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Role of Mooney-Rivlin constants in seal formulations under non-equilibrium conditions.

Elastomers are used in many critical service applications such as seals, gaskets, rocket fuel binders, etc. As a result, the estimation of aging, long term durability or the time to failure of elastomers is a subject of great importance to technologists that work with these materials. Testing in real time and with realistic in-service environments is ideal for such purposes, but the long term approach is generally not viable in many cases. So accelerated aging techniques are required. In rubbery polymers, free space exists between molecular chains. The kinetics of behavior of and changes in this free space are governed by Arrehenius relationships with regard to the influence of temperature. Similar to chemical kinetics which involve concentrations of reactants and products, the concentration of crosslinks is approximately proportionate to modulus or stiffness (ref. 1). Hence, measurements of changes in modulus from aging can be plotted logarithmically at each temperature. From a series of such aging plots at different temperatures, times to attain the same degree of modulus change can be used to develop the Arrehenius plot.

The Mooney-Rivlin equation (ref. 2) is useful in establishing a structure-property relationship. It is normally represented as

[Sigma]/[2([lambda] - [lambda.sup.2])] vs. 1/[lambda].

This plot on extrapolating to 1/[lambda] = 0 a value of [C.sub.1] is obtained and die slope is denoted as [C.sub.2]. By comparison with the theory of elasticity, it is proposed that [C.sub.1] = 0.5NRT, where N = crosslink density, R = gas constant and T = absolute temperature. In practice, the constant [C.sub.1] has proved to be a useful measure of the crosslink density. There is a linear dependence on [C.sub.1], on the concentration of sulfur. In many cases, an extrapolation to [C.sub.1] = 0 is not allowed since in the absence of chemical crosslinks the physical entanglements also contribute to [C.sub.1]. [C.sub.2] decreases as the chain cross section increases, i.e. as the polymer chain becomes stiffer and the conformational entropy of the network chains decreases. Such experiments are used to corroborate the idea that [C.sub.2] reflects the concentration of physical, more unstable crosslinks (such as entanglements, filler/filler and filler/ polymer interactions) (ref. 3). To assure near equilibrium response, stress-strain measurements are carried out at low strain rate, elevated temperature and sometimes in the swollen state.

Scope of the work

But in service conditions where there is no contact with solvents or oils, extension of lab results under the above suggested method may not be in order. Secondly, the influence of strain rate on stress-strain relationship is highly indeterminant in vulcanized elastomers due to its non-linear viscoelastic behavior. So a standard procedure, like ASTM D 412 for uniaxial tension at a specified strain rate, is more appropriate in that respect. Elastomeric seals based on nitrile rubber for contact with solvents and its counterpart EPDM used in `dry' but high temperature and other aging influences require Mooney-Rivlin plots constructed using simple laboratory techniques for better understanding of relative merits and limitations of these polymers under identical aging conditions. As both these elastomers are amorphous it is presumed that any variation in stress-strain behavior and trends in Mooney-Rivlin plots constructed are mainly attributed to the type of crosslinks (or cure system employed) and not to the backbone features. To normalize this possibility in our present investigation, we have employed sulfur based cure systems. It appears from literature that no such work has been done at least for academic purpose. Our present investigation makes an attempt towards this direction. Besides, given the conditions of current investigation on unswollen vulcanizates under non-equilibrium, the Mooney-Rivlin parameters were deduced from the respective plots where we observe typical Mooney-Rivlin behavior.


The rubber mixes were prepared on a lab size (150 mm x 300 mm) two roll mixing mill observing usual procedures at a friction ratio of 1:1.15. Tensile slabs were molded in an electrically heated hydraulic press uniformly at 155 [degrees] C. The cure times were set at [t.sub.90] (MDR[@ 155 [degrees] C]) of respective formulation + 2 min. Dumbbell specimens were punched out from the test slab according to ASTM D412 (type 2). Hot air aging was conducted as per ASTM D573 for 72 hrs. at 70 [degrees] C, 80 [degrees]C 90 [degrees]C and 105 [degrees]C. Similar aging at 100 [degrees]C for different period of exposure was also done. The test specimens were tested for tensile parameters under ambient conditions in a Zwick 1440 UTM at a strain rate of 500 mm/min.

Results and discussion

The formulations are given in table 1. In ACN/1, the asbestos pulp was added to enhance product reliability under `firing' conditions for a very short period. In ACN/4, a sulfur donor system was incorporated for better overall age resistance. The third monomer in Herlene 502 of EPDM/1 is ENB. So the cure system is not much different from any other olefinic elastomer. The MDR results are given in table 2. The energy of activation of cure was deduced using Arrehenius kinetics. ACN/3 is better activated compared to other formulations. It may be due to suitable combination of sulfur and MBT fairly at a higher dosage level. The `rubber moduli' at different elongation, tensile strength and elongation at break are given in table 3. The extension ratio ([lambda]) and the corresponding `reduced stress' ([Sigma]/[2([lambda] - [lambda.sup.2])]) were calculated from table 3 and are reported in table 4. Using Harvard Graphics (version 2.00) Mooney-Rivlin plots were constructed in and are represented in figures 1-5. For better representation of variation in temperature and exposure times for a given formulation, the plots were divided into two (a and b). Further, the linear portion of the plot is thought to represent the Mooney-Rivlin equation as follows


[Sigma]/[2([lambda] - [lambda.sup.2])] ([C.sub.1]+ [C.sub.2][lambda.sup.1]) (1) The intercept at [lambda.sup.1] = 1 gives [C.sub.1] + [C.sub.2] and [C.sub.2] is the slope of the line. A true Mooney-Rivlin material will give a straight line. Most elastomers do not give a straight line plot. From figures 1-5 we notice that both cases are present. It is also reported (ref. 2) that the initial shear modulus (G) could be related as G = 2([C.sub1] + [Csub.2]) Those values are given in table 5. These values are given only for those cases where we observe typical Mooney-Rivlin vulcanizates.


The following observations may be made on figures 1-5:

* ACN/1 has the highest G/2 value before aging and ACN/4 has the lowest. The cure system in ACN/1 has produced the highest crosslink density which resulted in a G value. The asbestos pulp supplements this phenomenon. On the other hand, in ACN/4, absence of elemental sulfur may have caused low but stable crosslinks. In spite of HAF being present, the need for more crosslinks may have caused low G value at least in the absence of additional (like hot air aging) heat history other than vulcanization.

* For a given time of exposure (72 hrs.), increase in temperature causes a steady rise in G value, which may be due to the formation of additional crosslinks. While at a given temperature (100 [degrees] C), with increase in duration of exposure, we notice a competing phenomena of cleavage of crosslinks and formation of additional crosslinks. Depending on the duration, the rate of one of these phenomena is prominent, which correspondingly reflects in the G values. So, either softening (drop in G) or stiffening (rise in G) is observed.

* In ACN/2, moderate increase in temperature for a given duration of air aging causes a drastic fall in G. This trend emphasizes the fact that for stable Mooney-Rivlin plots, not only thermally inert crosslinks but also adequate density are required. hi our case, sulfur @ 0.2 phr may not have been adequate to meet this requirement in spite of higher dosage of accelerators. But the series of aging @ 100 [degrees] C presents a different trend. Here we notice increase (i.e. stiffness) in G up to the duration of 288 hrs. It implies that additional crosslinks formed require much higher thermal acceleration. It may also be due to the contact with air for longer duration inside the aging chamber at a higher temperature. This condition may have been conducive exclusively for this formulation to undergo stiffening. Beyond 288 hrs. the role of scission is greater than the rate of formation of additional crosslinks and softening is observed.

* In ACN/3, moderate increase in temperature at a given duration of aging has not affected the G value. But aging at 100 [degrees] C for longer durations, the effects of competing reactions, namely formation of additional crosslinks and scission of labile crosslinks (polysulfidic/cyclic), are taking place.

* In ACN/4, steady rise in G is observed at moderate temperatures as expected in any usual NBR formulation. A similar trend, but with a higher starting value, is observed for longer durations at 100 [degrees] C. The role of `sulfur donor system only' is evident from this trend. The monosulfidic/disulfidic links formed are thermally inert and residual thiocarbamate derivative(s) formed during the vulcanization process enabled only the formation of additional crosslinks and scission has been substantially suppressed. The efficacy of the current investigation is well illustrated by this observation.

* The behavior of EPDM/1 has to be considered in the light of following features:

a) unsaturation only in the side chain; b) very low unsaturation just sufficient for vulcanization; and c) inherent resistance to oxidative degradation.

However, if the cure system per se significantly affects the Mooney-Rivlin plots, then in EPDM/1 we would also expect a similar trend. A gradual rise in `G' value up to 90 [degrees] C is noticed. Other aging conditions do not fit into a regular trend and in effect they are more complex. In case of an insulator compound used in rocket propulsion (ref. 4), the ENB based EPDM was reported to have better retention of mechanical properties on air aging. The structure of monosulfide -S- or/ and disulfide -S2- linkages in TMTD cured EPDM are suitable for scission to take place (ref. 5) and it takes place preferentially at crosslinks (ref. 6) during stress relaxation in air @ 110 [degrees] C. The main chain scission rate has been reported (ref. 7) to be 2.47 x [10.sup.-4] and for crosslinks it is 1.12 x [10.sup.-3]. The backbone of EPDM being free from unsaturation, we surmise that in our investigation, diffusion of air/[O.sup.2] at high temperatures also might influence the aging process which has resulted in complex Mooney-Rivlin plots.


A scheme of investigation to study the effect of air aging on Mooney-Rivlin plots was established.

* In nitrile rubber, curing system and fillers have greater influence on the variation in Mooney-Rivlin plots.

* Particularly the application of Mooney-Rivlin plots is exemplified in case sulfur donor system.

* In order to obtain stable Mooney-Rivlin plots, irrespective of aging conditions, the need for not only inert crosslinks but also in sufficient density was emphasized in our findings.

* Even though a similar crosslink pattern was expected in case of EPDM vulcanizate, the complexity of Mooney-Rivlin plots versus aging conditions provides a scope for similar work on diffusion study and change in crosslink system (viz., peroxide cure) which might throw more light on the role of crosslinks and backbone structure in altering the Mooney-Rivlin plots.


[1.] Roderick Martin and Robert Campion, Materials World, 4(4), 200, 1996.

[2.] Robert H. Finney, "Engineering with rubber, " Alan N. Gent (ed), Hanser Publishers, 1992.

[3.] Ulrich Eisele, "Introduction to polymer physics " chapter 10, Springer Verlag, 1990.

[4.] Arup S. Deuri and Anil K. Bhowmick, J. Appl. Polym. Sci. 34, pp. 2,205-2,222 (1987).

[5.] H.Z Jellinek (ed) "Aspects of degradation and stabilization of polymers" chapter 7, p. 341, Elsevier (1978).

[6] K. Murakami and S. Tamura, J. Polym. Sci., Part B, 11, 529 (1973).

[7.] K. Murakami and S. Tamura, Polym. J., 2, 330, (1971).
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Title Annotation:establishing elastomer structure-property relationships
Author:Seshadri, K.R.
Publication:Rubber World
Date:Nov 1, 1997
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