MSE 2100: Ceramics and Polymers

Comprehensive practice questions and answers for MSE 2100 Module 4 (Ceramics) and Module 5 (Polymers), covering crystal structures, stability rules, carbon allotropes, silicates, polymer synthesis, stereochemistry, crystallinity, and copolymer molecular weight calculations.

What are the two fundamental requirements for the structural stability of ceramic crystals?

1. Overall electrical neutrality, where total cation charge equals total anion charge.
2. The anions surrounding a cation must physically touch the cation without gaps or anion-anion crowding.

What are the primary applications and properties noted for silicon carbide ($\text{SiC}$), silicon nitride ($\text{Si}_3\text{N}_4$), and aluminum nitride ($\text{AlN}$)?

$\text{SiC}$ is hard and used for cutting tools; $\text{Si}_3\text{N}_4$ is strong at high temperatures and wear-resistant, used for turbine blades and bearings; $\text{AlN}$ has low thermal conductivity and is used for heat sinks in electronics.

How does the cation-to-anion radius ratio ($r_C/r_A$) dictate the coordination number in ceramic crystal structures?

• $r_C/r_A < 0.155 \rightarrow$ coordination number $2$
• $0.155\text{--}0.225 \rightarrow$ coordination number $3$
• $0.225\text{--}0.414 \rightarrow$ coordination number $4$
• $0.414\text{--}0.732 \rightarrow$ coordination number $6$
• $0.732\text{--}1.0 \rightarrow$ coordination number $8$

How many cations and anions are present per unit cell in Zinc Blende, Rock Salt ($\text{NaCl}$), and Cesium Chloride?

• Zinc Blende: $4$ cations and $4$ anions
• Rock Salt ($\text{NaCl}$): $4$ cations and $4$ anions
• Cesium Chloride: $1$ cation and $1$ anion

What are the four steps to determine the crystal structure of an AX-type ceramic?

1. Look up ionic radii for the cation and anion at the proper charge states to ensure neutrality.
2. Calculate the radius ratio ($r_C/r_A$).
3. Match the ratio to a coordination number using the radius ratio table.
4. Correlate the coordination number to the crystal structure ($4 \rightarrow$ Zinc Blende, $6 \rightarrow$ Rock Salt, $8 \rightarrow$ Cesium Chloride).

In the Fluorite ($\text{CaF}_2$) structure, what are the number of ions per unit cell and their respective coordination numbers?

There are $4$ cations ($\text{Ca}^{2+}$) and $8$ anions ($\text{F}^-$) per unit cell. The coordination number of the cation is $8$, and the coordination number of the anion is $4$.

How does the Antifluorite structure (e.g., $\text{K}_2\text{O}$) compare to the Fluorite structure?

Antifluorite is the direct inverse of fluorite with the positions of cations and anions swapped: it contains $8$ cations and $4$ anions per unit cell, with a cation coordination number of $4$ and an anion coordination number of $8$.

What formula is used to calculate the theoretical density ($\rho$) of a ceramic crystal?

$\rho = \frac{n'(\sum A_C + \sum A_A)}{V_c \times N_A}$, where $n'$ is the number of formula units per unit cell, $\sum A_C$ and $\sum A_A$ are the sums of atomic weights of cations and anions in one formula unit, $V_c$ is the unit cell volume, and $N_A$ is Avogadro's number ($6.022 \times 10^{23}$).

How do diamond and graphite differ in their bonding and structure?

Diamond has carbon atoms tetrahedrally bonded to four others by strong directional covalent bonds, forming an extremely hard lattice. Graphite consists of parallel layered sheets of hexagonal carbon arrays held together internally by covalent bonds, but between layers only by weak van der Waals forces.

What are fullerenes and carbon nanotubes?

Fullerenes are soccer-ball-shaped spherical clusters of $60$ carbon atoms ($\text{C}_{60}$). Carbon nanotubes consist of a sheet of graphite rolled into a seamless tube capped at both ends by fullerene hemispheres.

What is the basic structural unit of silicate ceramics and what are the three crystalline polymorphs of silica ($\text{SiO}_2$)?

The basic structural unit is the interconnected $\text{SiO}_4^{4-}$ tetrahedron. The three crystalline polymorphs of silica are quartz, cristobalite, and tridymite, which have a melting point of $1710\,^\circ\text{C}$.

What are the approximate chemical compositions of soda-lime glass and borosilicate glass?

• Soda-lime glass: approximately $70\%$ silica, $15\%$ soda, and $9\%$ lime.
• Borosilicate glass: approximately $78\%$ silica, $10\%$ boron oxide, $7\%$ soda, $3\%$ alumina, and $2\%$ zirconia.

What are the side groups on the polymer repeat units of polyethylene (PE), polypropylene (PP), and polyvinyl chloride (PVC)?

• Polyethylene (PE): all $\text{H}$ side groups
• Polypropylene (PP): one methyl group ($-\text{CH}_3$) per repeat unit
• Polyvinyl chloride (PVC): one chlorine atom ($-\text{Cl}$) per repeat unit

What are the specific functions of the common plastic additives: fillers, plasticizers, stabilizers, flame retardants, and colorants?

• Fillers: add volume
• Plasticizers: add flexibility
• Stabilizers: resist UV radiation and degradation
• Flame retardants: improve safety
• Colorants: add color

How do addition (chain-growth) polymerization and condensation (step-growth) polymerization differ in mechanism, byproducts, and monomer requirements?

• Addition polymerization: chain reaction adding monomers one at a time via initiation, propagation, and termination; requires double bonds (e.g., ethylene); yields no byproducts.
• Condensation polymerization: step-wise reaction between monomers forming larger molecules; does not require double bonds; releases small byproducts (such as water).

What is a free radical in polymer synthesis?

A highly reactive and electrically neutral molecule that contains one or more unpaired electrons, commonly formed by heating organic peroxides (such as benzoyl peroxide).

What is the difference between polymer conformation and polymer configuration?

Conformation describes shapes that change strictly through rotation around single bonds without breaking any bonds. Configuration refers to spatial arrangements that can only be altered by breaking and reforming primary chemical bonds (e.g., cis/trans isomerism and tacticity).

What is the structural difference between cis-isoprene and trans-isoprene, and what materials do they form?

They are configurational stereoisomers around a double bond. cis-isoprene forms natural rubber, whereas trans-isoprene forms gutta percha.

What do isotactic, syndiotactic, and atactic mean in terms of polymer tacticity?

• Isotactic: all $\text{R}$ side groups are positioned on the same side of the chain.
• Syndiotactic: $\text{R}$ side groups alternate regularly from side to side along the chain.
• Atactic: $\text{R}$ side groups are positioned randomly along the chain.

What are the four architectural types of copolymers?

1. Random: monomer units are randomly arranged along the chain.
2. Alternating: monomer units alternate systematically along the chain.
3. Block: large blocks of one monomer repeat alternate with large blocks of another.
4. Graft: branches composed of one monomer type are grafted onto a backbone chain composed of a different monomer.

Why are polymers semicrystalline rather than 100% crystalline, and what is the physical structure of their crystalline regions?

Polymers cannot achieve $100\%$ crystallinity because twisting, kinking, and chain misalignment inevitably create amorphous regions. Their crystalline regions consist of chain-folded platelets approximately $10\,\text{nm}$ thick that are denser than the surrounding amorphous matrix.

How do thermoplastics and thermosets differ in cross-linking, thermal behavior, and mechanical properties?

• Thermoplastics: have little to no cross-linking, soften and melt when heated, can be reshaped repeatedly, and are generally ductile (e.g., PE, PP, PC, PS).
• Thermosets: have heavily cross-linked 3D networks ($10\text{--}50\%$ of repeat units), cure irreversibly without softening when heated, and are hard and brittle (e.g., epoxies, vulcanized rubber, polyester resin).

How are number-average molecular weight ($\bar{M}_n$) and weight-average molecular weight ($\bar{M}_w$) calculated, and why is $\bar{M}_w \ge \bar{M}_n$?

$\bar{M}_n = \sum x_i M_i$ (where $x_i$ is the number fraction) and $\bar{M}_w = \sum w_i M_i$ (where $w_i$ is the weight fraction). $\bar{M}_w \ge \bar{M}_n$ always holds because heavier chains carry disproportionately higher mass, skewing the weight fraction upward.

How is the degree of polymerization (DP) calculated for a homopolymer and a copolymer?

For a homopolymer, $\text{DP} = \frac{\bar{M}_n}{m}$, where $m$ is the molecular weight of the single repeat unit. For a copolymer, $\text{DP} = \frac{\bar{M}_n}{\bar{m}}$, where $\bar{m} = \sum f_i m_i$ is the weighted average molecular weight of all repeat units based on their chain/number fractions ($f_i$).

For an alternating poly(styrene-butadiene) copolymer with $\bar{M}_n = 20000\,\text{g/mol}$, what is the average number of styrene and butadiene repeat units per molecule?

With repeat unit weights of $m_{\text{styrene}} = 104.16\,\text{g/mol}$ and $m_{\text{butadiene}} = 54.10\,\text{g/mol}$, alternating stoichiometry dictates $f = 0.5$ each, giving $\bar{m} = 0.5(104.16) + 0.5(54.10) = 79.13\,\text{g/mol}$. Total $\text{DP} = \frac{20000}{79.13} = 252.75$, resulting in $126.37$ styrene repeat units and $126.37$ butadiene repeat units per chain.

If a copolymer contains $20\,\text{wt}\%$ ethylene ($\text{C}_2\text{H}_4$, $m = 28.06\,\text{g/mol}$) and $80\,\text{wt}\%$ propylene ($\text{C}_3\text{H}_6$, $m = 42.09\,\text{g/mol}$), what are their respective number fractions ($f_A$ and $f_B$)?

In a $100\,\text{g}$ sample, there are $\frac{20}{28.06} = 0.713\,\text{mol}$ of ethylene and $\frac{80}{42.09} = 1.901\,\text{mol}$ of propylene (total $2.614\,\text{mol}$). Thus, $f_{\text{ethylene}} = \frac{0.713}{2.614} = 27.3\%$ ($0.273$) and $f_{\text{propylene}} = \frac{1.901}{2.614} = 72.7\%$ ($0.727$).