A Study of Chain-Addition Polymerizations With Temperature Variations- IV- Copolymerizations-Experiments With Styrene- AcrylonitriIe

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A Study o f Cha in -Add i t i on Po lymer i za t i ons w i th

Tem per a tur e Var ia t ions . IV .

Copo lymer i za t i ons -Exper imen ts w i th

Sty en e- Ac ry o n i r i e

D. H. SEBASTIAN arid J . A. BIESENBERGER

Department of Chemisty and Chemical Engineering

Stevens Institute of TechnologyHoboken New Jersey 07030

Free-radical copolymerizations were s tudied under non-

isothermal conditions with emphasis on their thermal runaway

and ignition behavior. Computational models are presented ingeneralized form and compared with experiments on the sys-

tem styrene-acrylonitrile.A new, useful method is proposed for

the evaluation of runaway parameters from scant kinetic data.

I NTRODUCTI ON

ecent work from t hese laboratories has focused on

R apid, high temperature addition polymerization

(1-6), with particular emphasis on the associated prob-

lems of thermal runaway (RA) and ins tability (2-6).

Thermal instability has been characterized for chain

addition homopolymerization (2-4). A blend of theory

and semi-empirical analysis was used to deve lop dimen-

sionless criteria which predict both the onset and

characte r of RA ( 2 ) .These were corroborated by numer-

ical simulation (3)and further tested with experiments

on free-radical styrene polymerization (4). In our most

recent work, RA theory was extended to include addi-

tion copolymerization (6). It was demonstrated that co-

polymerization parameters can be defined which are

analogous in physical interpretation to their

homopolymer counterpart s, and thus have direc t appli-

cation to our previously reported RA analysis.

This work is an experimental investigation of RA in

copolymerization and is a sequel to our experimentalwork on styrene, Part 111 in this series (4). The com-

onomer pair styrene-acrylonitrile (SAN) has be en cho-

sen as the subject ofcopolymerization analysis. T he pair

forms an industrially important engineering plastic, and

a great deal is known about th e properties and reactions

ofstyrene. However, the reaction kinetics of SAN are far

from ideal, and not well characterized. The reaction

medium changes from homogeneous to precipitous with

variation in comonomer feed composition. Even under

isothermal conditions the reaction exhibits autoac-

celeratory behavior which is attributable to two well

known phenomena. One is acceleration du e to precipita-tion of the polymer and is characteristic of bulk AN

homopolymerization. The other is the gel effect (GE)which occurs in homogeneous media. G E has been ob-

served in styrene polymerization but to a lesser degree

than was found in S A N copolymerization (7, 8).With the

190

added dimension of temperature variation, thermal

runaway constitutes an additional form of autoaccelera-

tion.

In spite of non-idealities, it is the claim of this work

that qualitative predictions of non-isothermal behavior

can be made on the basis of dimensionless criter ia whose

parameters have physical significance, independent of

any particular kinetic mechanism. These parameters a recharacteristic of general processes such as reactant con-

sumption or heat generation, and may be determined

experimentally in the absence of a detailed knowledge of

kinetic mechanism.

In a separate but related study, reaction kinetics of

free radical SAN copolymerization were reported (8).

Attempts to fit the data to kinetic models based upon

existing copolymerization termination mechanisms met

with limited success. Although initial rates could be re-

produced, subsequent reaction behavior could not. Of

greater significance to this work was the determination

of process time constants strictly from experimental dataand their application via dimensional analysis to describe

isotherma1 reaction behavior. Despi te the limitations of

existing kinetic models, this work will show that the

parameters necessary to evaluate RAcriteria may also be

evaluated directly from experimental data. Further-

more, the values of the dimensionless criteria are in

quantitative accord with the expectations drawn from

RA theory.

EXPERIMENTAL

Both comonomers were vacuum distilled to remove

commercially added inhibitors, then stored at 273K.Initiator azo-bis-isobutyronitrile (AIBN) was twice re-

crystal lized from chloroform with methanol, dr ied in

vacuo, and stored at 273K.

The thermal ignition point apparatus (TIPA) has been

described elsewhere (4).Some modifications were made

POLYMER ENGINEERING A ND SCIENCE, FEBRUARY, 1979, Vol . 19 No. 3



A Study of Chain-Addition Polymerizations wi th Temperature Variations

on the batch reactor, and the start-up procedure has

been changed. The reactor, pictured in F i g . 1 was

constructed of stainless steel. It maintains the same

outer dimensions of the original glass reactor, but the

change in material along with a reduced wall thickness

afforded better heat transfer. Under a new procedure,

comonomer feeds (50 ml) were prehea ted in a

pressurized vessel separate from the reactor. The vessel

was heated electrically, and controlled to a constant wall

tempe rature. With reactor in place in the TIPA, initiator

was loaded through the reactor entry pipe. When at the

desired temperature, the pre heate r was attached to the

reactor-entry pipe, and the hot monomer feeds were

flushed through the initiator, dissolving it, and sub-

sequently passing on to the reactor. Manipulation of

preheater temperature assured the same initial temper-

ature and coolant temperature.

Reactions were conducted at 4 atm pressure to pre-

vent boiling oft he monomers at the extremes of temper-

ature encount ered dur ing RA reactions. Reactions werestopped by a pressurized injection of 25 in1 of O.1M

p-benzoquinone in to luene . This solution provided both

a thermal and chemical quench as well as diluting the

products to a manageable consistency.

THEORY

Prior to any discussion of experimental results it is

necessary to establish the framework of the analysis with

a brief review of our RA theory for copolymerization. In

previous articles of this series it was shown that t hre e

ialor

mber

Flange

Reactor

F i g . I . TIPATatch reactor.

parameters could characterize the non-isothermal be-

havior of homopolymerizations (2-4).The parameter a

predicted the onset of RA, with a value ofa < 2 identify-

ing the transition to RA conditions for most polymeri-

zations. The parameters b and B related to the influence

of reactant consumption on RA sensitivity. Values ofb <100 indicated loss of sensitivity due to rapid initiator

decay, while B < 20 warned of monomer limited sen-

sitivity. In conjunction with weakened sensitivity, the

critical value a decreases from the value of two, and may

be depressed to values near one ( 3 ) .While all three of the above parameters follow di-

rectly from the dimensionless form of the balance equa-

tions, each has an independent significance when

viewed as the ratio of time constants for particular reac-

tion processes . Specifically,

where X i s a time constant for initiator consumption, A,,,

for monomer consumption, had for adiabatic reaction,

and AR for heat removal.

Ou r copolymerization analysis drew upon t he

rationalization of dimensionless crit eria as ratios of time

constants for competitive processes, and extended the

notion of characteristic times to lend physical in-

terpretations to each of these constants (6). Thus withtemperature and concentration made dimensionless,

the homopolymerization balances lead us to the conclu-

sion that the time constant for monomer decay is the

reciprocal of the initial rate, i.e.,

similarly for initiator

and for heat generation

= T o / ( ) for To = T R0

Furthermore, ARand h a d were shown to be related to the

temperatu re derivatives of the heat removal and genera-

tion functions in the batch thermal energy balance. Thus

and

where

d T G, - R ,C P X (9)

191OLYMER ENGINEERING AND SCIENCE, FEBRUARY, 1979 V o l . 19, No. 3



yields

and

The above were used as defining equations for A,,,,

, ,, time constants for copolymerization, while

and AR remain unchanged. Note that by generating

physical interpreta tions of the parameters, the analysis

transcends the kinetic forms of homopolymerization. It

becomes possible to extend the application of kinetic

theory intuitively to systems with kinetic schemes that

defy a Semenov-type analysis.

In contrast to their homopolymerization counter-

parts, time constants A,,,, , and , do not appear

explicity in the dimensionless balance equations.

Nevertheless , copolymerization reaction behavior con-

forms to the predictions by dimensionless criteria

formed from the direct substitution of these time con-

stants in place of their appropriate homopolymerization

counterpart s. Thus with a defined as in Eq 1 but with

d substituted for &, the same RA criteria hold for

copolymerization. Critical conditions are

The physical interpretation of these characteristic

times lends new significance to the dimensionless

criteria. For instance a is not a mere consequence of

mathematical manipulation associated with th e

Semenov-type RA analysis. It is actually a measure of

the relative rates at which competitive processes of heat

generation and removal increase with temperature . This

is clear from substitution ofEqs 7 and8 intoEq 1 giving:

Since the heat generation function contains the expo-

nentially increasing reaction rate term, while the re-

moval function is linearly dependent upon temperat ure,

one might expect that the initial removal rate must

exceed generation in order that it might keep pace as

temperatu re rises. Indeed, our RA criterion shows that

j0'2(+j

is a necessary condition to avoid RA.

With knowledge of a detailed kinetic model, it is of

course possible to derive analytical express ions for each

of the time constants based upon defining Eqs 4 8 . More

importantly, however, these parameters can still beevaluated in the absence ofa rigorous kinetic model. In a

paper on isothermal copolymerization kinetics (8), it was

shown that using experimental initial rate data the value

of A,,, could be calculated as in Eq 4 . These values

successfully united conversion histories taken under a

wide variety of conditions, when plotted in dimension-

less form, 4 vs with dimensionless time defined as 7=t/A,. Furthermore, the isothermal histories thus re-

duced behave in the same manner as dimensionless

homopolymerization trajectories.

A similar analysis can be applied to t herma l histories

to extract values for parameters from experimentally

measurable rates. When initial and reservoir tempera-

tures are equal, the initial value of the removal function,

is zero. Thus, from Eq 9 it follows that:

which combines with E q 6 to yield:

It is possible to evaluate f irectly from the initial slope

of a plot of temperature vs time.

Of equal importance in the formulation of RA criter ia

is L a dt too can be determined solely from initial

temperature-time slopes. Recall that when T o = TR, R e

is zero, thus:

Comput ing the change in initial slope with varying ini-

tial tempera ture provides th e means for evaluating 11 .

Induction period studies described in our kinetic

analysis give a ready means for determining for an

initiator in monomer solution (8). Our experimentalstudy of RA in styrene homopolymerization demon-

strated a technique for calculating AR from cooling curve

data (4). It is thus possible to evaluate all the parameters

necessary to formulate criteria 1-3 without a rigorous

kinetic model.

These experimentally determined time constants

have an added value beyond the qualitative predictions

drawn from the crit eria they form. In an earlier work, it

was shown that complex copolymerization kinetic

schemes could often be simulated by pseudohomo-

polymerization kinetics through substitution of appro-

priate copolymer forms in homopolymer balances. Thusexperimenta l data can be generalized for modeling pur-

poses by using the following balances.

dT m,1I2m E'T' (T TA)

dt n, exp[ 1 + T AR

(22)

All parameters can be determined from experimental

data, thus even details of conversion and temperature

D. . Sebast ian and J. A . Biesenberger

192 POLYMER ENGINEERING AND SCIENCE, FEBRUARY, 1979, Vol. 19, No. 3



A Study of Chain-Addition Polymerizations with Temperature Variations

histories may be available without resorting to complex

reaction mechanisms.

RESULTS

Non-isothermal copolymerizations were performed

for comonomer compositions of90,80, 70, 60,40and 20

percent SAN (note: percentage shall hereafter refer to

mole percen t styrene in monomer feed). RA behavior at

each of these compositions was examined at 373K, and

the 90, 80 and 70 percent levels at 363K as well (15).

Although these temperatures exceed the normal range

associated with AIBN initiated polymerization, this in-

itiator was chosen for the specific purpose of keeping

molecular weight low. Iosthermal studies showed that

SAN copolymerizations exhibited a strong gel-effect (8).

In order that experimenta l conditions most closely paral-

lel the assumptions implicit in RA theory, it was desired

to examine non-isothermal behavior devoid of late RA

brought on by anomolous kinet ic effects. A high ra te of

initiation leads to a high rate of reaction and low

molecular weight of the polymer product. The former

insures early runaway, i. e., RA at low conversion, and

the latter tends to postpone the onset of G E to higher

conversions and reduce its severity. However, both

ends are achieved at the expense of a decreased RA

sensitivity 3) making definition of the ignition point

more difficult.

All reactions were conduc ted at a single coolant flow

rate, so the heat transfer coefficient of U = 145 J/m2s K

holds for all reactions. Init iator feed concentration was

manipulated to provoke the occurrence of RA. Thus for

each comonomer composition, a family of temperatureprofiles was generated with initiator concentration as

the only variable parameter. Fi g ur es 2-6 illustrate these

families for all of the AIBN initiated copolymerizations

considered in this work. Additionally, a series ofbenzoyl

peroxide (BP)-initiated reactions were conducted with

70 perce nt SAN at 373K, and these are pictured in Fi g .

7 .The curves in Fi g s . 2-6 are computer reproductions of

experimental data. They are not, however, curve fits of

the data. They are point-to-point connections of data.

The raw data were smooth continuous curves on the

r 90 S I N A lB N

1 C l l = .03

2 .04

3 .05

4 .06

5 5 .07

z<t

n ‘

m

bI

*<

ODh

I6 0 180 3 00 4 2 0 5 4 0

T i m e s e c

Fig. 3. 90 percent SANIAIBN at 373K temperature history.

70 S I N I l B N1 “ l o = .01

2 . 0 1 5

3 ,0175

4 . 0 2

I1 00 3 0 0 5 0 0 7 00 900

Time scc

F i g. 4 . 70 percent SANIAIBN ut 373K temperature history.

I 40 S l N A l B N I1 [I] = ,0035

2 , 0 0 5

3 .01

4 . 0 3

I 90 S I N I l B N 1

mP

1 [ IIo= . 0 7

2 . 0 9

3 . I0

4 . 1 2

I I8 5 2 5 5 4 2 5 5 9 5 7 6 5

Time sec

F i g . 5 . 40 percent SANIAIBN at 373K tentperuture history.

I80 2 4 0 4 0 0 560 7 2 0

T ine sec

Fig . 2 . 90 percent SANIAIBN ut 360K teniperuture history.

chart recorder output. Selection of individual points to

transform to the temperature-time domain was arbi-

trary, indeed, an infinite number of points could be

chosen to generate these curves. Thus, actual experi-

POLYMER ENGINEERING AND SCIENCE, FEBRUARY, 1979 Yo/. 19. No. 3 193



D . H . Sebast ian and J. A . Biesenberger

20 11A l B N

1 CI&=.0025

2 0035

3 005

4 .01

5 .03

I100 300 500 700 900

Tint see

Fig. 6. 20 percent SANIAIBN ut 373K t e mpe ra ture h i s t o ry .

100 300 5 0 0 700 900

T i m see

Fig. 7. 70 percent S A N I B P u t 373K t e mpe ra t ure h i s t o ry .

mental points are not indicated in the figures, only the

resulting profiles a re shown.

A number of qualitative observations are immediately

apparent. Comparing polymerizations at 363K to those

at 37313, it is evident that a higher level of initiator is

required to cause RA at lower temperatures. It is alsoclear that the lower temperature RA transitions are

more sensitive in nature than the 37313 families. Com-

pare, for instance, Fi g s . 2 and 3 . Similar incremental

increases in initiator feed concentration bring greater

changes in thermal behavior at 363K than at 373K.

While start ing at a lower feed temperature, the 363K

runaway profiles rise higher above reservoir tempera-

ture than the runs at 373K3,and temperature spread

between successive curves is greater.

Note that change of initiator also affects sensitivity.

Compare Fig . 4 , the AIBN-initiated, with Fi g . 7, the

BP-initiated70 percent SAN reactions. BP is the slowerdecomposing initiator and its produces a more sensitive

RA transition. These reactions also exhibit an induction

period (the time before the onse t ofRA) which is roughly

twice that of the AIBN-initiated reactions. Ignition

theory predicts (9) and numerical simulation has

194

confirmed (3) that the induction period should be prop-

ortional to & d . This parameter depends inversely upon

reaction rate and thus should be proportional to R;'''.

Since all other reaction condit ions are identical , the ratio

of induction periods for the AIBN and BP reactions

should be inversely proportional to the square root of

the rate constant for decay of these initiators. Indeed,

evaluating kd for these initiators at 373K leads us topredict that BP induction periods should be 2 times

the value for AIBN.

Monomer feed composition variations introduce an

added dimension not present in homopolymerization.

Composition may affect both RA and RA sensitivi ty. In

Fig . 8 feed composition is the variable parameter, with

initiator feed concentration fixed at 0.03 m/l. Succes-

sively enriching AN content in the feeds brings about

runaway in much the same way as increased initiator

feed concentration. Observing Fi g s . 2-7, the qualitative

effect of composition on RA sensi tivity is appare nt. As

the range of90 to 20 percent styrene is traversed, th e RAtransitions increase in sensitivity. There is a much

sharper break between RA and quasi-isothermal tem-

perature profiles in the highest AN content reactions,

Fi g . 7, than in the highest styrene content reactions,

F i g . 3 .

In numerical simulation studies of runaway, families

of temperature profiles plot ted in dimensionless form vs

time made dimensionless by reduction with d , fol-

lowed a common trajectory during the induction period

prior to RA. A value of initial temperatu re is sufficient to

reduce temperature (T' = [T T,]/T,) but absence of a

kinetic expression for d prevents a p r i o r i determina-tion of this parameter. It is known that the rate of

homogeneous free-radical polymerization .is propor-

tional to the square root of the rate of initiation, and thus

is proportional to the square root of the initiator concen-

tration. From homopolymerization analysis it can be

concluded that &d is inversely proportional to the ini tid

rate of reaction. At a given temperature a nd feed com-

position, for a specific initiator, comonomer system Ld

must therefore be proportional to the inverse of the

square root of the initiator feed concentration. Thus for

SAN AlBNr l l ~ . o 3

60 180 300 4 2 0 540

T i m e s ec

F i g . 8 . Composi t ionul e ffec ts of AIBN-ini t ia ted reuct ions at

373K.

POLYMER ENGINEERING A ND SCIENCE, FEBRUARY, 1979, Vol . 19 No. 3



A Study of Chain-Addition Polymerizations wi th Temperature Variations

rsny temperatu re profile scaling time by multiplying by[I],'@ differs from T =tl d by only aconstant factor. This

factor is the same for all curves in any RA family since all

feed conditions are the same with th e exception of [I],.

Thus it is possible to transform th e tempe rature histories

ofFigs.2-7 to pseudo-dimensionless plots ofT' vs t [Z], ',

and these are shown in Figs. 8-12.

Note that the desired effect has been achieved. For

instance in F i g . 8, 90 percent SAN, it is clear that all

temperature paths coincide throughout the induction

period, This tre nd holds as styrene content is decreased

to 60 percent. At the 40 percent level, F i g. 1 1 , th e first

sign of a breakdown appears and is amplified at the 20

percent level. This should be anticipated since the half-

order dependence of rate on initiator concentration is a

characteristic of homogeneous kinetics. Studies of

heterogeneous bulk AN polymerization indicate a higher

order dependence, with values reported as 0.7-0.8(10).

Clearly a higher order would preferentially shift the

high concentration curves to the right, decreasing their

initial slope and increasing the induction period in

4OxSAW l B W

c13,=.0035

2 ,005

3 .01

5.

9 .

.r

4

I

m9

20 1 0 0 140 180

90 S W AlBN

1 cI1, = .07

2 .09

3 .10

4 .12

t [ 111.5

Fig. 9. 90 percent SANIAIBN at 363K pseu do- d imen s ion les sp l o t .

.03

I

m9

10 30 50 70 90

1 [ 1 ] y

Fig . 10. 70 percent SANIAIBN at 373K pseudo-dimensionlessp l o t .

.

4 .03

F i g . 11. 4 0 percent SANIAIBN at 3731<,pseudo-dimensionlessp l o t .

ZOf sS lN l B W

2 .0035

3 ,005

4 .01

5 .03

*N.

1 Lllo=.oo25

Fig . 1 2 . 20 percent SAN1AIB.V at 373K pseudo-dimensionlessp l o t .

pseudo-dimensionless form. This is the qualitative trend

necessary to achieve the same effect with high A N con-

tents as with high styrene contents.

Beyond qualitative generalizations, it is desired to

test the quantitative applicability of thermal RA theoryto copolymerization. To accomplish this in a manner

parallel to that for homopolymerization 4)equires that

values of feed parameters and kinetic constants be in-

ser ted in to the expressions for the various Characteristic

times, and that the dimensionless runaway parameters

subsequently be evaluated. However, earlier isother-

mal kinetic studies shbwed that no available kinetic

model adequately reproduced SAN reaction profiles.

This would pose an apparently insurmountable obstacle

to any quantitative evaluation of the experimental re-

sults. The physical approach to evaluating time con-

stants described in the previous section provides analternat ive to strictly analytical solutions. Values for the

time constants can be determined from experimental

data, obviating the need for a kinetic model.

Because the pseudo-dimensionless plots align to give

a common induction period trajectory, evaluation of

195OLYMER ENGINEERING AND SCIENCE, FEBRUARY, 19 79 , Vof . 19, No. 3



D . H . Sebast ian and J.

initial slopes is made considerably easier. Although in-

dividual slopes can be taken from each profile of th e real

temperature -time plots, the pseudo-dimensionless form

gives and averages over some five runs with different

values of [ I 1,.Recalling that the calculation of d requires the

change in initial slope with temperature, there are in-

sufficient data to calculate this parameter for th e 60, 40and 20 percent compositions, which were reacted at

only one temperature. Strictly, a wider range of data

than available for the 90,80and 70percent levels should

be used to calculate A a d in E q 19. F ro m t h e

homopolymerization expression for it is known tha t

) h d T:/exp(- E )

For values of E typical of free-radical polymerization,

and T o n the range of this study, th e ratio on the RHS of

E q 25 changes slowly with tem perat ure. Therefore to a

good approximation we should be able to express E q 19

as

This permits the use ofdataobtained at two temperature

levels separated by ten degrees, to estimate a value for

reduced by [I] , 2

for comonomer compositions of 90, 80 and 70 percent.

Also included in the table a re values of A, determined in

the isothermal kinetic study (8).The general trend is for

each parameter to decrease with increased temperature

or AN content, as both se rve to raise the rate ofreaction.

Table 2 lists each experimental run along with the

associated dimensionless RA parameters determined

from the A s in Table 1 in E qs 12, 1 3 , 1 4 , and2 3. From

Table 1. Experimentally Determined Time Constants

d .

Table 1 lists the values of it and

System T,, [\IA A m [1IA'* Ac [ I I ~ Aa d

17.2

13.6

12.5

90 SAN/AIBN 363 481 1262

373 21 5 430

80 SAN/AIBN 363 489 889

373 231 31 8

70 SAN/AIBN 363 387 1042

373 200 324

Table 2. Experimentally Determined Dimensionless RAParameters

~ ~

Oh ,, [I], Type' a b B E

0.90 0.03 NU 1.65 5.7 12.5 25.0

0.04 NU 1.43 6.6 12.5 25.0

0 05 RA 1.28 7.4 12.5 25.0

0.06 RA 1.17 8.1 12.5 25.0

0.07 RA 1.08 8.8 12.5 25.0

0.80 0.015 NU 1.78 5.9 17.0 24.3

0.02 NU 1.54 6.8 17.0 24.3

0.025 RA 1.38 7.6 17.0 24.3

0.03 RA 1.26 8.3 17.0 24.3

0.04 RA 1.09 9.6 17.0 24.3

0.70 0.01 NU 2.08 5.0 16.0 26.0

0.01 5 NR 1.70 6.2 16.0 26.0

0.01 75 NU 1.57 6.7 16.0 26.0

0.02 RA 1.47 7.1 16.0 26.0

0.03 RA 1.20 8.7 16.0 26.0

* RA-Runaway.NR-Non-runaway.

A. Biesenberger

values of b and B it is clear that all reactions were

conducted in a non-sensitive regime. Parameter b is an

order of magnitude smaller than the value at which

initiator consumption limits sensitivity. Monomer pa-

rameter B is quite close to the suggested value for the

disappearance of sensitivity. Under such conditions one

must expect that the value of a associated with the

transition t o RA will be depressed from two. RA bound-

aries of a - vs b generated by numerical simulation ofhomopolymerization (3) suggest that a e r should lie

somewhere between 1 .2 and 1.4. Indeed, our experi-

mentally determined values of a fell in this region.

It is important to remember that no specific kinetic

model was invoked to evaluate the parameters of Table

2. With no more than the knowledge of the order of

dependence of reaction rate upon each reactant, and the

physical interpreta tion of each characteristic time, it is

possible to directly interpre t experimental data in terms

of RA theory. The results so obtained match detailed

numerical simulations of homopolymerizations as wellas copolymerizations indicating a significance that trans-

cends th e details of any particular kinetic model.

The technique presented in this work has potential

application to reactor design and nee d not be restricted

to polymerization reactions. Our RA parameters have

analogs in explosion theory 11) and simple chemical

reaction kinetics such as the first-order conversion of

reactant to products (12). Although expressions for the

RA parameters differ in form owing to differences in

kinetics, their physical interpretation is identical to

ours. It is the underlying physical significance of these

parameters characterizing the competitive rates of reac-tion and t ransport processes that lends a universality to

this approach. RA behavior can be assessed without the

need for kinetic and thermodynamic properties neces-

sary to evaluate the analytical expressions for dimension-

less RA parameters. Detailed simulation, of course, re-

quires a precise model, however go-no go predictions of

RA can be made based solely upon experimen tation. In

fact, the unified behavior of dimensionless tempe rature

histories during the induction period makes non-

runaway profiles sufficient to calculate characteristic

times and evaluate RA criteria. Plant datacan b e used to

predict reactor response to changes in feed parameterswithout actually causing RA. Certainly a series of simple

bench scale experiments would be adequate to generate

data for a RA analysis.

Had we chosen to examine a kinetically well de-

scribed system such as styrene-methyl methacrylate,

our analysis might have bee n simplified. All parameters

could have been evaluated analytically from kinetic ex-

pressions since this system can be adequately described

by several kinetic schemes in the literature (13, 14).

However, by trea ting a complex system such as SAN we

were able to bett er elucidate th e anatomy of RA theory

as a collection of competing processes whose rates man-

ifest themselves in measurable quantities. The more

general meaning of each parameter is of far greater

importance than the details of their kinetic derivation

giving the analysis a broader range of applicability, be-

yond the scope of our original investigation.

196 POLYMER ENGINEERING AND SCIENCE, FEBRUARY, 1979, Vol. 19 No. 3



A Study of Chain-Addition Polymerizations wit h Temperature Variations

ACKNOW LEDGM ENT

This work was supported in part by a grant from the

National Science Foundation (ENG-7605053). The au-

thors also gratefully acknowledge Dr. Joseph Domine

and Dr. David Chappelear and their respective com-

panies, Union Carbide and Monsanto, for supplying us

with styrene monomer at no cost.

NOMENCLATURE

= wetted area for heat transfer

= )hd/)lRdimensionless ignition parameterA ,a

b =

B =

C,E’

E {

G ,

G :

[ ] = initiator concentration

[m] = monomer concentration; without brackets-

dimensionless = [ m ] / [ m ] ,

[m,] = fictitious initiator concentration = 2 [ 1 ] ;without

brackets-dimensionless = [ m , ] / [ m , ] ,

R ,

R:

t = time

T = temperature

Z”

U

t iR = volume of reactor

A = time constant

= heat capacity caVg K

= / h a d dimensionless activation energy

= E d / & T , dimensionless initiator activation

= thermal energy generation function = -AH R ,

= dimensionless generation function =

energy

for homopolymerization

- H R,/pC,T, for homopolymerization

= thermal energy removal function =

= dimensionless removal function =

UAduR(T - TR),

uAw/&pUR(T’ TA)

= dimensionless temperature = (T T , ) / T ,= overall heat transfer coefficient

A = copolymerization time constant

p = density

T = t/ & dimensionless time

Subscripts

ad = adiabatic conversion

cr = critical

G = heat generation

i = initiator conversion

m = monomer conversion

oR = heat removal

= initial condition, evaluated at feed conditions

REFERENCES

1. J . A. Biesenberger and R. Capinpin, Polym. E n g . Sci . , 14,737 (1974).

2. J. A. Biesenberger, R. Capinpin, and D. Sebastian, Appl.Polym. Symp. 26, 211 (1975).

3 . J . A . Biesenberger, R. Capinpin, and J C. Yang,Polym. Eng.

Sci . , 16, 101 (1976).4. D. H. Sebastian and J . A . Biesenberger,Polym. E n g . Sci., 16,

117 (1976).

5 . L. Valsamis and J. A. Biesenberger,CEPSymposium Series,160, 20 (1976).

6. D. H. Sebastian and J . A. Biesenberger, accepted f o r publi-cation by J.A p p l . Polym. Sci. (1978).

7 . G . Mino, J.Polym. Sci. 22, 369 (1956).

8. D. H. Sebastian and J . A. Biesenberger, (1978) ubmitted to

9. P. Gray and hl. J . Harper, Trans. Faraday Soc . 55, 581

J. Macromul. Sci.

(1959).

10. W . M . Thomas, Ado. in Polym. Sci . , 2, 401 (1961).

11. J . Adler and J . W. Enig, Comb. Flame, 8, 97 (1967).

12. C .H. Barklew,Chem. E n g . Prugr. Symp. Ser., 55,37( 1959).

13. H. W. Melville, B. Noble, and W. F. Watson, J . Polym. Sci.,

14. S . Russo and S. Munari, J. Macromol . Sci.-Chem., A-115,

15. D. H. Sebastian, PhD Thesis, Stevens Institute ofTechn ol-

2 , 229 (1947).

2159 (1967).

ogy (1977).

POLYMER ENGINEERING AND SCIENCE, FEBRUARY, 1979, Vol . 19, No. 3 197

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