HW Solutions Ch 7-9

# HW Solutions Ch 7-9 - CHAPTER 7 1. Consider a polyethylene...

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CHAPTER 7 1. Consider a polyethylene molecule ( C 2 H 4 ) n with n = 50. (a) What is the root-mean-square length (coiled length) of this molecule? (b) What is the length of this molecule when stretched? Note that the C-C-C angle is 109.5 ° . (c) When one suddenly releases a polymer from the stretched configuration, what will happen to its temperature? Why? Solution (a) For n = 50, there are 100 C-C bonds. The root-mean-square length of this molecule = 0.154 100 = 1.54 nm where each C-C bond length is 0.154 nm. (b) When fully stretched, the length of this molecule = 100 × 0.154 × sin 109.5 2 = 12.6 nm (c) When suddenly released from the stretched configuration, the temperature drops. This is due to the sudden increase in entropy dS , with a corresponding heat absorption of TdS , where T is the temperature. 3. Polyethylene (PE) with 100% crystallinity has a density of 1.01 g/cm 3 , while amorphous PE has a density of 0.90 g/cm 3 . The density of high-density polyethylene (HDPE) is 0.96 g/cm 3 . Show that the volume fraction of crystalline PE in HDPE is about 55%. Solution

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Assume that the volume fraction of crystalline PE = V x and that the volume fraction of amorphous PE = V a . Mass of 1 cm 3 of HDPE = 0.96 = 1.01 V x + 0.9 V a = 1.01 V x + 0.9(1 V x ) = 0.11 V x + 0.9 Solving, we have: V x = 0.55 9. Certain plastic containers and items are labeled as “dishwasher safe”. Discuss what this means along two lines: (a) What will happen to “unsafe” plastic containers after they are
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## This note was uploaded on 11/21/2011 for the course MAT SCI 201 taught by Professor Matsci during the Spring '10 term at Northwestern.

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HW Solutions Ch 7-9 - CHAPTER 7 1. Consider a polyethylene...

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