Academic literature on the topic 'Lennard-Jones interaction potential'

To model the car-following behavior more accurately, we carried out the molecular similarity analysis between the vehicles on the road and the inert gas system, comparing vehicles with microscopic particles in long and narrow pipes. The complex car-following interaction behavior is simplified into a dynamic process of the follower car that is constantly seeking to maintain the required safety distance from the leading vehicle. Through mathematical derivation of the Lennard–Jones potential function suitable for thermodynamic analysis of inert gas systems, the influence of each variable on the potential energy is clarified, and the existing problems of the existing molecular car-following model are analyzed, referring to the general Lennard–Jones potential function to build the vehicle interaction potential function. Considering the impact of the road wall potential generated by the lane boundary, a car-following model based on Lennard–Jones interaction potential is presented. The simulation test results show that compared with the existing molecular car-following model and IDM model, the average absolute error and root mean square error of the vehicle acceleration results obtained by this model and the actual data are lower, which proves that the vehicle is based on the Lennard–Jones interaction potential. The vehicle-following model based on Lennard–Jones interaction potential has a better fitting effect on the real vehicle-following behavior.

A unified atom model for describing interaction energy between C60 molecules was obtained by Liu and Wang based on the Smith–Thakkar potential function. In view of the mathematical resemblance between the Liu–Wang and the conventional Lennard-Jones (12-6) function (used in computational chemistry software for describing van der Waals energy), modified versions of the Lennard-Jones function are proposed for quantifying the potential energy between C60 molecules. In this way, the Liu–Wang parameters can be converted into Lennard-Jones parameters for ready execution in commercially available computational chemistry software with minimal hard-coding involved. It was found that the Lennard-Jones function reasonably approximates the Liu–Wang model when the former's indices are increased by a factor of (7/4), without introducing any change to the coefficients. A better agreement was found when m = 4n = 35.4857, which also requires the change in repulsive and attractive indices from 1 and 2 to (1/3) and (4/3), respectively.

This paper reports on the molecular dynamics simulation results of liquid bromine trifluoride (BrF3) at 299, 315, and 363 K. We have assumed that the molecules interact via Lennard–Jones 12–6 site–site pair potential and Lennard–Jones site–site + fractional charges over atomic sites. Lennard–Jones potential parameters of Singer et al. (Mol. Phys. 33, 1757 (1977)) have been used for Br–Br, and F–F interactions and cross interaction terms are calculated using Lorentz–Berthelot mixing rules. Fractional charges are assigned to reproduce the experimentally determined gaseous-state molecular dipole moment. Various structural and thermodynamic properties for liquid state are reported and compared in detail with results from diffraction studies (Mittkin et al. J. Struct. Chem. 28, 60 (1987)). Some mechanical properties such as mean-square force and torque, self-diffusion coefficient have also been calculated. The repulsive part of the proposed atom–atom pair potential is a good approximation since both molecular configurations are in good agreement with experimental results.

The oscillatory motion in nonlinear nanolattices having different interatomic potential energy functions is investigated. Potential energies such as the classical Morse, Biswas – Hamann and modified Lennard – Jones potentials are considered as interaction potentials between atoms in one-dimensional nanolattices. Noteworthy phenomena are obtained with a nonlinear chain, for each of the potential functions considered. The generalized governing system of equations for the interaction potentials are formulated using the well-known Euler – Lagrange equation with Rayleigh’s modification. Linearized damping terms are introduced into the nonlinear chain. The nanochain has statistical attachments of $40$ atoms, which are perturbed to analyze the resulting nonlinearities in the nanolattices. The range of initial points for the initial value problem (presented as second-order ordinary differential equations) largely varies, depending on the interaction potential. The nanolattices are broken at some initial point(s), with one atom falling off the slender chain or more than one atom falling off. The broken nanochain is characterized by an amplitude of vibration growing to infinity. In general, it is observed that the nonlinear effects in the interaction potentials cause growing amplitudes of vibration, accompanied by disruptions of the nanolattice or by the translation of chaotic motion into regular motion (after the introduction of linear damping). This study provides a computationally efficient approach for understanding atomic interactions in long nanostructural components from a theoretical perspective.

The article proposes a method of controlling the movement of a group of robots with a model used to describe the interatomic interactions. Molecular dynamics simulations were carried out in a system consisting of a moving groups of robots and fixed obstacles. Both the obstacles and the group of robots consisted of uniform spherical objects. Interactions between the objects are described using the Lennard-Jones potential. During the simulation, an ordered group of robots was released at a constant initial velocity towards the obstacles. The objects’ mutual behaviour was modelled only by changing the value of the interaction strength of the potential. The computer simulations showed that it is possible to find the optimal value of the potential impact parameters that enable the implementation of the assumed robotic behaviour scenarios. Three possible variants of behaviour were obtained: stopping, dispersing and avoiding an obstacle by a group of robots.

We study a transition from quasiperiodic to stochastic motion in one-dimensional classical systems consisting of N particles with the nearest-neighbor Lennard–Jones interaction, extensively by computer simulation. We find a new feature in the change of the Lyapunov spectrum and the maximal Lyapunov exponent by changing its energy in the intermediate region between quasiperiodic and stochastic motions. The characteristics of the Lennard–Jones system in the intermediate region is considered by means of properties of Hessian matrix of potential function. The applicability of random matrix approximation for high energy region is also investigated, comparing with the case of soft-core potential.

Abstract Langevin dynamics simulations are performed to examine how impurities affect two-dimensional dodecagonal quasicrystals. We assumed that the interaction potential between two particles is the Lennard–Jones–Gauss potential if at least one of these particles is a matrix particle and that the interaction potential between two impurities is the Lennard–Jones potential. Matrix particles and impurities impinge with constant rates on the substrate created by a part of a dodecagonal quasicrystal consisting of square and triangular tiles. The dependences of the twelve-fold rotational order and the number of shield-like tiles on the impurity density are examined after sufficient solid layers are grown. While the change in the twelve-fold rotational symmetry is small, the number of shield-like tiles in the solid increases greatly with increasing impurity density.

In this paper, methane adsorption in single-walled carbon nanotube (SWNT) has been simulated by using the grand canonical ensemble Monte Carlo (GCMC) method. Lennard-Jones (LJ) potential is used to represent the fluid-fluid interaction, Lennard-Jones potential and integral method are used to calculation of the potential between fluid molecules and carbon atoms, respectively. In the simulation, two methods of calculation of potential between fluid molecules and SWNT are compared. The potential calculated by the two methods are almost the same. Then the influence of diameter of SWNT on the usable capacity ratio (UCR) is analyzed, and the parameters of the SWNT which has the best adsorption performance at 300K is recommended under certain pressure.

A new kind of effective potential, which permits the calculation of the quantum equilibrium averages of configuration dependent observables in a classical-like way, is used for calculating the quantum pair correlation function of a two-body system. The main feature of this effective potential is the capability to fully account for the quantum harmonic effects, so it proves much more efficient than the analogous one defined by the Wigner expansion. Applications and comparisons with exact data are made for the Lennard-Jones interaction, with the characteristic parameters of helium atoms and hydrogen molecules.

We report dynamical instability of one-dimensional system with the nearest-neighbor Lennard–Jones interaction. A presence of new certain region between weakly and strongly chaotic region has been found in energy dependence of the maximal Lyapunov exponent. It is numerically shown that the presence of the region is enhanced by decrease of the particle density. The characteristics of the Lennard–Jones system, which are different from the FPU and soft-core system, are explained by means of a local instability of the potential surface. In addition, the relation between the presence of the new region and spatio-temporal pattern is also discussed in the low density cases.

Ce travail de thèse présente la modélisation théorique de l'expérience FORCA-G. L'objectif de cette expérience est la mesure des interactions à courte portée entre des atomes piégés dans un réseau optique et une surface massive à une grande précision. Nous nous sommes intéressés plus particulièrement à l'effet Casimir-Polder induit par la surface sur les atomes. Le but était de fournir la prédiction la plus précise possible des états atomiques. Ceci a consisté à considérer les effets de la température sur l'interaction Casimir-Polder et modéliser la surface de la manière la plus réaliste possible. Afin de résoudre le problème de divergence qu'impliquait un traitement perturbatif de l'interaction atome-surface, nous avons développé une méthode numérique pour un traitement non-perturbatif de l'interaction Casimir-Polder et modélisé l'interaction atome-surface à très courte distance par un potentiel de Lennard-Jones. Chaque effet et incertitude sur les états atomiques ont été évalués afin de déterminer s'ils seraient observables ou un facteur limitant en regard de la précision visée par l'expérience. Enfin nous nous sommes intéressés au cas d'un déséquilibre thermique entre la température du miroir et la température de l'environnement qui pourrait être induit par les lasers en présence ou un laser de chauffage. Nous avons calculé la correction du potentiel Casimir-Polder due au déséquilibre et évalué l'effet sur les niveaux d'énergie atomiques pour déterminer si cet effet pouvait être mesuré
This thesis presents the theoretical modeling of the experiment FORCA-G. The purpose of this experiment is to measure short-range interactions between trapped atoms in an optical lattice and a massive surface with a high precision. We are focused on Casimir-Polder effect induced by the surface on the atoms. The aim was to give the most possible precise prediction of atomic states. This work took the temperature effects on Casimir-Polder interaction into account, modelled the surface of the experiment. In order to solve the divergence problem due to the perturbative treatment of the atom-surface interaction, we developed a digital method for a non-perturbative treatment of the Casimir-Polder interaction and modelled the short-range atom-surface interaction by a Lennard-Jones potential. Each effect and uncertainties on the atomic states were evaluated so that we know if they could be observable or a limiting factor compared to the experiment precision. Finally we were focused on an out of thermal equilibrium situation between the miroir and environment temperature which may be induced by the lasers. We computed the correction to the Casimir-Polder potential due to this disequilibrium and evaluated the effect on the atomic states

Ce travail propose une nouvelle approche de la description des phénomènes physiques qui interviennent dans le cadre de la modélisation de l'interaction plasma-isolant. Pour cela un code de calcul de dynamique moléculaire à été réalisé pour décrire les mécanismes fondamentaux qui régissent cette interaction à l'échelle microscopique.
Une étude fondamentale de la dynamique moléculaire, basée sur l'utilisation des méthodes numériques particulières comme les intégrateurs symplétiques et l'exploitation des différents potentiels d'interactions existants (Morse, Lennard-Jones...), a abouti à deux modèles de polymère : le polyéthylène ou PE (CH2)n. Le premier modèle dit simplifié consiste à considérer un groupement CH2 comme un atome fictif de masse molaire 14g, tandis que le second plus complet traite la dynamique de l'atome d'hydrogène au sein de la macromolécule. Ces deux modèles sont utilsés, dans le cadre de ce travail, pour diverses interactions.
Par ailleurs, des mesures expérimentales de perte de masse des matériaux polymères qui interagissent avec un plasma, créé par l'explosion d'un fil de cuivre, sont exposées. Ces résultats sont corrélés par des calculs théoriques de thermodynamique qui montrent une différence de comportement des deux polymères testés : le polyéthylène et le polyoxyméthylène, POM ou Delrin (CH2O)n.

Adhesive forces, mediated by van der Waals’ and other interactions, dominate the contact response in the micron and sub-micron regimes. Understanding adhesion is especially important in biological systems (interaction of cells with pathogens, bio-locomotion, and drug delivery), mechanical systems (nano-indentation), and Micro-Electro-Mechanical Systems (MEMS), among many others. Classical adhesive contact models like the JKR, DMT, and Maugis’ models apply in the small-deformation regime for regular bodies. Despite attempts by Shull, Lin, and others, enabling large deformation and arbitrary shapes is infeasible in such semi-analytical schemes, necessitating the use of finite element analysis (FEA). Existing FE models use volume-to-volume (V2V), surface-to-surface (S2S), point to volume (P2V) or point to surface (P2S) interactions. S2S (e.g. Fan et al.) are computationally efficient but are not accurate enough to simulate strong adhesion in soft bodies due to inherent approximations. In these paradigms, a well-known FE scheme is the Coarse-Grained-Contact-Model (CGCM) developed by Sauer and co-workers. While CGCM is quite general, it uses a modification of the classical continuum, which is complicated to implement. More importantly, adhesion involves inherent ‘jump-to’ and ‘jump-off’ instabilities, which have not received adequate attention in the existing simulation literature. Moreover, these instabilities are more pronounced in soft materials, and necessitate new supporting algorithms and computational approaches for successful simulation. Lastly, for applications, it is important for solvers to demonstrate the ability to simulate adhesive systems with realistic material and interaction parameters. In the present work, a V2V, interaction-based, continuum FE model is developed for large deformation plane strain adhesive contacts, with all interacting bodies considered to be elastic. A tree-based, ultra-fine, structured mesh generator is developed to accurately model interactions while reducing the associated computational expense. A k-d tree based algorithm is implemented to compute the interactions, reducing the computational cost. Both quasi-static and implicit dynamic solvers are developed. The quasi-static solver uses a custom path-following algorithm which can tackle ‘jump-to’ and ‘jump-off’ instabilities for a wide range of problems. The dynamic solver provides an alternative solution strategy to resolve only the stable branches of the solution curve and is especially useful for soft materials with strong adhesion. The solutions obtained by the quasi-static solver and the dynamic solver in the low-velocity limit show good agreement, except, obviously, in the snap-back zone. In the past, dynamics solvers for adhesive problems (Johnson et al.; Jayadeep et al.) have typically focused on the impact ('unforced') regime rather than on the constant-velocity ('forced') regime, which is often more important in applications. Some studies were carried out to validate various aspects of these solvers, including checks on the accuracy of interaction force calculations, mesh convergence behavior, and various limiting cases. Several model applications were considered to study and test these solvers, including cylinders and elliptical cylinders interacting with half-spaces, and a multi-body problem involving two cylinders and a half-space. Apart from the load-displacement and load-gap curves, a complete set of sub-surface strain fields and transmitted contact tractions is presented. The temporal evolution of the pressure peaks near the edges of contact is clearly revealed, flipping from tensile to compressive as the bodies approach each other very closely. The simulations show that tensile peaks always occur near the 'edge of contact' even in a highly repulsion-dominated regime. The solvers developed in the present work are expected to be useful to explore a spectrum of adhesive contact problems that arise in applications.

Numerous electric field induced phenomena have been studied, for long, at various length scales. In particular, a concentrated electric field applied across a conductor, or equivalently an electric current of very high density passing through a conductor, can manifest in form of both destructive and constructive processes, depending on the requirements of an application. For example, electromigration, which is a diffusion-controlled electric field directed mass transport phenomenon, often leads to the formation of voids and hillocks near the cathode and the anode, respectively, metal interconnects in microelectronic devices. This results in failure of the device and hence this “destructive” manifestation of the electric field is considered as a “villain” in microelectronic interconnects. On the other hand, recently discovered electromigration in liquid metals may pave the path for various useful applications, such as maskless conformal coating, pattern formation, surface modification, etc. Besides the exploitation of the capability of the electric field for transporting matter (e.g., in liquid metals) in controlled and directed fashion in various applications, harnessing the unique potential of the electric field in inducing a chemical reaction in a controlled fashion in a confined region also provides new avenues for constructive usage. In particular, the electric field induced chemical reaction has been exploited for patterning at extremely small length scale, using scanning probe microscopes, such as atomic force microscope (AFM) and scanning tunneling microscope (STM). It is imperative to unambiguously understand the fundamentals of the concerned phenomenon before the aforementioned electric current induced phenomenon can be exploited to bear numerous technologies and applications. Here, we have studied two different electric field induced phenomena, namely electromigration in liquid metals and electric field-induced chemical reaction in solid thin metals1. The presentation of the study in form of this thesis is divided into three main parts, (i) Theoretical modelling of electromigration in liquid metals (or liquid electromigration), (ii) Study of the electric field induced chemical reaction in Cr film, including a detailed investigation of effects of ambient conditions on reaction kinetics, and (iii) Development of a tool for pattern drawing by the means of electric field-induced chemical reaction. As mentioned earlier, electromigration, irrespective of whether it is in solids or liquids, is a diffusion-controlled directional mass transport phenomenon that is driven by the applied electric field. The direction of the mass transport, in general, depends on the net force experienced by the positively charged ions due to the applied electric field and the momentum transferred from the colliding free-electrons. Hence, it is critical to understand the direction of this effective force in metal. Often it is from the cathode to the anode in a solid metal; however, it is not that straightforward in liquid metals. For example, the direction of the net mass transport in most of the liquid metals, e.g., Ga, In, Ga, etc., is in the direction of the electric field (i.e., from the anode to the cathode, which is contrary to the solid metals), whereas the direction of the flow is reversed in the liquid Pb. The reason for the dichotomy of the directionality in the liquid metal flow was not completely understood, and hence we performed detailed analytical and experimental work to resolve it. Here, we developed a theoretical model based on the cell model of liquids and incorporating Lennard-Jones interaction potential. The model considers the short-range order in liquid metals and calculates the force on the ions due to the momentum transferred by electrons during electron-ion collisions. The model not only successfully predicts the flow direction of numerous liquid metals, including liquid Pb, Ga, etc., but it also gives the value of effective charge number of liquid metals as the function of the temperature. Experiments were performed on selected liquid metals in order to validate the model. As mentioned earlier, electrical interaction between the tip and the metal (e.g., Cr) film may induce a chemical reaction in the localized region around the probe tip on the film. If the probe is translated over the metal film along a predefined path, then the chemical reaction induced controlled patterning of the film can be achieved. In the second segment of our work, the focus has been to understand the mechanism of the phenomenon of electric field-induced chemical reaction in Cr film by performing a series of experiments using a custom-built experimental setup, so that we can later exploit the gained understanding for lithography. The phenomenon was studied using a W-tip with a diameter of 20 μm under stationary tip condition. Although this length scale is relatively larger than that of using AFM or STM tip, it provides a significant amount of reaction product and allows easy maneuverability as well as better control of the experiments: Both of these are critical for an unambiguous understanding of the nature and kinetics of the chemical reaction. The study includes confirmation of observation of a chemical reaction induced process in presence of electric field (as per Faraday’s law) and the identification of the reactants (as Cr and H2O – in the form of both vapor and liquid) and the product (as CrO3) at the cathode. The ambient conditions affect the reaction kinetics at the cathode probe tip and hence the dimensions (as well as quality) of the patterns. Therefore, the phenomenon was studied under different ambient conditions, such as vacuum, gaseous (e.g., N2, O2 and air) environments, variable humidity, high and low temperature, etc. It was observed that the reaction did not occur in an environment unless water vapor (or water) was present. Furthermore, the reaction occurred without the generation of a significant amount of heat (and hence the negligible rise in the temperature was associated with this process). Finally, the reaction was favored at the locations of high current densities at or near the cathode. A study on the understanding of the nature of the reaction product revealed that CrO3 is highly hygroscopic and it quickly absorbs water from the air to become liquid. As the reaction product is soluble in water, the region where reaction had taken place could be easily removed by dipping the sample into water. The use of water in the reaction was further exploited to develop a new SPM based lithography process that can preclude the need to keep the sample and the tip into contact and proffers spontaneous removal of the reaction product. Overall, the results obtained in this segment of the work paves the path for developing a new tip-based lithography technique that is better suited to meet the challenges of tip wear, debris collection, low throughput, etc., which are often associated with other SPM based lithography techniques. In the last segment of the work, the understanding of the electric current induced chemical reaction in Cr film was applied to develop a tool for drawing patterns at the micrometer length scale. A considerable amount of effort was made to assemble a standalone lithography unit that can work in ambient as well as submerged in water conditions. Here, a micro-positioner was used to place the sample at the desired location relative to the tip, and a W-tip was traversed over the sample. The tip was brought into contact with (and detached from) sample using an “electromagnet-based lever-type drive.” A software-hardware interface was developed using LabView software, which was also capable of importing drawings made in third-party software, such as CleWin. Tool parameters, such as tip velocity, tip force, etc., were observed to have a significant impact on the pattern dimensions. Finally, several patterns, including closely spaced parallel lines, were generated using the developed tool in Cr films of different thicknesses and statistical information was obtained. In summary, this work, which includes both explorations of fundamentals and application of the learned fundamentals to develop new technology for lithography, confirms the constructive potential of the electric current and invites researchers to explore this area further.

Microcantilever sensor has gained much popularity because of its high sensitivity and selectivity. It consists of a micro-sized cantilever that is usually coated on one side with chemical/biological probe agents to generate strong attraction to target molecules. The interactions between the probe and target molecules induce surface stress that bends the microcantilever. This current work applied the molecular dynamics simulation to study the microcantilever system. Lennard-Jones potentials were used to model the target-target and target-probe interactions and bond bending potentials to model the solid cantilever beam. In addition, this work studied the effect of probe locations on the microcantilever deflection. The simulation results suggest that both target-target and target-probe interactions as well as the probe locations affect the arrangement of the bonds; in term of the bonding number, the area containing the bonded molecules, and the distances between them. All these factors influence the microcantilever deflection.

Since its discovery in 2004, the graphene global market had a huge/considerable growth. Such growth can be explained by the use of graphene in specific or targeted applications where it has a huge and clear advantage. Although graphene is growing and has many possible applications, its market fraction is insignificant compared to the carbon global market. This is simply explained because the industry still has challenges related to quality, costs, reproducibility and safety. In this chapter, we propose a new look on the mechanical exfoliation. Basically, based on the difference in binding energy between graphite, graphene and a substrate we can exfoliate. The binding energy is the energy between materials at equilibrium. When 3 materials A-B-C are interacting, if the binding energy between A-B is superior to B-C, then by moving A in the opposite direction, B will follow. Based on that, we calculated the interaction potential between graphite, graphene and a substrate using the standard Lennard-Jones potential. Conventional substrates like silicon and silicon dioxide cannot exfoliate while gold, silver and copper can at 3.2 to 3.3 Å. This difference may be because of their higher atomic density and modest lattice parameter compared to others substrates used in this study.

A numerical procedure for the surface deformation and adhesion between elastic half-spaces interacting by the Lennard-Jones surface potential is presented. The problem is solved based on the superposition of Boussinesq solutions for a half-space, with an iteration procedure to incorporate the nonlinear surface force-depression relation. First the axisymmetric contact between a sphere and a plane surface is demonstrated to show the validity of the procedure for a wide range of the Tabor parameter. The method is then applied to the contact between a sphere and a wavy surface, and the influence of the surface waviness on the adhesive behavior is illustrated.

A continuum model of adhesive interaction between elastic surfaces is presented. Surface interaction between two elastic spheres is modeled by the Lennard-Jones (L-J) potential. The analysis is based on the equivalent system of a rigid sphere of reduced radius in close proximity with an elastic half-space of effective elastic modulus. The critical gap at the instant of the “jump-in” and “jump-out” contact instabilities is determined by an elastic solution of the half-space surface displacement. A finite element model, in which surface interaction is modeled by nonlinear springs of a prescribed force-displacement governed by the L-J potential, is also used to analyze adhesive surface interaction. The analytical model is validated by finite element results of the critical central gap at the instant of jumpin and jump-out instabilities for different values of the Tabor parameter.

In typical atomistic simulations of simple liquids, the Lennard-Jones interatomic pair potential is truncated so that algorithms scale as Natoms rather Natoms2, which would be the case if an interaction were computed explicitly for all atom pairs. However, it is known that interfacial properties are sensitive to the cutoff radius selected. Corrections for the missing ‘tails’ of the potential can reduce the error, but cannot eliminate it because the liquid and vapor densities are also sensitive to the cutoff radius. In light of this, we have developed and implemented a NlogN particle-particle particle-mesh (P3M) algorithm to evaluate the 1/r6 dispersive forces between Lennard-Jones fluid molecules without truncation. Statistical expression for the surface tension also scale as N2 if potentials are not truncated, so we also developed a P3M formulation for computing surface tension. The techniques are demonstrated on a thin liquid film suspended in equilibrium with its own vapor. Simulations at several temperatures between the triple point and the critical point are compared with the available data. The expense of the algorithm is competitive for simple geometries and seems preferable in non-trivial geometries without the possibility of tail corrections.

We consider the bending of two nanotubes coupled together with van der Waal forces acting transverse to the axis, and subject to axial loads. The nanotubes are modeled as elastica while the interaction forces are derived from a Lennard-Jones 12-6 potential. The elastica are assumed to be a fixed distance apart at their ends, not necessarily equal to the equilibrium distance as identified from the Lennard-Jones potential. Therefore, the equilibrium configuration is not necessarily straight. As the compressive axial force increases, the beams can undergo buckling instability and the critical load depends not only on the material properties of the structure, but the geometry of the system as well. The continuum model is subjected to a Galerkin reduction to develop a reduced set of equations that can be used to calculate the equilibrium configuration of the system as well as the stability of these configurations. We show that the buckling instability in this model is significantly affected by the presence of the interaction force as well as the separation of the nanotubes at their ends.

A major challenge facing tumour treatment procedures, including hyperthermia, is the inadequate modelling of the bio-heat transfer process. Therefore, an accurate mathematical bio-heat transfer model has to precisely quantify the temperature distribution within a complex geometry of a tumour tissue, in order to help optimize unwanted side effects for patients and minimize (avoid) collateral tissue damage. This study examines the three-dimensional molecular dynamics (MDs) simulation of a Lennard-Jones fluid in the hope of contributing to the understanding of the propagation of a thermal wave in fluids causing phase change i.e. irreversible gelation. It is intended to establish, from such information, a useful benchmark for application to large scale phenomena involving macro scale heat transfer. Specifically, this study examines assemblies of N particles (N = 500 atoms) and analyses the microscopic simulation of double well interaction with permanent molecular bond formation at various temperatures within the range 1–2.5Kb/εT. The dynamics of the fluid is also being studied under the influence of a temperature gradient, dt/dx, where neighbouring particles (i.e. atoms/molecules) are randomly linked by permanent bonds to form clusters of different sizes. The atomic/molecular model consist of an isothermal source and sink whose particles are linked by springs to lattice sites to avoid melting, and a bulk of 500 atoms/molecules in the middle representing the Lennard-Jones fluid. Then, this study simulates the energy propagation following the temperature gradient between the heat source and heat sink at T1 = 2.5 and T2 = 1.5 respectively. The potential equation involved in this study is given by the Finitely Extensible Non Elastic (FENE) and Lennard-Jones (LJ) interaction potential. It is observed that the atoms of the bulk start to form a large cluster (∼ 300 atoms) with long time of simulation estimated by 106 time steps where τ = SQRT(ε/mσ2) and Δt = 10−3. It is also obtained that the potential energy of 13.65KbT across a barrier to establish permanent bonds giving rise to irreversible gel formation. All the parameters used in this study are expressed in Lennard-Jones units.

Abstract Molecular dynamics simulations are used to explore explosive boiling of thin water films on a gold substrate. In particular, water films of 2.5, 1.6 and 0.7 nanometer thickness were examined. Three different surface wettabilities with contact angles of 11, 47 and 110 degrees were simulated along with substrate temperatures of 400K, 600K, 800K and 1000K. The 11 degree contact angle was obtained using a Morse interaction potential between the water film and the gold substrate while the 47 and 110 degree contact angles were obtained via a Lennard-Jones potential. Evaporation was the first mode of phase change observed in all cases and explosive boiling did not occur until the substrate reached a temperature of 800K. When explosive boiling was present for all three contact angles, it was consistently shown to occur first for the surface with a 47 degree contact angle, contrary to the expectation that it would occur first on the substrate with an 11 degree contact angle. These results suggest that explosive boiling onset is strongly dependent on the particularities of the interaction potential. For instance, the Morse potential used to model the surface described by an 11 degree contact angle, is a softer potential as compared with Lennard-Jones, but has more interaction sites per molecule — two hydrogen atoms and one oxygen atom vs one oxygen atom. Thus, although the water film reaches a higher temperature with the Morse potential, explosive boiling onset is delayed as more interaction sites have to be disrupted. These results suggest that both the interaction strength and the number of atoms interacting at the interface must be considered when investigating trends of explosive boiling with surface wettability.

A method is proposed to estimate the enthalpy associated with the desorption of liquid molecules away from a solid surface as a function of temperature using a generic statistical thermodynamic formulation with known intermolecular potentials. This paper specifically focuses on coupling the well-known Redlich-Kwong fluid model with the interactive pair potential models between fluid molecules and a graphite surface. An example is applied where an approximate Lennard-Jones 6–12 intermolecular model dictates fluid-fluid molecule interaction, while the Steele potential is applied for the graphite-fluid interaction. Predictions suggest that the adsorption enthalpy of methanol on graphite is approximately 0.1 J/m2. A new metric is also established that suggests the qualitative magnitude of adsorption enthalpy for a variety of fluids, with alcohols and acetone appearing to be the most favorable.

The interaction stresses (pressure and shear stress) for (001) surface between a half-space consisting of a uniform material and a half-space with a spatially periodic material distribution have been derived based on the Lennard-Jones potential. The periodically distributed material property function is expanded as a complex Fourier series. The interaction pressures consist of non-fluctuation terms and fluctuation terms, while the shear stresses have only fluctuation terms. The interaction stresses for a distribution of two materials were then calculated as a typical example of a periodic material distribution. The basic characteristics of the interaction stresses are clarified.

Molecular dynamics (MD) simulations are carried out to calculate the surface tension of bubbles formed in a metastable Lennard-Jones (LJ) fluid. The calculated normal and transverse pressure components are used to compute a surface tension which is compared to the surface tension computed from the Young-Laplace equation. Curvature effects on surface tension are investigated by performing various sized simulations ranging from 6,912 to 256,000 LJ particles. Density profiles, pressures, and calculated surface tension are shown to have a strong dependence on the choice of the interaction cutoff radius. A cutoff radius of 8σ, significantly larger than that commonly used in the literature, is recommended for accurate calculations in liquid-vapor systems.

The interaction stresses acting between a half-space consisting of a uniform material and a half-space with a one-dimensional material distribution in the in-plane direction have been derived. Two patterns of the material distribution are considered: a periodic distribution of materials (Pattern 1) and a distribution of two materials with a single interface (Pattern 2). The interaction stresses for Pattern 1 were derived using a Fourier series, while the interaction stresses for Pattern 2 were derived as elementary functions. The basic characteristics of these interaction stresses were clarified.