

FOLLOWUS
State Key Laboratory of Chemical Engineering and Low-carbon Technology, Department of Chemical Engineering, Tsinghua University, Beijing 100084, China
ltyan@mail.tsinghua.edu.cn
Received:11 December 2025,
Accepted:25 December 2025,
Online First:02 February 2026,
Published:15 March 2026
Scan QR Code
Wang, Y. M.; Wei, W. J.; Wu, Y. B.; Yan, L. T. Physical origin of conformational entropy in polymers. Chinese J. Polym. Sci. 2026, 44, 611–622
Yu-Ming Wang, Wen-Jie Wei, Yi-Bo Wu, et al. Physical Origin of Conformational Entropy in Polymers[J]. Chinese Journal of Polymer Science, 2026, 44(3): 611-622.
Wang, Y. M.; Wei, W. J.; Wu, Y. B.; Yan, L. T. Physical origin of conformational entropy in polymers. Chinese J. Polym. Sci. 2026, 44, 611–622 DOI: 10.1007/s10118-025-3548-7.
Yu-Ming Wang, Wen-Jie Wei, Yi-Bo Wu, et al. Physical Origin of Conformational Entropy in Polymers[J]. Chinese Journal of Polymer Science, 2026, 44(3): 611-622. DOI: 10.1007/s10118-025-3548-7.
This review provides a conceptual framework unveiling several principles and rules of conformational entropy in governing structures and properties of polymers
from the perspective of fundamental physics and statistical mechanics.
Conformational entropy
one of the central concepts of polymer physics
is the key to revealing physical characteristics of polymers. Despite an increased repertoire of conformational-entropy effects in the structural formation
transition
and properties of polymer systems
the physical origin of conformational entropy remains less understood compared to interaction energy and other types of entropy. This review seeks to provide a conceptual framework unveiling several principles and rules of conformational entropy in governing the structures and properties of polymers
from the perspective of fundamental physics and statistical mechanics. First
we focus on the fundamentals of entropy in thermodynamics
leading to the theoretical basis for the elucidation of conformational entropy. Second
we delineate the physical nature of statistics and dissipation of conformational entropy and its essential dependence on the environmental heat bath. Next
we explore the principles of conformational entropy in driving the ordering transitions of various systems of polymers and their nanocomposites
elucidating the emergent and collective behaviors as well as the interplay between energetic interactions and entropy. Moreover
we demonstrate how the concept of conformational entropy is generalized to the biological systems and other soft matters. Finally
we discuss future directions to signify this framework originated from polymers.
Guth, E.; Mark, H. Zur innermolekularen, statistik, insbesondere bei kettenmolekiilen I. Monatsh. Chem. 1934 , 65 , 93−121..
[Kuhn, W. Über die gestalt fadenförmiger moleküle in lösungen. Kolloid-Zeitschrift 1934 , 68 , 2−15..
[Flory, P. J. in Principles of polymer chemistry . Cornell university press, New York, USA, 1953 ..
[Flory, P. J. in Statistical mechanics of chain molecules . Interscience, New York, USA, 1969 ..
[Wang, Z. G. 50th anniversary perspective: polymer conformation—a pedagogical review. Macromolecules 2017 , 50 , 9073−9114..
Zhu, G.; Huang, Z.; Xu, Z.; Yan, L. T. Tailoring interfacial nanoparticle organization through entropy. Acc. Chem. Res. 2018 , 51 , 900−909..
Yang, Y. L.; Zhang, H. D. A discussion o n the origins and development of polymer physics. Acta Polymerica Sinica (in Chinese) 2020 , 51 , 87−90..
Dai, X.; Wan, H. X.; Zhang, X.; Wei, W.; Chen, W.; Zhang, L.; Li, J.; Yan, L. T. Role of conformational entropy in complex macromolecular systems. Chem. Res. Chin. Univ. 2023 , 39 , 709−718..
Balazs, A. C.; Emrick, T.; Russell, T. P. Nanoparticle polymer composites: where two small worlds meet. Science 2006 , 314 , 1107−1110..
Bailey, E. J.; Winey, K. I. Dynamics of polymer segments, polymer chains, and nanoparticles in polymer nanocomposite melts: a review. Prog. Polym. Sci. 2020 , 105 , 101242..
Kao, J.; Thorkelsson, K.; Bai, P.; Rancatore, B. J.; Xu, T. Toward functional nanocomposites: taking the best of nanoparticles, polymers, and small molecules. Chem. Soc. Rev. 2013 , 42 , 2654−2678..
Zhu, G.; Xu, Z.; Yan, L.-T. Entropy at bio–nano interfaces. Nano Lett. 2020 , 20 , 5616−5624..
Frederick, K. K.; Marlow, M. S.; Valentine, K. G.; Wand, A. J. Conformational entropy in molecular recognition by proteins. Nature 2007 , 448 , 325−329..
Thaner, R. V.; Kim, Y.; Li, T. I.; Macfarlane, R. J.; Nguyen, S. T.; Olvera de la Cruz, M.; Mirkin, C. A. Entropy-driven crystallization behavior in DNA-mediated nanoparticle assembly. Nano Lett. 2015 , 15 , 5545−5551..
Zhu, G.; Xu, Z.; Yang, Y.; Dai, X.; Yan, L. T. Hierarchical crystals formed from dna-functionalized janus nanoparticles. ACS Nano 2018 , 12 , 9467−9475..
Liu, Z.; Guo, R.; Xu, G.; Huang, Z.; Yan, L. T. Entropy-mediated mechanical response of the interfacial nanoparticle patterning. Nano Lett. 2014 , 14 , 6910−6916..
Jhalaria, M.; Cang, Y.; Huang, Y.; Benicewicz, B.; Kumar, S. K.; Fytas, G. Unusual high-frequency mechanical properties of polymer-grafted nanoparticle melts. Phys. Rev. Lett. 2022 , 128 , 187801..
Hoheisel, T. N.; Hur, K.; Wiesner, U. B. Block copolymer-nanoparticle hybrid self-assembly. Prog. Polym. Sci. 2015 , 40 , 3−32..
Dong, B.; Huang, Z.; Chen, H.; Yan, L. T. Chain-stiffness-induced entropy effects mediate interfacial assembly of janus nanoparticles in block copolymers: from interfacial nanostructures to optical responses. Macromolecules 2015 , 48 , 5385−5393..
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..
Zha, L.; Zhang, M.; Li, L.; Hu, W. Entropy-driven segregation and its competition with crystal nucleation in the binary blends of stretched and free guest polymers. J. Phys. Chem. B 2016 , 120 , 12988−12992..
Zeng, W.; Liu, L.; Shen, Y.; Wu, Z.; Zhai, Y.; Liu, D.; Chen, H.; Zhang, K.; Yin, B.; Yang, W.; Yang, M. Conformational selection of polymer chains upon π-π interactions with small molecules. Phys. Rev. Lett. 2024 , 133 , 178101..
Cai, L.-H.; Panyukov, S.; Rubinstein, M. Hopping diffusion of nanoparticles in polymer matrices. Macromolecules 2015 , 48 , 847−862..
Dai, X.; Zhang, X.; Gao, L.; Xu, Z.; Yan, L. T. Topology mediates transport of nanoparticles in macromolecular networks. Nat. Commun. 2022 , 13 , 4094..
Frenkel, D. Order through entropy. Nat. Mater. 2015 , 14 , 9−12..
van Anders, G.; Klotsa, D.; Ahmed, N. K.; Engel, M.; Glotzer, S. C. Understanding shape entropy through local dense packing. Proc. Natl. Acad. Sci. U. S. A. 2014 , 111 , E4812−E4821..
Zhang, X.; Dai, X.; Gao, L.; Xu, D.; Wan, H.; Wang, Y.; Yan, L.-T. The entropy-controlled strategy in self-assembling systems. Chem. Soc. Rev. 2023 , 52 , 6806−6837..
Manoharan, V. N. Colloidal matter: packing, geometry, and entropy. Science 2015 , 349 , 1253751..
de Nijs, B.; Dussi, S.; Smallenburg, F.; Meeldijk, J. D.; Groenendijk, D. J.; Filion, L.; Imhof, A.; van Blaaderen, A.; Dijkstra, M. Entropy-driven formation of large icosahedral colloidal clusters by spherical confinement. Nat. Mater. 2015 , 14 , 56−60..
Geng, Y.; van Anders, G.; Dodd, P. M.; Dshemuchadse, J.; Glotzer, S. C. Engineering entropy for the inverse design of colloidal crystals from hard shapes. Sci. Adv. 2019 , 5 , eaaw0514..
Hou, C.; Gao, L.; Wang, Y.; Yan, L. T. Entropic control of nanoparticle self-assembly through confinement. Nanoscale Horiz. 2022 , 7 , 1016−1028..
Rovigatti, L.; Sciortino, F. Designing enhanced entropy binding in single-chain nanoparticles. Phys. Rev. Lett. 2022 , 129 , 047801..
Damasceno, P. F.; Engel, M.; Glotzer, S. C. Crystalline assemblies and densest packings of a family of truncated tetrahedra and the role of directional entropic forces. ACS Nano 2012 , 6 , 609−614..
Haji-Akbari, A.; Engel, M.; Keys, A. S.; Zheng, X.; Petschek, R. G.; Palffy-Muhoray, P.; Glotzer, S. C. Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra. Nature 2009 , 462 , 773−777..
Damasceno, P. F.; Engel, M.; Glotzer, S. C. Predictive self-assembly of polyhedra into complex structures. Science 2012 , 337 , 453−457..
Zhao, K.; Bruinsma, R.; Mason, T. G. Entropic crystal–crystal transitions of brownian squares. Proc. Natl. Acad. Sci. U. S. A. 2011 , 108 , 2684−2687..
Chen, Q.; Bae, S. C.; Granick, S. Directed self-assembly of a colloidal kagome lattice. Nature 2011 , 469 , 381−384..
Mao, X.; Chen, Q.; Granick, S. Entropy favours open colloidal lattices. Nat. Mater. 2013 , 12 , 217−222..
Cates, M. E. Entropy stabilizes open crystals. Nat. Mater. 2013 , 12 , 179−180..
Dijkstra, M.; Luijten, E. From predictive modelling to machine learning and reverse engineering of colloidal self-assembly. Nat. Mater. 2021 , 20 , 762−773..
Szleifer, I. Entropic templating. Nat. Mater. 2013 , 12 , 693−694..
Escobedo, F. A. Engineering entropy in soft matter: the bad, the ugly and the good. Soft Matter 2014 , 10 , 8388−8400..
Dai, X.; Zhang, X.; Gao, L.; Yan, L. T. Superentropy effect and macromolecular entropy control strategy. Acta Polymerica Sinica (in Chinese) 2021 , 52 , 1076−1099..
[Yan, L. T. in Entropy-controlled strategy of soft matter systems , Science Press, Beijing, 2021 ..
Li, B.; Zhou, D.; Han, Y. Assembly and phase transitions of colloidal crystals. Nat. Rev. Mater. 2016 , 1 , 1−13..
Onsager, L. The effects of shape on the interaction of colloidal particles. Ann. N. Y. Acad. Sci. 1949 , 51 , 627−659..
Yu, B.; Sun, P.; Chen, T.; Jin, Q.; Ding, D.; Li, B.; Shi, A. C. Confinement-induced novel morphologies of block copolymers. Phys. Rev. Lett. 2006 , 96 , 138306..
Liu, Z.; Zhang, J.; Zhao, S.; Yan, Y.; Li, X.; Zhang, X. Nonadditive effective interactions and entropy-driven non-close-packed self-assembly cluster of nanoparticle in ordered block copolymer structure. Macromolecules 2024 , 57 , 1478−1488..
[Rubinstein, M.; Colby, R. H. in Polymer physics , Oxford University Press, Oxford, 2003 ..
[Clausius, R. in Abhandlungen über die mechanische wärmetheorie , Friedrich Vieweg und Sohn, Berlin, 1864 ..
Clausius, R. Ueber verschiedene für die anwendung bequeme formen der hauptgleichungen der mechanischen wärmetheorie. Ann. der Phys. 1865 , 125 , 353−400..
[Boltzmann, L. in Vorlesungen über gastheorie ; Johann Ambrosius Barth, Leipzig, 1896 ..
Planck, M. Ueber das gesetz der energieverteilung im normalspectrum. Ann. der Phys. 1901 , 309 , 553−563..
Verlinde, E. On the origin of gravity and the laws of newton. J. High Energ. Phys. 2011 , 2011 , 1−27..
Georgi, H.; Glashow, S. L. Unity of all elementary-particle forces. Phys. Rev. Lett. 1974 , 32 , 438..
Yang, C. N.; Mills, R. L. Conservation of isotopicspin and isotopic gauge invariance. Phys. Rev. 1954 , 96 , 191−195..
Min, Y.; Akbulut, M.; Kristiansen, K.; Golan, Y.; Israelachvili, J. The role of interparticle and external forces in nanoparticle assembly. Nat. Mater. 2008 , 7 , 527−538..
Asakura, S.; Oosawa, F. On interaction between two bodies immersed in a solution of macromolecules. J. Chem. Phys. 1954 , 22 , 1255−1256..
Ball, P. The force of shape. Nat. Mater. 2014 , 13 , 1083−1083..
Wojtecki, R. J.; Meador, M. A.; Rowan, S. J. Using the dynamic bond to access macroscopically responsive structurally dynamic polymers. Nat. Mater. 2011 , 10 , 14−27..
[Xu, Z.; Dai, X.; Bu, X.; Yang, Y.; Zhang, X.; Man, X.; Zhang, X.; Doi, M.; Yan, L. T. Enhanced heterogeneous diffusion of nanoparticles in semiflexible networks. ACS Nano 2021 , 15 , 4608-4616..
Daniel, W. F.; Burdyńska, J.; Vatankhah-Varnoosfaderani, M.; Matyjaszewski, K.; Paturej, J.; Rubinstein, M.; Dobrynin, A. V.; Sheiko, S. S. Solvent-free, supersoft and superelastic bottlebrush melts and networks. Nat. Mater. 2016 , 15 , 183−189..
Danielsen, S. P.; Beech, H. K.; Wang, S.; El-Zaatari, B. M.; Wang, X.; Sapir, L.; Ouchi, T.; Wang, Z.; Johnson, P. N.; Hu, Y. Molecular characterization of polymer networks. Chem. Rev. 2021 , 121 , 5042−5092..
Broedersz, C. P.; MacKintosh, F. C. Modeling semiflexible polymer networks. Rev. Mod. Phys. 2014 , 86 , 995−1036..
[Yan, L. T. in Dynamics and transport in macromolecular networks: theory, modelling, and experiments , Wiley-VCH, Weinheim, 2023 ..
Zhang, X.; Dai, X.; Wan, H.; Jiao, Z.; Chen, W.; Wei, W.; Li, J.; Liu, K.; Yang, Z.; Yan, L.-T. Interfaces between nanoparticle and biomacromolecular network: dynamic behaviors, confinement and entropy. Adv. Funct. Mater. 2024 , 34 , 2314134..
Zhang, X.; Dai, X.; Habib, M. A.; Gao, L.; Chen, W.; Wei, W.; Tang, Z.; Qi, X.; Gong, X.; Jiang, L. Unconventionally fast transport through sliding dynamics of rodlike particles in macromolecular networks. Nat. Commun. 2024 , 15 , 525..
Zhang, X.; Dai, X.; Wei, W.; Chen, W.; Gao, L.; Yan, L. T. Dynamic heterogeneities of rod rotation in macromolecular networks. Macromolecules 2023 , 56 , 8428−8437..
Xu, D.; Wan, H. X.; Yao, X.-R.; Li, J.; Yan, L. T. Molecular simulations in macromolecular science. Chin. J. Polym. Sci. 2023 , 41 , 1361−1370..
Bao, Y.; Luo, Z.; Cui, S. Environment-dependent single-chain mechanics of synthetic polymers and biomacromolecules by atomic force microscopy-based single-molecule force spectroscopy and the implications for advanced polymer materials. Chem. Soc. Rev. 2020 , 49 , 2799−2827..
Cai, W.; Xu, D.; Qian, L.; Wei, J.; Xiao, C.; Qian, L.; Lu, Z. Y.; Cui, S. Force-induced transition of π-π stacking in a single polystyrene chain. J. Am. Chem. Soc. 2019 , 141 , 9500−9503..
Stokes, G. G. On the effect of the internal friction of fluids on the motion of pendulums. Trans. Camb. Philos. Soc. 1851 , 9 , 8−106..
Kivelson, S.; Kivelson, S. A. Defining emergence in physics. npj Quantum Mater. 2016 , 1 , 16024..
Maciołek, A.; Dietrich, S. Collective behavior of colloids due to critical casimir interactions. Rev. Mod. Phys. 2018 , 90 , 045001..
Cates, M. E.; Tailleur, J. Motility-induced phase separation. Annu. Rev. Condens. Matter Phys. 2015 , 6 , 219−244..
Huang, Z.; Lu, C.; Dong, B.; Xu, G.; Ji, C.; Zhao, K.; Yan, L. T. Chain stiffness regulates entropy-templated perfect mixing at single-nanoparticle level. Nanoscale 2016 , 8 , 1024−1032..
Sheiko, S. S.; Zhou, J.; Arnold, J.; Neugebauer, D.; Matyjaszewski, K.; Tsitsilianis, C.; Tsukruk, V. V.; Carrillo, J.-M. Y.; Dobrynin, A. V.; Rubinstein, M. Perfect mixing of immiscible macromolecules at fluid interfaces. Nat. Mater. 2013 , 12 , 735−740..
Xiao, R.; Pal, S.; Rademacher, C. P.; Chen, J.; Wang, Q.; Chen, W.; Shull, K. R.; Keten, S.; Wang, M. Real-time visualization of single polymer conformational change in the bulk state during mechanical deformation. Phys. Rev. Lett. 2025 , 134 , 148101..
Wang, Y.; Lu, H.; Jia, X.-M.; Shi, A.-C.; Zhou, J.; Zhang, G.; Liu, H. Entropy-induced localization and sliding dynamics of rings on polyrotaxane. Macromolecules 2024 , 57 , 1846−1858..
Mao, J.; Jia, X.-M.; Zhang, G.; Zhou, J. Excluded volume of slide rings in single-chain polyrotaxane. Macromolecules 2024 , 57 , 3841−3849..
Zhao, S.; Yu, J.; Liu, Z.; Zhang, J.; Yan, Y.; Dong, Q.; Shi, A.-C.; Zhang, X. Phase behavior of linear-star topology-transformable block copolymers. Macromolecules 2024 , 57 , 3831−3840..
Zhang, R.; Lee, B.; Stafford, C. M.; Douglas, J. F.; Dobrynin, A. V.; Bockstaller, M. R.; Karim, A. Entropy-driven segregation of polymer-grafted nanoparticles under confinement. Proc. Natl. Acad. Sci. U. S. A. 2017 , 114 , 2462−2467..
Wang, M.; Song, Z.; Liu, G.; Wang, D. Entropic origin of polymer nucleation at amorphous solid interfaces. Phys. Rev. Lett. 2025 , 135 , 018101..
Yeh, J. W., Chen, S. K., Lin, S. J., Gan, J. Y., Chin, T. S., Shun, T. T., Tsau, C. H., Chang, S. Y. Nanostructured high-entropy alloys with multiple principle elements: novel alloy design concepts and outcomes. Adv. Eng. Mater. 2004 , 6 , 299−303..
[Frenkel, D. Order through disorder: entropy-driven phase transitions. In Proceedings of the Sitges Conference on Complex Liquids Garrido, L., Eds.; Springer, New York, 1993 , pp. 137–148..
[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..
Liu, X. Y.; Yan, X. Y.; Liu, Y.; Qu, H.; Wang, Y.; Wang, J.; Guo, Q. Y.; Lei, H.; Li, X. H.; Bian, F. Self-assembled soft alloy with frank–kasper phases beyond metals. Nat. Mater. 2024 , 23 , 570−576..
Thompson, R. B.; Ginzburg, V. V.; Matsen, M. W.; Balazs, A. C. Predicting the mesophases of copolymer-nanoparticle composites. Science 2001 , 292 , 2469−2472..
Kim, B. J.; Chiu, J. J.; Yi, G. R.; Pine, D. J.; Kramer, E. J. Nanoparticle-induced phase transitions in deblock-copolymer films. Adv. Mater. 2005 , 17 , 2618−2622..
Kang, H.; Detcheverry, F. A.; Mangham, A. N.; Stoykovich, M. P.; Daoulas, K. C.; Hamers, R. J.; Müller, M.; de Pablo, J. J.; Nealey, P. F. Hierarchical assembly of nanoparticle superstructures from block copolymer-nanoparticle composites. Phys. Rev. Lett. 2008 , 100 , 148303..
Dai, X.; Chen, P.; Zhu, G.; Xu, Z.; Zhang, X.; Yan, L.-T. Entropy-mediated mechanomutable microstructures and mechanoresponsive thermal transport of nanoparticle self-assembly in block copolymers. J. Phys. Chem. Lett. 2019 , 10 , 7970−7979..
Gupta, S.; Zhang, Q.; Emrick, T.; Balazs, A. C.; Russell, T. P. Entropy-driven segregation of nanoparticles to cracks in multilayered composite polymer structures. Nat. Mater. 2006 , 5 , 229−233..
Wan, H.; Xu, D.; Gao, L.; Yan, L. T. Entropy-mediated nanoparticle cellular uptake. Small Sci. 2024 , 4 , 23000 78..
Wan, H. X.; Xu, D.; Dong, X. W.; Yang, K.; Yan, L. T. Insight into biophysicochemical principles of biopolymers through simulation and theory. Chinese J. Polym. Sci. 2023 , 41 , 1342−1354..
van der Lee, R.; Buljan, M.; Lang, B.; Weatheritt, R. J.; Daughdrill, G. W.; Dunker, A. K.; Fuxreiter, M.; Gough, J.; Gsponer, J.; Jones, D. T. Classification of intrinsically disordered regions and proteins. Chem. Rev. 2014 , 114 , 6589−6631..
Zeno, W. F.; Thatte, A. S.; Wang, L.; Snead, W. T.; Lafer, E. M.; Stachowiak, J. C. Molecular mechanisms of membrane curvature sensing by a disordered protein. J. Am. Chem. Soc. 2019 , 141 , 10361−10371..
Lolicato, F.; Joly, L.; Martinez-Seara, H.; Fragneto, G.; Scoppola, E.; Baldelli Bombelli, F.; Vattulainen, I.; Akola, J.; Maccarini, M. The role of temperature and lipid charge on intake/uptake of cationic gold nanoparticles into lipid bilayers. Small 2019 , 15 , 1805046..
Singh, A.; Soler, J. A.; Lauer, J.; Grill, S. W.; Jahnel, M.; Zerial, M.; Thutupalli, S. Two-component molecular mo tor driven by a gtpase cycle. Nat. Phys. 2023 , 19 , 1185−1192..
Ou, L.; Chen, H.; Yuan, B.; Yang, K. Membrane-specific binding of 4 nm lipid nanoparticles mediated by an entropy-driven interaction mechanism. ACS Nano 2022 , 16 , 18090−18100..
Xu, Z.; Liu, G.; Gao, L.; Xu, D.; Wan, H.; Dai, X.; Zhang, X.; Tao, L.; Yan, L.-T. Configurational entropy-enabled thermostability of cell membranes in extremophiles: from molecular mechanism to bioinspired design. Nano Lett. 2023 , 23 , 1109−1118..
Lee, J.; Im, W. Transmembrane helix tilting: insights from calculating the potential of mean force. Phys. Rev. Lett. 2008 , 100 , 018103..
Ren, C. L.; Ma, Y. Q. Structure and organization of nanosized-inclusion-containing bilayer membranes. Phys. Rev. E 2009 , 80 , 011910..
0
Views
11
Downloads
0
CSCD
Publicity Resources
Related Articles
Related Author
Related Institution
京公网安备11010802046900号