I'm trying to calculate thermal conductivity of graphene in Lammps. I started with LAMMPS's example script which uses LJ units. But, I'm not sure if it yields thermal conductivity in W/m-K units. I'm getting expected numbers though (in the vicinity of ~2000). Is there any modification need if I use LJ units? Thanks.
The Lennard-Jones potential is given by
U = 4 eps [(sig/r)^12 - (sig/r)^6]
LJ units mean that you are measuring energy in units of "eps" and length in units of "sig". This simplifies the potential to the form:
U* = 4 [(1/r*)^12 - (1/r*)^6]
where the U* and r* are now measured in LJ units. Also,when using LJ units, LAMMPS sets the masses of particles, and the Boltzmann constant to 1. So, assuming that the mass of Carbon atoms is m_c, we have:
m* = m / m_c
You can obtain the scaling factor of other physical quantities based on these. For example, for time:
t* = t x sqrt (eps / (m_c x sig ^ 2))
or your example, thermal conductivity:
kappa* = kappa x sig^2 x sqrt (m_c) / (eps^(3/2) x k_B)
where k_B is the Boltzmann factor. kappa* is what you get if you calculate the thermal conductivity based on the raw output from LAMMPS in LJ units.
A word of notice: the values of extensive quantities such as energy in LAMMPS's LJ units are reported as divided by the number of particles.
The Lennard-Jones potential is given by
U = 4 eps [(sig/r)^12 - (sig/r)^6]
LJ units mean that you are measuring energy in units of "eps" and length in units of "sig". This simplifies the potential to the form:
U* = 4 [(1/r*)^12 - (1/r*)^6]
where the U* and r* are now measured in LJ units. Also,when using LJ units, LAMMPS sets the masses of particles, and the Boltzmann constant to 1. So, assuming that the mass of Carbon atoms is m_c, we have:
m* = m / m_c
You can obtain the scaling factor of other physical quantities based on these. For example, for time:
t* = t x sqrt (eps / (m_c x sig ^ 2))
or your example, thermal conductivity:
kappa* = kappa x sig^2 x sqrt (m_c) / (eps^(3/2) x k_B)
where k_B is the Boltzmann factor. kappa* is what you get if you calculate the thermal conductivity based on the raw output from LAMMPS in LJ units.
A word of notice: the values of extensive quantities such as energy in LAMMPS's LJ units are reported as divided by the number of particles.
Glad to help! Though it seems that I had made a mistake. I had missed the time in the kappa* formula. I edited my answer. But I guess you can verify these yourself as well.
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