Why is the Polydispersity Index ($\text{PDI}$) equal to $1$ for natural polymers but $>1$ for synthetic polymers?

Natural polymers like proteins and DNA are monodisperse because biological synthesis is genetically dictated, producing identical chain lengths where $\bar{M}_w = \bar{M}_n$, making $\text{PDI} = 1$. Synthetic polymers undergo stochastic kinetic polymerization, forming a statistical distribution of chain lengths where $\bar{M}_w > \bar{M}_n$, resulting in $\text{PDI} > 1$.

What structural difference makes Bakelite thermosetting while Polythene is thermoplastic?

Polythene consists of linear or branched chains held together by weak van der Waals forces, allowing the polymer chains to slide over one another upon heating. Bakelite forms an irreversible 3D cross-linked covalent network via methylene bridges ($\text{-CH}_2\text{-}$) during molding, preventing softening or melting when reheated.

How do High-Density Polyethylene ($\text{HDPE}$) and Low-Density Polyethylene ($\text{LDPE}$) differ in synthesis?

$\text{LDPE}$ is synthesized under high pressure ($1000-2000\text{ atm}$) via free-radical polymerization, resulting in extensive branching and low packing density. $\text{HDPE}$ is synthesized using a Ziegler-Natta catalyst ($\text{TiCl}_4 + \text{Al(Et)}_3$) under low pressure ($1-7\text{ atm}$), forming linear, closely packed polymer chains with high density and melting point.

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Solved High-Yield Sample Questions

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Question #1NEET 2023

Which of the following polymers is synthesized by using $\varepsilon$ -caprolactam as the starting monomer unit?

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Step-by-Step Solution & Concept

Step 1

Identify the chemical structure of $\varepsilon$ -caprolactam, which is a seven-membered cyclic lactam containing $6$ carbon atoms and an amide linkage.

Step 2

Heating $\varepsilon$ -caprolactam at $533-543\text{ K}$ with water triggers hydrolytic ring-opening polymerization without eliminating small molecules.

Step 3

The resulting polyamide featuring repeating structural units of $[-\text{NH-(CH}_2)_5\text{-CO-}]_n$ is $Nylon\ 6$ .

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Question #2JEE Main 2023

A synthetic polymer sample contains $30\%$ molecules with molecular mass $M_1 = 20,000\text{ g/mol}$ and $70\%$ molecules with molecular mass $M_2 = 40,000\text{ g/mol}$ . Calculate the Polydispersity Index ( $\text{PDI}$ ) of the polymer sample.

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Step-by-Step Solution & Concept

Step 1

Calculate the number average molecular mass: $\bar{M}_n = \frac{(30 \times 20000) + (70 \times 40000)}{30 + 70} = \frac{600000 + 2800000}{100} = 34,000\text{ g/mol}$ .

Step 2

Calculate the weight average molecular mass: $\bar{M}_w = \frac{30(20000)^2 + 70(40000)^2}{34000 \times 100} = \frac{1.2 \times 10^{10} + 1.12 \times 10^{11}}{3.4 \times 10^6} = \frac{1.24 \times 10^{11}}{3.4 \times 10^6} \approx 36,470.59\text{ g/mol}$ .

Step 3

Compute the Polydispersity Index: $\text{PDI} = \frac{\bar{M}_w}{\bar{M}_n} = \frac{36470.59}{34000} \approx 1.07$ .

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Mastering Polymers: Formulas, Traps & Exam Strategy | ExamiFly

Chapter Overview

Core Subtopics & Syllabus Breakdown

Key Formulas & High-Yield Equations

Number Average Molecular Mass

Weight Average Molecular Mass

Polydispersity Index (PDI)

Degree of Polymerization

Ziegler-Natta Catalyst System

Repeat Unit Mass of Nylon 6

Common Mistakes & Traps to Avoid

Past Year Question (PYQ) Trends

Solved High-Yield Sample Questions

Frequently Asked Questions

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