Molecular dynamic simulation

From Thermal-FluidsPedia

The motion of each molecule $i$ in the system is described by Newton’s second law, i.e.,

$\sum\limits_{j = 1(j \ne i)}^N {{\mathbf{F}}_{ij} } = m_i \frac{{d^2 {\mathbf{r}}_i }} {{dt^2 }}, i = 1,2,3...n$ $i = 1,2,3...n\qquad \qquad(1)$

where $m i$ and ${{\mathbf{r}}_i}$ are the mass and position of the i^th molecule in the system. In arriving at eq. (1), it is assumed that the molecules are monatomic and have only three degrees of freedom of motion. For molecules with more than one atom, it is also necessary to consider the effect of rotation. As the simplest case, the intermolcular potential between the i^th and j^th molecules is obtained by the Lennard-Jones potential:

${\phi _{ij}} = 4\varepsilon \left[ {{{\left( {\frac{{{r_0}}}{{{r_{ij}}}}} \right)}^{12}} - {{\left( {\frac{{{r_0}}}{{{r_{ij}}}}} \right)}^6}} \right]\qquad \qquad(2)$

The intermolecular force between the i^th and j^th molecules can be obtained from

${{\mathbf{F}}_{ij}} = - \nabla {\phi _{ij}} = \frac{{24\varepsilon }}{{{r_o}}}\left[ {{{\left( {\frac{{{r_o}}}{{{r_{ij}}}}} \right)}^{13}} - {{\left( {\frac{{{r_o}}}{{{r_{ij}}}}} \right)}^7}} \right]\frac{{{{\mathbf{r}}_{ij}}}}{{{r_{ij}}}}\qquad \qquad(3)$

where $r i j$ is the distance between the i^th and j^th molecules.

References

Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA

Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.

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Molecular dynamic simulation

From Thermal-FluidsPedia

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