Linear vs. cross-linked/branched polymers: compared to linear chains, cross-linked or highly branched polymers generally exhibit which change in bulk mechanical behavior?

Introduction / Context:
Molecular architecture strongly influences polymer properties. Linear chains can slide past one another when heated or stressed, whereas cross-links and extensive branching impede mobility. This question asks for the dominant qualitative trend in mechanical behavior when moving from linear to cross-linked/branched structures.

Given Data / Assumptions:

• Cross-linking restricts chain mobility.
• Branching reduces crystallinity in many systems but increases entanglements.
• We consider room-temperature bulk properties in typical engineering polymers.

Concept / Approach:
Increasing cross-link density raises modulus and hardness, often reducing elongation at break and increasing brittleness. Many branched networks cannot truly melt; they soften slightly before degrading. While density and melting behavior depend on chemistry/crystallinity, the robust, exam-relevant trend is that cross-linked and heavily branched polymers are stiffer and more brittle than their linear analogs due to constrained molecular motion and reduced capacity for plastic deformation.

Step-by-Step Solution:

Verification / Alternative check:
Tensile stress–strain curves of thermosets vs. thermoplastics show higher modulus and lower elongation at break for cross-linked systems, consistent with increased brittleness.

Why Other Options Are Wrong:

• Higher density: not a universal outcome; varies by system.
• Higher melting point: cross-linked networks do not melt in the thermoplastic sense.
• Higher tensile with enhanced ductility: contradicts typical behavior.
• Lower Tg in all cases: Tg usually increases with cross-link density.

Common Pitfalls:
Assuming “stronger” means “tougher”; cross-linking often raises strength but reduces toughness/ductility.

Final Answer:
Higher hardness, rigidity, and brittleness