# Thermal conductivity of polymers using the Green-Kubo method

Hi all,

I have some questions about Green-Kubo method for determining thermal conductivity. My simulated media is polymethylmethacrylate(PMMA).
First question, I have some problems about determining timestep, correlation length and sample interval. Because I have a system of polymer (PMMA) and I know its heat flux is low for thermal gardiants, I tried some small correlation length and sample interval. And I found correlation length for 2 and sample interval for 1 give me a correct thermal conductivity at timestep equal 1. I found the right timestep by try and error too. I can simulate this system because I know the thermal conductivity of PMMA at 300K equal about 0.18 and ofcourse I must say I did not include the method’s error. My question is: what is the way of determining proper timestep, correlation length and sample interval?
Second question, about the dimentionality. I study a few about the Green-Kubo method and I found we took dimentionality equal 1 ( d=1 ). Then we must determine the interest in one dimension and because of this we take our simulation box in one dimension more larger that theothers. But my simulated box is equal in all direction. Am I should change my simulated data? Or I can do the job by this box?
Third question is determining thermal conductivity at different temperatures. When I found the right timestep, correlation length and sample interval for 300K I ran the simulation at different T s. I found when T is at the range of 150 till 450 the answer of the code is something near to reality. (Tg for PMMA can be given around 370K and Tm around 500K). But when T isn’t at this range specially for T s smaller than about 100K, I found that the answer of code is really not the true one. l tried to find the answer by seeing the algorithm of this code but I can’t find my answer. I would appreciate if anyone can tell me what is the problem with changing T in the Green-Kubo method?
And what is the best method for determining thermal conductivity for this simulation of polymer?

Any suggestion can help me alot and I would thanks if anyone can help me.

Regards,
Eliar

Hi Eliar,

Question 1. I think you need to first understand the method fully by studying a simple system such as solid or liquid argon described by the simple LJ potential (there is an example in KAPPA/).

Question 2. Is your system quasi-one-dimensional (like a wire?). If so, simply correct the final results by a proper scaling factor, using a proper “volume”.

Question 3. There is no difference for the Green-Kubo method used at different temperatures. Perhaps the time step for integration should be smaller at a higher temperature.

Suggestion: present the input script and the obtained results (preferably using figures plotting the running thermal conductivity as function of the correlation time).

Best,
Bruce