## 3 Results and Discussion
### Rubber Composites Preparation and Characterization
#### 3.2.6 Anisotropic Properties  
In order to investigate the anisotropic mechanical behavior of the systems, DMA tests were carried out on specimens taken from plates in shear-sandwich configuration. This approach was selected instead of using an RPA machine for two reasons. Firstly, the production process of the plate (two-roll mill followed by compression molding) favors a layered structuring of lamellar nanographite, as already investigated by some of the authors [31]. Secondly, the use of parallelepiped-shaped specimens enables modifying the loading configuration from a through-thickness (TT) to an in-plane (IP) application of the shear load (see Figure 1) without altering the specimen geometry.  
Table 7 shows the data of storage modulus at minimum (0.02%) and at maximum (21%) shear strain amplitude, both in IP and TT configuration (as specified in the subscripts): G\({}^{\prime}\)IP0,02% and G\({}^{\prime}\)TT,0.02% and G\({}^{\prime}\)IP21%, respectively. Moreover, it shows the maximum values for the loss modulus: G\({}^{\prime\prime}\)max,IP and G\({}^{\prime\prime}\)max,TT.  
For each of these parameters, the effect of anisotropy was evaluated in terms of a conveniently defined anisotropy index, calculated as the ratio of the value in IP over the value in TT configuration: anisotropy index equal to 1 indicates an isotropic behavior for the material, whereas a value higher than 1 means that the material has an anisotropic behavior. In the latter case, it was observed [31] that HSAG, in a rubber composite prepared with the same procedure adopted in the present work, led to an orthotropic and transversally isotropic behavior. All data are in Table 7.  
Figure 7: HKV curves of the rubber composites incorporating silica, silica/HSAG, and silica/HSAG-SP measured at day zero (dashed line) and after a 7-day aging (continuous line). The graph shows the amount of silica (in mm\({}^{3}\)) released by the instrument vs. time.  
Data in Table 7 indicate that the neat elastomeric matrix is isotropic, as expected. The systems with only HSAG showed an anisotropy index slightly higher than 1 only for storage moduli at small strain amplitude. It has been reported [31] that an anisotropic behavior of the rubber composite can be observed when HSAG is above its percolation threshold, and this is not the case of the material studied in this work. To account for the anisotropy index slightly higher than 1 at low strain, it could be commented that HSAG agglomerates present at rest some preferential orientation, which is disrupted by the strain application. Very similar results were obtained with the silica-filled composite. Silica aggregates are not expected to give rise to a clearly detectable anisotropy. It was reported [34] that aggregates of CB (CB N220) could show some anisotropy \"in the form of a reduction of aggregate breadth, or flatness, in one direction\". However, it was also reported that also perfectly spherical particles can give rise to an anisotropic behavior, if not homogeneously dispersed. The addition of HSAG, either pristine or functionalized, to the silica-based composite did not substantially modify the anisotropic behavior of the composite. However, an increase in the anisotropy index can be observed in Table 7, both at low and large strain amplitudes, as if the lamellar filler was able to provide an anisotropic behavior to the hybrid filler system.