---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '22288'
abstract:
- lang: eng
  text: 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  μ⁢m 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.
acknowledgement: The authors thank Katharine Jensen, Stefanie Heyden, Thomas Salez,
  Francesco Stellacci, Denis Bartolo, Francesco Picella, Hélène Delanoë-Ayari, Mathieu
  Leocmach, Antoine Bérut, Cécile Cottin-Bizonne, Anne-Laure Biance, and Oriane Talabart
  for useful discussions. We also thank the reviewers for excellent suggestions that
  substantively improved the manuscript.
article_number: '021063'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Nicolas
  full_name: Bain, Nicolas
  last_name: Bain
- first_name: Lawrence A.
  full_name: Wilen, Lawrence A.
  last_name: Wilen
- first_name: Dominic
  full_name: Gerber, Dominic
  last_name: Gerber
- first_name: Mengjie
  full_name: Zu, Mengjie
  id: 26dd9e7c-e86a-11eb-a854-82ac731c9ae2
  last_name: Zu
- first_name: Carl Peter
  full_name: Goodrich, Carl Peter
  id: EB352CD2-F68A-11E9-89C5-A432E6697425
  last_name: Goodrich
  orcid: 0000-0002-1307-5074
- first_name: Senthilkumar
  full_name: Duraivel, Senthilkumar
  last_name: Duraivel
- first_name: Kaarthik
  full_name: Varma, Kaarthik
  last_name: Varma
- first_name: Harsha
  full_name: Koganti, Harsha
  last_name: Koganti
- first_name: Robert W.
  full_name: Style, Robert W.
  last_name: Style
- first_name: Eric R.
  full_name: Dufresne, Eric R.
  last_name: Dufresne
citation:
  ama: Bain N, Wilen LA, Gerber D, et al. Multiscale interfacial mechanics of soft
    solids. <i>Physical Review X</i>. 2026;16(2). doi:<a href="https://doi.org/10.1103/8msx-l8s7">10.1103/8msx-l8s7</a>
  apa: Bain, N., Wilen, L. A., Gerber, D., Zu, M., Goodrich, C. P., Duraivel, S.,
    … Dufresne, E. R. (2026). Multiscale interfacial mechanics of soft solids. <i>Physical
    Review X</i>. American Physical Society. <a href="https://doi.org/10.1103/8msx-l8s7">https://doi.org/10.1103/8msx-l8s7</a>
  chicago: Bain, Nicolas, Lawrence A. Wilen, Dominic Gerber, Mengjie Zu, Carl Peter
    Goodrich, Senthilkumar Duraivel, Kaarthik Varma, Harsha Koganti, Robert W. Style,
    and Eric R. Dufresne. “Multiscale Interfacial Mechanics of Soft Solids.” <i>Physical
    Review X</i>. American Physical Society, 2026. <a href="https://doi.org/10.1103/8msx-l8s7">https://doi.org/10.1103/8msx-l8s7</a>.
  ieee: N. Bain <i>et al.</i>, “Multiscale interfacial mechanics of soft solids,”
    <i>Physical Review X</i>, vol. 16, no. 2. American Physical Society, 2026.
  ista: Bain N, Wilen LA, Gerber D, Zu M, Goodrich CP, Duraivel S, Varma K, Koganti
    H, Style RW, Dufresne ER. 2026. Multiscale interfacial mechanics of soft solids.
    Physical Review X. 16(2), 021063.
  mla: Bain, Nicolas, et al. “Multiscale Interfacial Mechanics of Soft Solids.” <i>Physical
    Review X</i>, vol. 16, no. 2, 021063, American Physical Society, 2026, doi:<a
    href="https://doi.org/10.1103/8msx-l8s7">10.1103/8msx-l8s7</a>.
  short: N. Bain, L.A. Wilen, D. Gerber, M. Zu, C.P. Goodrich, S. Duraivel, K. Varma,
    H. Koganti, R.W. Style, E.R. Dufresne, Physical Review X 16 (2026).
das_tickbox: '1'
dataavailabilitystatement: The data that support the findings of this article are
  openly available https://github.com/nicobain/Multiscale_interfacial_mechanics_soft_solids_data
date_created: 2026-07-13T09:40:54Z
date_published: 2026-06-30T00:00:00Z
date_updated: 2026-07-13T11:17:51Z
day: '30'
ddc:
- '530'
department:
- _id: CaGo
doi: 10.1103/8msx-l8s7
external_id:
  arxiv:
  - '2410.09158'
file:
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  date_created: 2026-07-13T11:16:47Z
  date_updated: 2026-07-13T11:16:47Z
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file_date_updated: 2026-07-13T11:16:47Z
has_accepted_license: '1'
intvolume: '        16'
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '06'
oa: 1
oa_version: Published Version
publication: Physical Review X
publication_identifier:
  issn:
  - 2160-3308
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
researchdata_availability: yes
scopus_import: '1'
status: public
supplementarymaterial: yes
title: Multiscale interfacial mechanics of soft solids
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  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
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...