Abstract
Aiming at the difficult problem of solving the conformation statistics of complex polymers, this study presents a novel and concise conformation statistics theoretical approach based on Monte Carlo and Neural Network method. This method offers a new research idea for investigating the conformation statistics of complex polymers, characterized by its simplicity and practicality. It can be applied to more complex topological structure, more higher degree of freedom polymer systems with higher dimensions, theory research on dynamic self-consistent field theory and polymer field theory, as well as the analysis of scattering experimental data. The conformation statistics of complex polymers determine the structure and response properties of the system. Using the new method proposed in this study, taking the semiflexible ring diblock copolymer as an example, Monte Carlo simulation is used to sample this ring conformation to construct the dataset of polymer. The structure factor describing conformation statistics are expressed as continuous functions of structure parameters by neural network supervised learning. This is the innovation of this work. As an application, the structure factors represented by neural networks were introduced into the random phase approximation theory to study the microphase separation of semiflexible ring diblock copolymers. The influence of the ring’s topological properties on the phase transition behavior was pointed out.
Similar content being viewed by others
References
Marko, J, F. Microphase separation of block copolymer rings. Macromolecules 1993, 26, 1442–1444.
Lecommandoux, S.; Borsali, R.; Schappacher, M.; Deffieux, A.; Narayanan, T.; Rochas, C. Microphase separation of linear and cyclic block copolymers poly(styrene-b-isoprene): SAXS experiments. Macromolecules 2004, 37, 1843–1848.
Poelma, J. E.; Ono, K.; Miyajima, D.; Aida, T.; Satoh, K.; Hawker, C. J. Cyclic block copolymers for controlling feature sizes in block copolymer lithography. ACS Nano 2012, 6, 10845–10854.
Kapnistos, M.; Lang, M.; Vlassopoulos, D.; Pyckhout-Hintzen, W.; Richter, D.; Cho, D.; Chang, T.; Rubinstein, M. Unexpected power-law stress relaxation of entangled ring polymers. Nat. Mater. 2008, 7, 997–1002.
Lee, E.; Jung, Y. Slow dynamics of ring polymer melts by asymmetric interaction of threading configuration: Monte Carlo study of a dynamically constrained lattice model. Polymers 2019, 11, 516.
Reigh, S. Y.; Yoon, D. Y. Concentration dependence of ring polymer conformationals from Monte Carlo simulations. ACS Macro Lett. 2013, 2, 296–300.
Shanbhag, S. Unusual dynamics of ring probes in linear matrices. J. Polym. Sci., Part B: Polym. Phys. 2017, 55, 169–177.
Henke, S. F.; Shanbhag, S. Self-diffusion in asymmetric ring-linear blends. React. Funct. Polym. 2014, 80, 57–60.
Gennes, P. G.; Witten, T. A. Scaling concepts in polymer physics. Physics 1980, 33, 51.
Leibler, L. Theory of microphase separation in block copolymers. Macromolecules 1980, 13, 34–36.
Gordon, M. Modern theory of polymer solutions. Brit. Poly. J. 1972, 4, 541–542.
Hammouda, B. Structure factors for regular polymer gels and networks. J. Chem. Phys. 1993, 99, 9182–9187.
Herschberg, T.; Carrillo, J. M. Y.; Sumpter, B. G.; Panagiotou, E.; Kumar, R. Topological effects near order-disorder transitions in symmetric diblock copolymer melts. Macromolecules 2021, 54, 7492–7499.
Qian, H. J.; Lu, Z. Y.; Chen, L. J.; Li, Z. S.; Sun, C. C. Computer simulation of cyclic block copolymer microphase separation. Macromolecules 2005, 38, 1395–1401.
Qiang, Y.; Li, W. Accelerated method of self-consistent field theory for the study of gaussian ring-type block copolymers. Macromolecules 2021, 54, 9071–9078.
Kim, J. U.; Yang, Y. B.; Lee, W. B. Self-consistent field theory of gaussian ring polymers. Macromolecules 2012, 45, 3263–3269.
Ryu, J. H.; Kim, Y.; Lee, W. B. Inhomogeneity of block copolymers at the interface of an immiscible polymer blend. Phys. Rev. E 2018, 97, 042502.
Fokin, V. V.; Sharpless, K. B. A practical and highly efficient aminohydroxylation of unsaturated carboxylic acids. Angew. Chem. Int. Ed. 2001, 40, 3455–3457.
Sun, P.; Chen, J.; Liu, J.; Zhang, K. Self-accelerating click reaction for cyclic polymer. Macromolecules 2017, 50, 1463–1472.
Li, Z.; Qu, L.; Zhu, W.; Liu, J.; Chen, J. Q.; Sun, P.; Wu, Y.; Liu, Z.; Zhang, K. Self-accelerating click reaction for preparing cyclic polymers from unconjugated vinyl monomers. Polymer 2018, 137, 54–62.
Kawaguchi, D. Direct observation and mutual diffusion of cyclic polymers. Polym. J. 2013, 45, 783–789.
Pasquino, R.; Vasilakopoulos, T. C.; Jeong, Y. C.; Lee, H.; Rogers, S.; Sakellariou, G.; Allgaier, J.; Takano, A.; Bras, A. R.; Chang, T.; Goossen, S.; Pyckhout-Hintzen, W.; Wischnewski, A.; Hadjichristidis, N.; Richter, D.; Rubinstein, M.; Vlassopoulos, D. Viscosity of ring polymer melts. ACS Macro Lett. 2013, 2, 874–878.
Chen, W.; Chen, J.; Liu, L.; Xu, X.; An, L. Effects of chain rigidity on conformational and dynamical properties of individual ring polymers in shear flow. Macromolecules 2013, 46, 7542–7549.
Takeshita, H.; Poovarodom, M.; Kiya, T.; Arai, F.; Takenaka, K.; Miya, M.; Shiomi, T. Crystallization behavior and chain folding manner of cyclic, star and linear poly(tetrahydrofuran)s. Polymer 2012, 53, 5375–5384.
Kitahara, T.; Yamazaki, S.; Kimura, K. Effects of topological constraint and knot entanglement on the crystal growth of polymers proved by growth rate of spherulite of cyclic polyethylene. Kobunshi Ronbunshu. 2011, 68, 694–701.
Chen, R.; Ling, J.; Hogen-Esch, T. E. Synthesis and spectroscopic studies of macrocyclic polystyrene containing two fluorene units and single 9,10-anthracenylidene group. Macromolecules 2009, 42, 6015–6022.
Zhang, H.; Zhou, N.; Zhu, X.; Chen, X.; Zhang, Z.; Zhang, W.; Zhu, J.; Hu, Z.; Zhu, X. Cyclic side-chain phenylazo naphthalene polymers: enhanced fluorescence emission and surface relief grating formation. Macromol Rapid Commun. 2012, 33, 1845–1851.
Cai, Y.; Lu, J.; Zhou, F.; Zhou, X.; Zhou, N.; Zhang, Z.; Zhu, X. Cyclic amphiphilic random copolymers bearing azobenzene side chains: facile synthesis and topological effects on self-assembly and photoisomerization. Macromol Rapid Commun. 2014, 35, 901–907.
Coulembier, O.; Deshayes, G.; Surin, M.; De Winter, J.; Boon, F.; Delcourt, C.; Leclere, P.; Lazzaroni, R.; Gerbaux, P.; Dubois, P. Macrocyclic regioregular poly(3-hexylthiophene): from controlled synthesis to nanotubular assemblies. Polym. Chem. 2013, 4, 237–241.
Kaitz, J. A.; Diesendruck, C. E.; Moore, J. S. Dynamic covalent macrocyclic poly(phthalaldehyde)s: scrambling cyclic homopolymer mixtures produces multi-block and random cyclic copolymers. Macromolecules 2013, 46, 8121–8128.
Chen, B.; Jerger, K.; Frechet, J. M. J.; Szoka, F. C., Jr. The influence of polymer topology on pharmacokinetics: differences between cyclic and linear pegylated poly(acrylic acid) comb polymers. J. Control. Rel. 2009, 140, 203–209.
Qian, Z.; Xu, X.; Amacher, J. F.; Madden, D. R.; Cormet-Boyaka, E.; Pei, D. Intracellular delivery of peptidyl ligands by reversible cyclization: discovery of a PDZ domain inhibitor that rescues CFTR activity. Angew. Chem. Int. Ed. 2015, 54, 5874–5878.
Wei, H.; Chu, D. S. H.; Zhao, J.; Pahang, J. A.; Pun, S. H. Synthesis and evaluation of cyclic cationic polymers for nucleic acid delivery. ACS Macro Lett. 2013, 2, 1047–1050.
Cortez, M. A.; Godbey, W. T.; Fang, Y.; Payne, M. E.; Cafferty, B. J.; Kosakowska, K. A.; Grayson, S. M. The synthesis of cyclic poly(ethylene imine) and exact linear analogues: an evaluation of gene delivery comparing polymer. architectures. J. Am. Chem. Soc. 2015, 137, 6541–6549.
Acknowledgments
This work was financially supported by the National Natural Science Foundation of China (No. 22173004).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare no interest conflict.
Electronic Supplementary Information
Rights and permissions
About this article
Cite this article
Qin, DY., Zhao, SD., Liu, ZX. et al. Microphase Separation of Semiflexible Ring Diblock Copolymers. Chin J Polym Sci 42, 267–276 (2024). https://doi.org/10.1007/s10118-023-3024-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10118-023-3024-1