**Modelling of polymer based materials and devices are at the basis of the development of materials and applications**. Proper understanding of the electrical, mechanical and magnetoelectric properties, among others will be achieved through computer simulations involving multiscale approaches, form molecular dynamics to finite element methods. Particular attention is paid to the coupling between the different scales.

### Material Properties Device Simulation

### Main References

### Material Properties

Figure represents the phase diagram of the same solution. Among the black line and the red line is the meta-stable region where the pore formation occurs. These vary as a function of temperature and volume fraction. Theoretical example of a simulation of the micro-structure of a polymer solution, according to the Cahn-Hilliard equation and the Flory-Huggins theory.

Conductivity versus volume fraction for three different aspect ratios. Inset log–log plot.

The conductivity increases with increasing aspect ratio. Applying the power law (Fig. 2 inset) defined by the percolation theory, results in t = 1.0. The latter value for the critical exponent is equal to that predicted by the effective medium theory.

Results for random and nematic materials with different aspect ratios (AR 10 and AR 50). In the inset the log–log plot for the nematic materials.

From the error bars, it is concluded that the standard error is higher for the random materials. This is related to the effect of the minimum distance and the rotation angle on the local capacitance. For the anisotropic materials, a decrease of the standard error is observed due to the orientation of the cylinders. Also, based in Fig. 2, it can be concluded that: (a) increasing the aspect ratio will increase the dielectric constant (in agreement with recent experimental results for the MWCNT/PVDF composites; (b) nematic materials have a lower dielectric constant compared to isotropic ones.

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Coupled Multiscale: Micro-Macro. We consider a material homogenous at macro scale (a), once we go deep to the microstructure (b), we will find some heterogeneities such as inclusions (blue and red in figure) and voids (white). Here, d ≪ l ≪ L. Representative Volume Element (RVE) is a statistically representative sub-region of the microstructure (b). Mechanical properties of the nanoscale polymer (c) were simulated through Molecular Dynamics. This data was then used as input parameters for local microstructure analysis (b).

FEM Simulation of the ME effect in laminates bonded with M-Bond epoxy with PVDF thickness of a) 110μm, b) 52μm, and c) 28μm. Profiles of each laminate present different charge distribution patterns due to the ME effect, concluding that the ME response of PVDF based ME composites increases with increasing the thickness of PVDF layer. The color scale of the FEM simulation is represented on the right side of the image.

FEM Simulation of the ME effect in laminates with a PVDF thickness of 110 μm, bonded with three different epoxies of a) M-Bond, b) Devcon, and c) Stycast. Profiles of each laminate present different charge distribution patterns due to the ME effect, concluding that in the ME response of PVDF based ME composites are strongly influenced by the epoxy mechanical properties. The highest ME response was obtained for the epoxy with lowest Young Modulus (M-Bond), and the lowest response was obtained for the epoxy with highest Young Modulus (Stycast). This reveals that with higher Young Modulus, the epoxy loses its ability to transmit the deformation from the magnetostrictive layer to the piezoelectric layer, revealing an interface detachment. The color scale of the FEM simulation is represented on the right side of the image.

### Device Simulation

Development of the theoretical model simulation using adequate software with objective of predicting the influence of some parameters at battery performance according to the objectives of the study.

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It is showed the acoustic beam response of a piston ultrasonic transducer. The result where obtained from a finite element method simulation using a 2D symmetric plane. The acoustic beam has a pattern characterized by its divergence angle, which depends on the transducer diameter and on the wavelength. In the figure 1 it is possible to see the near field, far field and the beam divergence angle (δ).

The Figure shows the acoustic pressure wave along the transducer thickness and the medium when positioned at the center of the acoustic pattern. The transducer dimensions were defined to operate at 1 MHz resonance frequency, resulting in a 2.05 mm thickness for PZT-5H and 1.125 mm for PVDF, and a diameter with 2.5 times the wavelengths.

These signals were obtained from a FEM simulations using Comsol Multiphysics platform in a 2D symmetric plane with the Piezo Strain Plane models for the active element actuation and the Pressure Acoustic model for the pressure waves. The selected mesh is divided in areas with triangular shape and a size of 10% of the wavelength. The simulations were performed with the following settings: fresh water as propagation medium, 20 C˚ of temperature.

### Main References

- Martins, M., Correia, V., Cabral, J.M., Lanceros-Mendez, S., Rocha, J.G. Optimization of piezoelectric ultrasound emitter transducers for underwater communications. Sensors and Actuators, A: Physical(2012), 184, pp. 141-148. DOI: http://dx.doi.org/10.1016/j.sna.2012.06.008.
- M. S. Martins, V. Correia, S. Lanceros-Mendez, J. M. Cabral, J. G. Rocha, "Comparative finite element analyses of piezoelectric ceramics and polymers at high frequency for underwater wireless communications", Proc. Eurosensors XXIV, September 5-8, 2010, Linz, Austria. DOI: http://dx.doi.org/10.1016/j.proeng.2010.09.057.
- M. Silva, S. Reis. C. S. Lehmann,P. Martins, S. Lanceros-Méndez, A. Lasheras, J. Gutierrez, J. M. Barandiaran. Optimization of the magentoelectric response of poly(vinylidene fluoride)/epoxy/Vitrovac laminates. ACS Appl. Mater. Interfaces (2013). Doi: 10.1021/am4031054.
- Ref para Figure2.tif: Simoes, R., Silva, J., Lanceros-Mendez, S., & Vaia, R. (2009). Influence of fiber aspect ratio and orientation on the dielectric properties of polymer-based nanocomposites. Journal of Materials Science, 45(1), 268–270. doi:10.1007/s10853-009-3937-2.
- Silva, J., Ribeiro, S., Lanceros-Mendez, S., & Simões, R. (2011). The influence of matrix mediated hopping conductivity, filler concentration, aspect ratio and orientation on the electrical response of carbon nanotube/polymer nanocomposites. Composites Science and Technology, 71, 643–646. Doi:10.1016/j.compscitech.2011.01.005.