Thermal conductivity (TC)

The thermal conductivity is commonly measured by flash laser method in axial direction of small cylinders, typically 6-15 mm diameter and 2-5 mm high. The small cylinders are machined in both parallel and perpendicular pressing directions in order to measure the thermal conductivity in parallel and perpendicular directions of pressing.

In opposite to CTE properties, TC of C/Cu composite materials is strongly linked with the thermal properties of the carbon fibres (CF) or vapor grown carbon nanofibres (VGCNF). Indeed, TC of CF along their main axis can go from 10 to 900 W/mK whereas TC are
constant perpendicular to CF main axis (close from 5 to 10 W/mK). Table 3 shows the evolution of CTE, TC and density of C/Cu composite materials for one type of CF (with TC = 140 W/mK in parallel to main axis). It can be seen that the thermal conductivity of composites materials decreases with volume fractions of fibres. However, the TC is strongly anisotropic, with 150 and 170 W. m-1.K-1 in perpendicular direction, and 210 and 250 W. m – 1.K-1 in parallel and perpendicular direction of multilayer samples for 40 and 30 vol. % fibres, respectively (table 3). Also, the strong anisotropy of carbon fibre properties (X// = -1 10-6 °C-1 in axis and X i=12 10-6 °C-1 in perpendicular axis of fibre) and orientation of fibres lead to strong anisotropic behaviour of thermal conductivity of Cu/C composite materials (table 3).

Material with %C

CTE

10-6 °C-1

Thermal Conductivity W. m-i. K-i

Density

Cu /10% C

15-16 1

270 //

8.1

Cu /20% C

13 1

230 //

7.5

Cu /30% C

11 1

260 1

180 //

6.8

Cu /40% C

9 1

220 1

160 //

6.1

Cu /50% C

7 1

180 1

120 //

5.5

Cu/5% carbon nanofibre (VGCNF)

17 1

450 //

8.5

Table 3. CTE and TC measures in parallel (//) and perpendicular (1) pressing direction on the copper carbon composites with pitch based carbon fibre (TC = 140 W/mK) [Geffroy et al., 2008] and with carbon nanofibre [Silvain et al., 2009].

The thermal conductivity obtained with Cu/C carbon composite is lower than one expected by inferior limit of Hashin and Shtrikman model [Hashin and Shtrikman, 1962]. This is likely due to the important thermal resistance of copper/carbon interface. Then, the thermal conductivity decreases strongly with an increase of carbon volume fraction. The thermal resistance of interface Cu/C decreases usually with an improvement of mechanical properties of interface copper/carbon by previous surface treatment of carbon fibre, as described in previous section. Indeed, the origin of thermal conduction in copper is electronic, while the one of carbon fibres is due to phonons. These different mechanisms of thermal conduction between copper matrix and carbon fibres explain likely that the interface carbon/copper has a large influence on thermal properties of composites, and is always one of the critical points of thermal properties of Cu/C composites.

Recent research results show that the TC of these composites materials can be improved with a higher thermal conductivity than copper (450 W. m-1.K-1) using a low amount (5% in volume) of carbon nanofibres [Silvain et al., 2009]. However, the elaboration of these composites requires, on the one hand, the previous surface treatment of short carbon fibres in order to improve the Cu/ C interface properties, on the other hand, the excellent dispersion of carbon nanofibres in copper matrix.