# regarding desired volume fraction of LJ particles in simulation box

Dear Lammps Users,

I am running simulations to compute viscosity of polydisperse LJ particles and would like to know what is the best course of action to have desired volume fraction (10%, 12% etc) without changing the box size.

How can one achieve desired volume fraction with four different particle sizes??

Any help or explanation is greatly appreciated.

Best regards
Raghav

• you say you are running simulations, but then you ask about how to set them up. so you want to run them? or what simulations are you running?
• you talk about “polydisperse”, but then only mention 4 particles sizes. polydisperse usually implies that each particle has a different size.
• you ask about volume fraction, but you are not really defining how this has to be interpreted. technically speaking, lennard-jones particles do not have a size. they are point particles. however, the shape of the potential results in an “effective” size depending on the sigma and epsilon parameters or all particles. since the interaction is “soft” the volume per particle type is not so well defined. one way to assign a volume would be voronoi tesselation, another would be to define an “effective radius” from radial distribution functions, but both methods can determine the relative volumes only after the fact. Or just derive it from sigma, but then the ratio between effective volume and assigned volume is dependent on the specific choice of parameters
• also, when packing (hard sphere) particles of different size, you may have different percentages of vacuum depending on the packing and how well the particles can re-arrange.

so can you clarify and be more specific as to what you already have done and where exactly you are stuck with figuring things out yourself.

axel.

Dear Dr. Kohlmeyer,

• I have a system prepared for 4 different particle sizes and the number and particles size information will be updated to 15 different particles mass/effective radius etc. The issue I wanted to be helped on was regarding the amount of simulation domain filled with these point particles?

• I understand the concept of polydispersity and for sure not in true sense but I am just calling my simulation system a polydisperse system due to size/mass differences of different particles (apologies if I have made the wrong statement).

• and yes, I was also thinking about the effective radius for the computation of volume fraction of individual particle type and collectively for the whole system. Thank you for the suggestions and I will try the Voronoi tessellation and/or radial distribution function to compute effective volume for the particles.

• As I am generating the particles randomly in my simulation domain, I just wanted to compute the volume fraction occupied by the particles generated in the simulation domain as I want to run simulations of volume fraction from 1:20%. Is there some procedure in lammps with which I can get this information directly by inserting specific commands in the input script or any “rule of thumb” to do the same?

Right now I am running simulations which are not dependent on volume fractions meaning I have a certain number of particles of each of 4 types and running the simulations to determine the viscosity.

Does that make sense??

Thank you for your time and suggestions.

Best regards
Raghav

Voronoi tessellation is the only assumption-free method to assign volumes to atoms, but you have to keep in mind that this divides the entire volume and assigns it to individual atoms. That will lead to undesired large volume assignments if you have open surfaces or voids in your system.
The other issue to keep in mind is that for a dynamical system, the values for individual atoms will change as the system changes, so for each atom type (and thus assigned value of sigma) you will get a distribution of volumes that can change over time. How you compute the desired volume fractions from that requires some assumptions or definitions that you will have to pick.

Axel.