polymer-stats

Numerical modelling of the electroelasticity of polymer chains consisting of dielectric monomers and polar monomers. Chains consisting of dielectric monomers can be simulated in either the fixed end-to-end vector (mean_field.jl) or fixed force ensembles (mcmc_eap_chain.jl). The fixed end-to-end vector ensemble is simulated using mean-field theory and numerical integration; whereas the fixed force ensemble is simulated using the Markov chain Monte Carlo method. As of now, chains consisting of polar monomers and dipole-dipole interactions (for either chain type) can only be simulated in the fixed force ensemble (mcmc_eap_chain.jl). The mean-field theory simulations tend to be faster, but more physics can be captured using the Markov chain Monte Carlo method.

Getting started

This research code is written in the julia language. In the scripts directory, there is a script for installing package dependences:

julia scripts/install_dependencies.jl

The main file for the mean-field theory simulations is mean_field.jl. You can see options by running:

julia mean_field.jl --help

The theoretical details of this code can be found in the first reference (in particular, sections 3 and 4.1) in the Citations section below.

The main file for the Markov chain Monte carlo method is mcmc_eap_chain.jl. You can see options by running:

julia mcmc_eap_chain.jl --help

An experimental algorithm for clustering of the chain is implmeneted in mcmc_clustering_eap_chain.jl. You can see options by running:

julia mcmc_clustering_eap_chain.jl --help

It has been verified against analytical results, so I am relatively confident in its correctness. The expectation is that the clustering algorithm will vastly improve the convergence rate for dielectric chains with monomer-monomer interactions, but this has not been studied yet.

Questions

Documentation of this work is still in progress. However, I am very receptive to questions and comments via email. You can email questions to [email protected].

Citations

There are a few papers associated with polymer-stats. If you found this code useful for your research, please be kind enough to cite it, using the DOIs 10.1039/D0SM00845A, 10.1073/pnas.2102477 and 10.1016/j.jmps.2021.104658, or the following BiBTeX entries:

@article{grasinger2020statistical,
    title={Statistical mechanical analysis of the electromechanical coupling in an electrically-responsive polymer chain},
    author={Grasinger, Matthew and Dayal, Kaushik},
    journal={Soft Matter},
    volume={16},
    number={27},
    pages={6265--6284},
    year={2020},
    publisher={Royal Society of Chemistry},
    doi={10.1039/D0SM00845A}
}

@article {grasinger2021flexoelectricity,
    author = {Grasinger, Matthew and Mozaffari, Kosar and Sharma, Pradeep},
    title = {Flexoelectricity in soft elastomers and the molecular mechanisms underpinning the design and emergence of giant flexoelectricity},
    volume = {118},
    number = {21},
    year = {2021},
    doi = {10.1073/pnas.2102477118},
    publisher = {National Academy of Sciences},
    issn = {0027-8424},
    journal = {Proceedings of the National Academy of Sciences}
}

@article{grasinger2021statistical,
    title={Statistical mechanics of a dielectric polymer chain in the force ensemble},
    author={Grasinger, Matthew and Dayal, Kaushik and deBotton, Gal and Purohit, Prashant K},
    journal={Journal of the Mechanics and Physics of Solids},
    pages={104658},
    year={2021},
    publisher={Elsevier}
}