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Nanomechanical resonators are built into phones, as filters or accelerometers, but they lack a knob to effectively tune the frequency at the nanoscale when it’s easy to tune on an octave the tone of a classical musical instrument like a guitar string. Moreover, the control of deformation in nanomaterials, as two-dimensional (2D) materials, to tailor their electronic properties, i.e., straintronic, opens up avenues for applications in force detection, bolometry or quantum emitters. An accurate control of the deformation within these materials is thus necessary to fully exploit their potential. The precise study of deformations in 2D materials involves measurements of vibration modes and nanomechanics. By using a suspended MoS₂membrane heated by the Joule effect, we induce a strong softening of the mechanical resonance frequency as a function of the electrothermal heating, over one octave. A simple electrical tension is used to modulate the thermal mechanical tuning. Its amplitude is very large, greater than 100% modulation for one volt, compared to other approaches on 2D or 1D materials and, moreover, a very wide frequency range is accessible. Finally, we have related a photo-induced softening of the membrane over very long times with the current measurements and a photothermal effect.

 

The synthesis of 1-butyl-2,3-dimethyl-4-vinylimidazolium triflate, its polymerization, and ion exchange to yield a trio of 1-butyl-2,3-dimethyl-4-vinylimidazolium polymers is described. Irrespective of the nature of the anion, substitution at the 2-position of the imidazolium moiety substantially increases the distance between the anion and cation. The methyl substituent at the 2-position also served to expose the importance of H-bonding for the attractive potential between imidazolium moiety and anions in polymers without a methyl group at the 2-position. The thermal characteristics of poly(1-butyl-2,3-dimethyl-4-vinylimidazolium) salts and corresponding poly(1-ethyl-3-methyl-4-vinylimidazolium) salts were evaluated. While the mid-point glass transition temperatures, Tg-mid, for 1-ethyl-3-methyl-4-vinylimidazolium polymers with CF3SO3−, (CF3SO2)2N− and PF6− counterions, were 153 °C, 88 °C and 200 °C, respectively, the Tg-mid values for 1-butyl-2,3-dimethyl-4vinylimidazolium polymers with corresponding counter-ions were tightly clustered at 98 °C, 99 °C and 84 °C, respectively. This dramatically reduced influence of the anion type on the glass transition temperature was attributed to the increased distance between the center of the anions and cations in the 1-butyl-2,3-dimethyl-4-vinylimidazolium polymer set, and minimal H-bonding interactions between the respective anions and the 1-butyl-2,3-dimethyl-4-vinylimidazolium moiety. It is believed that this is the first observation of substantial independence of the glass transition of an ionic polymer on the nature of its counterion. 

The flow in a Hele-Shaw cell with a time-increasing gap poses a unique shrinking interface problem. When the upper plate of the cell is lifted perpendicularly at a prescribed speed, the exterior less viscous fluid penetrates the interior more viscous fluid, which generates complex, time-dependent interfacial patterns through the Saffman–Taylor instability. The pattern formation process sensitively depends on the lifting speed and is still not fully understood. For some lifting speeds, such as linear or exponential speed, the instability is transient and the interface eventually shrinks as a circle. However, linear stability analysis suggests there exist shape invariant shrinking patterns if the gap $b(t)$ is increased more rapidly: $b(t)=\left (1-({7}/{2})\tau \mathcal {C} t\right )^{-{2}/{7}}$ , where $\tau$ is the surface tension and $\mathcal {C}$ is a function of the interface perturbation mode $k$ . Here, we use a spectrally accurate boundary integral method together with an efficient time adaptive rescaling scheme, which for the first time makes it possible to explore the nonlinear limiting dynamical behaviour of a vanishing interface. When the gap is increased at a constant rate, our numerical results quantitatively agree with experimental observations (Nase et al. , Phys. Fluids , vol. 23, 2011, 123101). When we use the shape invariant gap $b(t)$ , our nonlinear results reveal the existence of $k$ -fold dominant, one-dimensional, web-like networks, where the fractal dimension is reduced to almost unity at late times. We conclude by constructing a morphology diagram for pattern selection that relates the dominant mode $k$ of the vanishing interface and the control parameter $\mathcal {C}$ .