This set of Polymer Engineering Problems focuses on “Chain Length and Degree of Polymerization”.

1. What does the ratio R_{p}/R_{i} represent in polymerization?

a) chain length

b) monomer concentration

c) initiator concentration

d) none of the mentioned

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Explanation: The kinetic chain length is viewed as the ratio of rate of propagation to the rate of initiation or termination, since R

_{i}= R

_{t}.

2. The kinetic chain length represents the average number of monomer molecules in a polymer molecule. State true or false.

a) true

b) false

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Explanation: The kinetic chain length represents the average number of monomer molecules consumed by a primary radical, from its initiation to termination.

3. What is the expression for kinetic chain length for a purely thermal polymerization?

a) k_{p}/2(k_{i}k_{t})^{0.5}

b) k_{p}/2(k_{i}/k_{t})^{0.5}

c) k_{p}^{2}/2(k_{i}k_{t})^{0.5}

d) k_{p}/(k_{i}k_{t})^{0.5}

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Explanation: For pure thermal polymerization, Rp is given by-

R

_{p}= k

_{p}(k

_{i}/k

_{t})

^{0.5}[M]

^{2}

And the chain length is given by-

v =( k

_{p}

^{2}/2k

_{t}) ([M]

^{2}/R

_{p})

So, for pure thermal polymerization, the expression for kinetic chain length is given by, v = k

_{p}/2(k

_{i}k

_{t})

^{0.5}.

4. The kinetic chain length expression given by, v=( k_{p}^{2}/2k_{t})([M]^{2}/R_{p}) is applicable to all cases of termination, irrespective of the mechanism involved. State true or false.

a) true

b) false

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Explanation: The kinetic chain length expression given by, v=( k

_{p}

^{2}/2k

_{t})([M]

^{2}/R

_{p}) is applicable to all cases of termination, irrespective of the mechanism involved, combination or disproportionation and also irrespective of the nature of initiation mechanism.

5. For vinyl acetate polymerized at 50ᵒC, the value of the ratio k_{p}^{2}/k_{t} is 0.0138 l/mol-s. What is the value of chain length, when monomer concentration is 6.53 mol/l and rate of polymerization is 2.0*10^{-4}mol/l-s?

a) 1471

b) 2942

c) 2500

d) 225

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Explanation: The expression for kinetic chain length is-

v=( k

_{p}

^{2}/2k

_{t})([M]

^{2}/R

_{p})

Substituting the values, we get v as 1471.

6. What are the relative chain lengths of vinyl chloride and styrene, polymerized at 60ᵒC, having the values of ratio k_{p}^{2}/k_{t} as 0.126 l/mol-s and 0.0034 l/mol-s, respectively?

a) 37

b) 74

c) 50

d) 100

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Explanation: Assume the rate of polymerization and monomer concentration same for both the cases.

v

_{vc}/v

_{s}= ( k

_{p}

^{2}/k

_{t})

_{vc}/( k

_{p}

^{2}/k

_{t})

_{s}

= 0.126/0.0034

= 37.

7. What is the degree of polymerization for polyvinyl chloride, having kinetic chain length as 400 and terminated by coupling mechanism?

a) 400

b) 800

c) 200

d) none of the mentioned

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Explanation: For termination by combination,

X

_{n}= 2v

So, the value of degree of polymerization is 800.

8. For styrene polymerized at 70ᵒC, monomer concentration is 7.85mol/l and the value of the ratio (k_{p}^{2}/k_{t}) is 0.0015 l/mol-s. What is the rate of polymerization reaction, if the chain length is 300?

a) 0.092

b) 0.046

c) 0.08

d) 0.072

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Explanation: The kinetic chain length expression is given by,

v= (k

_{p}

^{2}/k

_{t})([M]

^{2}/R

_{p})

Substituting the values we get, R

_{p}as 0.046.

9. What is the ratio of degree of polymerization for a polymer when terminated by combination to disproportionation mechanism?

a) 2

b) 0.5

c) 1

d) 4

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Explanation: For termination by combination,

X

_{n}= 2v

And for termination by disproportionation,

X

_{n}= v

So, the ratio is 2.

10. What is the degree of polymerization for the product having ratio of incidences of termination by combination and by disproportionation, y is 5, when the chain length is 400?

a) 686

b) 343

c) 500

d) 2000

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Explanation: The number average degree of polymerization is related to kinetic chain length, when termination occurs simultaneously by combination and disproportionation, by the following expression-

X

_{n}= [2(y+1)/(y+2)]v

= 686.

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