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Water in motion: How charged semiflexible nanofibers affect self-diffusion of water

Hanno Holzinger1, Ahmad Reza Motezakker1, Sergey V. Dvinskikh2, Korneliya Gordeyeva1, Per Tomas Larsson1,3, and Daniel Söderberg1,3

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Phys. Rev. E 113, 065403 – Published 3 June, 2026

DOI: https://doi.org/10.1103/mbbj-6cnz

Abstract

Even at very low concentrations, the rheology of dispersions of charged semiflexible nanofibers differs from the rheology of the pure liquid, given the fiber charge, morphology, and interactions. At the nanoscale, the thermal motion of fibers is driven by the collective motion of the solvent molecules, but to what extent does the fiber presence and motion affect the self-diffusion of the liquid molecules? By studying the self-diffusion of water in dilute nanofiber dispersions using experiments and simulations, we can show that the interplay of fiber charge and motion on water mobility is more significant than the effect of the excluded volume caused by the charged particles.

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References (83)

  1. L. Feng, S. Li, and Y. Li, Super-hydrophobic surfaces: From natural to artificial, Adv. Mater. 14, 1857 (2002).
  2. Y. Zheng, H. Bai, Z. Huang, X. Tian, F. Q. Nie, Y. Zhao, J. Zhai, and L. Jiang, Directional water collection on wetted spider silk, Nature (London) 463, 640 (2010).
  3. E. L. Lindh, M. Bergenstråhle-Wohlert, C. Terenzi, L. Salmén, and I. Furó, Non-exchanging hydroxyl groups on the surface of cellulose fibrils: The role of interaction with water, Carbohydr. Res. 434, 136 (2016).
  4. M. Wohlert, T. Benselfelt, L. Wågberg, I. Furó, L. A. Berglund, and J. Wohlert, Cellulose and the role of hydrogen bonds: Not in charge of everything, Cellulose 29, 1 (2022).
  5. S. L. Berry and M. L. Roderick, Plant-water relations and the fibre saturation point, New Phytol. 168, 25 (2005).
  6. H. Voisin, L. Bergström, P. Liu, and A. P. Mathew, Nanocellulose-based materials for water purification, Nanomaterials 7, 57 (2017).
  7. K. Nakamura, T. Hatakeyama, and H. Hatakeyama, Studies on bound water of cellulose by differential scanning calorimetry, Text. Res. J. 51, 607 (1981).
  8. P. Chen, J. Wohlert, L. Berglund, and I. Furó, Water as an intrinsic structural element in cellulose fibril aggregates, J. Phys. Chem. Lett. 13, 5424 (2022).
  9. L. Solhi et al., Understanding nanocellulose-water interactions: Turning a detriment into an asset, Chem. Rev. 123, 1925 (2023).
  10. A. Etale, A. J. Onyianta, S. R. Turner, and S. J. Eichhorn, Cellulose: A review of water interactions, applications in composites, and water treatment, Chem. Rev. 123, 2016 (2023).
  11. H. O’Neill et al., Dynamics of water bound to crystalline cellulose, Sci. Rep. 7, 11840 (2017).
  12. L. Capolupo and V. Faraco, Green methods of lignocellulose pretreatment for biorefinery development, Appl. Microbiol. Biotechnol. 100, 9451 (2016).
  13. K. M. Roberts, D. M. Lavenson, E. J. Tozzi, M. J. McCarthy, and T. Jeoh, The effects of water interactions in cellulose suspensions on mass transfer and saccharification efficiency at high solids loadings, Cellulose 18, 759 (2011).
  14. P. Bettotti and M. Scarpa, Nanocellulose and its interface: On the road to the design of emerging materials, Adv. Mater. Interfaces 9, 2101593 (2022).
  15. A. R. Motezakker, A. Córdoba, T. Rosén, F. Lundell, and L. D. Söderberg, Effect of stiffness on the dynamics of entangled nanofiber networks at low concentrations, Macromolecules 56, 9595 (2023).
  16. N. Fakhri, F. C. MacKintosh, B. Lounis, L. Cognet, and M. Pasquali, Brownian motion of stiff filaments in a crowded environment, Science 330, 1804 (2010).
  17. M. Doi and S. F. Edwards, Dynamics of concentrated polymer systems. Part 1. Brownian motion in the equilibrium state, Chem. Soc., Faraday Trans. 74, 1789 (1978).
  18. T. Odijk, The statistics and dynamics of confined or entangled stiff polymers, Macromolecules 16, 1340 (1983).
  19. L. Leibler, M. Rubinstein, and R. H. Colby, Dynamics of reversible networks, Macromolecules 24, 4701 (1991).
  20. S. T. Milner, Unified entanglement scaling for flexible, semiflexible, and stiff polymer melts and solutions, Macromolecules 53, 1314 (2020).
  21. M. Fixman, Dynamics of semidilute polymer rods: An alternative to cages, Phys. Rev. Lett. 55, 2429 (1985).
  22. L. Geng, N. Mittal, C. Zhan, F. Ansari, P. R. Sharma, X. Peng, B. S. Hsiao, and L. D. Söderberg, Understanding the mechanistic behavior of highly charged cellulose nanofibers in aqueous systems, Macromolecules 51, 1498 (2018).
  23. I. Bitsanis, H. T. Davis, and M. Tirrell, Brownian dynamics of nondilute solutions of rodlike polymers. 1. Low concentrations, Macromolecules 21, 2824 (1988).
  24. J. H. Simpson and H. Y. Carr, Diffusion and nuclear spin relaxation in water, Phys. Rev. 111, 1201 (1958).
  25. K. Krynicki, C. D. Green, and D. W. Sawyer, Pressure and temperature dependence of self-diffusion in water, Faraday Discuss. Chem. Soc. 66, 199 (1978).
  26. W. S. Price, H. Ide, and Y. Arata, Self-diffusion of supercooled water to 238 K Using PGSE NMR diffusion measurements, J. Phys. Chem. A 103, 448 (1999).
  27. P. Garbacz and W. S. Price, 1H NMR diffusion studies of water self-diffusion in supercooled aqueous sodium chloride solutions, J. Phys. Chem. A 118, 3307 (2014).
  28. R. Hausser, G. Maier, and F. Noack, Nuclear magnetic measurements of self-diffusion coefficients in water and benzene up to the critical point, Z. fur Naturforsch.-J. Phys. Sci. 21, 1410 (1966).
  29. W. J. Lamb, G. A. Hoffman, and J. Jonas, Self-diffusion in compressed supercritical water, J. Chem. Phys. 74, 6875 (1981).
  30. K. R. Harris and L. A. Woolf, Pressure and temperature dependence of the self diffusion coefficient of water and oxygen-18 water, J. Chem. Soc. Faraday Trans. 76, 377 (1980).
  31. R. Mills, Self-diffusion in normal and heavy water in the range 1−45∘, J. Phys. Chem. 77, 685 (1973).
  32. L. G. Longsworth, The mutual diffusion of light and heavy water, J. Phys. Chem. 64, 1914 (1960).
  33. J. H. Wang, Self-diffusion and structure of liquid water. I. Measurement of self-diffusion of liquid water with deuterium as tracer, J. Am. Chem. Soc. 73, 510 (1951).
  34. J. H. Wang, Self-diffusion and structure of liquid water. II. Measurement of self-diffusion of liquid water with O18 as tracer, J. Am. Chem. Soc. 73, 4181 (1951).
  35. J. H. Wang, C. V. Robinson, and I. S. Edelman, Self-diffusion and structure of liquid water. III. Measurement of the self-diffusion of liquid water with H, H and O as tracers, J. Am. Chem. Soc. 75, 466 (1953).
  36. B. Medronho, A. Pereira, H. Duarte, L. Gentile, A. M. Rosa da Costa, A. Romano, and U. Olsson, Probing cellulose–solvent interactions with self-diffusion NMR: Onium hydroxide concentration and co-solvent effects, Carbohydr. Polym. 303, 120440 (2023).
  37. I. H. Sahputra, A. Alexiadis, and M. J. Adams, Effects of moisture on the mechanical properties of microcrystalline cellulose and the mobility of the water molecules as studied by the hybrid molecular mechanics–molecular dynamics simulation method, J. Polym. Sci. Part B Polym. Phys. 57, 454 (2019).
  38. S. Sudo, T. Kawaguchi, M. Asano, M. Fukuzaki, and S. Yagihara, Investigation of dynamical properties of free water in hydroxypropyl cellulose–water mixture by PFG-NMR, Phys. D Nonlinear Phenom. 438, 133348 (2022).
  39. A. Isogai, T. Saito, and H. Fukuzumi, TEMPO-oxidized cellulose nanofibers, Nanoscale 3, 71 (2011).
  40. D. H. Wu, A. Chen, and C. S. Johnson, An improved diffusion-ordered spectroscopy experiment incorporating bipolar-gradient pulses, J. Magn. Reson. Ser. A 115, 260 (1995).
  41. W. S. Price, Pulsed-field gradient nuclear magnetic resonance as a tool for studying translational diffusion: Part II, Experimental aspects Concepts Magn. Reson. 10, 197 (1998).
  42. E. O. Stejskal and J. E. Tanner, Spin diffusion measurements: Spin echoes in the presence of a time-dependent field gradient, J. Chem. Phys. 42, 288 (1965).
  43. M. Holz, S. R. Heil, and A. Sacco, Temperature-dependent self-diffusion coefficients of water and six selected molecular liquids for calibration in accurate H1 NMR PFG measurements, Phys. Chem. Chem. Phys. 2, 4740 (2000).
  44. See Supplemental Material at http://link.aps.org/supplemental/10.1103/mbbj-6cnz for tabulated diffusion coefficients, complementary experimental data and calculations as well as simulation details, which includes Refs. [45, 46, 47, 48, 49, 50, 51, 52].
  45. B. Ahlrichs and P. Dünweg, Lattice-Boltzmann simulation of polymer-solvent systems, Int. J. Mod. Phys. C 09, 1429 (2011).
  46. C. W. Jones, J. C. Wang, F. A. Ferrone, R. W. Briehl, and M. S. Turner, Interactions between sickle hemoglobin fibers, Farad. Discuss. 123, 221 (2003).
  47. I. Usov, G. Nyström, J. Adamcik, S. Handschin, C. Schütz, A. Fall, L. Bergström, and R. Mezzenga, Understanding nanocellulose chirality and structure–properties relationship at the single fibril level, Nat. Commun. 6, 7564 (2015).
  48. A. Paajanen, S. Ceccherini, T. Maloney, and J. A. Ketoja, Chirality and bound water in the hierarchical cellulose structure, Cellulose 26, 5877 (2019).
  49. S. K. Mudedla, M. Vuorte, E. Veijola, K. Marjamaa, A. Koivula, M. B. Linder, S. Arola, and M. Sammalkorpi, Effect of oxidation on cellulose and water structure: A molecular dynamics simulation study, Cellulose 28, 3917 (2021).
  50. W. M. Lee, Selection of barrier materials from molecular structure, Polym. Eng. Sci. 20, 65 (1980).
  51. A. Bondi, van der Waals volumes and radii, J. Phys. Chem. 68, 441 (1964).
  52. J. R. Scherer and B. A. Bolton, Water in polymer membranes. 5. On the existence of pores and voids, J. Phys. Chem. 89, 3535 (1985).
  53. A. R. Motezakker, L. G. Greca, E. Boschi, G. Siqueira, F. Lundell, T. Rosén, G. Nyström, and L. D. Söderberg, Stick, slide, or bounce: Charge density controls nanoparticle diffusion, ACS Nano 18, 28636 (2024).
  54. H. J. Limbach, A. Arnold, B. A. Mann, and C. Holm, ESPResSo-an extensible simulation package for research on soft matter systems, Comput. Phys. Commun. 174, 704 (2006).
  55. S. Ventura-Cruz and A. Tecante, Extraction and characterization of cellulose nanofibers from Rose stems (Rosa spp.), Carbohydr. Polym. 220, 53 (2019).
  56. W. T. Wulandari, A. Rochliadi, and I. M. Arcana, Nanocellulose prepared by acid hydrolysis of isolated cellulose from sugarcane bagasse, IOP Conf. Ser. Mater. Sci. Eng. 107, 012045 (2016).
  57. G. Zhang, F. Wu, T. Ma, B. Zhang, A. Manyande, and H. Du, Preparation and characterization of cellulose nanofibers isolated from lettuce peel, Cellul. Chem. Technol. 53, 677 (2019).
  58. J. D. Moon, T. R. Webber, D. R. Brown, P. M. Richardson, T. M. Casey, R. A. Segalman, M. S. Shell, and S. Han, Nanoscale water-polymer interactions tune macroscopic diffusivity of water in aqueous poly(ethylene oxide) solutions, Chem. Sci. 15, 2495 (2024).
  59. S. Beck-Candanedo, M. Roman, and D. G. Gray, Effect of reaction conditions on the properties and behavior of wood cellulose nanocrystal suspensions, Biomacromolecules 6, 1048 (2005).
  60. F. Cherhal, F. Cousin, and I. Capron, Influence of charge density and ionic strength on the aggregation process of cellulose nanocrystals in aqueous suspension, as revealed by small-angle neutron scattering, Langmuir 31, 5596 (2015).
  61. Y. N. Kryuchkov, Concentration dependence of the mean interparticle distance in disperse systems, Refract. Ind. Ceram 42, 390 (2001).
  62. A. Einstein, Investigations on the Theory of the Brownian Movement, new ed. (Dover, New York, 1978).
  63. I. L. Novak, P. Kraikivski, and B. M. Slepchenko, Diffusion in cytoplasm: Effects of excluded volume due to internal membranes and cytoskeletal structures, Biophys. J. 97, 758 (2009).
  64. B. Nyström, M. E. Moseley, W. Brown, and J. Roots, Molecular motion of small molecules in cellulose gels studied by NMR, J. Appl. Polym. Sci. 26, 3385 (1981).
  65. K. R. Hadley and C. McCabe, Coarse-grained molecular models of water: A review, Mol. Simul. 38, 671 (2012).
  66. F. Zipoli, T. Laino, S. Stolz, E. Martin, C. Winkelmann, and A. Curioni, Improved coarse-grained model for molecular-dynamics simulations of water nucleation, J. Chem. Phys. 139, 094501 (2013).
  67. O. O. Lebedenko, V. A. Salikov, S. A. Izmailov, I. S. Podkorytov, and N. R. Skrynnikov, Using NMR diffusion data to validate MD models of disordered proteins: Test case of N-terminal tail of histone H4, Biophys. J. 123, 80 (2024).
  68. I. C. Yeh and G. Hummer, System-size dependence of diffusion coefficients and viscosities from molecular dynamics simulations with periodic boundary conditions, J. Phys. Chem. B 108, 15873 (2004).
  69. I. Lado Touriño, A. C. Naranjo, V. Negri, S. Cerdán, and P. Ballesteros, Coarse-grained molecular dynamics simulation of water diffusion in the presence of carbon nanotubes, J. Mol. Graph. Model. 62, 69 (2015).
  70. R. A. Waggoner, F. D. Blum, and J. M. D. MacElroy, Dependence of the solvent diffusion coefficient on concentration in polymer solutions, Macromolecules 26, 6841 (1993).
  71. M. B. Mustafa, D. L. Tipton, M. D. Barkley, P. S. Russo, and F. D. Blum, Dye diffusion in isotropic and liquid crystalline aqueous (hydroxypropyl)cellulose, Macromolecules 26, 370 (1993).
  72. L. Masaro and X. X. Zhu, Physical models of diffusion for polymer solutions, gels and solids, Prog. Polym. Sci. 24, 731 (1999).
  73. P. Gao and P. E. Fagerness, Diffusion in HPMC gels. I. Determination of drug and water diffusivity by pulsed-field-gradient spin-echo NMR, Pharm. Res. 12, 955 (1995).
  74. R. I. Cukier, Diffusion of brownian spheres in semidilute polymer solutions, Macromolecules 17, 252 (1984).
  75. P. G. De Gennes, Dynamics of entangled polymer solutions. II. Inclusion of hydrodynamic interactions, Macromolecules 9, 594 (1976).
  76. H. Yasuda, C. E. Lamaze, and A. Peterlin, Diffusive and hydraulic permeabilities of water in water-swollen polymer membranes, J. Polym. Sci. Part A-2 Polym. Phys. 9, 1117 (1971).
  77. G. Choudalakis and A. D. Gotsis, Free volume and mass transport in polymer nanocomposites, Curr. Opin. Colloid Interface Sci. 17, 132 (2012).
  78. J. S. Mackie and P. Meares, The diffusion of electrolytes in a cation-exchange resin membrane I. Theoretical, Proc. A 232, 498 (1955).
  79. D. Topgaard and O. Söderman, Diffusion of water absorbed in cellulose fibers studied with H1 -NMR, Langmuir 17, 2694 (2001).
  80. V. Guccini, S. Yu, Z. Meng, E. Kontturi, F. Demmel, and G. Salazar-Alvarez, The impact of surface charges of carboxylated cellulose nanofibrils on the water motions in hydrated films, Biomacromolecules 23, 3104 (2022).
  81. E. L. Lindh, C. Terenzi, L. Salmén, and I. Furó, Water in cellulose: Evidence and identification of immobile and mobile adsorbed phases by H2 MAS NMR, Phys. Chem. Chem. Phys. 19, 4360 (2017).
  82. E. L. Perkins and W. J. Batchelor, Water interaction in paper cellulose fibres as investigated by NMR pulsed field gradient, Carbohydr. Polym. 87, 361 (2012).
  83. C. D. S. Brites et al., Decoding a percolation phase transition of water at ∼330 K with a nanoparticle ruler, J. Phys. Chem. Lett. 11, 6704 (2020).

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Phys. Rev. E 113, 065403– Published 3 June, 2026
  • Received 17 April 2025
  • Accepted 23 April 2026
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