Cure kinetics and variable temperature analysis methodologies for solving factory problems.
The reaction kinetics module can be accessed through the Eclipse software package. It enables the calculation of additional parameters such as reaction order, reaction rate constant and activation energy.
The reaction order can be forced between a value of O. 10 and 3.00, or the calculated optimal value within the range of 0.10 to 2.00 can be used. The user can either choose to use ML or true zero as the minimum value for the purposes of determining the conversion variable curve. Generally, MH is used as the maximum value. However, if a compound exhibits marching modulus, there is an option which establishes the maximum value as the point at which the slope of the torque curve falls below a certain threshold.
Up to ten cure points can be used to determine the reaction rate constant. Changing these values will allow the user to concentrate on and/or ignore particular parts of the curve. Enabling the activation energy calculation will allow the user to include up to eight tests in determining the activation energy of the compound. These tests should be run at various temperatures so that the Arrhenius equation can be applied.
In the reaction kinetics module, there are other tabs that enable the user to view the curves and results of the tests. Under the conversion variable tab, the torque curve is normalized by subtracting the minimum from each point and then dividing by (maximum-minimum). This allows the curve to be plotted in a range of 0.0 to 1.0, where each value corresponds to a cure point. For example, a value of 0.9 would represent the cure point tc90. Example conversion variable curves can be seen in figure 1.
The conversion curve will display the cure points on a log scale when the reaction order is one using the function log(1-X). However, the reaction rate constant will be calculated using the 1n(1-X). If the reaction order is not one, a normal scale will be used following the function [(1-X).sup.1-N]/(1-N), where N is the reaction order and X is the cure point or conversion. A linear regression is performed for each curve based on the cure points selected in the setup tab. The slope of the regression line is the reaction rate constant. Below is a derivation of the reaction rate solutions,
r = dC /dt = -k[C.sup.n] (1)
Where r is the reaction rate, C is the concentration, t is time, k is the reaction rate constant, and n is the reaction order. If n = 1, the solution is
1n C = 1n [C.sub.o] - kt (2)
where [C.sub.o] is the initial concentration. The conversion can be defined as
x = [C.sub.o]-C/[C.sub.o]=-C/[C.sub.o] (3)
Combining Equations (2) and (3) yields
1n(1-X)= -kt (4)
If n [not equal to] 1, the solution is
[C.sup.1-n] = [C.sub.o.sup.1-n] - kt(1-n) (5)
Utilizing equations (3) and (5), the following solution is formed,
[(1-X).sup.1-n] = 1 - (1-n)k[C.sub.o.sup.n-1]t (6)
[(1-X).sup.1-n]/1-n = 1/1-n- k[C.sub.o.sup.n-1]t (7)
Since k and [C.sub.o] are constants, they can be combined to form a new constant K as follows,
K = k[C.sub.o.sup.n-1] (8)
Substituting this equation into equation (7) gives
[(1-X).sup.1-n]/1-n = 1/1-n - Kt (9)
As you can see, these equations match the functions used for the scaling on the conversion curves. In figure 2, an example conversion curves plot is shown representing four tests run at different temperatures on the same compound.
The activation energy, [E.sub.a], is the final calculation. It is solved for using the Arrhenius equation
k = A[e.sup.-[E.sub.a]/RT] (10)
where A is the pre-exponential factor, R is the universal gas constant and T is the temperature. The Arrhenius equation can be linearized to the form
If a plot of 1n(k) versus 1/T is made, the slope of the linear regression line will be -[E.sub.a] /R and the intercept will be 1n(A). In figure 3, an example Arrhenius plot can be viewed that uses the same data as figures 1 and 2.
Once the activation energy, pre-exponential factor and reaction order are known, cure points can be calculated for any given temperature, and theoretical conversion and conversion variable curves can be plotted. The accuracy of the calculations and curves depends on various factors, including the compound formulation, the reaction chemistry and the chosen testing conditions (refs. 1-5).
Variable temperature analysis
Variable temperature analysis, or VTA, was available originally on the RPA in 1993. This use of digital technology for the first time allowed the RPA to replace the older analog cure simulator, which was used in the tire industry in the 1980s. Through the VTA feature, an RPA could now be programmed to follow exactly a time-temperature profile from a thermocouple tire cure study, just as the earlier cure simulators did (ref. 6). However, this VTA program could also be set up on the RPA to implement a precisely controlled linear, thermal ramp from a processability temperature, such as 100[degrees]C, up to a high cure temperature, such as 190[degrees]C (ref. 7). Figures 4 and 5 demonstrate how this linear thermal ramp is 50% more sensitive to differences in scorch time than a corresponding isothermal cure test.
Because of this improvement in statistical test sensitivity, a new Part C was added to the ASTM D6204 method for using the RPA as a processability tester (ref. 8).
Because this technique is commonly used in rubber technology today, it was felt that such a VTA configuration should also be used with our cure kinetics software to study the effects of deliberate changes in cure packages on curing properties.
A series of mixed stocks with controlled variations in curatives was completed with a BR laboratory internal mixer and blend mill.
All cure kinetics testing and analysis were performed on the Alpha Technologies MDR 2000 moving die rheometer with Eclipse software Advanced Module (which possesses the Reaction Kinetics option). [E.sub.a]ch compound was isothermally tested at three preselected cure temperatures. These temperatures were 160[degrees], 170[degrees] and 180[degrees]C for the majority of the compounds. However, NR and CPE were tested at 150[degrees], 160[degrees] and 170[degrees]C. For the purposes of this study, the conversion curves were derived from tc50, tc55, tc60, tc65, tc70, tc75, tc80, tc85, tc90 and tc95. By starting at tc50, we are reasonably certain to be taking measurements above the inflection point of the cure curve (ref. 10). However, the CPE compounds described in table 4 displayed marching modulus in their cure profiles. Therefore, just for the CPE compounds, we only used tc50 to tc80 in order to improve the accuracy of our [E.sub.a] calculations.
All variable temperature analysis (VTA) testing was per formed on the Alpha Technologies RPA 2000 rubber process analyzer with Pathfinder software which can be programmed to perform thermal ramps and do VTA. All VTA tests that were performed for this study included a linear thermal ramp from 100[degrees] to 180[degrees]C in exactly four minutes, followed by an additional isothermal cure plateau at 180[degrees]C for an additional four to ten minutes (total VTA cure times were eight to 14 minutes). All VTA tests were performed at 1.67 Hz and 7% strain. All conventional isothermal tests were also performed at 1.67 Hz and 7% strain. The VTA tests were compared to isothermal cure tests performed at 150[degrees]C.
Discussion of results
In the first experimental series given in table 1, compound variations in accelerator, oil and carbon black in SBR/NR were made, with results of the energy of activation ([E.sub.a)] and order of reaction (N) compared in table 7.
As observed in this study, variations in the accelerator, oil and carbon black resulted in changes in calculated [E.sub.a.] Specifically, changes in the accelerator loading caused a significant change in the computed order of reaction (N) in table 7 and a rise in calculated [E.sub.a.] Also, higher carbon black loading will increase the [E.sub.a]. Even a rise in naphthenic oil was found to increase the [E.sub.a].
In the second series of compound variations, shown in table 2, changes in accelerator and stearic acid (activator) levels resulted in significant changes in the calculated [E.sub.a] and order of reaction (N), as reported in table 8.
It was also observed that adjustments in stearic acid and CBS accelerator did increase the [E.sub.a]. This again shows the importance of accelerator concentration. Higher acceleration resulted in a higher calculated [E.sub.a].
In the experimental work shown in table 3, different types of accelerators were compared for their effect on the calculated [E.sub.a] and N. Accelerators selected for this comparison were thiazoles, sulfenamides, thiurams and dithiocarbamates. The resuits of this third study are reported in table 9.
A higher loading of MBTS (thiazole) significantly increased the [E.sub.a] to higher than 140 M/mole. Also, the zinc dithiocarbamate salts (ZnDEDC and ZnDBDC) both are effective at increasing the [E.sub.a]. All these variations affected the computed N, as well.
Table 4 gives the compositional variations for the chlorinated polyethylene (CPE or CM) model compounds. Table 10 gives the numerical results from the cure kinetics calculations.
From this comparison, it can be noted that the use of coagents increased the calculated [E.sub.a] vs. not using coagents in the model CPE compounds.
Lastly, table 5 gave the compositional variations of peroxide and coagents in this study to cure the FEPM fluoroelastomer compound. Table 11 gives the cure kinetic results from testing these compounds containing variations in the use of coagents with the DCP peroxide cure.
Unlike the previous studies of coagent variations in CPE, this last study actually showed less variation in the order of reaction N brought on by the use of different coagents with DCP (except for the TAC coagent).
Overall, three of these series of cure kinetics tests were arbitrarily repeated. The coefficient of variation from these replicate tests was calculated to be 1.6%.
Variable temperature analysis
The following are comparisons of VTA overlays vs. conventional isothermal cure overlays.
Figures 6 (VTA cure) vs. figure 7 (isothermal cure) both show the faster cure rates brought on by a higher accelerator level, as well as the slower cure rates and lower maximum torques brought on by higher oil loading. However, the VTA cure does a better job of giving the same information in less time compared to the isothermal cure.
Figures 8 and 9 make the same comparisons for variations in stearic acid in the NR model compound. Without the stearic acid activator, scorch safety is decreased significantly and state of cure is reduced. Increasing the stearic acid improves the scorch safety time, while helping to provide a tighter ultimate crosslink density. Again, the VTA cure curve is giving the same information, but in less time.
Figures 10 and 11 compare VTA vs. isothermal cure in evaluating the subtle differences in the cure profiles of commonly used ultra and conventional accelerators in the SBR model formulation. Since the VTA cures in figure 10 are more discerning for differences in the scorch event early in the cure process, it gives better separation for scorch time than the conventional isothermal cure profiles in figure 11.
Figure 12 (VTA cure)vs, figure 13 (traditional cure) compare different peroxide cure packages in a chlorinated polyethylene elastomer (CPE) compound. Here, the VTA is much better than the traditional cure in separating and distinguishing exactly what temperature and time differences exist for the points of rising torque. The VTA is very good in showing this, while the traditional cure is not as good. With the CPE recipe, both the PDM and the TAC stand out.
Figure 14 (VTA cure) vs. figure 15 (traditional cure) shows the effects of different coagents on the peroxide cure of fluoroelastomer. As can be seen, this FEPM recipe is much more sensitive to the specific coagent used than other recipes. The VTA cure in figure 14 shows much better sensitivity to differences in coagents than can be seen with the traditional isothermal cure curves in figure 15, where the scorch times appear to be indistinguishable. With the controlled rise in temperature of the VTA, one can note at what temperature and time that each different coagent reached the scorch point. Here, the VTA gives a very large advantage over the traditional isothermal cure. By having a linear controlled rise in temperature (much the way that a DSC analysis would proceed), much more useful information can be obtained rheologically.
* The reaction kinetics module of Eclipse software is very effective at measuring order of reaction (N) and energy of activation ([E.sub.a]) for the rubber compounds used in this study.
* Repeatability of these cure kinetics measurements, such as [E.sub.a] and N, were very good, with a coefficient of variation of 1.6% for the [E.sub.a].
Typically, conventional sulfur cures will be between 65 and 140 kJ/mole, while peroxide cures will be between 140 and 165 kJ/mole for [E.sub.a].
* Typically, conventional sulfur cures can deviate greatly from a first order reaction where many non-CPE peroxide cures can have an order of reaction (N) very close to unity.
* With conventional sulfur cures, increases in carbon black or oil can sometimes elevate the calculated [E.sub.a] of the compound.
* Increasing accelerator loading or changing to an ultra accelerator for sulfur cures can increase the energy of activation ([E.sub.a]).
* Adding a coagent to a peroxide cure can also increase the [E.sub.a].
* VTA can give better information (such as scorch times) during the early stages (onset) of cure.
* VTA can provide a better compromise in test lapse time for measuring changes that are occurring at the onset of cure vs. the ultimate state of cure.
* VTA is more sensitive to changes that occur at the onset of cure, especially with the peroxide cured halogenated elastomers (such as CPE and FEPM) in that not only the scorch time can be measured, but the VTA scorch temperature as well. Scorch temperature might be more sensitive to real differences with halogenated elastomer compounds than scorch time.
(1.) G. Matin and G. Yablonsky, Kinetics of Chemical Reactions, Decoding Complexity, Wiley-VCH, Weinheim, Germany, 2011.
(2.) M. Pilling and P Seakins, Reaction Kinetics, Oxford University Press, Norfolk, U.K., 1995.
(3.) K. Connors, Chemical Kinetics, The Stud)/' of Reaction Rates in Solution, VCH Publishers USA, 1990.
(4.) O. Levenspiel, Chemical Reaction Engineering, 3rd Ed., John Wiley & Sons, Hoboken, N J, 1999.
(5.) P Houston, Chemical Kinetics and Reaction Dynamics, Dover Publications, Mineola, NY.
(6.) J. Dick, "Variable temperature analysis' puts quality to the test, "' Rubber and Plastics News, November 3, 2008, p. 14.
(7.) J. Dick, C. Sumpter and B. Ward, "New effective methods for measuring processing and dynamic property performance of silicone compounds," KGK (Kautschuk Gummi Kunststof fe), September, 1999 (52, pp. 600-607).
(8.) J. Dick and T. Liotta, "New useful ASTM test methods and standards' now available internationally," Rubber World, Vol. 229, No. 4, January, 2004, p. 30.
(9.) S.K. Henning and W.M Boye, "Fundamentals of curing elastomers with peroxides and coagents II: Understanding the relationship between coagent and elastomer, "paper presented at the Rubber Division Meeting of the ACS, Louisville, KY, October 14-16, 2008.
(10.) J. Dick and H. Pawlowski, "Application for the curemeter maximum cure rate in rubber compound development, process control and cure kinetic studies," Polymer Testing 15, (1996) pp. 207-243.
by John S. Dick and Edward Norton, Alpha Technologies
Table 1 - changes in accelerator, carbon black and oil levels in SBR/NR MB301 Internal mix Compound no. A1 A2 A3 A4 A5 SBR 1502 (phr) 80.00 80.00 80.00 80.00 80.00 SMR 20 NR (ph 20.00 20.00 20.00 20.00 20.00 N299, carbon 50.00 50.00 50.00 50.00 60.00 black Naphthenic oil 10.00 10.00 15.00 20.00 10.00 Santoflex 13 3.00 3.00 3.00 3.00 3.00 Sunolite 240 2.00 2.00 2.00 2.00 2.00 TMQ, Flectol H 1.00 1.00 1.00 1.00 1.00 Zinc oxide 4.00 4.00 4.00 4.00 4.00 Stearic acid 1.50 1.50 1.50 1.50 1.50 Total 171.50 171.50 176.50 181.50 181.50 Mill mix Compound no. A1 A2 A3 A4 A5 Masterbatch 171.50 171.50 176.50 181.50 181.50 TBBS, Santocure NS 1.15 2.30 1.15 1.15 1.15 Sulfur 2.50 2.50 2.50 2.50 2.50 Total 175.15 176.30 180.15 185.15 185.15 Table 2 - changes in accelerator and stearic acid in NR MB301 Internal mix Compound no. B1 B2 B3 SMR 5 natural rubber (phr) 100.00 100.00 100.00 N330, carbon black 50.00 50.00 50.00 Aromatic oil 3.00 3.00 3.00 Zinc oxide 5.00 5.00 5.00 Total 158.00 158.00 158.00 Mill mix Compound no. B1 B2 B3 Masterbatch (phr) 158.00 158.00 158.00 CBS accelerator 0.80 0.40 1.15 Sulfur 2.50 2.50 2.50 Stearic acid 0.00 2.00 8.00 Total 161.30 162.90 169.65 Table 3 - changes in accelerators in SBR MB301 Internal mix Compound no. C1 C2 C3 C4 C5 SBR 1500 (phr) 100.00 100.00 100.00 100.00 100.00 N330 carbon black 50.00 50.00 50.00 50.00 50.00 Aromatic oil 8.00 8.00 8.00 8.00 8.00 Zinc oxide 4.00 4.00 4.00 4.00 4.00 Stearic acid 2.00 2.00 2.00 2.00 2.00 Total 164.00 164.00 164.00 164.00 164.00 Mill mix Compound no. CI C2 C3 C4 C5 Masterbatch (phr) 164.00 164.00 164.00 164.00 164.00 Sulfur 2.00 2.00 2.00 2.00 2.00 CBS 1.00 MBTS 2.40 TMTD 0.80 Zn DEDC 0.80 TBBS 1.00 MBS DCBS Zn DBDC CBS Total 167.00 168.40 166.80 166.80 167.00 MB301 Internal mix Compound no. C6 C7 C8 C9 SBR 1500 (phr) 100.00 100.00 100.00 100.00 N330 carbon black 50.00 50.00 50.00 50.00 Aromatic oil 8.00 8.00 8.00 8.00 Zinc oxide 4.00 4.00 4.00 4.00 Stearic acid 2.00 2.00 2.00 2.00 Total 164.00 164.00 164.00 164.00 Mill mix Compound no. C6 C7 C8 C9 Masterbatch (phr) 164.00 164.00 164.00 164.00 Sulfur 2.00 2.00 2.00 2.00 CBS MBTS TMTD Zn DEDC TBBS MBS 1.00 DCBS 1.00 Zn DBDC 0.80 CBS 1.00 Total 167.00 167.00 166.80 167.00 Table 4 - changes in coagents in CPE compounds MB301 Internal mix Phr Tyrin 0136 100 N550 carbon black 60 Ca[C0.sub.3] 40 DIDP 30 Maglite D 5 Agerite resin D 1 Total 236 Mill mix Compound no. 1 2 3 4 5 6 Phr Masterbatch 236 236 236 236 236 236 Di-Cup 40KE 7.5 7.5 7.5 7.5 7.5 7.5 TMA 5 HVPBD 5 PBDDA 5 PDM 5 TAC 5 Total 243.5 248.5 248.5 248.5 248.5 248.5 Table 5 - changes in coagents in FEPM compounds MB401 Internal mix Phr Aflas 150P 100 MT 990 carbon black 25 Sodium stearate 1 Total 126 Mill mix Compound no. 1 2 3 4 5 6 Phr Masterbatch 126 126 126 126 126 126 Di-Cup 40KE 7.5 7.5 7.5 7.5 7.5 7.5 TMA 5 HVPBD 5 PBDDA 5 PDM 5 TAC 5 Total 133.5 138.5 138.5 138.5 138.5 138.5 Table 6 - identification of coagents Coagent Chemical name Trade name Type (ref. 9) abbreviation TMA Trifunctional (meth) Sartomer I acrylate ester Saret SR517 HVPBD High vinyl Sartomer II poly (butadiene) Ricon 154 PBDDA Poly(butadiene) Sartomer Hybrid diacrylate SR307 PDM N,N'-m-phenylene Sartomer I dimaleimide SR525 TAC Triallyl Sartomer II cyanurate SR507 Table 7 - [E.sub.a] and N for SBR/NR compounds Compound [E.sub.a] kJ/ Order of no. Compound ID mole reaction (N) A1 SBR/NR control 85.81 0.94 A2 SBR/NR + 1.15 TBBS 93.66 1.19 A3 SBR/NR + 5 Oil 89.96 0.95 A4 SBR/NR + 10 Oil 87.21 0.95 A5 SBR/NR + 10 carbon black 91.98 0.97 Table 8 - Ea and N for NR compounds Compound [E.sub.a] Order of no. Compound ID (kJ/mole) reaction (N) B1 NR Cpd with 0 99.87 1.06 stearic acid/0.8 CBS B2 NR Cpd with two parts 104.85 0.85 stearic acid/0.4 CBS B3 NR Cpd with 8 phr 104.5 0.91 stearic acid/1.15 CBS Table 9 - [E.sub.a] and N for SBR compounds Compound Order of no. Compound ID [E.sub.a] reaction (N) C1 SBR with 1 phr CBS 100.98 0.97 C2 SBR with 2.4 phr MBTS 143.22 1.3 C3 SBR with 0.8 phrTMTD 102.88 1.22 C4 SBR with 0.8 phrZnDEDC 103.05 1.03 C5 SBR with 1 phrTBBS 89.51 0.97 C6 SBR with 1 phr MBS 104.54 0.95 C7 SBR with 1 phr DCBS 108.25 1.18 C8 SBR with 0.8phrZnDBDC 105.55 1.09 C9 SBR with 1 phr CBS 96.98 0.99 Table 10 - [E.sub.a] and N for CPE compounds Compound [E.sub.a], kJ/ Order of no. Compound ID mole reaction (N) F1 DCP 159.43 1.14 F2 DCP/TMA 171.52 1.36 F3 DCP/HVPBD 156.64 1.21 F4 DCP/PBDDA 163.15 1.17 F5 DCP/PDM 166.05 1.9 F6 DCP/TAC 160.76 1.15 Table 11 - [E.sub.a] and N for FEPM compounds Compound [E.sub.a], KJ/ Order of no. Compound ID mole reaction (N) G1 DCP 142.02 1 G2 DCP/TMA 138.02 1.02 G3 DCP/HVPBD 142.34 1.03 G4 DCP/PBDDA 150.72 1.02 G5 DCP/PDM 149.27 1.03 G6 DCP/TAC 147.59 1.31
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|Author:||Dick, John S.; Norton, Edward|
|Date:||Mar 1, 2013|
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