## 4 Properties
### Electrical Properties  
The introduction of conductive nanofillers in an insulator polymer matrix permits to modulate its electrical and dielectrical properties. Electrical properties are mainly investigated by analyzing the bulk conductivity by using a two probe method, or by surface conductivity. The conductivity of a typical polymer, such as APs, is in general less than \(10^{-12}\) ohm\({}^{-1}\)m\({}^{-1}\), that of semi-insulating or semiconductive materials covers the range \(10^{-12}\)-\(10\) ohm\({}^{-1}\)m\({}^{-1}\), and for semimetals and metals is greater than \(10\) ohm\({}^{-1}\)m\({}^{-1}\). Electrical conduction may occur through the movement of either electrons or ions. The volume resistivity is related to the measured resistance R between the electrodes by:  
\[\rho_{\rm V}=\frac{\rm RA}{1} \tag{3}\]  
where A and 1 are the cross-sectional area and the length of the specimen between the electrodes, respectively.  
The main problem in accurate measurement of resistivity is the contact resistance between the measurements electrode and specimens. This is clearly the case of samples with low resistivity. Contact resistance may be reduced by painting electrodes directly on to the surface of the specimen instead of relying on pressure contact with metal plates or foils. Suitable paints are silver dispersions. A much better way to deal with contact resistance is to use a 4-terminal, potentiometric method. The simplest configuration to be used with bulk is that of two current electrodes and two potential electrodes.  
The dielectric behavior of a conductive nanocomposite can be analyzed in a different range of frequencies. The complex permittivity of the materials can be viewed in terms of an equivalent parallel circuit, thus the specimen can be represented by a capacitance \(C\) in parallel with a Resistance \(R\). The total impedance will be given by:  
\[\frac{1}{Z}=\frac{1}{R}+i\omega C \tag{4}\]  
Application of the alternating voltage (V) represented by the real part of V will produce an out-of-phase or capacitive current (I\({}_{\rm c}\)) and an in-phase or resistive current (I\({}_{\rm R}\)).  
The analysis of the total impedance of the specimen in different frequency ranges allows for the understanding of the complex relative permittivity and dielectric loss that, in turn allows us to analyze the dielectric relaxation process.  
In AP-based nanocomposites it has been observed that the electrical conductivity increased with the CNT introduction and with the CNT weight content with respect to the neat polymer matrix. In fact, CNTs are conductive nanofillers with high aspect ratio: a higher amount of nanotubes create a larger path for the electrical current through the material. This effect is observed in polymers as PLLA, but also in PBCE and its copolymers, and it is mainly due to the CNT network formation, related to the CNT aspect ratio and processing method, which affected the filler dispersion [10; 11; 12; 13]. Some differences between the polymers can be observed for lower CNTs loadings, where the effect of the polymer matrix on the overall nanocomposite conductivity seems to be more relevant [10; 11; 12; 13]. Dielectric analyses confirmed that the conductive nature is predominant at low frequencies, while at higher frequencies the capacitive behavior provides a constant value for the phase curve [38].