Abstract
Crosslinked network formation occurs when multifunctional precursors react to form a three-dimensional polymer network. In attempting to link network topology to physical properties, materials are typically characterized by the functionality of the crosslink nodes, the typical chain length between crosslinks and the concentration of the crosslink junctions. Statistical models that are in common usage calculate average values of these quantities and do not determine the possible variation in these properties. Molecular dynamics studies show not only how networks form and whether the average values conform to the predictions of these statistical theories, but also how they vary locally. An important result from the simulations is that there are significant regions where there are few bonds connecting neighboring chains. In addition, very long loops and dangling chains occur. None of this should be surprising in a system where the reactions and spatial arrangements are influenced by random chance and there are such a huge number of precursor molecules and possibilities that a number of nonideal configurations are possible. The simulations permit visualizations of these imperfections and show how large they are. Many of the end use properties of polymer networks depend on the continuity of the network, so this heterogeneity must have an impact on the physical properties. Here, the simulations use coarse-grained techniques that are not specific to any reactive chemistry, but such research may indicate how networks can be assembled that are less prone to large heterogeneities and are thus more robust.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Flory, P.J.: Network structure and the elastic properties of vulcanized rubber. Chem. Rev. 135, 51–75 (1944)
Flory, P.J.: Principles of Polymer Chemistry. Cornell University Press, Ithaca (1953)
Stockmayer, W.H.: Theory of molecular size distribution and gel formation in branched-chain polymers. J. Chem. Phys. 11(2), 45–55 (1943)
Stockmayer, W.H.: Theory of molecular size distribution and gel formation in branched polymers II. General cross linking. J. Chem. Phys. 12(40), 125–131 (1944)
Dušek, K.: Crosslinking and networks. Makromol. Chem. Suppl. 2, 35–49 (1979)
Cail, J.I., Stepto, R.F.T.: The gel point and network formation—theory and experiment. Polym. Bull. 58(1), 15–25 (2007)
Zhou, H., Woo, J., Cok, A.M., Wang, M., Olsen, B.D., Johnson, J.A.: Counting primary loops in polymer gels. Proc. Natl. Acad. Sci. USA. 109(47), 19119–19124 (2012)
Duering, E.R., Kremer, K., Grest, G.S.: Structure and relaxation of end-linked polymer networks. J. Chem. Phys. 101, 8169–8192 (1994)
Duering, E.R., Kremer, K., Grest, G.S.: Structural properties of randomly crosslinked polymer networks. Progr. Colloid Polym. Sci. 90, 13–15 (1992)
Gordon, M.: Good’s theory of cascade processes applied to the statistics of polymer distributions. Proc. R. Soc. Lond. A Math. Phys. Sci. 268, 240–256 (1962)
Treloar, L.R.G.: The Physics of Rubber Elasticity. Clarendon Press, Oxford (1958)
Flory, P.J., Rehner, J.: Statistical mechanics of swelling of crosslinked polymer networks. Chem. Phys. 11, 521–526 (1943)
Coniglio, A., Stanley, H.E., Klein, W.: Site-bond correlated-percolation problem: a statistical mechanical model of polymer gelation. Phys. Rev. Lett. 42(8), 513–522 (1979)
Gujrati, P.D.: Thermal and percolative transitions and the need for independent symmetry breakings in branched polymers on a Bethe lattice. J. Chem. Phys. 98(2), 1613–1634 (1993)
Dušek, K.: My fifty years with polymer gels and networks and beyond. Polym. Bull. 58, 321–338 (2007)
Dušek, K., Dušková-Smrčková, M.: Network structure formation during crosslinking of organic coating systems. Prog. Polym. Sci. 25, 1215–1260 (2000)
Dušek, K., Dušková-Smrčková, M., Huybrechts, J., Ďuračková, A.: Polymer networks from preformed precursors having molecular weight and group reactivity distributions. Theory and application. Macromolecules. 46, 2767–2784 (2013)
Miller, D.R., Macosko, C.W.: Molecular weight relations for crosslinking of chains with length and site distribution. J. Polym. Sci. B Polym. Phys. 25, 2441–2469 (1987)
Miller, D.R., Macosko, C.W.: Network parameters for crosslinking of chains with length and site distribution. J. Polym. Sci. B Polym. Phys. 26, 1–54 (1988)
Dušek, K., Spĕváček, J.: Cyclization in vinyl–divinyl copolymerization. Polymer. 21, 750–756 (1980)
Tiemersma-Thoone, G.P.J.M., Scholtens, B.J.R., Dušek, K., Gordon, M.: Theories for network formation in multistage processes. J. Polym. Sci. B Polym. Phys. 29, 463–482 (1991)
Flory, P.J.: Statistical thermodynamics of random networks. Proc. R. Soc. Lond. A Math. Phys. Sci. 351, 351–380 (1976)
Queslel, J.P., Mark, J.E.: Molecular interpretation of the moduli of elastomeric polymer networks of known structure. Adv. Polym. Sci. 85, 135–176 (1984)
Flory, P.J.: Elastic activity of imperfect networks. Macromolecules. 15, 99–100 (1982)
Grest, G.S., Kremer, K.: Statistical properties of random cross-linked rubbers. Macromolecules. 23, 4994–5000 (1990)
Stevens, M.J.: Interfacial fracture between highly cross-linked polymer networks and a solid surface: effect of interfacial bond density. Macromolecules. 34, 2710–2718 (2001)
Tsige, M., Stevens, M.J.: Effect of cross-linker functionality on the adhesion of highly crosslinked polymer networks: a molecular dynamics study of epoxies. Macromolecules. 37, 630–637 (2004)
Tsige, M., Lorenz, C.D., Stevens, M.J.: Role of network connectivity on the mechanical properties of highly cross-linked polymers. Macromolecules. 37, 8466–8472 (2004)
Zee, M., Feickert, A.J., Kroll, D.M., Croll, S.G.: Cavitation in crosslinked polymers: molecular dynamics simulations of network formation. Prog. Org. Coat. 83, 55–63 (2015)
Plimpton, S.: Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995)
Pascault, J.-P., Sautereau, H., Verdu, J., Williams, R.J.J.: Thermosetting Polymers. Marcel Dekker, New York (2002)
Gillham, J.K.: Formation and properties of thermosetting and high Tg polymeric materials. Polym. Eng. Sci. 26(20), 1429–1433 (1986)
Herrmann, H.J., Hong, D.C., Stanley, H.E.: Backbone and elastic backbone of percolation clusters obtained by the new method of ‘burning’. J. Phys. A Math. Gen. 17, L261–L266 (1984)
Kroll, D.M., Croll, S.G.: Influence of crosslinking functionality, temperature and conversion on heterogeneities in polymer networks. Polymer. 79, 82–90 (2015)
Martin, M.G.: MCCCS Towhee: a tool for Monte Carlo molecular simulation. Mol. Simul. 39(14–15), 1212–1222 (2013)
Smit, B.: Phase diagrams of Lennard-Jones fluids. J. Chem. Phys. 96, 8639–8640 (1992)
Ge, J., Wu, G.-W., Todd, B.D., Sadus, R.J.: Equilibrium and nonequilibrium molecular dynamics methods for determining solid–liquid phase coexistence at equilibrium. J. Chem. Phys. 119, 11017–11023 (2003)
Ahmed, A., Sadus, R.J.: Effect of potential truncations and shifts on the solid liquid phase coexistence of Lennard-Jones fluids. J. Chem. Phys. 133, 124515 (2010)
Witten, T.A., Sander, L.M.: Diffusion-limited aggregation. Phys. Rev. B. 27(9), 5686–5697 (1983)
Meakin, P.: Diffusion-limited aggregation in three dimensions: results from a new cluster–cluster aggregation model. J. Colloid Interface Sci. 102(2), 491–504 (1984)
Heinson, W.R., Chakrabarti, A., Sorensen, C.M.: Divine proportion shape invariance of diffusion limited cluster–cluster aggregates. Aerosol Sci. Technol. 49(9), 786–792 (2015)
Erath, E.H., Spurr, R.A.: Occurrence of globular formations in thermosetting resins. J. Polym. Sci. 35(129), 391–399 (1959)
Racich, J.L., Koutsky, J.A.: Nodular structure in epoxy resins. J. Appl. Polym. Sci. 20(8), 2111–2129 (1976)
Morsch, S., Liu, Y., Lyon, S.B., Gibbon, S.R.: Insights into epoxy network nanostructural heterogeneity using AFM-IR. ACS Appl. Mater. Interfaces. 8, 959–966 (2016)
Sahagun, C.M., Morgan, S.E.: Thermal control of nanostructure and molecular network development in epoxy-amine thermosets. ACS Appl. Mater. Interfaces. 4, 564–572 (2012)
Cuthrell, R.E.: Epoxy polymers II. Macrostructure. J. Appl. Polym. Sci. 12(6), 1263–1278 (1968)
Labana, S.S., Newman, S., Chompff, A.J.: Chemical effects on the ultimate properties of polymer networks in the glassy state. In: Chompff, A.J., Newman, S. (eds.) Polymer Networks, pp. 453–477. New York, Plenum Press (1971)
Zee, M.: Structures of crosslinked networks. Master’s thesis, North Dakota State University. ProQuest Dissertations Publishing, 1589686 (2015)
Acknowledgements
The authors are glad to acknowledge computer access, financial, and administrative support from the North Dakota State University Center for Computationally Assisted Science and Technology and the U.S. Department of Energy through Grant No. DESC0001717.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Kroll, D.M., Croll, S.G. (2017). Heterogeneity in Crosslinked Polymer Networks: Molecular Dynamics Simulations. In: Wen, M., Dušek, K. (eds) Protective Coatings. Springer, Cham. https://doi.org/10.1007/978-3-319-51627-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-51627-1_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-51625-7
Online ISBN: 978-3-319-51627-1
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)