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Confinement-driven emergence of hyperuniform fluids

Fabio Leoni1,*, Giancarlo Franzese2,3,†, Erdal C. Oğuz4,5,6,‡, and Fausto Martelli1,7,§

  • *Contact author: fabio.leoni@uniroma1.it
  • †Contact author: gfranzese@ub.edu
  • ‡Contact author: ecoguz@iphy.ac.cn
  • §Contact author: fausto.martelli@cnr.it
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Phys. Rev. Research 7, 043305 – Published 16 December, 2025

DOI: https://doi.org/10.1103/9xrg-4684

Abstract

Controlling emergent structural order in spatially constrained systems is a fundamental challenge. Using large-scale simulations of a model fluid at equilibrium conditions, we show that geometric confinement alone can stabilize fluid and hyperuniform labyrinthine phases. Moreover, confinement can induce self-assembly into distinct regimes—ranging from nonhyperuniform to antihyperuniform configurations—providing a robust mechanism for tuning spatial order. Our results identify confinement as a minimal design principle for engineering systems with target structural properties, including (anti)hyperuniformity, without relying on genetic or chemical specificity, and with broad applications in multiple disciplines and technologies.

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References (70)

  1. J. M. Drake and J. Klafter, Dynamics of confined molecular systems, Phys. Today 43(5), 46 (1990).
  2. F. Leoni and G. Franzese, Structural behavior and dynamics of an anomalous fluid between attractive and repulsive walls: Templating, molding, and superdiffusion, J. Chem. Phys. 141, 174501 (2014).
  3. F. Leoni, C. Calero, and G. Franzese, Nanoconfined fluids: Uniqueness of water compared to other liquids, ACS Nano 15, 19864 (2021).
  4. J. Mittal, T. M. Truskett, J. R. Errington, and G. Hummer, Layering and position-dependent diffusive dynamics of confined fluids, Phys. Rev. Lett. 100, 145901 (2008).
  5. M. C. Stewart and R. Evans, Phase behavior and structure of a fluid confined between competing (solvophobic and solvophilic) walls, Phys. Rev. E 86, 031601 (2012).
  6. A. Zaragoza, M. A. González, L. Joly, I. López-Montero, M. A. Canales, A. L. Benavides, and C. Valeriani, Molecular dynamics study of nanoconfined TIP4P/2005 water: How confinement and temperature affect diffusion and viscosity, Phys. Chem. Chem. Phys. 21, 13653 (2019).
  7. L. B. Krott and M. C. Barbosa, Anomalies in a waterlike model confined between plates, J. Chem. Phys. 138, 084505 (2013).
  8. T. M. Truskett, P. G. Debenedetti, and S. Torquato, Thermodynamic implications of confinement for a waterlike fluid, J. Chem. Phys. 114, 2401 (2001).
  9. A. Zaccone and K. Trachenko, Explaining the low-frequency shear elasticity of confined liquids, Proc. Natl. Acad. Sci. USA 117, 19653 (2020).
  10. T.-D. Li and E. Riedo, Nonlinear viscoelastic dynamics of nanoconfined wetting liquids, Phys. Rev. Lett. 100, 106102 (2008).
  11. I. Williams, E. C. Oğuz, T. Speck, P. Bartlett, H. Löwen, and C. P. Royall, Transmission of torque at the nanoscale, Nat. Phys. 12, 98 (2016).
  12. C. Alba-Simionesco, B. Coasne, G. Dosseh1, G. Dudziak, K. E. Gubbins, R. Radhakrishnan, and M. Sliwinska-Bartkowiak, Effects of confinement on freezing and melting, J. Phys.: Condens. Matter 18, R15 (2006).
  13. H. K. Christenson, Confinement effects on freezing and melting, J. Phys.: Condens. Matter 13, R95 (2001).
  14. A. D. Virgiliis, R. L. C. Vink, J. Horbach, and K. Binder, Colloid-polymer mixtures between asymmetric walls: Evidence for an interface localization transition, Europhys. Lett. 77, 60002 (2007).
  15. V. Kapil, C. Schran, A. Zen, J. Chen, C. J. Pickard, and A. Michaelides, The first-principles phase diagram of monolayer nanoconfined water, Nature (London) 609, 512 (2022).
  16. P. Ravindra, X. R. Advincula, C. Schran, A. Michaelides, and V. Kapil, Quasi-one-dimensional hydrogen bonding in nanoconfined ice, Nat. Commun. 15, 7301 (2024).
  17. S. Wan, X. Xi, H. Zhang, J. Ning, Z. Zheng, Z. Zhang, Y. Long, Y. Deng, P. Fan, D. Yang, T. Li, and A. Dong, Shape-mediated oriented assembly of concave nanoparticles under cylindrical confinement, ACS Nano 16, 21315 (2022).
  18. B. de Nijs, S. Dussi, F. Smallenburg, J. D. Meeldijk, D. J. Groenendijk, L. Filion, A. Imhof, A. van Blaaderen, and M. Dijkstra, Entropy-driven formation of large icosahedral colloidal clusters by spherical confinement, Nat. Mater. 14, 56 (2015).
  19. Y. Chen, Z. Yao, S. Tang, H. Tong, T. Yanagishima, H. Tanaka, and P. Tan, Morphology selection kinetics of crystallization in a sphere, Nat. Phys. 17, 121 (2021).
  20. E. G. Teich, G. V. Anders, D. Klotsa, J. Dshemuchadse, and S. C. Glotzer, Clusters of polyhedra in spherical confinement, Proc. Natl. Acad. Sci. USA 113, E669 (2016).
  21. F. Deißenbeck, H. Löwen, and E. C. Oğuz, Ground state of dipolar hard spheres confined in channels, Phys. Rev. E 97, 052608 (2018).
  22. P. Ball and R. Evans, The density profile of a confined fluid, Mol. Phys. 63, 159 (1988).
  23. J. F. Lutsko, Density functional theory of inhomogeneous liquids. II. A fundamental measure approach, J. Chem. Phys. 128, 184711 (2008).
  24. R. Messina and H. Löwen, Reentrant transitions in colloidal or dusty plasma bilayers, Phys. Rev. Lett. 91, 146101 (2003).
  25. L. B. Krott, T. Puccinelli, and J. R. Bordin, Core-softened colloid under extreme geometrical confinement, Soft Matter 20, 4681 (2024).
  26. F. Martelli, H.-Y. Ko, C. C. Borallo, and G. Franzese, Structural properties of water confined by phospholipid membranes, Front. Phys. 13, 136801 (2018).
  27. M. Chiricotto, F. Martelli, G. Giunta, and P. Carbone, Role of long-range electrostatic interactions and local topology of the hydrogen bond network in the wettability of fully and partially wetted single and multilayer graphene, J. Phys. Chem. C 125, 6367 (2021).
  28. F. Martelli, J. Crain, and G. Franzese, Network topology in water nanoconfined between phospholipid membranes, ACS Nano 14, 8616 (2020).
  29. Z. Wei, M. Chiricotto, J. D. Elliott, F. Martelli, and P. Carbone, Wettability of graphite under 2D confinement, Carbon 198, 132 (2022).
  30. A. Gabrielli, M. Joyce, and F. S. Labini, Glass-like universe: Real-space correlation properties of standard cosmological models, Phys. Rev. D 65, 083523 (2002).
  31. S. Torquato and F. H. Stillinger, Local density fluctuations, hyperuniformity, and order metrics, Phys. Rev. E 68, 041113 (2003).
  32. S. Atkinson, G. Zhang, A. B. Hopkins, and S. Torquato, Critical slowing down and hyperuniformity on approach to jamming, Phys. Rev. E 94, 012902 (2016).
  33. C. Laurent, P. M. Chaikin, J. P. Gollub, and D. J. Pine, Random organization in periodically driven systems, Nat. Phys. 4, 420 (2008).
  34. C. E. Zachary, Y. Jiao, and S. Torquato, Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings, Phys. Rev. Lett. 106, 178001 (2011).
  35. R. Xie, G. G. Long, S. J. Weigand, S. C. Moss, T. Carvalho, S. Roorda, M. Hejna, S. Torquato, and P. J. Steinhardt, Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor, Proc. Natl. Acad. Sci. USA 110, 13250 (2013).
  36. J. H. Weijs, R. Jeanneret, R. Dreyfus, and D. Bartolo, Emergent hyperuniformity in periodically driven emulsions, Phys. Rev. Lett. 115, 108301 (2015).
  37. D. Hexner and D. Levine, Hyperuniformity of critical absorbing states, Phys. Rev. Lett. 114, 110602 (2015).
  38. F. Martelli, S. Torquato, N. Giovambattista, and R. Car, Large-scale structure and hyperuniformity of amorphous ices, Phys. Rev. Lett. 119, 136002 (2017).
  39. F. Carollo, J. P. Garrahan, I. Lesanovsky, and C. Pérez-Espigares, Fluctuating hydrodynamics, current fluctuations, and hyperuniformity in boundary-driven open quantum chains, Phys. Rev. E 96, 052118 (2017).
  40. Q.-L. Lei, M. P. Ciamarra, and R. Ni, Nonequilibrium strongly hyperuniform fluids of circle active particles with large local density fluctuations, Sci. Adv. 5, eaau7423 (2019).
  41. Y. Zheng, L. Liu, H. Nan, Z.-X. Shen, G. Zhang, D. Chen, L. He, W. Xu, M. Chen, Y. Jiao, and H. Zhuang, Disordered hyperuniformity in two-dimensional amorphous silica, Sci. Adv. 6, eaba0826 (2020).
  42. T. Yanagishima, J. Russo, R. P. A. Dullens, and H. Tanaka, Towards glasses with permanent stability, Phys. Rev. Lett. 127, 215501 (2021).
  43. F. Martelli, Steady-like topology of the dynamical hydrogen bond network in supercooled water, PNAS Nexus 1, pgac090 (2022).
  44. M. Formanek, S. Torquato, R. Car, and F. Martelli, Molecular rotations, multiscale order, hyperuniformity, and signatures of metastability during the compression/decompression cycles of amorphous ices, J. Phys. Chem. B 127, 3946 (2023).
  45. S. D. Cengio, R. Mari, and E. Bertin, Giant density fluctuations in locally hyperuniform states, Phys. Rev. E 112, L042101 (2025).
  46. F. Martelli, B. G. Elmegreen, M. J. Zimoń, and K. M. Yeo, Hyperuniform and nearly hyperuniform neural networks, U.S. Patent Application US20240202508A1 (2024), https://patents.google.com/patent/US20240202508A1/en.
  47. Y. Wang, Z. Qian, H. Tong, and H. Tanaka, Hyperuniform disordered solids with crystal-like stability, Nat. Commun. 16, 1398 (2025).
  48. N. Oppenheimer, D. B. Stein, M. Y. B. Zion, and M. J. Shelley, Hyperuniformity and phase enrichment in vortex and rotor assemblies, Nat. Commun. 13, 804 (2022).
  49. Z. Ge, The hidden order of turing patterns in arid and semi-arid vegetation ecosystems, Proc. Natl. Acad. Sci. USA 120, e2306514120 (2023).
  50. W. Hu, L. Cui, M. Delgado-Baquerizo, R. Solé, S. Kéfi, M. Berdugo, N. Xu, B. Wang, Q.-X. Liu, and C. Xu, Causes and consequences of disordered hyperuniformity in global drylands, Proc. Natl. Acad. Sci. USA 122, e2504496122 (2025).
  51. S. Torquato, Hyperuniform states of matter, Phys. Rep. 745, 1 (2018).
  52. P. Vilaseca and G. Franzese, Isotropic soft-core potentials with two characteristic length scales and anomalous behaviour, J. Non-Cryst. Solids 357, 419 (2011).
  53. P. Vilaseca and G. Franzese, Softness dependence of the anomalies for the continuous shouldered well potential, J. Chem. Phys. 133, 084507 (2010).
  54. F. Leoni and G. Franzese, Effects of confinement between attractive and repulsive walls on the thermodynamics of an anomalous fluid, Phys. Rev. E 94, 062604 (2016).
  55. A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in 't Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, R. Shan, M. J. Stevens, J. Tranchida, C. Trott, and S. J. Plimpton, LAMMPS—A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales, Comput. Phys. Commun. 271, 108171 (2022).
  56. See Supplemental Material at http://link.aps.org/supplemental/10.1103/9xrg-4684 for additional details about the simulated model and supplementary analysis, which includes Ref. [70].
  57. Z. Ma and S. Torquato, Random scalar fields and hyperuniformity, J. Appl. Phys. 121, 244904 (2017).
  58. E. C. Oğuz, J. E. S. Socolar, P. J. Steinhardt, and S. Torquato, Hyperuniformity and anti-hyperuniformity in one-dimensional substitution tilings, Acta Cryst. A 75, 3 (2019).
  59. J. Kim and S. Torquato, Effect of imperfections on the hyperuniformity of many-body systems, Phys. Rev. B 97, 054105 (2018).
  60. Y. Zheng, Y.-W. Li, and M. P. Ciamarra, Hyperuniformity and density fluctuations at a rigidity transition in a model of biological tissues, Soft Matter 16, 5942 (2020).
  61. N. Osterman, D. Babic, I. Poberaj, J. Dobnikar, and P. Ziherl, Observation of condensed phases of quasiplanar core-softened colloids, Phys. Rev. Lett. 99, 248301 (2007).
  62. A. J. Dickstein, S. Erramilli, R. E. Goldstein, D. P. Jackson, and S. A. Langer, Labyrinthine pattern formation in magnetic fluids, Science 261, 1012 (1993).
  63. H. Feng, M. Dolejsi, N. Zhu, S. Yim, W. Loo, P. Ma, C. Zhou, G. S. W. Craig, W. Chen, L. Wan et al., Optimized design of block copolymers with covarying properties for nanolithography, Nat. Mater. 21, 1426 (2022).
  64. Y. Norizoe and T. Kawakatsu, Particle Monte Carlo simulation of string-like colloidal assembly in two and three dimensions, J. Chem. Phys. 137, 024904 (2012).
  65. D. P. Richman, R. M. Stewart, J. Hutchinson, and V. S. Caviness, Mechanical model of brain convolutional development, Science 189, 18 (1975).
  66. K. Efimenko, M. Rackaitis, E. Manias, A. Vaziri, L. Mahadevan, and J. Genzer, Nested self-similar wrinkling patterns in skins, Nat. Mater. 4, 293 (2005).
  67. E. Cerda, K. Ravi-Chandar, and L. Mahadevan, Wrinkling of an elastic sheet under tension, Nature (London) 419, 579 (2002).
  68. G. Malescio and G. Pellicane, Stripe phases from isotropic repulsive interactions, Nat. Mater. 2, 97 (2003).
  69. F. Leoni and Y. Shokef, Attraction controls the inversion of order by disorder in buckled colloidal monolayers, Phys. Rev. Lett. 118, 218002 (2017).
  70. S. Torquato, Structural characterization of many-particle systems on approach to hyperuniform states, Phys. Rev. E 103, 052126 (2021).

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Phys. Rev. Research 7, 043305– Published 16 December, 2025
  • Received 9 June 2025
  • Revised 13 October 2025
  • Accepted 26 November 2025
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