Abstract
In this work, we will make an energetic and structural characterization of three-dimensional linear chains generated from a simple self-avoiding random walk process in a finite time, without boundary conditions, without the need to explore all possible configurations. From the analysis of the energy balance between the terms of interaction and bending (or correlation), it is shown that the chains, during their growth process, initially tend to form clusters, leading to an increase in their interaction and bending energies. Larger chains tend to “escape” from the cluster when they reach a number of “steps” \(N>\sim 1040\), resulting in a decrease in their interaction energy, however, maintaining the same behavior as flexion energy or correlation. This behavior of the bending term in the energy allows distinguishing chains with the same interaction energy that present different structures. As a complement to the energy analysis, we carry out a study based on the moments of inertia of the chains and their radius of gyration. The results show that the formation of clusters separated by “tails” leads to a final “prolate” structure for this type of chain, the same structure evident in real polymeric linear chains in a good solvent.
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References
Flory, P.J.: Principles of Polymer Chemistry. Cornell University Press, Ithaca (1953)
Flory, P.J.: The configuration of real polymer chains. J. Chem. Phys. 17(3), 303–310 (1949)
Madras, N., Sokal, A.: The pivot algorithm: a highly efficient Monte Carlo method for self-avoiding walk. J. Stat. Phys. 50(1–2), 109–186 (1988)
Slade, G.: Self-avoiding walks. Math. Intell. 16(1), 29–35 (1994). https://doi.org/10.1007/BF03026612
Figueirêdo, P.H., Moret, M.A., Coutinho, S., Nogueira, J.: The role of stochasticity on compactness of the native state of protein peptide backbone. J. Chem. Phys. 133, 08512 (2010)
Boglia, R.A., Tiana, G., Provasi, D.: Simple models of the protein folding and of non-conventional drug design. J. Phys. Condens. Matter 16(6), 111 (2004)
Tang, C.: Simple models of the protein folding problem. Phys. A Stat. Mech. Appl. 288(1), 31–48 (2000)
Grosberg, A.Y., Khokhlov, A.R.: Statistical Physics of Macromolecules. AIP Press, New York (1994)
Rubinstein, M., Colby, R.H.: Polymer Physics. Oxford University Press, New York (2003)
Teraoka, I.: Polymer Solutions: An Introduction to Physical Properties. Wiley Inter-science, New York (2002)
Hsu, H.P., Paul, W., Binder, K.: Standard definitions of persistence length do not describe the local “intrinsic” stiffness of real polymers. Macromolecules 43(6), 3094–3102 (2010)
Landau, L.D., Lifshitz, E.M.: Theory of Elasticity. Elsevier Sciences, New York (1986)
Schöbl, S., Sturm, S., Janke, W., Kroy, K.: Persistence-length renormalization of polymers in a crowded environment of hard disks. Phys. Rev. Lett. 113(23), 238302 (2014)
Amit, D.J., Parisi, G., Paliti, L.: Asymptotic behavior of the “true” self-avoiding walk. Phys. Rev. B 27(3), 1635–1645 (1983)
Solc, K.: Shape of random-flight chain. J. Chem. Phys. 55(1), 335–344 (1971)
Rudnick, J., Gaspari, G.: The asphericity of random walks. J. Phys. A: Math. Gen. 30(11), 3867–3882 (1997)
Hadizadeh, S., Linhananta, A., Plotkin, S.S.: Improved measures for the shape of a disordered polymer to test a mean-field theory of collapse. Macromolecules 44(15), 6182–6197 (2011)
Aronovitz, J., Nelson, D.: Universal features of polymer shapes. J. Phys. 47(9), 1445–1456 (1986)
Cannon, J.W., Aronovitz, J.A., Goldbart, P.: Equilibrium distribution of shapes for linear and star macromolecules. J. Phys. I Fr. 1(5), 629–645 (1991)
Alim, K., Frey, E.: Shapes of semi-flexible polymer rings. Phys. Rev. Lett. 99(19), 198102 (2007)
Dokholyan, N.V., Buldyrev, S.V., Stanley, H.E., Shakhnovich, E.I.: Discrete molecular dynamics studies of the folding of a protein-like model. Fold. Des. 3(6), 577–587 (1998)
Theiler, J.: Estimating fractal dimension. J. Opt. Soc. Am. A, OSA 7(6), 1055–1073 (1990)
Blavatska, V., Janke, W.: Shape anisotropy of polymers in disordered environment. J. Chem. Phys. 133(18), 184903 (2010)
Rawdon, E.J., et al.: Effect of knotting on the shape of polymers. Macromolecules 41(21), 8281–8287 (2008)
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Avellaneda B., D.R., González, R.E.R., Ariza-Colpas, P., Morales-Ortega, R.C., Collazos-Morales, C.A. (2021). Structural Characterization of Linear Three-Dimensional Random Chains: Energetic Behaviour and Anisotropy. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2021. ICCSA 2021. Lecture Notes in Computer Science(), vol 12949. Springer, Cham. https://doi.org/10.1007/978-3-030-86653-2_13
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DOI: https://doi.org/10.1007/978-3-030-86653-2_13
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