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Negative normal stress in semiflexible biopolymer gels

Nature Materials volume 6, pages 48–51 (2007)Cite this article

Abstract

When subject to stress or external loads, most materials resist deformation. Any stable material, for instance, resists compression—even liquids. Solids also resist simple shear deformations that conserve volume. Under shear, however, most materials also have a tendency to expand in the direction perpendicular to the applied shear stress, a response that is known as positive normal stress1. For example, wet sand tends to dilate when sheared, and therefore dries around our feet when we walk on the beach. In the case of simple solids, elastic rods or wires tend to elongate when subject to torsion2. Here, we show that networks of semiflexible biopolymers such as those that make up both the cytoskeleton of cells and the extracellular matrix exhibit the opposite tendency: when sheared between two plates, they tend to pull the plates together. We show that these negative normal stresses can be as large as the shear stress and that this property is directly related to the nonlinear strain-stiffening behaviour of biopolymer gels3.

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Figure 1: Relationship of normal stress to shear strain for semiflexible and flexible polymer hydrogels.
Figure 2: Negative normal stress is a common feature of semiflexible biopolymer gels.
Figure 3: Schematic diagram of the deformations leading to negative normal stress.
Figure 4: Concentration dependence of normal stress in fibrin gels and comparison with theoretical predictions.

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Acknowledgements

This work was supported by the US National Institutes of Health, the NSF MRSEC program, the CompInt program of the Elitenetzwerk Bayern, the (Netherlands) Foundation for Fundamental Research on Matter (FOM) and the NSF through the Kavli Institute for Theoretical Physics at the University of California. We are grateful to T. Lubensky and R. Bucki for helpful discussions.

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Authors and Affiliations

  1. Institute for Medicine and Engineering, University of Pennsylvania, 3340 Smith Walk, Philadelphia, Pennsylvania, 19104, USA

    Paul A. Janmey, Margaret E. McCormick, Sebastian Rammensee, Jennifer L. Leight & Penelope C. Georges

  2. Department of Physics and Astronomy, University of Pennsylvania, 209 S 33rd St, Philadelphia, Pennsylvania, 19104, USA

    Paul A. Janmey

  3. Physik-Department E22 Biophysik, Technische Universität, München, James-Franck-Str. 1, 85747, Garching, Germany

    Sebastian Rammensee

  4. Department of Physics and Astronomy, Vrije Universiteit Amsterdam, De Boelelaan, 1081, 1081HV Amsterdam, The Netherlands

    Fred C. MacKintosh

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  1. Paul A. Janmey
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Correspondence to Paul A. Janmey or Fred C. MacKintosh.

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Janmey, P., McCormick, M., Rammensee, S. et al. Negative normal stress in semiflexible biopolymer gels. Nature Mater 6, 48–51 (2007). https://doi.org/10.1038/nmat1810

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