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Multiscale Interfacial Mechanics of Soft Solids

Nicolas Bain1,2,*, Lawrence A. Wilen3, Dominic Gerber2, Mengjie Zu4, Carl P. Goodrich4, Senthilkumar Duraivel5, Kaarthik Varma6, Harsha Koganti5, Robert W. Style2 et al.

Eric R. Dufresne2,5,6

  • *Contact author: nicolas.bain@cnrs.fr
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Phys. Rev. X 16, 021063 – Published 30 June, 2026

DOI: https://doi.org/10.1103/8msx-l8s7

Abstract

Soft solids and their surface deformations control the response of many natural and artificial systems. Yet, their underlying properties are vigorously debated, particularly for polymer networks. While molecular-scale theories predict no interfacial changes with macroscopic deformation, multiple experiments suggest otherwise. To settle this issue, we measure displacement fields near the interface of a silicone gel, in the limit of small deformations. We discover an unexpected multiscale response. The shear modulus decreases smoothly by half with 20  μm of the interface. At the same time we observe a surface excess elasticity, that depends on history and outer medium composition. These results reveal the fundamentally multiscale nature of polymeric surfaces, and call for further experimental and theoretical investigations into the basic understanding of soft solid interfaces.

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While the deformation of soft solids underlies the function of many systems, from living cells to biomedical adhesives, their underlying mechanical response is vigorously debated. The confounding factor is that while the mechanical response of a typical solid is distributed throughout its bulk, a significant part of a soft solid’s response is localized to its surface. Here, we use high-precision 3D location and tracking of nanotracers to measure the deformation of a silicone gel. We find an unexpected multiscale response. Close to the interface we report a large elasticity gradient, over tens of microns, and an environment- and history-dependent surface elasticity, arising from a mechanical discontinuity over a submicron length scale. These results contrast with the scale-free elastic models widely used throughout science and engineering, and call for new experimental and theoretical investigations to understand, model, and design soft interfaces that account for their multiple intrinsic length scales.

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Phys. Rev. X 16, 021063– Published 30 June, 2026
  • Received 3 November 2025
  • Accepted 11 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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