What does the Flory-Fox equation express for polymers?

What does the Flory-Fox equation express for polymers?

• A. P = RT/(V - b) - a/V^2
• B. ΔP = 8 μ L Q /(π r^4)
• C. T_g = T_g,∞ + K / M_n
• D. k = A e^(-Ea/RT)

Answer: (C)

The Flory-Fox relationship shows how a polymer’s glass transition temperature depends on its molecular weight. Tg is the temperature where the polymer transitions from a hard, glassy state to a softer, rubbery state as chains gain mobility. When chains are short (low Mn), mobility is higher and Tg is lower. As Mn increases, chains are longer and movement is more restricted, so Tg rises and approaches a limiting value Tg,∞ that would be reached if the chains were infinitely long. The equation captures this with a correction term that scales with 1/Mn, meaning the influence of molecular weight diminishes as Mn grows. The constant K sets how strongly Mn affects Tg for the specific polymer. In short, this equation expresses that Tg approaches a fixed high-temperature limit with increasing molecular weight, with the rate of approach governed by the inverse of Mn. The other formulas shown describe unrelated phenomena (gas behavior, flow resistance, and Arrhenius temperature dependence) and do not describe how Tg depends on molecular weight.

The Flory-Fox relationship shows how a polymer’s glass transition temperature depends on its molecular weight. Tg is the temperature where the polymer transitions from a hard, glassy state to a softer, rubbery state as chains gain mobility. When chains are short (low Mn), mobility is higher and Tg is lower. As Mn increases, chains are longer and movement is more restricted, so Tg rises and approaches a limiting value Tg,∞ that would be reached if the chains were infinitely long. The equation captures this with a correction term that scales with 1/Mn, meaning the influence of molecular weight diminishes as Mn grows. The constant K sets how strongly Mn affects Tg for the specific polymer.

In short, this equation expresses that Tg approaches a fixed high-temperature limit with increasing molecular weight, with the rate of approach governed by the inverse of Mn. The other formulas shown describe unrelated phenomena (gas behavior, flow resistance, and Arrhenius temperature dependence) and do not describe how Tg depends on molecular weight.