Questions: Polymer Mechanical Behavior and Viscoelasticity

Question 1

A rubber band is stretched and held taut, then placed in boiling water (100°C). Compared to room temperature, what happens to its elastic restoring force, and why?

• A. The restoring force decreases — higher temperature weakens the covalent bonds that store elastic energy in the stretched rubber
• B. The restoring force increases — higher temperature strengthens the entropic driving force that pulls stretched chains back toward their coiled, higher-entropy conformations
• C. The restoring force stays the same — rubber elasticity is purely mechanical and temperature-independent
• D. The rubber softens and loses elasticity at 100°C because it approaches its glass transition temperature

Answer: (B)

Rubber elasticity is entropic, not energetic. Stretching rubber forces chains into less probable, low-entropy conformations. The restoring force arises from the Second Law driving the system back toward higher entropy, and this force is proportional to absolute temperature (F ∝ TΔS/ΔL). Higher temperature strengthens the restoring force. This is the opposite of metals, which soften at high temperatures because energetic bond forces weaken with thermal expansion. Rubber stiffening on heating is counterintuitive but experimentally confirmed and theoretically derivable from polymer chain statistics.

Question 2

A polymer gasket in a mechanical seal is placed under constant compressive stress. After one year of service, the seal has begun leaking despite no change in applied load. Which viscoelastic phenomenon best explains this?

• A. Stress relaxation — under constant strain, stress decreases as chains rearrange, reducing the sealing force
• B. Creep — under constant stress, strain increases over time as polymer chains slowly flow; the gasket has permanently deformed, reducing contact pressure and allowing leakage
• C. Glass transition — the gasket cooled below Tg during service and became brittle, fracturing under load
• D. Elastic recovery — the gasket is springing back to its original shape, opening a gap

Answer: (B)

Creep is the time-dependent increase in strain under constant stress — the viscous component of viscoelastic behavior. Polymer chain segments slowly rearrange under sustained load, allowing the gasket to permanently deform over months or years. This reduces the contact pressure between sealing surfaces and causes leakage. Stress relaxation (option A) would describe decreasing stress at constant strain — relevant for a stretched O-ring that cannot move, not a compressed gasket under constant load. This is why engineers use creep data and time-temperature superposition to predict long-term seal performance.

Question 3

The glass transition temperature Tg is a sharp, precisely defined temperature at which a polymer transitions from glassy to rubbery behavior, analogous to a melting point.

• T. True
• F. False

Answer: False

Tg is NOT a sharp equilibrium transition like melting. It is a kinetic phenomenon — the temperature range over which the time scale of segmental chain motion matches the observation time scale. Because it is rate-dependent, Tg shifts to higher values when measured at faster heating rates or higher frequencies. The transition occurs over a range of tens of degrees, not at a single temperature. This matters for engineering: a material appearing glassy in a fast impact test may behave as a soft rubber in a slow creep application at the same temperature.

Question 4

Rubber elasticity is driven by entropy: stretching forces polymer chains into less probable configurations, and the system pulls back to restore higher-entropy coiled states.

• T. True
• F. False

Answer: True

An unstretched crosslinked rubber network has chains in their most probable, highly coiled conformations — maximum conformational entropy. Stretching forces chains toward extended, less probable conformations — lower entropy. The restoring force arises from the Second Law's tendency to maximize entropy, not from stretching covalent bonds. This entropic origin explains why rubber stiffens at higher temperatures (greater thermal driving force for entropy maximization) and why rubber under constant elongation maintains its restoring force differently than a metal spring would.

Question 5

Explain why rubber stiffens (its elastic modulus increases) as temperature rises, while metals soften at higher temperatures.

Model answer: Rubber elasticity is entropy-driven: the restoring force comes from stretched polymer chains seeking to return to higher-entropy coiled conformations. The entropic restoring force is proportional to absolute temperature (F ∝ TΔS), so increasing temperature directly increases the stiffness. Metal elasticity is energy-driven: the restoring force comes from stretching atomic bonds, and higher temperature reduces effective bond stiffness (thermal vibrations broaden potential energy wells, weakening the restoring force). The opposite physical origin of elasticity produces opposite temperature dependences.

This distinction can be demonstrated experimentally: hang a weight from a rubber band and heat the band — the weight rises as rubber stiffens. The same experiment on a metal spring shows the weight dropping as the spring softens. Understanding entropic elasticity is also essential for interpreting the WLF equation and time-temperature superposition: temperature governs chain mobility, which governs all viscoelastic relaxation behavior in polymers.