Radial breathing mode frequencies of carbon nanotubes for determination of their diameters

In this paper, exact formulas are obtained for the radial breathing mode (RBM) frequencies of triple-walled carbon nanotubes (TWCNTs) using symbolic package in MAPLE software. For this purpose, TWCNT is considered as triple concentric elastic thin cylindrical shells, which are coupled through van der Waals (vdW) forces between two adjacent tubes. Lennard–Jones potential is used to calculate the vdW forces between adjacent tubes. Then, explicit formulas for RBM frequencies of single-walled (SW), and double-walled (DW) CNTs have been deduced from TWCNT formulas that show an excellent agreement with the available experimental results and the other theoretical model results. The advantage of this analytical approach is that the elastic shell model considers all degrees of freedom in the vibrational analysis of CNTs. To demonstrate the accuracy of this work, the RBM frequencies of different multi-walled carbon nanotubes (MWCNTs) are compared with the available experimental or atomistic results with relative errors of less than 1.5%. To illustrate the application of this approach, the diameters of DWCNTs are obtained from their RBM frequencies which show an excellent agreement with the available experimental results. Also, this approach can be used to determine the diameters of the TWCNTs and MWCNTs. The influence of changing the geometrical and mechanical parameters of a TWCNT on its RBM frequencies has been investigated, too.     

Molecular dynamic simulation of Copper and Platinum nanoparticles Poiseuille flow in a nanochannels

In this paper, simulation of Poiseuille flow within nanochannel containing Copper and Platinum particles has been performed using molecular dynamic (MD). In this simulation LAMMPS code is used to simulate three-dimensional Poiseuille flow. The atomic interaction is governed by the modified Lennard–Jones potential. To study the wall effects on the surface tension and density profile, we placed two solid walls, one at the bottom boundary and the other at the top boundary. For solid–liquid interactions, the modified Lennard–Jones potential function was used. Velocity profiles and distribution of temperature and density have been obtained, and agglutination of nanoparticles has been discussed. It has also shown that with more particles, less time is required for the particles to fuse or agglutinate. Also, we can conclude that the agglutination time in nanochannel with Copper particles is faster that in Platinum nanoparticles. Finally, it is demonstrated that using nanoparticles raises thermal conduction in the channel.     

Analytical equations of state for multi-Yukawa fluids based on the Ross variational perturbation theory and the Percus-Yevick radial distribution function of hard spheres

Analytical expressions for equation of state and thermodynamic properties have been derived for the multi-Yukawa fluids, based on the Ross variational perturbation theory and the analytical Percus–Yevick (PY) expression for the radial distribution function of hard spheres. It is shown that the variational procedure is absolutely convergent and the calculations are convenient and fast. By using the parameters fitted to the Lennard–Jones 12–6 potential from the literature, numerical calculations have been made within wide temperature and density ranges. Comparison with computer simulations shows that the precision of the analytical Ross theory based on the Yukawa-type potential is equivalent to the non-analytical Ross theory based on the Lennard–Jones 12–6 potential. It is concluded that the analytical theory based on the Yukawa-type potential can be applied to research practical fluids within wide temperature and density ranges.     

Long range relationship between Morse and Lennard–Jones potential energy functions

Arising from the use of the Morse function–which is well-known for its applicability for describing bonded interaction energy–in van der Waals systems, an attempt is made herein to express parameters of the Lennard–Jones potential function in terms of the Morse function to enable normalized comparison. In a departure from previous work where the parameter relationships enforce equal curvature at the minimum well-depth, the present approach replaces this rule with equal area above the curves for 1?≤?(r/R)?≤?∞. Results show good approximations of the Morse function to the Lennard–Jones curve and vice versa. Comparison with the previous relation for short range interaction shows that the present relations offer superior agreement with the Lennard–Jones function over a longer range. The conversion relations provide a cost-effective, less time-consuming and reasonably reliable method for obtaining Morse parameters from those of the Lennard–Jones function and vice versa.     

Liquid–vapour equilibrium of n -alkanes using interface simulations

Molecular Dynamics simulations were performed to calculate liquid–vapour coexisting properties of n-alkane chains up to 16 carbon atoms using interface simulations. The lattice sum or Ewald method on the dispersion forces of the Lennard–Jones potential was applied to calculate the full interaction. The liquid and vapour coexisting densities were obtained for two flexible force field models, NERD and TraPPE-UA, where the intermolecular interactions are of the Lennard–Jones type. We have recently shown [P. Orea, J. López-Lemus, and J. Alejandre, J. Chem. Phys. 123, 114702 (2005)] that the liquid–vapour densities for simple fluids do not depend on interfacial area and therefore it is possible to use a small number of molecules in a simulation. We show that the same trend is found on the simulation of these hydrocarbon molecules. The phase diagram of ethane/n-decane binary mixtures is also obtained at 410.95 K for the NERD model. The simulation results from this work were compared with those obtained using methods with interfaces using large cut-off distances and with methods without interfaces for the same potential model. In both comparisons, excellent agreement was found. The results of liquid density from the TraPPE-UA model are in good agreement with experimental data while those from the NERD model are underestimated at low temperatures. Our findings are consistent with results published by other authors for small hydrocarbons.     

Density functional theory of vapor to liquid heterogeneous nucleation: Lennard–Jones fluid on solid substrate

Density functional theory has been applied to investigate the vapor to liquid heterogeneous nucleation on a flat solid surface, by invoking a model free energy density functional along with an exponential density model. The effects of supersaturation of the vapor and the strength of the solid-fluid interaction on the nucleation barrier have been investigated for Lennard–Jones fluid with 12–6 fluid–fluid and 9–3 solid–fluid interaction model. The spinodal decomposition of vapor has been observed at higher supersaturation or at higher strength of the solid–fluid interaction. The shape, density profile and the free energy of formation of droplets of any arbitrary size have been obtained in this work.     

Exploring the utility of coarse-grained water models for computational studies of interfacial systems

Molecular dynamics simulations have become a standard tool for the investigation of biological and soft matter systems. Water models serve as the basis of force fields used in molecular dynamics simulations of these systems. This article reports on an examination of the utility of a set of coarse-grained (CG) water models, with different resolutions, interaction potentials (Lennard–Jones, Morse), and cut-off distances. The relationships between the parameters under specific choices of the above options and the thermodynamic properties, such as density, surface tension, and compressibility, were found to fit simple mathematical equations. The limits of applicability of these CG water models were explored by checking the melting temperature. If a CG site is mapped to one or two real water molecules, a simple model with appropriate combinations of cut-off distances, functional forms, and parameters can be found to simultaneously match the experimental values of density, surface tension, and compressibility under ambient conditions. If more water molecules are included in a CG site, either the melting temperature approaches or surpasses room temperature, or the surface tension and compressibility cannot both be matched simultaneously. In striving for computational efficiency, it is still possible to find a simple CG water model with three water molecules contained in a CG bead that generates a liquid state of water with realistic values of density, surface tension and compressibility at ambient condition, but coarser models are not recommended.     

Phase diagram of hard colloidal platelets: a theoretical account

We construct the complete liquid crystal phase diagram of hard plate-like cylinders for variable aspect ratio using Onsager's second virial theory and employing the Parsons–Lee decoupling approximation to account for higher-body interactions in the isotropic and nematic fluid phases. The stability of the solid (columnar) state at high packing fraction is included by invoking a simple equation of state based on a Lennard–Jones–Devonshire cell model which has proven to be quantitatively reliable over a large range of packing fractions. By employing an asymptotic analysis based on the Gaussian approximation we are able to show that the nematic–columnar transition is universal and independent of particle shape. The predicted phase diagram is in qualitative agreement with simulation results.     

Surface tension of hydrocarbon chains at the liquid–vapour interface

Molecular dynamics simulations were performed at constant temperature to obtain the surface tension of hydrocarbon chains at the liquid–vapour interface. The Ewald sum was used to calculate the dispersion forces of the Lennard–Jones potential to take into account the full interaction. The NERD and TraPPE_UA flexible force field models were used to simulate molecules from ethane to hexadecane along the coexistence curve. The simulation results for the TraPPE_UA model are in good agreement with experimental data, whereas the NERD model predicts slightly higher values.     

Calculation of the surface tension and the surface energy of Lennard–Jones fluids from the radial distribution function in the interface zone

A detailed study is presented of the calculation of the surface tension and the surface energy of Lennard–Jones fluids from the radial distribution function and the density profile. To do so, a modification is made to Lekner and Henderson's statistical mechanics approach by introducing two simple analytical expressions for the radial distribution function of the interface zone. In these expressions the radial distribution functions of the liquid and vapour phases are weighted via step or exponential variations. The well- known exponential model for the density profile in the interface zone is considered. Finally, results are compared with values from experiment, from computer simulation and from relevant theoretical developments. It is shown that the use of the proposed radial distribution function in the interface zone represents a significant improvement in applying Lekner and Henderson's approach.     

Perturbation and variational approach for the equation of state for hard-sphere and Lennard-Jones fluids

The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state (EOS) for a mixture of hard sphere (HS), Lennard–Jones (LJ) fluids. A suitable flexible functional form for the radial distribution function G(R) is assumed for the mixture, with R as a variable. The function G(R) has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m. For m = 0.75 and m = 0.83 results are close to molecular dynamics (MD) result for pure HS and LJ fluid respectively.     

Surface phase transitions of multiple-site associating fluids

Surface phase transitions of Lennard–Jones (LJ) based two- and four-site associating fluids have been studied for various associating strengths using grand-canonical transition matrix Monte Carlo simulations. Our results suggest that, in the case of a smooth surface, represented by a LJ 9-3-type potential, multiple-site associating fluids display a prewetting transition within a certain temperature range. However, the range of the prewetting transition decreases with increasing associating strength and increasing number of sites on the fluid molecules. With the addition of associating sites on the surface, a quasi-2D vapor–liquid transition may appear, which is observed at a higher surface site density for weaker associating fluids. The prewetting transition at lower associating strength is found to shift towards the quasi-2D vapor–liquid transition with increasing surface site density. However, for highly associating fluids, the prewetting transition is still intact, but shifts slightly towards the lower temperature range. Adsorption isotherms, chemical potentials and density profiles are used to characterize surface phase transitions.     

Interfacial properties of Morse fluids

The interfacial properties as reflected in the interfacial tension values and the density profile of Morse fluids has been studied. The parameter range is chosen to coincide with that describing the behaviour of solid metals. The interfacial tension has been found to follow Guggenheim's and MacLeod's relations. However, the constants, while independent of temperature for each metal, are not the universal values predicted; with the exception of Macleod's exponent p. The density profile illustrates the change in densities across the interface dividing the coexisting vapour and liquid phases. The correlation length is also found to follow the universal relation with temperature, but again the constants, while independent of temperature, are dependent on the type of metal. The value of constant ν is found to be different for all five metals considered and is found to differ from the three-dimensional Ising model value of ν?=?0.630, which is also predicted by applying the Lennard–Jones model.     

A new equation of state for associating Lennard–Jones fluids with two sites: small bond angle

ABSTRACT

We developed a new equation of state for Lennard–Jones spheres with two short-ranged, directional association sites. The theory is novel in that association is dependent on bond angle between the two sites, and formation of self-assembled linear and cyclic clusters is predicted in the model. The competition between ring and chain formations at various densities and temperatures is predicted by the theory and verified by Monte Carlo simulations. It was found that closed-loop structures become important at low temperatures and densities. Also, at fixed association energy, intensifying the Lennard–Jones energy reduces the extent of association in the fluid. The theory and simulation are in excellent agreement.     

Dependence of in—tube doping on the radius and helicity of single—wall carbon nanotubes

Using the Lennard－Jones interaction potential between the impurity atom and carbon atom, we have studied the dependence of in-tube impurity doping on the radius of a single-wall carbon nanotube (SWNT), as well as its helicity. The obtained results show that the radius of the most stably doped SWNT is different for different kinds of impurity atoms. This is useful for producing the required doped SWNT. In addition, it is found that the helicity of tube has a strong effect on the potential energy of the atoms doped in the SWNT.     

Surface tension calculations of the cationic (CTAB) and the zwitterionic (SB3-12) surfactants using new force field models: a computational study

Actual CTAB and SB3-12 surfactant force field models fail to reproduce one of the most important thermodynamic property of those molecules, the surface tension. Molecular dynamics simulations were conducted to construct new force fields of the cationic surfactant, Cetyl Trimethyl Ammonium Bromide (CTAB), and the non-ionic, cocoamidopropyl betaine, surfactants using united atom models. By scaling the Lennard Jones parameters, the well depth potential (ε) and the intermolecular distance (σ), we constructed an united atom model of the cationic and the betaine surfactants. The new models were tested with actual experiments reported in the literature. With the correct parameters, surface tensions of both surfactants were calculated at different temperatures and different areas per molecule. Electrostatic properties and micelle structures were also calculated with the new set of parameters and radius of gyrations, i.e. micelle radius, were evaluated showing good affinity with experimental data. The new force fields were proved with two different water models, TIP4P/ε and SPC/E, having good agreement with actual experiments     

Estimation of the Electron–Phonon Coupling Constants for Graphene and Metallic and Nonmetallic Substrates

Two modes of graphene–substrate interaction have been considered: a weak van der Waals bond and a strong covalent bond. The Lennard–Jones potential and Harrison bond-orbital method are used in the former and latter cases, respectively. Analytical expressions for the electron–phonon interaction constants, which contain only two parameters (binding energy E _B for graphene and a substrate and distance d between them) have been obtained. The constants have been calculated for metallic, semiconductor, and dielectric substrates.

     

Spontaneous translation of nanodroplet over a heterogeneous surface due to thermal cycles: role of solid–liquid interfacial fluctuations

ABSTRACT

We study the molecular-scale features of the solid surface that result in the spontaneous motion of a nanodroplet due to the periodic variation of temperature. We first employ a thermodynamic model to predict the variation of solid–fluid interfacial properties that can result in the above motion. The model identifies a composite (surface couple) made of two surfaces that are characterised by a large difference between the entropic parts of the solid–liquid interfacial free energies. In order to understand the molecular-scale features of the two surfaces that may form a surface couple, we performed grand canonical Monte Carlo simulations of Lennard Jones fluid and crystalline surfaces made of Lennard Jones-like atoms. We then used the cumulant expansions of the perturbation formulas to divide the interfacial entropy into two parts: The one that is directly affected by the solid–fluid attraction (direct part), and the other (indirect part) that is indirectly affected by the solid–fluid attraction via the alteration of interfacial fluctuations. Our results indicate that two surfaces form a surface couple if the differences between their chemical natures lead to large differences in the indirect part of the interfacial entropy, while the direct part remains relatively unaffected.