(a) Briefly explain why porosity decreases the thermal conductivity of ceramic and polymeric materials, rendering them more thermally insulative. (b) Briefly explain how the degree of crystallinity affects the thermal conductivity of polymeric materials and why.

Porosity is the presence of voids or pores within a material, which can occur in both ceramics and polymers. The presence of these pores creates air gaps within the material, and since gases have much lower thermal conductivity compared to solids, the overall thermal conductivity of the material decreases as porosity increases. Additionally, the presence of these pores disrupts the lattice structure of the material, leading to impediments to the flow of heat due to phonon scattering. This combination of factors results in a decrease of thermal conductivity and an increase of thermal insulation in porous materials.

The degree of crystallinity in a polymeric material refers to the amount of ordered, crystalline regions in the polymer compared to the amorphous, disordered regions. Crystalline regions tend to have a more organized molecular structure, allowing for more efficient transport of heat through the material due to a lower degree of phonon scattering. As the crystallinity increases, so does the overall thermal conductivity of the polymeric material. In contrast, amorphous regions in the polymer are characterized by irregular, disordered molecular structures, which can disrupt the flow of heat and cause increased phonon scattering. This results in a decrease in thermal conductivity in comparison to the more ordered crystalline regions. Therefore, the degree of crystallinity in a polymeric material will affect its thermal conductivity as it determines the balance between higher conducting crystalline regions and lower conducting amorphous regions. Increasing the degree of crystallinity increases the thermal conductivity of the material due to a decrease in phonon scattering and a more efficient heat transfer through the material.