Polymer Chemistry Course, KTE 080, 2016 Patric Jannasch ————————————————————————————————

Exercises in polymer chemistry

Polymer & Materials Chemistry

Contents

1 Step-Growth Polymerization 3

2 Free Radical Polymerization 9

3 Emulsion Polymerization 14

4 Ion and Coordination Polymerization 16

5 Copolymerization 18

6 Polymers in Solution 21

7 Polymer characterization - Molar masses 25

Answers 30

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Chapter 1 Step-Growth Polymerisation 1.1. Can the following alkyd recipe be carried to ”complete” conversion without gelling?

(Rudin A. The Elements of Polymer Science and Engineering 1982)

1.2. Following is a simplified alkyd recipe:

a) Calculate the number average degree of polymerization when the esterification reaction is complete (p = 1). b) An operator makes up this mixture and forgets to add the ethylene glycol. He tries to run the reaction to completion. At what extent of conversion will he notice the results of this omission? (Rudin A. The Elements of Polymer Science and Engineering 1982)

CH2OH

CH2OH

HOH2C

CH2OH

Pentaerythritol Phthalic anhydride Tricarballylic acid

1.21 mole 0.5 mole 0.49 mole

O

O

O

COOH

COOH

COOH

CH (CH2 )7COOHCH3 (CH2 )7CHoleic acid phthalic acid glycerol ethylene glycol

1.00 mole 1.31 mole 1.30 mole 0.5 mole

COOH

COOH

OH OH OH

OH OH

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1.3. Calculate the extent of reaction at which gelation occurs for the following mixtures: a) phthalic anhydride and glycerol in stoichiometric amounts, b) phthalic anhydride and glycerol in the molar ratio 1.500:0.980 c) phthalic anhydride, glycerol and ethylene glycol in the molar ratio 1.500:0.990:0.002 d) phthalic anhydride, glycerol and ethylene glycol in the molar ratio 1.500:0.500:0.700 Compare the gel points calculated from Carothers equation (and its modifications) with those using the statistical approach. (Odian G. Principles of Polymerization 1981) 1.4. When will the gel point be reached in a system containing 2 mole RA3 and 3 mole of R´B2 provided the only reaction occurring is that between A- and B-groups? 1.5. Ethylene glycol is polymerized with an impure sample of terephthalic acid which contains 1.0 % benzoic acid. a) How does this impurity affect the limiting degree of polymerization at very high conversions? b) Calculate the number average molecular weight at very high conversions. (Rudin A. The Elements of Polymer Science and Engineering 1982) 1.6. The polymerization between equimolar amounts of a diol and diacid proceeds with an equilibrium constant of 200. What will be the expected degree of polymerization and extent of reaction if the reaction is carried out in a closed system without removal of the by-product water? To what level must [H2O] be lowered in order to obtain a degree of polymerization of 200 if the initial concentration of carboxyl groups is 2 M? (Odian G. Principles of Polymerization 1981)

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1.7. A polymerization reaction was run in order to produce a polyester. A sample was taken from the reaction vessel after 20 minutes. The sample was titrated with KOH and 52 % of the acid groups had reacted. The monomers used in the reaction were phthalic acid (1.2 mole), maleic acid (1.2 mole), diethylene glycol (2 mole) and pentaerythritol (0.2 mole). The reactivities of the functional groups are assumed to be equal. The reaction was carried out in toluene with a strong acid as a catalyst. The water produced was continually removed and replaced by toluene. a) In this polymerizarion gelation will occur. At what conversion will that happen? b) At which reaction time will the gel point be reached? 1.8. When an equilibrium step-growth polymerization is 99.5 % complete, what fraction of the reaction mixture is still monomer a) on mole basis? b) on weight basis? (Rudin A. The Elements of Polymer Science and Engineering 1982) 1.9. A step-growth polymer is found to have a number average degree of polymerization equal to 100. Assuming a most probable distribution and a degree of conversion of functional groups close to unity (p = 0.9999), calculate X w. (Rudin A. The Elements of Polymer Science and Engineering 1982) 1.10. A polyester was prepared by condensation polymerization of 6-hydroxy hexanoic acid (HO(CH2)5COOH). The reaction was carried out in a solvent and was catalyzed by a mineral acid. The water produced by the reaction was continually removed by distillation, and the total volume was kept constant by adding solvent. The reaction rate equation was:

d((COOH)

dt- = k(COOH)2

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The reaction was followed by titration of small samples. A sample was taken after 3 h and 20 min., and 95 % of the functional groups were found to be reacted. The desired product should have a M n = 8 000 g/mole. a) How long reaction time was necessary for obtaining the desired product? b) What should M w for the desired product be? 1.11. Nylon-11 is poly(11-amino undecanoic acid). This polymer has a crystal melting point around 190 °C and has lower water absorption than nylon-6,6 or nylon-6. It can be used to make mechanical parts, packaging films, bristles, monofilaments, and sprayed and fluidized coatings. n H2N(CH2)10COOH -(- NH(CH2)10CO -)-n + n H2O In step-growth polymerization of this monomer a) how much monomer (in terms of weight fraction of the reaction mixture) is left when 90 % of the functional groups have reacted? b) Calculate M n and M w of the reaction mixture at this stage. (Rudin A. The Elements of Polymer Science and Engineering 1982) 1.12. A polyester is produced by condensation of 6-hydroxy hexanoic acid (HO(CH2)5COOH) in a solvent using a catalyst. The produced water is continually removed by destillation and solvent is added to keep the total volume constant. The reaction can be described as a second order reaction. After 2 hours and 30 minutes reaction time 96 % of the functional groups have reacted. a) How long time must the reaction proceed to reach a number average molecular weight of 9 000 g/mole? b) What is the weight average molecular weight of the product? 1.13. Show that the time required to go from p = 0.98 to p = 0.99 is very close to the time to reach p = 0.98 from the start of polymerization for the external acid catalysed polymerization of an equimolar mixture of a diol and diacid. (Odian G. Principles of Polymerization 1981)

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1.14. Flory has studied acid catalyzed polyesterification. In one experiment he used p-toluene sulfonic acid (0.2 %) to catalyze the reaction between equivalent molar amounts of diethylene glycol and adipic acid at 109 °C. The reaction was performed with specially purified chemicals in a nitrogen atmosphere. Samples were taken from the reaction mixture and titrated with potassium hydroxide. Table 1.15.I shows the results from the experiment. Table 1.15.I

Time (min.)

Number average chain length

25 2.9845 5.2167 8.4998 14.13126 18.45163 25.35190 29.34223 35.90265 44.30308 53.50363 63.60415 73.70

(Flory, P. J., J. Am. Soc. 62, 1062 (1940)) Show the order of the reaction and express the number average chain length as a function of time. 1.15. Compare the maximum theoretical average molecular weight possible if 0.1 % and 1 % of the diethylene glycol in the experiment described in 1.14. was distilled off.

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Chapter 2 Free Radical Polymerization 2.1. Rate constants for termination kt may be of the order of 108 l/mole s in free radical polymerization. Consider the polymerization of styrene initiated by di-t-butyl peroxide at 60 °C. For a solution of 0.01 M peroxide and 1.0 M styrene in benzene, the initial rate of polymerization is 1.5*10-7 mole/l s and M n of the polymer produced is 138 000 g/mol. a) From the above information estimate kp for styrene at 60 °C. b) What is the average lifetime of a macro radical during the initial stages of the polymerization in this system? (Rudin A. The Elements of Polymer Science and Engineering 1982) 2.2. The benzoyl peroxide initiated polymerization of a monomer follows the simplest kinetic scheme, that is, Rp = kp[M](fkd[I]/kt)

1/2 with all rate constants and f being independent of conversion. For a polymerization system with [M]0 = 2 M and [I]0 = 10-2 M, the limiting conversion p∞ is 10 %. To increase p∞ to 20 %: a) Would you increase or decrease [M]0, and by what factor? b) Would you increase or decrease [I]0, and by what factor? How would the rate and degree of polymerization be affected by the proposed changes in [I]0 ? c) Would you increase or decrease the reaction temperature for the case of thermal initiated polymerization? Ed, Ep and Et are 64, 32 and 8 kJ/mole, respectively. (Odian G. Principles of Polymerization 1981) 2.3. The half-life time, t1/2,for decomposition of di-t-butyl peroxide and bis(1-hydroxy cyclohexyl) peroxide have been determined at different temperatures: T (°C) 90 100 110 120 130 t1/2 (h) di-t-butyl peroxide 800.0 210.0 65.0 20.0 6.5 t1/2 (h) bis(1-hydroxy cyclohexyl) peroxide 9.8 4.5 2.0 1.0 0.5 Calculate the activation energy of the decomposition, Ed, of the initiator. The kinetics are of the first order, and theArrhenius equation kd = A e(-Ed/RT) is followed.

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2.4. One hundred liters of methyl methacrylate is reacted with 10.2 moles of an initiator at 60 °C. kp = 5.5 l/mole s kt = 25.5*106 l/mole s Density of monomer = 0.94 g/cm3 t1/2 for this initiator = 50 h f = 0.3 a) What is the kinetic chain length in this polymerization? b) How much polymer has been made in the first 5 h of reaction? (Rudin A. The Elements of Polymer Science and Engineering 1982) 2.5. Styrene is bulk polymerized with 2-azobisisobutyronitrile (AIBN) as initiator. The initiator concentration is 0.01M. What number average chain length is reached at low conversion: a) at 60 °C? b) at 80 °C? The following data are known at 60 °C:

kp = 0.145*103 l/mole s kt = 2.9*107 l/mole s kd = 0.85*10-5 s-1 Ep = 32.0 kJ/mole Et = 8.0 kJ/mole Ed = 123.5 kJ/mole f = 0.6 The parameters k and E are rate constants and activation energies at 60 °C respectively, for propagation (p), termination (t) and initiator decomposition (d). Any consideration concerning chain transfer to monomer is not needed. The density of styrene is 910 kg/m3 and its molecular weight is 104.14 g/mole. Termination occurs by combination.

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2.6. 1.0 mole styrene and 1.0*10-4 2-azo-bis-isobutyronitrile (AIBN) is used to carry out a polymerization in 1 dm3 benzene. What molecular weight would be expected if every initiator fragment initiates one chain and: a) all chains start to grow at the same time, terminate only by disproportionation, and are of the same length? b) same as in a) but with termination by combination? c) same as in a) but 6.0*10-4 mole n-butyl mercaptan is added and each mercaptan molecule acts as chain transfer agent only once. 2.7. Suspension polymerization has been used to produce porous, spherical polystyrene particles. A mixture of toluene and isooctane was used to create permanent pores in the particles. Calculate the propagation constant and the number average molecular weight of the produced polymers. Termination occurs only by combination. Initiator efficiency = 0.80 Polymerization rate = 2.5*10-4 mole/(l s) Termination constant = 1.6*107 l/(mole s) Initiator decomposition constant = 4.5*10-5 s-1 Density of styrene = 0.909 g/cm3 M(AIBN) = 164 g/mole Recipe: Water 100 g AIBN (initiator) 0.03 g Styrene 30 g Solvent 15 ml Stabilizer 1 g 2.8. A sample of polystyrene with M n = 80 000 g/mole was prepared by using bulk polymerization to low conversion at 60 °C with AIBN as initiator. A chain transfer agent CCl4 was used to regulate the molecular weight. In the first experiment the mol ratio CCl4/styrene was 0.0413 and a polystyrene with M n = 200 000 g/mole was obtained. What ratio CCl4/styrene should be used in a second experiment to make the desired product? Identical conditions as in the first experiment was used. The chain transfer constant for CCl4 in this system was 0.0091. Termination occurs only by combination.

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2.9. Vinyl acetate was polymerized in a free radical reaction. The initial monomer concentration was 1 mole/l and its concentration after 1 h was 0.85 mole/l. Chloroform was present as a chain transfer agent, with concentrations 0.01 mole/l at time zero and 0.007 mole/l after 1 h. What is the chain transfer constant C in this case? (Rudin A. The Elements of Polymer Science and Engineering 1982) 2.10. Dibenzoyl peroxide is dissolved in acrylonitrile to a concentration of 0.01 mole/l. The acrylonitrile is suspension polymerized at 60 °C with 40 % of the reaction mixture (by volume) being acrylonitrile droplets. a) What is the initial steady state rate of polymerization (g polyacrylonitrile/l reaction mixture/s)? b) What is M n of the polymer made during this stage of the reaction? For dibenzoyl peroxide take kd = 3*10-6 s-1, f = 0.4; for acrylonitrile: density = 0.8 g/cm3, molecular weight = 53 g/mole, kp = 1960 l/(mole s), kt = ktc = 780 l/(mole s), CM = 0.3*10-4. (Rudin A. The Elements of Polymer Science and Engineering 1982) 2.11. Styrene was polymerized with a peroxide initiator (6.6*10-3 mole/l) to low conversion. The polymerization rate (assumed constant) was determined to 1.79*10-3 g/(mole min) by weighing amount produced polymer. At the temperature used was kd = 3.25*10-4 min-1 and the density for styrene was 910 g/l. a) Estimate the maximum degree of polymerization (DP n) for the polymer and state what assumptions this estimate is based on. b) Is the molecular weight distribution narrower or wider than the most probable one? Explain why! c) Calculate the rate of polymerization if the initiator concentration is 25*10-3 mole/l. 2.12. Poly(vinyl acetate) of number-average molecular weight 100 000 is hydrolyzed to poly(vinyl alcohol). Oxidation of the latter with periodic acid to cleave 1,2-diol linkages yields a poly(vinyl

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alcohol) with X n = 200. Calculate the percentages of head-to-tail and head-to-head linkages in the poly(vinyl acetate). (Odian G. Principles of Polymerization 1981) 2.13. For a radical polymerization with bimolecular termination, the polymer produced contains 1.30 initiator fragments per polymer molecule. Calculate the relative extent of termination by disproportionation and coupling, assuming that no chain transfer reactions occur. (Odian G. Principles of Polymerization 1981) 2.14. Styrene is bulk polymerized isothermally at 60 °C with AIBN as initiator. Calculate the amount of initiator needed to reach 90 % conversion of the styrene. kp

2/kt = 1.18*10-3 l/(mole s) rstyrene = 0.907 g/cm3 kd = 0.96*10-5 s-1 f = 1

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Chapter 3 Emulsion Polymerisation 3.1. Following is a recipe for the production of a polyacrylate latex. All quantities are in parts by weight. Ethyl acrylate 93 2-Chloroethyl vinyl ether 5 Divinyl benzene 2 Sodium lauryl sulfate (emulsfier) 3 Sodium pyrophosphate (pH buffer) 0.7 K2S2O8 (initiator) 1 Water 133 Time 8 h Temperature 60 °C Yield 100 % What effects do the following changes have on the polymerization rate in interval II? a) Using 6 parts sodium lauryl sulfate. b) Using 2 parts K2S2O8. c) Using 6 parts sodium lauryl sulfate and 2 parts K2S2O8. d) Adding 0.1 parts lauryl mercaptan (chain transfer agent). (Rudin A. The Elements of Polymer Science and Engineering 1982) 3.2. a) What happens to the rate of emulsion polymerization if more monomer is added to the reaction mixture during interval II polymerization? b) What happens to the number average degree of polymerization? (Rudin A. The Elements of Polymer Science and Engineering 1982) 3.3. Estimate the number of polymer chains in a latex particle with a diameter of 0.05 µm. The density of the polymer is 1 g/cm3, DP n = 10 000 and the molecular weight of the monomer is 100 g/mole.

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3.4. Styrene is polymerized in emulsion with K2S2O8.as initiator. Every initiator molecule gives two radicals. a) If the rate constans for initiator decomposition is 0.08 h-1 and the initiator concentration 5 mM, what is the rate of radical production in mole/l s? b) At 15 % conversion exists 1018 particles/l in which polymerization can occur. No radicals are lost to the aqueous phase and termination occurs immediately when a second radical enters the particle. Calculate the lifetime of a radical in a particle. c) During the above polymerization, 103 monomer molecules are added per second to a growing chain. What is the average degree of polymerization and the molecular weight of the polymer in the particle? 3.5. Calculate the polymerization rate and the average degree of polymerization when styrene is polymerized at 60 °C. The emulsion contains 3.2*1013 polymer particles per cm3, the concentration of monomer is 5 M and the rate of radical production is 1.1*1012 cm-3 s-1. kp = 145 l/(mole s). 3.6. Compare the rate and degree of polymerization when styrene is polymerized in bulk at 60 °C with an emulsion polymerization (Case 2 behavior: n = 0.5) containing 1.0*1015 polymer particles per milliliter. Assume that [M] = 5.0 molar, Ri = 5.0*1012 radicals per milliliter per second and all rate constants are the same for both systems. For each polymerization system, indicate the various ways (if any) by which the polymerization rate can be affected without affecting the degreee of polymerization. (Odian G. Principles of Polymerization 1981) 3.7. A particular emlsion polymerization yields polymer with M n = 500 000. Show how you would adjust the operation of a semibatch emulsion process to produce a polymer with M n = 250 000 in interval II without changing the rate of polymerization, reaction temperature or particle concentration. (Rudin A. The Elements of Polymer Science and Engineering 1982)

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Chapter 4 Ion and Coodination Polymerisation 4.1. Styrene is polymerized in tetrahydrofuran with butyllithium as initiator. a) What reactions occur? b) Calculate the molecular weight for the polymer if every initiator molecule starts one polymer chain, the intiation is momentary and termination and chain transfer do not occur. The concentration of initiator is 10-4 mole/l and the concentration of styrene 0.15 mole/l. c) What is the ratio M w/M n? 4.2. A scrupulously clean and dry solution of styrene (5 g) in 50 ml tetrahydrofuran was held at -70 °C. Sodium (1.0 g) and naphthalene (6.0 g) were stirred together in 50 ml dry tetrahydrofuran to form a dark green solution of sodium naphthalene. When 1.0 ml of this green solution was injected into the styrene solution the latter turned reddish orange. After a few minutes the reaction was complete. The color was quenched by adding a few milliliters methanol. The reaction mixture was allowed to warm to room temperature, and the polymer formed was precipitated and washed with methanol. What is M n of the polystyrene formed in the absence of side reactions? What should M w of the product be if the polymerization were carried out so that the growth of all macromolecules was started and ended simultaneously? (Rudin A. The Elements of Polymer Science and Engineering 1982) 4.3. Anionic polymerization of styrene can be initiated by potassium amide, KNH2, in liquid ammonia. The reaction of the amide ions with styrene determine the reaction rate. Termination occurs by a chain transfer reaction with the solvent. a) Show all the reactions. b) Derivate an expression relating the polymerisation rate to the concentrations of initiator, monomer and solvent. c) Derive an expression for the kinetical chain length. d) Discuss the temperature dependence of the polymerisation rate when En =-16.7 kJ/mol and Ei = 54.4 kJ/mol.

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4.4. Isobutylene is polymerized under conditions where chain transfer to monomer is the predominant chain-breaking reaction. A 4.0 g sample of the polymer was found to discolor 6.0 ml of an 0.01 M solution of bromine in carbo tetrachloride. Calculate the number average molecular weight of the polyisobutylene. (Odian G. Principles of Polymerization 1981) 4.5. 1.0*10-3 mole of sodium naphthalene is dissolved in tetrahydrofuran and then 2.0 moles of styrene is introduced into the system by a rapid injection technique. The final total volume of the solution is 1 liter. Assume that the injection of the styrene results in instantaneous homogeneous mixing. It is found that half of the monomer is polymerized in 2 000 s. a) Calculate the propagation rate constant. b) Calculate the degree of polymerization at 2 000 s and at 4 000 s of reaction time. (Odian G. Principles of Polymerization 1981) 4.6. Isobutene is polymerized commercially by a cationic mechanism initiated by strong acids like AlCl3. It is not polymerized by free radicals or anionic initiators. Acrylonitrile is polymerized commercially by free radical means. It can also be polymerized by anionic initiators like potassium amide but does not respond to cationic initiators. Account for the difference in behavior of isobutene and acrylonitrile in terms of monomer structure. (Rudin A. The Elements of Polymer Science and Engineering 1982)

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Chapter 5 Copolymerization 5.1. Calculate the copolymer composition (in mole percent) formed at an early stage of the reaction of: a) methyl methacrylate (monomer 1) at 5 mole/l and 5-ethyl-2-vinyl pyridine (monomer 2) at 1 mole/l concentration. Reactivity ratios are r1 = 0.40 and r2 = 0.69. b) What molar ratio of monomers in the feed produces a copolymer composition which is the same as the feed composition? (Rudin A. The Elements of Polymer Science and Engineering 1982) 5.2. A copolymer consisting of acrylic acid and acrylamide can be produced in two ways, either from acrylic acid or sodium acrylate copolymerized with acrylamide. Usually acrylamide and sodium acrylate in aqueous solution are used and fed into the reactor at a molar ratio 35:65 and the reaction proceeds until all monomer is consumed. If instead acrylic acid is used, is it possible to get a product with the same amount of monomer units in the polymer and the same average monomer sequence length? In which ratio should the reactant be feed if the copolymer at low conversion should have similar total composition as in the sodium acrylate case? The polymerization is carried out at 60 °C. The reactivity ratios for acrylamide (M1) and acrylic acid (M2) are r1 = 1.38 and r2 = 0.36, and for acrylamide (M1) and sodium acrylate acid (M2) r1 = 1.10 and r2 = 0.35. 5.3. At anionic and cationic polymerization the reactivity of the active center changes when the solvent is changed. The reactivity depends on the ability of the solvent to shield charges and depends on the polarity of the solvent. This phenomenon is reflected in the reactivity ratios. Copolymerization of styrene (M1) and isoprene (M2) with organic lithium compounds as initiators gave the following reactivity ratios: Solvent r1 r2 Toluene 0.35 3.20 Triethylamine 0.50 0.25 Tetrahydrofuran 2.65 0.15 a) Draw a plot showing the initial copolymer composition as a function of the comonomer feed composition. Are there any azeotropic compositions for the copolymer?

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b) A copolymer having the average sequence length of styrene twice as that for isoprene is to be produced. At what feed compositions will the polymerization give this sequence distribution in the different solvents? 5.4. Copolymerization of methyl methacrylate (MMA, r1 = 1.322) and acrylonitrile (AN, r2 = 0.138) gives the following plot

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

f1

In one experiment the initial molar ratio of MMA/AN was 70/30. The polymerization was carried out to complete conversion. The polymer produced in the end of the reaction was a homopolymer. Which one? Explain your answer. 5.5. The copolymerization of ethylene and propylene is found to be essentially random (r1r2~1) with (C2H5)2AlCl/VO(C2H5)3 catalyst in chlorobenzene at 30 °C. The control of such systems is frequently on monomer concentration in the gas phase over the reaction mixture. This is because gas phase concentrations vary less with temperature, pressure and solvent. What monomer composition in the gas phase is needed to produce a copolymer containing 30 mole % propylene? The reactivity ratio of ethylene (r1) has been found to be 5, based on gas phase concentration. (Rudin A. The Elements of Polymer Science and Engineering 1982)

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5.6. What copolymer composition is initially obtained when butadiene (M1) and styrene (M2) is copolymerized at 50 °C and the monomers are mixed in equimolar amounts? r1 = 1.35 and r2 = 0.58. 5.7. Copolymerization of methacrylic acid (M1) and methacrylonitrile (M2) gives a polymer with the following composition:

Monomer composition mole-% M1

Polymer composition mole-% M1

0 0.0 10 15.5 20 29.2 30 41.3 40 52.1 50 61.0 60 70.8 70 79.0 80 86.5 90 93.5 100 100.0

Estimate the reactivity ratios r1 and r2 for the monomer. 5.8. It has been suggested that free radical polymerization would be a useful way to react an equimolar mixture of allyl acetate and methyl methacrylate. Is this a good idea? (Allyl acetate: e = -1.13, Q = 0.028; methyl methacrylate: e = 0.40, Q = 0.74). (Rudin A. The Elements of Polymer Science and Engineering 1982) 5.9. Calculate the monomer reactivity ratios for the comonomer pairs styrene-butadiene and styrene-methyl methacrylate. Styrene: e = -0.80, Q = 1.00; butadiene: e = -1.05, Q = 2.39; methyl methacrylate: e = 0.40, Q = 0.74. (Odian G. Principles of Polymerization 1981)

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Chapter 6 Polymers in Solution 6.1. Which of the following polymers in table 6.1.I are persistent against gasoline? Table 6.1.I Polymer Molecular weight of monomer

(g/mole)

(cal/cm3)1/2 Polyethylene 28.05 7.9 Polystyrene 104.14 9.1 PVC 68.50 9.7 SBR 25 mol-% styrene, 75 mol-% butadien BUNA 25 mol-% akrylnitril, 75 mol-% butadien The value for gasoline is between 6 and 8 (cal/cm3)1/2. 6.2. Toluene (molecular weight = 92 g/mole, density = 0.87 g/cm3) boils at 110.6 °C at 1 atm pressure. Calculate its solubility parameter at 25 °C. [The enthalpy of vaporization may be approximated from the normal boiling point Tb (K) of a solvent: H(25 °C) = 23.7Tb + 0.020Tb

2 - 2950 cal/mol (J. Hildebrand and R. scott, ”The Solubility of Non Electrolytes”, 3rd ed. Van Nostrand Reinhold, New York, 1949).] (Rudin A. The Elements of Polymer Science and Engineering 1982) 6.3. Calculate the solubility parameter for a methyl methacrylate-butadiene copolymer containing 25 mole % methyl methacrylate. (poly(methyl methacrylate)) = 19.0 (J/cm3)1/2; (polybutadiene) = 17.1 (J/cm3)1/2. (Rudin A. The Elements of Polymer Science and Engineering 1982) 6.4. What relative amounts of methyl ethyl ketone, ethanol, and a hydrocarbon fraction will give the same solution properties as n-butyl acetate? LÖSNINGSMEDEL d p h n-butyl acetate 8.5 7.7 1.8 3.1 MEK 9.3 7.8 4.3 2.5 Ethanol 13.0 7.7 4.4 9.5 Hydrocarbon fraction 8.0 8.0 0.2 0.3

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6.5. Which of the following polymers will dissolve in tetrahydrofuran? Use the molar attraction constants in table 6.5.I to calculate . THF = 9.5 (cal/ cm3)1/2. a) Polystyrene, = 1.05 g/cm3 b) Poly(methyl methacrylate), = 1.19 g/cm3 c) Polyacrylonitrile, = 1.18 g/cm3 Guidance: = *Fi/M0 Table 6.5.I Group Molar attraction Fi

(cal*cm3)1/2/mol Group Molar attraction Fi

(cal*cm3)1/2/mol -CH3 148.3 -H acidic dimer -50.47

-CH2- 131.5 OH aromatic 170.99

>CH- 85.99 NH2 226.56

-C-

32.03

- NH

180.03

CH2= olefin 126.54 - N -

61.08

-CH= olefin 121.53 CN 354.56

>C= olefin 84.51 NCO 358.66

-CH= aromatic 117.12 -S- 209.42

>C= aromatic 98.12 Cl2 342.67

-O- (ether, acetal) 114.98 Cl primary 205.06

-O- (epoxide) 176.20 Cl secondary 208.27

-COO- 326.58 Cl aromatic 161.0

>C=O 262.96 Br 257.88

-CHO 292.64 Br aromatic 205.60

(CO)2O 567.29

-OH-> 225.84 F 41.33

Structure feature Structure feature

Conjugation 23.26 6-membered ring -23.44

Cis -7.13 Ortho substitution 9.69

Trans -113.50 Meta substitution 6.6

4-membered ring 77.76 Para substitution 40.33

5-membered ring 20.99

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6.6. A copolymer of methyl methacrylate and acrylonitrile is produced form a 70/30 (MMA/AN) mixture of the monomers. The copolymer is composed of polymer chains containing from 79 mol-% methyl methacrylate to 100 mol-% acrylonitrile because of the reactivity ratios. Select a good solvent from table 6.6.I for the produced copolymer. Table 6.6.I Solvent

((cal/cm3)1/2) Diisodecyl phthalate 7.2 Isoamyl acetate 7.8 Methyl isobutyl ketone 8.4 Tetrahydrofuran 9.3 1,4-Dioxane 10.0 Furfural 11.2 Dimethyl sulfoxide 12.0 (poly(methyl methacrylate) = 9.3 (cal/cm3)1/2 (polyacrylonitrile) = 12.7 (cal/cm3)1/2

Help: c = wii |1-2|<2 (cal/cm3)1/2 soluble 6.7. The molecular weight and radius of gyration of a monodisperse preparation of polymethylene were measured in a theta solvent, and found to be 22 400 g/mole and 6.5 nm, respectively. Calculate the mean square end-to-end distance and the characteristic ratio. The carbon-carbon bond length is approximately 0.153 nm. (Richard E.G. An introduction to physical properties of large molecules in solution 1980)

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6.8. The radius of gyration and second virial coefficient of a sample of atactic polystyrene dissolved in cyclohexane were measured (by light-scattering methods) at a series of temperatures with the results in table 6.8.I. Estimate the unperturbed root mean square end-to-end distance and the theta temperature in this solvent. What is the expansion factor () at 320 K? Table 6.8.I

T (K)

S (nm)

A2 (arbitrary units)

305.7 47.9 -0.40 307.2 51.8 -0.20 311.2 57.6 0.37 318.2 62.5 0.95 328.2 66.5 1.58

(Richard E.G. An introduction to physical properties of large molecules in solution 1980) 6.9. A series of polystyrene samples of varying molecular weights were dissolved in cyclohexane. The solutions were cooled until they just became opalescent. The temperatures at which this occurred were recorded, and are given in table 6.9.I together with the molecular weights. Assume that the volume for one monomer unit is the same as that of a cyclohexane molecule, and estimate the theta temperature of polystyrene in cyclohexane. Table 6.9.I

Tc (°C)

M (g/mole)

31.3 920 000 27.8 182 000 23.9 63 900 19.5 31 500

(Richard E.G. An introduction to physical properties of large molecules in solution 1980) 6.10.

24

Use the answer from problem 6.9. to calculate the second virial coefficient at 40 °C of each fraction of polystyrene, assuming that the solutions are concentrated and that the density of pure cyclohexane is 0.9. (Richard E.G. An introduction to physical properties of large molecules in solution 1980)

25

Chapter 7 Polymer characterization - Molar masses 7.1. Polystyrene was fractionated from a methyl ethyl ketone solution by additions of methanol. The osmotic pressure, was measured at 25 °C for one of the fractions dissolved in toluene at different concentrations, c. The results obtained are given in table 7.1.I. Calculate the number average of molar mass, and the second and third virial coefficient in the expansion of /c against c. Table 7.1.I

c (kg/m3)

(N/m2)

1.75 30.4 2.85 52.0 4.35 86.3 6.5 146.0 8.85 231.0

(Bawn, Freeman and Kamaliddin, Trans. Farady Soc. 46, 862 (1950)) 7.2. The data given in table 7.2.I are obtained from osmotic pressure measurements of nitrocellulose in acetone at 20 °C. Table 7.2.I

c (g/dm3)

(cm H2O)

1.16 0.62 3.66 2.56 8.38 8.00 19.0 25.4

Calculate ( /c)0 och M n. 7.3. In an ideal membrane osmometry experiment, a plot of /cRT against c gives a straight line with intercept 1/M . Similarly, an ideal light scattering experiment at zero viewing angle yields a straight line plot of Hc/t against c with intercept 1/M . For a given polymer sample, solvent and temperature, a) are the M values the same from osmometry and light scattering? b) are the slopes of the straight line plots the same? Explain your answers briefly. (Rudin A. The Elements of Polymer Science and Engineering 1982)

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7.4. Acetonitrile is a -solvent for poly(methyl methacrylate) at 302 K. Calculate the osmotic pressure for a solution containing a polymer with M n = 191 kg/mol and a concentration of 20 g/dm3. 7.5. Calculate the constants in the Mark-Houwink equation for polystyrene in tetrahydrofuran at 25 °C from the data given in table 7.5.I. Table 7.5.I

M v (g/mole)

[] (dl/g)

867 000 2.07 411 000 1.25 173 000 0.67 89 000 0.44 51 000 0.28 20 000 0.14

7.6. Viscosity measurements of poly methyl methacrylate in chloroform gave the following flow times: Flow time

(s)

chloroform 200.78 200.79 200.79 200.79 200.79

co = 4.988 g/dm3 222.77 222.76 222.74 222.74 222.74

chloroform 200.79 200.78 200.79 200.76 200.76

c1 = 4.000 g/dm3 218.13 218.13 218.18 218.14 218.24

chloroform 200.84 200.88 200.83 200.81 200.77

c2 = 3.015 g/dm3 213.74 213.82 213.80 213.84 213.76

chloroform 200.83 200.78 200.82 200.78 200.77

c3 = 2.013 g/dm3 209.33 209.32 209.35 209.38 209.38

a) Calculate the limiting viscosity number [] and the Huggins constant kH. Make the calculation in two ways, i.e., from sp/c and lnr/c. b) Calculate the molecular weight of the polymer when K[] = 3.3*10-6 and a = 0.85.

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7.7. Two ”monodisperse” polystyrenes are mixed in equal quantities by weight. One polymer has a molcular weight of 39 000 g/mol and the other a molecular weight of 292 000 g/mol. What is the intrinsic viscosity of the blend in benzene at 25 °C? The Mark-Houwink constants for polystyrene (benzene are K = 9.18*10-5 dl/g and = 0.74. (Rudin A. The Elements of Polymer Science and Engineering 1982) 7.8. Calculate the molecular weight of three different polystyrenes (PS1, PS2 and PS3) from the data in table 7.8.I measured at 25 °C: Table 7.8.I conc. polymer Flow time

(s)

(g/ml) PS1 PS2 PS3 0.01 155.8 148.5 140.2

0.0083 145.7 140.2 133.7 0.0071 138.8 134.5 129.1

The polystyrene is dissolved in toluene and the constants in the Mark-Houwink equation are 0.017 ml/g and 0.69. Flow time for pure toluene is 103.0 s. 7.9. In a laboratory experiment, bulk polymerization of methyl methacrylate (MMA) was studied at 60 °C with AIBN (0.14 mol/l) as initiator. A sample of the reaction mixture was taken 10 min after the polymerization had started. The analysis showed what the conversion was 7 %. Some of this sample was dissolved in chloroform and the flow time of four solutions with different concentrations were measured in an Ostwald viscosimeter at 20 °C, table 7.9.I. Table 7.9.I. Flow times for solutions of PMMA in chloroform at 20 °C.

[PMMA] (g/dl)

Flow time (s)

0 83.3 0.125 89.9 0.250 97.0 0.500 116.9 1.000 159.7

According to the literature PMMA in chloroform at 20 °C apply to :

log X n = 3.261 + 1.256log[] [] in dl/g. At 60 °C is the propagating rate constant for MMA 750 l/(mol s) and the density 0.85 g/cm3.

28

Termination occurs only by disproportionation. Calculate the termination constant. 7.10. A sample of polystyrene consists of fractions with various molecular weights:

Fraction Weight (g)

Molecularweight(g/mole)

A 0.23 21 000 B 0.28 35 000 C 0.22 49 000 D 0.15 73 000 E 0.12 102 000

Calculate the number average and the weight average molecular weights. 7.11. Calculate M n and M w for a sample of polystyrene with the following composition (i = degree of polymerization).

i 20 25 30 35 40 45 50 60 80 >80 w-% 30 20 15 11 8 6 4 3 3 0

(Rudin A. The Elements of Polymer Science and Engineering 1982) 7.12. Four different polystyrene samples were prepared using different amounts of CCl4 as chain transfer agent, see table 7.12.I. Unfortunately, when the GPC measurements were performed the sample names were mixed up. Calculate the number average molecular weights for the four samples and match the samples with the correct molecular weight. Table 7.12.I

PS sample Styrene (g)

CCl4 (mmol)

A 30.00 0 B 30.00 2.00 C 30.00 4.00 D 30.00 8.00

Table 7.12.II PS standard M n Elution volume

29

(g/mole) (ml) 1 332 200 30.5 2 190 680 32.1 3 115 500 33.8 4 82 700 35.0

Elution volumes for the PS samples 30.80 ml, 32.40 ml, 31.45 ml and 30.00 ml

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Answers 1.1. No, gelation at p = 0.89 1.2. a) X n = 8.33 b) Gelation at p = 0.9972 1.3. . a) pc(Carothers) = 0.833 pc(statistical) = 0.707 b) pc(Carothers) = 0.844 pc(statistical) = 0.714 c) pc(Carothers) = 0.838 pc(statistical) = 0.710 d) pc(Carothers) = 0.931 pc(statistical) = 0.826 1.4 p = 0.833 1.5. a) X n(p = 1) = 200 b) M n=19 200 g/mole 1.6. X n = 15 and p = 0.93 in a closed system If X n = 200 is to be obtained at the starting concentration of acid groups of 2 M, the concentration of water has to be decreased to 0,01 1.7. a) p = 0.9583 b) 7 hours and 4 minutes 1.8. a) x1 = 0.005 b) w1 = 0.000 025 1.9. X w = 200 1.10. a) 12 hours and 7 minutes b) 15 900 g/mole 1.11. a) w1 = 0.01 = 1 weight-% b) M n = 1 848 g/mole M w = 3 495 g/mole 1.12. a) t = 8 hours and 6 minutes b) M w = 17 900 g/mole 1.13. The reaction is of the second order 1.14. M n(0.1 %) = 216 000 g/mole M n(1 %) = 21 500 g/mole 2.1. 141 l/mole s

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2.2. a) Increase [M]0 by 1.125 b) Increase [I]0 by 4.49. DP n will decrease by 2.13 c) Decrease the reaction temperature 2.3. Ed(1) = 146 kJ/mole Ed(2) = 91 kJ/mole 2.4. a) = 14.9 b) 620 g 2.5. a) DP n(60 °C) = 1042 b) DP n(80 °C) = 523 2.6. a) M n = 0.52*106 g/mole b) M n = 1.04*106 g/mole c) M n = 1.30*105 g/mole 2.7. a) kp = 450 l/mole s b) M n = 190 000 g/mole 2.8. [CCl4]/[M] = 0.127 2.9. Ctr = 2.19 2.10. a) Rp = 6.15 g polymer/(l monomer + polymer) s = = 2.46 g polymer/ (l reaction mixture) s b) M n = 1.77*106 g/mole 2.11. a) DP n = 69.9, assuming f = 1 b) Narrower than most probable one. The probability that a long chain combinates with a short one is higher than the probability that it combinates with a chain of similar size. c) Rp2 = 2.92*10-4 mole/l min 2.12. 99.5 % head to tail 0.5 % head to head 2.13. 0.46 by coupling and 0.54 by disproportionation 2.14. [I]0 = 0.0108 mole/l 3.1. a) Rp increases with 20.6 b) Rp increases with 20.4 c) Rp increases with 2

32

d) No difference 3.2. a) No difference b) No difference 3.3. 39 3.4. a) 2.22*10-7 mole/l s b) 7.47 s c) 7.78*105 g/mole 3.5. Rp = 1.93*10-5 mole/l s DP n = 21 100 3.6. Increase the emulsifying agent concentration and the initiator concentration at the same time. 3.7. Use a chain transfer agent 4.1. a) see Cowie s 100 b) M n = 156 000 g/mole

c) M wM n

1

4.2. M n = 11 500 g/mole M w = 11 700 g/mole 4.3. a) see Cowie s 94

b) R p k i k p

kt r

KNH2 M 2

NH 3

c)

kp

ktr

M

NH3 d) Rp increases with temperature 4.4. M n = 67 000 g/mole 4.5. a) kp = 0.35 l/mole s b) X n (t = 2 000 s) = 2 000 X n (t = 4 000 s) = 3 000 5.1. a) 72 mole % methyl methacrylate and 28 mole % 5-ethyl-2-vinylpyridine b) 34 mole % methyl methacrylate and 66 mole % 5-ethyl-2-vinylpyridine

33

5.2. Yes, 33 mole % acrylamide and 67 mole % acrylic acid, the monomer sequence distribution is almost the same. 5.3. a) Yes in triethylamine b) Toluene: 85.6 mole % styrene 14.4 mole % isoprene Triethylamine: 70.7 mole % styrene 29.3 mole % isoprene Tetrahydrofuran: 36.5 mole % styrene 63.5 mole % isoprene 5.4. AN. MMA is consumed first 5.5. 31.8 mole % ethylene and 68.2 mole % propylene 5.6. 60 mole % butadiene and 40 mole % styrene 5.7. Finemann and Ross: r1 = 1.59 and r2 = 0.61 Slope: r1 = 1.54 and r2 = 0.65 5.8. No, initially will the copolymer consist of 93.8 mole % methyl methacrylate and 6.2 mole % allylacrylate. Methyl methacrylate is consumed and in the end will the polymer consist of only allylacrylate. 5.9. Styrene(1) - butadiene(2): r1 = 0.51 and r2 = 1.84 Styrene(1) - methyl methakrylate(2): r1 = 0.52 and r2 = 0.46 6.1. PE not resistant PS probably resistant PVC resistant SBR probably not resistant BUNA probably resistant = 18.3 (J/cm3)1/2 = 9.0 (cal/cm3)1/2 6.3. = 17.8 (J/cm3)1/2 = 8.7 (cal/cm3)1/2 6.4. MEK = 11 vol-% EtOH = 28 vol-% CHfraction = 61 vol-% 6.5. a) PS soluble b) PMMA soluble c) PAN not soluble 6.6. Furfural 6.7. r 2 = 254 (nm)2

= 6.77

34

6.8. r 21 /2

= 132 nm

= 1.17 6.9. = 34 °C 6.10. A2 = 2.09*10-4 cm3 mole/g2 7.1. M n = 167 000 g/mole A2 = 4.98*10-4 mole*m3/kg2 A3 = 2.6*10-5 mole*m6/kg3 7.2. (/c0) = 0.0518 Nm/g M n = 47 000 g/mole 7.3. a) No, osmometry gives M n and light scattering M w b) No, osmometry slope = A2 and light scattering slope = 2A2 7.4. 263 Pa 7.5. = 0.71 and K = 1.2*10-4 dl/g 7.6. a) From Huggins: [] = 0.02071; kH = 0.542 From Kreamer: [] = 0.02065; kH = 0.571 b) M v = 29 300 g/mole 7.7. [] = 0.62 dl/g 7.8. M n(PS1) = 86 400 g/mole M n(PS2) = 78 000 g/mole M n(PS3) = 62 600 g/mole 7.9. ktd = 2.17*107 l/mol s 7.10. M n = 37 500 g/mole M w = 48 600g/mole 7.11. M n = 2 880 g/mole M w = 3 270 g/mole 7.12. M n(PSA) = 390 000 g/mole M n(PSB) = 299 000 g/mole M n(PSC) = 242 000 g/mole M n(PSD) = 179 000 g/mole