# How to calculate free volume for polymers

Hello lammps community, i am using 2 Aug 2023 lammps my system consists of polymers and want to compute free volume in my system, according to the manual voronoi/atom command can do but the volume obtained from that command is equal to the total volume which i get from thermo_style, and their is another method which mention by prof.@akohlmey to find average volume per atom but i do not know this method, professor @akohlmey would it possible to explain how to find out average volume per atom with much respect.
thank you so much

When you quote somebody, you should provide a reference from where you have that quote from. As a scientist this should be your second nature. In my home country, several highly respected people have lost their (well paid) jobs because they didnâ€™t quote their sources properly in their respective PhD theses. That wonâ€™t happen to you here any now, but it is always a good idea to make proper citing a habit so it doesnâ€™t bit you in the backside later.

As for your question. The volume of an atom is an ill-defined property and so is volume of any molecule or polymer at the atomic level. Even the volume per atom of a homogeneous bulk system is dependent on the packing, and if you build a crystal of two kinds of atoms with different effective radii, you can stuff more atoms into the same volume since the smaller ones can better fill the â€śholesâ€ť of the packing of the larger ones. Voronoi tesselation does not determine the volume per atom, but it partitions the volume according to some geometrical rules.

So to determine the â€śfreeâ€ť volume you have to make some assumptions and approximations. E.g. you can try to build a filled system (but see the caveats from above) compute from that the effective volume per atom and then determine the occupied volume by summing over the effective volumes of the atoms, but that can be tricky if you have a mix of hydrogen and carbon/oxygen/nitrogen. You can take a â€śprobe particleâ€ť with an empirically chosen radius, try to place it on random locations in the box and get the ratio between occupied and unoccupied by whether the probe particle is overlapping with any of the atoms in the system. You can cut the entire simulation cell in very small boxes (or voxels, i.e. like pixels, but in 3d). Now you check the voxels, if they overlap with any atoms (plus either their covalent or VDW radius or LJ sigma) and then count the occupied and unoccupied voxels and from that count the free volume.

None of these methods is exact and without empirical choices. Some are available with external tools (e.g. VMD or OVITO) or could be implemented with a little scripting etc.

Thank you so teacher for your help,
teacher if i used this formula

variable Rc equal 0.72 #radius of corban atom in Armstrong
variable vcorbon equal (4/3)pi (r^3)

from this i will get the volume of atom and than multiple the number of atom with this calculated volume, it will give me the occupied volume. After this the occupied volume subtracted from the total volume, from this i will get the free volume

is this is a valid method

thank you so much

I am not your teacher. I am just some random dude on the internet.

Please see the forum guidelines about how to correctly quote input files so the forum will not interpret special characters as markup symbols. Please also watch your spelling and watch out for valid LAMMPS input syntax (this will create an error when used like this).

It is not my job to give you a thumbs up or thumbs down. You cannot write in your report/thesis â€śThis random dude on the internet said it was OK, so I used this.â€ť You have to make a convincing scientific argument and you do not have to convince me but rather yourself and your reviewers.

I already wrote a lengthy response about my perspective on this topic and that all attempts to put a number to this will be ultimately wrong since you have an ill-defined and in this specific case a fractal property. I have nothing of substance to add to my previous post since the discussion of what is the occupied/unoccupied volume is not a LAMMPS topic but rather a question of the general science.

In my society we used â€śteacherâ€ť for respect.

it,s my bad luck i make some spelling mistake, sorry for that,

thank you so much sir for your help.

Correct spelling is not a matter of luck.

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Years ago I have used 3V: Voss Volume Voxelator to compute the solvent-accessible-surface of a substrate. Depending of what you need to compute exactly, you could do that in post-processing using the trajectory.

thank you so much @hothello,
basically, I want to find free volume of un-crosslinked and crosslinked polymers as the density of crosslinking increases the free volume is also increasing in the polymer system. My aim to calculate the relation of crosslinking density with the increase in the free volume.

thank you so much for your help.

Hello,

I am not sure if LAMMPS has any in-built tools to do this calculation. You can use open-source tools that are specifically designed for computing free volume in atomistic models. As Dr. Kohlmeyer explained, you may need to implement the â€śprobe particleâ€ť approach. Here are some available tools online -

1. Another Void Program
2. PSDSOLV
3. trj_cavity
There are many other codes online you can look into.

Best,
PD

@Prathamesh_Deshpand1, thank you so much for your help, definitely i will try these tools.
know i am trying vmd, from vmd i get density_out.dx file but i do not understand how i can calculated free volume from that file,