# Temperature fluctuations in graphene

I am studying heat transfer in single layer graphene sheet. Equilibration is ok.
I apply two thermostats through fix temp/rescale to two groups of atoms in the sheet to establish heat transfer. I define three computes. One each for the two ends (heat source and sink) and one in the middle (somewhere in between the heat source and the sink.) While the temperature of the heat source and sinks obtained from the compute are indeed at desired thermostatted temperatures and fluctuates may be 1-2% from the thermostatted temperature, the temperature obtained from the compute in the middle group is in between the source and sink temperature (that’s fine) but with time, fluctuates highly. For example if I set the source and sink temperatures 300 and 100K then the middle compute gives temperatures varying from 210 to 280 K. That is pretty large. Similar fluctuations exist for other temperature ranges as well. I am using rebo force field (CH.Airebo file).

In my simulations, few atoms at the boundary of the sheet are fixed so that the sheet does not move around. Also I am using non periodic ‘s’ boundary condition in all directions. There are no charge interactions. I am also recording temperature profile along the heat transfer direction using fix ave/spatial at different instants of time . However, the temperature profile obtained fluctuates a lot less (within 5-10 % of average). I am wondering is there any reason why the temperature obtained from the compute in the middle is fluctuating a lot ?

My objective is to maintain different temperatures at different regions in the sheet to initiate and maintain heat transfer and record temperature at some specific regions in the sheet as a result of heat transfer. Is there a better way than how am I doing it?

Thanks and regards,

Souvik.

For starters, don't use temp/rescale. It is a bad method to manipulate kinetic energy, particularly for a system like yours. Axel.

How big is your system?
How many atoms are in your compute in the middle region?
Has steady state been reached?

Compute gives you instantenous temperature. So, dont expect it roo be same at all times where you are not themostating the system. at boundraies, you r forcing the temperature to be something with quite a high frequency, hence less fluctuations. Also in graphene, thermal fluctuations take a while to decay because of its 2d crystalline nature.

It's good that you are paying attention to the variation in your
temperature profile. There is nothing fundamentally wrong with your
observed temperature fluctuations in the range 210K to 280K. This
level of fluctuation can be explained by a combination of equilibrium
fluctuations in the kinetic energy of that group of atoms and also
fluctuations due to the dynamics of energy transfer between the hot
and cold regions. It is important to recognize that the measured
average heat transfer rate in your simulation will be influenced by
many factors, including system size, thermostatting method, duration
of simulation, even the timestep size. You should experiment with
these variables to get a sense of how well-converged your results are.
Also, don't expect perfect agreement with experiment, as classical MD
simulations leave out some important effects, such as electronic heat
transfer. There are prior publications on heat transfer in carbon
structures that you can compare to.

Finally, get a second and third opinion by using alternative methods:

Aidan

Thank you all for the valuable suggestions. Some more details about my simulation:

Timestep: 0.4 femtoseconds.

Duration of heat transfer run: 5 nanoseconds

Total system size: ~4000 atoms

The steady state will have to be determined in terms of either heat flux or temperature. Although the temperature in the target domain fluctuates, its average value remains constant over time. So we can say that a pseudo steady state has been achieved.

I am now trying the other thermostatting methods with different time step and duration to see how different is the system temperature variation are in these cases. I will also try longer simulation duration to see if that reduces the fluctuations a little bit.

Thanks and regards,
Souvik.

I just forgot to mention, the number of atoms in the middle compute group is ~200.

Souvik,

Are you seeing periodicity in the fluctuations in the central compute as well ? How long is your system along heat transfer direction? If the system is not long enough, the fluctuations could very well be due to phonons bouncing back and forth between hot and cold thermostat.

Regards,
Vikas