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Entropic force between biomembranes

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Abstract

Undulation force, an entropic force, stems from thermally excited fluctuations, and plays a key role in the essential interactions between neighboring surfaces of objects. Although the characteristics of the undulation force have been widely studied theoretically and experimentally, the distance dependence of the force, which constitutes its most fundamental characteristic, remains poorly understood. In this paper, first, we obtain a novel expression for the undulation force by employing elasticity and statistical mechanics and prove it to be in good agreement with existing experimental results. Second, we clearly demonstrate that the two representative forms of the undulation force proposed by Helfrich and Freund were respectively the upper and lower bounds of the present expression when the separation between membranes is sufficiently small, which was intrinsically different from the existing results where Helfrich’s and Freund’s forms of the undulation force were only suitable for the intermediate and small separations. The investigations show that only in a sufficiently small separation does Helfrich’s result stand for the undulation force with a large wave number and Freund’s result express the force with a small wave number. Finally, a critical acting distance of the undulation force, beyond which the entropic force will rapidly decay approaching zero, is presented.

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Acknowledgments

The project was supported by the programs in the National Natural Science Foundation of China (Grants 11232013 and 11472285). L. Li thanks L.B. Freund and R. Lipowsky for insightful discussions. F. Song is very grateful to Y.L. Bai of State Key Laboratory of Nonlinear Mechanics and F.J. Ke of Beijing University of Aeronautics and Astronautics for helpful discussions.

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Authors and Affiliations

  1. State Key Laboratory of Nonlinear Mechanics (LNM) and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China

    Long Li & Fan Song

  2. School of Engineering Science, University of Chinese Academy of Sciences, Beijing, 100049, China

    Long Li & Fan Song

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  1. Long Li
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  2. Fan Song
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Correspondence to Fan Song.

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Li, L., Song, F. Entropic force between biomembranes. Acta Mech. Sin. 32, 970–975 (2016). https://doi.org/10.1007/s10409-016-0588-9

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  • DOI: https://doi.org/10.1007/s10409-016-0588-9

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