For each of the following pairs of polymers, do ( the following: (1) State whether it is possible to decide whether one polymer has a higher tensile modulus than the other; (2) if this is possible, note which has the higher tensile modulus and cite the reason(s) for your choice; and (3) if it is not possible to decide, state why. (a) Branched and atactic poly(vinyl chloride) with a weight-average molecular weight of \(100,000 \mathrm{~g} / \mathrm{mol}\); linear and isotactic poly(vinyl chloride) having a weight-average molecular weight of \(75,000 \mathrm{~g} / \mathrm{mol}\) (b) Random styrene-butadiene copolymer with \(5 \%\) of possible sites crosslinked; block styrene-butadiene copolymer with \(10 \%\) of possible sites crosslinked (c) Branched polyethylene with a number-average molecular weight of \(100,000 \mathrm{~g} / \mathrm{mol}\); atactic polypropylene with a number-average molecular weight of \(150,000 \mathrm{~g} / \mathrm{mol}\)

Step by step solution

01

a) Branched and atactic poly(vinyl chloride) vs linear and isotactic poly(vinyl chloride)

We can compare the tensile modulus of these two polymers because they have well-defined structures. The higher tensile modulus is observed in the linear and isotactic poly(vinyl chloride). The reasons for the higher tensile modulus are: 1. The isotactic structure leads to a more ordered and crystalline structure, which provides better mechanical properties. 2. The linear chain arrangement has better packing efficiency than the branched one, leading to a more rigid and resistant structure. Even though the linear and isotactic PVC has a lower molecular weight (75,000 g/mol) than the branched and atactic PVC (100,000 g/mol), its ordered and linear structure provides a higher tensile modulus.

02

b) Random styrene-butadiene copolymer vs block styrene-butadiene copolymer

It is difficult to decide which one of the given styrene-butadiene copolymers will have a higher tensile modulus without more information. The different crosslinking percentages (5% and 10%) alone are not enough to make a conclusion. The tensile modulus depends not only on the crosslinking but also on the distribution and arrangement of the styrene and butadiene units within the polymer, which is not provided in the problem.

03

c) Branched polyethylene vs atactic polypropylene

We can compare the tensile modulus of these two polymers because they have well-defined structures. The higher tensile modulus is observed in the branched polyethylene. The reasons for the higher tensile modulus are: 1. Polyethylene, in general, has higher crystallinity than atactic polypropylene. The crystalline structure provides better mechanical properties. 2. Polyethylene has a somewhat more ordered structure than atactic polypropylene which further contributes to the higher tensile modulus. Even though the branched polyethylene has a lower molecular weight (100,000 g/mol) than the atactic polypropylene (150,000 g/mol), its higher crystallinity and order will result in a higher tensile modulus.

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