scholarly journals Surface Energy of Curved Surface Based on Lennard-Jones Potential

Nanomaterials ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 686
Author(s):  
Dan Wang ◽  
Zhili Hu ◽  
Gang Peng ◽  
Yajun Yin
Keyword(s):  
Surface Energy ◽  
Flat Surface ◽  
Convex Surface ◽  
Pair Potential ◽  
Spherical Geometry ◽  
Surface Geometry ◽  
Jones Potential ◽  
Lennard Jones ◽  
Local Principle ◽  
Geometrical Effect

Although various phenomena have confirmed that surface geometry has an impact on surface energy at micro/nano scales, determining the surface energy on micro/nano curved surfaces remains a challenge. In this paper, based on Lennard-Jones (L-J) pair potential, we study the geometrical effect on surface energy with the homogenization hypothesis. The surface energy is expressed as a function of local principle curvatures. The accuracy of curvature-based surface energy is confirmed by comparing surface energy on flat surface with experimental results. Furthermore, the surface energy for spherical geometry is investigated and verified by the numerical experiment with errors within 5%. The results show that (i) the surface energy will decrease on a convex surface and increase on a concave surface with the increasing of scales, and tend to the value on flat surface; (ii) the effect of curvatures will be obvious and exceed 5% when spherical radius becomes smaller than 5 nm; (iii) the surface energy varies with curvatures on sinusoidal surfaces, and the normalized surface energy relates with the ratio of wave height to wavelength. The curvature-based surface energy offers new insights into the geometrical and scales effect at micro/nano scales, which provides a theoretical direction for designing NEMS/MEMS.

On the transport properties of simple liquids

1986 ◽  
Vol 64 (2) ◽  
pp. 211-214
Author(s):  
S. K. Datta
Keyword(s):  
Shear Viscosity ◽  
Pair Potential ◽  
Viscosity Coefficient ◽  
Simple Fluids ◽  
Jones Potential ◽  
Simple Liquids ◽  
Lennard Jones ◽  
Approximate Nature ◽  
Real Fluids ◽  
Analytical Expressions

Closed analytical expressions for the diffusion coefficient and shear-viscosity coefficient of dense, simple fluids characterized by the Lennard-Jones potential function have been obtained using the Weeks, Chandler, and Andersen criterion for the division of the pair potential. The expressions are then used to calculate these properties for some real fluids. The deviations between the estimated and measured values of the coefficients are attributed mostly to the approximate nature of the Kirkwood and Rice expressions for shear viscosity and the friction coefficient used to calculate those properties.

scholarly journals The FHH Multilayer Expression: Effects of Particle Size

1986 ◽  
Vol 3 (3) ◽  
pp. 123-140 ◽  
Author(s):  
B. D. Adkins ◽  
P. J. Reucroft ◽  
B. H. Davis
Keyword(s):  
Particle Size ◽  
Surface Energy ◽  
Spherical Particle ◽  
Flat Surface ◽  
Experimental Results ◽  
High Coverage ◽  
Lennard Jones ◽  
Surface Areas ◽  
Primary Particles ◽  
Adsorption Data

Frenkel-Halsey-Hill (FHH) plots are presented using the adsorption data from eleven silicas with surface areas between 40 and 1200 m2 g−1. These materials consist of regular nonporous primary particles which have been approximated as monomodal size distributions of spheres. Two models (semi-infinite slab and spherical particle) were used to make the FHH plots. The results from these plots indicate that the FHH coefficient and exponent vary with particle size. A model is proposed for a particle having a featureless Lennard-Jones surface which predicts (a) that the actual variation is in the coefficient alone, which depends upon coverage as well as particle size, but (b) on a ‘spherical particle’ FHH plot, this variation will manifest itself as a particle size dependence of both coefficient and exponent. However, the model predicts that the exponent should decrease with particle size; experimental results show it to increase. The model also predicts that ‘flat surface’ FHH plots should be less linear than the ‘spherical particle’ plots, and should deviate downwards at high coverage, when in fact the ‘flat surface’ plots are more linear. Predictions obtained by recalculating the model in the absence of the surface energy term are in much better agreement with the experimental results, indicating that the surface energy correction is possibly excessive, e.g. if the particles were actually polyhedral instead of spherical.

scholarly journals Calculated Self-Diffusion Coefficients for Liquid Argon

1972 ◽  
Vol 25 (5) ◽  
pp. 529 ◽  
Author(s):  
RA Fisher ◽  
RO Watts
Keyword(s):  
Diffusion Coefficients ◽  
Pair Potential ◽  
Liquid Argon ◽  
The Self ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Self Diffusion ◽  
Lennard Jones ◽  
Method Of Molecular Dynamics ◽  
Experimental Values

The method of molecular dynamics has been applied with the Barker?Bobetic pair potential for argon interactions to calculate the self-diffusion coefficients of liquid and dense gaseous argon. These self-diffusion coefficients are compared with experimental values and with values obtained from the Lennard?Jones potential. There are significant differences between the calculated and experimental values at high densities.

Molecular Dynamics Study of Wetting on Brushlike Nanopillar and Wavelike Nanorough Surfaces

2007 ◽  
Author(s):  
Claudiu Valentin Suciu
Keyword(s):  
Molecular Dynamics ◽  
Flat Surface ◽  
Mechanical Energy ◽  
Equilibrium Temperature ◽  
Nanoporous Materials ◽  
Base Surface ◽  
Jones Potential ◽  
Alkyl Chains ◽  
Lennard Jones ◽  
Linear Chains

A Molecular Dynamics technique is proposed to simulate the motion of water nano-droplets on brushlike nanopillar and wavelike nanorough surfaces. Firstly, a brushlike nanopillar structure is obtained by deposition of a hexagonal packing of alkyl linear chains CnH2n+1 (n = 1–18) on a (0001) type flat surface, consisted of hexagonal packed carbon atoms. Distance between the grafted alkyl chains is selected in the 0.5–1.4 nm range, and the distance between the carbon atoms of the base surface is set to 0.1421nm. Next, the (0001) type flat surface is folded in order to obtain a wavelike nano-roughness. Water cluster is consisted of 729–2197 molecules, and after 25ps it reaches a diameter of 3–5 nm, which corresponds to a liquid phase of 1g/cm3 density, at an equilibrium temperature of 293K. Lennard-Jones potential is used to describe all the interactions into the considered system. By the appropriate input of the Lennard-Jones parameters one controls the hydrophilic level of the base surface. Influences of the intermolecular distance and the length of the grafted alkyls, as well as the influences of the nano-wavelength and the hydrophilic level of the base surface on the contact angle are illustrated. Such results are useful for the appropriate design of ultrahydrophobic nano-surfaces, and for the optimal design of nanoporous materials, able to produce surface dissipation of the mechanical energy.

Self Diffusion Parameters from Non-empirical Pair Potentials

1992 ◽  
Vol 291 ◽  
Author(s):  
S. Dorfman ◽  
D. Fuks ◽  
J. Pelleg ◽  
S. Rashkeev
Keyword(s):  
Electronic Structure ◽  
First Principles ◽  
Pair Potential ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Self Diffusion ◽  
Lennard Jones ◽  
Pair Potentials ◽  
Diffusion Parameters ◽  
And Migration

ABSTRACTA scheme for construction of the pair potential from non-empirical calculations of electronic structure of solids is suggested. As an example, parameters of Lennard-Jones potential are obtained for fccCs, based on LMTO calculations of energy parameters. Vacancy formation and migration energies for fccCs are calculated from this first-principles pair potential. In addition, the frequency of vibration and the jump probability of an atom are calculated and it is shown that they are direction dependent.

scholarly journals Inferring Single-Cell 3D Chromosomal Structures Based on the Lennard-Jones Potential

2021 ◽  
Vol 22 (11) ◽  
pp. 5914
Author(s):  
Mengsheng Zha ◽  
Nan Wang ◽  
Chaoyang Zhang ◽  
Zheng Wang
Keyword(s):  
Single Cell ◽  
Loss Function ◽  
Gaussian Function ◽  
Three Dimensional ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Cubic Lattice ◽  
Lennard Jones ◽  
3D Fish ◽  
Well Depth

Reconstructing three-dimensional (3D) chromosomal structures based on single-cell Hi-C data is a challenging scientific problem due to the extreme sparseness of the single-cell Hi-C data. In this research, we used the Lennard-Jones potential to reconstruct both 500 kb and high-resolution 50 kb chromosomal structures based on single-cell Hi-C data. A chromosome was represented by a string of 500 kb or 50 kb DNA beads and put into a 3D cubic lattice for simulations. A 2D Gaussian function was used to impute the sparse single-cell Hi-C contact matrices. We designed a novel loss function based on the Lennard-Jones potential, in which the ε value, i.e., the well depth, was used to indicate how stable the binding of every pair of beads is. For the bead pairs that have single-cell Hi-C contacts and their neighboring bead pairs, the loss function assigns them stronger binding stability. The Metropolis–Hastings algorithm was used to try different locations for the DNA beads, and simulated annealing was used to optimize the loss function. We proved the correctness and validness of the reconstructed 3D structures by evaluating the models according to multiple criteria and comparing the models with 3D-FISH data.

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