scholarly journals The Size and Shape Effects on the Melting Point of Nanoparticles Based on the Lennard-Jones Potential Function

Nanomaterials ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 2916
Author(s):  
Anwar Al Al Rsheed ◽  
Saad Aldawood ◽  
Omar M. Aldossary
Keyword(s):  
Melting Point ◽  
Potential Function ◽  
Lennard Jones Potential ◽  
Spherical Nanoparticles ◽  
Melting Points ◽  
Jones Potential ◽  
Lennard Jones ◽  
Model Based ◽  
Shape Effects ◽  
Experimental Values

A model is proposed to calculate the melting points of nanoparticles based on the Lennard-Jones (L-J) potential function. The effects of the size, the shape, and the atomic volume and surface packing of the nanoparticles are considered in the model. The model, based on the L-J potential function for spherical nanoparticles, agrees with the experimental values of gold (Au) and lead (Pb) nanoparticles. The model, based on the L-J potential function, is consistent with Qi and Wang’s model that predicts the Gibbs-Thompson relation. Moreover, the model based on the non-integer L-J potential function can be used to predict the melting points of nanoparticles.

Intermolecular forces and properties of fluid. I. The automatic calculation of higher virial coefficients and some values of the fourth coefficient for the Lennard-Jones potential

1960 ◽  
Vol 254 (1279) ◽  
pp. 487-498 ◽  
Keyword(s):  
Virial Coefficient ◽  
Mathematical Problem ◽  
Virial Coefficients ◽  
Intermolecular Forces ◽  
Lennard Jones Potential ◽  
Intermolecular Potentials ◽  
Jones Potential ◽  
Lennard Jones ◽  
Experimental Values ◽  
First Time

The prediction of the virial coefficients for particular intermolecular potentials is generally regarded as a difficult mathematical problem. Methods have only been available for the second and third coefficient and in fact only few calculations have been made for the latter. Here a new method of successive approximation is introduced which has enabled the fourth virial coefficient to be evaluated for the first time for the Lennard-Jones potential. It is particularly suitable for automatic computation and the values reported here have been obtained by the use of the EDSAC I. The method is applicable to other potentials and some values for these will be reported subsequently. The values obtained cannot yet be compared with any experimental results since these have not been measured, but they can be used in the meantime to obtain more accurate experimental values of the lower coefficients.

Water Molecule and Atoms Inside C60 Fullerene

2020 ◽  
Vol 17 (7) ◽  
pp. 2955-2961
Author(s):  
Prangsai Tiangtrong
Keyword(s):  
Water Molecule ◽  
Interaction Energy ◽  
Potential Function ◽  
External Force ◽  
Exact Formula ◽  
C60 Fullerene ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Lennard Jones ◽  
Single Water Molecule

In this research, we are interested in the non-bonded interactions between a single water molecule and the atoms Li, Na, K, Rb, Cs, Ca, Ni, Zn and Pb inside a C60 fullerene using the Lennard-Jones potential function. We assume that a single water molecule is inside the endofullerene and determine the exact formula of the interaction energy between the water molecule and the fullerene. Then we determine the interaction energy between an atom and the endofullerene to consider the interaction behaviours of each atom inside the fullerene. The results show that a water molecule does not desire to be encapsulated inside the fullerene. Similarly, Rb, Cs and Pb act the same behaviour, where they are not stable inside the fullerene. However, some atoms which are Li, Na, K, Ca, Ni and Zn can be inside the endofullerene. Hence, the creation of endofullerene with a single water molecule or Rb, Cs and Pb inside, an external force must be applied while that force is not necessary for Li, Na, K, Ca, Ni and Zn.

A new method of solving the Born-Green equation for the radial distribution function

1952 ◽  
Vol 210 (1103) ◽  
pp. 509-517 ◽  
Keyword(s):  
Distribution Function ◽  
Radial Distribution Function ◽  
Numerical Integration ◽  
Potential Function ◽  
Radial Distribution ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Lennard Jones ◽  
Central Molecule ◽  
Close Range

A solution of the Born-Green equation for the radial distribution function may be found as a series in ascending powers of the density. This method is applied to a fluid of rigid spherical molecules, and the results are compared with those which Kirkwood, Maun & Alder obtained by means of numerical integration. For such molecules it is possible to show that the close-range structure at a distance between n and n + 1 diameters from a central molecule is of the order of the density raised to the n th power ( n integral). When the Lennard-Jones potential function is employed, the first and second approximations to the radial distribution function thus obtained are shown to be identical with those resulting from a rigorous development of this function in powers of the density.

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