# Density confusion in LJ units

Hi All,

I’m newbie in molecular world and I’m almost confused with using lj reduced unit density in lattice command. First of all, I assume density in lj reduced units is Number Density right? because in description of lj units on lammps manual density is defined as mass/volume however its reduced units definition has only length unit in it so I assume number density is what has been applied, right?
Now based on manual we have scale = reduced density rho* (for LJ units) so

does that mean in lammps examples directory the “flow” simulation, where a 2d couette flow is being simulated, a fluid with reduced density of 0.7 (# of molecules/Area) and T* = 1.0 is being simulated?

Is this density of the walls too? as they’ve not been introduced a different density.

so basically based on the defined region ( region box block 0 20 0 10 -0.25 0.25 ) and reported number of atoms in accompanied log file ( Created 420 atoms ) I thought I have to get the applied reduced density of 0.7 by 420/(20*10) ( # of molecules / area of the region) which apparently is not right! Would you please let me know what’s wrong with my interpretation of calculating the density?

How can I get the density of the fluid that is being simulated?

Thanks,

Kasra.

Hi All,

I'm newbie in molecular world and I'm almost confused with using lj reduced
unit density in lattice command. First of all, I assume density in lj
reduced units is Number Density right? because in description of lj units on
lammps manual density is defined as mass/volume however its reduced units
definition has only length unit in it so I assume number density is what has
been applied, right?

only if you have only one type of particle and that has the mass 1.
neither length nor mass have a conventional "unit" attached.
mass is the ratio to the reference mass and length the ratio
with the reference sigma.

Now based on manual we have scale = reduced density rho* (for LJ units) so

does that mean in lammps examples directory the "flow" simulation, where a
2d couette flow is being simulated, a fluid with reduced density of 0.7 (#
of molecules/Area) and T* = 1.0 is being simulated?

Is this density of the walls too? as they've not been introduced a different
density.

so basically based on the defined region ( region box block 0 20 0
10 -0.25 0.25 ) and reported number of atoms in accompanied log file (
Created 420 atoms ) I thought I have to get the applied reduced density of
0.7 by 420/(20*10) ( # of molecules / area of the region) which apparently
is not right! Would you please let me know what's wrong with my
interpretation of calculating the density?

How can I get the density of the fluid that is being simulated?

on the molecular level, density is only a well defined
property, if you have a (uniform) bulk system with
periodic boundaries. it is non-trivial to define the
volume of a group of atoms.

axel.

• isn’t density = mass/volume nondimensionalized as rho* = rho m^-1sigma^3? unless we define density = #molecules/volume which is nondimensionalized as in the manual (rho = rho sigma^3)

• Then when I choose a LJ type material in liquid phase say T*=1.0 and rho*=0.7 for couette simulation, how can I actually make sure that I’m applying correct density in my simulation? isn’t it deviding number of molecules of the fluid by volume ( area in 2d like “flow” example) of the region defined for fluid molecules?

Thanks,
Kasra.

isn't density = mass/volume nondimensionalized as rho* = rho m^-1*sigma^3?
unless we define density = #molecules/volume which is nondimensionalized as
in the manual (rho* = rho sigma^3)

molecules have no meaning for computing density in lammps.

Then when I choose a LJ type material in liquid phase say T*=1.0 and
rho*=0.7 for couette simulation, how can I actually make sure that I'm
applying correct density in my simulation? isn't it deviding number of
molecules of the fluid by volume ( area in 2d like "flow" example) of the
region defined for fluid molecules?

but how do you define the volume (or area) *exactly*?

what is the *exact* volume of an atom? you can only
approximate it by averaging over a large sample where
the error from approximating atoms as point particles
is vanishing.

there is no "correct" density on the scale of nanometers.
think about it for a bit and you'll see.

axel.

So what do I get by deviding number of atoms by the size of the box defined in lammps? Is has nothing to do with density?

Kasra.

So what do I get by deviding number of atoms by the size of the box defined in lammps? Is has nothing to do with density?

it is an approximation and it will be a worse
approximation the smaller the volume gets.

remember, you have point particles that have
no volume, so you only have a well defined
volume, if you have a homogeneously filled
periodic cell.