# [lammps-users] query regarding equivalence of reduced density and real density in polymer systems

Hi all,

I hope my mail will reach many polymer simulation experts who can guide me out of my confusion.

This query is regarding the equivalence of reduced density and real density and the effect of its difference on polymer property like entanglement length.

I am modeling Polyethylene using full atomistic model rather than coarse grained one.

Generally, the polymer simulation community working with coarse grained simulations prefers reduced density values of 0.85 and using same they reach various entanglement length values of these systems.

For my PE system e.g. if I have the following parameters:

N (No of atoms in simulation box) = 9500, LJ_sigma = 4.28 Angstrom, Box_length (corresponding to real density of 0.77 grms/cc) = 65.74 Angstrom.

Then, the equivalent reduced density (rho_real) = N * LJ_sigma^3 / Box_length^3 = 2.62

So, my query is that with this big difference in reduced density, is it advisable to compare Entanglement length Values of two systems (coarse grained & full atomistic)?

Other query is: why this magic number 0.85 for reduced density in coarse grained systems?

In case, my query is bit immature then I will really appreciate if someone can suggest me some good references!!

Looking forward for enlightenmentâ€¦

Hi Dhiraj Mahajan,

First, a reduced density of 0.85 corresponds to the triple point density of a Lennard-Jones fluid. It is chosen for many coarse-grained polymer systems merely as a convenience to ensure that the simulated system is a dense fluid. That model allows for the investigate of the physics of polymers without getting distracted by the chemical details. Therefore, comparisons with that model for specific numerical values of entanglement length may be meaningless. With a fully atomistic system, you will want to compare with experiment or other simulations that are chemically detailed and at the same density as your simulation.

Second, of course it appears that you have a huge reduced density because you have incorrectly reduced the density. Either you need to take into account the multiple types of atoms you have in the simulation or you need to reduce on a higher unit basis than merely an atom. If you still really want to compare with coarse-grained models, what you need to do is calculate a reduced density based on persistence length.

Follow-up to Joanne's comment - if your PE is an all-atom model,
are you including the H atoms in N? I don't think you should - but rather
just the backbone atoms, or some count of monomer units that are
a characteristic size of sigma=4.28.

Steve