Environmental Engineering Reference
In-Depth Information
origin from the thermal interface resistance between heat bath and
the middle region, thus cannot be eliminated by tuning parameter.
With further increase of
τ
(0.2
<τ <
300), temperature profile
becomescorrectandstable:bothheatfluxandtemperaturegradient
become insensitive to
τ
, thus the calculated thermal conductivity in
Fig.1.9disalmostaconstantwithsmallfluctuation.Next,when
τ>
300, temperature gradientbecomessmallerandheatfluxdecreases
quickly. This is because in the large
τ
range, the distribution of
ς
δ
-function [27]. As a result, it would require longer
simulation times in order to ensure the decay of correlations. This
prevents the heat bath from reaching the aimed temperature due to
thelimitedsimulationtime,andalsoasmallertemperaturegradient.
Therefore,fromtheconsiderationofapracticalcomputationaltime,
oneshould notchoose an extremely large
τ
.
For Langevin heat bath, in the weak damping limit
λ
→
0
(e.g.,
λ
=
0.1 in Fig. 1.9b), the heat bath cannot reach the aimed
temperature. However, in the strong damping limit (e.g.,
λ
=
500 in Fig. 1.9b), although the heat bath can reach the aimed
temperature, large TJ is observed at the boundary. In both cases,
smalltemperaturegradientisgenerated,whichinducesasmallheat
current. In the middle range of
λ
, a temperature profile with correct
heat bath temperature and small TJ can be established. This causes
heat flux and thermal conductivity first increase then decrease with
theincreaseof
λ
as shown in Fig. 1.9c, d.
In MD calculation, it must be confirmed that the temperature
profileiscorrectandatemperaturegradientcanbewellestablished
in order to achieve accurate prediction results. Based on these
considerations and the results shown in Fig. 1.9, an intermediate
value of
becomes a
(from 1 to 100) is recommended for Langevin heat
bath. For NH heat bath, Fig. 1.9 suggests
λ
τ
from 0.2 to 300 is
the optimal choice in numerical simulation when NH heat bath is
applied. Moreover, we can see from Fig. 1.9d that the discrepancy of
thermal conductivity in Fig. 1.6d is mainly due to the choice of heat
bath parameter: the same result can be obtained if the parameter is
chosen properly.
In addition to homogeneous materials, heterogeneous materials
suchascarbonnanotubebased[44]andgraphenebased[45]nano-
junctionsarepromisingcandidatesforthermalrectifierapplication.
