Skip to main content
SpringerLink
Log in

Inferring the Physics of Structural Evolution of Multicomponent Polymers via Machine-Learning-Accelerated Method

  • Research Article
  • Published:
Chinese Journal of Polymer Science Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

Dynamic self-consistent field theory (DSCFT) is a fruitful approach for modeling the structural evolution and collective kinetics for a wide variety of multicomponent polymers. However, solving a set of DSCFT equations remains daunting because of high computational demand. Herein, a machine learning method, integrating low-dimensional representations of microstructures and long short-term memory neural networks, is used to accelerate the predictions of structural evolution of multicomponent polymers. It is definitively demonstrated that the neural-network-trained surrogate model has the capability to accurately forecast the structural evolution of homopolymer blends as well as diblock copolymers, without the requirement of “on-the-fly” solution of DSCFT equations. Importantly, the data-driven method can also infer the latent growth laws of phase-separated microstructures of multicomponent polymers through simply using a few of time sequences from their past, without the prior knowledge of the governing dynamics. Our study exemplifies how the machine-learning-accelerated method can be applied to understand and discover the physics of structural evolution in the complex polymer systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Thurn-Albrecht, T.; Schotter, J.; Kastle, C. A.; Emley, N.; Shibauchi, T.; Krusin-Elbaum, L.; Guarini, K.; Black, C. T.; Tuominen, M. T.; Russell, T. P. Ultrahigh-density nanowire arrays grown in self-assembled diblock copolymer templates. Science 2000, 290, 2126–2129.

    CAS  PubMed  Google Scholar 

  2. Meuler, A. J.; Hillmyer, M. A.; Bates, F. S. Ordered network mesostructures in block polymer materials. Macromolecules 2009, 42, 7221–7250.

    CAS  Google Scholar 

  3. Müller, M.; Abetz, V. Nonequilibrium processes in polymer membrane formation: theory and experiment. Chem. Rev. 2021, 121, 14189–14231.

    PubMed  Google Scholar 

  4. Huang, C. H.; Zhu, Y. Y.; Man, X. K. Block copolymer thin films. Phys. Rep. 2021, 932, 1–36.

    CAS  Google Scholar 

  5. Fraaije, J. G. E. M.; van Vlimmeren, B. A. C.; Maurits, N. M.; Postma, M.; Evers, O. A.; Hoffmann, C.; Altevogt, P.; Goldbeck-Wood, G. The dynamic mean-field density functional method and its application to the mesoscopic dynamics of quenched block copolymer melts. J. Chem. Phys. 1997, 106, 4260–4269.

    CAS  Google Scholar 

  6. Morita, H.; Kawakatsu, T.; Doi, M. Dynamic density functional study on the structure of thin polymer blend films with a free surface. Macromolecules 2001, 34, 8777–8783.

    CAS  Google Scholar 

  7. Müller, M.; Schmid, F. Incorporating fluctuations and dynamics in self-consistent field theories for polymer blends. Adv. Polym. Sci. 2005, 185, 1–58.

    Google Scholar 

  8. Wang, G.; Ren, Y.; Müller, M. Collective short-time dynamics in multicomponent polymer melts. Macromolecules 2019, 52, 7704–7720.

    CAS  Google Scholar 

  9. Sides, S. W.; Fredrickson, G. H. Parallel algorithm for numerical self-consistent field theory simulations of block copolymer structure. Polymer 2003, 44, 5859–5866.

    CAS  Google Scholar 

  10. Hall, D. M.; Lookman, T.; Fredrickson, G. H.; Banerjee, S. Hydrodynamic self-consistent field theory for inhomogeneous polymer melts. Phys. Rev. Lett. 2006, 97, 114501.

    PubMed  Google Scholar 

  11. Zhang, L.; Sevink, A.; Schmid, F. Hybrid lattice Boltzmann/dynamic self-consistent field simulations of microphase separation and vesicle formation in block copolymer systems. Macromolecules 2011, 44, 9434–9447.

    CAS  Google Scholar 

  12. Arora, A.; Qin, J.; Morse, D. C.; Delaney, K. T.; Fredrickson, G. H.; Bates, F. S.; Dorfman, K. D. Broadly accessible self-consistent field theory for block polymer materials discovery. Macromolecules 2016, 49, 4675–4690.

    CAS  Google Scholar 

  13. Mehta, P.; Wang, C.-H.; Day, A. G. R.; Richardson, C.; Bukov, M.; Fisher, C. K.; Schwab, D. J. A high-bias, low-variance introduction to machine learning for physicists. Phys. Rep. 2019, 810, 1–124.

    PubMed  PubMed Central  Google Scholar 

  14. Carleo, G.; Cirac, I.; Cranmer, K.; Daudet, L.; Schuld, M.; Tishby, N.; Vogt-Maranto, L.; Zdeborová, L. Machine learning and the physical sciences. Rev. Mod. Phys. 2019, 91, 045002.

    CAS  Google Scholar 

  15. Brunton, S. L.; Noack, B. R.; Koumoutsakos, P. Machine learning for fluid mechanics. Annu. Rev. Fluid Mech. 2020, 52, 477–508.

    Google Scholar 

  16. Keith, J. A.; Vassilev-Galindo, V.; Cheng, B.; Chmiela, S.; Gastegger, M.; Müller, K. R.; Tkatchenko, A. Combining machine learning and computational chemistry for predictive insights into chemical systems. Chem. Rev. 2021, 121, 9816–9872.

    CAS  PubMed  PubMed Central  Google Scholar 

  17. Colen, J.; Han, M.; Zhang, R.; Redford, S. A.; Lemma, L. M.; Morgan, L.; Ruijgrok, P. V.; Adkins, R.; Bryant, Z.; Dogic, Z.; Gardel, M. L.; de Pablo, J. J.; Vitelli, V. Machine learning active-nematic hydrodynamics. Proc. Natl. Acad. Sci. U. S. A. 2021, 118, e2016708118.

    CAS  PubMed  PubMed Central  Google Scholar 

  18. Li, H.; Jin, Y.; Jiang, Y.; Chen, J. Z. Y. Determining the nonequilibrium criticality of a Gardner transition via a hybrid study of molecular simulations and machine learning. Proc. Natl. Acad. Sci. U. S. A. 2021, 118, e2017392118.

    CAS  PubMed  PubMed Central  Google Scholar 

  19. LeCun, Y.; Bengio, Y.; Hinton, G. Deep learning. Nature 2017, 521, 436–444.

    Google Scholar 

  20. Carrasquilla, J.; Melko, R. G. Machine learning phases of matter. Nat. Phys. 2017, 13, 431–434.

    CAS  Google Scholar 

  21. Bapst, V.; Keck, T.; Grabska-Barwińska, A.; Donner, C.; Cubuk, E. D.; Schoenholz, S. S.; Obika, A.; Nelson, A. W. R.; Back, T.; Hassabis, D.; Kohli, P. Unveiling the predictive power of static structure in glassy systems. Nat. Phys. 2020, 16, 448–454.

    CAS  Google Scholar 

  22. Zhao, S.; Cai, T.; Zhang, L.; Li, W.; Lin, J. Autonomous construction of phase diagrams of block copolymers by theory-assisted active machine learning. ACS Macro Lett. 2021, 10, 598–602.

    CAS  PubMed  Google Scholar 

  23. Coli, G. M.; Boattini, E.; Filion, L.; Dijkstra, M. Inverse design of soft materials via a deep learning-based evolutionary strategy. Sci Adv. 2022, 8, eabj6731.

    PubMed  PubMed Central  Google Scholar 

  24. Aoyagi, T. Deep learning model for predicting phase diagrams of block copolymers. Comput. Mater. Sci. 2021, 188, 110224.

    CAS  Google Scholar 

  25. Tu, K.; Huang, H.; Lee, S.; Lee, W.; Sun, Z.; Alexander-Katz, A.; Ross, C. A. Machine learning predictions of block copolymer self-assembly. Adv. Mater. 2020, 32, 2005713.

    Google Scholar 

  26. Schneider, L.; de Pablo, J. J. Combining particle-based simulations and machine learning to understand defect kinetics in thin films of symmetric diblock copolymers. Macromolecules 2021, 54, 10074–10085.

    CAS  Google Scholar 

  27. Pathak, J.; Hunt, B.; Girvan, M.; Lu, Z.; Ott, E. Model-free prediction of large spatiotemporally chaotic systems from data: a reservoir computing approach. Phys. Rev. Lett. 2018, 120, 024102.

    CAS  PubMed  Google Scholar 

  28. Raissi, M.; Perdikaris, P.; Karniadakis, G. E. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 2019, 378, 686–707.

    Google Scholar 

  29. Zhao, H.; Storey, B. D.; Braatz, R. D.; Bazant, M. Z. Learning the physics of pattern formation from images. Phys. Rev. Lett. 2020, 124, 060201.

    CAS  PubMed  Google Scholar 

  30. Bar-Sinai, Y.; Hoyer, S.; Hickey, J.; Brenner, M. P. Learning data-driven discretizations for partial differential equations. Proc. Natl. Acad. Sci. U. S. A. 2019, 116, 15344–15348.

    CAS  PubMed  PubMed Central  Google Scholar 

  31. Kemeth, F. P.; Bertalan, T.; Thiem, T.; Dietrich, F.; Moon, S. J.; Laing, C. R.; Kevrekidis, I. G. Learning emergent partial differential equations in a learned emergent space. Nat. Commun. 2022, 13, 3318.

    PubMed  PubMed Central  Google Scholar 

  32. Vlachas, P. R.; Byeon W.; Wan, Z. Y.; Sapsis, T. P.; Koumoutsakos, P. Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks. Proc. R. Soc. A 2018, 474, 20170844.

    PubMed  PubMed Central  Google Scholar 

  33. Vlachas, P. R.; Arampatzis, G.; Uhler, C.; Koumoutsakos, P. Multiscale simulations of complex systems by learning their effective dynamics. Nat. Machine Intelligence 2022, 4, 359–366.

    Google Scholar 

  34. Montes de Oca Zapiain, D., Stewart, J. A.; Dingreville, R. Accelerating phase-field-based microstructure evolution predictions via surrogate models trained by machine learning methods. NPJ Comput. Mater. 2021, 7, 1–11.

    Google Scholar 

  35. Hu, C.; Martin, S.; Dingreville, R. Accelerating phase-field predictions via recurrent neural networks learning the microstructure evolution in latent space. Comput. Methods Appl. Mech. Engrg. 2022, 397, 115128.

    Google Scholar 

  36. Qi, S.; Schmid, F. Dynamic density functional theories for inhomogeneous polymer systems compared to brownian dynamics simulations. Macromolecules 2017, 50, 9831–9845.

    CAS  Google Scholar 

  37. Pearson, K. On lines and planes of closest fit to systems of points in space. Philos. Mag. 1901, 2, 559–572.

    Google Scholar 

  38. Jolliffe, I. T. Principal Component Analysis; Wiley: Chichester, U.K., 2002.

    Google Scholar 

  39. Hochreiter, S.; Schmidhuber, J. Long short-term memory. Neural Comput. 1997, 9, 1735–1780.

    CAS  PubMed  Google Scholar 

  40. Greff, K.; Srivastava, R. K.; Koutnik, J.; Steunebrink, B. R.; Schmidhuber, J. LSTM: a search space odyssey. IEEE Trans. Neural Netw. Learn. Syst. 2017, 28, 2222–2232.

    PubMed  Google Scholar 

  41. Cho, K.; Van Merriënboer, B.; Bahdanau, D.; Bengio, Y. On the properties of neural machine translation: encoder-decoder approaches. 2014, arXiv preprint arXiv:1409.1259.

  42. Cho, K.; Van Merriënboer, B.; Gulcehre, C.; Bahdanau, D.; Bougares, F.; Schwenk, H.; Bengio, Y. Learning phrase representations using RNN encoder-decoder for statistical machine translation. 2014, arXiv preprint arXiv:1406.1078.

  43. Bray, A. J. Theory of phase-ordering kinetics. Adv. Phys. 1994, 43, 357–459.

    Google Scholar 

  44. Sung, L.; Karim, A.; Douglas, J. F.; Han, C. C. Dimensional crossover in the phase separation kinetics of thin polymer blend films. Phys. Rev. Lett. 1996, 76, 4368.

    CAS  PubMed  Google Scholar 

  45. Siggia, E. D. Late stages of spinodal decomposition in binary mixtures. Phys. Rev. A: At., Mol., Opt. Phys. 1979, 20, 595–602.

    CAS  Google Scholar 

  46. Shiwa, Y.; Taneike, T.; Yokojima, Y. Scaling behavior of block copolymers in spontaneous growth of lamellar domains. Phys. Rev. Lett. 1996, 77, 4378.

    CAS  PubMed  Google Scholar 

  47. Bahiana, M.; Oono, Y. Cell dynamical system approach to block copolymers. Phys. Rev. A: At., Mol., Opt. Phys. 1990, 41, 6763.

    CAS  Google Scholar 

  48. Yokojima, Y.; Shiwa, Y. Ordering process in quenched block copolymers at low temperatures. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2000, 62, 6838.

    CAS  Google Scholar 

  49. Singh, M.; Wu, W.; Nuka, V.; Strzalka, J.; Douglas, J. F.; Karim, A. Late stage domain coarsening dynamics of lamellar block copolymers. ACS Macro Lett. 2021, 10, 727–731.

    CAS  PubMed  Google Scholar 

Download references

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (Nos. 22073028, 21873029 and 22073004) and the Fundamental Research Funds for the Central Universities.

Author information

Authors and Affiliations

  1. School of Chemistry, Center of Soft Matter Physics and Its Applications, Beihang University, Beijing, 100191, China

    Kai-Hua Zhang & Ying Jiang

  2. Shanghai Key Laboratory of Advanced Polymeric Materials, School of Materials Science and Engineering, East China University of Science and Technology, Shanghai, 200237, China

    Liang-Shun Zhang

Authors
  1. Kai-Hua Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ying Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liang-Shun Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Ying Jiang or Liang-Shun Zhang.

Ethics declarations

The authors declare no interest conflict.

Electronic Supplementary Information

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, KH., Jiang, Y. & Zhang, LS. Inferring the Physics of Structural Evolution of Multicomponent Polymers via Machine-Learning-Accelerated Method. Chin J Polym Sci 41, 1377–1385 (2023). https://doi.org/10.1007/s10118-023-2891-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10118-023-2891-9

Keywords

Search

Navigation