- Access by Xinjiang University
Miscibility phase diagram of ring-polymer blends: A topological effect
Phys. Rev. E 93, 042502 – Published 21 April, 2016
DOI: https://doi.org/10.1103/PhysRevE.93.042502
Abstract
The miscibility of polymer blends, a classical problem in polymer science, may be altered, if one or both of the component do not have chain ends. Based on the idea of topological volume, we propose a mean-field theory to clarify how the topological constraints in ring polymers affect the phase behavior of the blends. While the large enhancement of the miscibility is expected for ring-linear polymer blends, the opposite trend toward demixing, albeit comparatively weak, is predicted for ring-ring polymer blends. Scaling formulas for the shift of critical point for both cases are derived. We discuss the valid range of the present theory, and the crossover to the linear polymer blends behaviors, which is expected for short chains. These analyses put forward a view that the topological constraints could be represented as an effective excluded-volume effects, in which the topological length plays a role of the screening factor.
Physics Subject Headings (PhySH)
Article Text
References (32)
- T. McLeish, Science 297, 2005 (2002).
- D. Richter, S. Gooßen, and A. Wischnewski, Soft Matter. 11, 8535 (2015).
- J. D. Halverson, J. Smrek, K. Kremer, and A. Y. Grosberg, Rep. Prog. Phys. 77, 022601 (2014).
- M. E. Cates and J. M. Deutsch, J. Phys. 47, 2121 (1986).
- S. P. Obukhov, M. Rubinstein, and T. Duke, Phys. Rev. Lett. 73, 1263 (1994).
- M. Müller, J. P. Wittmer, and M. E. Cates, Phys. Rev. E 53, 5063 (1996).
- A. Takano, Polym. Prepr. Jpn. 56, 2424 (2007).
- T. Vettorel, A. Yu. Grosberg, and K. Kremer, Phys. Biol. 6, 025013 (2009).
- J. Suzuki, A. Takano, T. Deguchi, and Y. Matsushita, J. Chem. Phys. 131, 144902 (2009).
- T. Sakaue, Phys. Rev. Lett. 106, 167802 (2011).
- T. Sakaue, Phys. Rev. E 85, 021806 (2012).
- M. Lang, J. Fischer, and J.-U. Sommer, Macromolecules 45, 7642 (2012).
- S. Y. Reigh and D. Y. Yoon, ACS Macro Lett. 2, 296 (2013).
- A. Y. Grosberg, Soft Matter 10, 560 (2014).
- A. Rosa and R. Everaers, Phys. Rev. Lett. 112, 118302 (2014).
- S. Obukhov, A. Johner, J. baschnagel, H. Meyer, and J. P. Wittmer, Europhys. Lett. 105, 48005 (2014).
- S. Gooßen, A. R. Brás, M. Krutyeva, M. Sharp, P. Falus, A. Feoktystov, U. Gasser, W. Pyckhout-Hintzen, A. Wischnewski, and D. Richter, Phys. Rev. Lett. 113, 168302 (2014).
- J. Roovers, Macromolecules 18, 1359 (1985).
- G. B. McKenna et al., Macromolecules 20, 498 (1987).
- M. Kapnistos et al., Nat. Mater. 7, 997 (2008).
- S. T. Milner and J. D. Newhall, Phys. Rev. Lett. 105, 208302 (2010).
- J. D. Halverson, G. S. Grest, A. Y. Grosberg, and K. Kremer, Phys. Rev. Lett. 108, 038301 (2012).
- Y. Doi et al., Macromolecules 48, 3140 (2015).
- T. Ge, S. Panyukov, and M. Rubinstein, Macromolecules 49, 708 (2016).
- A. R. Khokhlov and S. K. Nechaev, J. Phys. II (France) 6, 1547 (1996).
- A. Yu. Grosberg, Phys. Rev. Lett. 85, 3858 (2000).
- M. D. Frank-Kamenetskii, A. V. Lukashin, and A. V. Vologodskii, Nature 258, 398 (1975).
- P.-G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, 1979).
- T. Sakaue and E. Raphaël, Macromolecules 39, 2621 (2006).
- A. Grosberg and A. Khokhlov, Statistical Physics of Macromolecules (AIP, NY, 1994).
- T. A. Kavassalis and J. Noolandi, Phys. Rev. Lett. 59, 2674 (1987).
- M. Daoud, P. Pincus, W. H. Stockmayer, and T. Witten, Macromolecules 16, 1833 (1983).