Ind. Eng. Chem. Res. 2007, 46, 3321-3327
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Optimization of Alkyl Methacrylate Terpolymer Properties as Lubricating Oil Rheology Modifier Ante Jukic´ , Marko Rogosˇic´ , and Zvonimir Janovic´ * Faculty of Chemical Engineering and Technology, UniVersity of Zagreb, Marulic´ eV trg 19, P.O. Box 177, HR-10000, Zagreb, Croatia
Solution terpolymerization processes of methyl methacrylate, dodecyl methacrylate, and octadecyl methacrylate using bifunctional 1,1-di(tert-butylperoxy)-3,3,5-trimethylcyclohexane or monofunctional tert-butylperoxy2-ethylhexanoate initiator were investigated. The first set of terpolymerizations was performed in 2 M xylene solutions, isothermally at 91, 100, 105, and 115 °C. The terpolymerization kineticssconcentrations of molecular species, kinetic chain length, molar mass averages as functions of the reaction timeswas modeled by the Villermaux-Blavier tendency kinetic model for radical polymerization. Complete monomer conversions and high molar masses of terpolymers were achieved in a simple batch process with bifunctional initiator. The second set of polymerization reactions was performed in 2 M mineral base oil solutions, under isothermal conditions at 115 and 120 °C, using the bifunctional initiator. By varying the monomer mixture composition and concentrations of the initiator and chain transfer agent, n-dodecyl mercaptan, the terpolymers of different composition and molar mass were obtained. The solution properties of alkyl methacrylate terpolymers as lubricating oil rheology modifiersskinematic viscosity, viscosity index, shear stability, and pour pointswere established. A strong correlation between molar mass distribution of synthesized polymers and rheological properties of polymer solutions was revealed by an applied optimization procedure. 1. Introduction
2. Experimental
Alkyl methacrylate copolymers belong to a group of important rheology modifiers for lubricating mineral oils, where they serve as viscosity index improvers and pour point depressants.1,2 They are composed of two to three monomers with different lengths of lateral alkyl chains, C1-C20. The corresponding monomer unit ratio is optimized to ensure the best application properties. Besides composition, the properties of modifiers depend also on copolymer structural parameters, such as molar mass and molar mass distribution (MMD), temperature induced conformational changes, and polymer/solvent interaction, i.e., the properties of the solvent, mineral base oil. Such polymers, besides exhibiting high solution viscosities, should also be stable against high shear rates developed in lubricating conditions. Alkyl methacrylate copolymers are usually produced by solution copolymerization processes using monofunctional free radical initiators. Isothermal batch processes with stepwise addition of initiator are applied to ensure the necessary polymer product properties and uniformity.3,4 Recently, bifunctional peroxide initiators were introduced in vinyl-based (mostly styrene) systems to obtain both high conversions and high molar masses in short reaction times.5-15 In this study, a bifunctional peroxide, 1,1-di(tert-butylperoxy)3,3,5-trimethylcyclohexane was used to initiate the solution terpolymerization of methyl methacrylate (MMA), dodecyl methacrylate (DDMA), and octadecyl methacrylate (ODMA). A tendency model was applied to describe the solution terpolymerization kinetics. In the second part of the study, a procedure for the determination of optimal process conditions in order to obtain the best application properties was described. This work continues the investigations on the same system with the use of a conventional monofunctional peroxide initiator.16
Chemicals. Polymerization grade monomers, methyl methacrylate, dodecyl methacrylate, and octadecyl methacrylate (MMA, DDMA, and ODMA, respectively) were from RohMax Chem. Co. and were used as received. The initiators used were either bifunctional 1,1-di(tert-butylperoxy)-3,3,5-trimethylcyclohexane (Trigonox 29, Akzo Nobel) or monofunctional tertbutylperoxy-2-ethylhexanoate (Trigonox 21, Akzo Nobel). The chain transfer agent was n-dodecyl mercaptan (Atochem). Solvents used were xylene (p.a. Kemika, Zagreb, Croatia) and two different grades of mineral base oil (INA Refinery Rijeka, Croatia), i.e., SN150 with a kinematic viscosity of ν ) 25.7 mm2 s-1 at 40 °C, viscosity index of 97, and pour point of -12 °C and SN200 with a kinematic viscosity of ν ) 40.6 mm2 s-1 at 40 °C, viscosity index of 104, and pour point of -9 °C.
* To whom correspondence should be addressed. Tel.: +385-14597-125. Fax: +385-1-4597-142. E-mail:
[email protected].
Polymerizations. (A) Kinetic Investigations. Terpolymerizations of methacrylate monomer mixtures in xylene were performed isothermally at temperatures of 91 and 100 °C (the monofunctional initiator case) or 105 and 115 °C (the bifunctional initiator case), in a 1 dm3 reactor, under nitrogen atmosphere. The total monomer concentration was 2 mol dm-3; x(MMA)/x(DDMA)/x(ODMA) was 0.18/0.66/0.16. Two concentrations of initiators, c ) 0.005 or 0.01 mol dm-3, were applied. Samples of reaction mixtures were withdrawn at different polymerization times; overall monomer conversions were determined gravimetrically. (B) Application Properties. Mineral base oil terpolymerizations were performed isothermally at temperatures of 115 and 120 °C, using the bifunctional initiator, in a 1 dm3 reactor,
10.1021/ie060890c CCC: $37.00 © 2007 American Chemical Society Published on Web 04/04/2007
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Table 1. Kinetic Experiments Setup Data (Initiator Type; Initiator Concentration, cI; Temperature, T; Initiator Half-Life Time, t1/2; Final Polymerization Time, tp) and Optimization Results (Propagation Rate Coefficient, kp; Transfer-to-Monomer Rate Coefficient, ktm; Objective Function Final Value, OF)a experiment
initiator type
cI/(mol dm-3)
T/°C
t1/2/min
tp/min
kp/(dm3 mol-1 s-1)
ktm/(dm3 mol-1 s-1)
OF
1 2 3 4
mono bi mono bi
1 × 10-2 1 × 10-2 1 × 10-2 0.5 × 10-2
91 105 100 115
60 60 20 20
180 180 150 150
4590 7940 4330 7460
7.71 10.4 8.94 15.7
0.078 0.230 0.035 0.036
a
The total monomer concentration was 2 mol dm-1; the monomer feed composition was xMMA/xDDMA/xODMA ) 0.18/0.66/0.16.
under nitrogen atmosphere. SN150 mineral base oil was used as a solvent; the total monomer concentration was 2 mol dm-3. By changing the concentrations of initiator (w ) 0.25 and 0.5 mass %, relative to monomers) and chain transfer agent (w ) 0.0, 0.05, and 0.1 mass %, relative to monomers), a set of terpolymers of different molar masses was obtained. By changing the monomer mixture ratio, the terpolymer composition was varied, too. In order to establish the reproducibility, for a given set of operational conditions each experiment was performed twice. For terpolymerizations in mineral oil, the kinematic viscosity of resultant batch solution was measured. Only negligible differences in examined values were found, and rheological and structural parameters were measured for the second batches of each experiment pair. For batches in xylene, the conversion of monomers was estimated. Small differences in conversion values (2-5%) were found only for terpolymerizations with monofunctional initiators at the very beginning of exothermal reaction. Methods. Number and weight average molar masses (Mn and Mw, respectively) of terpolymer samples were determined by the size exclusion chromatography (SEC) method on a Polymer Laboratories GPC 20 instrument, at room temperature. The narrow-distribution polystyrene standards were used for calibration. Tetrahydrofuran at the flow rate of 1.0 cm3 min-1 was used as a solvent/eluent. The polydispersity index (PI) was calculated as Mw/Mn. Rheological properties of polymeric additive solutions in the SN200 mineral base oil were determined by the standardized test methods. Viscosity and viscosity index were calculated using ASTM methods ASTM D-445 and ASTM D2270, respectively. Kinematic viscosity measurements were carried out at 40.0 and 100.0 °C, using the calibrated Cannon-Fenske capillary viscometers immersed in a constant temperature bath. The shear stability of an oil is measured by using the DIN-51382 test method. First, the viscosity of an engine (polymer containing) oil is measured. Then, the oil is exposed to severe shearing conditions by repeatedly pumping it through a specially sized diesel fuel injection nozzle at high pressure. After shearing the oil, its viscosity is measured again. The percentage of viscosity lost is determined by comparing the second viscosity measurement with the original viscosity measurement. The viscosity loss reflects polymer degradation due to shear at the nozzle. Pour points were measured by ISO method 3016. The pour point was defined as the coldest temperature at which the sample still poured. The pour points were determined by placing a test jar with 50 mL of the sample submerged into a cooling medium. The sample temperature was measured in 1 °C increments at the top of the sample until the liquid stopped pouring. This point is defined when the sample did not flow when the jar is held in a horizontal position for 5 s. The set point temperature of the cooling media was determined based on the expected pour point of the sample. All viscosity and pour point measurements were run in duplicate, and the average values were reported.
Figure 1. Overall monomer conversion (cM) vs polymerization time (tp). Symbols and lines represent experimental and calculated data, respectively. (a and b) Experiments corresponding to the initiator half-life times of 60 and 20 min, respectively.
3. Results and Discussion Kinetic InvestigationssExperimental Data. In our recent article,17 we have published some results considering the lowconversion kinetics of MMA-DDMA-ODMA terpolymerizations, initiated by mono- and bifunctional peroxy initiators. The results presented here deal with high-conversion kinetics in the same system. In Table 1, basic experimental setup data for kinetic experiments are given. In Figure 1, the overall monomer conversion is shown as a function of reaction time for both mono- and bifunctional initiators. In Figure 1a, the experimental data complying with the initiator half-life times of 60 min18 are shown. One observes that the required high conversions of monomers are obtained in somewhat lower reaction times for the bifunctional initiator experiment. However, this may be due to the higher overall concentration of peroxy groups as well as to the higher temperature in the bifunctional initiator case. In Figure 1b, the data corresponding to the initiator half-life times of 20 min are shown. Here, the bifunctional initiator concentration was one-half of that of the monofunctional initiatorsi.e., the peroxy group concentration was the same. Now, similar conversions were obtained in the same reaction times, proving that the effect of initiator concentration on conversion is more significant than that of the temperature. The free radical bulk polymerization of lower n-alkyl methacrylates is characterized by autoacceleration or the gel effect after definite conversions of the monomers. Still, the intensity of autoacceleration decreases with increase in the alkyl group length in the ester as well as with an increase of the polymerization temperature.19-21
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Figure 2. Number average molar mass (Mn) vs polymerization time (tp). Symbols and lines represent experimental and calculated data, respectively. (a and b) Experiments corresponding to the initiator half-life times of 60 and 20 min, respectively.
experiments with the bifunctional initiator, as in previously studied vinyl-based systems.5-15 Kinetic InvestigationssModeling. It is well-established that in copolymerization reaction monomers with similar structure, such as methacrylic esters, aside from differences in terms of alkyl group size, have similar copolymerization reactivities. Hence, their mixture will give copolymers with a statistical distribution of repeated units and composition equal to that of the monomer mixture. Accordingly, the copolymerization reactivity ratios for the investigated system are all close to unity.23-26 Therefore, the terpolymerization reaction in this particular case might be approximated by the homopolymerization,26,27 which made kinetic modeling rather simple. The Villermaux-Blavier tendency kinetic model for isothermal batch homopolymerization was applied for the description of concentrations of molecular species in the reacting mixture and prediction of the polymer structural properties (kinetic chain length, MMD, and MMD averages) as functions of polymerization time.21-23 The modeling of polymerization using bifunctional initiator based on the mechanism of polymerization using monofunctional initiator is in principle not precise, since a new type of radical which contains one living radical on one end and another undecomposed peroxide on the other chain end is present. A mass balance of this type of radical should be included in the modeling. However, the manufacturer describes the decomposition kinetics of bifunctional diperoxy initiator by a single pair of constants (A ) 7.59 × 1013 s-1, Ea ) 127.5 kJ mol-1)18 dealing only with the total radical concentration, as in the model proposed. The scope of this study was to synthesize some terpolymer additives with improved structural properties where the kinetic modeling was simplified with no intention to study the polymerization mechanism in detail, but only to set up a tendency model giving the right trends in conversion of monomers and main structure parameters of the polymer product. So, we make the assumption that this model has an interpolation capability, as it is based on the simplified mechanism derived from reasonable approximations. The corresponding model equations are the following:
cA ) cA0 exp(-kdt) cR )
( ) fkdcA kt
cM ) cM0 exp cP ) cP0 + Figure 3. Weight average molar mass (Mw) vs polymerization time (tp). Symbols and lines represent experimental and calculated data, respectively. (a and b) Experiments corresponding to the initiator half-life times of 60 and 20 min, respectively.
In the paper of Lazar et al.,22 it was found that bulk free radical polymerization of n-dodecyl methacrylate proceeds with a low gel effect in the temperature region from 60 to 90 °C. In our case, terpolymerizations were performed in xylene solution with a total monomer concentration of 2 mol dm-3, at temperatures of 115 and 120 °C, and with a high share of long chain alkyl methacrylates in monomer mixtures; the gel effect was not observed. In Figures 2 and 3, molar mass averages are shown as a function of reaction time. Considering the molar masses of the prepared terpolymers, higher MMD averages were found in
L)
1/2
∫0t(-kpcR) dt
(2) (3)
∫0t(ktcR2 + ktmcMcR) dt
(4)
kpcMcR 2fkdcA + ktmcMcR
(5)
µ1cP ) (µ1cP)0 +
∫0tkpcMcR dt
µ1cP hM M hn)M cP µ2cP ) (µ2cP)0 +
(1)
∫0t(6ktcR2L2 + 2ktmcMcRL2) dt
µ2cP hM M hw)M µ1cP
(6) (7) (8) (9)
In these expressions, cA, cR, cM, and cP stand for the concentrations of initiator, free radicals, monomers, and polymers, respectively. L is the kinetic chain length, µ1cP and µ2cP are the
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Table 2. Monomer Feed and Terpolymer Composition, (xM,i ) xP,i)/mol %; Kinematic Viscosity at Indicated Temperatures, ν; Viscosity Index, VI; Shear Stability Index, SSI; Weight Average Molar Mass, Mw; Number Average Molar Mass, Mn; and Polydispersity Index, PI, of Terpolymers of Methyl Methacrylate (MMA), Dodecyl Methacrylate (DDMA), and Octadecyl Methacrylate (ODMA) in Mineral Base Oil serial no. x/%
MMA DDMA ODMA
t/°C w (I)/% at ΣMi w (CTA)/% at ΣMi ν (100 °C, conc sol) shear stability test
40 °C
V before V after SSI V before V after SSI
100 °C VI before VI after pour point/°C Mw/kg mol-1 Mn/kg mol-1 PI ) Mw/Mn
1
2
3
4
5
6
7
8
9
10
11
12
8 74 18 115 0.25 0 733 102 79.3 20.7 16.3 12.5 21.7 172 156 -33 214 71 3.01
8 74 18 120 0.25 0 699 102 79.0 21.1 15.5 11.9 21.7 161 146 -33 220 100 2.20
8 74 18 115 0.25 0.05 588 94.9 78.1 16.5 14.5 11.8 17.2 158 145 -32 188 90 2.08
8 74 18 115 0.5 0.1 297 75.0 70.0 6.18 11.8 10.9 6.59 151 146 -30 105 37 2.86
8 74 18 120 0.5 0 273 74.6 68.9 7.13 11.8 10.8 7.62 153 146 -30 116 39 3.00
8 74 18 120 0.25 0.1 180 67.1 63.5 4.95 10.7 10.1 5.20 148 144 -30 103 46 2.24
18 66 16 115 0.25 0 934 105 79.7 22.4 16.4 12.2 23.9 169 150 -33 240 104 2.30
18 66 16 115 0.25 0.05 705 95.3 77.7 17.3 14.9 12.0 18.4 164 149 -32 198 88 2.26
18 66 16 115 0.5 0 583 88.8 74.5 14.9 14.2 11.8 15.5 165 154 -32 156 43 3.61
18 66 16 115 0.25 0.1 359 78.0 70.1 9.38 12.5 11.2 10.1 159 151 -31 132 47 2.83
18 66 16 120 0.25 0 336 77.3 68.4 10.7 12.5 11.0 11.5 161 151 -31 145 55 2.64
18 66 16 120 0.5 0.1 254 68.1 65.3 3.68 10.8 10.3 4.26 150 145 -30 89 35 2.57
Polymerization time: tp ) 3.5 h, w (I) and w (CTA) stand for the mass % of initiator and chain transfer agent with the respect to sum of monomers, respectively.
first and second kinetic moment, respectivelysthe parameters related to the statistical distribution of polymer chain length. Mn and Mw are the number and weight average molar mass, respectively. MM is the average molar mass of the monomer mixture, and f is the initiator efficiency. The subscript 0 denotes the initial value of the corresponding variable. The model was tested against the terpolymerization experiments described previously. Some of the kinetic parameters were taken from the literature. Initiator decomposition rate coefficients were given as temperature functions:18 kd/s-1 ) 1.54 × 1014 exp[-124 900/(RT)] and kd/s-1 ) 7.59 × 1013 exp[-127 520/ (RT)] for monofunctional and bifunctional initiator, respectively. The termination rate coefficient was the following:21 kt/(dm3 mol-1 s-1) ) 1.36 × 109 exp[-11 900/(RT)]. The value of initiator efficiency was fixed to f ) 0.5. The values of the propagation (kp) and transfer-to-monomer (ktm) rate coefficients were chosen as fitting parameters; the following optimization function was minimized:
OF )
1
n
∑
n i)1
(
) [(
exp ccalc M - cM
cexp M
2
+
1
m
∑
2m i)1
)
exp Mcalc n - Mn
Mexp n
(
2
+
)]
exp Mcalc w - Mw
Mexp w
2
(10)
By choosing such a function, we tried to give equal weight to gravimetric (monomer conversion) determination and SEC (MMD) measurements. The terms n and m are the total numbers of conversion and SEC samples, respectively. The minimization procedure was performed by the NelderMead simplex method for each of the four kinetic runs performed. The best fitting kp and ktm parameters and optimal OF values are given in Table 1, together with corresponding experimental setup data. In Figure 1, experimental and calculated monomer concentrations are compared. The model fits the experimental data well for both the initiators studied. A satisfactory agreement between experimental and calculated Mn and Mw values is found for the monofunctional initiator experiments, too (Figures 2 and 3). However, regarding the bifunctional initiator experiments, only the general trend of Mn and Mw vs tp functions is predicted
correctly by the model; the model somewhat overestimates the Mn values and underestimates the Mw values. Probably, the model applied is too simple to correctly describe the complex kinetic mechanism of copolymerization initiated by the bifunctional peroxy initiator.6-12 Calculated kp values are significantly different for the monoand diperoxy-initiated terpolymerization processes. The two peroxy groups in the bifunctional initiator are characterized by different decomposition rates, the literature value being the average one.6,18 This means that the primarily grown and terminated polymer molecules contain unreacted peroxy groups and are subject to reinitiation and subsequent repropagation. Therefore, the differences in kp values are probably due to the differences in the mechanism. It is interesting to note that the Arrhenius equation ktm/(dm3 mol-1 s-1) ) 7.37 × 105 exp[34 900/(RT)] fits the calculated ktm values well, regardless of the initiator type. Application Properties. Some application properties of a series of polymer solutions in mineral base oil, obtained by diperoxy-initiated terpolymerization processes, were investigated, i.e., viscosity, viscosity index, shear stability index, and pour point. Kinematic viscosity was measured for the synthesized batches at 100 °C, as well as for the batches diluted by the base oil to the polymer concentration of 5 mass %, at 40 and 100 °C. Pour point measurements are performed at polymer concentrations of 0.5 mass % in mineral base oil. The data are given in Table 2, together with the process conditions and some structural characteristics of synthesized terpolymers. Monomer mixture composition, xM,i, is considered equal to the terpolymer composition, xP,i, regarding the complete conversion of monomers to polymer. The viscosity index describes the temperature-dependent viscosity change of polymer solutions; higher values of viscosity-temperature gradients are characterized by lower viscocity indices. In the investigated systems, VI generally increases with molar mass. The data show that all the investigated terpolymermineral base oil systems exhibit high viscosity index values. Therefore, all the copolymers may be used as viscosity index improvers for lubricating mineral oils.1,2 In Figure 4, the kinematic viscosity at 100 °C, as well as the shear stability index (permanent viscosity loss due to shear stress applied) of diluted polymer solutions (5 mass %) in mineral base oil are shown as
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Figure 4. Kinematic viscosity at 100 °C and shear stability index of diluted solutions (5 mass %) of terpolymeric additives in mineral base oil as functions of average MMA/DDMA/ODMA terpolymer molar mass (xMMA ) 8 mol % (b, 9) and 18 mol % (O, 0)). Lines indicate observed linear trends.
functions of polymer molar mass. Obviously, polymer molar mass strongly influence both properties. Shear stability index increases with the molar mass increase, i.e., larger molecules are more susceptible to cleavage under high shear stresses. The lowered molar mass of the polymeric additive after the performed test is sensed in the lowered viscosity of the solution. According to presented results, the lowering of the viscosity is less than 5% of its original pretest value for solutions with terpolymer Mw up to 100 kg mol-1. For Mw values in the range of 100-150 kg mol-1, the lowering of the viscosity is less than 13%, and for Mw larger than 200 kg mol-1, the viscosity is significantly lowered, >20%. On the other hand, higher molar masses of polymers contribute to higher viscosities of oil solutions. This is clearly visible in Figure 4, where a linear kinematic viscosity vs polymer molar mass relationship is established. The pour points of all investigated oil solutions (at terpolymeric additive concentrations of 0.5%) are in the narrow temperature range between -30 and -33 °C, proving the wellknown use of the investigated class of copolymers as excellent mineral oil pour point depressants.1,2,31 Two terpolymer compositions with molar fractions of MMA of 8 and 18% were chosen to cover the solubility range of investigated terpolymeric additive in mineral oil, at application temperatures of lubricating oils (the upper limit of solubility is reached at an MMA molar fraction of approximately 20%). Seemingly, the terpolymer composition (MMA molar fraction) affects neither the shear stability index nor kinematic viscosity values, at least not significantly, since data points may be approximated by single lines in Figure 4. The best lubricating properties of mineral oils are obtained with additives giving high VI values and low shear stability index (SSI) values at the same time. One of those key properties increases with Mw, while the other decreases. Therefore, an optimization of Mw is required. Optimization Procedure. The most important application properties of lubricating mineral oils containing polymeric additives are functions of the polymer structure.1,2,27 Here, number average molar mass, Mn, polydispersity index, PI, and methyl methacrylate molar fraction, xMMA, may serve as the main structural parameters. The unknown functional dependence may be described by a polynomial function:27
( )( )(
Pi ) a i
Mn Mn0
bi
PI PI0
ci
1 + xMMA 1 + xMMA0
)
di
(11)
For i ) 1, the application property of interest is the shear
Figure 5. Experimental vs correlated shear stability index (SSI) values. Table 3. Parameters of the Functional Dependence of Shear Stability Index, SSI, and Viscosity Index, VI, Respectively, on Number Average Molar Mass, Mn, Polydispersity Index, PI, and Methyl Methacrylate Feed Mole Fraction, xMMAa ln ai bi ci di Ri2 a
SSI (i ) 1)
VI (i ) 2)
-1.782 ( 0.424 1.824 ( 0.133 2.387 ( 0.329 -0.025 ( 0.119 0.9600
4.681 ( 0.054 0.130 ( 0.017 0.232 ( 0.042 0.026 ( 0.015 0.8913
Ri2 is the linear regression coefficient.
stability index, P1 ) SSI; for i ) 2, the corresponding application property is the viscosity index, P2 ) VI. The previous expression may be transformed to the linear form by applying the logarithmic function:
( ) ( ) (
ln Pi ) ln ai + bi
)
Mn 1 + xMMA PI + ci + di Mn0 PI0 1 + xMMA0
(12)
Parameters of the polynomial functions (12) were determined by the linear regression method. In previous equations, Mn0, PI0, and xMMA0 were the normalization constants, the corresponding average values for the whole set of experimental data. The optimal correlation parameters, as well as corresponding linear regression coefficients, are given in Table 3. The number of distinct xMMA experimental values (two points, 8 and 18%) was too small to allow for the reliable determination of parameter di. (Anyhow, higher methyl methacrylate content would have caused precipitation of the terpolymer from the mineral oil, due to its poor solubility.) The reliability of the tested correlations is illustrated in Figures 5 and 6. Here, it is useful to introduce the so-called index of end-use properties, or the performance index, J, which may serve as a tool, i.e., a function for the optimization of structural parameters to obtain the desired product quality. In this work, the performance index was deliberately defined as
VIn SSI + VI SSIn
J)z
(13)
where VI stands for the viscosity index and SSI is the shear stability index. In this particular case, lower values of 1/VI and SSI mean better application properties, oil viscosity being less dependent on the effects of temperature and mechanical shear. Appropriate normalization constants VIn and SSIn, i.e., the mean values of corresponding experimental data sets, were applied to make the previous expression dimensionless. Here, z was the factor used to balance the relative weights of particular
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The very existence of such a relationship proves that Mn and PI are not to be considered as independent variables. As such, for a monodisperse polymer (PI ) 1), the molar mass of Mn ) 104.2 kg mol-1 gives optimal product properties. However, this case is highly unrealistic for industrial radical polymerizations. Usually, practically attainable MMDs are much broader (PI ) 2-4), and this decreases the end-use properties of the lubricating mineral oil. The structure and composition of the polymeric additive are varied in accordance with the specific application requirements. The obtained relationships between rheological and structural properties enable the additive manufacturer to fulfill the necessary requirements more accurately in order to ensure the best lubricant application properties. As revealed in the previous discussion, performance index J will take its minimal (optimal) value for the monodisperse polymeric additive. The investigated terpolymerization processes with bifunctional initiator are capable to produce polymers of low PI value and high molar mass simultaneously. The products are obtained in a simple batch isothermal process, in shorter reaction times in comparison to the previously studied processes with monofunctional initiators, either in isothermal or in adiabatic conditions.16,27 Moreover, the processes with bifunctional initiators may be performed without any changes in the equipment used in processes using monofunctional peroxide initiators.
Figure 6. Experimental vs correlated viscosity index (VI) values.
4. Conclusion
Figure 7. Polymer additive performance index, J, as a function of the number average molar mass, Mn, and polydispersity index, PI, with constant methyl methacrylate feed mole fraction (xMMA ) 9%): a contour plot. The descending direction is indicated by an arrow.
factors to the quality of product. In the normalized form, the numerical range of experimental VI values was approximately ten times lower in comparison to that of the SSI values. Accordingly, the z value was set to 10. In the previous procedure, we have determined the VI and SSI indices as the polynomial functions of structural variables, Mn, PI, and xMMA. Minimization of the J function was performed by the gradient method of steepest descent. The obtained results showed that the J function did not exhibit any true extremum in the physically reliable parameter domain. Instead, a minimum was observed in the margin of the function domain. In order to simplify the graphic representation of the J function, the value of xMMA ) 9%, that corresponds to a commercial methacrylate terpolymer additive product, was set constant. Then, the performance index became a function of two variables only, to be easily represented by a contour diagram as shown in Figure 7. A valley in the diagram is immediately observed, inclined to the region of low PI values. The minimum of the J function was found in the margin of the physically significant function domain (PI ) 1, monodisperse polymer). By fixing the polydispersity index to a value characteristic for the particular terpolymerization process, J becomes a function of the single variable, Mn. Now, minima of the J(Mn) function for various PI values may be described by the simple linear relationship, in this case:
(Mn)opt ) 136 - 32.0PI
(14)
In this paper, the procedure for the determination of optimal structural molecular properties of polymer additives for lubricating mineral oils is described. Terpolymers of methyl methacrylate, dodecyl methacrylate, and octadecyl methacrylate were synthesized by the batch isothermal radical polymerization processes in mineral base oil solution. The bifunctional initiator 1,1-di(tert-butylperoxy)-3,3,5-trimethylcyclohexane was used. The simple tendency kinetic model was applied for the calculation of concentrations of reacting species and polymer structural properties. A good agreement with experimental data was found. The correlation between the structural properties of polymeric additives (MMD parameters) and application properties of lubricating mineral oils (viscosity index and shear stability index) was established. The simple batch terpolymerization processes with bifunctional initiator were found to be advantageous over the similar processes with conventional monofunctional initiators, since the former are capable of producing polymers of low PI value and high molar mass at the same time and at a high polymerization rate. Nomenclature cA ) molar concentration of the initiator in the feed, mol dm-3 cA0 ) initial molar concentration of the initiator in the feed, mol dm-3 cM ) molar concentration of all monomers in the feed, mol dm-3 cM0 ) initial molar concentration of all monomers in the feed, mol dm-3 cP ) molar concentration of the polymer in the feed, mol dm-3 cP0 ) initial molar concentration of the polymer in the feed, mol dm-3 cR ) molar concentration of the radicals in the feed, mol dm-3 f ) initiator efficiency factor J ) polymeric additive performance index kd ) initiatior decomposition rate coefficient, s-1
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kp ) propagation rate coefficient, dm3 mol-1 s-1 kt ) termination rate coefficient, dm3 mol-1 s-1 ktm ) transfer-to-monomer rate coefficient, dm3 mol-1 s-1 L ) kinetic chain length, 1 MM ) average molar mass of comonomers, kg mol-1 Mn ) number average molar mass, kg mol-1 Mw ) weight average molar mass, kg mol-1 PI ) polydispersity index SSI ) shear stability index t ) polymerization time, s T ) temperature, °C V0 ) initial volume of the feed, dm3 VI ) viscosity index w ) mass fraction, % xMi ) molar fraction of the comonomer i in the feed, % xPi ) molar fraction of the comonomer unit i in the copolymer, % µ1cP ) first kinetic moment of the molar mass distribution, mol dm-3 (µ1cP)0 ) initial value of the first kinetic moment of molar mass distribution, mol dm-3 µ2cP ) second kinetic moment of the molar mass distribution, mol dm-3 (µ2cP)0 ) initial value of the second kinetic moment of molar mass distribution, mol dm-3 ν ) kinematic viscosity, mm s-1 Literature Cited (1) Mortimer, R. M.; Orszulik, S. Y. Chemistry and technology of lubricants; Chapman & Hall: London, 1997. (2) Ver Strate, G.; Struglinski, M. J. Polymers as lubricating oil viscosity modifiers. In Polymers as rhelogy modifiers; Schulz, D. N., Glass, J. E., Eds.; American Chemical Society: Washington, D.C., 1991; pp 256-272. (3) (a) McCormick, H. W.; Nummy, W. R. Poly-alkylstyrene viscosity index improver. U.S. Patent 3,318,813, May 9, 1967. (b) Auschra, C.; Pennewiss, H. Lubricant Additives. U.S. Patent 5,756,433, May 26, 1998. (c) Lachowicz, D. R.; Holder, C. B. Lubricating Composites Containing Methacrylate Ester Graft Copolymers as Useful Viscosity Index Improvers. U.S. Patent No. 4,026,809, May 31, 1977. (d) Sutherland, R. J.; DuBois, D. A. Star Polymers of Dienes, Vinylarenes and Alkyl Methacrylates as Modified Viscosity Index Improvers. U.S. Patent 5,496,898, March 5, 1996. (e) Sutherland, R. J.; DuBois, D. A. Star Polymers of Dienes, Vinylarenes and Alkyl Methacrylates as Modified Viscosity Index Improvers. U.S. Patent 5,344,887, September 6, 1994. (f) Seebauer, J. G.; Bryant, C. P. Viscosity Improvers for Lubricating Oil-Compositions. U.S. Patent 6,271,184, August 7, 2001. (g) Bryant, C. P.; Grisso, B. A.; Cantiani, R. Dispersant-Viscosity Improvers for Lubricating Oil Compositions. U.S. Patent 6,881,780, April 19, 2005. (h) Seebauer, J. G.; Bryant, C. P. Viscosity Improvers for Lubricating Oil Compositions. U.S. Patent 6,124,249, September 26, 2000. (i) Yuki, T.; Ota, Y. Viscosity Index Improver and Lube Oil Containing the Same. U.S. Patent 6,746,993, June 8, 2004. (j) Sivik, M. R.; Bryant, C. P. Dispersant-Viscosity Improvers for Lubricating Oil Compositions. U.S. Patent 6,639,034, October 28, 2003. (4) Janovic´, Z.; Saric´, K.; Sertic´-Bionda, K. Polymerization and polymer properties of some alkylmethacrylates as lubricating oil viscosity modifiers. Chem. Biochem. Eng. Q. 1998, 12, 19. (5) Kamath, V. R. New initiators for PS offer big efficiencies. Mod. Plast. 1981, 58, 106. (6) Dhib, R.; Gao, J.; Penlidis, A. Simulation of free radical bulk/solution homopolymerization using mono- and bi-functional initiators. Polym. React. Eng. 2000, 8, 299. (7) Kim, K. J.; Liang, W.; Choi, K. Y. Bulk free radical polymerization of styrene with unsymmetrical bifunctional initiators. Ind. Eng. Chem. Res. 1989, 28, 131. (8) Choi, K. Y.; Liang, W. R.; Lei, G. D. Kinetics of bulk styrene polymerization catalyzed by symmetrical bifunctional initiators. J. Appl. Polym. Sci. 1988, 35, 1547.
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ReceiVed for reView July 11, 2006 ReVised manuscript receiVed January 29, 2007 Accepted February 26, 2007 IE060890C
