7.6 An amorphous polymer fiber is being treated to form polymer crystals. You may assume that...

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7.6 An amorphous polymer fiber is being treated to form polymer crystals. You may assume that the fiber is thin enough to be treated as a one-dimensional solid. (a) Write an equation for the functional relationship between the fraction of the amorphous polymer that has crystallized (F) and time (t). Assume that the nucleation of crystals is homogeneous and that the rate of nucleation is constant. Assume also that the rate of crystal growth is constant. (b) After 1 hour of the treatment, 10% of the polymer fiber is crystalline. How long will it take for 50% of the fiber to become crystalline? (c) Will your answer to part a be changed if the nucleation is heterogeneous, and all the nuclei become active at the beginning of the transformation (t = 0)? If so, how? 7.6 An amorphous polymer fiber is being treated to form polymer crystals. You may assume that the fiber is thin enough to be treated as a one-dimensional solid. (a) Write an equation for the functional relationship between the fraction of the amorphous polymer that has crystallized (F) and time (t). Assume that the nucleation of crystals is homogeneous and that the rate of nucleation is constant. Assume also that the rate of crystal growth is constant. (b) After 1 hour of the treatment, 10% of the polymer fiber is crystalline. How long will it take for 50% of the fiber to become crystalline? (c) Will your answer to part a be changed if the nucleation is heterogeneous, and all the nuclei become active at the beginning of the transformation (t = 0)? If so, how?