A simulation approach to study of entropic elasticity properties of polymer chain molecules using atomic scale Monte-Carlo
DOI:
https://doi.org/10.15587/1729-4061.2014.27988Keywords:
Monte-Carlo, model, simulation, entropy, elasticity, polymers, monomers, properties, radius, gyrationAbstract
This paper describes atomic scale Monte–Carlo studies of entropic elasticity properties of individual polymer chain molecules. An efficient numerical Monte –Carlo sampling approach is outlined and used to evaluate the entropic contribution to the total elastic force.Theoretic predictions of mechanical properties of polymer molecules, particularly complex bio-molecules (proteins, lipids, etc.), are difficult due to effects of entropic elasticity. Entropic elastic force can be a significant contributor to the free energy F of the polymer chain and can even exceed interatomic potential energy U under external mechanical load. Monte-Carlo based approach allows to achieve atomic resolution for molecular structure in contrast to analytical methods. Specific load-extension curves are obtained numerically for a group of molecules with degenerate potential energy profiles. Results of the atomistic modeling are compared with the limiting continuum model of the same type of polymers. The extent of the linear and nonlinear elastic regimes and dependence on the molecular weight and geometric parameters of the molecules are discussed. A significant divergence with the continuummodel behavior is observed at smaller bond angles for all elongationsof the molecule. Linearity of the entropic force exists in a wide range ofthe elongations, however, molecules with low gyration radii(densely packedpolymers) are linear mostly in extensionor unfolding, while very sparsely packed molecules are linear mostly in thecontraction mode. The achieved result cannot be reproduced withinthe settings of the continuum model and required an application of atomic scale Monte-Carlo approach developed by our group.
References
1.Zuckerman, D. M. (2010).Statistical Physics of Biomolecules: An Introduction. CRC Press, 356. 10.5860/choice.48-2065
2.Bhutani, S. P. (2010). Chemistry of Biomolecules. CRC Press, 304.
3.Stroble, G. (2007). The Physics of Polymers: Concepts for Understanding Their Structures and Behavior. Springer, 518.
4.Broedersz, C. P., Storm, C., MacKintosh, F. C. (2008). Nonlinear elasticity of composite networks of stiff biopolymers with flexible linkers. Phys. Rev. Lett., 101(11), 118103–118107. DOI: 10.1103/PhysRevLett.101.118103
5. Landau, L. D., Lifshitz E. M. (1980). Statistical Physics. 3rd ed. (Course of TheoreticalPhysics, Vol. 5). Butterworth-Heinemann, 544.
6. Laurendeau, N. (2005). Statistical Thermodynamics for Ideal Gas Mixtures. Fundamentals and Applications, 205–222. DOI:10.1017/cbo9780511815928.015
7.Strick, T. R., Dessinges, M. N., Charvin, G. (2003). Stretching of macromolecules and proteins.Reports on Progress in Physics, 66, 1–45. DOI: 10.1088/0034-4885/66/1/201
8. Gardiner, C. W. (2004). Handbook of Stochastic Methods. Springer, 442.
9.Karpov, E. G., Chaichenets, S., Liu, W. K. (2010).Mechano-kinetic coupling approach for functional materials with dynamic internal structure.Philosoph. Mag. Lett. 90(7), 471–480. DOI: 10.1080/09500831003761933
10.Borsali, R., Pecora, R. (2008). Soft-Matter Characterization. Springer, 1452. DOI: 10.1007/978-1-4020-4465-6
11.Karpov, E. G., Grankin. M. V. (2012). Atomic Scale Monte-Carlo Studies of Entropic Elasticity Properties of Polymer Chain Molecules.Adv. inSoftMatterMech., 147–163. doi: 10.1007/978-3-642-19373-6_5
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2014 Михаил Викторович Гранкин, Анатолий Алексеевич Каргин, Эдуард Григорьевич Карпов

This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.