Download Calculating the thermal conductivity with Forcite using the imposed

Calculating the thermal conductivity with Forcite using the imposed flux method
Disclaimer: This custom script is compatible with Materials Studio version 5.5. It is provided
"as is" and is NOT supported by Accelrys nor is it warranted for any purpose whatsoever. The
user assumes responsibility for any malfunctions or bugs.
Background
The thermal conductivity is an important materials property measuring the ability of the material
to transfer heat. Materials with high thermal conductivity, such as metals, transfer heat at a
faster rate than materials with low thermal conductivity, such as polymers. Consequently the
former are widely used in heat exchanger, and the latter find application as thermal insulation.
Some typical values are given in the table below:
Material
Thermal conductivity (W/m/K)
Air
0.025
Rubber
0.16
Polypropylene 0.25
Water (liquid)
0.6
Water (solid)
2
Mercury
8.3
Lead
35.3
Silver
429
Graphene
5000
With the Materials Script ThermalConductivity.pl the thermal conductivity can be calculated.
The script requires the Forcite module in Materials Studio for molecular dynamics simulations.
The script implements a nonequilibrium method, in which an energy flux is imposed on the
system (Müller-Plathe (1997), Jund (1999)). The resulting temperature gradient is measured.
The ratio is the thermal conductivity:
Eq. 1
where J is the energy flux in the z-direction, and dT/dz the temperature gradient. Since the
direction of the flux is opposite from the gradient, the thermal conductivity is always positive.
The flux is imposed by exchanging, every time interval ∆t, an energy ∆E between two fixed
layers in the system:
Eq. 2
where A is the area perpendicular to the flux direction, and the factor 2 is due to periodic
boundary conditions, since an amount ∆E/2 flows in or out either sides of the layer.
Figure 1. The distribution of the average temperature in space. Kinetic energy is exchanged at set
intervals between one or more particles in a hot layer (red) and a cold layer (blue), imposing an energy
flux through the system. The layers are repeated due to periodic boundary conditions. Also shown is a
projection of the density in the system (bottom); the density decreases with temperature.
The script implements two variants of the imposed flux method: the Reverse Non Equilibrium
Molecular Dynamics (RNEMD) method of Müller-Plathe (1997) and the imposed flux method of
Jund (1999). In the RNEMD method the energy exchange is carried out by exchanging the
kinetic energy of two particles: the hottest particle in the cold layer and the coldest particle in
the hot layer. The energy ∆E is therefore variable and needs averaging over many exchanges. In
the method of Jund the energy ∆E is fixed, and involves all particles in the hot and cold layers.
Both methods conserve total linear momentum and energy of the system. The method of Jund
also conserves the total linear momentum of the hot and cold layer, i.e. no momentum is
exchanged.
The script supports exchange of kinetic energy of different objects: atoms, molecules, repeat
units, and subunits. The objects may differ in mass, by using the momentum conserving
extension due to Nieto-Draghi (2003). In order to use molecules, repeat units, or subunits, such
objects must be present in the structure.
Running the script
The script is run by filling in the settings array and providing a document. The script provides a
Run method that takes both arguments. Optionally any setting supported by Forcite can be
provided as a third argument.
Run(<document>, <settings>, <Forcite settings>)
Description
Performs a thermal conductivity calculation using Forcite on the specified 3D Atomistic
document.
Parameters
Parameter
Default
Optional/Required value
Document
Required
Description
3D Atomistic Document containing the
structure.
Settings
Required
Settings that control this calculation.
Forcite
settings
Optional
Settings to customize Forcite.
Settings
The following settings are required to run the thermal conductivity calculation:
Setting
Default
Values
Description
NumLayers
40
>0
The number of layers in which the direction of
flux is divided. Increasing the number of
layers can increase the accuracy of the
gradients, but too many layers will lead to
large fluctuations in the layer temperatures.
ObjectType
ATOMS
ATOMS
MOLECULES
REPEATUNITS
SUBUNITS
The type of object to use in the energy
exchange. ATOMS will exchange kinetic
energy between atoms; MOLECULES will
exchange kinetic energy between molecules;
REPEATUNITS will exchange kinetic energy
between repeat units in a polymer;
SUBUNITS will exchange kinetic energy
between subunits;
ExchangeType
VARIABLE VARIABLE
FIXED
The type of exchange method to use.
VARIABLE will exchange a variable energy
between one object in the hot layer and one
in the cold layer. FIXED will exchange a
constant energy between all hot objects in
the hot layer and all objects in the cold layer.
ExchangeEnergy
1.0
>0
The amount of energy to exchange in each
step when using the FIXED exchange type, in
kcal/mol. The flux is determined by the ratio
of ExchangeEnergy and NumberOfSteps.
NumExchangesEqui
500
≥0
The number of exchanges during the
equilibration stage. During the equilibration
stage a thermostat acts on the system.
NumExchangesProd 1000
>0
The number of exchanges during the
production stage. The production stage is
carried out at constant energy.
CalculateFields
Yes
Yes
No
Whether to generate 3D field output as part
of the calculation.
FieldsInterval
10
>0
Number of exchanges in between two field
updates. Increase this number to avoid
overhead of field calculations.
TimeStep
1
>0
Time step to be used in the simulation in
femto seconds.
NumberOfSteps
100
>0
Number of time steps in between two
exchanges. Decreasing the NumberOfSteps
leads to higher fluxes and increases the
temperature gradient. Too small values
should be avoided as these will introduce
nonlinear effects and may impact
performance.
Results
A study table is returned with the same name as the input document. Charts can be created
using the Plot Graph functionality in Materials Studio, for instance the Temperature as a function
of the distance, or the thermal conductivity as a function of time. The study table output
contains three sheets:
Summary Sheet
This sheet contains a list of the input parameters, and the average properties after the last step.
Profile Sheet
This sheet contains various properties for each layer.:
Distance: The distance from the cold layer (in Å).
Temperature: The average temperature in the layer (in K).
Variance: The variance of the temperature in the layer (in K2).
Standard deviation: The standard deviation of the temperature in the layer (in K).
Density: The average mass density of the layer (in g/cc).
Variance: The variance of the density in the layer (in (g/cc)2).
Standard deviation: The standard deviation of the density in the layer (in g/cc).
Analysis Sheet
This sheet contains various derived properties for each exchange.:
Time: The time since the start of the production run (in ps).
Thermal conductivity: The thermal conductivity (in W/m/K).
Energy flux: The average energy flux (in GW/m2).
Standard deviation: The average temperature gradient, averaged over both regions (in
GK/m = 0.1 K/Å).
-Gradient Hot to Cold: Negated average temperature gradient between the hot and cold
layer (in GK/m).
Gradient Cold to Hot: Average temperature gradient between the cold and hot layer (in
GK/m).
Preparation of the input structure
To run the script a document must be provided containing a 3D atomistic structure. The
structure is typically an amorphous cell of molecules, representing a fluid, although solids should
be possible also. The structure should be equilibrated at the average temperature for which the
thermal conductivity is required. The script will also do some equilibration, but with the energy
flux imposed.
For best performance the box should be extended in the z-direction, corresponding to the
direction of the flux. A ratio of at least 1:3 is recommended, see Müller-Plathe (1999). Input
structures are readily created using the Amorphous Cell module in Materials Studio, which also
preserves molecules, subunits, etc, if used.
Example
An example is provided of argon at density 0.2652 g/cc and temperature 500 K. The
experimental thermal conductivity at this state point is is 0.0352 W/m/K (Stewart (1989)).
The initial structure was constructed using the Amorphous Cell module in Materials Studio. The
system has 3000 atoms in a tetragonal box elongated in the z-direction to 200 Å. The system is
divided into 40 layers, or 75 atoms per layer. The Universal force field is used at Medium quality
with a time step of 5 fs. The system is then equilibrated with the Forcite module at constant
temperature of 500 K.
A velocity exchange was performed every 250 steps (1.25 ps). After a transient period of 500
exchanges (625 ps), a production stage was run over 1000 exchanges (1.25 ns). The resulting
flux is 0.396 GW/m2. The resulting gradient is 11.7 GK/m. The resulting thermal conductivity
therefore is 0.396/11.7 = 0.0337 W/m/K.
Known issues
All-atom forcefields, such as COMPASS and pcff, tend to overestimate the thermal conductivity.
This has been attributed to the fact that such force fields treat all bonds and angles as flexible,
whereas in reality they are fixed since the thermal energy is not sufficient to excite some bonds
and angles (Zhang (2005) and Lussetti (2007)). For instance a CH stretch mode has an energy
of 3300 cm-1, whereas at room temperature the thermal energy is just 207 cm-1. Consequently,
at room temperature, such a mode is not available for energy transport, since it cannot store
more energy than that of the ground state.
It is possible to correct for quantum effects, by assuming that all degrees of freedom contribute
equally to the thermal conductivity. With Nf the number of inactive degrees of freedom, and N
the total number, a corrected value is obtained by multiplying with (N-Nf)/N. In practice,
however, some degrees of freedom are more effective in transporting energy than others and
the correction becomes more complicated.
References
Bedrov, D.; Smith, G.D., "Thermal conductivity of molecular fluids from molecular dynamics
simulations: Application of a new imposed-flux method.", J. Chem. Phys., 113, 8080-808
(2000).
Jund, P.; Jullien, R., "Molecular dynamics calculation of the thermal conductivity of vitreous
silica.", Phys. Rev. B, 59, 13707-13711 (1999).
Lussetti, E.; Terao, T.; Müller-Plathe, F., "Nonequilibrium molecular dynamics calculation of the
thermal conductivity of amorphous polyamide-6,6.", J. Phys. Chem. B, 111, 11516-11523
(2007).
Müller-Plathe, F., "A simple nonequilibrium molecular dynamics method for calculating the
thermal conductivity.", J. Chem. Phys., 106, 6082-6085 (1997).
Nieto-Draghi, C.; Bonet Avalos, J., "Non-equilibrium momentum exchange algorithm for
molecular dynamics simulation of heat flow in multicomponent systems.", Mol. Phys., 101,
2303-2307 (2003).
Stewart, R. B.; Jacobsen, R. T., "Thermodynamic properties of argon from the triple point to
1200 K with pressures to 1000 MPa.", J. Phys. Chem. Ref. Data, 18, 639-798 (1989).
Zhang, M.; Lussetti, E.; de Souza, L. E. S.; Müller-Plathe, F., "Thermal conductivities of
molecular liquids by reverse nonequilibrium molecular dynamics.", J. Phys. Chem. B, 109,
15060-15067 (2005).