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Spherical Confinement Generates Entropic Force to Accelerate Polymer Chain Detachment

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Abstract

To understand the dynamic process of polymer detachment, it is necessary to determine the mean detachment time of a single breakable link, which is modeled as a spring. Normally, this time can be viewed as the escape of a Brownian particle from the potential well of the spring. However, as the free dangling length of the polymer chain increases, the conformational entropy of the chain is affected by geometric confinement. It means that the wall exerts a repulsive force on the chain, resulting in accelerated link detachment from a macroscopic perspective. In this work, we investigate the effect of entropy on the detachment rate in the case where the substrate is spherical. We demonstrate that spherical confinement accelerates chain detachment both inside and outside the sphere. An analytical expression for the mean detachment time of breakable links is given, which includes an additional pre-factor that is related to the partition function. Additionally, we analyze the expressions for entropic forces inside the sphere, outside the sphere, and on a flat wall, comparing their magnitudes to explain the difference in mean detachment time.

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Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (No. 51965057), Xinjiang Tianchi PhD Project (No. TCBS202113), the Natural Science Foundation of Xinjiang (No. 2022D01C34), Xinjiang Basic Research Funds for Universities (No. XJEDU2022P017), Robot-Intelligent Equipment Technology Innovation (No. 2022D14002) and Xinjiang Tianshan Science Technology Innovation Leading Talents Program (No. 2022TSYCLJ0044).

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Authors and Affiliations

  1. Mechanical Engineering, Xinjiang University, Urumqi, 830002, China

    Yu-Shan Zheng, Jian-Ping Zhou, Yan Xu & Kai Li

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  1. Yu-Shan Zheng
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  2. Jian-Ping Zhou
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  3. Yan Xu
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Correspondence to Yan Xu or Kai Li.

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Zheng, YS., Zhou, JP., Xu, Y. et al. Spherical Confinement Generates Entropic Force to Accelerate Polymer Chain Detachment. Chin J Polym Sci 42, 407–416 (2024). https://doi.org/10.1007/s10118-023-3049-5

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