# [lammps-users] Why periodic boundary condition?

Dear All,

Is it meaningful to use a non-periodic boundary condition( for example shrink-wrapped boundary condition) in the calculation of thermal conductivity on nanowires?

In most of the literature, the periodic boundary condition is used to calculate the thermal conductivity of nanowires. In my opinion, for the large simulation system, it is an appropriate choice to calculate the thermal conductivity using the periodic boundary condition. Actually, I don’t know why people still use it in a small simulation system, like thin nanowires. Is it just for the simplification of the simulation model?

Any discussion and comment will be highly appreciated.

Regards,

kaviany

Periodic along which direction? Along the nanowire axis or transverse to it? Is the length of the nanowire finite? Is the finite length important?

Dear Robert Hoy,
The non-periodic boundary condition means the derections both along the nanowire axis and transverse to it is not periodic boundary ,for example: boundary f f f or boundary s s s.
I noticed some paper mentioned that the reciprocal of the thermal conductivity was found to be linearly related to the nanowire length[Schelling,2002], and for SW Si at 500 K, the mean-free path is about 100 nm; some other paper found that the thermal conductivity values become length independent when the wire is longer than 8.56 nm [Volz&G.Chen,1999]. The two conclusion apparently are contradictory. which one is correct?
When some paper investigate the relationship between length of finite nanowires and the value of thermal conductivity, they also used the periodic boundary condition along the nanowire axis. Why don’t they use the non-periodic boundary condition?
Is the finite length not important?

Thanks!!

Regards,

kaviany

Hi kaviany,

I guess the usage of PBC is to reduce the end effects, which would definitely create a interface at the wire end. For the thermal conduction calculation, many papers have been talking about the length dependant thermal conductivity, but i think it is a seperate topic. Someone has compared the results of PBC and non-PBC, as far as I know.

Best,

AC

Think. The conductivity of a normal wire depends on its length (simply, related to the MFP). The conductivity of a nanowire will obviously also depend on its length (less simply). Generally, there are always finite-size effects - the idea of using pbcs is to get rid of “edge” or “end” effects, but the tradeoff is introducing periodicity.

Hi , Robert Hoy, AJING CAO and Navin Kumar. Thanks for your comment!

Actually, I still don’t know why people use pbcs to get rid of “edge” or “end” effects by introducing periodicity, when their paper’s aim is to investigate the relationship between thermal conductivity and the size of cross section and length. In my opinion, If you want to discuss the relationship between thermal conductivity and the size of nanowires, you should make sure your nanowires has finite size, and they should have “edge” or “end” .

Thanks!!

Regards,

kaviany

Simply because the simulation cell is much smaller than the real case. For example, CNT always has 1-10 micron in length direction while our simulation models usually smaller than 300 nm.

Best,

AC