# Gradient Thermal Linear Lennard-Jones Fluids

Dear ,

I need to induce a temperature gradient ( z axis ) to a linear Lennard- Jones fluid confined between two plates at different temperatures. To simulate the plates I want to use fix wall / lj93 with different parameters. However , we still do not know how to get the right temperature linear profile .
Can I do this with lammps ?
It is correct to use fix wall / lj93 or there is another more appropriate way to define this wall ?, for example with virtual particles.

regards



Dear ,

I need to induce a temperature gradient ( z axis ) to a linear Lennard-
Jones fluid confined between two plates at different temperatures. To

what is a "linear fluid"?

simulate the plates I want to use fix wall / lj93 with different parameters.

an analytical wall potential like this cannot impose a temperature on
other atoms.

However , we still do not know how to get the right temperature linear
profile .
Can I do this with lammps ?

LAMMPS can do a lot of things, however, it is not quite clear what you
want to learn from the simulation. you definitely can impose a
temperature gradient using a temperature bias, but would be more like
doing an animation.

It is correct to use fix wall / lj93 or there is another more appropriate
way to define this wall ?, for example with virtual particles.

you can set up tethered particles (using fix spring/self) and then
thermalize those and study the imposed kinetic energy transfer to the
neighboring liquid. you can also simply use an analytic wall
potential, and then just define a region where you apply a
thermalization (e.g. using fix langevin) and then just do regular time
integration via fix nve for the rest of the system. there are more way
to set up a simulation with the general properties you look at, but
without knowing what it is that you want to study, it is difficult to
make a suggestion. the best suggestion is to consult with your
adviser, since you have to be clear about what it is what you want to
learn from the simulation and how the model should be set up, before
you can seriously look into which features in LAMMPS to use. on top of
that, it is highly recommended to check out what other people have
done (i.e. check the literature) and make some simple experiments with
small systems to see, if what you have decided that you want to do, is
viable and can produce the kind of answer you are looking for.

axel.

> Dear ,
>
> I need to induce a temperature gradient ( z axis ) to a linear Lennard-
> Jones fluid confined between two plates at different temperatures. To

what is a "linear fluid"?

Sorry , I meant linear temperature gradient in the z axis.

> simulate the plates I want to use fix wall / lj93 with different
parameters.

an analytical wall potential like this cannot impose a temperature on
other atoms.

> However , we still do not know how to get the right temperature linear
> profile .
> Can I do this with lammps ?

LAMMPS can do a lot of things, however, it is not quite clear what you
want to learn from the simulation. you definitely can impose a
temperature gradient using a temperature bias, but would be more like
doing an animation.

My ultimate goal is to study thermophoretic effects a colloidal system
subjected to a temperature gradient and a high confinement . Study effects
of confinement and temperature gradient to the collective behavior of the
colloid in the direction perpendicular to the temperature gradient .
For that I have to measure Soret coefficient , thermal conductivity and
diffusion among other things.

First I want to model the Lennard- Jones fluid , then a fluid model with
SRD and ultimately shape the final system :
SRD + solid colloid sphere.

In the literature I have read that the walls can be simulated with virtual
particles at different kinetic energies or use termoestatos . The important
thing is that the wall behaves like a solid wall at a certain temperature .
Another thing is that the temperature gradient is linear , to make use of
the Fourier law.

In the end I wish to maintain a nonequilibrium steady state with constant
temperature gradient to the colloidal system confined within the walls .

any suggestions would be appreciated,

thanks

Hi Christopher,

Here are some references for NEMD algorithms of thermal gradients, which might be useful. The “heat exchange algorithm” (Refs. 1&2) and the RNEMD method (Ref. 8) are implemented in LAMMPS. If you are interested in thermostatted walls, the algorithm proposed by Ashurst (Ref. 5) or Ciccotti and Tenenbaum (Ref. 7) might be an option.

For a slab geometry and sufficiently far away from the reservoirs/walls most of these algorithms generate a linear temperature profile, as you can see in the papers.

Peter

[1] B. Hafskjold, T. Ikeshoji, and S. Ratkje, “On the molecular mechanism of thermal diffusion
in liquids,” Molecular Physics 80, 1389–1412 (1993).

[2] T. Ikeshoji and B. Hafskjold, “Non-equilibrium molecular dynamics calculation of heat
conduction in liquid and through liquid-gas interface,” Molecular Physics 81, 251–261
(1994).

[3] D. J. Evans and W. G. Hoover, “Flows far from equilibrium via molecular dynamics,”
Annual Review of Fluid Mechanics 18, 243–264 (1986).

[4] D. J. Evans, “Homogeneous NEMD algorithm for thermal conductivity–application of
non-canonical linear response theory,” Physics Letters A 91, 457–460 (1982).

[5] W. T. Ashurst, “Determination of thermal conductivity coefficient via non-equilibrium
molecular dynamics,” in Advances in Thermal Conductivity: 13th International Conference
on Thermal Conductivity, Lake Ozark, Nov. 1973, Papers (1974) pp. 89–98.

[6] A. Baranyai, “Heat flow studies for large temperature gradients by molecular dynamics

simulation,” Physical Review E 54, 6911–6917 (1996).

[7] G. Ciccotti and A. Tenenbaum, “Canonical ensemble and nonequilibrium states by molec-

ular dynamics,” Journal of Statistical Physics 23, 767–772 (1980).

[8] F. Müller-Plathe, “A simple nonequilibrium molecular dynamics method for calculating

the thermal conductivity,” Journal of Chemical Physics 106, 6082–6085 (1997).

[10] S. Kuang and J. D. Gezelter, “A gentler approach to RNEMD: Nonisotropic velocity scaling

for computing thermal conductivity and shear viscosity,” Journal of Chemical Physics 133,
164101 (2010).

Hi Christopher,

What’s already been said is good advice. I would only add that you don’t need a linear temperature gradient to use Fourier’s law - though we often assume that the thermal conductivity is a constant, in reality it varies with T. Rather than having to fit a straight line to dT/dz, you can determine the local gradient of the curve to determine \lambda(T), as described in JCP 140 016102 (2014) Thanks, Niall

Dear Peter ,

thanks for the information . Indeed while the wall are sufficiently separated the temperature gradient is linear .
I will continue checking in particular how to use thermostatted walls and no periodic boundary conditions in the direction of the gradient using a NEMD .

Thanks for the references.

Hi Niall,

Thank you for the suggestion. I will take it into account.

regards

Christopher