646
Ind. Eng. Chem. Res. 1991,30, 646-653
MATERIALS AND INTERFACES Development of a Reaction Injection Molding Encapsulant System. 3. Gel Times for the Anionic Bulk Polymerization of Styrene with Divinylbenzene George D. Karles, Walter H. Christiansen, John G. Ekerdt, Isaac Trachtenberg, and Joel W. Barlow* Department of Chemical Engineering and Center for Polymer Research, The University of Texas at Austin, Austin, Texas 78712
The respective influences on gel time of butyllithium initiator concentration (0.01-0.17 M), butyl isomer (n-butyl or sec-butyl) present in the initiator, temperature (0-18 "C),and the molar ratio, R,, of styrene to divinylbenzene (7-90) are experimentally determined. Solutions initiated with sec-butyllithium (sec-BuLi) are found to gel u p to 5 times more rapidly than those initiated with n-butyllithium (n-BuLi), a result that may be related to the lower initiation rate of n-BuLi. Generally, gel time is reduced when reaction temperature is increased and when R, is reduced, although deviations are seen at low R, when n-BuLi is used. A predictive model for gel time is developed that combines Flory's criterion for incipient gelation with measurements and analysis of styrene/divinylbenzene copolymerization kinetics. The model is able to predict gel times to within 15% relative error for R, > 44.
Introduction Our laboratory has been developing a reaction injection molding (RIM) process for encapsulation of electronic components with rapidly polymerizing, cross-linked, compositions that contain substituted styrene. The motivation for this approach and kinetics information for the anionic polymerization of styrene are presented in part 1of this series (Your et al., 1989). In part 2 (Christiansen et al., 1990) an experimental protocol and fundamentally based model for predicting the viscosity rise during the bulk linear polymerization of styrene, anionically initiated by butyllithium, is presented. This paper, part 3, considers the potentially more difficult to predict case of nonlinear polymerization where the viscosity rise results from the formation of a three-dimensional network due to the presence of divinylbenzene (DVB) in the reacting mixture. As in the previous study, part 2, we are particularly interested in using results of studies of polymerization rates together with fundamental relationships between viscosity and molecular sizes and functionality to build a model for predicting the viscosity rise, gel, time of the reacting mixture. Such information is obviously useful for determining the maximum allowable mold fill time for the composition and operating temperature of interest. Unfortunately, very little data exist in the literature for the anionic bulk copolymerization of styrene and DVB, and the reactivity ratios that do exist are inconsistent (Worsfold, 1970; Popov and Schwachula, 1981). For this reason, we also include rates of copolymerization, measured for this system by a gas chromatographic method. Materials and Procedures Characterization of Materials. All of the materials used in this study were purchased from the Aldrich Chemical Company. Styrene was received as 99% mo-
nomer, inhibited with 10-15 ppm 4-tert-butylcatechol. The divinylbenzene, DVB, was a technical grade mixture containing 55.5 wt % m-DVB and p-DVB isomers and 42 w t '70 3- and 4-ethylvinylbenzene, as determined by a Hewlett-Packard Model 5880A gas chromatograph which was equipped with a 25-m, BP10,0.53-mm-i.d., capillary column and a flame ionization detector. The gas chromatograph was operated with 10 mL/min helium carrier gas, and the column temperature was programmed from 45 to 80 "C. The estimated uncertainty in the measured compositions is about 2%. The DVB was inhibited by the supplier with approximately 900-1100 ppm 4-tert-butylcatechol. The isomer content of the DVB components in the mixture was measured to be 33 mol % pDVB and 67 mol '70m-DVB by this same technique. The elution order of the DVB isomers needed for this determination was established by measuring elution times for the DVB isomers which were separated from the technical grade DVB by the methods of Rubenstein et al. (1965). Both normal and secondary isomers of butyllithium, BuLi, were used in these studies. sec-BuLi and n-BuLi were supplied as 1.3 and 1.6 M concentrations in cyclohexane and isomers of hexane, respectively. These concentrations were verified to within fO.O1 M by use of the double titration method developed by Gilman and Carteledge (1964). Prior to polymerization, oxygen, water, and carbon dioxide were stripped from the monomer by bubbling either argon or oxygen-free nitrogen at 40-80 mL/min through no more than 25 mL of monomer for at least 30 min. Stripping is necessary to prevent preferential reaction of these materials with the BuLi initiator, as detailed in previous studies (Your et al., 1989; Christiansen et al., 1990). Typically, stripping of styrene lowered the active M, as determined by contaminant level to (2-5) x titration with BuLi, using an end point defined by the
0888-588519l 12630-0646$02.50/0 0 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 4,1991 647
Therm 0 coup Ie -b
f
To Data &cqulsition System
Rubber Septum
Table I. Summary of Reaction Conditions concentration, M run no, styrene DVB sec-BuLi 1 2 3 4
Vial Monomer
5 6 7 8 90 100
Refrigerated Bath Magnetic Stirring Bar
11
12 13 14 15 16
Magnetic Stirrer
Figure 1. Schematic of apparatus for measuring gel times.
persistence of the orange styryllithium complex (Morton et al., 1970; Worsfold and Bywater, 1972). Titration of the DVB with BuLi indicated a 18 X M active impurity concentration after stripping. The approximate difference in impurity concentrations between M. This differnce DVB and styrene is roughly 14 X corresponds to a Ctert-butylcatechol concentration of lo00 ppm, provided each catechol molecule terminates two BuLi molecules. This is the expected result based on the two pendant hydroxyl groups per catechol molecule, and the observed difference in impurity concentrations between DVB and styrene is simply due to the presence in the DVB of roughly 1000 ppm catechol inhibitor. The titration procedures, outlined above, were used to estimate the active BuLi and styryllithium concentrations. The concentrations reported in this paper are corrected for scavenging by contaminants through use of this titration method. Measurement of Gelation Times. The apparatus for measuring gel time is simply a clean, purged, 6-dram vial, equipped with a magnetic stir bar and a rubber septum, Figure 1. Purified monomers with a total volume of 4 mL were placed in the vial. The vial was then placed in a refrigerated water bath and vigorously stirred to reach thermal equilibrium. A thermocouple was placed through the septum and extended into the liquid to measure temperature during the polymerization. Temperature was recorded with the computer-based data acquisition system described previously (Your et al., 1989). At thermal equilibrium, the butyllithium was rapidly injected into the mixture to initiate polymerization. Gelation time was easily determined to be the time at which the stir bar ceased to rotate. At this time, the solution was a gel that would not flow when the vial was tilted. The uncertainty in determining this point, as estimated from repeated experiments, was generally about * 5 % . The temperature during gelation experiments could be maintained to within *2 "C over the range of experimental temperatures between 4 and 18 "C and for R, ratios between l and infinity, after an initial 2 "C increase, associated with the rapid initial formation of styryllithium, was observed. The temperatures reported are the average observed values after styryllithium formation. Attempts to measure the viscosity rise preceding and accompanying gelation with the torque rheometer, described previously (Christiansen et al., 1990), were not successful. The initially formed gel has very low mechanical strength and is easily disintegrated by the shear fields in this apparatus at torque or shear stress levels that are too low to be accurately detected by the instrument.
8.5 8.2 8.3 8.3 8.0 8.4 8.4 8.1 8.3 8.6 8.0 7.8 7.7 7.3 8.0 6.5
0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.19 0.10 0.10 0.27 0.26 0.30 0.49 0.19 0.92
0.0144 0.0391 0.0283 0.0335 0.0561 0.0250 0.0205 0.0218 0.0250 0.0250 0.0208 0.0425 0.0144 0.0374 0.0353 0.0237
T,O C 1.5 f 0.2 3.4 f 0.3 2.7 f 0.3 2.9 f 0.3 3.4 f 0.3 1.5 f 0.2 1.6 f 0.2 3.0 i 0.3 18 2 -22.0 f 0.5 2.6 f 0.4 3.2 i 0.3 1.8 i 0.3 3.0 f 0.3 3.0 f 0.3 1.5 f 0.3
Initiated directly with sec-BuLi. All others initiated with styryllithium formed from the separate reaction of sec-BuLi with styrene.
Measurement of Polymerization Rates. Bulk polymerizations were carried out in dried 25-mL Erlenmeyer flask reactors which were equipped with magnetic stir bars and capped with rubber septa. sec-BuLi was used as the initiator to avoid any potential complications due to the known slower initiation of styrene by n-BuLi (Hsieh, 1965). To further guarantee that initiation would be rapid, the sec-BuLi was first reacted with enough styrene to form, on average, dimeric units of poly(styryl1ithium). This material was then used to initiate all of the polymerizations used in reaction kinetics studies, unless otherwise stated. The bulk copolymerizations were run isothermally at either 0 or -22 "C by immersing the reactor in ice-water or in dry ice-carbon tetrachloride mixtures, respectively. These subambient temperatures were necessary to slow the polymerizations sufficiently to maintain the reaction temperature constant to within f0.5 "C, as measured by a J-type thermocouple in the reacting fluid. Initiator concentrations used in these studies were of the order of 10" M, after correcting for scavenging by impurities. For the initiator concentrations, reactor configuration, and cooling system described, the polymerizations were too rapid to maintain isothermal conditions when the temperature was near ambient, and temperature changes of as much as 4 "C were observed, as shown in the summary of reaction conditions, Table I. The polymerizations were slow enough to permit the use of the gas chromatograph, described above, to measure the quantities of unreacted styrene, p-divinylbenzene b-DVB), and m-divinylbenzene (m-DVB), m-ethylvinylbenzene, and p-ethylvinylbenzene in the reaction mixture. Results and Discussion Polymerization Kinetics. Provided the molar ratio of styrene to DVB, R,, exceeds roughly 25, the polymerization is observed to be first order with respect to each of the primary reactants. The polymerizations are observed to follow -dM/dt = k'M (1) or
Jg [E] = In
= -$k'dt
= -k't = k P t (2)
where M is the molar concentration of either p-DVB, m-DVB, ethylvinylbenzene, or styrene, M ois the initial
648 Ind. Eng. Chem. Res., Vol. 30, No. 4, 1991 2 1.8 1.6 1.4
1.2 1 0.8 0.6 0.4
0.2 0
0
100 200
300
400
500
600
700
800
900
time (sec)
Figure 2. Disappearance of species with reaction time at R, = 83, 2.9 "C,and [I0] = 33.5 mM. (m) p-DVB; (0) m-DVB; (X) styrene; (+) m-ethylvinylbenzene, Table 11. List chemical no. 1 2 3 4 5 6
7 8
9
of Chemical Names name styrene p-DVB, unreacted p-divinylbenzene p-DVB1, half-reacted p-divinylbenzene m-DVB, unreacted m-divinylbenzene m-DVB1, half-reacted m-divinylbenzene p-DVB2, completely reacted p-divinylbenzene m-DVB2, completely reacted m-divinylbenzene p-EVB, p-ethylvinylbenzene m-EVB, m-ethylvinylbenzene
concentration of the respective species, k'is a lumped rate constant which includes a term for initiator concentration, I, and order, n, and t is the elapsed reaction time. As shown in Figure 2, the polymerizations are first order in these species to conversions in excess of 30%. The presence of good straight lines in Figure 2 suggests that the lumped rate constants, k', really are constant. This, in turn, suggests that I" is independent of reaction time, a situation that is possible provided the rate of initiation is much higher than that of propagation or polymerization and the termination rate is negligible. The use of styryllithium avoids delays due to initiation directly with BuLi. The use of anionic initiator guarantees negligible termination during the polymerization process. To describe the reaction mechanism completely, we potentially have the nine species, listed in Table 11, to consider. Monomers 8 and 9 are contaminants that are present in the technical grade DVB used in these experiments. In Figure 2, monomer 9 is shown to have reactivity similar to styrene, monomer 1, and one can reasonably assume that monomer 8 is also similar to styrene. By considering monomers 8 and 9 to be kinetically identical with monomer 1,only five reactive species, monomers 1-5, need be examined. Monomer, 3, p-DVB1, is the monomer that exists after the first vinyl group on p-DVB has been reacted. Similarly, monomer 5 is formed by reacting one of the vinyl groups on monomer 4. Barring intramolecular cyclization reactions, an intermolecular cross-link,p-DW32, is formed when the second vinyl group on p-DVB1 is reacted. A cross-link also forms when the second vinyl group on m-DVB1, monomer 5, is reacted. Although the propagation rates are first order with respect to monomer, a description of the polymerization kinetics of this system is potentially quite complicated. For example, the rate of disappearance of monomer 1 (together with the ethylvinylbenzenes) could be given by -d[Ml] /dt = [MJ Ckil[M;Li+]"(') i
(3)
where the counter, i, corresponds with reactants 1-5 cited above, [MI] is the concentration of monomer 1, [M;Li+]
is the concentration of the propagating ionic end resulting from the reaction of monomer i with the growing ionic end, and kil describes the reaction rate of ionic end M:Li+ with monomer 1. Potentially, five rate constants and five different reaction orders with respect to the propagating ions, n(i),need to be provided to describe the disappearance of styrene. When equations similar to (3) are written for each monomer, one is required, in principle, to evaluate 25 unknown rate constants, and 5 unknown reaction orders to describe the polymerization system. Furthermore, the extra relationships that derive from the standard assumption of the existence of steady-state radical concentrations in free-radical copolymerizations (Alfrey et al., 1952; Billmeyer, 1962) may not be appropriate for anionic copolymerizations where no termination step exists (0'Driscoll, 1962). For anionic copolymerizations all one can really say is that the total ion content should be constant. Several simplifications are possible for the present system. Since monomers 3 and 5 are similar to monomers 8 and 9, respectively, one can also set kS1, klS, k13, and kB1 equal to kll. The most important simplification, however, arises where the experiments are constructed to provide a dominant term in the series, (3). In our initial studies, we have deliberately set compositions where styrene monomer molar concentrations are at least 40 times higher than those of other species to guarantee that styryllithium ion, I = MfLi+, is the dominant ion in the system. Under these conditions, (3) can be approximated by -d In ([M,])/dt = kll[I]n(l) = Cll
(4)
and the rate of disappearance of component j in the mixture is similarly -d In ([Mj])/dt = klj[I]"(l) = C ,
(5)
The relative reactivity of monomer j , Rj, in the reacting mixture is then found by dividing (5) by (4) to yield R; = d In ([Mjl)/d In ([MJ = In ([Mjl/[Mj~l)/ln ([Mll/[M101) = kl,/kll
(6)
From the slopes of the lines in Figure 3, one can determine that R2and R4 are 6.6 and 2.0, respectively. These resulta suggest that both isomers of DVB are more reactive than styrene. The observed rank order of reactivities, p-DVB > m-DVB > styrene, agrees with the assessment that the propagating carbanion reacts more rapidly with monomers that possess higher electronic density of opposite sign on the vinyl bond (Landler, 1952). From Figure 2, the reactivity of the m-ethylvinylbenzene contaminant in the DVB is similar to that of styrene in the reaction mixture. Due to its low concentration in the reaction mixture, p-ethylvinylbenzene is not easily characterized and its relative reactivity in the mixture is not known with sufficient accuracy to warrant publication. A good direct comparison of the results from Figure 3 with literature vJues does not exist; however it is still interesting to examine what has been reported. Using W spectroscopy, Worsfold (1970) studied the anionic copolymerization of styrene with p D V B in the presence of toluene solvent and tetrahydrofuran promoter. He determined that the first vinyl group on p-DVB was about 10 times more reactive than styrene, compared to our estimate of 6.6 times. He also determined that the first group on p-DVB was about 14 times more reactive than the remaining vinyl group. In contrast, Popov and Schwachula (1981), using a gas chromatographic technique similar to our technique, report that styrene is more re-
Ind. Eng. Chem. Res., Vol. 30, No. 4,1991 649
ec!
0.7
0
0.6
0.18 1
0.5
0.15
3
0.4
9
0.3
2 =
-0
0.09
,e
0.06
E
v
0.1
~
"
~
'
~
'
~
'
~
'
1
'
~
1 ~.
-
'
"
"
1
0.12
z
0.2
320 640 960 1280 1600 1920 2240 2560 2880 3200
0.03
0 0
0.05
0.1
0.2
0.15
0.25
0.3
0.35
0
In(Sto/St) 0.4
$ ,b O
9 %
v
2 1.8 1.6 1.4 1.2
5 .
-c
v
1
0.8 0.6 0.4 0.2 0
0.36 0.32 0.28 0.24 0.2 0.16 0.12 0.08 0.04
0 I .4
0
In (S to/ S t )
Figure 3. Constructions showing reactivitiesof p-DVB and m-DVB relative to styrene. Data are taken from runs 3-5,7,9, 13, and 16 in Table I.
active than p-DVB and less reactive than m-DVB. Figure 4 summarizes the effect of temperature on the reaction rates of monomers 1,2, and 4, over the temperature range -22 to 18 "C a t R, = 81. As before, these reaction rates are clearly first order with respect to monomer and increase as the temperature is raised. From (2), the slopes of these lines are simply kl", and plots of ln(kI") vs 1/T yield straight lines from which the activation energy, Mi,can be evaluated for each propagation reaction; see Figure 5. The measured activation energies range and 13.5 f 0.6 from 13.2 f 0.6 kcal/mol for p-DVB, M2, kcal/mol for m-DVB, M4, to 14.7 f 0.4 kcal/mol for styrene, M1.The value for styrene polymerization, A&, agrees well with the value, AEI = 14.4 f 0.6 kcal/mol, obtained previously for styrene bulk polymerization by two different methods (Your et al., 1989). Within the limits of uncertainty, AE4 = AEz, and the observation that k12 > k14 must then suggest that the prefactor A12 > Ale Without assuming a reaction order with respect to the are found, initiator, the combined rate parameters, C1., from Figure 5, for R, > 43 and I = 0.025 4 to be styrene c11
= (7.78 f 7) X p-DVB
= kIl[I]"(')
lo7 exp(-14700 c 1 2
F
400/RT)
T
~
l
~
l
~1
1l
.
'
-
5 . :
0.84 0.7
-e
l
0
0.56 0.42 0.28 0.14 0 0
320 640 960 1280 1600 1920 2240 2560 2880 3200
timc (sec)
Figure 4. Effect of temperature on the rates of disappearance of styrene, m-DVB, and p-DVB, reacted near R, = 85 and [Io] = 25.0 mM. Data taken from runs 6 , 9 , and 10 in Table I. (w) 18 "C; (0) 1.5 "C; (0) -22 "C. -5
-6
-7 -8 -9
-10, -1 1
-12
1
3.4
.
I
3.5
.
t
3.6
.
I
3.7
.
I
3.8
.
l
3.9
.
I
4
llTxlOOO (IIK)
l/s
(7)
= k12[I]"(1)
= (4.38 f 3) X 10' exp(-13200 m-DVB
l
1.26 1.12 0.98
0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.3
600/RT) l / s
(8)
C14 = kl4[IIn(l) = (2.09 f 2) X 10' exp(-13500 7 600/RT) l / s (9) At room temperature, the rate constant for the disappearance of styrene monomer from the multicomponent
Figure 5. Constructions used for obtaining activation energies from data in Figure 4. (m) p-DVB; (0)m-DVB; (0) styrene.
reaction mixture is, within a factor of 2, that observed in bulk polymerization of pure styrene at the same initiator concentration and temperature (Your et al., 1989). The difference is probably the result of uncertainties in the present measurements. For example, the effed of initiator concentration on the reaction of monomer 2, p-DVB, in styrene at R, = 81 is illustrated in Figure 6. The 5-1070 uncertainty in initiator concekration, shown here, results from uncertainties in determining the concentration of contaminants that react with the butyllithium initiator. Our previous kinetics studies (Your et al., 1989) avoided
~
l
~
650 Ind. Eng. Chem. Res., Vol. 30, No. 4, 1991
. E 5. -
styryllithium chain ends dimerize (Morton and Fetters, 1964; Morton et al., 1970). The criterion for gelation of the living polymerization is then simply
2 1.8 1.6 1.4 1.2 1 0.8
where [M6] and [M7] are the concentrations of doubly reacted p- and m-DVB, respectively, in the copolymerizing system at any time. Gelation is, therefore, predicted when the concentration of doubly reacted DVB molecules rises to 1/4 of the initial initiator concentration. Walling (1945) has shown that the Flory criterion (Flory, 1953) for critical conversion, xC, at the gel point
0.6 0.4 0.2 0
xc
-5.3
-
-
-6 .-
-- ;=
I7Lf!L.l -6 8 -7 -72
-5
-4 7 -4 4 -4 I -3 8 -3 5 -3 2 - 2 9 -2 6 -2 3
-2
I I1 Io
Figure 7. Construction, using slopes in Figure 6, for determining reaction order with respect to initiator for p-DVB at R, > 80. (m) At reaction temperature; (0)shifted to 3.4 'C.
this problem by determining the molecular weight of the linear polymer by gel permeation chromatography. The molecular weight was then used to calculate the effective initiator concentration. This approach is not possible for the present system which forms a three-dimensional, insoluble, network. The reaction order, n(l), can be determined by the construction shown in Figure 7. The reaction temperatures were not all identical, and the appropriate shift in the kl"(') product was made by using the measured activation energy, pE2 = 13.2 kcal/mol, (8) above. As illustrated in Figure 7, the best linear fit of the shifted data gives an apparent reaction order of n(1) = 0.82 f 0.3. The uncertainty in the initiator concentrations is responsible for the uncertainty in reaction order. Despite this uncertainty, the reaction order with respect to initiator still seems higher than the 0.5 values observed for styrene polymerizations in the absence of DVB (Youret al., 1989). The reason for this behavior is not known but may be related to the potentially greater stability of the DVBcontaining ionic complex, relative to styrene, which results from the higher number of conjugated states possible in the more complex DVB molecule. Gelation Behavior of Systems with R, 1 44. Although the kinetic information for the styrene-DVB system is limited to the styrene-rich regime, it is still interesting to attempt to use this and additional information to predict gel time. The additional information required is the criterion for incipient gelation. According to Flory (1953),incipient gelation is expected when one cross-link exists for every two primary chains. That is, the ratio of cross-links to primary chains is 1:2. When R, is large, the effective number of primary chains in the living styreneDVB system is approximately [10]/2, where the factor of 2 arises from the fact that the living
= l/(PoY,)
(11)
where po is the molar fraction of divinyl groups in the initial monomer mixture and yw the weight-average degree of polymerization of the primary chains (those that would exist if all cross-links were severed), was approximately followed by two systems. Unfortunately, (11)has been held to be inappropriate for the styrene-DVB system (Worsfold, 1970; Mikos et al., 1986),because intramolecular cyclization reactions apparently exist that can lead to delays in observed gel times, relative to predicted values. The lower reactivity of the second DVB group, noted in the present study, may also contribute to an increase in gel time relative to that calculated from Flory's assumption that all vinyl groups have the same reactivity. The higher reactivities of the DVB vinyls relative to styrene could likewise be expected to shorten the gel time relative to that predicted by statistical arguments alone at high DVB concentrations. It should be possible to use the combined reaction rate constants, described above, to predict vinyl group consumption without assuming equal reactivity. These results could then be used with (10) to predict gelation times. Assuming the same reaction order with respect to initiator for all reactions, the balances for once reacted DVB, monomers 3 and 5, are d[M,I/dt = CdM41 - C15[M51
(13)
where
c,
= Itlj[10]"(')
(14)
The rates of cross-link formation are proportional to the concentrations of once reacted p-DVB and m-DVB, [M3] and [M5],respectively: d[M6i/dt = C16[M31
(15)
d[M,I/dt = CidM51
(16)
The rates of disappearance of M2 and M4 are observed to follow the form of (5). These can be integrated to give (17) [M21= W 2 0 1 exp(-C12t) [M41 = [M401exP(-Cid) (18) Equations 17 and 18 were sukstituted into (12) and (13) and the results integrated (Spiegel, 1968) to determine [M3] and [M,] , respectively:
Ind. Eng. Chem. Res., Vol. 30, No. 4, 1991 661 Table 111. Comparison of Experimental with Predicted Gel Times
R, 81
I,. mol/L 0.035
44
0.025 0.035
28
0.025 0.035 0.025
eel time, min predicted T.OC exDtl n = 0.5 n = 0.8 4.0 15.5 f 1.5 19.9 f 1.9 17.9 f 1.9 4.4 17.4 f 1.5 19.0 f 1.9 17.2 f 1.9 9.5 10.0 f 0.5 11.9 f 1.9 10.9 f 1.9 9.3 10.1 f 0.8 11.4 f 1.8 11.4 f 1.9 4.4 13.5 f 0.5 12.5 f 1.3 11.4 f 1.3 9.3 f 0.3 9.1 f 1.3 8.2 f 1.3 8.0 11.2 6.7 f 0.3 6.8 f 1.3 6.2 f 1.3 3.8 f 0.1 3.8 f 1.2 3.4 f 1.2 18.0 7.8 f 0.4 7.8 f 1.2 7.8 f 1.2 9.3 6.1 10.4 f 0.4 12.7 f 1.8 8.6 f 0.4 11.1 f 1.8 7.8 3.7 f 0.1 5.1 f 1.4 18.0 9.3 7.6 f 0.4 10.0f 1.8
Equations 19 and 20 can be combined with (15) and (16), respectively, and the results integrated analytically to yield
[ i13
C12C13[M201
[%I =
~ 1 -3 c ~ Z
-(exp(-C13t)
w-
3.4
3.6
3.5
1iTemperature
( O K )
3.7
(~1000)
Figure 8. Natural log of gelation time versus 1/T. (0) R, = 6.9, [b]= 0.024 M;(A)R, = 44, [I,] = 0.035 M.
12 l4
li----l
- 1) -
0
1 -bp(-Cl4t) Cl.4
= Cy([Io] /0.025)”(’)
0.04
0.OB
0.12
Io, M
- 1)
Figure 9. Comparison of predicted and observed gel times at R , =
The rate constants, CI3and C15,are unknown; however, it is not unreasonable to approximate these parameters to be the same as the rate constant for polystyrene, CI1. The similarity in structure between half-reacted p-DVB or m-DVB and ethylvinylbenzene and the similarity in reactivity between ethylvinylbenzene and styrene, Figure 2, suggest that this approximation is reasonable. A comparison of observed and calculated gel times, from (lo), (21), and (22), are presented in Table 111. Predicted gel times are seen to agree, within 15% relative error, with experimentally observed values for values of R, from 27 to 81. The uncertainty reported for observed gel times is that determined from repeated runs, whereas that reported for predicted values is estimated from uncertainties in the rate constants and activation energies employed. The predicted gel times for R, = 44 and R, = 81 were determined by using the C, parameten reported in (7)-(9). The effect of initiator concentration is computed by CIj(Z0)
~
3.3
(23)
where C is the measured parameter reported in (7)-(9) and C,(& is the estimated value of that parameter at an initiator concentration Io. This estimation obviously requires knowledge of the order of the reaction with respect to initiator, n. Two predictions, one for n = 0.5 and one for n = 0.8, are presented in Table 111. The differences between these predictions are small because the maximum excursion in initiator concentration from the value, Io = 0.025 M, used in the measurements of the Clj values is small. The success of these predictions suggests that the rate constants in these equations are independent of R, for R, 1 44. A good prediction can also be made for R , = 28, provided one is willing to evaluate the kinetic rate data by doing experiments for which R , = 28. As mentioned earlier, the reaction rates are no longer first order
44 as a function of initiator concentration at 12 OC. (B) Experimental. (-) Lower line calculated from (71410)and (21)and (22); upper line calculated by reducing rates in (7)-(9)by 15%. Both lines calculated using n = 0.80. (- - -1 Calculated using (7)-(10) and (21) and (22)with n = 0.5.
with respect to monomer, are lower than rates at R, L 44, and are functions of R, when R, < 44. However, rate “constants” can be evaluated from experimental data which can give reasonable estimates of gel time, as illustrated by the case R, = 28 in Table 111. The results in ,Table I11 suggest that the model does a reasonable job of predicting the temperature dependency of gel time over a narrow range of temperature. To the extent that the whole process of polymerization is pseudo first order in overall conversion with gelation time proportional to a critical conversion, one can write In (tc) = AEa/RT + C (24) where tG is the gel time, AE, the apparent activation energy, and C a constant that contains information about the conversion, rate constant, and initiator concentration. As shown in Figure 8, experimental observations seem to follow the form suggested by, (22) for both R, = 44 and R, = 6.9, even though the kinetic rates cannot be described in detail at the lower R, value. The apparent activation energy, ma, is determined to be 14.8 f 0.7 kcal/mol for both cases. This value is very similar to for pure styrene polymerization, discussed earlier, and the similarity seems to suggest the dominance of styrene and styryllithium ends in the polymerization process, even at styrene to DVB ratios as low as R, = 6.9. As shown in Figure 9, the gel time for R, = 44 is experimentally observed to decrease with increasing butyllithium concentration. The model, (10) and (21)-(23), predicts either that the gel time should increase with increasing initiator concentration, when n = 0.5, or that gel
652 Ind. Eng. Chem. Res., Vol. 30, No. 4,1991
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.-K
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.-
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I
I
I
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.-E c
-
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Temperature ( " C ) Figure 10. Effect of temperature and initiator type on gel time for R, = 6.9. (A)70 mM n-BuLi; (0)24 m M sec-BuLi.
time should decrease with increasing initiator concentration, when n = 0.8. The prediction of gel times is quite sensitive to the magnitudes of the rate expressions. The lower solid curve in Figure 9 is obtained by using the rate constants listed in (7)-(9) and n = 0.8. The upper solid curve is similarly calculated from rate expressions that are 15% lower than the values listed in (7149). Within this level of uncertainty, the model and the data agree quite well, provided n = 0.8 is used in the model calculation. The model is quite sensitive to the assumed reaction order, and quite good agreement between the model and experiment can be obtained for n = 0.8, the value obtained from the construction in Figure 7. Figure 9 clearly suggests that n = 0.8 does a better job of predicting the influence of initiator concentration on gel time than n = 0.5; however, no physical significance can be associated with this fractional reaction order. Typically, the presence of a fractional reaction order, such as n = 0.8, suggests that the actual reaction mechanism is more complex than the one we postulated. Our assumption that n should be the same for all reactions with the styryllithium end could also well be in error. Unfortunately, the experimental difficulties, described above, preclude accurately knowing the active initiator concentration in this cross-linking system. Until this problem can be resolved, there is little point in postulating additional reaction mechanisms. Gelation Behavior of Systems with R, < 44. Due to the lack of reliable kinetic information, prediction of gelation for systems that contain high ratios of DVB to styrene cannot be made. The gelation behavior of such systems is still of practical interest, however, and some features are described below. In contrast to the experiments described in the previous sections, those described below do not use the prereacted styryllithium as initiator. Instead, the BuLi is simply added to the reaction mixture at the beginning of the reaction. Figure 10 shows that increasing the temperature will reduce the gel time for systems with R, = 6.9. This result is qualitatively consistent with the findings at high R, values, summarized in Figure 8. The large difference in the apparent activities of the n-BuLi and sec-BuLi initiators is surprising. Depending on the temperature of comparison, systems initiated with n-BuLi take roughly 5 times longer to gel than those initiated with one-third less sec-BuLi, an observation that agrees with the qualitative comments by Popov and Schwachula (1980). These two initiators are conversely found to give nearly equivalent polymerization rates when used to initiate pure styrene (Your et al., 1989). The difference in behavior is related to the presence of DVB as well as to differences in the initiators. The addition of BuLi to purified styrene/DVB mixtures results in the formation of a dark-red
0' 0.00
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I
I
0.05
0.1 0
0.1 5
0.20
Initiator Concentration (molil) Figure 11. Effect of initiator concentrations and type on gel time for R, = 6.9. (A)n-BuLi at 23 "C;(0) sec-BuLi at 17 "C.
color which is probably indicative of the formation of a lithium-DVB complex (Worsfold, 1970). The onset of the red color occurs typically within 15 s after addition of sec-BuLi to the styrene/DVB mixture and persists throughout the polymerization. When n-BuLi is used,the orange color which is characteristic of styryllithium first appears about 1 min after addition of the initiator. The red color does not appear until several minutes into the polymerization. These observations suggest that n-BuLi initiates styrene more rapidly than it does DVB. While the reason for this behavior is not understood, that it occurs could qualitatively explain the differences in gel times with initiator type observed in Figure 10. Figure 11shows the effect of initiator concentration and type on gel times for R, = 6.9. Again, one sees the generally lower reaction rate that leads to longer gel times of n-BuLi-initiated systems, relative to those containing sec-BuLi. As was observed for R, > 44, the gel times initially decrease as the concentration of either initiator increases. For n-BuLi concentiations greater than about 20 mM, howeve!, gel time is observed to increase with increasing initiator concentration. This trend may be related to the tendency for n-BuLi to preferentially initiate styrene over DVB, discussed above. At any rate, gel times do not increase with increasing initiator concentration when the initiator is sec-BuLi.
Summary and Conclusions The kinetic complexity and cross-linkingassociated with reactions of p-DVB and m-DVB in polymerizing styrene prevent a detailed kinetic description of the polymerization process for all ratios of styrene to DVB. At high ratios of styrene to DVB, R, > 43, tbe analysis of the reacting system is simplified by the predominance of styryllithium propagating species. In this regime, the rates of disappearance of each monomer, styrene, p-DVB, and m-DVB, appear to be first order with respect to the same monomer, and the relative reactivities of these species, p-DVB > m-DVB > styrene, can be easily determined experimentally. These results appear to follow those suggested by Landler (1952). Due to uncertainties in measurements of initiator concentrations, the precise evaluation of reaction orders with respect to initial initiator concentration is not possible. The order appears to be n = 0.8, a value that is higher than the n = 0.5 value obtained in studies of bulk anionic homopolymerization with butyllithium (Your et al., 1989). The Flory criterion for incipient gelation appears to work quite well for R, > 43, provided the strong dimerization of the propagating polymeric ends is included in the analysis. Calculations of gel times from the Flory criterion
Ind. Eng. Chem. Res., Vol. 30, No. 4 , 1 9 9 1 653 and the kinetic model generally agree with experimental observations to within 15% relative error, provided the overall reactions order with respect to initiator is set to be n = 0.8, the value found from analysis of experimental reaction rates in this study. Although n = 0.8 probably suggests only that our model of the reacting system is incomplete, the ability to predict gel times at least suggests a measure of internal consistency. Within the band of uncertainties in both data and calculation, it is difficult to determine the influence, if any, of intramolecular cyclization reactions, such as those suggested by several investigators (Dusek and Spevacek, 1980; Fink, 1981; Soper et al., 1972). Given the high R, values used in this study, it is reasonable to expect intramolecular cyclization to not be a problem.
Acknowledgment Support for this work by the State of Texas Advanced Technology Program is gratefully acknowledged. Registry No. (Styrene)(DVB) (copolymer), 9003-70-7; DVB, 1321-74-0; styrene, 100-42-5; s-BuLi, 598-30-1; BuLi, 109-72-8.
Literature Cited Alfrey, T., Jr.; Bohrer, J. J.; Mark, H. Copolymerization; Interscience: New York, 1952; Chapters I, 11, VI, XI, XII. Billmeyer, F. W., Jr. Textbook of Polymer Science; Interscience: New York, 1962; Chapter 11. Christiansen, W.H.; Ekerdt, J. G.; Trachtenberg, I.; Barlow, J. W. Development of a Reaction Injection Molding Encapsulant System. 2. Chemorheology of the Anionic Bulk Polymerization of Styrene. Ind. Eng. Chem. Res. 1990,29,463-470. Dusek, K.; Spevacek, J. Cyclization in Vinyl-Divinyl Copolymerization. Polymer 1980, 21, 750-756. Fink, J. K. Kinetics of Crosslinking Copolymerization of Styrene with Symmetric Divinyl Compounds. J. Polym. Sci. Polym Chem. Ed. 1981, 18,195-202. Flory, P. J. Principles of Polymer Chemistry; Cornel1 University Press: Ithaca, NY, 1953; pp 356-393.
Gilman, H.; Carteledge, F. K. The Analysis of Organolithium Compounds. J. Organomet. Chem. 1964,2,447-454. Hsieh, H. L. Kinetics of Polymerization of Butadiene, Isoprene, and Styrene with Alkyllithiums. Part 1. Rate of Polymerization. Part 2. Rate of Initiation. Part 3. Rate of Propagation. J.Polym. Sci. 1965, A-3, 153-180. Landler, Y. On Anionic Copolymerization. J. Polym. Sci. 1952,8 (l), 63-72. Mikos, A. G.; Takoudis, C. G.; Peppas, N. A. Kinetic Modeling of CoDolvmerization/Cross-Linking Reactions. Macromolecules i9Ss, is,2174-2182. Morton, M.; Fetters, L. J. Homogeneous Anionic Polymerization V. Association Phenomena in Organolithium Polymerization. J. Polym. Sci.: Part A 1964, 2, 3311-3326. Morton, M.; Fetters, L. J.; Pett, R. A.; Meier, J. F. The Association Behavior of Polystyryllithium, Polyisopropenyllithium, and Polvbutadienyllithium in Hydrocarbon Solvents. Macromolecules i970,3, 32j-332. ODriscoll, K. F. Anionic Copolymerization. J. Polym. Sci. 1962,57, 721-726. Popov, G.; Schwachula,G. Styren-Divinylbenzen-Copolpem. XXI. Polymerisationkinetishes Verhalten des Anionischen Styren-Divinylbenzen-Systems. Plaste Kautsch. 1981,24372-374. Rubenstein, D.; et al. Separation of Para and Meta Isomers of Divinylbenzene. United States Patent No. 3,217,051, Nov 9, 1965. Soper, B.; Haward, R. N.; White, E. F. T. Intramolecular Cyclization of Styrene-p-Divinylbenzene Copolymers. J. Polym. Sci. Part A-1, 1972,10, 2545-2464. Spiegel, M. R. Mathematical Handbook; Schaum’s Outline Series; McGraw-Hill: New York, 1968; p 104. Walling, C. Gel Formation in Addition Polymerization. J. Am. Chem. SOC. 1945,67,441-447. Worsfold, D. J. Anionic Copolymerization of Styrene with p-Divinylbenzene. Macromolecules 1970,3,514-517. Worsfold, D. J.; Bywater, S. Degree of Association of Polystyryl-, Polyisopropenyl-, and Polybutadienyllithium in Hydrocarbon Solvents. Macromolecules 1972,5, 393-397. Your, J.-J. A.; Karles, G. D.; Ekerdt, J. G.; Trachtenberg, I.; Barlow, J. W. Development of a Reaction Injection Molding Encapsulant System. 1. Kingtic Studies of Butyllithium-Catalyzed Styrene Polymerization. Ind. Eng. Chem. Res. 1989,28, 1456-1463. Received for review June 25, 1990 Accepted October 15,1990
