SOLUTIONS MANUAL FOR

by

Introduction to PolymersThird Edition

Robert J. YoungPeter A. Lovell

SOLUTIONS MANUAL FOR

by

Introduction to PolymersThird Edition

Robert J. YoungPeter A. Lovell

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Part I Problems

Concepts, Nomenclature

and

Synthesis of Polymers

1

Chapter 1 Concepts and Nomenclature

1.1 Polystyrene has the repeat unit structure

Hence

M0 = (8 x 12 g mol-1) + (8 x 1 g mol-1) = 104 g mol-1

Neglecting contributions from end-groups (which is reasonable because M n is high), then xn can be calculated using a rearranged form of Equation (1.1)

xn = M n / M0

xn =

89 440 g mol−1

104 g mol−1= 860

Molar-mass dispersity ĐM is defined by ĐM = Mw / M n and so if ĐM = 1.5, then

Mw = 1.5 x 89 440 g mol-1 = 134 160 g mol-1

1.2 The mean repeat unit molar mass of the copolymer M0

cop is given by Equation (1.2), which requires knowledge of the mole fraction Xj and the molar mass M0

j of each type j of repeat unit. Since there are only two types of repeat unit, it is necessary to calculate Xj for only one of the two repeat units (because XE + XVAc = 1). The two repeat units are of structure:

and so

M0E = (2 x 12 g mol-1) + (4 x 1 g mol-1) = 28 g mol-1

M0VAc = (4 x 12 g mol-1) + (6 x 1 g mol-1) + (2 x 16 g mol-1) = 86 g mol-1

2

Thus

X E = (100−12.9 g (100 g cop)−1 / 28 g mol−1

{(100−12.9 g (100 g cop)−1) / 28 g mol−1}+{12.9 g (100 g cop)−1 / 86 g mol−1}

XE = 0.954 Hence

XVAc = 1 – 0.954 = 0.046

M0cop can now be calculated from Equation (1.2)

M0cop = (0.954 x 28 g mol-1) + (0.046 x 86 g mol-1)

M0cop = 30.67 g mol-1

Finally, using a rearranged form of Equation (1.1)

xn

cop = 39 870 g mol−1

30.67 g mol−1=1300

1.3 (a) M n and Mw can be calculated using, respectively, Equations (1.4) and (1.9) with N1 = N2 = N3 = N:

M n =

(N ×10 000 g mol−1)+ (N × 30 000 g mol−1)+ (N ×100 000 g mol−1)N + N + N

M n = 46 667 g mol-1

Mw = {N × (10 000 g mol−1)2}+{N × (30 000 g mol−1)2}+{N × (100 000 g mol−1)2}

(N ×10 000 g mol−1)+ (N × 30 000 g mol−1)+ (N ×100 000 g mol−1)

Mw = 78 571 g mol-1

Mw / M n = 1.68

(b) M n and Mw can be calculated using, respectively, Equations (1.7) and (1.8) with w1 = w2 = w3 =

13

:

M n =1

(13

/ 10 000 g mol−1)+ (13

/ 30 000 g mol−1)+ (13

/ 100 000 g mol−1)

M n = 20 930 g mol-1

Mw = (1

3×10 000 g mol−1) + (1

3× 30 000 g mol−1) + (1

3×100 000 g mol−1)

Mw = 46 667 g mol-1

Mw / M n = 2.23

3

(c) The calculations are carried out as in (b) but with w1 = 0.145, M1 = 10 000 g mol-1 and w2 = 0.855, M2 = 100 000 g mol-1 :

M n =

1(0.145 / 10 000 g mol−1)+ (0.855 / 100 000 g mol−1)

M n = 43 384 g mol-1

Mw = (0.145×10 000 g mol−1)+ (0.855×100 000 g mol−1)

Mw = 86 950 g mol-1

Mw / M n = 2.00

The calculations for mixtures (a) and (b) show that, compared to mixing by equal numbers of molecules, mixing polymer samples with different molar masses by equal weight greatly increases the number of molecules of low molar mass and so reduces M n and Mw .

The calculations also highlight the inadequacies of using Mw / M n to assess molar mass distributions. The molar mass distribution for each mixture is multi-modal and this cannot be interpreted from Mw / M n . Furthermore, despite Mw / M n = 2 for the mixture in (c), this mixture does not have a molar mass distribution consistent with the most probable distribution or other common distributions for which Mw / M n = 2, thereby highlighting the deficiencies in using Mw / M n as the only means of assessing the functional form of molar mass distributions.

4

Chapter 2 Principles of Polymerization

2.1 Formation of high molar mass polymer at low overall monomer conversion, as in polymerization of vinyl chloride, is indicative of chain polymerization. Commercial production of poly(vinyl chloride) is carried out using methods of free-radical chain polymerization. Formation of high molar mass polymer only at high extents of reaction of functional groups, as for polymerization of ethylene glycol with terephthalic acid, is indicative of step polymerization. Poly(ethylene terephthalate) is produced commercially by melt-phase step polymerization of ethylene glycol with terephthalic acid.

2.2 The esterification rate coefficient kester defines the intrinsic reactivity of the carboxylic acid group towards a hydroxyl group in the formation of an ester link. The kester data show that the reactivity of a carboxylic acid group rapidly reaches a constant value (within experimental error) as the size of the molecule to which it is attached increases. The conclusion from these (and other such) data obtained in the early days of Polymer Science is that a single rate coefficient is capable of describing all the individual esterification reactions that occur during formation of a polyester by step polymerization. The observation that the intrinsic reactivity of a reactive species is independent of molecular size is more generally true and simplifies massively the treatment of polymerization kinetics (as is demonstrated in the chapters which consider polymerization kinetics, e.g. see Chapters 3–5). This assumption of equal reactivity of functional groups fails only for very short chains, so for formation of long chains (the usual situation), the assumption is entirely reasonable.

2.3 Methyl methacrylate is difunctional (the C=C π-bond provides for two links in the polymer backbone) and so its opening in polymerization produces linear poly(methyl methacrylate). Ethylene glycol dimethacrylate possesses two C=C bonds and so is tetrafunctional. Hence its inclusion in copolymerization with methyl methacrylate will lead initially to branching, but ultimately to the formation of a 3-dimensional network polymer (see Chapter 4, Section 4.6.1).

5

Chapter 3 Step Polymerization

3.1 (a)

CO

ClCH2C

8

O

ClCH2 NH2H2N

6n n

CH28

CH2 NHH2N6

n-1

CO

CO

ClCH2

8

OCH2 NHNH

6C

OC + (2n - 1) HCl

(b)

(c)

6

3.2 (I) is a polyurethane produced by polyaddition of

(II) is a polyester produced by polycondensation of

(III) is a polyamide produced by polycondensation of

3.3 The initial reaction is between two molecules of ω-amino carboxylic acid:

H2N R CONH R C OH

OH2N R C OH

O

H2N R C OHO

H2O++

and in general the polymerization can be represented by:

NH R C OHO

Hnn

n H2O( - 1)+H2N R C OHO

For the calculations, the data should be plotted according to 2nd and 3rd order kinetics (see Section 3.2.3.3) to determine which gives the best fit: For 2nd order kinetics a plot of 1/c against t should be a straight line For 3rd order kinetics a plot of 1/c2 against t should be a straight line

t / h c / mol dm-3 (1/c) / dm3 mol-1 (1/c)2 / dm6 mol-2 0 3.10 0.323 0.104 0.5 1.30 0.769 0.592 1.0 0.83 1.205 1.452 1.5 0.61 1.639 2.687 2.0 0.48 2.083 4.340 2.5 0.40 2.500 6.250 3.0 0.34 2.941 8.651

7