present alternative and simple proofs of these theorems, by consideration of the canonical or Bloch density matrix and its relation to the kinetic energy density. The explicit analytical forms of the Bloch density matrix are used for the above-mentioned potentials to achieve the proofs. For the case of linear potential, we obtain a more general result for the so-called semilocal virial theorem, and for the harmonic oscillator potential case we derive a new relationship between the diagonal part of the canonical bloch density and the kinetic energy density.

Dispersion interactions and reactive collisions of ultracold polar molecules

Progress in ultracold experiments with polar molecules requires a clear understanding of their interactions and reactivity at ultralow collisional energies. Two important theoretical steps in this process are the characterization of interaction potentials between molecules and the modeling of the reactive scattering mechanism. Here, we report on the ab initio calculation of isotropic and anisotropic van der Waals interaction potentials for polar KRb and RbCs colliding with each other or with ultracold atoms. Based on these potentials and two short-range scattering parameters, we then develop a single-channel scattering model with flexible boundary conditions. Our calculations show that, at low temperatures (and in the absence of an external electric field), the reaction rates between molecules or between molecules and atoms have a resonant character as a function of the short-range parameters. We also find that both the isotropic and anisotropic van der Waals coefficients have significant contributions from dipole coupling to excited electronic states. Their values can differ dramatically from those solely obtained from the permanent dipole moment. A comparison with recently obtained reaction rates of fermionic 40K87Rb shows that the experimental data cannot be explained by a model where the short-range scattering parameters are independent of the relative orbital angular momentum or partial wave.

Argon Solid Response upon Rydberg Photoexcitation of the NO Chromosphore: Case of Using ab Initio Potential Energy Surfaces and Comparison to Similar Studied Systems

Molecular dynamics simulations of NO-doped Ar solid upon Rydberg photoexcitation of the impurity have been carried out taking into account angular dependent potential energy surfaces (PESs) in the ground and excited states. To go beyond isotropic potentials simulations, the effects of anisotropy of potentials on the structure, dynamics, and energetics are investigated by taking into account two cases, namely, the whole PESs and the isotropic parts. Results have been compared to those obtained in previous works for similar NO-doped rare gas systems. Radial distribution functions (RDF) for the ground and excited state indicate that for both cases the shell structure of the lattice is kept ordered and is characterized by well-defined bands. No influence of the anisotropy of potentials has been detected in the RDFs since the anisotropy is rather manifested at short distances. The well part, which has been proven to be unimportant for the dynamics in previous works, arises here to be important for the right simulation of the spectrum. In general, our results show a reasonable agreement with respect to the experimental values for the dynamics and energetics when ab initio potentials are used, although better results can be obtained if higher level ab initio PESs are used.

Analysis of pair interparticle interaction in nonideal dissipative systems

A new method is proposed for determining the interaction forces between particles in nonideal dissipative systems with isotropic pair potentials. The method is based on the solution of the inverse problem describing the motion of interacting particles by a system of Langevin equations and allows one to recover the parameters of the external confining potential without referring to a priori information on the friction coefficients of the particles. This procedure was tested by a numerical simulation of the problem in a wide range of parameters typical of experimental conditions in a laboratory dusty plasma. The results of the first experimental approbation of the method as applied to the analysis of the interaction of dust particles in a laboratory high-frequency capacitive discharge plasma are presented.

A First Principles Development of a General Anisotropic Potential for Polycyclic Aromatic Hydrocarbons.

Standard empirical atom-atom potentials are shown to be unable to describe the binding of polycyclic aromatic hydrocarbon (PAH) molecules in the variety of configurations seen in clusters. The main reason for this inadequacy is the lack of anisotropy in these potentials. We have constructed an anisotropic atom-atom intermolecular potential for the benzene molecule from first principles using a symmetry-adapted perturbation theory based on density functional theory (SAPT(DFT)), interaction energy calculations and the Williams-Stone-Misquitta method for obtaining molecular properties in distributed form. Using this potential as a starting point, we have constructed a transferable anisotropic potential to model intermolecular interactions between PAHs. This new potential has been shown to accurately model interaction energies for a variety of dimer configurations for four different PAH molecules, including certain configurations which are poorly modeled with current isotropic potentials. It is intended that this potential will form the basis for further work on the aggregation of PAHs.

Equation of state for gaseous ethane determined from isotropic model potentials

A four-term virial equation of state was combined with isotropic model potentials to predict accurate volu- metric and caloric thermodynamic properties of ethane in the gas phase. The parameters of the model potentials were determined from a fit to speed-of-sound data alone; no other data were used. The approximation used for the fourth virial coefficient included all interactions that contain up to two triplet potentials. Predicted ordinary second and third virial coefficients are in agreement with the data of Funke et al. (8); we believe that predicted fourth virial coefficients are reliable and accurate. In the subcritical temperature region, the equation of state predicted compressibility factors that deviate by less than 0.04 percent at densities of up to 2.7 mol/dm 3 (≈0.4ρc). At supercritical temperatures, com- pressibility factors deviate by less than 0.02 percent at densities of up to 2.6 mol/dm 3 ; also, in this region predicted isobaric heat capacity agrees with available data to within uncertainties of 0.4 percent at densities above 3 mol/dm 3 . We demonstrated that the four-term virial equation is more accurate than the three-term analogue.

Equation of state for gaseous nitrogen determined from isotropic model potentials

AbstractA four‐term virial equation of state was combined with isotropic potential models to predict accurate volumetric and caloric thermodynamic properties of nitrogen in the gas phase. The parameters of the model potentials were determined from a fit to acoustic data alone; no other data was used. For nitrogen, it was only necessary to approximate the fourth virial coefficient at the level of interactions that contained no more than one triplet potential; higher order approximations offered no further advantage. It was shown that the four‐term virial equation was more accurate than the three‐term analogue. It was found that predicted virial coefficients became consistent with experimental values when temperature was >150 ± 30 K; conversely, below this range virial coefficients predicted by the model did not agree with experiment. It was believed that predicted fourth virial coefficient was reliable and accurate only above about 150 K. Predicted compressibility factors deviated by <0.05% at pressures of up to 10–12 MPa, or densities up to 4 mol/dm3 (≈0.4ρc), only when temperature was >220 K. Values of enthalpy predicted from the equation of state showed good agreement with experimental data.

Thermodynamic characteristics of two-dimensional fluids with isotropic pair interaction potentials

A simple semi-empirical approximation of the energy density in two-dimensional liquids is proposed for the different types of isotropic pair potentials, commonly used for simulation of repulsion in kinetics of interacting particles. Coefficients of this approximation were obtained by the best fitting of the numerical data by the suggested analytical function. The proposed analytical expression of the energy density may be used for determination of any thermodynamic functions using the known formulae of thermodynamics. Comparisons of theoretical results with the numerical data are presented.

Theoretical study on self-assembly in organic materials

Theoretical work related to the self-assembly of organic materials was dealt with, and the various mechanisms leading to self-assembly, such as transition metal mediated self-assembly, constraint induced self-assembly, covalent bond based self-assembly and van der Waals interaction driven self-assembly, etc., were discussed. The formation of ordered structures could be attributed to the competition between short range attractive forces and long-range repulsion, which was arising from dipole interaction or may result from a different mechanism based on a purely repulsive isotropic short-range pair potential with two characteristic length scales. Such mechanism could be exploited in the study of self-assembly process. First principles SAPT(DFT) interaction energy calculations, combined with the Williams-Stone-Misquitta method, offer the ability to improve the molecular dynamics (MD) accuracy which could in turn be used in the prediction of crystal structures and self-assembly tendency. The combination of experimental and theoretical studies could open new breakthroughs over the design, synthesis, and characterization of self-assembled materials.

MOMENTUM MAPS, INDEPENDENT FIRST INTEGRALS AND INTEGRABILITY FOR CENTRAL POTENTIALS

It is shown that all the motions of a natural Hamiltonian H(q, p) = ½‖p‖2+V(q) lie on planes through 0 ∈ Rn if and only if V is a central potential, i.e. H admits SO(n) symmetry. Then, using the momentum maps associated to their natural symmetry groups, we study in detail the functional independence of first integrals of a general central potential, of the isotropic harmonic potential and of the Kepler potential. We show that all the smooth first integral of the isotropic harmonic oscillator are dependent of the angular momentum tensor L and of the Fradkin tensor H, and that all the smooth first integrals of the Kepler system on the region of negative energy are dependent of the angular momentum tensor L and of the Laplace–Runge–Lenz vector B.

A finite element framework for continnua with boundary potentials

AbstractThis contribution deals with the implications of the anisotropic boundary potential energies on deformational mechanics in the framework of the two‐dimensional finite element method at finite strains. In the first part of this work ([6])) only the isotropic boundary potentials were considered, however, in this contribution we allow for the anisotropic contributions from the boundary energies, too. The boundary effects sometimes play a dominant role in the material behavior, e.g. surface tension in fluids. The boundary potentials, in general, are allowed to depend not only on the boundary deformation gradient but also on the spatial curve‐tangent, as well. For the finite element implementation, a suitable curvilinear coordinate system attached to the boundary is defined and corresponding derivations are carried out. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Finite-temperature dynamics of a single vortex in a Bose-Einstein condensate: Equilibrium precession and rotational symmetry breaking

We consider a finite-temperature Bose-Einstein condensate in a quasi-two-dimensional trap containing a single precessing vortex. We find that such a configuration arises naturally as an ergodic equilibrium of the projected Gross-Pitaevskii equation, when constrained to a finite conserved angular momentum. In an isotropic trapping potential, the condensation of the classical field into an off-axis vortex state breaks the rotational symmetry of the system. We present a methodology to identify the condensate and the Goldstone mode associated with the broken rotational symmetry in the classical-field model. We also examine the variation in vortex trajectories and thermodynamic parameters of the field as the energy of the microcanonical field simulation is varied.

Technique for analysis of interparticle interaction in nonideal dissipative systems with isotropic pair potentials

A new technique for determining interaction forces between the particles in nonideal dissipative systems with isotropic pair potentials is presented. This technique is based on solving of the inverse problem describing movement of dust particles by a system of Langevin equations. Numerical simulations in a wide range of the parameters typical for dusty plasma experiments were performed to verify the solutions of inverse problem.

Role of the Range in the Fluid−Crystal Coexistence for a Patchy Particle Model

We evaluate the phase diagram of the four-site Kern-Frenkel patchy particle model [Kern, N.; Frenkel, D. J. Chem. Phys. 2003, 118, 9882.], a model representative of particles interacting via short-range orientational interactions, for several values of the interaction range. Similar to what has been found for isotropic potentials, the liquid phase disappears as an equilibrium phase for values of the range on the order of 15% of the particle diameter. For smaller ranges, the gas-liquid phase separation becomes metastable with respect to crystallization into a diamond-like structure. Interestingly, and differently from the isotropic case, the supersaturation of the fluid at the critical point does not significantly increase upon going toward the adhesive (vanishing interaction range) limit.

On the Local Relaxation of Solid Neon upon Rydberg Excitation of a NO Impurity: The Role of the NO(A)−Ne Interaction Potential and Zero-Point Quantum Delocalization

The local relaxation of solid neon subsequent to the impulsive excitation of the NO chromophore to its A(3s sigma) Ryberg state is investigated using molecular dynamics simulations. This study makes use of empirical NO(X,A)-Ne isotropic pair potentials as well as a recently developed ab initio triatomic potential energy surface for the excited state. The role of these interaction potentials is analyzed, including many-body effects. In particular, empirical potentials, designed to reproduce correctly both the NO X-A steady-state absorption and emission bands, are shown to lead to a good description of the subpicosecond relaxation dynamics. The 600 fs expansion of the electronic bubble fairly agrees with experimental data. This relatively long time scale with respect to solid Argon, which was previously attributed to the range of the NO(A)-Ne interaction, is presumably related to the quantum nature of the medium. The time-resolved local relaxation of the Ne solid is understandably intermediate between that of classical solids (e.g., Ar) and that of quantum solids (e.g., H(2)).

Classical isotropic two-body potentials generating martensitic transformations

An isotropic interaction potential for classical particles is devised in such a way thatthe crystalline ground state of the system changes discontinuously when someparameter of the potential is varied. Using this potential we model martensitictransformations, and are able to study in detail the processes that are usuallyassociated with them: the shape memory effect and superelasticity, as well asmany details concerning the dynamics of the transformations, particularly thecharacteristics of the martensitic texture obtained as a function of parameters affecting thetransformation rate. Here we introduce the interaction potentials and present some basicresults concerning the transformations that they can be used to describe, for theparticular cases of two-dimensional triangular–rhombohedral and triangular–squaretransformations.