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Chapter 15: Problem 30

For each of the following pairs of polymers plot and label schematic specific volume versus temperature curves on the same graph (i.e., make separate plots for parts a, b, and c). (a) Linear polyethylene with a weightaverage molecular weight of \(75,000 \mathrm{g} / \mathrm{mol}\); branched polyethylene with a weightaverage molecular weight of \(50,000 \mathrm{g} / \mathrm{mol}\) (b) Spherulitic poly(vinyl chloride), of \(50 \%\) crystallinity, and having a degree of polymerization of \(5000 ;\) spherulitic polypropylene, of \(50 \%\) crystallinity, and degree of polymerization of 10,000 (c) Totally amorphous polystyrene having a degree of polymerization of \(7000 ;\) totally amorphous polypropylene having a degree of polymerization of 7000

Short Answer

Expert verified
Question: Plot and label schematic specific volume versus temperature curves for (a) linear polyethylene with a weight average molecular weight of 75000 g/mol and branched polyethylene with a weight average molecular weight of 50000 g/mol, (b) spherulitic poly(vinyl chloride) with 50% crystallinity and a degree of polymerization of 5000 and spherulitic polypropylene with 50% crystallinity and a degree of polymerization of 10000, and (c) totally amorphous polystyrene with a degree of polymerization of 7000 and totally amorphous polypropylene with a degree of polymerization of 7000. Answer: When plotting the specific volume versus temperature curves for each pair of polymers, (a) linear polyethylene will have a lower specific volume and a steeper increase in specific volume with increasing temperature compared to branched polyethylene, (b) spherulitic poly(vinyl chloride) and spherulitic polypropylene will have similar trends but with varying magnitudes based on their degree of polymerization and crystallinity percentages, and (c) the trend for totally amorphous polystyrene and totally amorphous polypropylene will be relatively similar, with variations primarily due to differences in their degree of polymerization.

Step by step solution

01

Part a: Linear and branched polyethylene

Step 1: Determine the specific volume for each type of polyethylene Linear polyethylene: The specific volume of linear polyethylene varies with temperature and is generally lower than that of branched polyethylene. Branched polyethylene: The specific volume of branched polyethylene also varies with temperature and is generally higher than that of linear polyethylene due to the presence of branches that allow for higher free volume. Step 2: Plot the specific volume versus temperature Plot the specific volume on the y-axis and temperature on the x-axis. Linear polyethylene will have a lower specific volume and a steeper increase in specific volume with increasing temperature compared to branched polyethylene. Label both curves with the respective polymer types and molecular weights.
02

Part b: Spherulitic poly(vinyl chloride) and spherulitic polypropylene

Step 1: Determine the specific volume for each type of polymer Spherulitic poly(vinyl chloride): The specific volume of spherulitic poly(vinyl chloride) varies with temperature and is affected by the degree of polymerization and crystallinity. Spherulitic polypropylene: The specific volume of spherulitic polypropylene also varies with temperature and is determined by the degree of polymerization and crystallinity. Step 2: Plot the specific volume versus temperature Plot the specific volume on the y-axis and temperature on the x-axis. Spherulitic poly(vinyl chloride) and spherulitic polypropylene will have similar specific volume vs. temperature trends, with the main difference being the magnitude of the specific volume based on their degree of polymerization and crystallinity. Label both curves with the respective polymer types, degree of polymerization, and crystallinity percentages.
03

Part c: Totally amorphous polystyrene and totally amorphous polypropylene

Step 1: Determine the specific volume for each type of polymer Totally amorphous polystyrene: The specific volume of totally amorphous polystyrene varies with temperature and is determined by the degree of polymerization. Totally amorphous polypropylene: The specific volume of totally amorphous polypropylene also varies with temperature and is determined by the degree of polymerization. Step 2: Plot the specific volume versus temperature Plot the specific volume on the y-axis and temperature on the x-axis. The specific volume vs. temperature trend for totally amorphous polystyrene and totally amorphous polypropylene will be relatively similar, with variations primarily due to differences in their degree of polymerization. Label both curves with the respective polymer types and degrees of polymerization.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molecular Weight of Polymers
The molecular weight of polymers is a critical factor influencing their physical properties, such as tensile strength, impact resistance, and melting temperature. It represents the mass of a mole of chains, calculated as the sum of the atomic weights of all atoms in a polymer molecule. As molecular weight increases, polymers tend to exhibit higher mechanical strength and higher resistance to solvents and chemicals.

When plotting the specific volume versus temperature for polymers, such as linear and branched polyethylene, those with higher molecular weights generally exhibit a tighter packing arrangement of the molecular chains, leading to a lower specific volume. However, increased molecular weight can also increase the chain entanglement, which affects the temperature at which the polymer softens or melts. In the provided step-by-step solution, the higher molecular weight polymer (linear polyethylene) is expected to have lower specific volume compared to the branched counterpart.
Degree of Polymerization
Polymer chains consist of repeated monomer units, and the degree of polymerization (DP) quantifies the number of these repeating units in a single polymer chain. It is directly related to the molecular weight of the polymer since the molecular weight is essentially the product of DP and the molecular weight of the monomer unit.

When considering the specific volume versus temperature, polymers with a higher DP generally have more extensive chains that can lead to higher degrees of entanglement and influence the thermal properties. For example, spherulitic polypropylene with a DP of 10,000 will likely have a different volume-temperature plot from spherulitic poly(vinyl chloride) with a DP of 5,000, primarily because the longer chains in polypropylene may result in more significant volume change with temperature due to increased molecular motion. The solution method correctly takes into account the different DPs of the two spherulitic polymers when comparing their specific volumes.
Spherulitic Crystallinity
Spherulitic crystallinity refers to a semi-crystalline structure where polymer chains fold into ordered regions called spherulites. These regions are interspersed in an amorphous matrix, giving the polymer distinct mechanical and thermal properties. A polymer's crystallinity significantly impacts its density, melting point, and mechanical properties. Spherulites can act as stress concentrators and influence the toughness of the material.

Polymers with higher spherulitic crystallinity typically exhibit less thermal expansion, resulting in a more stable specific volume with temperature changes. However, crystallinity can be disrupted by imperfections or irregularities in the chain structure, such as branching. Therefore, even with the same degree of polymerization, the spherulitic polyvinyl chloride and polypropylene indicated in the step-by-step solution may have different volume-temperature behaviors due to the intrinsic differences in how these polymers form spherulites and their response to temperature fluctuations.

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Most popular questions from this chapter

Cite five important characteristics for polymers that are to be used in thin- film applications.

The tensile strength and number-average molecular weight for two poly(methyl methacrylate) materials are as follows: $$\begin{array}{cc}\hline \begin{array}{c}\text { Tensile Strength } \\\\\text { (MPa) }\end{array} & \begin{array}{c}\text { Number-Average } \\ \text { Molecular Weight (g/mol) }\end{array} \\\\\hline 50 & 30,000 \\\150 & 50,000 \\\\\hline\end{array}$$ Estimate the tensile strength at a numberaverage molecular weight of \(40,000 \mathrm{g} / \mathrm{mol}\).

Nylon 6,6 may be formed by means of a condensation polymerization reaction in which hexamethylene diamine \(\left[\mathrm{NH}_{2}-\left(\mathrm{CH}_{2}\right)_{6}-\right.\) \(\left.\mathrm{NH}_{2}\right]\) and adipic acid react with one another with the formation of water as a byproduct. What masses of hexamethylene diamine and adipic acid are necessary to yield \(20 \mathrm{kg}\) of completely linear nylon \(6,6 ?\) (Note: the chemical equation for this reaction is the answer to Concept Check \(15.12 .\) )

For the vulcanization of polyisoprene, compute the weight percent of sulfur that must be added to ensure that \(10 \%\) of possible sites will be crosslinked; assume that, on the average, 3.5 sulfur atoms are associated with each crosslink.

For thermoplastic polymers, cite five factors that favor brittle fracture.
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