Modified Morse Potential Research Articles

Thermoelectric Properties of a Monolayer Bismuth

The structural and electronic properties of a two-dimensional monolayer bismuth are studied using density functional calculations. It is found that the monolayer forms a stable low-buckled hexagonal structure, which is reminiscent of silicene. The electronic transport properties of the monolayer bismuth are then evaluated by using Boltzmann theory with the relaxation time approximation. By fitting first-principles total energy calculations, a modified Morse potential is constructed, which is used to predicate the lattice thermal conductivity via equilibrium molecular dynamics simulations. The room temperature ZT value of a monolayer bismuth is estimated to be 2.1 and 2.4 for the n- and p-type doping, respectively. Moreover, the temperature dependence of ZT is investigated and a maximum value of 4.1 can be achieved at 500 K.

Nonlinear Multi-Scale Finite Element Method to Predict Tensile Behavior of Carbon Nanotube-Reinforced Polymer Composites

The ability of carbon nanotubes (CNTs) to consider as the strongest and stiffest elements in nanoscale composites remains a powerful motivation for the research in this area. This paper describes a finite element (FE) approach for prediction of the mechanical behavior of polypropylene (PP) matrix reinforced with single walled carbon nanotubes (SWCNTs). A representative volume element is proposed for modeling the tensile behavior of aligned CNTs/PP composites. The CNT is modeled with solid elements. Modified Morse potential is used for simulating the mechanical properties of an isolated carbon nanotube. The matrix is modeled as a continuum medium by utilizing an appropriate nonlinear material model. A cohesive zone model is assumed between the nanotube and the matrix with perfect bonding until the interfacial shear stress exceeds the bonding strength. Using the representative volume element, a unidirectional CNT/PP composite was modeled and the results were compared with corresponding rule-of-mixtures predictions. The effect of interfacial shear strength on the tensile behavior of the nanocomposite was also studied. The influence of the SWCNT within the polymer is clearly illustrated and discussed. The results showed that polymer's Young's modulus and tensile strength increase significantly in the presence of carbon nanotubes.

Parameterizing the Morse potential for coarse-grained modeling of blood plasma

Multiscale simulations of fluids such as blood represent a major computational challenge of coupling the disparate spatiotemporal scales between molecular and macroscopic transport phenomena characterizing such complex fluids. In this paper, a coarse-grained (CG) particle model is developed for simulating blood flow by modifying the Morse potential, traditionally used in Molecular Dynamics for modeling vibrating structures. The modified Morse potential is parameterized with effective mass scales for reproducing blood viscous flow properties, including density, pressure, viscosity, compressibility and characteristic flow dynamics of human blood plasma fluid. The parameterization follows a standard inverse-problem approach in which the optimal micro parameters are systematically searched, by gradually decoupling loosely correlated parameter spaces, to match the macro physical quantities of viscous blood flow. The predictions of this particle based multiscale model compare favorably to classic viscous flow solutions such as Counter-Poiseuille and Couette flows. It demonstrates that such coarse grained particle model can be applied to replicate the dynamics of viscous blood flow, with the advantage of bridging the gap between macroscopic flow scales and the cellular scales characterizing blood flow that continuum based models fail to handle adequately.

Nonlinear failure analysis of carbon nanotubes by using molecular-mechanics based models

Equivalent nonlinear fracture models for pristine and reconstructed one- and two-atom vacancy defected single wall carbon nanotubes are developed by using the molecular mechanics based models where the initial reconstructed nanotube models are obtained by using molecular dynamic simulations and nonlinear characteristic of the covalent bonds are obtained by using the modified Morse potential. As a result of analyses, it is concluded that fractures of all types of nanotubes are brittle, armchair nanotubes are stiffer than zigzag nanotubes and vacancy defects significantly affect the mechanical behavior of nanotubes. In brief, fracture stress and strain values of pristine armchair nanotubes are respectively 30% and 32% larger than those of pristine zigzag nanotubes, and predicted failure stress and strain values of vacancy defected nanotubes are respectively 27% and 52% smaller than those of pristine ones. It is shown that large deformation and nonlinear geometric effects are important on fracture behavior of nanotubes. Comparisons are made with the failure stress and strain results reported in literature that show good agreement with our results.

Optimization of a Coarse-Grained Force Field for Biological Simulations

The substantial gains in computational power over recent years have been the result of increased processor parallelization. For atomistic simulation, parallelization of spatial dimensions is a viable approach, leading to large length scale simulation. Parallelization of time, on the other hand, can be achieved by averaging of fast time scale motions. Coarse-Grained (CG) models accomplish this by replacing common groups of atoms with 0-dimension points (beads) and defining potentials between the beads. The challenge then is to choose functional forms and parameters for these potentials that accurately reproduce the behavior of equivalent atomistic and experimental systems. In this work, we consider the fundamental unit of water to be a bead representing four water molecules. The beads are made polarizable by the addition of a variable angular term between three charged points on each charge neutral site. Ionic beads are defined as equivalent to four water molecules solvating one atomistic ion. Further, building blocks of linear alkanes are beads of either 3 or 4 carbon units. Non-bonded, non-Coulomb interactions between beads are described by a modified Morse potential which addresses the complexity of multi-atomic beads by decoupling the short-range and long-range behavior. Instead of using a potential of relatively simple form, the comparatively complex potential is computed by lookup table. Optimization of force-field parameters is performed using FFOpt, an in-house software package. The method explores parameter space using Nelder-Mead, a simplex optimization algorithm. The error function for optimization is defined by comparison of CG simulation results to either those of atomistic simulation or experimental values. Analysis used is optimization includes density profile, diffusion coefficient, dielectric constant, and solvation free energies.

Nonlinear fracture analysis of single-layer graphene sheets

In this paper, an atomistic based finite element model for prediction of fracture behavior of single-layer graphene sheets is developed by considering large deformation and nonlinear geometric effects. Euler–Bernoulli beam elements are used to represent covalent bonds and non-linear characteristic of the beam elements are obtained by using the modified Morse potential. Formulation underlying the proposed approach is applied to defect-free, and Stone–Wales and one atom vacancy defected zigzag and armchair graphene sheets. It is shown that large deformation and nonlinear geometric effects are important on the fracture behavior of graphene sheets. The results show that graphene sheets exhibits an orthotropic fracture behavior and these defects significantly affect the mechanical performance of the graphene sheets. In addition, fracture initiation and crack propagation direction issues are studied. It is observed that the fractures of all types of graphene sheets are brittle.

A modified Morse potential accounting for non-zero temperature in molecular statics for Nickel crystals

A modified Morse interatomic potential, which allows extension of the classical Molecular Statics (MS) to non-zero temperatures, is introduced. Accordingly, the constants defining the traditional interatomic potential become temperature-dependent. In this paper they are determined based on experimentally known coefficients of thermal expansion for Nickel. The stress–strain data for a 3D Nickel crystal at different temperatures is found numerically and the results are compared against known experimental data and similar results obtained by the Molecular Dynamics (MD) method. This comparison confirms the validity of the concept of temperature-dependent interatomic potential in MS simulations.

Multiscale calculations of thermoelectric properties ofn-type Mg2Si1−xSnxsolid solutions

The band structure of Mg${}_{2}$Si${}_{1\ensuremath{-}x}$Sn${}_{x}$ solid solutions with 0.250 \ensuremath{\leqslant} $x$ \ensuremath{\leqslant} 0.875 is calculated using the first-principles pseudopotential method. It is found that the low-lying light and heavy conduction bands converge and the effective mass reaches a maximum value near $x$ $=$ 0.625. Using the semiclassical Boltzmann transport theory and relaxation-time approximation, we find that the system with $x$ $=$ 0.625 exhibits both higher Seebeck coefficient and higher electrical conductivity than other solid solutions at intermediate temperatures. By fitting first-principles total energy calculations, a modified Morse potential is constructed, which is used to predicate the lattice thermal conductivity via equilibrium molecular dynamics simulations. Due to relatively higher power factor and lower thermal conductivity, the Mg${}_{2}$Si${}_{0.375}$Sn${}_{0.625}$ is found to exhibit enhanced thermoelectric performance at 800 K, and additional Sb doping is considered in order to make a better comparison with experiment results.

Theoretical Prediction of Tensile Behavior of Single-Walled Carbon Nanotubes

Based on molecular mechanics, a finite element model is proposed to evaluate the tensile behaviour of single-walled carbon nanotubes (SWCNT). The SWCNT is modelled as a space-frame structure. The bonds between the carbon atoms are simulated as beam members to carry the loads, while the carbon atoms are the joints of the members. The modified Morse potential is adopted to characterize the non-linear behaviour of C-C bonds. The simulation are carried out for two well-known SWCNTs, armchair and zigzag with different diameters to investigate the influence of chirality and diameter on the mechanical properties including the Youngs modulus, tensile strength and fracture strain of SWCNTs. It is found that the Youngs moduli of both armchair and zigzag nanotubes increase monotonically with the increase of diameter. The armchair nanotube exhibits larger stress-strain response than the zigzag nanotube. Numerical simulations reveal that the Youngs modulus and tensile strength of armchair nanotubes are larger than that of zigzag nanotubes. These results are in good agreement with the existing numerical and experimental results.

Limit load analysis of graphene with pinhole defects: A nonlinear structural mechanics approach

In this paper, a fully nonlinear spring-based structural mechanics approach, incorporating the modified Morse potential, is presented. Defects are defined as holes developed due to atom vacancies, as opposed to the perfect nanostructure of a graphene sheet. Appropriate boundary conditions are applied to evaluate the proposed method, under tensile and shear loadings, using finite element analysis. Material properties like stress–strain curves and elastic and fracture related properties of both pristine and defective graphene sheets, are predicted. The effect of defect size on mechanical response of the graphene with respect to its zigzag and armchair directions is explored. Analytical expressions of mechanical properties are obtained, using regression analysis of numerical results. The proposed method is validated by comparing predicted properties to data obtained from the literature.

Critical and phase-equilibrium properties of an ab initio based potential model of methanol and 1-propanol using two-phase molecular dynamics simulations

Two-phase molecular dynamics simulations employing a Monte Carlo volume sampling method were performed using an ab initio based force field model parameterized to reproduce quantum-mechanical dimer energies for methanol and 1-propanol at temperatures approaching the critical temperature. The intermolecular potential models were used to obtain the binodal vapor-liquid phase dome at temperatures to within about 10 K of the critical temperature. The efficacy of two all-atom, site-site pair potential models, developed solely from the energy landscape obtained from high-level ab initio pair interactions, was tested for the first time. The first model was regressed from the ab initio landscape without point charges using a modified Morse potential to model the complete interactions; the second model included point charges to separate Coulombic and dispersion interactions. Both models produced equivalent phase domes and critical loci. The model results for the critical temperature, density, and pressure, in addition to the sub-critical equilibrium vapor and liquid densities and vapor pressures, are compared to experimental data. The model's critical temperature for methanol is 77 K too high while that for 1-propanol is 80 K too low, but the critical densities are in good agreement. These differences are likely attributable to the lack of multi-body interactions in the true pair potential models used here.

Evaluation of Mechanical Properties of Single-Walled Carbon Nanotubes

A micromechanical finite element model incorporated with molecular mechanics is employed to determine the mechanical properties of single-walled carbon nanotubes (SWCNT). The SWCNT is modelled as a space-frame structure. The bonds between the carbon atoms are simulated as beam members to carry the loads, while the carbon atoms are the joints of the members. The modified Morse potential is adopted to characterize the non-linear behavior of C-C bonds. In this work, the mechanical properties of SWCNT such as the Young’s modulus, ultimate strength and strain are investigated. To verify the proposed FE model and evaluate its performance, the effects of diameter and chirality on the mechanical properties of SWCNT are presented. It is found that both the Young’s modulus and ultimate strength of SWCNT increase monotonically with the increase of diameter. The Young’s modulus of armchair is larger than that of zigzag SWCNTs. These results are in good agreement with the existing numerical and experimental results.

Non linear adjustments with external conditions

A new non linear adjustment algorithm is proposed that includes the possibility to satisfy conditions involving non linear analytical functions of the adjustment parameters. It is based on the Levenberg-Marquardt algorithm and makes use of Lagrange multipliers to fulfill external conditions. As an application, the method is used to derive a modified Morse potential to represent the potential energy function of the 2Π1/2 ground state of nitric oxide (NO), while having both an acceptable description of the equilibrium bond length, the vibrational overtone spectrum to up to the 6th overtone, the energy and the dispersion coefficient at dissociation NO → N + O.

Liquid–vapour interface of simple fluids interacting by the modified Morse potential

The liquid–vapour diagram and the surface tension of simple fluids were calculated by means of molecular dynamics. The Morse function is modified including an extra adjustment parameter and this new function is the interaction law among the particles. This same function was already employed for estimating transport properties of liquid alkali metals near the melting point [F. Juan-Coloa et al. Mol. Sim. 33 (2007), pp. 1167–1172]. The surface tension and the orthobaric densities related to this kind of fluid are shown for the first time in this work. These same quantities are calculated for three cut-off radii , and . As a relevant result, we found that the complete interaction is estimated using a cut-off distance of . Furthermore, it is verified whether both Morse and modified Morse potentials follow the law of the corresponding state.

Predicting the Young’s Modulus of Single-Walled Carbon Nanotubes using Finite Element Modeling

A finite element simulation technique for estimating the mechanical properties of Single-Walled Carbon Nanotube (SWCNT), polymer composites is developed. In the present modeling work, individual carbon nanotube is simulated as a frame-like structure and the primary bonds between two nearest-neighboring atoms are treated as 3D beam elements. The beam element nonlinear properties are determined via the concept of energy equivalence between molecular dynamics and structural mechanics using Modified Morse potential. Young’s modulus of SWCNTs is estimated to illustrate the accuracy of this simulation technique. Results show that the obtained mechanical properties of nanotubes by the present method are in good agreement with their comparable results.

A modified Morse Potential for Coarse Grained Water-Alkane Interaction

We have developed a coarse grained (CG) model based on the Morse potential with bulk densities, thermodynamical data and surface tensions as targets, for the molecules (n-alkanes and water) that are model components of phospholipid membranes [1]. In this work, a modified Morse potential was used to characterize the CG water-alkane and water-water interactions. The Morse parameters for the alkane-alkane interaction were taken from our previous work [1]. Alkane-water interfacial tensions, solvation free energies of water (alkanes) in alkanes (water) were used as targets for the parameterization. Correct interfacial tension is an essential ingredient in models of phospholipid mebranes since the driving force of self-assembly in aqueous amphiphilic enviornments is the segregation of hydrophic and hydrophobic regions. The so obtained CG force field parameters yields simulated thermodynamical data such as transfer free energies of water (alkane) from liquid water (alkane) to liquid alkane (water) in good agreement with the experimental data available in literature.Reference:[1] See-Wing Chiu, H. Larry Scott, and Eric Jakobsson. J. Chem. Theo. Comput. 6, 851, 2010.

Continuum states of modified Morse potential

Using a proper approximation scheme to the centrifugal term, we study any l-wave continuum states of the Schrödinger equation for the modified Morse potential. The normalised analytical radial wave functions are presented, and a corresponding calculation formula of phase shifts is derived. It is shown that the energy levels of the continuum states reduce to those of the bound states at the poles of the scattering amplitude. Some numerical results are calculated to show the accuracy of our results.

Tensile behaviors of graphene sheets and carbon nanotubes with multiple Stone–Wales defects

An atomistic based finite bond element model has been developed to study the effects of multiple Stone–Wales (5-7-7-5) defects on mechanical properties of graphene sheets and carbon nanotubes. The element formulation includes 8 degrees of freedom reducing computational cost compared to the 12 degrees of freedom used in other FE type models. The coefficients of the elements are determined based on the analytical molecular structural mechanics model developed by the authors. The model uses the modified Morse potential to predict the Young's modulus and stress–strain relationship of perfect and defective nanotubes and graphene sheets. The variation of ultimate stress, strain at failure, and Young's modulus values of carbon nanotubes and graphene sheets have been examined as a function of the distance between two defects aligned in the axial and hoop directions. The mechanical properties as a function of the number of defects in the hoop direction are also studied. It is found that the moduli are sensitive to the tube lengths when the total tube length is used to compute the strain. If one uses a local defective length to define the strain, a size independent modulus can be obtained for the defective region. The diameter of the affected region (2 nm) from a single defect is defined as the defective length and is used for all different tube lengths examined in the present study. The effects of defect density on mechanical properties of tubes of any lengths are also discussed.

Design and identification methods of effective mechanical properties for carbon nanotubes

Atomic arrangement and configuration of carbon nanotubes (CNTs) imposes the necessity of the use of transversely isotropic or specially orthotropic material models in the description of their effective material properties instead of isotropic one. Therefore, in the present paper an identification technique based on the analysis of natural vibrations is introduced. Theoretical values of natural vibrations are derived with the use of theoretical relations valid for thin orthotropic cylindrical shells. They are compared with numerical ones calculated utilizing a three-dimensional finite element (FE) model for armchair and zigzag single-walled carbon nanotubes (SWCNTs). The numerical model development is consistent with molecular mechanics formulations and it is based on the assumption that carbon nanotubes, when subjected to free vibrations, behave like space-frame structures. In order to compare the numerical and theoretical values of eigenfrequencies two forms of the interatomic potentials are considered: the modified Morse potential and REBO potential. In order to avoid local modes of deformations the axisymmetric modes are investigated only. A detailed study of results demonstrates that CNTs should be considered as orthotropic structures.

Analytical solution for estimation of temperature-dependent material properties of metals using modified morse potential

Summary An atomic-level analytical solution, together with a modified Morse potential, has been developed to estimate temperature-dependent thermal expansion coefficients (CTE) and elastic characteristics of bulk metals. In this study, inter-atomic forces are considered as a set of anharmonic oscillator networks which can be described by Morse potential, while the material properties can be defined by these inter-atomic forces; when temperature increases, the vibration of the anharmonic oscillator causes the phenomenon of temperature-dependent material properties. The results of analysis showed that the original Morse potential can give a reasonable prediction of the thermal expansion coefficients and elastic constants of metals at room temperature; however, it has difficulties in giving an accurate result at low and high temperatures. Therefore, to overcome the deficiency, a temperaturedependent modified Morse potential is developed and validated with various metals.