For each of the following pairs of materials, decide which has the larger thermal conductivity. Justify your choices. (a) Pure silver; sterling silver \((92.5\) wt\% \(\mathrm{Ag}-7.5 \mathrm{wt} \% \mathrm{Cu})\) (b) Fused silica; polycrystalline silica (c) Linear and syndiotactic poly(vinyl chloride) \((D P=1000) ;\) linear and syndiotactic polystyrene \((D P=1000)\) (d) Atactic polypropylene \(\left(\bar{M}_{w_{5}}=10^{6} \mathrm{~g} / \mathrm{mol}\right)\); isotactic polypropylene \(\left(\bar{M}_{w}=10^{5} \mathrm{~g} / \mathrm{mol}\right)\)

In the realm of materials science, thermal conductivity is a fundamental property that defines how well a material can conduct heat. This depends on several factors, such as atomic structure, electron mobility, and the presence of defects or impurities. For instance, pure metals generally have free electrons that facilitate heat transfer, resulting in higher thermal conductivity when compared to alloys, where additional elements can disrupt the electron flow and increase resistance to heat transfer.

When comparing pure silver to sterling silver, materials science principles suggest that the uninterrupted lattice of pure silver allows electrons to move more freely than in sterling silver, which contains copper. The copper atoms create scattering points for silver's conduction electrons, reducing thermal conductivity. This concept is foundational in understanding how the composition and purity levels of metal can affect its ability to conduct heat.

Diving deeper into the world of polymer structures, it's important to understand the various arrangements of polymer chains and how these affect properties like thermal conductivity. Polymers can be linear, with chains arranged in a straightforward sequence, or they can be branched, where side chains extend from the main chain. Additionally, the arrangement of side groups can be isotactic, where all side groups are on the same side; syndiotactic, with alternating sides; or atactic, where the placement is random.

For instance, isotactic polypropylene's regular side group placement creates an orderly structure which enhances heat flow. Conversely, atactic polypropylene's random placement leads to a more disordered arrangement, disrupting thermal pathways and reducing conductivity. Understanding these structures is critical to predicting and tailoring the thermal properties of polymers for specific applications.

When discussing thermal conductivity in materials, the distinction between crystalline and amorphous materials is paramount. Crystalline materials are characterized by a highly ordered, repeating atomic arrangement. This periodicity facilitates the seamless transfer of heat as atoms vibrate in a predictable manner. In contrast, amorphous materials lack this order, leading to a more complex pathway for heat transfer due to the irregular arrangement of atoms or molecules.

In the example of fused silica and polycrystalline silica, it is the ordered, repeating structure of polycrystalline silica that enables higher thermal conductivity. This example is illustrative of how understanding the atomic structure of materials can directly inform predictions about their physical properties, such as thermal conductivity. It's one of the core principles in materials science that determines why, for instance, glasses and ceramics (typically amorphous) are excellent insulators compared to metals (typically crystalline).