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Particle Distribution Informed by Chain Rigidity in Diblock Copolymer Melts: The Effect of Entropy

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Abstract

We study the effect of chain rigidity on tailoring the nanoparticle locations for neutral and selective particles embedded in the lamellar morphology formed by semiflexible diblock copolymer chains using self-consistent field calculations. The nanoparticles are modeled through a cavity function, and the semiflexible chains are represented by the continuous Kratsky-Porod chain model. In general situation, the nanoparticles prefer to stay at the interface in order to reduce the interface areas and thus the system free energy. However, the particle distribution at the domain center is subtle, and the underlying physics is intrinsically different depending on the polymer flexibility. In the case of flexible chains, the entropy just contributes a constant shift to the free energy when the nanoparticles move around the domain center indicating that the local metastable state if appears at the domain center is wholly attributed to the local minimum in the enthalpy. If the polymers are rigid, the variation of the particle distribution at the domain center has a close relation with the polymer rigidity and nanoparticle size. In the case of strongly rigid polymers with small nanoparticles, a nearly uniform particle distribution at the domain center is observed, while in other cases, a local enhancement of particle distribution there is found. In contrast to the case of flexible chains, further analysis reveals the crucial role of entropy in controlling the shape of particle distributions at the phase domain. Specifically, the local metastable state appears in the domain center is determined by the large entropy there which arises from the weak coupling of bond orientations that allows the polymer chains to be relatively relaxed. When the particle becomes selective, its distribution in the phase domain exhibits a shift almost uniformly rather than changes its profile, and the underlying physics still holds. In all, our study establishes a strong coupling between the chain rigidity and effect of entropy.

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References

  1. Al-Saleh, M. H. Influence of polymer structure on the electrical resistivity of nanocomposite materials. Synth. Met. 2020, 256, 116409.

    Article  Google Scholar 

  2. Yang, Y.; He, J. L.; Li, Q.; Gao, L.; Hu, J.; Zeng, R.; Qin, J.; Wang, S. X.; Wang, Q. Self-healing of electrical damage in polymers using superparamagnetic nanoparticles. Nat. Nanotechnol. 2018, 14, 151–155.

    Article  ADS  Google Scholar 

  3. Huang, Y.; Ellingford, C.; Bowen, C.; McNally, T.; Wu, D.; Wan, C. Y. Tailoring the electrical and thermal conductivity of multi-component and multi-phase polymer composites. Int. Mater. Rev. 2019, 65, 129–163.

    Article  Google Scholar 

  4. Bockstaller, M. R.; Thomas, E. L. Proximity effects in self-organized binary particle-block copolymer blends. Phys. Rev. Lett. 2004, 93, 166106.

    Article  ADS  PubMed  Google Scholar 

  5. Wang, Y.; Liu, X.; Li, S.; Li, T.; Song, Y.; Li, Z.; Zhang, W.; Sun, J. Transparent, healable elastomers with high mechanical strength and elasticity derived from hydrogen-bonded polymer complexes. ACS Appl. Mater. Interfaces 2017, 9, 29120–29129.

    Article  CAS  PubMed  Google Scholar 

  6. Yang, Q.; Ye, C.; Zhao, J.; Chen, D.; Weng, B.; You, J.; Li, Y. Shape memory polymers with interconnected nanopores and high mechanical strength. J. Polym. Sci., Part B: Polym. Chem. 2017, 56, 125–130.

    Article  ADS  Google Scholar 

  7. Sharma, U.; Concagh, D.; Core, L.; Kuang, Y.; You, C.; Pham, Q.; Zugates, G.; Busold, R.; Webber, S.; Merlo, J.; Langer, R.; Whitesides, G. M.; Palasis, M. The development of bioresorbable composite polymeric implants with high mechanical strength. Nat. Mater. 2017, 17, 96–103.

    Article  ADS  PubMed  Google Scholar 

  8. Bosquetti, M.; da Silva, A. L.; Azevedo, E. C.; Berti, L. F. Analysis of the mechanical strength of polymeric composites reinforced with sisal fibers. J. Nat. Fibers 2019, 18, 105–110.

    Article  Google Scholar 

  9. Zhao, X.; Liu, J.; Li, J.; Liang, Z.; Zhou, W.; Peng, S. Strategies and techniques for improving heat resistance and mechanical performances of poly(lactic acid) (PLA) biodegradable materials. Int. J. Biol. Macromol. 2022, 218, 115–134.

    Article  CAS  PubMed  Google Scholar 

  10. Peelman, N.; Ragaert, P.; Ragaert, K.; Erkoç, M.; Brempt, W. V.; Faelens, F.; Devlieghere, F.; Meulenaer, B. D.; Cardon, L. Heat resistance of biobased materials, evaluation and effect of processing techniques and additives. Polym. Eng. Sci. 2017, 58, 513–520.

    Article  Google Scholar 

  11. Ozerin, S. A.; Vdovichenko, A. Y.; Streltsov, D. R.; Davydov, A. B.; Orekhov, A. S.; Vasiliev, A. L.; Zubavichus, Y. V.; Grigoriev, E. I.; Zavyalov, S. A.; Oveshnikov, L. N.; Aronzon B. A.; Chvalun, S. N. Structure and magnetic properties of Ni-poly(p-xylylene) nanocomposites synthesized by vapor deposition polymerization. J. Phys. Chem. Solids 2017, 111, 245–253.

    Article  ADS  CAS  Google Scholar 

  12. Barrera, G.; Tiberto, P.; Allia, P.; Bonelli, B.; Esposito, S.; Marocco, A.; Pansini, M.; Leterrier, Y. Magnetic properties of nanocomposites. Appl. Sci. 2019, 9, 212.

    Article  CAS  Google Scholar 

  13. Sanida, A.; Stavropoulos, S. G.; Speliotis, T.; Psarras, G. C. Investigating the effect of Zn ferrite nanoparticles on the thermomechanical, dielectric and magnetic properties of polymer nanocomposites. Materials 2019, 9, 3015.

    Article  ADS  Google Scholar 

  14. Balazs, A. C.; Emrick, T.; Russell, T. P. Nanoparticle polymer composites: where two small worlds meet. Science 2006, 314, 1107–1110.

    Article  ADS  CAS  PubMed  Google Scholar 

  15. Harijan, M.; Singh, M. Zwitterionic polymers in drug delivery: A review. J. Mol. Recognit. 2021, 35, e2944.

    Article  PubMed  Google Scholar 

  16. Li, M.; Zhang, W.; Li, J.; Qi, Y.; Peng, C.; Wang, N.; Fan, H.; Li, Y. Zwitterionic polymers: addressing the barriers for drug delivery. Chin. Chem. Lett. 2023, 108177.

    Google Scholar 

  17. Fu, X.; Hosta-Rigau, L.; Chandrawati, R.; Cui, J. Multi-stimuli-responsive polymer particles, films, and hydrogels for drug delivery. Chem 2018, 4, 2084–2107.

    Article  CAS  Google Scholar 

  18. Kolate, A.; Baradia, D.; Patil, S.; Vhora, I.; Kore, G.; Misra, A. PEG — A versatile conjugating ligand for drugs and drug delivery systems. J. Control. Rel. 2014, 192, 67–81.

    Article  CAS  Google Scholar 

  19. Jeon, S. J.; Yang, S. M.; Kim, B. J.; Petrie, J. D.; Jang, S. G.; Kramer, E. J.; Pine, D. J.; Yi, G. R. Hierarchically structured colloids of diblock copolymers and Au nanoparticles. Chem. Mater. 2009, 21, 3739–3741.

    Article  CAS  Google Scholar 

  20. Nuopponen, M.; Tenhu, H. Gold nanoparticles protected with pH and temperature-sensitive diblock copolymers. Langmuir 2007, 23, 5352–5357.

    Article  CAS  PubMed  Google Scholar 

  21. Kim, B. J.; Fredrickson, G. H.; Hawker, C. J.; Kramer, E. J. Nanoparticle surfactants as a route to bicontinuous block copolymer morphologies. Langmuir 2007, 23, 7804–7809.

    Article  CAS  PubMed  Google Scholar 

  22. Jang, J.; Li, X. L.; Oh, J. H. Facile fabrication of polymer and carbon nanocapsules using polypyrrole core/shell nanomaterials. Chem. Commun. 2004, 794.

    Google Scholar 

  23. Hamdoun, B.; Ausserré, D.; Joly, S.; Gallot, Y.; Cabuil, V.; Clinard, C. New nanocomposite materials. Journal de Physique II 1996, 6, 493–501.

    Article  ADS  CAS  Google Scholar 

  24. Lauter-Pasyuk, V.; Lauter, H. J.; Ausserre, D.; Gallot, Y.; Cabuil, V.; Hamdoun, B.; Kornilov, E. I. Neutron reflectivity studies of composite nanoparticle - copolymer thin films. Phys. B Condens. Matter 1998, 248, 243–245.

    Article  ADS  CAS  Google Scholar 

  25. Dong, B.; Guo, R.; Yan, L. T. Coassembly of Janus nanoparticles in asymmetric diblock copolymer scaffolds: unconventional entropy effect and role of interfacial topology. Macromolecules 2014, 47, 4369–4379.

    Article  ADS  CAS  Google Scholar 

  26. Tabedzki, C.; Krook, N. M.; Murray, C. B.; Composto, R. J.; Riggleman, R. A. Effect of graft length and matrix molecular weight on string assembly of aligned nanoplates in a lamellar diblock copolymer. Macromolecules 2022, 55, 3166–3175.

    Article  ADS  CAS  Google Scholar 

  27. Aviv, Y.; Altay, E.; Fink, L.; Raviv, U.; Rzayev, J.; Shenhar, R. Quasi-two-dimensional assembly of bottlebrush block copolymers with nanoparticles in ultrathin films: combined effect of graft asymmetry and nanoparticle size. Macromolecules 2018, 52, 196–207.

    Article  ADS  Google Scholar 

  28. Hamley, I. W. Developments in block copolymer science and technology, Wiley, New York, 2004.

    Book  Google Scholar 

  29. Bates, F. S. Block copolymers - designer soft materials. Physics Today 1999, 52, 32–38.

    Article  CAS  Google Scholar 

  30. Bates, F. S.; Hillmyer, M. A.; Lodge, T. P.; Bates, C. M.; Delaney, K. T.; Fredrickson, G. H. Multiblock polymers: Panacea or Pandora’s box? Science 2012, 336, 434–440.

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  31. Leibler, L. Theory of microphase separation in block copolymers. Macromolecules 1980, 13, 1602–1617.

    Article  ADS  CAS  Google Scholar 

  32. Chiu, J. J.; Kim, B. J.; Kramer, E. J.; Pine, D. J. Control of nanoparticle location in block copolymers. J. Am. Chem. Soc. 2005, 127, 5036–5037.

    Article  CAS  PubMed  Google Scholar 

  33. Gu, J.; Zhang, R.; Zhang, L.; Lin, J. Epitaxial assembly of nanoparticles in a diblock copolymer matrix: precise organization of individual nanoparticles into regular arrays. Macromolecules 2021, 54, 2561–2573.

    Article  ADS  CAS  Google Scholar 

  34. Bockstaller, M. R.; Mickiewicz, R. A.; Thomas, E. L. Block copolymer nanocomposites: perspectives for tailored functional materials. Adv. Mater. 2005, 17, 1331–1349.

    Article  CAS  PubMed  Google Scholar 

  35. Zhang, L.; Lin, J.; Lin, S. Self-Assembly behavior of amphiphilic block copolymer/Nanoparticle mixture in dilute solution studied by self-consistent-field theory/density functional theory. Macromolecules 2007, 40, 5582–5592.

    Article  ADS  CAS  Google Scholar 

  36. Jin, J.; Wu, J.; Frischknecht, A. L. Modeling microscopic morphology and mechanical properties of block copolymer/nanoparticle composites. Macromolecules 2009, 42, 7537–7544.

    Article  ADS  CAS  Google Scholar 

  37. Lindsay, B. J.; Composto, R. J.; Riggleman, R. A. Equilibrium field theoretic study of nanoparticle interactions in diblock copolymer melts. J. Phys. Chem. B 2019, 123, 9466–9480.

    Article  CAS  PubMed  Google Scholar 

  38. Matsen, M. W.; Thompson, R. B. Particle Distributions in a block copolymer nanocomposite. Macromolecules 2008, 41, 1853–1860.

    Article  ADS  CAS  Google Scholar 

  39. Jiang, Y.; Zhang, W. Y.; Chen, J. Z. Y. Dependence of the disorder-lamellar stability boundary of a melt of asymmetric wormlike AB diblock copolymers on the chain rigidity. Phys. Rev. E 2011, 84, 041803.

    Article  ADS  Google Scholar 

  40. Jiang, Y.; Chen, J. Z. Y. Influence of chain rigidity on the phase behavior of wormlike diblock copolymers. Phys. Rev. Lett. 2013, 110, 138305.

    Article  ADS  PubMed  Google Scholar 

  41. Uchida, K.; Mita, K.; Yamamoto, S.; Tanaka, K. Local orientation of polystyrene at the interface with poly(methyl methacrylate) in block copolymer. ACS Macro Lett. 2020, 9, 1576–1581.

    Article  CAS  PubMed  Google Scholar 

  42. Aldaye, F. A.; Palmer, A. L.; Sleiman, H. F. Assembling materials with DNA as the guide. Science 2008, 321, 1795–1799.

    Article  ADS  CAS  PubMed  Google Scholar 

  43. Zhou, C.; Duan, X.; Liu, N. DNA-nanotechnology-enabled chiral plasmonics: from static to dynamic. Acc. Chem. Res. 2017, 50, 2906–2914.

    Article  CAS  PubMed  Google Scholar 

  44. Spakowitz, A. J.; Wang, Z. G. End-to-end distance vector distribution with fixed end orientations for the wormlike chain model. Phys. Rev. E 2005, 72, 041802.

    Article  ADS  Google Scholar 

  45. Kratky, O.; Porod, G. Röntgenuntersuchung gelöster Fadenmoleküle. Recueil des Travaux Chimiques des Pays-Bas 1949, 68, 1106–1122.

    Article  CAS  Google Scholar 

  46. Saitô, N.; Takahashi, K.; Yunoki, Y. The statistical mechanical theory of Stiff chains. J. Phys. Soc. Jpn. 1967, 22, 219–226.

    Article  ADS  Google Scholar 

  47. Chen, Y.; Zhang, X.; Jiang, Y. The influence of side-chain conformations on the phase behavior of bottlebrush block polymers. Soft Matter 2020, 16, 8047–8056.

    Article  ADS  CAS  PubMed  Google Scholar 

  48. Matsen, M. W. Melts of semiflexible diblock copolymer. J. Chem. Phys. 1996, 104, 7758–7764.

    Article  ADS  CAS  Google Scholar 

  49. Vorselaars, B.; Kim, J. U.; Chantawansri, T. L.; Fredrickson G. H.; Matsen, M. W. Self-consistent field theory for diblock copolymers grafted to a sphere. Soft Matter 2011, 7, 5128–5137.

    Article  ADS  CAS  Google Scholar 

  50. Thompson, R. B.; Rasmussen, K. O.; Lookman, T. Improved convergence in block copolymer self-consistent field theory by Anderson mixing. J. Chem. Phys. 2004, 120, 31–34.

    Article  ADS  CAS  PubMed  Google Scholar 

  51. Matsen, M. W. Fast and accurate SCFT calculations for periodic block-copolymer morphologies using the spectral method with Anderson mixing. Eur. Phys. J. E 2009, 30, 361.

    Article  CAS  PubMed  Google Scholar 

  52. Bockstaller, M. R.; Lapetnikov, Y.; Margel, S.; Thomas, E. L. Size-selective organization of enthalpic compatibilized nanocrystals in ternary block copolymer/particle mixtures. J. Am. Chem. Soc. 2003, 125, 5276–5277.

    Article  CAS  PubMed  Google Scholar 

  53. Thompson, R. B.; Ginzburg, V. V.; Matsen, M. W.; Balazs, A. C. Predicting the mesophases of copolymer-nanoparticle composites. Science 2001, 292, 2469–2472.

    Article  CAS  PubMed  Google Scholar 

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Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (No. 22173002). S.Q. acknowledges the Fundamental Research Funds for the Central Universities (No. YWF-22-K-101). J.Y. acknowledges the Fundamental Research Funds for the Central Universities from Beihang University. The SCF calculations were carried out on the high performance computer cluster at Beihang University.

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  1. School of Chemistry, Beihang University, Beijing, 100191, China

    Yuguo Chen, Shuanhu Qi & Ying Jiang

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  1. Yuguo Chen
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Correspondence to Shuanhu Qi or Ying Jiang.

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Chen, Y., Qi, S. & Jiang, Y. Particle Distribution Informed by Chain Rigidity in Diblock Copolymer Melts: The Effect of Entropy. Chin J Polym Sci 42, 388–399 (2024). https://doi.org/10.1007/s10118-023-3053-9

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