Electrical conductivity is one of several outstanding features of graphene–polymer nanocomposites, but calculations of this property require the intricate features of the underlying conduction processes to be accounted for. To this end, a novel Monte Carlo method was developed. We first established a randomly distributed graphene nanoplatelet (GNP) network. Then, based on the tunneling effect, the contact conductance between the GNPs was calculated. Coated surfaces (CSs) were next set up to calculate the current flow from the GNPs to the polymer. Using the equipotential approximation, the potentials of the GNPs and CSs met Kirchhoff’s current law, and, based on Laplace equation, the potential of the CSs was obtained from the potential of the GNP by the walk-on-spheres (WoS) method. As such, the potentials of all GNPs were obtained, and the electrical conductivity of the GNP polymer composites was calculated. The barrier heights, polymer conductivity, diameter and thickness of the GNP determining the electrical conductivity of composites were studied in this model. The calculated conductivity and percolation threshold were shown to agree with experimental data.
In this paper, the magnetoelectric (ME) effect is investigated in two kinds of A-line shape Terfenol-D/PZT-5A structures by changing the position of the NdFeB permanent magnet. The experimental results show that both ME composite structures had multiple resonance peaks. For the ME structure with acrylonitrile-butadiene-styrene (ABS) trestles, the resonance peak was different for different places of the NdFeB permanent magnet. Besides, the maximum of the ME coefficient was 4.142 V/A at 32.2 kHz when the NdFeB permanent magnet was on top of the Terfenol-D layer. Compared with the ME coefficient with a DC magnetic field, the ME coefficient with NdFeB magnets still maintained high values in the frequency domain of 65~87 kHz in the ME structure with mica trestles. Through Fourier transform analysis of the transient signal, it is found that the phenomenon of multiple frequencies appeared at low field frequency but not at high field frequency. Moreover, the output ME voltages under different AC magnetic fields are shown. Changing the amplitude of AC magnetic field, the magnitude of the output voltage changed, but the resonant frequency did not change. Finally, a finite element analysis was performed to evaluate the resonant frequency and the magnetic flux distribution characteristics of the ME structure. The simulation results show that the magnetic field distribution on the surface of Terfenol-D is non-uniform due to the uneven distribution of the magnetic field around NdFeB. The resonant frequencies of ME structures can be changed by changing the location of the external permanent magnet. This study may provide a useful basis for the improvement of the ME coefficient and for the optimal design of ME devices.
Graphene agglomeration tends to develop with the increase of graphene loading. In this article, we present a unified model that first considers the evolution of graphene agglomeration and then incorporates it into the calculation of electrical and mechanical properties of agglomerated graphene/polymer nanocomposites. In the evolution of graphene agglomerates, a modified nanoparticle distance in terms of yield strength is introduced, while in the calculation of composite properties, a two‐scale framework that consists of the graphene‐rich agglomerates and the remainder as the graphene‐poor region is constructed. In electrical conduction, electron tunneling is modeled through Simmons formula and its difference with the widely used Cauchy function is compared. We highlight that both Simmons and Cauchy functions could well describe the interfacial tunneling activity, but the former is physics‐based while the latter is statistics‐based. In the calculation of nonlinear elastoplastic response, a field‐fluctuation method is adopted. We also demonstrated how the presented model gives rise to experimentally consistent electrical and mechanical properties of graphene/polypropylene nanocomposites, and how filler agglomeration hinders the performance of the materials.
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