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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
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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
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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
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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-
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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.
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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
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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
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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
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