# Thermal conductivity of system with temperature gradient

Hi,

I am modelling liquid argon inside a channel where its two walls are of different temperatures (fixed using the temp/rescale command). What is the best way to calculate the thermal conductivity of the liquid argon?

I tried the Green-Kubo method but the autocorrelation function for the y direction (direction perpendicular to the walls) converges to a non zero value. This means that the bigger my correlation length is, the higher the thermal conductivity is since the integral will will be taken over a larger area.

On the other hand, is the Muller-Plathe method a good idea when thermostats are used?

Thanks in advance for any help

Hi Michael,

I think you might be confusing a couple of different methods here.

The Green-Kubo method is for calculating thermal conductivities at equilibrium (i.e., when there's no temperature gradient in your system). This would be applicable in a sample of bulk Ar at constant temperature. A failure to decay to zero is normally a consequence of finite size effects in your system. Make everything the same temperature, and you should see the autocorrelation function get closer to zero as you make your system larger and larger.

There are also non-equilibrium methods. You can use non-equilibrium MD (NEMD), which involves applying a temperature gradient to your system (using something like temp/rescale) and measuring the resultant heat flux. Alternatively, there's reverse-NEMD (or rNEMD), which is Mueller-Plathe's algorithm. You apply the heat flux directly by swapping the momenta of some particles, and measure the resulting temperature different. In both cases, you apply Fourier's law to work out the conductivity.

Niall

Dear Niall,

Thank you very much for your response.

So since I already have the thermostats (and hence a temperature gradient), all I need is the heat flux vector (which I am already calculating for the Green Kubo method) and the temperature profiles which I can get using the fix ave/spatial?

Mike