Solution Manual Polymer Science and Technology 3rd Joel Fried .PDF PDF

Preview

Summary

Access Full Complete Solution Manual Here https://www.book4me.xyz/solution-manual-polymer-science-and-technology-fried/ TABLE OF CONTENTS Chapter 1 1 Chapter 2 5 Chapter 3 14 Chapter 4 24 Chapter 5 28 Chapter 7 36 Chapter 11 40 Chapter 12 51 Chapter 13 52 CHAPTER 1 1-1 A polymer sample combines five...

Description

Access Full Complete Solution Manual Here https://www.book4me.xyz/solution-manual-polymer-science-and-technology-fried/

TABLE OF CONTENTS Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 7 Chapter 11 Chapter 12 Chapter 13

1 5 14 24 28 36 40 51 52

CHAPTER 1 1-1 A polymer sample combines five different molecular-weight fractions, each of equal weight. The molecular weights of these fractions increase from 20,000 to 100,000 in increments of 20,000. Calculate M n , M w , and M z . Based upon these results, comment on whether this sample has a broad or narrow molecular-weight distribution compared to typical commercial polymer samples. Solution Fraction # 1 2 3 4 5 Σ 5

M n = ∑Wi N = i =1

Mi (×10-3) 20 40 60 80 100 300

Wi 1 1 1 1 1 5

Ni = Wi/Mi (×105) 5.0 2.5 1.67 1.25 1.0 11.42

5 = 43,783 1.142 × 10−4

5

Mw =

∑W M i

i =1

∑W 5

∑W M i =1 5

i

300,000 = 60,000 5

=

4 × 108 + 16 × 108 + 36 × 108 + 64 × 108 + 100 × 108 = 73,333 3 × 105

2 i

∑W M i =1

=

i

i =1

Mz =

i

5

i

i

M z 60,000 = = 1.37 (narrow distribution) M n 43,783

1-2 A 50-gm polymer sample was fractionated into six samples of different weights given in the table below. The viscosity-average molecular weight, M v , of each was determined and is included in the table. Estimate the number-average and weight-average molecular weights of the original sample. For these calculations, assume that the molecular-weight distribution of each fraction is extremely narrow and can 1

https://www.book4me.xyz/solution-manual-polymer-science-and-technology-fried/

be considered to be monodisperse. Would you classify the molecular weight distribution of the original sample as narrow or broad? Fraction 1 2 3 4 5 6

Solution Let M i ≈ M v

6

M n = ∑Wi N = i =1

Weight (gm) 1.0 5.0 21.0 15.0 6.5 1.5

Fraction

Wi

Mi

1 2 3 4 5 6 Σ

1.0 5.0 21.0 15.0 6.5 1.5 50.0

1,500 35,000 75,000 150,000 400,000 850,000

Mv 1,500 35,000 75,000 150,000 400,000 850,000 Ni = Wi/Mi (×106) 667 143 280 100. 16.3 1.76 1208

WiMi 1500 175.000 627,500 2,250,000 2,600,000 1,275,000 7,929,000

50.0 = 41,322 1.21 × 10−3

6

Mw =

∑W M i

i =1

6

∑W

i

=

7,930,000 = 158,600 50.0

i

i =1

M w 158, 600 = = 3.84 (broad distribution) Mn 41,322

1-3 The Schultz–Zimm [11] molecular-weight-distribution function can be written as

W (M ) =

a b +1 M b exp ( − aM ) Γ ( b + 1)

where a and b are adjustable parameters (b is a positive real number) and Γ is the gamma function (see Appendix E) which is used to normalize the weight fraction. (a) Using this relationship, obtain expressions for M n and M w in terms of a and b and an expression for M max , the molecular weight at the peak of the W(M) curve, in terms of M n . Solution Mn =

∫

∞

0

∞

WdM

∫ (W 0

M ) dM

let t = aM 2

https://www.book4me.xyz/solution-manual-polymer-science-and-technology-fried/

∫

∞

0

∞ a b +1 a b +1 1 ∞ b 1 b t a exp − t d t a = t exp ( −t ) dt = Γ ( b + 1) = 1 ( ) ( ) ( ) ∫ Γ ( b + 1) 0 Γ ( b + 1) a b +1 ∫0 Γ ( b + 1)

WdM =

∞

∫0 (W

M ) dM =

∞ a b +1 a b +1 1 b −1 t a exp − t d t a = ( ) ( ) ( ) Γ ( b + 1) ∫0 Γ ( b + 1) a b

∫

∞

0

t b −1 exp ( −t ) dt =

a b +1 1 Γ (b) = Γ ( b + 1) a b

a a Γ (b) = bΓ ( b ) b

Mn =

1 b = ab a

Mw =

∫

∞

0

∫

WMdM

∞

0

∞

= ∫ WMdM = 0

WdM

b +1 ∞ a b +1 a b +1 Γ ( b + 2 ) t exp − = = a t d t a ( ) ( ) ( ) Γ ( b + 1) ∫0 Γ ( b + 1) a b + 2

( b + 1) Γ ( b + 1) = b + 1 aΓ ( b + 1) a (b) Derive an expression for Mmax, the molecular weight at the peak of the W(M) curve, in terms of M n . Solution dW a b +1 = bM b −1 exp ( − aM ) + M b ( − a ) exp ( − aM ) = 0 dM Γ ( b + 1) bM b − a = aM b

b = M a = M n (i.e., the maximum occurs at M n ) a

(c) Show how the value of b affects the molecular weight distribution by graphing W(M) versus M on the same plot for b = 0.1, 1, and 10 given that M n = 10,000 for the three distributions. Solution b a= 10,000 b a W=

0.1 1×10-5

1 1×10-4

10 1×10-3

a b +1 M b exp ( − aM ) dM Γ ( b + 1)

where Γ ( b + 1) = ∫

∞

0

( aM )

b

exp ( − aM ) dM .

Plot W(M) versus M Hint:

∫

∞

0

x n exp ( − ax ) dx = Γ ( n + 1) a n +1 = n ! a n +1 (if n is a positive interger).

3

https://www.book4me.xyz/solution-manual-polymer-science-and-technology-fried/

1-4 (a) Calculate the z-average molecular weight, M z , of the discrete molecular weight distribution described in Example Problem 1.1. Solution 3

Mz =

∑W M i =1 3

i

2 i

∑W M i =1

i

1(10,000 ) + 2 ( 50,000 ) + 2 (100,000 ) 2

= i

2

1(10,000 ) + 2 ( 50,000 ) + 2 (100,000 )

2

= 80,968

(b) Calculate the z-average molecular weight, M z , of the continuous molecular weight distribution shown in Example 1.2. Solution 105

Mz

∫ = ∫

3

M 2 dM

10 105 103

MdM

( M 3) = ( M 2) 3

105

2

103 105

= 66,673

103

(c) Obtain an expression for the z-average degree of polymerization, X z , for the Flory distribution described in Example 1.3.

4...