Elastic Constant for polymer system

Dear Sir,

I want to calculate the elastic constant for my system( Polymer + water molecules). I checked the examples available in LAMMPS installation directory- examples/ELASTIC_T/BORN_MATRIX.
Examples available only for crystal systems (Argon and Silicon).

My question is, Can I apply this concept to polymer systems?


Hi @Sachin_varshney,
This is actually a tricky question as it depends of what your polymer system actually is.

The Born method results depend on the statistical exploration of the configurational phase space which is a tricky problem as it can be very long for polymeric systems like melted bulk. In such case the system will give you values that are “glassy”, that is way to high at high temperature in some preferred directions that will depend on your configuration. Those can be averaged out with a large number of replicas to get back anisotropic behaviour but will always remain in a glassy like regime.

However I think they can be used for reticulated systems where polymer molecules diffusion is very much limited by the network they form. In the case of diluted molecules, I think the result would likely give the compressibility of the fluid but I’ve never tried that.

Some published work related to those questions were done by @evoyiatzis here.

If you want to know more about the implementation in LAMMPS, see the related paper.

Thanks, Sir

I have tried to calculate the elastic proiperties of an epoxy network (i dont knoi if this is the polymer case you are modeling). In fact I do not suggest this method due to the very large computational times required to explore the configurational phase space in polymers in addition with the calculation of the born and stress term in this formula. In fact you may also need to use a large system (over 30k atoms) which will increase the computational time drastically. I suggest looking to other methods. See for example this work or this.

Just to put numbers in perspective, the computation of stress is rather straight forward in MD since the forces and velocities are mandatory for the simulation.

The Born term is actually fast to converge in the case of crystals, so I personally think it does not need to be computed that often for polymers. As for the computation, if you use analytical implementation, you only need one more pass per atom pairs, bonds, angles… so count it as another force computation. If you use a numerical differentiation method, you have to count for two more force computing loops so it is roughly up to a factor 3 if you compute it every step.

I agree with you that this method is not really usable in the case of polymer bulk, I am more circumspect in the case of polymerized resins.

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As you suggested, I read the paper which you provided in the link.
" Molecular dynamics simulations of EPON-862/DETDA epoxy networks: structure, topology, elastic constants, and local dynamics"
In that paper, three methods are suggested. Which one I should follow?

Do you have a sample input script for that method?