

FOLLOWUS
a.State Key Laboratory of Polymer Science and Technology, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China
b.School of Applied Chemistry and Engineering, University of Science and Technology of China, Hefei 230026, China
c.State Key Laboratory of Molecular Engineering of Polymers, Fudan University, Shanghai 200433, China
d.School of Metallurgy and Environment, Central South University, Changsha 410083, China
dwsun@ciac.ac.cn
Received:14 August 2026,
Accepted:07 September 2026,
Online First:28 October 2026,
Published:2026-10
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Li, H.; Li, H.; Sun, D. W.; An, L. J. Process-directed self-assembly of perforated lamellar mesostructure with P6/mmm symmetry in linear multiblock copolymers. Chinese J. Polym. Sci. https://doi.org/10.1007/s10118-026-3874-4
Hao Li, Hong Li, De-Wen Sun, et al. Process-directed Self-assembly of Perforated Lamellar Mesostructure with
Li, H.; Li, H.; Sun, D. W.; An, L. J. Process-directed self-assembly of perforated lamellar mesostructure with P6/mmm symmetry in linear multiblock copolymers. Chinese J. Polym. Sci. https://doi.org/10.1007/s10118-026-3874-4 DOI:
Hao Li, Hong Li, De-Wen Sun, et al. Process-directed Self-assembly of Perforated Lamellar Mesostructure with
The rugged free-energy landscape of block copolymers features a multitude of local free-energy minima in addition to the only global free-energy minimum
giving rise to long-lived metastable states and enabling the fabrication of desired
metastable mesostructure in a process-accessible manner. Considering that the fabrication of perforated lamellar mesostructures in block copolymers
via
the stabilization strategy by either fine-tuning the chain architecture of the block copolymer or blending cannot fix the stacking sequence of hexagonally perforated layers in experiments due to similar free energies of different stacking sequences an
d leads to limited stable regions
using general symmetry considerations
we design a symmetry-conserving process to obtain the desired perforated lamellar mesostructure. The thermodynamically stable iHP
a
with
P
6/
mmm
symmetry of No. 191 space group in linear
$$ {B}_{1}{A}_{1}{B}_{2}{A}_{2}{B}_{3} $$
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pentablock copolymer melts is chosen as the initial
equilibrium mesophase
based on which the desired
starting
unstable states are generated using the isothermal
alchemical conversion process of the
C
-blocks of linear
$$ {\tilde{B}}_{1}{\tilde{C}}_{1}{A}_{1}{B}_{2}{A}_{2}{C}_{3} $$
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$$ {C}_{1}{A}_{1}{B}_{2}{A}_{2}{C}_{3} $$
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and
$$ {C}_{1}{A}_{1}{\tilde{C}}_{2}{\tilde{B}}_{2}{A}_{2}{C}_{3} $$
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multiblock copolymers from
B
to
A
. Ensuing from the corresponding starting
unstable states
the perforated lamellar mesostructure exhi
biting only the AA… sequence of perforated lamellar layers with
P
6/
mmm
symmetry as well can be process-accessibly obtained with large fabrication ranges. Field theory is employed to implement our explorations.
Bates, F. S.; Fredrickson, G. H. Block copolymers—designer soft materials. Phys. Today 1999 , 52 , 32−38..
Bates, F. S. Network phases in block copolymer melts. MRS Bull. 2005 , 30 , 525−532..
Meuler, A. J.; Hillmyer, M. A.; Bates, F. S. Ordered network mesostructures in block polymer materials. Macromolecules 2009 , 42 , 7221−7250..
Bates, F. S.; Fredrickson, G. H. Block copolymer thermodynamics: theory and experiment. Annu. Rev. Phys. Chem. 1990 , 41 , 525−557..
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..
Matsen, M. W.; Bates, F. S. Unifying weak- and strong-segregation block copolymer theories. Macromolecules 1996 , 29 , 1091−1098..
Zhang, C. Z.; Wang, Z. G. Random isotropic structures and possible glass transitions in diblock copolymer melts. Phys. Rev. E 2006 , 73 , 031804..
Ren, Y.; Müller, M. Kinetics of pattern formation in symmetric diblock copolymer melts. J. Chem. Phys. 2018 , 148 , 204908..
Dorfman, K. D.; Wang, Z. G. Liquid-like states in micelle-forming diblock copolymer melts. ACS Macro Lett. 2023 , 12 , 980−985..
Li, W.; Nealey, P. F.; de Pablo, J. J.; Müller, M. Defect removal in the course of directed self-assembly is facilitated in the vicinity of the order-disorder transition. Phys. Rev. Lett. 2014 , 113 , 168301..
Li, W.; Müller, M. Directed self-assembly of block copolymers by chemical or topographical guiding patterns: optimizing molecular architecture, thin-film properties, and kinetics. Prog. Polym. Sci. 2016 , 54/55 , 47−75..
Ryu, H. J.; Fortner, D. B.; Rohrer, G. S.; Bockstaller, M. R. Measuring relative grain-boundary energies in block-copolymer microstructures. Phys. Rev. Lett. 2012 , 108 , 107801..
Matsen, M. W. Kink grain boundaries in a block copolymer lamellar phase. J. Chem. Phys. 1997 , 107 , 8110−8119..
[Schoen, A. H. Infinite periodic minimal surfaces without self-intersections. NASA Technical Note 1970 , No. TN D-5541..
Müller, M.; Sun, D. W. Directing the self-assembly of block copolymers into a metastable complex network phase via a deep and rapid quench. Phys. Rev. Lett. 2013 , 111 , 267801..
Müller, M.; Sun, D. W. Process-directed self-assembly of block copolymers: a computer simulation study. J. Phys. Condens. Matter 2015 , 27 , 194101..
Sun, D. W.; Müller, M. Process-accessible states of block copolymers. Phys. Rev. Lett. 2017 , 118 , 067801..
Lord, E. A.; MacKay, A. L. Periodic minimal surfaces of cubic symmetry. Curr. Sci. 2003 , 85 , 346−362..
Jiang, K.; Wang, C.; Huang, Y.; Zhang, P. Discovery of new metastable patterns in diblock copolymers. Commun. Comput. Phys. 2014 , 14 , 443−460..
Cho, J. Two new triply periodic bicontinuous network structures for molten block copolymers. Macromol. Res. 2018 , 26 , 380−387..
Cho, J. Identification of some new triply periodic mesophases from molten block copolymers. Polymers 2019 , 11 , 1081..
[Li, H.; Geng, X. J.; Sun, D. W.; An, L. J. Polymeric self-consistent field calculations in block copolymers using the spectral method on graphics processing units. Chinese J. Polym. Sci . 2026 , doi: 10.1007/s10118-026-3825-0..
[In Ref. [17 ] , this periodically ordered network mesostructure with Ia $$ \overline{3} $$ d symmetry was named as cubic single-DIAmond network (DIA) on the basis of Ref. [19 ] . In Ref. [22 ] , it was named as cubic single 4-fold network (S4F) since (I) it has a single 4-fold network domain and (II) cubic single-diamond network commonly refers to the periodically ordered network mesostructure with Fd $$ \overline{3} $$ m symmetry, i.e ., SD. In this study, S4F is also utilized to indicate this ordered network mesostructure..
Geng, X. J.; Li, H.; Yang, X.; An, L. J.; Müller, M.; Sun, D. W. Process-directed self-assembly of the frank-kasper A15 structure in linear, conformationally symmetric block copolymers. Phys. Rev. Lett. 2025 , 134 , 118102..
[Gray, A.; Abbena, E.; Salamon, S. in Modern differential geometry of curves and surfaces with mathematica , Chapman & Hall/CRC, Boca Raton, FL, 2006 ..
Li, W.; Müller, M. Defects in the self-assembly of block copolymers and their relevance for directed self-assembly. Annu. Rev. Chem. Biomol. Eng. 2015 , 6 , 187−216..
Nagpal, U.; Müller, M.; Nealey, P. F.; de Pablo, J. J. Free energy of defects in ordered assemblies of block copolymer domains. ACS Macro Lett. 2012 , 1 , 418−422..
Sun, D. W.; Müller, M. Numerical algorithms for solving self-consistent field theory reversely for block copolymer systems. J. Chem. Phys. 2018 , 149 , 214104..
Müller, M. Process-directed self-assembly of copolymers: results of and challenges for simulation studies. Prog. Polym. Sci. 2020 , 101 , 101198..
Sun, D.; An, L. Process-directed self-assembly of block copolymers: theories and computer simulations. Chem. Res. Chin. Univ. 2026 , 42 , 1124−1147..
Foerster, S.; Khandpur, A. K.; Zhao, J.; Bates, F. S.; Hamley, I. W.; Ryan, A. J.; Bras, W. Complex phase behavior of polyisoprene-polystyrene diblock copolymers near the order-disorder transition. Macromolecules 1994 , 27 , 6922−6935..
Khandpur, A. K.; Foerster, S.; Bates, F. S.; Hamley, I. W.; Ryan, A. J.; Bras, W.; Almdal, K.; Mortensen, K. Polyisoprene-polystyrene diblock copolymer phase diagram near the order-disorder transition. Macromolecules 1995 , 28 , 8796−8806..
Matsen, M. W.; Schick, M. Stable and unstable phases of a diblock copolymer melt. Phys. Rev. Lett. 1994 , 72 , 2660−2663..
Matsen, M. W. The standard Gaussian model for block copolymer melts. J. Phys. Condens. Matter 2002 , 14 , R21−R47..
Matsen, M. W. Effect of architecture on the phase behavior of AB-type block copolymer melts. Macromolecules 2012 , 45 , 2161−2165..
Jiang, W.; Qiang, Y.; Li, W.; Qiu, F.; Shi, A. C. Effects of chain topology on the self-assembly of AB-type block copolymers. Macromolecules 2018 , 51 , 1529−1538..
Xie, Q.; Qiang, Y.; Chen, L.; Xia, Y.; Li, W. Synergistic effect of stretched bridging block and released packing frustration leads to exotic nanostructures. ACS Macro Lett. 2020 , 9 , 980−984..
Xie, Q.; Qiang, Y.; Li, W. Single gyroid self-assembled by linear BABAB pentablock copolymer. ACS Macro Lett. 2022 , 11 , 205−209..
Hou, L.; Xu, Z.; Dong, Q.; Shi, A. C.; Li, W. Stabilizing DG, DD, and DP bicontinuous network phases in pure AB-type block copolymers beyond relieving packing frustration. Macromolecules 2024 , 57 , 2165−2175..
Chen, H.; Dong, Q.; Qiang, Y.; Peng, L.; Huang, X.; Li, W. Mechanisms of multiple reentrant transitions between frank-kasper and classical spherical phases in AB-type dendron-like copolymer. Macromolecules 2025 , 58 , 10192−10202..
Matsen, M. W. Stabilizing new morphologies by blending homopolymer with block copolymer. Phys. Rev. Lett. 1995 , 74 , 4225−4228..
Matsen, M. W. Phase behavior of block copolymer/homopolymer blends. Macromolecules 1995 , 28 , 5765−5773..
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 , 361−369..
Zhu, L.; Huang, P.; Cheng, S.; Ge, Q.; Quirk, R.; Thomas, E.; Lotz, B.; Wittmann, J. C.; Hsiao, B.; Yeh, F.; Liu, L. Dislocation-controlled perforated layer phase in a PEO- b-PS diblock copolymer. Phys. Rev. Lett. 2001 , 86 , 6030−6033..
Zhu, L.; Huang, P.; Chen, W. Y.; Weng, X.; Cheng, S. Z. D.; Ge, Q.; Quirk, R. P.; Senador, T.; Shaw, M. T.; Thomas, E. L.; Lotz, B.; Hsiao, B. S.; Yeh, F.; Liu, L. “Plastic deformation” mechanism and phase transformation in a shear-induced metastable hexagonally perforated layer phase of a polystyrene- b -poly(ethylene oxide) diblock copolymer. Macromolecules 2003 , 36 , 3180−3188..
[Henry, N. F. M.; Lonsdale, K. in International tables for X-ray crystallography , Kynoch, Birmingham, 1969 ..
Zhang, J.; Zhang, Y.; Chen, F.; Zhang, W.; Zhao, H. Self-assembly of photoswit chable diblock copolymers: salt-induced micellization and the influence of UV irradiation. Phys. Chem. Chem. Phys. 2015 , 17 , 12215−12221..
Huebner, D.; Rossner, C.; Vana, P. Light-induced self-assembly of gold nanoparticles with a photoresponsive polymer shell. Polymer 2016 , 107 , 503−508..
Brunsen, A.; Cui, J.; Ceolín, M.; del Campo, A.; Soler-Illia, G. J. A. A.; Azzaroni, O. Light-activated gating and permselectivity in interfacial architectures combining “caged” polymer brushes and mesoporous thin films. Chem. Commun. 2012 , 48 , 1422−1424..
Fredrickson, G. H.; Ganesan, V.; Drolet, F. Field-theoretic computer simulation methods for polymers and complex fluids. Macromolecules 2002 , 35 , 16−39..
[Fredrickson, G. H. in The equilibrium theory of inhomogeneous polymers , Oxford University Press, Oxford, 2006 ..
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..
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..
Maurits, N. M.; Fraaije, J. G. E. M. Mesoscopic dynamics of copolymer melts: from density dynamics to external potential dynamics using nonlocal kinetic coupling. J. Chem. Phys. 1997 , 107 , 5879−5889..
Kawakatsu, T. Effects of changes in the chain conformation on the kinetics of order-disorder transitions in block copolymer melts. Phys. Rev. E 1997 , 56 , 3240−3250..
Reister, E.; Müller, M.; Binder, K. Spinodal decomposition in a binary polymer mixture: dynamic self-consistent-field theory and Monte Carlo simulations. Phys. Rev. E 2001 , 64 , 041804..
Lyakhova, K. S.; Zvelindovsky, A. V.; Sevink, G. J. A. Kinetic pathways of order-to-order phase transitions in block copolymer films under an electric field. Macromolecules 2006 , 39 , 3024−3037..
Müller, M.; de Pablo, J. J. Computational approaches for the dynamics of structure formation in self-assembling polymeric materials. Annu. Rev. Mater. Res. 2013 , 43 , 1−34..
Grzetic, D. J.; Wickham, R. A.; Shi, A.-C. Statistical dynamics of classical systems: a self-consistent field approach. J. Chem. Phys. 2014 , 140 , 244907..
[Flory, P. J. in Principles of polymer chemistry , Cornell University Press, Ithaca, New York, 1953 ..
Hohenberg, P. C.; Halperin, B. I. Theory of dynamic critical phenomena. Rev. Mod. Phys. 1977 , 49 , 435−479..
Wang, G.; Ren, Y.; Müller, M. Collective short-time dynamics in multicomponent polymer melts. Macromolecules 2019 , 52 , 7704−7720..
[As pointed out by Ref. [62], on times that are shorter than the single-chain relaxation time, the assumption of DSCFT that the chain configurations are in equilibrium with the instantaneous densities becomes invalid and the relaxation of the chain configurations imparts memory effects onto the Onsager coefficient of Cahn-Hilliard dynamics.
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