Exploration of mechanical, thermal conductivity and electromechanical properties of graphene nanoribbon springs

Abstract

Recent experimental advances [Liu et al., npj 2D Mater. Appl., 2019, 3, 23] propose the design of graphene nanoribbon springs (GNRSs) to substantially enhance the stretchability of pristine graphene. A GNRS is a periodic undulating graphene nanoribbon, where undulations are of sinus or half-circle or horseshoe shapes. Besides this, the GNRS geometry depends on design parameters, like the pitch's length and amplitude, thickness and joining angle. Because of the fact that parametric influence on the resulting physical properties is expensive and complicated to examine experimentally, we explore the mechanical, thermal and electromechanical properties of GNRSs using molecular dynamics simulations. Our results demonstrate that the horseshoe shape design GNRS (GNRH) can distinctly outperform the graphene kirigami design concerning the stretchability. The thermal conductivity of GNRSs was also examined by developing a multiscale modeling, which suggests that the thermal transport along these nanostructures can be effectively tuned. We found that however, the tensile stretching of the GNRS and GNRH does not yield any piezoelectric polarization. The bending induced hybridization change results in a flexoelectric polarization, where the corresponding flexoelectric coefficient is 25% higher than that of graphene. Our results provide a comprehensive vision of the critical physical properties of GNRSs and may help to employ the outstanding physics of graphene to design novel stretchable nanodevices.

Fig. 1. Unit cell representation and definition of various structural parameters for the (a) sinus shape and (b) horseshoe shape graphene nanosprings.

Fig. 2. Stress–strain curves for (a) parameter set s_p – s_t – s_a in the GNRS, and (b) h_θ and h_r – h_t for the GNRH. (c) Standard deviation of the z− coordinates for the selected GNRS and GNRH systems. (d) Variation of the rupture strain and tensile strength (TS) for GNRS and GNRH systems with arc length. Solid lines indicate RS and dashed lines correspond to TS.

Fig. 3. Tensile deformed atomic configurations for (a–e) 18 – 3.2 – 5 GNRS and (f–j) 5 – 3.2 – 45° GNRH. The strain levels for the atomic snapshots are as follows: (a and f) 0.0, (b) 0.18, (c) 0.30, (d) 0.42, (e) 0.54, (g) 1.42, (h) 2.0, (i) 2.17 and (j) 2.23. The color bar indicates the stress values.

Fig. 4. Room temperature thermal conductivity for (a) parameter set s_p – s_t – s_a in the GNRS, (b) h_θ and (c) h_r – h_t for the GNRH as a function of correlation time. (d) Thermal conductivity of the graphene nanosprings at room temperature as a function of arc lengths. The insets in (d) illustrate the finite element modeling results for temperature distribution of the GNRS and GNRH in the diffusive regime.

Fig. 5. (a) Variation of polarization P_x with tensile strain. (b) Bending induced polarization P_z response with respect to the strain gradient. (c) Dependence of the flexoelectric coefficient μ_zxzx on the arc length of GNRS and GNRH systems. Legends indicate the respective atomic configurations used.

Fig. 6. Atomic configurations colored with dipole moment p_z for a strain gradient of 0.006 nm⁻¹. (a) 9 – 1.6 – 2.5 GNRS design. GNRH design with the inner radius 2.5 nm, thickness 1.6 nm and connecting angle h_θ at (b) 0°, (c) 15°, (d) 30° and (e) 45°. The dashed line indicates the middle portion of the atomic system.