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Ind. Eng. Chem. Res. 2006, 45, 1300-1306
Modeling and Simulation of Diimide Hydrogenation of Nitrile Butadiene Rubber Latex Xingwang Lin, Qinmin Pan, and Garry L. Rempel* Department of Chemical Engineering, UniVersity of Waterloo, Waterloo, Ontario N2L 3G1, Canada
A comprehensive simulation of the diimide hydrogenation process is carried out by taking into account the diimide generation reaction, the hydrogenation reaction, the side reaction between hydrogen peroxide and diimide, the disproportionation of diimide, and the diimide diffusion process. The relative magnitude of these rate constants with the diffusivity of diimide is estimated. It is found that the diimide diffusion interferes with the diimide hydrogenation of the latex of nitrile butadiene rubber (NBR), even though the particle diameter is as small as 72 nm. The interference of diimide diffusion makes it very difficult to achieve above 90% of hydrogenation without significant gel formation. Using core-shell latex with an NBR shell may help to solve the low hydrogenation efficiency and the gel formation at the same time. 1. Introduction Direct hydrogenation of nitrile butadiene rubber (NBR) in latex form has been of special interest to the industry since Wideman1 invented a diimide hydrogenation method in 1984. Diimide generated from the reaction between hydrazine (N2H4) and hydrogen peroxide (H2O2) can be used to saturate NBR latex without using organic solvents and complex catalysts.2-15 Four main reactions have been identified in the diimide hydrogenation system: (1) the reaction between N2H4 and H2O2 to produce diimide, (2) the reaction between diimide and carbon-carbon double bonds (CdC) to form hydrogenated polymer, (3) the reaction between diimide and H2O2 to generate nitrogen, and (4) the reaction between two diimide molecules to produce one molecule of N2H4 and to release one nitrogen molecule.
N2H4 + H2O2 f N2H2 + 2H2O
(1)
N2H2 + R1HCdCHR2 f N2 + R1H2CsCH2R2
(2)
N2H2 + H2O2 f N2 + 2H2O
(3)
2N2H2 f N2H4 + N2
(4)
Reaction 1 occurs at the particle interface where the aqueousphase-borne reactants can meet the interface-borne catalyst; reaction 2 occurs in the rubber phase when diimide diffuses into the rubber phase to meet CdC; reaction 3 occurs only at the interface; and reaction 4 most likely occurs in the rubber phase by way of a radical mechanism. The concentration of diimide cannot be measured, which makes it difficult to estimate the rate constants for these reactions. It has been identified that reaction 4 is the radical source for gel formation during hydrogenation.13 Reactions 3 and 4 consume diimide and decrease hydrogenation efficiency HE (HE is defined as the portion of H2O2 that is actually used for the hydrogenation of CdC14). Therefore, low HE and gel formation are generally observed for the diimide hydrogenation process. It is highly desirable to solve the two problems and to commercialize the diimide hydrogenation process. Process * To whom correspondence should be addressed. E-mail: grempel@ cape.uwaterloo.ca. Tel.: (519) 888-4567 ext. 2702. Fax: (519) 7464979.
simulation conducted in this work intends to provide a systematic description of this process, reasonable estimates for the rate constants, and solutions to optimize this process. 2. Experimental Section Two types of experiments were carried out in this investigation. The procedures for the semibatch hydrogenation experiment14 and the pressure buildup experiment15 have been published before. 3. Process Simulation Reaction 1 is first-order with respect to [N2H4] and [H2O2].15 The kinetic equation is
r1 ) k1f([Cat],[N2H4])[H2O2]
(5)
where r1 is the rate of reaction 1 and also the total consumption of hydrazine and f is an overall effectiveness factor of reaction 1. Because transition metal catalysts used in this reaction are not stable in the hydrazine and latex mixture, the amount of active catalyst cannot be quantified. Therefore, the effect of catalyst concentration is incorporated into the factor f. Hydrazine is normally kept in large excess in the diimide hydrogenation process. Its effect is also incorporated into the factor f. The reaction rates for reactions 2-4 are expressed as follows,
r2 ) k2[CdC][N2H2] ) -
d[CdC] dt
(6)
r3 ) k3[N2H2][H2O2]
(7)
r4 ) k4[N2H2]2
(8)
where r2, r3, and r4 are the rates of reactions 2, 3, and 4, respectively, and k2, k3, and k4 are the corresponding kinetic constants. The locations for the four reactions are illustrated in Figure 1. Vp is the total volume of the NBR rubber particles, which is the reaction location for reactions 2 and 4. Vs is the volume of the interface. It is an interfacial layer in which the catalyst, aqueous-phase-borne hydrazine and hydrogen peroxide, and organic-phase-borne diimide can contact each other. Va is the volume of the aqueous phase. [N2H4] and [H2O2] are
10.1021/ie0507575 CCC: $33.50 © 2006 American Chemical Society Published on Web 01/24/2006
Ind. Eng. Chem. Res., Vol. 45, No. 4, 2006 1301
(
)
3 Vp d[N2H2] k1f([Cat],[N2H4])[H2O2] ) -Dorg R Vs dr
|r)R
+
k3[N2H2]s[H2O2] + 2k4[N2H2]s2 (12) The other boundary condition for eq 9 is given by eq 13.
d[N2H2] )0 dr |r)0 Figure 1. Diagram of a latex particle and reaction locations for the diimide hydrogenation.
calculated based on Va. It is assumed that the concentrations are equal for the aqueous phase and the interface for both N2H4 and H2O2. 3.1. Assumptions. To simplify the simulation, certain assumptions are made. It is shown that different types of CdC have different reaction activities toward diimide. The rate of diimide hydrogenation of the vinyl CdC is 2.29 times that of the trans-CdC, as in the case of a homogeneous solution,16 i.e., the apparent rate ratio is kvinyl/ktrans ) 2.29. However, the vinyl and the cis-CdC content is only 10% of the total CdC. The presence of the 10% more active CdC groups would not alter the reaction kinetics significantly. Thus, in this simulation, it is assumed that there is only one type of CdC. The CdC has the same reaction activity toward diimide. It is assumed that all the particles inside the latex have the same radius R. The particle size distribution of typical latex is quite narrow. This assumption is generally accepted for latex. 3.2. Process Description. In this system, [CdC] and [N2H2] change with time spatially. Inside the particle, a mole balance over diimide in a differential region gives
-r
-2
(
)
∂[N2H2] (9) ∂t
One of the boundary conditions for eq 9 is defined by the mole balance over diimide at the interface.
( ) dNN2H2 dt
r1
(
) (
dNN2H2 dt
+ -
r3,s
)
dNN2H2 dt
r4,s
(
)
d[N2H2] dr
|r)R
(10b)
N is the total number of latex particles in the reaction system, and
N)
Vp 4 3 πR 3
Equation 10 can be converted to
(14)
The change of [CdC] is governed by eq 6.The initial condition for eq 6 is
[CdC]|t)0 ) [CdC]0
(15)
HD is defined as
HD(r,t) ) 1 HD(t) ) 1 -
[CdC] [CdC]0
[CdC] 3r2 dr 3 0 R
∫0R [CdC]
(16)
(17)
HE includes two parts. The HE from the competition of reaction 3 is
HEaqu ) 1 -
2k3[N2H2]|r)R k1f([N2H4],[Cat]) + k3[N2H2]|r)R
HEorg )
r
(18)
2
∫0R r2 +22r4 3rR3 dr
(19)
The total hydrogenation efficiency is
HE ) HEaquHEorg
(10a)
where (dNN2H2/dt)r1, (-dNN2H2/dt)r3,s, and (-dNN2H2/dt)r4,s are used to express the total amount of diimide generated by reaction 1 per unit time and the total amounts of diimide consumed per unit time by reactions 3 and 4, respectively, in Vs. WR is the diffusion flux via the particle surface, which can be expressed as follows
WR ) -Dorg
[N2H2]t)0 ) 0
(20)
Reaction 4 is the radical source. The major concern about cross-linking is at the interface, which is most probably being cross-linked. The ratio of reaction 4 to reaction 2 at the interface can be used to evaluate the degree of cross-linking.
) WR4πR2N + -
The initial condition for eq 9 is
The HE from the competition of reaction 4 is
∂[N2H2] ∂ 2 r Dorg + k2[CdC][N2H2] + ∂r ∂r 2k4[N2H2]2 ) -
(13)
(11)
Cross-linking ∝
|
r4 r2
(21) r)R
The simulation begins with eqs 6 and 9 by using those boundary conditions and initial conditions defined in eqs 10-15. On the basis of the input of Dorg, k1f, k2, k3, k4, and [CdC]0, the simulation will produce the course of hydrogenation and cross-linking according to eqs 16-20. However, the parameters Dorg, k2, k3, and k4 are not available from the literature. The analytical solution of simplified cases carried out below may provide insights into these parameters. 3.3. Simulation of Reaction-Controlled Processes. When the diimide diffusion is much faster than the reaction, [N2H2] would remain the same all over the particle; hydrogenation proceeds at the same rate all over the particle. Because diimide is a highly reactive intermediate, its concentration in the system is quite low. The total amount of diimide in the system at any time is much less than that generated in the system. Therefore, PSSH (pseudo-steady-state hypothesis) can be assumed for this
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system. A mole balance over diimide gives the following:
b0 )
diimide generated per unit time by reaction 1 ) diimide consumed per unit time by reactions 2-4 (22)
2[H2O2]0 + a0
Combining eq 29 with eq 31 and integrating eq 29 gives
i.e.,
r1Vs ) r2Vp + r3Vs + 2r4Vp
(23)
Let
(
( ))
a0 a0 Vs 1 NN2 ) NT - Va b0e- k1ftb1 + a0 ln(b1) - ln 2 Va 2 b0
(32)
with
r3Vs k3Vs [H2O2] γ1 ) ) r2Vp k2Vp [CdC]
(24)
r4Vp k4 [N2H2] ) γ2 ) r2Vp k2 [CdC]
(25)
b 1 ) e-
k1fVs[H2O2]
1 [N2H2] ) k2Vp[CdC] 1 + γ1 + 2γ2 HEaqu )
Vp(r2 + 2r4) 2Vsr3 + Vp(r2 + r4) HEorg )
)
dt
x
e-2
Vsk1ft a0 + Va b0
{
(
)}
a0 2[H2O2]0 1 NT ) Va [H2O2]0 + ln 1 + 2 2 a0
(26)
(33)
The average HE for H2O2 would then be expressed as
1 + 2γ2 1 + 2γ1 + 2γ2
(27)
r2 1 ) 2r4 + r2 1 + 2γ2
(28)
3.3.1. Simulation of the Pressure-Buildup Experiment. To acquire estimates of these rate constants, the specially designed pressure-buildup experiment was conducted. For the pressurebuildup experiment, a batch reaction of N2H4 and H2O2 was investigated in a closed container. The nitrogen generation course was recorded. N2H4 and CdC were kept at a large excess. [N2H4] and [CdC] were, therefore, assumed to be unchanged during the reaction. This process is controlled by reaction rather than mass transfer of diimide because only the surface layer of the rubber is hydrogenated. The percentage of reaction 4 is negligible when compared to that of reaction 2. For a batch reaction, when the initial concentration of H2O2 ([H2O2]0) is much less than [CdC]0, [CdC] will not change. HD ) 0 is assumed. The nitrogen production rate is
dNN2
Vsk1ft + Va
and the total amount of nitrogen generated from the reactions can be expressed as
Then,
) Vsr1 ) Vsk1f([Cat],[N2H4])[H2O2]
(29)
The H2O2 consumption rate can be simplified by omitting the r4 item.
-
[H2O2]02
(
Vs [H2O2] d[H2O2] Vs ) (r1 + r3) ) k1f[H2O2] 1 + dt Va Va [H2O2] + a0
)
HEaqu )
2NT [H2O2]0
-1)
ln(1 + 2γ1t)0) , 2γ1t)0 γ1t)0 )
k3 Vs [H2O2]0 (34) k2 Vp [CdC]0
This expression of HEaqu fits the HE data very well (Figure 2). Regression gives
k2 Vp ) 0.012 ( 0.002 M (95% confidence) k3 Vs
(35)
From this equation, the rate ratio of the hydrogenation to the side reaction of diimide at the interface can be estimated. Unfortunately, similar data is absent in the literature and, therefore, cannot be compared. This ratio is quite small when compared to 1, which means the in situ [H2O2] must be much lower than [CdC] to make the hydrogenation reaction dominate over the side reaction of H2O2 decomposition (reaction 3). 3.3.2. Simulation of the Semibatch Hydrogenation Process. As suggested by He et al.,8 the diimide hydrogenation of latex with small particle size (such as a diameter of 50 nm) was mainly a reaction-controlled process. A homogeneous model was proposed for this case. On the other hand, the hydrogenation of latex with large particle size (such as a diameter of 230 nm) was a diffusion-controlled process. The layer model was proposed for the diffusion-controlled process.
(30) with
a0 )
k2[CdC]0Vp k3Vs
Integrating eq 30 gives
[H2O2] ) ewith
(
Vsk1ft Vs b0e- k1ft + Va Va
x
b02e-2
)
Vsk1ft + a0b0 (31) Va Figure 2. HE at different [H2O2]0 ([N2H4] ≈ 2.2 M, T ) 25.0 °C, [H3BO3] ≈ 0.063 M, and solid content ) 3.8 wt %).
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In the semibatch hydrogenation of latex with a particle size of ∼72 nm, it was observed that HE was virtually 100% before HD reached 60% when boric acid was used as the catalyst,14 which means the disproportionation reaction 4 is negligible all through the major part of the hydrogenation process. The high efficiency suggests that the concentration of diimide is quite low and that the hydrogenation reaction 2 is quite slow when compared with the diimide diffusion process. Therefore, the hydrogenation of latex with an average diameter of 72 nm is probably a reaction-controlled process before HD reaches 60%. This simulation begins with a reaction-controlled assumption. The resultant hydrogenation curve from this simulation will be compared to that from the hydrogenation experiment to check whether this assumption is supported. The differential equations for [CdC], [N2H2], [H2O2], and [N2H4] are given by
d[CdC] ) -r2 dt
(36)
Vs d[N2H2] ) (r1 + r3) - r2 - 2r4 dt Vp
(37)
d[H2O2] qa - Vs(r1 + r3) - qv[H2O2] ) dt (V0 + qvt)
(38)
-Vsr1 d[N2H4] ) dt (V0 + qvt)
(39)
Figure 3. Simulation of HD curves at different k4 values (k2 ) 0.1 (sM)-1, k3 ) 2.0 (sM)-1, Vp ) 0.015 L, Vs ) 0.0015 L, and k4 in (sM)-1).
where qa is defined as the H2O2 addition rate in mol/s and qv is defined as the addition rate of H2O2 aqueous solution in L/s. The initial conditions are
[CdC]t)0 ) [CdC]0
(40)
[N2H2]t)0 ) 0
(41)
[H2O2]t)0 ) 0
(42)
[N2H4]t)0 ) [N2H4]0
(43)
The actual simulation is based on a semibatch hydrogenation process with the assumption of kinetic control. NBR latex (100.0 mL) with 15.0 wt % solid content, 17.4 g of hydrazine hydrate (2.0 times CdC in mole units), and 1.3 g of boric acid composed the reaction medium with the addition of 29.6 g of hydrogen peroxide aqueous solution (30.0 wt %) over a period of 10 h. This simulation aims at checking the effects of the values of these parameters upon the HD curve. Values of k2, k3, and k4 are related to the diimide concentration level, which, however, cannot be measured directly. During this simulation, k2 is preset at 0.1 (sM)-1. k3 is estimated from eq 35 with some adjustment to accommodate the difference with [H3BO3]. k4 is then changed over a range to compare the HD curves. When k2 and k3 are increased by a factor of 10 and k4 is increased by a factor of 100, [N2H2] will be just one-tenth of that with k2 ) 0.1 (sM)-1. Figures 3 and 4 clearly show that the increase in side reactions r3 or r4 would result in the decrease in HE. To accommodate the experimental results, HEorg is close to 100% before HD reaches 35%; HEaqu is close to 100% when [H2O2] is below 0.009 M; and both k3 and k4 have to be set below 20 when k2 is set at 0.1 (sM)-1. In Figures 3 and 4, HD can reach 98% or more when the hydrogenation efficiency is close to 100% at low HD range (such as the case of k3 < 20 (sM)-1 and k4 < 20
Figure 4. Simulation of HD curves at different k3 values (k2 ) 0.1 (sM)-1, k4 ) 2 (sM)-1, Vp ) 0.015 L, Vs ) 0.0015 L, and k3 in (sM)-1).
Figure 5. Hydrogenation of NBR latex (catalyst ) 1.3 g of boric acid, 40 °C, (N2H4/CdC) ) 2.0; H2O2/N2H4 ) 0.75, addition over 10.0 h).
(sM)-1). HD increases almost linearly with time, which fits well with the experimental results (Figure 5). However, it is very hard to reach greater than 98% of HD in the semibatch hydrogenation experiments (Figure 6). In this experiment, the NBR latex was hydrogenated to 85.6% (HD) in the first step. The residual [CdC] was 1.67 M. The resultant latex was aged over 24 h so that no H2O2 remained in the latex. After supplementing an additional 8.7 g of N2H4, the reaction
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Figure 6. Hydrogenation of latex partially saturated by diimide (catalyst ) boric acid, 10.0 wt % of NBR; 45 °C, (N2H4/CdC) ) 7.0 (newly added); (H2O2/CdC) ) 1.5; H2O2 addition over 8.0 h; [CdC]0 )1.67 M).
Figure 8. HD, HE, HEaqu, and HEorg curves for the case with k2 ) 800 (sM)-1, k3 ) 1.6 × 105 (sM)-1, k4 ) 5.12 × 109 (sM)-1, and R ) 36 nm.
Figure 7. [H2O2] dynamics for the semibatch hydrogenation process.
was resumed at the same addition rate of hydrogen peroxide aqueous solution, which was diluted by a factor of 7. The hydrogenation curve is presented in Figure 6. HE is much lower than that in the first step. Even after two cycles of hydrogenation, there is still 1.5% of the initial CdC left (Figure 6). This difference between simulation curves (Figures 3 and 4) with actual HD curves (Figures 5 and 6) would suggest that a pure reaction-controled mechanism cannot be assumed for the latex with an average particle size of 72 nm. Mass transfer interference would increase diimide buildup. The second-order side reaction r4 would be accelerated significantly and would dominate over r2. The hydrogenation of residual CdC can only be achieved at a very low HE. A long tail of the hydrogenation curve would be observed as the result. The hydrogenation experiments on latex with different particle sizes by He et al.8 have shown that higher HD can be achieved on latex with a smaller particle size, which suggests that the hydrogenation on latex with a particle diameter of 230 nm is interfered with by diimide diffusion. The simulation carried out here shows that diimide mass transfer is a problem even for the latex with a particle diameter of 72 nm. This simulation also indicates that, in order to achieve high efficiency over a low HD range up to 60%, k3 has to be smaller than 20 (sM)-1 and k4 has to be smaller than 20 (sM)-1 (when k2 is set at 0.1 (sM)-1). 3.4. Simulation of Diffusion-Interfered Semibatch Hydrogenation Process. A steady state for [H2O2] can be assumed for the hydrogenation process. The solution of eq 38 shows that [H2O2] reaches a steady state at 0.0181 M in just 1800 s (just 5.0% of the total reaction time, Figure 7). In the actual hydrogenation reaction, [N2H4] decreases and [H2O2] increases to compensate each other and to make sure that no accumulation of hydrogen peroxide occurs.
The simulation on simplified cases above has given a relative range for the values of k2, k3, and k4. Dorg can be set at 5 × 10-13 m2/s based on the general magnitude of diffusivity in solids.17 Using this diffusivity data and the hydrogenation phenomena observed for this system, this simulation can provide reasonable estimates for these parameters. Increasing k2, k3, and k4 simultaneously would render the process diffusion-controlled; decreasing k2, k3, and k4 simultaneously would render the process reaction-controlled. To further narrow down the value ranges for the three rate constants, the hydrogenation data from He et al.8 on latex with different particle sizes are taken into consideration. On the basis of their experiments, the hydrogenation of latex with a particle diameter of 230 nm is controlled by diimide mass transfer, while the effect of mass transfer significantly decreases when the particle diameter is decreased to 50 nm. By setting k2 ) 800 (sM)-1, k3 ) 1.6 × 105 (sM)-1, and k4 ) 5.12 × 109 (sM)-1, the simulation results on latex with different particle sizes fit well to the observation by He et al.8 and the results of the experiments for this investigation. As an example, the simulation results for latex particles with a diameter of 72 nm are illustrated in Figures 8 and 9, and the typical results of the simulation for representative particles are briefed here: the final HD is 0.6174 for the latex with a diameter of 230 nm, 0.9324 for the latex with a diameter of 72 nm, and 0.9531 for the latex with a diameter of 50 nm. 3.5. Limitation of This Simulation. A steady state is assumed for the reactions outside of the latex particle in this simulation. However, [N2H4] would decrease as the reaction proceeds; [H2O2] would increase at the same time. The changes would result in a slower supply of diimide at the end of this process. An ideal simulation can divide the whole reaction time into a number of sections, such as 100 parts. The steady state can be assumed for each part of this process. This improved simulation would be able to provide a more accurate description of the latter part of this process. Because cross-linking increases together with hydrogenation, the relaxation of rubber molecule chains may be restrained at a high HD range. The rate constant for hydrogenation may decrease as a result, and the diffusivity of diimide in the crosslinked rubber may also decrease. Nevertheless, it is very difficult to evaluate these effects.
Ind. Eng. Chem. Res., Vol. 45, No. 4, 2006 1305
Figure 9. Development of cross-linking, [N2H2] at the surface, [N2H2] distribution in the particle, and the residual CdC distribution curves for the case with k2 ) 800 (sM)-1, k3 ) 1.6 × 105 (sM)-1, k4 ) 5.12 × 109 (sM)-1, and R ) 36 nm.
4. Summary This comprehensive simulation of the semibatch hydrogenation process reveals the relative rates of the four reactions. It is indicated that k2 ) 800 (sM)-1, k3 ) 1.6 × 105 (sM)-1, and k4 ) 5.1 × 109 (sM)-1 at the temperature of 25 °C are reasonable estimations for these rate constants, providing that Vs/Vp ) 0.1 and Dorg of diimide ) 5 × 10-13 m2/s are assumed. This estimation has taken into consideration the three key experimental phenomena observed. HE is high at the low HD range. HE becomes quite low when HD reaches above 90%. Mass transfer affects the hydrogenation: hydrogenation of latex with a particle diameter of 230 nm is a totally mass-transfer controlled process, and when the diameter is 50 nm, mass transfer of diimide is not a problem. It is concluded from this simulation that diimide diffusion interferes with the hydrogenation reaction for the latex with an average particle diameter of 72 nm. Because of the mass transfer limitation, it is very difficult to reach above 95% HD without significant gel formation. Therefore, it is suggested that specially designed core-shell latex with an inert core and an NBR shell should be used for the diimide hydrogenation process. By using core-shell latex, both the low efficiency problem and the crosslinking problem can be eased significantly. It is also shown that radical generation in the organic phase is always part of this system. Cross-linking increases with HD. Therefore, the NBR latex should have relatively low molecular weight to allow for some degree of cross-link formation. The hydrogenated rubber would still be processable after a limited cross-link formation. Acknowledgment The financial support from Natural Sciences and Engineering Research Council of Canada (NSERC) and LANXESS Inc. is greatly appreciated. Nomenclature a0 ) (k2/k3)Vp/Vs[CdC]0, kmol/m3 b0 ) [H2O2]02/2[H2O2]0 + a0, kmol/m3 [Cat] ) catalyst concentration, kmol/m3 Dorg ) diffusivity of diimide in NBR rubber, m2/s
f ) effectiveness factor HD ) degree of hydrogenation HE ) hydrogenation efficiency HEaqu ) HE in the aqueous phase HEorg ) HE in the organic phase k1 ) rate constant for r1, l/s k2 ) rate constant for r2, m3/kmol/s k3 ) rate constant for r3, m3/kmol/s k4 ) rate constant for r4, m3/kmol/s ktrans ) the rate constant for the reaction between trans-CdC and diimide, 1/s kvinyl ) the rate constant for the reaction between vinyl CdC and diimide, 1/s N ) the total number of NBR particles in the reaction medium [N2H2]s ) dimide concentration on the interface of a NBR particle, kmol/m3 NBR ) acrylonitrile-butadiene rubber NN2H2 ) mole number of N2H2 NN2 ) mole number of nitrogen produced NT ) total mole number of nitrogen produced qa ) H2O2 addition rate, mole/s qv ) addition rate of H2O2 aqueous solution, Lliter/s R ) the average radius of latex particles, m r ) radius variable, m r1 ) reaction rate of reaction 1, i.e., the reaction between hydrazine and hydrogen peroxide r2 ) reaction rate of reaction 2, i.e., the reaction of diimide with CdC r3 ) reaction rate of reaction 3, i.e., the reaction between hydrogen peroxide with diimide r4 ) reaction rate of reaction 4, i.e., the disproportionation of diimide t ) time, s V0 ) volume of aqueous phase at t ) 0, m3 Va ) total volume of the aqueous phase at t, m3 Vp ) total volume of rubber phase in the latex, m3 Vs ) total volume of the interface, m3 WR ) diffusion flux at the particle surface, kmol/s/m2 Literature Cited (1) Wideman, L. G. U.S. Patent 4,452,950, 1984, assigned to The Goodyear Tire & Rubber Company (Akron, OH). (2) Parker, D. K.; Roberts, R. F.; Schiessl, H. W. Rubber Chem. Technol. 1994, 67 (2), 288-298. (3) Parker, D. K.; Ruthenburg, D. M. U.S. Patent 5,442,009, 1995, assigned to The Goodyear Tire & Rubber Company (Akron, OH). (4) Schiessl, H. W.; Migliaro, F. W., Jr. U.S. Patent 5,057,601, 1991, assigned to Olin Corporation (Cheshire, CT). (5) (a) Belt, J. W.; Vermeulen, J. A. A.; Kostermann, M. U.S. Patent 6,521,694, 2003; WO 00/09576, 2000; WO 00/09568, 2000, assigned to DSM N.V. (Heerlen, NL). (b) Belt, J. W.; Vermeulen, J. A. A.; Singha, N. K.; Aagaard, O. M.; Kostermann, M. U.S. Patent 6,552,132, 2003, assigned to DSM N.V. (Heerlen, NL). (6) Zhang, J.; Zhou, S.; Yao, M. Hecheng Xiangjiao Gongye (China Synthetic Rubber Industry) 2003, 26 (2), 78-80. (7) (a) Wang, J.; Zhou, S.; Zhang, J. Hecheng Xiangjiao Gongye (China Synthetic Rubber Industry) 2003, 26 (3), 141-143. (b) Xu, G.; Zhou, S.; Wang, J.; Zhang, J.; Xu, R. China Patent CN 1472232A, 2004, assigned to Nandi Chemical Industry Co. Ltd. (8) He, Y.; Daniels, E. S.; Klein, A.; El-Aasser, M. S. J. Appl. Polym. Sci. 1997, 64 (10), 2047-2056. (9) Xie, H.-Q.; Li, X.-D.; Liu, X.-Y.; Guo, J.-S. J. Appl. Polym. Sci. 2002, 83 (6), 1375-1384. (10) De Sarkar, M.; De, P. P.; Bhowmick, A. K. Polymer 2000, 41 (3), 907-915; J. Appl. Polym. Sci. 1997, 66 (6), 1151-1162. (11) Li, X.; Xie, H. Hecheng Xiangjiao Gongye (China Synthetic Rubber Industry) 2002, 25 (5), 282-285. (12) Zhou, S.; Bai, H.; Wang, J. J. Appl. Polym. Sci. 2004, 91 (4), 20722078.
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(13) Lin, X.; Pan, Q.; Rempel, G. L. J. Appl. Polym. Sci. 2005, 96 (4), 1122-1125. (14) Lin, X.; Pan, Q.; Rempel, G. L. Appl. Catal., A 2004, 276 (1-2), 123-128. (15) Lin, X.; Pan, Q.; Rempel, G. L. Appl. Catal., A 2004, 263 (1), 27-32. (16) Lin, X. Hydrogenation of Unsaturated Polymers in Latex Form. Ph.D. Thesis, Department of Chemical Engineering, University of Waterloo, Ontario, Canada, Feb 2005.
(17) Fogler, H. S. Elements of Chemical Reaction Engineering, 3rd ed.; Prentice Hall PTR: Upper Saddle River, NJ, 2002.
ReceiVed for reView June 26, 2005 ReVised manuscript receiVed December 19, 2005 Accepted December 21, 2005 IE0507575
