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Polystyrene samples used in pyrolysis - NIST · polystyrene sample of molecular weight 230,000...

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/ JOURNAL OF RESEARCH of the National Bureau of Standards-A. Physics and Chemistry Vol. 66A, No.4, July- Augu st 1962 Thermal Degradation of Fractionated High and Low Mo- lecular Weight Polystyrenes 1 S. L. Madorsky, D. McIntyre, 1. H. O'Mara, and S. Straus (April 16 , 1962) In previous work on the thermal d egrad at i on of polystyrene of average molecul ar weight of 230,000, carried out in a vac uum in the temperature range 318 to 348 ° C, the rate cur ves exhibited di st in ct maximums when perc entage loss of sampl e per minute was pl otted as a fun ct ion of percentage vo lat ilization. Th ese maximums correspond to a vol at ilization of about 35 to 45 percent and te nd to flatt en with decreased temperature of pyro lysis. A similar st udy of rat es of thermal d eg radation at 307.5 °C h as now been made on two groups of polymers: (1) l ow mol ec ul ar weight, 24,000; 51,000; and 66,000 ; and (2) high molecular weight, 2,000,000; 2,250,000; an d 5, 000,000. Whole polymers an d also fraction s of narrow- ran ge molec ular weight were used. The rate curves for t he 24,000 an d 51,000 molecular- weight sampl es ex hibit very high initial rate s, but no max i mums; the 66,000 sample showed a maxi mum at 45 percent volatilization. Th e rate curves for the 2,000,000, 2,250,000, and 5,000,000 molecul ar -wei ght sa mples exhibit a gradual rise up to about 25 percent vol atiliza- tion; then, instead of forming max imums, they follow pl ateaus to about 50 percent vol at iliza- tio n. These pl ateaus are ind i cat ive of a zero-order react ion in the range that they cover, and the r ates co rr espond in g to them fit well on t he Arrh enius activat ion-ener gy curve obtain ed previously for pol ystyrene sa mpl es at higher temperatures. 1. Introduction Th e rates of thermal degradaLion of polystyrene in a vacuum have b ee n s Lud ied extensivel y by J ellin ek [1,2],2 Maclorsky [3,4], and Grassie [5 , 6] . However, the exaet me chani sm of degradation has b ee n uncertain . Th e reacLion docs no t fo llow a simple process of random initiaL ion or end initiation. In stead, there appears to be a complex mechanism th at has b een explained by assuming random initia- tion, with a cons id erabl e amount of intramolecular an d intermolecular transfer of free radicals, ac- companied by unzipping at free-radical chain ends [7,8, 9] . In addition to this, s tructural irr eg ulariti es, so-called "weak links," in the backbone of the chains hav e been postul ated to account for some of the degradation of the chains [1,2,5, 6]. approach a zero-order at low temperatur es . In order to ehlCid ate this mechanism a seri es of experi- ment s were carried out at relatively low tempera- t ur es, usin g pol ystyrenr sa mpl es of hi gh purity, frac tionated and unIra ctionat rd, and oI bo Lh high and low mol ecul ar weigh t. In the earlier st udies on thermal degrad at ion a pol ystyrene sample of molecul ar weight 230,000 (osmotic pressure) was pyrolyzed in the temperature range of about 33 0 to 400 °C. C urv es of the rates of degradation in perc ent of original sample plotted as a function of percentage degra dation exhibit maximums in the rang e of about 35 to 45 percent d egradation [ 3]. These curves approach a horizontal line at decreased temperatures of degrad ation, as shown in fi g ur e 1. At 299 .5 °C th e middle portion of the rate curv e approaches very closely a horizontal lille [4], which is indicative oI a zero-order reaction. Thus, although at the hi gh er temperatures the me ch- anism of r eact ion is rather cOlIlplicated, it seems to 1 Th is paper was presented at the 14J st meeting of the American Chemical Society in WashiJlgton, D.C., March 20- 29, 1962. , Figures in brackets indicate the literat ure references at the end of this paper. I. I 1.0 .9 '" 2 ::; a: .s w Q. f- .7 u a: w 0.. .:. .6 '" z a i= .5 '" o '" a: t3.4 o u. o w .3 !;; a: .2 I I-- J / 6 / V / .; 0 V"- / .... ,,--0 0/ ,..-0---0- / r ___ 0- 348 0 /' --- ,7 "" \ - - / __ 0- \'", /0 1\ 1 \ '" ---<>- 333 0 "" , ", \ \ ...-- '----- "'\ 1 \ \, '\ \ - ......... 0 -0--.. \ .-c. o= 323 0 c--£--- -0--' 0 3i'8. 0_ 0 _ o- o---r _o --<L 0- 0_ :>-- 0 0-. 0 _ 0 o o 10 20 30 40 50 60 70 so 90 100 DEGRA DATION, PERCENT FIGURE 1. Rat es of thermal degradation of unfmctionated pol ys tyrene of molecular weight of 230,000. Rate of sample loss, K, is measured in percent of original sample. Fi gure is taken from references [31 and [41. 307
Transcript
Page 1: Polystyrene samples used in pyrolysis - NIST · polystyrene sample of molecular weight 230,000 (osmotic pressure) was pyrolyzed in the temperature range of about 330 to 400 °C. Curves

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JOURNAL OF RESEARCH of the National Bureau of Standards-A. Physics and Chemistry Vol. 66A, No.4, July- August 1962

Thermal Degradation of Fractionated High and Low Mo­lecular Weight Polystyrenes 1

S. L. Madorsky, D. McIntyre, 1. H. O'Mara, and S. Straus

(April 16, 1962)

In p revious work on the t hermal degradation of polystyrene of average molecular weight of 230,000, carried out in a vac uum in the temperature range 318 to 348 °C, t he rate curves exhibited distinct maximums when percentage loss of sample per minute was plotted as a function of percentage volatili zation. These maximums correspond to a volatilization of abo ut 35 to 45 percent and tend to flatten with decreased temperature of pyrolysis. A similar study of rates of thermal d egradation at 307.5 °C has now been made on two groups of polymers: (1) low molecular weight, 24,000; 51,000; and 66,000 ; and (2) high molecular weight, 2,000,000; 2,250,000; and 5,000,000. Whole polymers and also fractions of narrow­range molecular weight were used. The rate curves for t he 24,000 and 51,000 molecular­weight samples exhibit very high initial rates, but no maximums; the 66,000 sample showed a maximum at 45 percent volatilization. The rate curves for the 2,000,000, 2,250,000, and 5,000,000 molecular-weight samples exhibit a gradual rise up to about 25 percent volatiliza­t ion; t hen, instead of formin g maximums, they follow plateaus to about 50 percent volatiliza­tio n. These plateaus are indicative of a zero-order reaction in the range that they cover, an d t he rates correspond ing to them fit well on t he Arrhenius activat ion-energy curve obtain ed previo usly for polystyrene samples at higher temperatures.

1. Introduction

The rates of thermal degradaLion of polystyrene in a vacuum have b een sLud ied extensively by J ellinek [1,2],2 Maclorsky [3,4], and Grassie [5 ,6] . However, the exaet mechanism of degradation has b een uncertain. The reacLion docs no t follow a simple process of random initiaLion or end initiation. Instead, there appears to be a complex m echanism that has been explained by assuming random initia­tion, with a considerable amount of intramolecular and intermolecular transfer of free radicals, ac­companied by unzipping at free-radical ch ain ends [7,8, 9] . In addition to this, s tructural irregularities, so-called "weak links," in the backbon e of the chains have been postulated to account for some of the degradation of the chains [1,2,5,6].

approach a zero-order at low temperatures. In order to ehlCidate this mechanism a series of experi­ments were carried out at relatively low tempera­tures, usin g polystyrenr samples of high purity, fractionated and unIractionatrd, and oI boLh high and low mol ecular weigh t.

In the earlier studies on thermal degradation a polystyrene sample of molecular weight 230,000 (osmotic pressure) was pyrolyzed in the temperature range of about 330 to 400 °C. Curves of the rates of degradation in percent of original sample plotted as a function of percentage degradation exhibit maximums in the range of about 35 to 45 percent degradation [3]. These curves approach a horizontal line at decreased temperatures of degradation, as shown in figure 1. At 299 .5 °C the middle portion of the rate curve approaches very closely a horizontal lille [4], which is indicative oI a zero-order reaction . Thus, although at the higher temperatures the mech­anism of reaction is rather cOlIlplicated, it seems to

1 Th is paper was presented at the 14J st meeting of the American Chemical Society in WashiJlgton, D .C., March 20- 29, 1962.

, Figures in brackets indicate the literature references at the end of this paper.

I. I

1.0

~ .9

'" 2 ::; a: .s w Q.

f-

~ .7 u a: w 0...:. .6

'" z a i= .5

'" o

'" a: t3.4 o u. o w .3 !;; a:

.2

I

I--~! J

/ 6 / V

/ .; ~/ 0 V"-/ ....,,--0

0/ ,..-0---0-/ r

___ 0 - 348 0

/' ~ ---,7 "" \ -

·~o-~ -

/ '~ I~ __ 0 - ~so \'", ~

/0 ~ 1\ 1\ '" ---<>-

333 0 "", ", \ \ ...-- '-----o~ "'\ 1\ \,

32 S ~ '\ \ -

......... 0 -0--.. .~ \~ \ .-c.o= 323 0

o~ c--£---

-0--' 03i'8. 0_0 _

,~<> ~:~ o-o---r _ o --<L 0 - 0 _ :>-- 0

0-.0

_

0

o o 10 20 30 40 50 60 70 so 90 100

DEGRA DATION, PERCENT

FIGURE 1. Rates of thermal degradation of unfmctionated polystyrene of molecular weight of 230,000.

R ate of sample loss, K, is measured in percent of original sample. Figure is taken from references [31 and [41.

307

Page 2: Polystyrene samples used in pyrolysis - NIST · polystyrene sample of molecular weight 230,000 (osmotic pressure) was pyrolyzed in the temperature range of about 330 to 400 °C. Curves

2 . Apparatus and Experimental Procedure In earlier studies on rates of thermal degradation

of polymer a tungsten helical spring microbalance was used for the higher temperatures; in the present work an E lmic electronic microbalance was used because it was more suitable for meaSUTements of the slower rates obtained at the relatively low tempera­tUTe of 307.5 °0. This electronic balance auto­matically recorded the tempel'atUTe and loss of weig'ht of the sample, and could be operated for long periods of time without attention.

The experimental procedure using this balance has been described in detail [4]. A 4 to 5 mg sample of the polymer in a small platinum crucible was suspended from the arm of the balance enclosed in a glass housing. The system was evacuated to about 10-5 mm Hg. An electric furnace which w~s preheated to the required temperature was then raIsed around the glass housing for pyrolysis of the sample. A chromel-chromel constantan thermo­couple directly under the crucible reached the operating temperature in about 15 min. Very little loss of weight OCCUlTed during the warming-up period. The thermocouple was precalibl'ated against a similar thermocouple placed in the crucible in contact with its bottom . The temperature was kept constant to within ± 0.2 °0 by means of an electronic thermostat.

3. Materials Eastman styrene, stabilized with p-tert-butyl­

catechol, was used in the preparation of the polymer. It was first washed with 7 percent N aOH then with distilled water, and finally dried with 0~S04' The dri~d monomer was distilled at 18 mm Hg. The pUrIfied dry monomer was degassed in a high­vacuum line and distilled in to dilatorneters. Two batches of polymers were prepared: polymer A and polymer B. No initiator was used for either of these two polymers.

Polymer A : This polymer was polymerized for a year at room temperature to about 50 pereent conversion. The reaction mixture was poured into methanol. The precipitated polymer was then dried . The viscosity-average molecular weight of the whole polym er was 2,250,000 . The fractionation was begun a t a concentration of 0.5 p ercent of polymer in methyl ethyl ketone using isopropyl alcohol as a precipitant. Several fractions and subfractions were r ecovered .

Polymer B: This polymer was polymerized at 180 °0 to about 30 percen t conversion. The re­action mixtUTe was poured into methanol and then precipitated with water. The viscosity-average molecular weight of the whole polymer was 51 ,000. Fractionation b egan with an initial concentration of 0.6 percent of the polymer in a methyl-ethyl ketone acetone mixture (1: 1) using methanol as a pre­cipitant. Twelve fractions were recovered.

Pertinent data on the unfractionated and fraction­ated materials used in this paper are shown in table 1. The molecular weights of these materials were determined by the viscosity method. The

TABLE 1. Polystyrene samples used in pyrolysis

Sample No. Fraction Mol.wt.

A- uf Unfract ionated 2,250,000 A-hf High fra ction 5,000,000 A-If Low fraction 2,000, 000

B -uf Unfractionatcd 51 , 000 B-hf High fra ct ion 66, 000 B-If Low fraction 24, 000

intrinsic viscosities were determined in benzene at 40 °0 using an Ubbelohde viscometer. Molecular weights were calculated from the relation

[1J]= 1.00 X 1O - 4.Mwo.75

which is very close to the relation given by F lory [10] for the intrinsic viscosity and weight-average molecular weight of fractions of polystyrene.

4 . Experimental Work

4 .1 . Molecular Weight of Degraded Polymers

Samples of polystyrene fraction A-H, molecular weight 2,000,000 (table I) , were pyrolyzed in a vacuum for various periods of time at temperatures ranging from 304 to 312 °0. The residues were dissolved in benzene and freeze-dried prior to deter­mining their average molecular weight by viscosity and osmotic-pressure methods.

The viscosity method has been described above . The osmotic-pressure determinations were made in cyclohexane at 35 °0 in Stabin osmometers using "never-dried" gel cellophane No. 600. Results of these pyrolysis experiments are shown in table 2. I,n figure 2 the r esults of molecular weight determina­tlOns of the residues by the viscosity and the osmotic­pressure methods for sample A-If are compared with similar results obtained previously [3] using the osmotic-pressure method for an unfractionated thermally prepared polystyrene sample of molecular weight 230,000. The r esults indica te a r apid drop of molecular weight during t1le initial 10 percent loss of weight to about 70,000 to 80,000. This drop is similar for both the fractionated polystyrene of average molecular weight 2,000,000 and the unfrae­tiona ted sample of molecular weight 230,000. Beyond 10 percent loss the drop is less dras tic and the curve shows a tendency to level off at about 50 ,000 (osm.otic-pressure molecular weigh t ) for both polymers.

T A B L E 2. Molecu lar wei ghts of degraded polystyrene fraction A-If

T emp . Dura.t ion Volatiliza-t ion

l\f.evisc.) J l n(os. p r.) M ./I\1n

° C min % 304 180 1. 3 335, 000 200, 000 1.68 312 240 5. 7 168,000 98, 600 1. 70 310 660 16. 6 9(), 500 61,100 1.48 304 960 41.0 65, 000 36, 600 1. 78 310 1260 51.0 50, 000 30,600 1. 63 310 1500 61. 0 41,000 25,600 1.60

A verage __ .. ______ ___ ___ - - -- --- -- -- - - . . - . - ---- -- --- -- --- . - -- ---- ---- 1. 64

308

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I

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Page 3: Polystyrene samples used in pyrolysis - NIST · polystyrene sample of molecular weight 230,000 (osmotic pressure) was pyrolyzed in the temperature range of about 330 to 400 °C. Curves

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:<!: 300 w :::> 0

Vi W Q:

u. 0

200 >-l: ~

Ui 150 ~

Q:

<l 100 ...J

:::> u w ...J 0 50 ~

70

AM OU NT VOL ATILIZED , PERCENT

FIGURE 2. Drop in the molecular weight oj polystyrene, fmction A-iJ, molecular weight 2,000,000 A- by the viscosity method; B- by the osmotic-pressurc method. Cur ve C is from ear! ier work [3], for un fractiona ted

polymer, molecular weight 230,000 by the osmotic-pressure m ethod.

4.2. Rates of Degradation

The whole polymers A and B , and t heir two fractions (table 1) were studied. P ertinent details of the rate experiments are shown in table 3. In figure 3 cumulative loss of weight, in percent of sample, is plotted as a function o[ time. Fractions A-hf and A-lf of 5,000,000 and 2,000,000 molec ular weight, respectively, show the sa me pyrolysis cur ve. These high molecular-weight curves show inflexions and resemble those obtn,ined previously for unfrac­tiona ted, thermally prepared polystyrene, molecular weight, 230,000, and or two fractions from this polymer of molecular weigh ts 106,000 and 584,000 [3 ].

TABLE 3. Rates of degradation of polystyrene at 307.5 °C

Sample No. Mol. IVt. Duration Volatilization Max. rate

liT % %/min A-uf 2,250,000 30 73.0 0.0480 A-hf 5,000,000 30 62.5 .0450 A-H 2,000,000 30 62.5 . 0450 B-uf 51,000 22 74.0 '.0555 B-hf 66,000 30 73.0 . 0534 B-lf 24,000 22 73.0 .0690 ,

• This rate corresponds to an inflection on the rate curve instead of to a m axi­mum rate.

In figure 4 the rates , calculated from the curves in figure 3, are plotted in percent of sample volatilized per minute as a function of percentage volatilized. The high molecular weight polymers, both unfrac­tionated and fractionated, show a gradual rise in rate up to about 25 percent loss, then there is a plateau extending to abou t 50 percent loss, followed by a drop in rate tending toward zero at 100 percent volatilization. The ntte curve for B-hf fraction, 66,000 molecular weight, r esembles those for the high molecular weight polymers, excep t that it does not have a plateau. The 24,000 B-lf fraction indi­cates a co nstant rate up to about 30 percen t volatili-

637358- 62--4 309

zation, followed by a drop toward 100 percent volatilization. The 51,000 B-uf sample starts at a very higlt rate and exhibi ts a pronounced inflexion between 40 to 45 percent volatilization , followed by a gradual decrrltse in !'ILlc.

70

60

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~ 40

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FIGURE 3.

00 0

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T IME FROM START OF EXPERIMEN T, HOURS

Cmnlllative thermal degradation oj polystyrene samples .

----------

Page 4: Polystyrene samples used in pyrolysis - NIST · polystyrene sample of molecular weight 230,000 (osmotic pressure) was pyrolyzed in the temperature range of about 330 to 400 °C. Curves

.090

.080

51,000

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.060

66,000

.050 2,250,000

2,000,000 OR 5,000,000

.010 -

5 . Discussion

As the high lllOlecular weight polystyrene under­goes pyrolysis, its (M) drops rapidly during tbe first 5 to 10 percent loss of weight and stabilizes at about 40,000 to 60,000. The level of stabilization seems to be independent of the initial molecular weight or of the molecular distribution in the polymer species, provided the initial (M) is not below the stabilization level. The initial drop in molecular weight may be due partially to scissions at weak-link bonds caused by impurities in the polymers, but is mainly due to thermal scissions in the chain. This continues to a point where the drop in weight caused by random scissions is counter-balanced by the disappearance of smaller chains through unzipping, mainly into monomers. According to Staudinger and Stein­hofer [11] and Madorsky and Straus [12], the degrada­tion products from polystyrene consist of about 40 percent monomers, 20 percent dimer, 20 percent trimer, and some larger fragments. Unzipping takes place at free-radical chain ends, presumably as follows :

:H H H :0 H H H IT o 0 :/ H , 0 0 0 0

IT/ H , H / H, H / : , H / H , H / H H / H , H / H, H L----'--'---'-----'--'--'-----'--'--'-----':---'--!-:---'-----:'::-~___::C H4 0 0 0: 0 0 ~~ 2~ 0 0 o·

80 </> </> </>: </> </> </> </> </> 10 20

FIGU RE 4.

- .6

o - .8

'" o ..J

-1.0

-1.2

-1.4

AMOUNT VOLATILIZED , PERCENT

Rates of thermal degradation of polystY1'ene samples.

TE M PE RATU R E,·C·

328 323 318

() 1

~l

-1.6IL.6-0--I..LS 2--1..L64--1.-'-6-6--1...!..6-8--1--'.7-0----:1.7'-::'2----:1.7'-::'4-~,.76

FIGURE 5. Arrhenius plot for the rates of thermal degradation of polystY1'ene.

o-Polystyrene molecular weight 230,000 0 - Polystyrene sample B-hf C.-Polystyrene sample A-uf

@- PolystYl'enesample A-hf and A-If

310

then

also,

H H H 0 , O · o H',: / H

H / H , H / :,H / I'H O 0 '0

</> </> : </>

: H H :OUJ o :/ H 0 IT/ H , H / : ~®/H"H

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H H o O· IT

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monomer

H H H o 0 0

H / H, H H~ / IT, H ~~O O· + 0 O+H

</> </> </> </>

dimer

At this point stabiliza tion sets in. Since loss here is mainly due to loss by unzipping at ends of chains, the rate is constant as long as the number of chain ends stays constant. This explains the plateau in the rate curves of the high molecular weight species. However, the average molecular weight drops grad­ually during this period, as is indicated in figure 2. Thus, as shown in figure 4, the portions of the rate curves from about 25 to 50 percent weight loss in the case of the three highest molecular weigh t samples point to a zero-order reaction . Beyond 50 percent volatilization a decrease in rate takes place due to a decrease in the number of chain ends. This is predicated on the assumption that in the range of conversion of 25 to 50 percent, the rate of disap­pearance of chain-ends by unzipping is equal to the rate of formation of new chain ends through random scission, while in the initial and final stages, the rate of disappearance of chains is respectively slower or faster than the rate of formation of new chain ends.

In the thermal degradation at 299 .3 °C of un­fractionated polystyrene of molecular weight 230,000, the rate curve shows a plateau in the range of about

1

Page 5: Polystyrene samples used in pyrolysis - NIST · polystyrene sample of molecular weight 230,000 (osmotic pressure) was pyrolyzed in the temperature range of about 330 to 400 °C. Curves

20 to 50 percent volatilization [4]. However , at higher temperatures, 318 to 348 00, the rate curves for this polymer show maxima instead of plateaus at about 35 to 45 percent volatilization [3]. This could be explained on the ground that with the rise in th e temperature of pyrolysis the various reactions in­vol ved are speeded up and overlap so that the r egion of stabilization narrows down from a plateau to a peak.

Simha and Wall [8] predict, on theoretical grounds, the occurrence of maximums in the rate curves for the thermal degradation of polystyren e at about 25 percent degradation, in disagreem ent with the present and the earlier work.

Polystyrene fraction B-hf has a molecular weigh t (66,000) which is in the r egion at which stabilization occurs. Although the temperature of degradation is low enough for a plateau to occur, stabiliza tion of molecular weight and of rate of loss of weight is of shor t duration and th ey begin to drop soon after stabilization sets in. As a r esult, the curve in figure 4 exhibi ts a maximum insteftd of a plate:1.u . Th e whole polymer, B-uf , molecul:1.r weight 51,000, h:1.s appar­ently a large propor tion of very short chains. Th e curve shows a high initi:1.1 r ate, followed by a short interv:1.1 of stabilization at abo ut 40 percent volfttili­zation . Fron1. h ere on, this cur ve follows the sam e trend as the oth er curves. Low fraction B-lf, molec­ular weight 24,000, apparently h as :1. narrow 11101ec­ulftr weight distribution and is [ree from vcry shor t chain molecules. It decomposes initially in a m anner of a, zero-order re:1.ction , but :1.t a high r~),te , up to about 30 percent loss. B eyond th is, t he n tLe drops gradually due to the disappearance or some o[ the shorter molecules, while [ew scission s occur to COJll ­

pensate for th e decrease in the number of elmill enels.

311

Figure 5 r epresents an Arrhenius plot for the activation energy of the thermal degradation of polystyrene. The rate l{[ r epresents a rate of loss of weight in percent of the orig inal sample per minute as :1. function of percentage volatilization. Th e points in this plot r epresent maximums of t be rate curve shown in figure 1 for polystyrene of molecular weight 230,000, the peak of the rate curve shown in figure 4 for polym er fraction B-hf, and for the plateau rates in the same figure of polymer smnple A-uf and its fractions, A-hf and A-If. The slope of the curve indicates a n activation energy of 55 kcal/mole. A similar value was obtained by plotting ini tial K2 rates for polystyrene of molecular weight 230,000 [3, 4] . The initial K2 rates were obtained by extrap­olating to zero the degrada tion rates expressed in percent of r esidue per minute as a fun ction of per­centage volatilization.

6. References

[1] H. I-1. G. J eHinck, J . Polymcr Sci. 3, 850 (1948) . [21 H. H . G . J cllinck, J . Polymcr Sci. 4, 13 (1949) . [3] S. L. Madorsky, J . Polymer Sci. 9, 133 (1952) . [4] S. L. Madorsky, J. Research NBS 62, 219 (1959). [5] N. Grassie a nd W. W. Kerr, Trans. Faraday Soc. 53, 23,[

(1957) . [6] N. G rass ic and W. W. K elT, Trans. FamchlY Soc. 55, 1050

(1959) . [71 R. Simha and L. A. Wall , J. Phvs. C he ll1 . 56, 707 (1952) . [8] R. Simh a, L. A. 'Wa ll , and J . Bram , J . Chcm. Phys. 29,

894 (1958). [9] S. Straus and S. L. :vrado r~ k.\·, J . Research NBS 65A

(Phys. and C llCm.) 243 (196 1). [10] .1'. J. F lo ry, Principlcs of P oly mer Chemist ry, Cornell

Uuiv. Press, p. 312, (1953) . [11] II. Staudin gc r a nd A. Steinhofer, Ann. Che mic 517, 35

(Ul35). [12] f-l . L. M ado rsky and S. Straus, J . Research NBS '10, 417

(H)48) . (Pl1per 66A4- 163)


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