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... The LJ fluid simulations are used to demonstrate the application of important physical chemistry concepts such as Newtonian mechanics, the Van der Waals equation of state, and the kinetic theory of gasses, while minimizing complexity and computing hardware requirements (any laptop is sufficient) thanks to the venerable, simple but effective, Lennard-Jones interaction potential. 8,9 This simplified fluid model is centered around a two parameter intermolecular pair potential that, despite decades of research since its introduction, is still a subject of current interest, 10,11 as is the development of coarse-grained models in general. [12][13][14][15] In addition to standalone LJ fluid simulations, the LJ potential is also utilized in many of the most widely used molecular dynamics (MD) force fields used to simulate proteins, nucleic acids, and other complex systems. ...

... C) This eight-point incomplete grid was produced from the function in panel A using the inputs 8, 10, and .75. Note how the function determines the positions for the nearest perfect square number of points(9) and returns all but the last to give 8 positions. ...

Most computational chemistry instructional activities are based around students running chemical simulations via a graphical user interface (GUI). GUI-based activities offer many advantages, as they enable students to run chemical simulations with a few mouse clicks. Although these activities are excellent for introducing students to the capabilities of chemical simulations, the disadvantage is that the students’ experience is not representative of how professional computational chemists work. Just as it is important that students in an organic chemistry instructional lab gain hands-on experience with equipment commonly used by professional organic chemists, students of computational chemistry must gain hands-on experience with coding, as professional computational chemists do not rely on GUIs; we write code. Motivated by the need for instructional activities that provide hands-on experience with computer code, a pair of activities were created around a free lightweight (runs on standard laptops) open-source Lennard-Jones (LJ) fluid simulation code written in Python, a programming language that prioritizes readability. The first activity, aimed at undergraduate physical chemistry lab courses, involves students writing Python code in a Jupyter Notebook that is used to run LJ simulations and fit a Van der Waals gas model to data produced by the LJ fluid simulations. The second is a jigsaw activity, aimed at advanced undergraduate or graduate students, where students are assigned different sections of the LJ fluid simulation code, and must demonstrate the functionality of their section to the class by both giving an oral presentation and sharing a Jupyter Notebook demonstration of their own design.

... Advances in ML and the automation of the development of large computational databases have driven the field of materials modeling to develop new approaches. In the past, interatomic classical potentials were developed based on physically motivated forms, following from the quantum mechanical treatment of electronic bonding to "integrate out" the electronic degrees of freedom [40][41][42][43][44][45][46][47][48]. While there is a strong benefit in relying on physical intuition in the development of models, the advantages of ML combined with the increasing availability of large-scale computational resources to generate large densityfunctional theory (DFT)-based databases has greatly changed the approaches to modeling interatomic potentials; see [49][50][51][52][53][54][55][56][57][58][59]. ...

... This form has shown sufficient flexibility to study both metals and semiconductors, but its use for multicomponent systems remains limited due to the lack of optimized parameters for multicomponent systems. The spline MEAM form itself can be thought of as a superset of other interatomic potentials from Lennard-Jones [40] (LJ), to the embedded-atom method [42] (EAM), the original modified embedded-atom method [43] (MEAM), the famous silicon Stillinger-Weber [45] (SW) potential and Tersoff [44] potentials. A recent study [39] showed the overlap of the traditional interatomic potentials with ML approaches. ...

We present an overview of four challenging research areas in multiscale physics and engineering as well as four data science topics that may be developed for addressing these challenges. We focus on multiscale spatiotemporal problems in light of the importance of understanding the accompanying scientific processes and engineering ideas, where “multiscale” refers to concurrent, non-trivial and coupled models over scales separated by orders of magnitude in either space, time, energy, momenta, or any other relevant parameter. Specifically, we consider problems where the data may be obtained at various resolutions; analyzing such data and constructing coupled models led to open research questions in various applications of data science. Numeric studies are reported for one of the data science techniques discussed here for illustration, namely, on approximate Bayesian computations.

... DFT exists along a spectrum of methods to calculate the energy and forces of an atomic configuration that trade off computation time and accuracy. On one end there are traditional force fields, which include simple classical physics-inspired terms like the Lennard-Jones potential [24]. These potentials can be rapidly evaluated, but often lack transferability and/or accuracy. ...

We present evidence that learned density functional theory (``DFT'') force fields are ready for ground state catalyst discovery. Our key finding is that relaxation using forces from a learned potential yields structures with similar or lower energy to those relaxed using the RPBE functional in over 50\% of evaluated systems, despite the fact that the predicted forces differ significantly from the ground truth. This has the surprising implication that learned potentials may be ready for replacing DFT in challenging catalytic systems such as those found in the Open Catalyst 2020 dataset. Furthermore, we show that a force field trained on a locally harmonic energy surface with the same minima as a target DFT energy is also able to find lower or similar energy structures in over 50\% of cases. This ``Easy Potential'' converges in fewer steps than a standard model trained on true energies and forces, which further accelerates calculations. Its success illustrates a key point: learned potentials can locate energy minima even when the model has high force errors. The main requirement for structure optimisation is simply that the learned potential has the correct minima. Since learned potentials are fast and scale linearly with system size, our results open the possibility of quickly finding ground states for large systems.

... In MDS of Ar and Pt-based samples, the interatomic potential of atoms was according to the UFF and EAM [42][43][44]. The LJ potential calculates the interactions between the Pt and Ar particles (Eq. 1) [45]. here, r ij and r c represent the particles' distance and cut-off radius. ...

Nanochannels (NCs) are hopeful structures for mass transfer (MT) and heat transfer (HT) procedures in actual usages. Prior reports displayed the atomic behavior of various fluids inside perfect NCs. This examination uses the molecular dynamics simulation (MDS) approach to examine the impact of obstacle numbers on argon flow inside Platinum-based NCs. Simulation outputs were presented by calculating physical quantities like temperature (T), potential energy(PE), density (D)/temperature (T)/velocity (V) profiles, and interaction energy(IE). MDS results show that as the number of obstacles (N.Os) increases, the maximum D increases from 0.093 to 0.099 atom/Å³. The maximum V decreases from 0.0031 to 0.0025 Å/ps by the expansion of the N.Os. The maximum T decreases from 329.46 to 318.43 K. By the N.Os increments, the fluid particles' oscillations (FP) and their temperature also decrease. This mechanism can reduce the temperature in the HT process. In addition, with the enhancement of the N.Os from 1 to 4, the IE increases from -60.52 to 70.86 - eV. This increase in IE can reduce the atomic stability of platinum NCs. This behavior reduces the lifetime of NCs in heat/mass transfer processes. Therefore, it is expected that with the outcomes of the current examination and the control of the N.Os, we will be able to optimize the various processes like MT and HT for industrial purposes.

... The Lennard -Jones potential (proposed by [4]) was originally developed to describe the potential energy of interaction between two nonbonding atoms or molecules based on their distance of separation. According to [5], the potential was also developed to treat noble gases but it is often used to describe metals and other forms of solids and liquids. ...

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.

... Review where A, B, and C are adjustable constants. There is a mathematically and computationally simpler form of eq 22 known as the "Lennard−Jones (L−J) 12−6" pair potential, where the exponential term is replaced with a ∼ 1/r 12 power term, chosen for its numerical efficiency, 246 describes closely enough the exponential soft repulsive wall, not too far from the equilibrium distance of two nonbonded atoms: ...

Carbon nanodots (CNDs) are the latest and most shining rising stars among photoluminescent (PL) nanomaterials. These carbon-based surface-passivated nanostructures compete with other related PL materials, including traditional semiconductor quantum dots and organic dyes, with a long list of benefits and emerging applications. Advantages of CNDs include tunable inherent optical properties and high photostability, rich possibilities for surface functionalization and doping, dispersibility, low toxicity, and viable synthesis (top-down and bottom-up) from organic materials. CNDs can be applied to biomedicine including imaging and sensing, drug-delivery, photodynamic therapy, photocatalysis but also to energy harvesting in solar cells and as LEDs. More applications are reported continuously, making this already a research field of its own. Understanding of the properties of CNDs requires one to go to the levels of electrons, atoms, molecules, and nanostructures at different scales using modern molecular modeling and to correlate it tightly with experiments. This review highlights different in silico techniques and studies, from quantum chemistry to the mesoscale, with particular reference to carbon nanodots, carbonaceous nanoparticles whose structural and photophysical properties are not fully elucidated. The role of experimental investigation is also presented. Hereby, we hope to encourage the reader to investigate CNDs and to apply virtual chemistry to obtain further insights needed to customize these amazing systems for novel prospective applications.

... Although obviously first introduced by Mie [36], U * LJ (r * ) nowadays is known as the Lennard-Jones (n-m) potential [12,14,37]. It has two adjustable parameters n and m. ...

We investigate the reduced collision integrals $$\Omega ^{(\ell ,s)*}(T^*)$$ Ω ( ℓ , s ) ∗ ( T ∗ ) for $$1 \le \ell \le 4$$ 1 ≤ ℓ ≤ 4 , $$\ell \le s \le 7$$ ℓ ≤ s ≤ 7 and $$\ell + s \le 8$$ ℓ + s ≤ 8 for several isotropic potential energy functions: the Lennard–Jones $$(n-m)$$ ( n - m ) , the Hulburt–Hirschfelder, and Tang–Toennies potential. It is observed that for a given $$\ell$$ ℓ and s , $$\Omega ^{(\ell ,s)*}(T^*)$$ Ω ( ℓ , s ) ∗ ( T ∗ ) shows a mutual intersection region at a reduced temperature $$0.39< T^*=T^*_{\ell s} < 2.22$$ 0.39 < T ∗ = T ℓ s ∗ < 2.22 which is nearly independent of the potential energy function used.

... exponent. 2 This model has been extensively utilized in the different studies of interatomic interactions with good validation. However, debate as to the lack of a physical basis for the inverse power-law repulsion has been offered despite their experimental validation. ...

... To determine the Lennard-Jones forces from formula (7), it is necessary to determine the quantities A and B. Formula (8) is used to determine the magnitude of B [21,22]. The quantities αSi and αSn in formula (8) are the polarity of silicon and tin in solution. ...

Silicon epitaxial layers were grown on a silicon (Si<111>) substrate in the range of 1323÷1073 K with initial crystallization temperatures from the silicon-tin (Si-Sn) solution. To determine the forces acting between the silicon nanoclusters in solution and the tin (Sn) particles and the silicon (Si) surface, the dielectric constant values of silicon, tin at selected temperatures were found experimentally. Given the Gibbs energy of the system to obtain the perfect epitaxial layers and structures of the crystal, optimal technological growth conditions are given.

... MD and other approaches numerically solving Newton's equations of motion require the use of semi-empirical atomistic potentials, which enable calculations of the total energy and interatomic forces. Early atomistic simulations employed pair potentials, usually of the Lennard-Jones or Morse type [21,22], but they give only qualitative agreement with the experimental data. A few decades later, Daw and Baskes [23] and Finnis and Sinclair [24] proposed a more advanced potential form called the embedded atom method (EAM). ...

Classical molecular dynamics and x-ray diffraction have been used to establish the origin of the paracrystalline structure of silver nanoparticles at the atomic scale. Models based on the face-centred cubic structure have been computer generated and their atomic arrangements have been optimized by the molecular dynamics with the embedded-atom model (EAM) potential and its modified version (MEAM). The simulation results are compared with the experimental x-ray diffraction data in reciprocal and real spaces, i.e., the structure factor and the pair distribution function. The applied approach returns the structural models, defined by the Cartesian coordinates of the constituent atoms. It has been found that most of the structural features of Ag nanoparticles are better reproduced by the MEAM. The presence of vacancy defects in the structure of the Ag nanoparticles has been considered and the average concentration of vacancies is estimated to be 3 at.%. The average nearest-neighbour Ag-Ag distances and the coordination numbers are determined and compared with the values predicted for the bulk Ag, demonstrating a different degree of structural disorder on the surface and in the core, compared to the bulk crystalline counterpart. It has been shown that the paracrystalline structure of the Ag nanoparticles has origin in the surface disorder and the disorder generated by the presence of the vacancy defects. Both sources lead to network distortion that propagates proportionally to the square root of the interatomic distances.

... In fact, in most cases, it defines the quality of the performed simulation. Some potential models have been successfully developed, like Lenard-Jones [8][9][10], Embedded Atom Method (EAM) [11][12][13], Tersoff [14], Tight Binding [15], Brenner [16], Finnis-Sinclair [17] and so on. Every interatomic potential model developed is most likely used specifically for a particular material, for instance, EAM many-body potential that has been developed for use in the investigation of metallic materials like Cu, Ag, Au, Ni, Pd, Pt [12]. ...

Carbon-nanotubes (CNTs) and Nanowires (NWs), the two nanomaterials with outstanding properties, are
the materials with which their behaviour and properties have long been drawing attention to researchers. However,
the tiny nature of these two materials causes difficulties in describing and estimating their behaviour and properties,
thus a numerical technique that considers the tiny nature of the materials like Molecular Dynamics (MD) simulation
is a promising solution to this problem. Since the early utilization of MD simulation in the investigation of the
behaviour of carbon-nanotubes and nanowires, it provides the researcher with an excellent description of how the
two materials behave at atomic-scale and then estimate their properties. Recently, MD simulation of CNTs and NWs
exhibit growth in the simulation size as with the growth of the computing capabilities. The size of the materials being
simulated by MD simulation increased significantly in the recent year, thus giving possibility to achieve a better
description of the behaviour and a more precise estimation of the properties. In this review, we provide an overview
of the recent advances in the investigation of the joining processes and properties of carbon-nanotubes and nanowires
at atomic-scale utilizing molecular dynamics simulation.

... The Lennard-Jones potential is the power source of atomic interaction force [30,54]. To describe the mathematical model of interaction force, the sum of the forces acting on the ith atom can be defined as (1). ...

Atom search optimization (ASO) is a newly developed metaheuristic algorithm inspired by molecular basis dynamics. The paramount challenge in ASO is that it is easily trapped into the local optima and premature convergence. To address these issues, this paper presented an improved atom search optimization with three strategies, global topology with secant factor, non-linear inertia weight and update learning. First, the global topology provides the best solution for each individual and enriches the information exchange of the population, and prevents premature convergence under the effect of the secant factor. Second, smooth properties of non-linear inertia weights are introduced to balance exploration and exploitation. Third, update learning provides more opportunities to jump out of the local optima. Thus, these three strategies are used to improve the performance of ASO, which is called GNUASO. Finally, the proposed GNUASO algorithm was evaluated in the CEC2017 benchmark functions and two real-world engineering problems, compared with some excellent algorithms to confirm the performance of the proposed GNUASO. Experimental results and statistical analysis show that the proposed GNUASO algorithm outperforms the other selected algorithms in CEC2017 benchmark functions and engineering design problems.

... 2. The interatomic pair potentials [258,259] ...

The physical phenomena are described by physical quantities related by specific physical laws. In the context of a Physical Theory, the physical quantities and the physical laws are described, respectively, by suitable geometrical objects and relations between these objects. These relations are expressed with systems of (mainly second order) differential equations. The solution of these equations is frequently a formidable task, either because the dynamical equations cannot be integrated by standard methods or because the defined dynamical system is non-integrable. Therefore, it is important that we have a systematic and reliable method to determine their integrability. This has led to the development of several (algebraic or geometric) methods, which determine if a dynamical system is integrable/superintegrable or not. Most of these methods concern the first integrals (FIs), that is, quantities that are constant along the evolution of the system. The FIs appear in the literature with many names such as constants of motion, conserved currents, and conservation laws. FIs are important, because they can be used to reduce the order of the system of the dynamical equations and, if there are `enough' of them, even to determine its solution by means of quadratures. In the latter case, the dynamical system is said to be Liouville integrable and it is associated with a canonical Lagrangian, whose kinetic energy defines a metric tensor known as kinetic metric. It is proved that there is a close relation between the geometric symmetries (collineations and Killing tensors) of this metric and the quantities defining the FIs. This correspondence makes it possible to use powerful results from Differential Geometry in the study of the integrability of dynamical systems. In this thesis, we study this correspondence and geometrize the determination of FIs by developing a new geometric method to compute them.

... Therefore, MD simulations are performed by collapsing the range to 0.2 nm [37] . The vdW interactions are modeled using the Lennard-Jones (L-J) potential [38] U L-J = 4 σ r i j 12 − σ r i j 6 (2) where σ = 3 . 4 Å and = 2 . ...

Here, we characterize the axial response of helical single-walled carbon nanotubes (HSWCNTs) to mechanical and electrostatic loads, separately. The study considers low-pitch (closed) and high-pitch (open) HSWCNTs of different number of turns in their natural states. The computations are carried out using molecular dynamics near 0 K and at 300 K. Under mechanical loading, the low-pitch HSWCNTs show a bilinear load (F) - strain (ϵ) relation up to their elastic limit by overcoming; (i) the inter-coil van der Waals and the elastic restoring forces, and (ii) only the elastic restoring forces, in that order. However, a tunable plastic-like region emerges between the two linear regimes which is dependent of the number of active coils. Unloading of low-pitch HSWCNTs within the elastic limit exhibits hysteresis in F−ϵ graph. However, unloading both low- and high-pitch HSWCNTs from a point beyond their elastic limits results in accumulation of plastic strain. Electrostatic loading of HSWCNTs causes inter-coil Coulombic repulsion which after overcoming the van der Waal’s attraction between them and the mechanical restoring forces, produces a net elongation. Interestingly, the charge per atom (q) – strain (ϵ) graphs for the high-pitch HSWCNTs up to their elastic limit are found to follow the power law: q∝ϵ3/5. Discharging the HSWCNTs completely from a point beyond their elastic limit shows plastic deformation. Mechanical and electrostatic loading, unloading, and reloading of the HSWCNTs up to the fracture point are also examined. The study shows a direction towards developing nano-electro-mechanical actuators and precise positioners based on HSWCNTs.

... We assume that the interaction potential between two strangeons is described by the Lennard-Jones potential (Jones 1924;Lai & Xu 2009;Gao et al. 2022), ...

The strong interaction at low energy scales determines the equation of state (EOS) of supranuclear matters in neutron stars (NSs). It is conjectured that the bulk dense matter may be composed of strangeons, which are quark clusters with nearly equal numbers of $u$, $d$, and $s$ quarks. To characterize the strong-repulsive interaction at short distance and the nonrelativistic nature of strangeons, a phenomenological Lennard-Jones model with two parameters is used to describe the EOS of strangeon stars (SSs). For the first time, we investigate the oscillation modes of non-rotating SSs and obtain their frequencies for various parameterizations of the EOS. We find that the properties of radial oscillations of SSs are different from those of NSs, especially for stars with relatively low central energy densities. Moreover, we calculate the $f$-mode frequency of nonradial oscillations of SSs within the relativistic Cowling approximation. The frequencies of the $f$-mode of SSs are found to be in the range from $6.7\,$kHz to $ 8.7\,\rm{kHz}$. Finally, we study the universal relations between the $f$-mode frequency and global properties of SSs, such as the compactness and the tidal deformability. The results we obtained are relevant to pulsar timing and gravitational waves, and will help to probe NSs' EOSs and infer nonperturbative behaviours in quantum chromodynamics.

... We used the Lennard-Jones 6−12 (LJ) [25] + Coulomb potentials to describe the interactions between the host and the sorbate atoms. Each atom of the host or the guest was treated explicitly. ...

In the present work, the interaction strength of Carbon Monoxide (CO) with a set of forty-two, strategically selected, functionalized benzenes was calculated. Our ab initio calculations at the MP2/6-311++G** level of theory reveal that phenyl hydrogen sulfate (-OSO3H) showed the highest interaction with CO (−19.5 kJ/mol), which was approximately three times stronger compared with the unfunctionalized benzene (−5.3 kJ/mol). Moreover, the three top-performing functional groups (-OSO3H, -OPO3H2, -SO3H) were selected to modify the organic linker of IRMOF-8 and test their ability to capture CO at 298 K for a wide pressure range. Our Grand Canonical Monte Carlo (GCMC) simulations showed a significant increase in the CO uptake in the functionalized MOFs compared with the parent IRMOF-8. It is distinctive that for the volumetric uptake, a 60× increase was observed at 1 bar and 2× was observed at 100 bar. The proposed functionalization strategy can be applied for improving the CO uptake performance not only in MOFs but also in various other porous materials.

... The collision integral Ω AB is obtained from the Lennard-Jones parameters. For example, one of the well-known correlations for expressing intermolecular energy ψ in terms of intermolecular distance r is given from the Lennard-Jones potential model [132][133][134]: ...

The existence of various native or nonnative species/fluids, along with having more than one phase in the subsurface and within the integrated production and injection systems, generates unique challenges as the pressure, temperature, composition and time (P-T-z and t) domains exhibit multi-scale characteristics. In such systems, fluid/component mixing, whether for natural reasons or man-made reasons, is one of the most complex aspects of the behavior of the system, as inherent compositions are partially or all due to these phenomena. Any time a gradient is introduced, these systems try to converge thermodynamically to an equilibrium state while being in the disequilibrium state at scale during the transitional process. These disequilibrium states create diffusive gradients, which, in the absence of flow, control the mixing processes leading to equilibrium at a certain time scale, which could also be a function of various time and length scales associated with the system. Therefore, it is crucial to understand these aspects, especially when technologies that need or utilize these concepts are under development. For example, as the technology of gas-injection-based enhanced oil recovery, CO2 sequestration and flooding have been developed, deployed and applied to several reservoirs/aquifers worldwide, performing research on mass-transfer mechanisms between gas, oil and aqueous phases became more important, especially in terms of optimal design considerations. It is well-known that in absence of direct frontal contact and convective mixing, diffusive mixing is one of most dominant mass-transfer mechanisms, which has an impact on the effectiveness of the oil recovery and gas injection processes. Therefore, in this work, we review the fundamentals of diffusive mixing processes in general terms and summarize the theoretical, experimental and empirical studies to estimate the diffusion coefficients at high pressure—temperature conditions at various time and length scales relevant to reservoir-fluid systems.

... The simplest potentials only consider pairwise interactions and are called pair-potential. For example, the widely used Lennard-Jones potential [Jones, 1924] is a pairpotential. Its expression is ...

Les réseaux de neurones profonds ont permis récemment d'importants progrès dans les problèmes d’apprentissage en grande dimension, notamment en classification d'images et en régression d'énergie en physique. Ces deux problèmes sont de nature multi-échelle. En effet, l'énergie des molécules et des solides résulte d'interactions à différentes échelles, avec par exemple les liaisons ioniques et covalentes à petite échelle, les interactions de Van-der-Waals aux échelles moyennes et les interactions de Coulomb à grande échelle. De même, on peut classifier une image en utilisant des informations de texture à petite échelle, des informations de motif à moyenne échelle ou des informations de forme à l'échelle de l’objet. De plus, il existe une analogie naturelle entre les techniques de classification d'images dites locales, basées sur des petits patch d'image, et les techniques de régression énergétique dites locales, basées sur la description de petits voisinages atomiques dans les molécules ou les solides. Dans ce manuscrit, nous étudions l'efficacité des méthodes locales pour la classification d'images et la régression d'énergie en physique. On observe que les méthodes locales sont étonnamment performantes pour ces deux problèmes, et ce malgré la nature multi-échelle de ces problèmes.Tout d'abord, nous étudions comparativement des techniques multi-échelles et locales pour la régression d'énergie de molécules et solides. Nous constatons que les méthodes locales sont très performantes, même pour les solides avec des composantes énergétiques à longue portée.Nous présentons une nouvelle méthode pour la régression d'entropie vibrationnelle dans les solides. Là encore, nous observons qu'une méthode utilisant des descripteurs locaux donne de bien meilleurs résultats que la stratégie multi-échelle étudiée. Pour la classification d'images, nous présentons un réseau de neurones convolutif structuré basé sur l'encodage de patch. Cette architecture donne des performances comparables à des réseaux convolutifs standards sur la base de données ImageNet. Enfin nous présentons un classificateur d'images basé sur des calculs de K-plus-proches-voisins de patch d’images, et dont les performances surprenantes suggèrent une forme de basse dimension des patch d’images. Nous terminons cette dissertation par une ouverture sur les dispositifs interactifs humain-machine pour la création artistique.

... Therefore, MD simulations are performed by collapsing the range to 0.2 nm [37] . The vdW interactions are modeled using the Lennard-Jones (L-J) potential [38] U L-J = 4 σ r i j 12 − σ r i j 6 (2) where σ = 3 . 4 Å and = 2 . ...

... Intra-molecular interactions are retained at this stage for technical reasons (discussed later). When deactivating the intermolecular interactions care should be taken to avoid potentials with singularities at the origin e.g. the Lennard-Jones potential 31,32 . In our calculations we use softcore potentials 33 , which remove the singularity at r = 0. ...

We present a general method for computing interfacial free energies from atomistic simulations, which is particularly suitable for solid/liquid interfaces. Our method uses an Einstein crystal as a universal reference state and is more flexible than previous approaches. Surfaces with dipoles, complex reconstructions, and partially dissolved species are all easily accommodated within the framework. It may also be extended to calculating the relative free energies of different phases and other types of defect. We have applied our method to interfaces of bassanite and gypsum with water and obtained interfacial free energies of the order of 0.15 J/m ² , of which approximately 50 % is due to entropic contributions. Our calculations of the interfacial free energy of NaCl with water obtained a value of 0.13 J/m ² of which only 19 % is from entropic contributions. We have also predicted equilibrium morphologies for bassanite and gypsum that compare well with experiments and previous calculations.

By combining interface-pinning simulations with numerical integration of the Clausius–Clapeyron equation, we accurately determine the melting-line coexistence pressure and fluid/crystal densities of the Weeks–Chandler–Andersen system, covering four decades of temperature. The data are used for comparing the melting-line predictions of the Boltzmann, Andersen–Weeks–Chandler, Barker–Henderson, and Stillinger hard-sphere approximations. The Andersen–Weeks–Chandler and Barker–Henderson theories give the most accurate predictions, and they both work excellently in the zero-temperature limit for which analytical expressions are derived here.

A modification of the structural phase-field crystal (XPFC) model for a Lennard-Jones (LJ) pair interaction potential is presented. Formation of 1D and 2D structures for the LJ-potential was studied numerically. The equilibrium lattice parameters for the obtained structures were found consistent to the correspondent LJ-distance parameters. The lattice parameter of 2D triangle's structure matches the periodical in 1D, which is consistent to the theory of freezing from the isotropic liquids. Numerically obtained phase diagram of two-dimensional structures qualitatively reproduces classical PFC diagram and coincides with the melting region of high-temperature part of LJ diagram.

Self-assembly of dilute sequence-defined macromolecules is a complex phenomenon in which the local arrangement of chemical moieties can lead to the formation of long-range structure. The dependence of this structure on the sequence necessarily implies that a mapping between the two exists, yet it has been difficult to model so far. Predicting the aggregation behavior of these macromolecules is challenging due to the lack of effective order parameters, a vast design space, inherent variability, and high computational costs associated with currently available simulation techniques. Here, we accurately predict the morphology of aggregates self-assembled from sequence-defined macromolecules using supervised machine learning. We find that regression models with implicit representation learning perform significantly better than those based on engineered features such as k-mer counting, and a recurrent-neural-network-based regressor performs the best out of nine model architectures we tested. Furthermore, we demonstrate the high-throughput screening of monomer sequences using the regression model to identify candidates for self-assembly into selected morphologies. Our strategy is shown to successfully identify multiple suitable sequences in every test we performed, so we hope the insights gained here can be extended to other increasingly complex design scenarios in the future, such as the design of sequences under polydispersity and at varying environmental conditions.

Experimental isotherms of N2 and CO2 on carbon‐based porous materials and models of the physisorption of gases on surfaces are used to obtain the pore size distribution (PSD). An accurate modelization of the physisorption of N2 and CO2 on the surface of carbon‐based porous materials is important to obtain accurate N2 and CO2 storage capacities and reliable PSDs. Physisorption depends on the dispersion interactions. High precision ab initio methods, such as CCSD(T), consider accurately the dispersion interactions, but they are computationally expensive. Double hybrid, hybrid and DFT‐based methods are much less expensive. In the case of graphene, there are experimental data of the adsorption of N2 and CO2 on graphite that can be used to build the Steele interaction potential of these gases on graphene. The goal is to find out hybrid and/or DFT methods that are as accurate as the CCSD(T) on benzene and as accurate as the experimental results on graphene. Calculations of the interaction energy curves of N2 and CO2 on benzene and graphene have been carried out using the CCSD(T) method and several double hybrid, hybrid, and DFT methods that consider the dispersion interactions. The energy curves on benzene have been compared to the CCSD(T) and the energy curves on graphene have been compared with the Steele energy curves. The comparisons indicate that double hybrids with dispersion corrections and ωB97 based DFT methods are accurate enough for benzene. For graphene, only the PBE‐XDM functional has a good agreement with the Steele energy curves. N2 and CO2 physisorption on benzene and graphene.

Compactly, this thesis encompasses two major parts to examine mechanical responses of polymer compounds and two dimensional materials: 1- Molecular dynamics approach is investigated to study transverse impact behavior of polymers, polymer compounds and two dimensional materials. 2- Large deflection of circular and rectangular membranes is examined by employing continuum mechanics approach. Two dimensional materials (2D), including, Graphene and molybdenum disulfide (MoS2), exhibited new and promising physical and chemical properties, opening new opportunities to be utilized alone or to enhance the performance of conventional materials. These 2D materials have attracted tremendous attention owing to their outstanding physical properties, especially concerning transverse impact loading. Polymers, with the backbone of carbon (organic polymers) or do not include carbon atoms in the backbone (inorganic polymers) like polydimethylsiloxane (PDMS), have extraordinary characteristics particularly their flexibility leads to various easy ways of forming and casting. These simple shape processing label polymers as an excellent material often used as a matrix in composites (polymer compounds). In this PhD work, Classical Molecular Dynamics (MD) is implemented to calculate transverse impact loading of 2D materials as well as polymer compounds reinforced with graphene sheets. In particular, MD was adopted to investigate perforation of the target and impact resistance force . By employing MD approach, the minimum velocity of the projectile that could create perforation and passes through the target is obtained. The largest investigation was focused on how graphene could enhance the impact properties of the compound. Also the purpose of this work was to discover the effect of the atomic arrangement of 2D materials on the impact problem. To this aim, the impact properties of two different 2D materials, graphene and MoS2, are studied. The simulation of chemical functionalization was carried out systematically, either with covalently bonded molecules or with non-bonded ones, focusing the following efforts on the covalently bounded species, revealed as the most efficient linkers. To study transverse impact behavior by using classical MD approach , Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software, that is well-known among most researchers, is employed. The simulation is done through predefined commands in LAMMPS. Generally these commands (atom style, pair style, angle style, dihedral style, improper style, kspace style, read data, fix, run, compute and so on) are used to simulate and run the model for the desired outputs. Depends on the particles and model types, suitable inter-atomic potentials (force fields) are considered. The ensembles, constraints and boundary conditions are applied depends upon the problem definition. To do so, atomic creation is needed. Python codes are developed to generate particles which explain atomic arrangement of each model. Each atomic arrangement introduced separately to LAMMPS for simulation. After applying constraints and boundary conditions, LAMMPS also include integrators like velocity-Verlet integrator or Brownian dynamics or other types of integrator to run the simulation and finally the outputs are emerged. The outputs are inspected carefully to appreciate the natural behavior of the problem. Appreciation of natural properties of the materials assist us to design new applicable materials. In investigation on the large deflection of circular and rectangular membranes, which is related to the second part of this thesis, continuum mechanics approach is implemented. Nonlinear Föppl membrane theory, which carefully release nonlinear governing equations of motion, is considered to establish the non-linear partial differential equilibrium equations of the membranes under distributed and centric point loads. The Galerkin and energy methods are utilized to solve non-linear partial differential equilibrium equations of circular and rectangular plates respectively. Maximum deflection as well as stress through the film region, which are kinds of issue in many industrial applications, are obtained.

In the current computational work, the atomic behaviour of Hydrogen (H) atoms (as fluid) inside 2D Platinum (Pt) nanochannel (NC) in the presence of obstacles is described using molecular dynamics simulation (MDS) for clinical applications. This simulation method is reported by temperature (T), total energy, profiles of density/velocity/T and interaction energy of simulated compounds. Computationally, a fluid-NC system modelled with Universal Force Field (UFF) and Embedded Atom Model (EAM) potentials (force-fields). MD outputs indicated the potential energy of samples converged to a negative amount after 5 ns. This physical behaviour shows the stability of the defined system at T=300 K. Furthermore, the simulation results show the atomic behaviour of H fluid optimized by atomic obstacle radius optimizing. By using NC with an obstacle, the interaction energy between fluid atoms and NC walls reach -40.44 eV and by this process occur, mass transfer phenomenon optimized for clinical aims.

Fine granular media are pivotal in thermochemical energy storage technology. Reactors based on granular materials store the heat using reversible reactions at high temperatures. Yet, powders become increasingly cohesive in those conditions. The rise of powder cohesion at high temperatures is one of the most irksome phenomena still limiting the scalability of this technology. We found titania coatings comprise an excellent solution to control cohesion in fine limestone powders at high temperatures. Limestone is the main component in granular flows running solid-based storage circuits based on the calcium looping process. It is also involved in many other industrial applications. Titania layers were used to shape stiffer carbonate surfaces at high temperatures (close to the Tamman point). The experiments conducted in this work investigated the benefits of these layers, examining the powder cohesion as the contact between particles evolved from rigid to plastic surfaces. In doing so, samples were subjected to different temperatures varying from 25 °C to 500 °C and preconsolidations up to 2 kPa. The results revealed that titania coatings shield (mechanically) carbonate particles, making surfaces more resilient to deformation while particles interact. The efficiency of titania layers was compared with samples coated with nanosilica, which is a solution broadly accepted nowadays for limestone powders. The experiments tackled one of the weaknesses of nanosilica coatings, namely their efficiency when particles are barely coated. Interestingly, at high temperatures, samples treated with titania outperformed those layered with nanosilica for surface coverages around 9%. Moreover, despite such a moderate amount of coverage, samples coated with titania reached an easy-flow regime even at high temperatures. However, samples treated with nanosilica fluidized less uniformly, and their flowability fell into a cohesive-flow regime in similar conditions. In conclusion, titania coatings represent an excellent alternative to deal with those flowability issues that still limit the scalability of solid-based storage technology.

The study of the reactivity of solid catalysts requires assessing chemical kinetics and mechanism in the absence of mass transport artifacts. These artifacts consist of the formation of concentration gradients either on the external or internal (inside nanopores) surface of the solid. Despite the existence of models and criteria for assessing the presence of mass transfer limitations during catalytic tests for gas-phase reactions in isothermal fixed bed reactors, the literature does not present straightforward protocols for performing the latter calculations. In this work, we present a systematic and complete protocol for the calculations above. The developed protocol serves as a tutorial for students and researchers. Particularly, the effectiveness factor for external and the Weisz-Prater number for the internal mass transfer limitations were developed. The oxidation of propane over mixed vanadium-aluminum (hydr)oxides was taken as a case study. Based on these protocols we perform a sensitivity study of the models for the following modifications: (i) the equation of state for modeling the thermodynamic properties of the gas phase, (ii) the particle size, (iii) the conversion of propane at two different temperatures and, (iv) the reactant used as a basis of the calculations; i.e., switching from propane to oxygen. Results showed that the model for calculating the effectiveness factor was poorly sensitive to all the above modifications. Meanwhile, the Weisz-Prater number was much more sensitive to the studied modifications, even reaching deviations up to ~200%.

Various fluids are implemented for mass/heat transfer procedures in industrial applications. These structures' behavior inside the metallic nanochannels (NCs) in the presence of the obstacle was described. To this end, the Molecular Dynamics Simulation (MDS) method is performed by the LAMMPS package. The various atomic forces in defined structures are defined using Universal Force Field (UFF) and Embedded Atom Model (EAM). In addition, physical parameters such as temperature (T), potential energy (PE), Radial Distribution Function (RDF), profiles of density (D)/velocity(V)/T, position histogram, trajectory lines, and interaction energy are reported for nanofluid (NF) behavior description. MDS results display the equilibrium of Ar (as fluid) and Pt (as NC) in the presence of obstacles after t=20 ns. Also, our simulations predict that the obstacles increase/decrease the average values of fluid adsorption/mobility inside the NC.

The breakup of liquid drops is an important phenomenology for many applications. We approach this problem with the objective of improving methods for modeling the impulse and impact dispersal of liquids in transportation accident scenarios. These scenarios can be distinguished from many other simpler problems due to the quantity of liquid and the complexity of the intermediate liquid morphology. These differences necessitate alternative (lower computational cost and lower fidelity) approaches to the problem compared to much of the historical modeling work. This work leverages a recently implemented model for inter-particle forces in a Lagrangian/Eulerian computational fluid dynamics (CFD) code. The inter-particle force model is inspired by molecular dynamics methods. It employs a Lennard-Jones (LJ) attractive force and a spring-based repulsive force that is governed by LJ parameters. The LJ parameters are related to the bulk fluid properties through a theoretical relationship to the surface tension. Methods are developed for modifying the single particle aerodynamic drag term, depending on the new notion of particle connectivity. These methods are evaluated for potential utilization in practical simulations. Breakup experiments for drops in flows from prior studies suggest a critical Weber number relating to the onset of breakup for a drop. These data are replicated with the proposed model and it is shown that the proposed method can reasonably reproduce aspects of breakup for a range of scales with only a single tuned parameter.

Investigation of the behavior of cancer cells and their mechanical and physical characteristics can play an important role in the early diagnosis and treatment of cancer. In this paper, the molecular dynamics method (MDM) investigates cancer cells' atomic behavior and stability under different external forces and initial pressures. To investigate the atomic behavior of the simulated structures, the parameters of gyration radius, interaction energy, and interaction force were studied. The results show that by increasing the external force to 0.05 kcal/mol Å, the radius of gyration increases to 0.49 Å. Also, with the application of external force, interaction energy and force increase to − 533.44 kcal/mol and − 190.06 kcal/mol Å. In addition, increasing the initial pressure up to 5 bar changes the mentioned quantities of the radius of gyration, interaction energy, and interaction force to 68.46 Å, − 535.55 kcal/mol, − 195.44 kcal/mol Å, respectively. Since structures' atomic behavior and stability are important factors in diagnosing any disease, we expect that the MDM performed in this paper will be useful in treating and preventing diseases, including cancer.

The wettability of rock affects the interaction between CO2, brine, and shale formation, which affects CO2 sequestration with enhanced gas recovery (CS–EGR) project. However, under reservoir conditions, there is limited research on the surface wettability of shale organic matter, and its internal interaction mechanism is unclear. In this study, the effects of temperature, pressure, mineralization, and concentration ratio of CO2 to CH4 on the contact angle were studied using molecular dynamics (MD), and the results were compared with the previous experimental data. Under a certain pressure, the water wettability increases with the increase in temperature. At a fixed temperature, the contact angle of water on graphene increases with the increase of CO2 pressure. Above the critical pressure, water at different temperatures is wetted by CO2 on the surface of graphene, and the wettability reversal occurs. The water wettability decreases with the increase in solution salinity. Under the same concentration of droplets, Mg²⁺ and Ca²⁺ have a greater effect on the wetting angle than Na⁺. The adsorption capacity of the graphene surface for CO2 is stronger than that of CH4. Finally, the order of wettability is verified by interaction energy. This study will contribute to alleviating the greenhouse effect.

In today’s world, energy consumption was increased dramatically. This increase in consumption has led to many advances in heat transfer (HT) and phase change (PC) in mechanical processes. This study investigated the thermal conductivity (TC) and PC of Cu-Ammonia nano-refrigerant (NR). This study used the molecular dynamics (MD) method in an aluminium nanochannel (NC). This simulation examines the effect of external electric field amplitude (EFA) and the initial pressure (IP) on atomic (temperature (T) and density (D) profiles) and thermal properties (TP) of the NR. The kinetic energy (KE) and total energy (TE) are examined to appraise the stability process. The results show that increasing the IP to 5 bar increases the maximum D value to 0.03 atoms/Å³, which indicates an improvement in the sample's atomic properties (AP). The PC particle rate increases with increasing IP from 53 to 59 %. Also, increasing the IP decreases PC duration (from 2.96 to 2.89 ns) and increases the TC of structures (0.76 to 0.80 W/m.K). On the other hand, by investigating the increase in the EFA applied to the NR from 1 to 5 Å, the maximum D increases from 0.028 to 0.029 atoms/Å³, and the rate of PC particles decreases to 49 %. Also, an increase in the EFA causes an increase in the PC duration and a reduction in TC in the sample.

A carbon nanotube (CNT) is a promising structure for nanoscale heat and mass transfer processes and targeted drug delivery (TDD). These appropriate behavior of CNTs cause this nanometric arrangement to be used in various clinical purposes, as drug delivery process. Here, we report nanopumping behavior of CNT sample in presence of an atomic defect and external heat flux (HF). Molecular Dynamics (MD) approach in this computational research consists of two main steps. In first step, equilibrium of defined compounds is described by Temperature (T) and Total Energy (TE) reporting. Results indicated that defined samples reach an equilibrium state after 1 ns. Next, nanopumping process is done by implementing external HF and metallic tips oscillating in vicinity of defected CNT as second step. Physical quantities such as T, TE, radial distribution function (RDF), nanopumping time, kinetic energy (KE), and Velocity (V)/T profiles of defined compounds were reported after two main processes were done. MD outputs indicated C20 molecule (target particle in nanopumping process) displaced inside CNT after 46.68 (ps), and by defining external flux, this time decreased to 43.12 (ps). Finally, we concluded that atomic defect and HF are important parameters that can be controlled nanopumping process in various clinical applications.

The Riesz potential fs(r)=r−s$f_s(r)=r^{-s}$ is known to be an important building block of many interactions, including Lennard‐Jones–type potentials fn,mLJ(r):=ar−n−br−m$f_{n,m}^{\rm {LJ}}(r):=a r^{-n}-b r^{-m}$, n>m$n>m$ that are widely used in molecular simulations. In this paper, we investigate analytically and numerically the minimizers among three‐dimensional lattices of Riesz and Lennard‐Jones energies. We discuss the minimality of the body‐centered‐cubic (BCC) lattice, face‐centered‐cubic (FCC) lattice, simple hexagonal (SH) lattices, and hexagonal close‐packing (HCP) structure, globally and at fixed density. In the Riesz case, new evidence of the global minimality at fixed density of the BCC lattice is shown for s<0$s<0$ and the HCP lattice is computed to have higher energy than the FCC (for s>3/2$s>3/2$) and BCC (for s<3/2$s<3/2$) lattices. In the Lennard‐Jones case with exponents 3<m<n$3<m<n$, the ground state among lattices is confirmed to be an FCC lattice whereas an HCP phase occurs once added to the investigated structures. Furthermore, phase transitions of type “FCC‐SH” and “FCC‐HCP‐SH” (when the HCP lattice is added) as the inverse density V increases are observed for a large spectrum of exponents (n,m)$(n,m)$. In the SH phase, the variation of the ratio Δ between the interlayer distance d and the lattice parameter a is studied as V increases. In the critical region of exponents 0<m<n<3$0<m<n<3$, the SH phase with an extreme value of the anisotropy parameter Δ dominates. If one limits oneself to rigid lattices, the BCC‐FCC‐HCP phase diagram is found. For −2<m<n<0$-2<m<n<0$, the BCC lattice is the only energy minimizer. Choosing −4<m<n<−2$-4<m<n<-2$, the FCC and SH latices become minimizers.

The Discovery of a drug with pharmaceutical actions goes through several stages, such as Hit to Lead and Lead Optimization. Hit to Lead comprises the phase in which small molecules are evaluated about their activity and their interaction with the target to generate lead compounds. Data analysis such as potency, selectivity, and other physicochemical properties play an important role in this step, as they form the basis for optimizing the next leads. The final stage of drug discovery is called Lead Optimization, whose function is to maintain or improve the desired properties present in selected compounds and, at the same time, reduce any deficiencies found in their structure. Studies of modifications in compounds for improvement can be carried out in experimental ways such as magnetic resonance and mass spectrometry or also by computational methods. Computational methods used in this phase include pharmacophore studies, molecular docking, molecular dynamics, QSAR, among others. This chapter reports the computational techniques used for the lead optimization stage to present which paths can be followed and used for the rational discovery of new drugs.

Nanomotors serve as nanoscale engines by converting various energies into mechanical energy. In addition to the huge number of existing nanomotors, we propose a simple nanomotor based on the hollow carbon nanosphere (i.e., fullerene) that is full of gas. We investigate the acceleration of the nanosphere by leakage of gas through a nanopore by molecular dynamics simulations. The nanosphere can be driven to a high speed of 100 m/s under proper simulation conditions, which can be further tuned by temperature, gas density, and pore diameter. We observe rotation of the pore direction during the acceleration process for a nanosphere of different pore diameters. The acceleration process can be well described by the Meshchersky theory. We also simulate the deceleration process of the nanosphere due to the damping force of the gas, which can be analyzed in terms of the kinetic motion of gas molecules. The nanomotor proposed in this work shall be realizable in experiments and may be useful in driving the mechanic motion of fullerenes.

Mixed wet pores are abundant in shales, yet there is little to no information on the behavior of fluids confined within pores characterized by one hydrophilic and one hydrophobic surface. This mixed wettability can impact fluid storage, distribution, capillary pressures and transport. In this study, we use molecular dynamics simulations to describe the initial distribution of reservoir fluids, such as multicomponent hydrocarbon mixtures and water, in mixed-wet pores. This is an essential pre-requisite to additional studies documenting fluid transport in such pores. The molecular model of the mixed wet pore used consists of kerogen separated by some distance from two clay surfaces. We evaluate spatial distribution of water and individual hydrocarbon species, at varying values of water concentration. Throughout the entire study, the results from the equilibrated system indicate a high affinity between the heavy components, such as the asphaltene/resin fraction and the kerogen surfaces. The more surprising result is the hydrogen bonding observed between the polar constituents in the asphaltene/resin fraction and water. This creates a situation where the asphaltene/resin fraction shows an affinity towards water. When this happens, the hydrophilic clay surface effectively becomes hydrophobic. A pore bounded by an asphaltene layer on one side and kerogen on the other is more oil-wetting than mixed-wet. The presence of asphaltenes can therefore expect to create conditions of modified wettability that will impact oil recovery, oil transport and distribution. Another surprising result in this work is that water forms structures that bridge between opposing surfaces of the model. These water bridges are seen to happen for water concentration values larger than 20%. In other words, water is not merely just adsorbed on to the clay surfaces, but also forms these bridge-like structures. Nevertheless, we still observe a strong affinity between the asphaltene/resin fraction and water leading to a lesser degree of mixed wettability. This study is the first, to the best of our knowledge, that considers water and multicomponent hydrocarbon mixtures in mixed-wet pores with realistic surface chemistry and constitutes a necessary first step towards additional studies related to water and hydrocarbon transport and EOR processes in shale nanopores.

The use of atomistic simulations for mechanical characterization and energetic stability has been in use for the last few decades. These simulations have been equally employed in conventional as well as advanced materials. Traditionally, the prevalent forcefields have not been much successful in predicting the synthesis and growth reactions for materials. However, recently developed ReaxFF, a quantum chemistry-based forcefield, has been successfully employed for predicting growth and synthesis reactions along with defect dynamics, with excellent success. These simulations have been particularly employed for nanomaterials such as graphene, h-BN, MoS2, and WSe2. This chapter discusses the origin, development and application of ReaxFF for the synthesis reactions of nanomaterials.KeywordsReaxFFBulk propertiesDefectNanomaterialsAtomistic scale simulations

For a long time, graphene-based nanomaterials have broad application prospects because of their excellent multi-functional properties. Here, combined with coarse-grained molecular dynamics simulations, the compressive mechanical behavior and impact resistance of graphene-assembled hollow nanospheres (GAHNs) with interlayer binders have been explored systematically. It was found that, the introduction of binders between graphene nanosheets (GNs) can effectively improve the interfacial stress-transfer, by which the compression strength and modulus can be increased by ∼ 100% and ∼ 300%, respectively, with a low content of 4.23%. Meanwhile, it is found that the role of binders is changed under different impacting velocities. When the impact velocity is small, the strong connection between layers inhibits the impact force from decomposing to neighbor graphene nanosheets, while when the velocity is high, it will help maintain the structure from being torn. The tensile-shear tests reveal the contribution of binders to stress transfer theoretically. This work provides a theoretical insight for carbon hollow spheres into the mechanical response and impact resistance under different interface situation and lays the foundation for impacting resistance application.

Analytical relations for the mechanical response of single polymer chains are valuable for modeling purposes, on both the molecular and the continuum scale. These relations can be obtained using statistical thermodynamics and an idealized single-chain model, such as the freely jointed chain model. To include bond stretching, the rigid links in the freely jointed chain model can be made extensible, but this almost always renders the model analytically intractable. Here, an asymptotically correct statistical thermodynamic theory is used to develop analytic approximations for the single-chain mechanical response of this model. The accuracy of these approximations is demonstrated using several link potential energy functions. This approach can be applied to other single-chain models, and to molecular stretching in general.

A significant research effort in the past few years has been devoted to engineering synthetic mimics of naturally occurring eumelanin. One such effort has involved the assembly of oligomers of 5,6-dihydroxyindole (DHI), a synthetic precursor of polydopamine (PDA), into melanin-mimicking nanoparticles for use in a variety of applications with desired optical, photonic, thermal, and electrical properties. In many of these applications, the PDA nanoparticles are mixed with other polymers or oligomers, thus motivating this specific study to understand how the surface characteristics of the assembled PDA-nanoparticles affect their interaction with poly(ethylene glycol) (PEG) chains in aqueous solution. We use molecular dynamics (MD) simulations to study the interaction of linear 20-mer PEG chains with different PDA-nanoparticles assembled using four types of oligomers of 5,6-DHI: two isomers of 5,6-DHI 2-mers with the monomers bonding either at the 2-2' position (A-type isomer) or 7-7' position (B-type isomer), denoted as A:2-mer and B:2-mer, respectively, and a 4-mer and an 8-mer of B-type chemistry denoted as B:4-mer and B:8-mer, respectively. Using explicit-solvent atomistic MD simulations, we find that PDA-nanoparticle surfaces assembled from B:8-mer exhibit smaller density fluctuations of water molecules and, as a result, are relatively more hydrophilic than the PDA-nanoparticle surfaces assembled from A:2-mer, B:2-mer, and B:4-mer. The surface composition of PDA-nanoparticles assembled from A:2-mer contains relatively fewer hydroxyl (-OH) groups compared to PDA-nanoparticles assembled from a B:2-mer, B:4-mer, or B:8-mer, yet the sample of PEG chains show more collapsed and adsorbed conformations on A:2-mer nanoparticles' surface. To explain the atomistically observed behavior of PEG chains on the nanoparticles' surfaces, we use coarse-grained (CG) MD simulations and explain the roles of the pattern formed by the attractive sites (e.g.,-OH groups) exposed on the surface and the roughness of the surface on interactions with a genric PEG-like copolymer chain. By comparing atomistic and CG MD simulation results, we confirm that the -OH groups' pattern on the surface of the PDA-nanoparticle assembled from A:2-mer is patchier than the random or string-like patterns on the PDA-nanoparticle assembled from B:2-mer, B:4-mer, or B:8-mer, and it is this -OH groups' surface pattern that dictates the PEG chain conformations and adsorption on the PDA-nanoparticle surface. Overall, these results guide the design of chemically and physically heterogeneous nanoparticle surfaces for the desired polymer interaction and conformations.

To design increasingly tough, resilient, and fatigue-resistant elastomers and hydrogels, the relationship between controllable network parameters at the molecular level to macroscopic quantities that govern damage and failure must be established. Constitutive models based upon statistical mechanics have used variants of the freely jointed chain (FJC) model with rigid links. However, since the free energy state of a polymer chain is dominated by enthalpic bond distortion effects as the chain approaches its rupture point, bond extensibility ought to be accounted for if the model is intended to capture chain rupture. To that end, a new bond potential is supplemented to the FJC model (as derived in the uFJC framework of Buche and colleagues), which we have extended to yield a tractable, closed-form model that is amenable to constitutive model development. Inspired by the asymptotically matched uFJC model response, a simple, quasi-polynomial, and anharmonic bond potential energy function is derived. Using this bond potential, approximate yet highly-accurate analytical functions for bond stretch and chain force dependent upon chain stretch are established. Then, using this polymer chain model, a stochastic thermal fluctuation-driven chain rupture framework is developed. This framework is based upon a force-modified tilted bond potential that accounts for distortional bond potential energy, allowing for the calculation of dissipated chain scission energy. The model is fit to single-chain mechanical response data collected from atomic force microscopy tensile tests for validation and to glean deeper insight into the molecular physics taking place. Due to their analytical nature, this polymer chain model and the associated rupture framework can be straightforwardly implemented in finite element models accounting for fracture and fatigue in polydisperse elastomer networks.

High-entropy alloys (HEAs) are promising to provide effective antiballistic capability because of their superior mechanical properties. However, the twinning-active Cantor alloy is found less ballistic resistant, compared with its Mn-free companion. It is unclear how the HEAs resist ballistic impact and why Mn does not benefit the ballistic resistance. Here, we used molecular dynamics simulations to investigate the ballistic resistances of CrMnFeCoNi and CrFeCoNi and elucidate underlying mechanisms. It is shown that the alloys’ ballistic resistances dominantly benefit from active dislocations generated at higher strain rates. Stronger atomic bonding and higher dislocation densities make the CrFeCoNi easier to be strain hardened with elevated toughness to resist high-speed deformation, while weaker atomic bonding and easier occurrence of dislocation tangling make CrMnFeCoNi less resistant to failure under ballistic impact. This work helps better understand the antiballistic behavior of HEAs and guide the design of armor and energy-absorption materials.

The gas permeation through nanoscale membranes like graphene has been extensively studied by experiments and empirical models. In contrast to planar membranes, the single-walled carbon nanotube has a natural confined hollow structure, which shall affect the gas permeation process. We perform molecular dynamics simulations to investigate the effect of the nanotube diameter on the gas permeation process. It is found that the permeance constant increases with the increase of the nanotube diameter, which can not be explained by existing empirical models. We generalize the three-state model to describe the diameter dependence for the permeance constant, which discloses a distinctive confinement-induced adsorption phenomenon for the gas molecule on the nanotube's inner surface. This adsorption phenomenon effectively reduces the pressure of the bulk gas, leading to the decrease of the permeance constant. These results illustrate the importance of the adsorption within the confined space on the gas permeation process.

In this article we develop an algorithm for the efficient simulation of electrolytes in the presence of physical boundaries. In previous work the discrete ion stochastic continuum overdamped solvent (DISCOS) algorithm was derived for triply periodic domains, and was validated through ion-ion pair correlation functions and Debye-Hückel-Onsager theory for conductivity, including the Wien effect for strong electric fields. In extending this approach to include an accurate treatment of physical boundaries we must address several important issues. First, the modifications to the spreading and interpolation operators necessary to incorporate interactions of the ions with the boundary are described. Next we discuss the modifications to the electrostatic solver to handle the influence of charges near either a fixed potential or dielectric boundary. An additional short-ranged potential is also introduced to represent interaction of the ions with a solid wall. Finally, the dry diffusion term is modified to account for the reduced mobility of ions near a boundary, which introduces an additional stochastic drift correction. Several validation tests are presented confirming the correct equilibrium distribution of ions in a channel. Additionally, the methodology is demonstrated using electro-osmosis and induced-charge electro-osmosis, with comparison made to theory and other numerical methods. Notably, the DISCOS approach achieves greater accuracy than a continuum electrostatic simulation method. We also examine the effect of under-resolving hydrodynamic effects using a “dry diffusion” approach, and find that considerable computational speedup can be achieved with a negligible impact on accuracy.

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