Terpolymerization Parameters - Advances in Chemistry (ACS

Jul 22, 2009 - DOI: 10.1021/ba-1969-0091.ch004 ... Abstract: The rational design of a reaction system to produce a desired polymer is more feasible to...
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4 Terpolymerization Parameters A. RAVVE and J. T. KHAMIS Corporate R & D, Continental Can Co., Chicago, Ill.

In the terpolymerization

of styrene, 2-ethylhexyl

acrylate,

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and glycidyl acrylate a continuous-addition type of technique was used, and attempts were made to achieve maximum

conversions.

Relationships

were

sought

between

molecular weights, molecular weight distributions, reaction temperature, initiator concentration, half-life of the initiator, and rate of monomer-initiator

addition.

weights of the products depended temperature

The

molecular

strongly upon reaction

and on the rate of initiator

decomposition.

Narrower molecular weight distributions resulted from the use of initiators with shorter half-lives.

*Tphe theory of free-radical addition polymerization, described in numerous publications (2, 3, 4, 17, 21), makes it clear that radical chaingrowth reactions of polymers are regulated by statistical laws. Because of their statistical character the products from these reactions must be heterodisperse. The ranges extend from a single unit upward, depending upon kinetic details of the reactions. W i t h changes occurring i n concentrations of the reacting species during the reaction, the probability that the radical w i l l propagate also changes progressively. This results i n wider average molecular weight distributions than the most probable ones. As a result, molecular weight distributions occurring i n vinyl polymers follow complicated patterns and force annoying qualifications upon all attempts at generalizations. It was shown that i n m u l t i c h a i n polymers the m o l e c u l a r weight distribution, Xw/Xn, is equal to 2 when j^hain transfer is taking place. When, however, chain transfer is absent, Xw/Xn = 1.5. In actual practice, typical Xw/Xn values for vinyl polymers prepared to high conversion seldom exceed 5. Special cases like autoacceleration are exceptions where values as high as Xw/Xn = 10 were reported ( 5 ) . The ratio of monomer to catalyst must be maintained constant or as close to constant as possible during the reaction to obtain polymer chains 64

Platzer; Addition and Condensation Polymerization Processes Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

4.

RAWE AND KHAMis

Terpolymerization

Parameters

65

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of uniform length. In practice, the initiator tends to be depleted at a rate different from the monomer. To minimize this phenomenon, multiple charges of initiator and/or monomer are often conducted when polymerizations are carried to high conversions. Hoffman and co-workers (11) demonstrated how polymers may be obtained which have narrower distributions by feeding initiators or monomers to batch polymerizations at rates determined from basic equations. Further (18, 19), monomer and initiator can be added simultaneously at such rates that steady-state conditions might tend to predominate, leading to somewhat narrower distributions. Scope of This

Work

This is a study of solution polymerization of styrene, 2-ethylhexyl acrylate, and glycidyl acrylate. Such a terpolymer is typical of components in commercial thermosetting systems (20). As such, in commercial batch preparations, high conversions are desirable, and control is needed over molecular weights of the products. In addition, narrow molecular weight distribution often offers many rheological advantages (JO). Information was sought, therefore, on the extent of reproducibility and on the degree of variation occurring in both molecular weight and its distribution. The terpolymerizations described were carried out by a continuous feed method, unless stated otherwise, where both the monomer mixture and the initiator were added together continuously to the reaction kettle (18). The variables studied were (1) effects of initiators with different half-lives, (2) effects of variations in temperature, and (3) effects of variations in concentrations of initiators. Attempts were also made to study the extent of heterogeneity in the products. Most polymerization reactions were carried out on two commercial mixtures of monomers without any prior purification or removal of inhibitors. The products were compared with polymers from reactions with purified monomers and against other batches of commercial monomers to test reproducibility. Commercial monomers were used to approximate industrial conditions, where economic considerations may often make purification steps undesirable. Experimental

The monomers used were ( 1 ) styrene, rubber grade, D o w Chemical Co., 99.2% of pure styrene with 12 p.p.m. of p-terf-butylcatechol inhibitor; (2) 2-ethylhexyl acrylate (Celanese Corp.) 99.0% purity by weight with 50 p.p.m. of monomethyl ether of hydroquinone; (3) glycidyl acrylate ( D o w Chemical Co.) 90% purity with 0.1% monomethyl ether of hydro-

Platzer; Addition and Condensation Polymerization Processes Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

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66

ADDITION

AND CONDENSATION

POLYMERIZATION

PROCESSES

quinone. Most of the impurity i n this monomer was epichlorohydrin. Mixture A contained by weight 50% styrene, 35% 2-ethylhexyl acrylate, and 15% glycidyl acrylate with a total of 174 p.p.m. of inhibitors. Mix­ ture Β contained by weight 68.5% styrene, 20% 2-ethylhexyl acrylate, and 11.5% glycidyl acrylate, with a total of 133 p.p.m. of inhibitors. Mono­ mers used for kinetic studies were purified b y fractional vacuum distillation. Polymerization. A l l liter-size batches were carried out i n threenecked, round-bottomed flasks equipped with mechanical stirrers, reflux condensers, dropping funnels, nitrogen atmosphere, a thermowell for a thermocouple, and a heating mantle connected to an electronic tempera­ ture controller (temperatures were controlled within d z l ° C ) . A 133gram portion of the solvent was placed into the flask, the temperature raised to the desired level, and 400 grams of monomer mixture containing the initiator were added dropwise over the desired time. Larger batches were prepared i n an identical manner except that pilot plant stainless steel kettles were utilized, with temperature control of ± 2 ° C . However, when a 150-gallon kettle was used, control of only ± 4 ° C . was achieved. The extent of conversion was obtained by determining the total polymer present and by vapor phase chromatography ( V P C ) of the solution. Molecular Weight Determinations. The polymers obtained were sub­ jected to gel permeation chromatography (15) using three, 4-foot gelled polystyrene columns (Waters Associates), pore sizes 10 δ , 10 4 , ΙΟ 3 Α., with tetrahydrofuran as the solvent. The weight and number average molecular weights were then calculated with the aid of a General Electric basic language digital computer. The average weight per angstrom of 53.5 was obtained from calculations using molecular models. Light scattering measurements were carried out on a Brice-Phoenix photometer i n three solvents—tetrahydrofuran, toluene, and methyl isobutyl ketone. The values of HC/T and sin 2 0/2 + 10c were calculated, where c is concentration, with the aid of a computer. Number average molecular weights were determined in toluene using a Mechrolab high speed membrane osmometer with Schleicher and Schuell, type U . O . very dense cellophane membranes. Previous work has established that under these conditions diffusion of this type of polymer through the membrane is not detectable at molecular weights down to about 6000 ( I S ) . Viscosities of the terpolymers were measured i n toluene at 2 0 ° C . i n an Oswald-Fenske viscometer. Analyses for oxirane oxygen were carried out by titrating with H B r i n acetic acid (19). Polymer Fractionations. The first type was conducted by separating a whole polymer into different molecular sizes using gel permeation chromatography ( G P C ). The effluent was passed into a fraction collector which collected 5-cc. portions. The second fractionation was carried out by selective precipitations. A whole polymer was dissolved i n acetone, and methanol was added until a haze developed. The solution was cooled overnight at —20°C.

Platzer; Addition and Condensation Polymerization Processes Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

4.

RAWE AND KHAMis

Terpolymerization

Parameters

67

A precipitate separated, yielding Fraction 1. This procedure was repeated several times until a haze would no longer develop from successive alcohol additions. The resulting liquid was evaporated on a rotary evaporator to yield the last fraction (Fraction 4). Results

and

Discussion

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Reactivity ratios for the three-component system used in this investi­ gation were reported by Khamis (13): styrene, r12 = 0.91, rVA = 0.73; 2-ethylhexyl acrylate, r 2 i = 0.29, r 2 3 = 0.98; glycidyl acrylate, r:n = 0.25, r 3 2 = 1.08. From the Alfrey-Goldfinger equation ( I ) , the composition of the product from monomer mixture A should be: -[^styrene) 3 . 5 5 (2-ethylhexyl acrylate) 2 2 0 (glycidylacrylate) 1 0 ] n Analysis of the products obtained by continuous feed type polymerization at 1 3 8 ° C . with 3% dicumyl peroxide was: After 0.5 hours: -f^styrene) S Q 2 (2-ethylhexyl acrylate) 2 2 6 (glycidyl acrylate) 1 0 ] n and upon completion of the addition (1.5 hours): - f f styrene) 3 2 0 (2-ethylhexyl acrylate) 2.or> (glycidyl acrylate) 1 0 ] w Here styrene entered the chains faster at the outset of the reaction, but as it progressed, chains with amounts of glycidyl acrylate greater than theoretical formed. When monomer-initiator addition was complete and heating and stirring maintained for an additional 1.5 hours (holding period), the polymer composition, found by combustion analysis, was: C = 79.75%; H = 9.1%; Ο = 11.24%. This corresponds to a terpolymer composition of: -ffstyrene) 3 . 3 3 (2-ethylhexyl acrylate) 2 3 3 (glycidyl acrylate)i. 0 ]« (Calculated: C = 79.6% ; Η = 8.59% ; Ο = 11.7% ) Upon completion of the addition of the monomers-initiator mixture, at the end of the 90-minute period, some unreacted monomers were still present in the reaction vessel. When heating and stirring were continued for an additional 90 minutes, all the monomer was polymerized. Thus, to achieve maximum conversion, a holding period appears necessary. Dur­ ing such a holding period more chain transferring can be expected, with the result that the products will have broader molecular weight distributions. Nevertheless, if the greatest conversion can be achieved during the feed period, then final products may not be drastically affected. This appears true at least with the monomers and conditions used in these experiments as shown i n Table I.

Platzer; Addition and Condensation Polymerization Processes Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

68

ADDITION

Table I.

AND CONDENSATION

POLYMERIZATION

Effect of Holding Time during Terpolymerizationα Molecular

Time Past Addition,

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a

PROCESSES

——

hrs.

M

0 1.0 1.5

38,200 41,500 40,000

Weight by GPC —

——ΖΓ

Mn

Mw/Mn

16,800 16,200 16,400

2.3 2.6 2.5

w

A t 1 3 8 ° C , 3% dicumyl peroxide, monomer mixture B, and xylene solvent.

Table II shows molecular weight distributions of products from monomer mixtures A and Β using 3% dicumyl peroxide as initiator. The molecular weight distributions of the products from the six polymeriza­ tions are 3 or less. When, however, the percent of dicumyl peroxide was decreased i n the reaction mixture, considerably wider molecular weight distributions resulted (Table III). W i t h less initiator, the chains grow longer and terminate more often by chain transfer. Table II.

Polymerization with 3% Dicumyl Peroxide Initiator" Monomer Mixture

Molecular M

Weight by GPC ~ ——~Mn Mw/Mn

Polymer

Batch Size

I II ΙΠ VII

1 liter 10 gal. 10 gal. 150 gal.

A

62,700 60,900 70,800 77,000

20,800 23,100 29,800 30,000

3.0 2.6 2.4 2.6

IV V VI

10 gal. 10 gal. 10 gal.

Β

43,100 39,700 40,800

16,000 14,800 16,600

2.7 2.7 2.5

w

At 1 3 8 ° C , addition time, 1.5 hours; hold time, 1.5 hours; conversion, essentially 100%.

a

Table I V shows the effect of initiator concentration when tert-buty\ peroxide, an initiator with a longer half-life is used. Increasing the amount of this initiator from 1 to 3% by weight has resulted in a decrease in both the molecular weight and in the molecular weight distribution. However, the molecular weight distributions were still quite wide. Further, when purified monomers were used, the product had a lower molecular weight and a narrower molecular weight distribution. Thus, an appreciable number of initiating radicals appear to be lost to inhibitors in such commercial reaction mixtures. The amount of thermal initiation which takes place at 1 3 8 ° C . and its effect on molecular weights and their distributions were also studied. Two batches were polymerized thermally using monomer mixture A .

Platzer; Addition and Condensation Polymerization Processes Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

4.

RAWE AND KHAMis

Table III.

Τ erpolymerization

Parameters

Effect of Initiator Concentration Using Dicumyl Peroxide" Molecular

Weight by GPC

Mw/M,

Initiator, %

Mw

VIII IX X

1 2 3

148,300 84,200 62,700

33,100 21,700 20,800

4.5 3.9 3.0

XI6 Pure monomers

2 2

102,400

27,562 23,800 (by osmotic pressure )

4.1

Polymer

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69





"Monomer mixture A, 138°C., 1-liter size; conversion, essentially 100%. 6 This batch was not prepared by continuous feed method. Instead, a 50% solution of all reactants in xylene was placed into the flask, and the reaction mixture was heated to 138°C. and stirred under N 2 till full conversion was achieved. Table IV.

Effect of Initiator Concentration Using Di-ieri-butyl Peroxide" Molecular

Weight by GPC

Polymer

Initiator, %

Mw

Mn

XII Avg. for 4 batches as shown in Table VII XIII

1

568,000

63,900

8.9

2 3

228,000 124,300

35,600 23,900

6.4 5.2

Purified monomers

2

144,193

25,000

5.8

At 138°C, addition time, 1.3 hrs.; hold time, 1.5 hrs.; size, 1 liter; conversion, essen­ tially 100%, monomer mixture A. a

Table V.

Effect of Temperature on Molecular Weight and on Its Distribution" Molecular

Polymer

XVI Avg. for 4 batches as shown in Table VII XXVIIP

Weight by GPC

Reaction Temp., °C.

Mw

Mn

Mw/M,

130

572,500

59,700

9.6

138 150

228,000 73,600

35,600 17,700

6.4 4.2

a 2% Di-terf-butyl peroxide, monomer mixture A, batch size, 1 liter; conversion, essen­ tially 100%. Mn by osmotic pressure = 18,500. b

Platzer; Addition and Condensation Polymerization Processes Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

70

ADDITION

AND CONDENSATION

POLYMERIZATION

PROCESSES

Table VI. Effect of Molecular

Monomer Mixture

Polymer

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X XIII XVII XVIII XIXh

Initiator,'

A A A Β A

%

M

DCP,3 DTBP,3 BzP,3 BPIC,3 AZBN,2

w

62,700 124,300 36,800 38,600 33,100

Addition time, 1.5 hrs.; hold time, 1.5 hrs.; size of batch, 1 liter. Legend: DCP, dicumyl peroxide. DTBP, di-teri-butyl peroxide. BzP, benzoyl peroxide. BPIC, butyl peroxy isopropyl carbonate. AZBN, azobisisobutyronitrile. α c

Table VII.

Reproducibility of Polymerizations" Molecular

Weight by GPC

M ,w / M n

Polymer

Mw

XX XXI6 XXII XXIII

229,200 236,400 226,600 219,800

43,000 30,200 38,500 31,000

5.3 7.8 5.9 7.1

Average

228,000

35,600

6\4

Monomer mixture A, 2% terf-butyl peroxide, 138°C, in xylene. Batch size, 1 liter; conversion, essentially quantitative. M„ by osmotic pressure = 30,400. a

6

One reaction was not carried out by continuous addition but as a 50% solution i n xylene at 138 ° C . for eight hours. Mw was found by G P C to be 301,000 and Mn to be 113,700 with MJMn = 2.6. The second reaction was carried out by continuous addition. Here the conversion was some­ what lower (8-10% ). The Mw was found to be 318,600, and Mn was 115,400. Mw/Mn = 2.8. Thus, it appears that ©nly small amounts of thermal polymerizations occur at this temperature and that their contri­ butions to the product are relatively small. Table V illustrates the effect of variation i n temperature and Table V I the effect of using initiators of different half-lives. The results of these effects are predictable. The reproducibility of these polymerizations was studied by pre­ paring four batches under identical conditions. The results are presented in Table V I I . The average of the molecular weights for these four batches was then used to compare with other batches where effects of variations

Platzer; Addition and Condensation Polymerization Processes Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

4.

RAVVE AND

KHAMIS

Terpolymerization

Parameters

71

Different Initiators0 Weight by GPC

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.20,800 23,900 16,700 15,400 15,700

Mw/Mn

Solvent

Reaction Temp., °C.

Half-Life of Init. Reaction Temp., hours

3.0 5.2 2.2 2.5 2.2

Xylene Xylene Toluene Xylene Benzene

138 138 110 138 80

0.7 3.0 0.12 0.1 0.9

b After 8 hours the conversion was still only 63%. Reaction was not carried out by the continuous feed method but instead in a 50% benzene solution.

in batch sizes were_studied. Results are presented in Table V I I I . The high ratios of Mw/Mn for the polymers listed are probably caused by autoacceleration. W h e n both monomer and initiator are added simultaneously, the rate of monomer and initiator addition to the reaction doesn't appear to be very critical. This was shown in a study of homopolymerization of styrene ( 19) and appears to be true in this terpolymerization (Table I X ) . Variations in Mic/Mn appear small. However, there is a decrease in Mw Table VIII.

Effect of Batch Sizes" Molecular

Polymer

Batch Size

Avg. for 4 batches shown in Table VII XXV a

M

w

Weight by GPC M„

Mw/M„

1 liter

228,000

35,600

6.4

10 gal.

243,000

38,000

6.4

2% Di-teri-butyl peroxide, monomer mixture A, 138°C, in xylene. Table IX.

Effects of Monomer-Initiator Addition Rate Molecular Addition

Polymer

Time, hrs.

—— Mw

Weight by GPC ZZ — n

M

Mw/M„

XXII Η 226,800 38,500 5.9 XXVI6 2" 187,100 31,400 6.0 XXVII 3 165,900 26,800 6.2 "Monomer mixture A, 2% DTBP, 138°C, in xylene; holding time, 1V2 hrs.; conver­ sion, essentially 100%. Mby osmotic pressure = 27,000. b

Platzer; Addition and Condensation Polymerization Processes Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

72

ADDITION

A N D CONDENSATION

POLYMERIZATION

PROCESSES

with an increase i n addition time. This may be caused by lower con­ centration of monomers i n the solvent during the early stages of the reactions. Polymer X V I ( Table V ) was fractionated into four portions by frac­ tional precipitation. The molecular weights of each fraction were then determined by G P C . The intrinsic viscosity of each fraction was obtained and used to calculated Κ and a values of the Mark-Houwink equation (12, 16) using Mw determined by G P C . This is presented in Table X .

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Table X . Fractionation of Polymer X V I a

these data, Κ =

Mv

572,500 802,300 161,400 37,941 13,746

858,769 140,700 38,673 12,838



Whole Polymer Fraction 1 Fraction 2 Fraction 3 Fraction 4 • From

M w by GPC 1.525 0.3650 0.1315 0.0530

3.1097 X10"5; a = 0.79047;

M=



3.1097 Χ ΙΟ^Μ,ο.79047.

Infrared data on a l l fractions of Polymer X X (Table X ) collected by both methods of fractionation revealed no discernible differences b y comparison of any two fractions. However, to test polymer heterogeneity, which we believe must exist, light scattering data were obtained on this polymer i n three different solvents: toluene, tetrahydrofuran, and methyl isobutyl ketone. Bushuk and Benoit ( 7 ) demonstrated that inordinately high molecu­ lar weights (apparent) w i l l result from light scattering data for co­ polymers owing to fluctuations i n their chain compositions. Thus, a comparison of Mw obtained with light scattering i n solvents of different polarities should be a significant aid i n establishing heterogeneity. The weight average molecular weights were found to be: in tetrahydrofuran, 338,000; i n toluene, 234,500; and i n methyl isobutyl ketone, 345,000. This information coupled with results of chemical analysis indicates that the terpolymer is heterogeneous. Analysis of data obtained from reactions with mixtures of purified monomers (18) permitted calculations of Kp2/Kt and kinetic chain lengths for these terpolymerization reactions using the following two relationships (6,9): and

Kp*/Kt

= 2 R*/K*/Kt

v=

= 2 R P 2 / [ M P [I] / kd

Kp[M]/2(KtfK my* d

where Rp is the rate of polymerization, M is the monomer concentration, I is the initiator concentration, / is the initiator efficiency, and ν is the

Platzer; Addition and Condensation Polymerization Processes Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

4.

Terpolymerization

RAWE AND K H A M i s

73

Parameters

kinetic chain length. The information on the kinetic chain length then in turn permitted estimation of M n by using an average for the weight of the units in the terpolymer. Thus, the terpolymer formed from monomer mixture A w i l l have an average unit weight of 134. For polymerization at 1 3 8 ° C , using 2% terf-butyl peroxide, values were calculated which are shown in Table X I . Initiator efficiency, f, for diluted systems (9), was assumed to be 0.5.

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Table XI. Time, sec.

Calculated Values of Kp2/Kh Kinetic Chain Length, and Molecular Weights Rp,

moles/liter

χ

3.55 7.01 8.39 8.75 7.54

600 1200 1800 3600 5400 a

ίο-*

V/Kt

V

0.2346 0.2894 0.3071 0.3732 0.4038

182 232 230 205 184

24,800 31,600 31,400 28,000 25,000

Average M„ calculated from the kinetic chain length = 28,200.

The average value of M shown above, compared with the measured values (18) of 27,500, _suggests that much of the termination is by transfer. The measured M n values for terpolymers formed under the same conditions but with commercial monomer mixtures averaged M = 37,400 (Table V I I I ) . Such higher molecular weights are probably results of initiator loss to inhibitors. The results evolved from the data obtained on polymerizations initiated by 2% dicumyl peroxide are shown in Table X I I . n

n

Table XII. Time, sec.

600 1200 1800 3600 5400

Calculated Values of Kp2/Kt> Kinetic Chain Length, and Molecular Weights

K VK , p

t

X

moles/liter io-1

1.21 1.51 1.64 2.08 2.26

V

95.2 126 130 138 118

12,700 16,900 17,400 18,500 15,800

"Average M„ calculated from kinetic chain length = 16,300. The above values are also based on an assumed initiator efficiency of 0.5 owing to the presence of solvent_(9). Comparison of the calculated M n with the measured value (18) ( M „ = 23,830) indicates that a con­ siderable amount of termination occurred by combination.

Platzer; Addition and Condensation Polymerization Processes Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

ADDITION AND CONDENSATION POLYMERIZATION PROCESSES

74 Conclusions

The general conclusions which can be drawn from the data pre­ sented are: ( 1 ) The molecular weights of the products depend strongly on tem­ perature; hence, good control is essential. (2) Choice of initiators must include considerations of reaction con­ ditions, initiator efficiency, and rate of initiator decomposition. ( 3 ) Narrower molecular weight distributions resulted from use of initiators with shorter half-lives.

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Literature Cited (1) Alfrey, T., Jr., Goldfinger, G., J. Chem. Phys. 12, 322 (1944). (2) Bamford, C. H., Barb, W. G., Jenkins, A. D., Onyon, P. F., "The Kinetics of Vinyl Polymerization by Radical Mechanisms," Academic Press, New York, 1958. (3) Bevington, J. C., "Radical Polymerization," Academic Press, New York, 1961. (4) Billmeyer, Jr., F. W., "Textbook of Polymer Science," Interscience, New York, 1962. (5) Billmeyer, Jr., F. W., Stockmayer, W. H., J. Polymer Sci. 5, 121 (1950). (6) Burnett, G. M., "Mechanisms of Polymer Reactions," Interscience, New York, 1954. (7) Bushuk, W., Benoit, H., Can.J.Chem. 36, 1616 (1958). (8) Durbetaki, A.J.,Anal. Chem. 28, 2000 (1956). (9) Flory, P.J.,"Principles of Polymer Chemistry," Cornell University Press, Ithaca, Ν. Y., 1953. (10) Hanle, J. E., Merz, E. H., Mesrobian, R. B., J. Polymer Sci. C-12, 185 (1966). (11) Hoffman, R. F., Schreiber, S., Rosen, G., Ind. Eng. Chem. 56 (5), 51 (1964). (12) Houwink, R.,J.Prakt. Chem. 157, 15 (1940). (13) Huque, M. M., Jaworzyn, J., Goring, D. A. I., J. Polymer Sci. 39, 9 (1959). (14) Khamis, J. T., Polymer 6, 98 (1965). (15) Maley, L. E.,J.Polymer Sci. C-8, 253 (1965). (16) Mark, H., Z. Elektrochem. 40, 413 (1934). (17) Ravve, Α., "Organic Chemistry of Macromolecules," M. Dekker, Inc., New York, 1967. (18) Ravve, Α., Khamis, J. T., Mallavarapu, L. X., J. Polymer Sci. A-3, 1775 (1965). (19) Ravve, Α., Khamis, I. T., J. Macromol. Sci. A1 (8), 1423 (1967). (20) Ravve, Α., Khamis, J. T., U. S. Patent 3,306,883 (Feb. 28, 1967); 3,323,946 (June 6, 1967). (21) Tanford, C., "Physical Chemistry of Macromolecules," Wiley, New York, 1961. RECEIVED October 2,

1967.

Platzer; Addition and Condensation Polymerization Processes Advances in Chemistry; American Chemical Society: Washington, DC, 1969.