Understanding thin sheets, ranging from the macro to the nanoscale, can allow control of mechanical properties such as
deformability. Out-of-plane buckling due to in-plane compression can be a key feature in designing new materials. While
thin-plate theory can predict critical buckling thresholds for thin frames and nanoribbons at very low temperatures, a
unifying framework to describe the e↵ects of thermal fluctuations on buckling at more elevated temperatures presents
subtle difficulties. We develop and test a theoretical approach that includes both an in-plane compression and an outof-
plane perturbing field to describe the mechanics of thermalised ribbons above and below the buckling transition. We
show that, once the elastic constants are renormalised to take into account the ribbon’s width (in units of the thermal
length scale), we can map the physics onto a mean-field treatment of buckling, provided the length is short compared
to a ribbon persistence length. Our theoretical predictions are checked by extensive molecular dynamics simulations of
thin thermalised ribbons under axial compression.
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This content will become publicly available on January 1, 2025
Vibrations and transitions across barrier of strained nanoribbons at finite temperature
Crystalline sheets (e.g., graphene and transition metal dichalcogenides) liberated from a substrate are a paradigm for materials at criticality, because flexural phonons can fluctuate into the third dimension. Although studies of static critical behaviors (e.g., the scale-dependent elastic constants) are plentiful, investigations of dynamics remain limited. Here, we use molecular dynamics to study the time dependence of the midpoint (the height center of mass) of doubly clamped nanoribbons, as prototypical graphene resonators, under a wide range of temperature and strain conditions. By treating the ribbon midpoint as a Brownian particle confined to a nonlinear potential (which assumes a double-well shape beyond the buckling transition), we formulate an effective theory describing the ribbon's transition rate across the two wells and its oscillations inside a given well. We find that, for nanoribbbons compressed above the Euler buckling point and thermalized above a temperature at which the nonlinear effects due to thermal fluctuations become significant, the exponential term (the ratio between energy barrier and temperature) depends only on the geometry but not the temperature, unlike the usual Arrhenius behavior. Moreover, we find that the natural oscillation time for small strain shows a nontrivial scaling
τ
o
∼
L
z
0
T
−
η
/
4
, with
L
0
being the ribbon length,
z
=
2
−
η
/
2
being the dynamic critical exponent,
η
=
0.8
being the scaling exponent describing scale-dependent elastic constants, and
T
being the temperature. These unusual scale- and temperature-dependent dynamics thus exhibit dynamic criticality and could be exploited in the development of graphene-based nanoactuators.
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- Award ID(s):
- 2011754
- NSF-PAR ID:
- 10500514
- Publisher / Repository:
- APS
- Date Published:
- Journal Name:
- Physical Review Materials
- Volume:
- 8
- Issue:
- 1
- ISSN:
- 2475-9953
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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