, Volume 19, Issue 6, pp 1821–1836 | Cite as

Deformation of cellulose nanocrystals: entropy, internal energy and temperature dependence

  • Jakob WohlertEmail author
  • Malin Bergenstråhle-Wohlert
  • Lars A. Berglund
Original Paper


An in-depth analysis was performed of the molecular deformation mechanisms in cellulose during axial stretching. For the first time, it was demonstrated that entropy affects the stiffness of cellulose nanocrystals significantly. This was achieved through Molecular Dynamics simulations of model nanocrystals subject to constant stress in the axial direction, for nanocrystals of varying lateral dimensions and at different temperatures. The simulations were analyzed in terms of Young’s modulus E, which is a measure of the elastic response to applied stress. A weak but significant temperature dependence was shown, with ∂E/∂T =  −0.05 Gpa K−1 at room temperature, in agreement with experimental numbers. In order to analyze the respective contributions from internal energy and entropy, a decomposition of the total response of the free energy with respect to strain was made. It was shown that the decrease in E with increasing T is due to entropy, and that the magnitude of the decrease is 6–9 % at room temperature compared to the value at 0 K. This was also shown independently by a direct calculation of the vibrational entropy of the cellulose crystal. Finally, it was found that internal hydrogen bonds are contributing to the stiffness by 20 %, mainly by stabilizing the cellulose internal structure.


Elastic modulus Cellulose nanocrystals Molecular dynamics Temperature dependence 



The authors thank Y. Nishiyama for bringing the work of Nakamoe and Nishino (1998) to their attention, C. Smith for helping with the translation, and P. T. Larsson for helpful discussions. Computer time was provided by PDC Center for High Performance Computing at KTH Royal Institute of Technology. Molecular graphics were produced using VMD (Humphrey et al. 1996).

Supplementary material

10570_2012_9774_MOESM1_ESM.pdf (51 kb)
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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Jakob Wohlert
    • 1
    Email author
  • Malin Bergenstråhle-Wohlert
    • 1
  • Lars A. Berglund
    • 1
  1. 1.Wallenberg Wood Science CenterKTH Royal Institute of TechnologyStockholmSweden

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