**2.1 Definition of thermal conductivity in polymers**

In general, heat transfer takes place through three different mechanisms: convection, conduction, irradiation.

In a solid, the main mechanism of heat transport is the conduction corresponding to the transfer of particle vibration energy to the adjacent particles without any motion of the matter but exclusively due to collision [12].

In steady state condition, Fourier' law (Eq. (1)) [15] describes the heat conduction across a slab of solid material of surface area A and thickness Y whose sides are set at two different temperatures T1 e T0, respectively, in the direction normal to a slab surface (see **Figure 1**):

$$\mathbf{Q} = \mathbf{k} \, A \, \frac{\Delta T}{Y} \, \tag{1}$$

In Eq. (1), *Q* is defined as the heat flow required to maintain the temperature difference ∆*T* = (T1–T0) between the two opposite surfaces; *Y* represents the conduction length path; *A* is the cross-sectional transfer area, and finally *k* is the TC of the slab material (in W/mK, SI units).

In the 1932, Debye introduced the concept of mean free path of thermal waves, simply called phonons, for explaining the thermal conduction in a dielectric crystal, in which the electrons are not free to move. In this case, the TC has been described through the following expression, also called Debye equation (Eq. (2)):

$$k = \frac{c\_p \text{ ou } l}{3} \tag{2}$$

where *cp* is the specific heat capacity per unit of volume, *l* is the phonon mean free path and υ is the average phonon velocity.

Usually, the thermal conduction occurs through these phenomena: (i) by charge carriers as electrons and holes,also defined as energized electron motion; (ii) by phonons, i.e., energy quanta of atomic lattice vibrations due to atom interaction and collision and (iii) by photon conductivity verifiable only in the case of high temperature. Depending on the material's nature, the different phenomena do not always

**Figure 1.** *Heat conduction across a slab of a solid material.*

happen simultaneously, but one can dominate over the others. For example, in metals, the electronic contribution exceeds the phonon one; whereas in insulators, phonons contribution prevails over the electrons one [11–14]. Polymers are thermal insulators, and due to defects, grain boundaries, and/or scattering with other phonons the mean free path of phonons (l) is very low and consequently also their TC [16]. For most of thermoplastics, the TC at 25°C falls in the range of 0.11 W/mK (for polypropylene) and 0.44 W/mK (for high density polyethylene) [17].
