Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-13T08:45:47.051Z Has data issue: false hasContentIssue false
  • English
  • Français

Phase behavior of polymer blends with reversible crosslinks—A self-consistent field theory study

Published online by Cambridge University Press:  08 November 2013

Thomas Gruhn  and
Heike Emmerich
Thomas Gruhn*
Affiliation:
Material and Process Simulation (MPS), University of Bayreuth, D-95447 Bayreuth, Germany
Heike Emmerich*
Affiliation:
Material and Process Simulation (MPS), University of Bayreuth, D-95447 Bayreuth, Germany
*
a)Address all correspondence to these authors. e-mail: thomas.gruhn@uni-bayreuth.de
b)e-mail: heike.emmerich@uni-bayreuth.de
Get access

Abstract

An extended version of self-consistent field (SCF) theory that was recently introduced by the authors [Li et al., J. Chem. Phys.137, 024906, (2012)] is used to study the phase behavior of a polymer blend with reversible crosslinks. The system consists of symmetric AB diblock copolymers and homopolymers of type A and B. We consider reversible crosslinks that can form between the diblock copolymers with a crosslink strength z and crosslink weights ωA and ωB for monomers of type A and B, respectively. Crosslinks between homopolymers are disabled. We present a phase diagram as a function of the A fraction of homopolymers $\phi _{\rm{\alpha }}^{{\rm{rel}}}$, the crosslink strength z, and the crosslink asymmetry ∆ω = ωA − ωB. A hexagonal phase is found for suitably large $\phi _{\rm{\alpha }}^{{\rm{rel}}}$, and suitably small z and $\left| {\Delta {\rm{\omega }}} \right|$. Otherwise the system forms a lamellar phase. A deeper insight into the phase behavior is gained from analyzing the free energy contributions in the hexagonal and the lamellar phase with the help of the capabilities of the extended SCF theory developed by us.

Keywords

polymernanostructurephase transformation
Type
Invited Feature Papers
Information
Journal of Materials Research , Volume 28 , Issue 22 , 28 November 2013 , pp. 3079 - 3085
Copyright
Copyright © Materials Research Society 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Litvinov, V.M., Orzy, R.O., Klüppel, M., van Duin, M., and Magusin, P.C.M.M.: Rubber filler interactions and network structure in relation to stress-strain behavior of vulcanized, carbon black filled EPDM. Macromolecules 44, 4887 (2011).CrossRefGoogle Scholar
Buenger, D., Tupoz, F., and Groll, J.: Hydrogels in sensing applications. Prog. Polym. Sci. 37, 1678 (2012).CrossRefGoogle Scholar
Tang, J., Wu, J., Lin, S., Fan, S., and Hu, D.: A multifunctional poly(acrylic acid)/gelatin hydrogel. J. Mater. Res. 24, 1653 (2009).CrossRefGoogle Scholar
Fletcher, D.A. and Mullins, R.D.: Cell mechanics and the cytoskeleton. Nature 463, 485 (2010).CrossRefGoogle ScholarPubMed
Vincent, R.R.R., Mansel, B.W., Kramer, A., Kroy, K., and Williams, M.A.K.: Micro-rheological behaviour and nonlinear rheology of networks assembled from polysaccharides from the plant cell wall. New J. Phys. 15, 035002 (2013).CrossRefGoogle Scholar
Secchi, E., Roversi, T., Buzzaccaro, S., Piazza, L., and Piazza, R.: Biopolymer gels with “physical” cross-links: Gelation kinetics, aging, heterogeneous dynamics, and macroscopic mechanical properties. Soft Matter 9, 3931 (2013).CrossRefGoogle Scholar
Park, S-Y., Sul, W-H., and Chang, Y-J.: A study on the selectivity of toluene/ethanol mixtures on the micellar and ordered structures of poly(styrene-b-4-vinylpyridine) using small-angle x-ray scattering, generalized indirect Fourier transform, and transmission electron microscopy. Macromolecules 40, 3757 (2007).CrossRefGoogle Scholar
Shenoga, N.B., Tsige, M., Patnaik, S.S., and Mukhopadhyay, S.M.: Molecular modeling approach to prediction of thermo-mechanical behavior of thermoset polymer networks. Macromolecules 45, 5307 (2012).CrossRefGoogle Scholar
Li, Y., Kröger, M., and Liu, W.K.: Primitive chain network study on uncrosslinked and crosslinked cis-polyisoprene polymers. Polymer 52, 5867 (2011).CrossRefGoogle Scholar
Quesada-Pérez, M., Ibarra-Armenta, J.G., and Martín-Molina, A.: Computer simulations of thermo-shrinking polyelectrolyte gels. J. Chem. Phys. 135, 094109 (2011).CrossRefGoogle ScholarPubMed
Chelakkota, R. and Gruhn, T.: Length dependence of crosslinker induced network formation of rods: A Monte Carlo study. Soft Matter 8, 11746 (2012).CrossRefGoogle Scholar
Chelakkot, R., Lipowsky, R., and Gruhn, T.: Self-assembling networks and bundle structures in systems of filaments and crosslinkers: A Monte Carlo study. Macromolecules 39, 7138 (2006).CrossRefGoogle Scholar
Weisgraber, T.H., Gee, R.H., Maiti, A., Clague, D.S., Chinn, S., and Maxwell, R.S.: A mesoscopic network model for permanent set in crosslinked elastomers. Polymer 50, 5613 (2009).CrossRefGoogle Scholar
Li, D., Yang, H.L., and Emmerich, H.: Phase field model simulations of hydrogel dynamics under chemical stimulation. Colloid Polym. Sci. 289, 513 (2011).CrossRefGoogle Scholar
Binder, K. and Milchev, A.: Polymer brushes on flat and curved surfaces: How computer simulations can help to test theories and to interpret experiments. J. Polym. Sci., Part B: Polym. Phys. 50, 1515 (2012).CrossRefGoogle Scholar
Wang, J., Müller, M., and Wang, Z-G.: Nucleation in A/B/AB blends: Interplay between microphase assembly and macrophase separation. J. Chem. Phys. 130, 154902 (2009).CrossRefGoogle Scholar
Müller, M. and Schmid, F.: Incorporating fluctuations and dynamics in self-consistent field theories for polymer blends. Adv. Polym. Sci. 185, 1 (2005).CrossRefGoogle Scholar
Fredrickson, G.H., Ganesan, V., and Drolet, F.: Field-theoretic computer simulation methods for polymers and complex fluids. Macromolecules 35, 16 (2002).CrossRefGoogle Scholar
Schmid, F.: Self-consistent-field theories for complex fluids. J. Phys. Condens. Matter 10, 8108 (1998).CrossRefGoogle Scholar
Edwards, S.F.: The statistical mechanics of polymers with excluded volume. Proc. Phys. Soc. 85, 613 (1965).CrossRefGoogle Scholar
Helfand, E. and Yukiko, T.: Theory of the interface between immiscible polymers. II. J. Chem. Phys. 56, 3592 (1972).CrossRefGoogle Scholar
Benhamou, M., Derouiche, A., Bettachy, A., and Elhajjaji, F.: Critical microphase properties of crosslinked polymer blends with quenched random impurities. Eur. Phys. J. E 34, 3 (2011).CrossRefGoogle ScholarPubMed
Mao, X., Goldbart, P.M., Xing, X., and Zippelius, A.: Soft random solids and their heterogeneous elasticity. Phys. Rev. E 80, 031140 (2009).CrossRefGoogle ScholarPubMed
Ulrich, S., Mao, X., Goldbart, M., and Zippelius, A.: Elasticity of highly cross-linked random networks. Europhys. Lett. 76, 677 (2006).CrossRefGoogle Scholar
Li, D., Gruhn, T., and Emmerich, H.: Mean field theory for a reversibly crosslinked polymer network, J. Chem. Phys. 137, 024906 (2012).CrossRefGoogle ScholarPubMed
Gruhn, T., Li, D., and Emmerich, H.: Calculating structural properties of reversibly crosslinked polymer systems using self-consistent field theory. Prog. Colloid Polym. Sci., submitted.Google Scholar
Wu, C., Ying, A., and Ren, S.: Fabrication of polymeric micelles with core–shell–coronastructure for applications in controlled drug release. Colloid. Polym. Sci. 291, 827 (2013).CrossRefGoogle Scholar
Yue, J., Wang, R., Liu, S., Wu, S., Xie, Z., Huang, Y., and Jing, X.: Reduction-responsive shell-crosslinked micelles prepared from Y-shaped amphiphilic block copolymers as a drug carrier. Soft Matter 8, 7426 (2012).CrossRefGoogle Scholar
Helfand, E.: Theory of inhomogeneous polymers: Fundamentals of the Gaussian random-walk model, J. Chem. Phys. 62, 999 (1975).CrossRefGoogle Scholar
Düchs, D., Ganesan, V., Fredrickson, G.H., and Schmid, F.: Fluctuation effects in ternary AB+A+B polymeric emulsions, Macromolecules 36, 9237 (2003).CrossRefGoogle Scholar
Bates, F.S., Maurer, W.W., Lipic, P.M., Hillmyer, M.A., Almdal, K., Mortensen, K., Fredrickson, G.H., and Lodge, T.P.: Polymeric bicontinuous microemulsions, Phys. Rev. Lett. 79, 849 (1997).CrossRefGoogle Scholar
Hillmyer, M.A., Maurer, W.W., Lodge, T.P., Bates, F.S., and Almdal, K.J.: Model bicontinuous microemulsions in ternary homopolymer/block copolymer blends, Phys. Chem. 103, 4814 (1999).Google Scholar
Adelsberger, J., Metwalli, E., Diethert, A., Grillo, I., Bivigou-Koumba, A.M., Laschewsky, A., Müller-Buschbaum, P., and Papadakis, C.M.: Kinetics of collapse transition and cluster formation in a thermoresponsive micellar solution of P(S-b-NIPAM-b-S) induced by a temperature jump. Macromol. Rapid Commun. 33, 254 (2012).CrossRefGoogle Scholar
Matsen, M.W. and Bates, F.S.: Unifying weak- and strong-segregation block copolymer theories, Macromolecules 29, 1091 (1996).CrossRefGoogle Scholar
Huck, W.T.S.: Materials chemistry: Polymer networks take a bow. Nature 472, 425 (2011).CrossRefGoogle Scholar