**2.2 Methods for measuring the thermal conductivity of polypropylene-based materials**

The classical steady state (SS) and non steady-state (NSS) methods are the two main techniques for evaluating the TC of a material. In the first case, the measurement is carried out after reaching the equilibrium state, while in the second case, the test is performed during the heating phase [18].

The SS mode allows measurements on glass, polymers, insulators, ceramics, metals, composites with an uncertainty of 2–3%; the NSS mode permits to extend the testing also of liquids, gases or powders with an uncertainty up to 10% [12]. However, the first approach is more time consuming and not suitable for shaped samples as concentric cylinder or sphere.

In the SS method, the principle of operation is based on Fourier' law, while in the NSS method, the TC is indirectly evaluated by measuring the thermal diffusivity (α), according to Eq. (3):

$$k = \mathbf{u} \, c\_p \, \text{p} \tag{3}$$

Here, *cp* and ρ are the heat capacity and the density of the tested material, respectively.

The common apparatuses for evaluating the performance in heat transport of PP and its related compounds are: the "Guarded Hot Plate Method (GHPM)" and the "Heat Flow Meter Method (HFMM)", based on SS approach, or the "Flash Method (FM)" and the "Transient Hot Wire Method (THWM)", instead based on NSS approach.

The differences among these techniques are found essentially in required time for testing and operation mode [19].

The GHPM (**Figure 2a**) is constituted by a hot plate, placed between two samples of the examining material. The outer side of each specimen is in contact with a cold surface. A known heat flow (i.e., the heating power) is applied to one side of the sample and passes through it by establishing a temperature gradient between the two opposite faces of the sample. At steady-state, the TC is evaluated by measuring the difference in temperature and applying the Eq. (1).

The layout of the HFMM (**Figure 2b**) is very close to the GHPM apparatus designed for a single sample, but the first arrangement is faster and more accurate with respect to the second one [18]. The principal difference concerns the replacement of the main heater with heat flux sensor (HFT) [12].

In the FM (**Figure 2c**), a short but intense energy pulse is sent to one side of the sample and the temperature increase is measured on the opposed side in function of time. The thermal diffusivity can be calculated by Parker Formula (Eq. (4)) [20]:

$$\mathbf{u} = \frac{\mathbf{1}.38 \, d^2}{\mathbf{t}\_{1/2}} \tag{4}$$

**41**

Eq. (5) [21]:

**Figure 2.**

*<sup>k</sup>* <sup>=</sup> *<sup>q</sup>* \_\_\_\_\_\_\_\_\_\_

radius and T0 is the cell temperature.

*Thermal Conductivity of Polypropylene-Based Materials DOI: http://dx.doi.org/10.5772/intechopen.84477*

The THWM (**Figure 2d**) implicates vertical or cylindrical geometry in which a wire, generally of platinum, is crossed by a constant electric current. A radial heat flow takes place around the wire that spreads in the tested sample. The TC is estimated, knowing the temperature profile on time (T(t)) and the heat output by

*Schematic representation of TC measuring devices: (a) GHPM; (b) HFMM; (c) FM; (d) THWM.*

<sup>4</sup>*π*(*T*(*t*) <sup>−</sup> *<sup>T</sup>*0) *ln*(

in which ln C is the Euler's constant, q is the applied thermal flow, r is the wire

Finally, also differential scanning calorimetry (DSC) has been considered as a technique for measuring the TC of solid materials. The analysis has been performed by incorporating a temperature sensor [22] or a made in-house accessory into the common apparatus [23]. It is possible also utilized the standard DSC machine, without any special modification or calibration, by setting a specific temperature-

The TC of polymers is affected by several factors as crystallinity, chemical constituent, bond strength, molecular weight, side pendent groups, defects or

Anderson [16] reported that the TC of polymers decreased as the disorder increased: imperfections, by decreasing the order of the molecular structure, caused a large phonon scattering that reduced the heat transport. Since the polymeric

time profile and recording the dynamic response of the sample [24].

**2.3 Factors affecting the thermal conductivity of polypropylene**

structural faults, processing conditions and temperature [14].

\_\_\_ 4*t*

*<sup>r</sup>*<sup>2</sup>*C*) (5)

where d is the sample's thickness and t1/2 is the time required for the signal to reach the 50% of its maximum value.

*Thermal Conductivity of Polypropylene-Based Materials DOI: http://dx.doi.org/10.5772/intechopen.84477*

*Polypropylene - Polymerization and Characterization of Mechanical and Thermal Properties*

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].

the test is performed during the heating phase [18].

samples as concentric cylinder or sphere.

for testing and operation mode [19].

**materials**

according to Eq. (3):

respectively.

approach.

**2.2 Methods for measuring the thermal conductivity of polypropylene-based** 

The classical steady state (SS) and non steady-state (NSS) methods are the two main techniques for evaluating the TC of a material. In the first case, the measurement is carried out after reaching the equilibrium state, while in the second case,

The SS mode allows measurements on glass, polymers, insulators, ceramics, metals, composites with an uncertainty of 2–3%; the NSS mode permits to extend the testing also of liquids, gases or powders with an uncertainty up to 10% [12]. However, the first approach is more time consuming and not suitable for shaped

In the SS method, the principle of operation is based on Fourier' law, while in the NSS method, the TC is indirectly evaluated by measuring the thermal diffusivity (α),

*k* = α *cp* ρ (3)

The common apparatuses for evaluating the performance in heat transport of PP and its related compounds are: the "Guarded Hot Plate Method (GHPM)" and the "Heat Flow Meter Method (HFMM)", based on SS approach, or the "Flash Method (FM)" and the "Transient Hot Wire Method (THWM)", instead based on NSS

The differences among these techniques are found essentially in required time

The GHPM (**Figure 2a**) is constituted by a hot plate, placed between two samples of the examining material. The outer side of each specimen is in contact with a cold surface. A known heat flow (i.e., the heating power) is applied to one side of the sample and passes through it by establishing a temperature gradient between the two opposite faces of the sample. At steady-state, the TC is evaluated

The layout of the HFMM (**Figure 2b**) is very close to the GHPM apparatus designed for a single sample, but the first arrangement is faster and more accurate with respect to the second one [18]. The principal difference concerns the replace-

In the FM (**Figure 2c**), a short but intense energy pulse is sent to one side of the sample and the temperature increase is measured on the opposed side in function of time. The thermal diffusivity can be calculated by Parker Formula (Eq. (4)) [20]:

*t*1/2

where d is the sample's thickness and t1/2 is the time required for the signal to

(4)

by measuring the difference in temperature and applying the Eq. (1).

ment of the main heater with heat flux sensor (HFT) [12].

<sup>α</sup> <sup>=</sup> 1.38 *<sup>d</sup>*<sup>2</sup> \_\_\_\_\_\_\_\_\_\_

reach the 50% of its maximum value.

Here, *cp* and ρ are the heat capacity and the density of the tested material,

**40**

**Figure 2.** *Schematic representation of TC measuring devices: (a) GHPM; (b) HFMM; (c) FM; (d) THWM.*

The THWM (**Figure 2d**) implicates vertical or cylindrical geometry in which a wire, generally of platinum, is crossed by a constant electric current. A radial heat flow takes place around the wire that spreads in the tested sample. The TC is estimated, knowing the temperature profile on time (T(t)) and the heat output by Eq. (5) [21]:

$$k = \frac{q}{4\pi (T(t) - T\_0)} \ln\left(\frac{4ta}{r^2 C}\right) \tag{5}$$

in which ln C is the Euler's constant, q is the applied thermal flow, r is the wire radius and T0 is the cell temperature.

Finally, also differential scanning calorimetry (DSC) has been considered as a technique for measuring the TC of solid materials. The analysis has been performed by incorporating a temperature sensor [22] or a made in-house accessory into the common apparatus [23]. It is possible also utilized the standard DSC machine, without any special modification or calibration, by setting a specific temperaturetime profile and recording the dynamic response of the sample [24].

## **2.3 Factors affecting the thermal conductivity of polypropylene**

The TC of polymers is affected by several factors as crystallinity, chemical constituent, bond strength, molecular weight, side pendent groups, defects or structural faults, processing conditions and temperature [14].

Anderson [16] reported that the TC of polymers decreased as the disorder increased: imperfections, by decreasing the order of the molecular structure, caused a large phonon scattering that reduced the heat transport. Since the polymeric

structure order of the amorphous is lower than of the crystalline, the related thermal behaviour of the former has been expected to be lower compared to the latter, and also TC temperature dependence has changed in different ways depending on substance state. In details, below the glass temperature, as the temperature grew up, the TC of the amorphous remained the same or increased with temperature (probably for the effect of raising chain mobility), while for crystalline the TC initially remained the same and then diminished. Probably, in this second case, a decrease or/ and breakup of the crystalline portions have been promoted by higher temperatures after which the conductivity of the amorphous has been risen. These considerations were confirmed by studies of Bashirov et al. [25] and Osswald et al. [26],developed not only on PP, but also on high-density polyethylene (HDPE), low-density polyethylene (LDPE) and other polymers. On the contrary, an opposite trend of the TC of PP against temperature was found by dos Santos et al. [11]. In their work, the authors measured the TC of semi-crystalline and amorphous polymers starting from room temperature and going up to melting temperature (for semi-crystalline polymers) or glass transition (for amorphous polymers). Results showed that initially, as the temperature rose between 25 and 125°C, the TC of PP slight decreased from 0.25 to 0.15 W/mK; then, it underwent a sudden increase reaching a peak of approximately 0.47 W/mK during the melting process, and finally it decreased. In the temperature range of 2–100 K the TC of polypropylene was evaluated by Choy et al. [27]. In the case of isotropic crystalline conditions, an increasing trend that exhibited a maximum near 100 K was detected; then, when the sample was extruded and a marked anisotropy of TC was induced, the heat transport resulted in an order of magnitude increase in the extrusion direction. Finally, a nearly linear temperature dependence without any detectable plateau of the TC of PP copolymer was observed by Barucci et al. in the range of temperature from 0.1 to 4 K [28].

Most of the TC measurements of polymers have been carried out at atmospheric pressure, which is far from the operating process conditions. At regard, some measurements have been reported in order to verify the effect of pressure on TC of polymers. Dawson et al. [29] measured the thermal parameter for polypropylene at pressures of 20, 80 and 120 MPa over the temperature range from 250 to 50°C. For each pressure, the isobaric curve of TC as a function of temperature showed a "Z shaped", probably attributed to a phase transition (crystallization during cooling). Beyond an increase encountered during this phase, the TC remained fairly constant with the temperature. At an equal temperature, an increase of TC was always verified with pressure, approximately of 20% going from 20 to 120 MPa. Andersson et al. [30] performed measurements of heat conduction of PP at 300°K by changing pressure in the range between 0 and 37 bar. They concluded that, when the pressure was exercised on the sample, a stress in the longitudinal direction was generated, greater than in the radial direction, by leading to anisotropy of the properties in the tested material. Experimental data, related both to atactic and isotactic PP, demonstrated that the TC increased strongly with pressure with a continuous change in the slope of curve until it reached an asymptotic value.

From the above, the actualizing the anisotropy in a sample has implied an influence of its thermal transport behaviour. In fact, when the orientation has been induced in the polymer, its TC became higher in the direction of a molecular orientation and lower in a direction normal to the orientation [31]. This attitude was confirmed in the case of injection molding and extrusion [32] or foaming [33] processes during which a macromolecular orientation of polymer chain was inferred.

Finally, a characterization of the heat transport directly on the melted PP has been carried out because of in a common process the material was usually in the molten state. In fact, in a solid state the TC of semi-crystalline thermoplastics was greater with respect to melt state due to an increase of density upon the solidification. At regard,

**43**

**materials**

**Table 1.**

*Thermal Conductivity of Polypropylene-Based Materials DOI: http://dx.doi.org/10.5772/intechopen.84477*

*Data reported in literature on TC values of polypropylene.*

investigations about the effect of hydrostatic pressure, temperature, and chemical structure on the thermal conduction of melted PP have been performed [26]. These studies confirmed that, as the hydrostatic pressure increased on melt state, also the TC of thermoplastics in general, and of PP in particular, increased for a reduction in free volume. Furthermore, the TC of PP in molten form was not significantly affected by temperature but it appeared to be a complex function of the molecular weight distribution and possible long chain branching [34]. Generally, an increment of the TC of polymers by raising the molecular weight was verified since a larger number of energy

**Polypropylene TC (W/mK)** Han et al. [14] 0.11 Goswami et al. [35] 0.12–0.17 Maier et al. [36] 0.17–0.22 Tripathi [4], Guo et al. [37], Birley [38] 0.22

transactions took place in a substance with shorter chains [16]. In **Table 1** the TC values for polypropylene are shown.

**3.1 Thermally conductive fillers in polypropylene**

cal insulation of the starting material [39].

**3. Enhancement of thermal conduction in polypropylene-based** 

In general, the common approach for enhancing the thermal transport behaviour of plastics foresees the addition of thermally conductive particles. By balancing in the polymeric resin the filler content and type, it is possible to obtain the desired features in the final products. Yet, the use of an extremely high percentage of reinforcement (approximately more than 30% in vol.), is needed to achieve the TC values in the composites, required for the modern technologies. This quantity represents a real challenge for the processability of the material and makes difficult or impossible extrusion and injection molding processes [14]. In the last few decades, great attention has been devoted to polymeric nanomaterials, born from the introduction into the matrix of filler having at least one dimension in the order of 1–100 nm. Based on the geometric characteristics, three groups of nanosize particles are distinguished: one-dimensional (nanotubes and nanofibres), two-dimensional (layered minerals), three-dimensional (spherical particles). Small size and large surface area (for a given volume) of nanofiller are considered the key factors for the development of exceptional and unexpected properties with respect to macroworld as in the fields of mechanical properties, barrier resistance, flame retardancy, scratch/wear resistance, as well as optical, magnetic, TC and electrical properties [17]. Thermally conductive fillers can be divided into three categories: metallic powders, ceramic particles and carbon-based materials, and have been chosen depending on the needs to act both on the heat and current transport. For example, by adding carbon-based or metallic particles, the final compounds earned not only in terms of the thermal conduction but also in terms of the electric one; yet, metallic particles, having high specific gravities, could not be applied in the case of the lightweight target and carbon-based reinforcements have been preferred. Conversely, the introduction of ceramic fillers allowed acting on heat transfer of the neat matrix without compromising the electri*Thermal Conductivity of Polypropylene-Based Materials DOI: http://dx.doi.org/10.5772/intechopen.84477*


### **Table 1.**

*Polypropylene - Polymerization and Characterization of Mechanical and Thermal Properties*

structure order of the amorphous is lower than of the crystalline, the related thermal behaviour of the former has been expected to be lower compared to the latter, and also TC temperature dependence has changed in different ways depending on substance state. In details, below the glass temperature, as the temperature grew up, the TC of the amorphous remained the same or increased with temperature (probably for the effect of raising chain mobility), while for crystalline the TC initially remained the same and then diminished. Probably, in this second case, a decrease or/ and breakup of the crystalline portions have been promoted by higher temperatures after which the conductivity of the amorphous has been risen. These considerations were confirmed by studies of Bashirov et al. [25] and Osswald et al. [26],developed not only on PP, but also on high-density polyethylene (HDPE), low-density polyethylene (LDPE) and other polymers. On the contrary, an opposite trend of the TC of PP against temperature was found by dos Santos et al. [11]. In their work, the authors measured the TC of semi-crystalline and amorphous polymers starting from room temperature and going up to melting temperature (for semi-crystalline polymers) or glass transition (for amorphous polymers). Results showed that initially, as the temperature rose between 25 and 125°C, the TC of PP slight decreased from 0.25 to 0.15 W/mK; then, it underwent a sudden increase reaching a peak of approximately 0.47 W/mK during the melting process, and finally it decreased. In the temperature range of 2–100 K the TC of polypropylene was evaluated by Choy et al. [27]. In the case of isotropic crystalline conditions, an increasing trend that exhibited a maximum near 100 K was detected; then, when the sample was extruded and a marked anisotropy of TC was induced, the heat transport resulted in an order of magnitude increase in the extrusion direction. Finally, a nearly linear temperature dependence without any detectable plateau of the TC of PP copolymer was observed by Barucci

et al. in the range of temperature from 0.1 to 4 K [28].

slope of curve until it reached an asymptotic value.

Most of the TC measurements of polymers have been carried out at atmospheric

pressure, which is far from the operating process conditions. At regard, some measurements have been reported in order to verify the effect of pressure on TC of polymers. Dawson et al. [29] measured the thermal parameter for polypropylene at pressures of 20, 80 and 120 MPa over the temperature range from 250 to 50°C. For each pressure, the isobaric curve of TC as a function of temperature showed a "Z shaped", probably attributed to a phase transition (crystallization during cooling). Beyond an increase encountered during this phase, the TC remained fairly constant with the temperature. At an equal temperature, an increase of TC was always verified with pressure, approximately of 20% going from 20 to 120 MPa. Andersson et al. [30] performed measurements of heat conduction of PP at 300°K by changing pressure in the range between 0 and 37 bar. They concluded that, when the pressure was exercised on the sample, a stress in the longitudinal direction was generated, greater than in the radial direction, by leading to anisotropy of the properties in the tested material. Experimental data, related both to atactic and isotactic PP, demonstrated that the TC increased strongly with pressure with a continuous change in the

From the above, the actualizing the anisotropy in a sample has implied an influence of its thermal transport behaviour. In fact, when the orientation has been induced in the polymer, its TC became higher in the direction of a molecular orientation and lower in a direction normal to the orientation [31]. This attitude was confirmed in the case of injection molding and extrusion [32] or foaming [33] processes during which a macromolecular orientation of polymer chain was inferred. Finally, a characterization of the heat transport directly on the melted PP has been carried out because of in a common process the material was usually in the molten state. In fact, in a solid state the TC of semi-crystalline thermoplastics was greater with respect to melt state due to an increase of density upon the solidification. At regard,

**42**

*Data reported in literature on TC values of polypropylene.*

investigations about the effect of hydrostatic pressure, temperature, and chemical structure on the thermal conduction of melted PP have been performed [26]. These studies confirmed that, as the hydrostatic pressure increased on melt state, also the TC of thermoplastics in general, and of PP in particular, increased for a reduction in free volume. Furthermore, the TC of PP in molten form was not significantly affected by temperature but it appeared to be a complex function of the molecular weight distribution and possible long chain branching [34]. Generally, an increment of the TC of polymers by raising the molecular weight was verified since a larger number of energy transactions took place in a substance with shorter chains [16].

In **Table 1** the TC values for polypropylene are shown.
