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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Late Stage Domain Coarsening Dynamics of Lamellar Block Copolymers
The block copolymer (BCP) phase separation is an intriguing phenomenon, the dynamics of which can be expected to differ significantly from that of the polymer blends due to the chain connectivity constraints. The BCP phase separation dynamics has been studied theoretically, but there has been little experimental evidence to confirm the BCP domain growth scaling laws put forward by theoretical studies. Here, we demonstrate the dynamics of late-stage lamellar BCP domain coarsening and show that the scaling exponent for domain growth is ≈1/6 (0.17) irrespective of the annealing temperature, which is close to the scaling exponent of 0.2 shown by theoretical studies. Furthermore, we show that the pre-factors in the domain coarsening equation show Arrhenius dependence on temperature indicating that the BCP domain growth dynamics is Arrhenius.
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- Award ID(s):
- 1905996
- NSF-PAR ID:
- 10233587
- Editor(s):
- Segalman, Rachel
- Date Published:
- Journal Name:
- ACS Macro Letters
- Volume:
- 10
- ISSN:
- 2161-1653
- Page Range / eLocation ID:
- 727 to 731
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1021/acsmacrolett.1c00105
