The Thermal Properties of Composite Materials

This thesis describes experiments on the thermal conductivity of some two-phase composites between 2 K and room temperature. The composites are made from particulate, non-metallic fillers of glass, crystalline quartz and alumina, and diamond embedded in a matrix of a thermosetting epoxy resin, Araldite MY 740. Filler particles, ranging from a size of 2 to 150 mierons have been used in this work.
Chapter 2 gives a review of the theory of heat transport in insulating crystals and amorphous glasses and polymers. There is also an account of the various methods predicting the thermal conductivity of two-phaae composites with particulate fillers.
Chapter 3 gives a general account of epoxy resins, the type of fillers used in epoxy resins and the effect of fillers on various physical properties of the system, A description of the specimen preparation is also given. The specimens were all prepared in the same way and the same epoxy has been used throughout this work.
Chapter 4 describes the experimental techniques and apparatus. The thermal conductivity was measured by the conventional steady-state method using cryostats of straight-forward design. Differential gold-iron (0.03 at %) versus chromel thermocouples were used for tenperature measurement from liquid hydrogen temperatures down to 2 K. Above these temperatures differential copper versus constantan thermocouples were used. Great care was taken to minimize errors due to radiation from the sides of specimen at temperatures of 78 K and above.
Chapter 5 describes some experiments on the unfilled epoxy and chapter 6 some experiments on the filled epoxies. The effect on the composite thermal conductivity of the filler thermal conductivity, filler volume concentration and filler particle size and shape has been studied.
Above helium temperatures the thermal conductivity of the two phase composites is dependent on the thermal conductivities of the epoxy matrix and filler, the volune concentration of the filler and the shape of the filler particles. The size of the particles is also important for crystalline filling materials when their thermal conductivity becomes size dependent due to the frequency independent phonon mean free path of boundary scattering.
At helium temperatures a pronounced size effect is found in which the smaller the particle size the lower is the resulting composite thermal conductivity, all other things belng equal. This size dependence is found to be much greater than would be expected from considerations of the size dependent thermal conductivity of crystalline filler materials in the boundary scattering region. This discrepancy is believed to be a result of the presence of a thermal contact resistance at the filler-epoxy interface due to phonon mismatch at the interface.
Generally, bulk displacement of the epoxy with a filler whose thermal conductivity is higher than that of the matrix produces composites whose thermal conductivity is higher than that of the epoxy, and increasing filler volume concentration results in increasing composite conductivity. At helium temperature this may not be so. The presence of a thermal contact resistance between the matrix and filler can result in composites whose thermal conductivities are substantially lower than that of the matrix and an increase in the filler concentration produces a decrease in the composite thermal conductivity.
The experimental results have been compared with the various predictions of the thermal conductivity of two-phase composites. At liquid hydrogen temperatures and above predictions using the theory of Maxwell and Rayleigh to which an extra factor to take account of the shape of the particle are in reasonable agreement with the experimental results. At liquid helium temperatures the presence of a thermal contact resistance will result in this theory predicting values which are much higher than those found by experiment. An attempt has been made to include the effect of this thermal contact resistance in the theoretical predictions and this does enable a fairly satisfactory explanation to be given of the low temperature measurements.