Journal of Colloid and Interface Science 291 (2005) 229–235 www.elsevier.com/locate/jcis
Influence of surface characteristics of carbon blacks on cure and mechanical behaviors of rubber matrix compoundings Soo-Jin Park a,∗ , Min-Kang Seo a , Changwoon Nah b a Advanced Materials Division, Korea Research Institute of Chemical Technology, P.O. Box 107, Yusong, Daejon 305-600, South Korea b Department of Polymer Science and Technology, Chonbuk National University, Chonju, Chonbuk 561-756, South Korea
Received 3 January 2005; accepted 28 April 2005 Available online 12 July 2005
Abstract In this work, the effect of chemical modification on the surface energetics and cure kinetics of carbon blacks (CBs) modified with KOH and C6 H6 was investigated by contact angle and rheometer measurements, respectively. Also, the resulting mechanical properties of the CBs/styrene–butadiene composites were studied in terms of tensile and dynamic mechanical analysis. As experimental results, the polar basic and nonpolar chemical treatments showed an increase of the London dispersive component (γSL ) of γS of the CBs without significantly changing the surface properties and microstructures that resulted from the deaggregation of microstructures and decrease of the swollen weight of the sample in the equilibrium state. Also, it was clearly revealed that the increase of γS of the CBs could largely affect the vulcanization and mechanical properties of the composites, resulting from the increase in γSL of the CBs. These results were evident that the mechanical properties of the composites were controlled more by the γSL of γS than by the specific (or polar) component (γSSP ), including electron acceptor and donor parameters on CB surfaces in an organic matrix composite system. 2005 Elsevier Inc. All rights reserved. Keywords: Chemical modification; Surface energetics; Carbon blacks (CBs); Styrene–butadiene rubber (SBR); Mechanical properties
1. Introduction Solid carbon materials are available in a variety of crystallographic forms, typically classified as diamond, graphite, and amorphous carbon. Among them, carbon black is widely used as a filler to enhance the performance of rubbers and other polymeric materials. The reinforcement of elastomers by particulate fillers has been studied in depth in numerous investigations, and it is generally accepted that this phenomenon is, to a large extent, dependent on the physical interactions between the filler and the rubber matrix, which can determine the degree of adhesion at interfaces [1–3]. Generally, it is dependent on the active functional groups, surface energy, and energetically different crystallite faces of the filler surfaces [4–8]. * Corresponding author.
E-mail address:
[email protected] (S.-J. Park). 0021-9797/$ – see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2005.04.103
A prerequisite of good adhesion between filler and polymer remains the surface energy of fillers, which must be greater than or equal to the surface energy of the polymer. The virgin carbons exhibit a small surface energy and are apparently unable to form strong adhesive bonds with the polymer. Surface treatments are therefore needed to improve the wettability of carbon surfaces by promoting the formation of hydrophilic groups, which increase the surface energetics. By appropriate surface treatments, the physical properties, such as optical, reflection, adhesion, friction coefficient, surface energy (or wettability), permeability, surface conductivity, and biocompatibility, of conventional materials can be easily modified. Generally, the surface modification of different materials gives rise to a change of their surface energy, which has recently been interpreted by acid–base interactions [4,9,10]. Recently, Park et al. [11–13] have treated carbon black surfaces with strong polar (electron acceptor and donor) and
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nonpolar chemicals and measured the surface free energy in terms of the London dispersive and the specific components based on contact angle measurement by the sessile drop method [14]. They have found that the London dispersive component is closely related to the resulting mechanical properties of rubber compounds. Moreover, the surface free energy (or work of adhesion) of a solid is believes to be of much greater importance than the nature of their chemical elements with regard to the resulting mechanical properties [4,9,15–17]. Van Oss et al. [18] denoted the work of adhesion of various liquids and solids resulting from Lifshitz–van der Waals intermolecular interactions of hydrophobic or as hydrophilic (polar) character. However, a means of determining the work of adhesion at interfaces between solid and solid is not easy and sometimes encounters difficulties in the physical acid–base (or electron acceptor–donor interactions). Meanwhile, the surface energetics of carbon blacks is believed to be of much greater importance than their elemental nature, with regard to the resulting mechanical properties of the filled elastomers. The surface free energy is a physical adsorption caused by the intermolecular interactions at interfaces, i.e., London dispersive force, Debye inductive force, Keesom orientational forces, hydrogen bonding, Lewis acid–base interactions, and energetically homogeneous and heterogeneous interactions [4,19–22]. In this study, the change of chemically modified carbon blacks (CBs) is investigated in terms of surface energetics and cure kinetics, and the effect of the surface free energy on the mechanical properties of the resulting CBs/styrene– butadiene rubber (SBR) composites is also studied in tensile and dynamic mechanical analysis. The change of surface characteristics, including the London dispersive component of surface free energy, has been also discussed, together with the mechanical test results obtained from the rubber composites.
2. Experimental 2.1. Materials and sample preparation A carbon black of N-220 type (VCB, Korea Carbon Black Co.) was selected as a reinforcement, and the loading level was fixed to be 50 phr. In order to create the polar functional groups on carbon black surfaces, the CBs were immersed in two different solutions of 0.1 N KOH and C6 H6 (BCB and NCB, respectively) for 24 h. Prior to use after analysis, the residual chemicals used were removed by Soxhlet extraction by boiling with acetone at 80 ◦ C for 2 h. Finally, the carbon blacks were washed several times with distilled water and dried in a vacuum oven at 90 ◦ C for 12 h. A styrene– butadiene rubber (SBR-1500, bound styrene: 23.5%, cis-1,4: 17%, trans-1,4: 68%, 1,2-vinyl: 15%, Kumho Petrochem. Co. of Korea) was selected as a rubber in this study. TBBS
Table 1 Compounding formulations of the work studied Ingredients
Loading (phr)
SBR-1052 Carbon blacks (N-220) ZnO Stearic acid Acceleratorb Sulfur
100 50 (type varied)a 5 2 1 2
a VCB: virgin, BCB: KOH-treated, and NCB: benzene-treated carbon blacks. b N -t -butyl-2-benzothiazole sulfonamide.
Table 2 Surface tensions and their components for the liquids, measured at 20 ◦ C (mJ/m2 ) Testing liquid
γL
γLL
γLSP
γL+
γL−
Water Diiodomethane Ethylene glycol
72.8 50.8 48.0
21.8 50.8 29.0
51.0 0.38 19.0
25.5 0.0 1.92
25.5 0.0 47.0
(N -t-butyl-2-benzothiazol sulfonamide) and sulfur were selected as the cure system. The compounding formulations are listed in Table 1. The mixing of compound ingredients was performed using an internal mixer (82BR, Farrel Co., USA) at about 150 ◦ C for 6 min according to the procedure described in ASTM D3184. Then the sulfur and accelerator curatives were added using a two-roll mill (M8422AX, Farrel Co., USA) at about 100 ◦ C for 3 min. Vulcanized rubber sheets about 2 mm in thickness were pressed and vulcanized using an electrically heated press (Carver 2518, USA) at 145 ◦ C for a given period of time determined by a torque rheometer (R-100, Monsanto, USA). 2.2. Measurements 2.2.1. Surface energetics Early, Fowkes [15] suggested that the surface free energy of a solid, γS , was the sum of two components: dispersive London, γSL , and specific, γSSP , components. The surface free energy of a solid could be obtained by measuring the contact angle formed between the solid and a liquid of known surface free energy characteristics. In this work, the surface free energy of carbon blacks was determined at 20 ± 1 ◦ C using a sessile drop method [14] (Rame–Hart goniometer). About 5 µl of wetting liquids was used for each measurement at 20 ◦ C, and more than 10 drops were tested for each of the CBs studied. Three different wetting liquids, distilled water, diiodomethane, and ethylene glycol, were selected as an apolar liquid, which must be used with apolar and polar liquids for the determination of their components including acid and base parameters of the surface free energy of carbon blacks. The basic characteristics of surface free energy of the liquids are given in Table 2 [9,11,12,23].
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2.2.2. Cure behaviors The cure characteristics of mixed rubber compounds were measured at 145 ◦ C using a torque rheometer (R-100, Monsanto, USA) with a frequency of 100 cycles/min and ±1.5 arc. 2.2.3. Mechanical properties Hardness was measured using a spring-type hardness tester (Shore Durometer A-2 type), according to the ASTM D2240. To measure tensile properties, dumbbell-shaped specimens were cut from the vulcanized rubber sheets. Stress–strain curves were obtained using a tensile tester (Instron 6021, USA) at room temperature and at a crosshead speed of 500 mm/min, according to the ASTM D412. The dynamic mechanical properties were measured over a wide temperature range from −70 to 70 ◦ C using a dynamic mechanical analyzer (Gabo Qualimeter, Eplexor-150, Germany). The dynamic frequency and deformation were set to be 11 Hz and 0.1%, respectively, and the measurement was performed by the ASTM D2231.
3. Results and discussion 3.1. Surface energetics It is accepted that knowledge of surface energies at a given temperature of a solid has recently allowed significant progress in many scientific and engineering fields, such as, adsorption wettability, catalysis, permeation, dyeability, painting, and adhesion [4,24], because it determines intermolecular interactions at the interfaces of a solid surface with its environment and has two nonidentical molecular interactions at a certain intermolecular distance. Therefore, in this work, we concentrate on the role of the intermolecular interactions at interfaces based on the surface free energy at a given temperature, and the work of adhesion at interfaces between unlike solid substances is also investigated from a viewpoint of intermolecular interactions. Surface science is greatly related to the adhesion force, supposing that the strength of an adhesive bond is proportional to the work of adhesion. The surface free energies (γS ) of solids (both carbon black (CB) and rubber (R)) between the solid and liquid are calculated according to the following equation using van der Waals acid–base parameters [9,18], L + γ + γ − + γ − γ + , (1) γ L,i (1 + cos θ ) = 2 γSL γL,i S L,i S L,i where γ L is the surface free energy of the liquid, θ the contact angle, γ L the London dispersive component of surface free energy associated with Lifshitz–van der Waals interactions that encompass London dispersion forces, γ + stands for the electron–acceptor parameter, γ − for the electron– donor parameter of the specific polar component of surface free energy (or tension), the subscript i is the experimental testing liquid, such as, water, diiodomethane, or ethylene
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Table 3 Surface tensions and their components for the carbon blacks and SBR, measured at 20 ◦ C (mJ/m2 ) Specimen
γS
γSL
γSSP
γS+
γS−
VCB BCB NCB SBR
64.2 77.8 56.5 35.8
31.1 34.5 33.7 27.6
33.1 43.2 22.8 8.2
15.0 16.1 10.1 5.2
18.3 29.0 12.9 3.2
glycol, and the subscripts L and S are liquid and solid states, respectively. Meanwhile, it is noted that the London dispersive component of the surface free energy is influenced by the particle size or specific surface area, whereas the polar component is dependent on the surface activity, which is related to the surface functional groups, such as hydroxyl, carbonyl, carboxyl, ether, phenol, lactone, pyrone, and chromene groups [4]. Table 3 summarizes the results of the London dispersive component and the specific component, including the electron acceptor and donor, of surface free energy for the carbon blacks studied in the contact angles. As a result, the BCB gives a maximum total surface free energy, which is mainly due to their higher specific polar components, γSSP . These increases in the specific polar component of surface free energy, including in both γS+ and γS− , can largely be attributed to the polar basic surface groups produced on carbon blacks after basic chemical modifications. And the increase of γSL (or decrease of γSSP ) of NCB of surface free energies can be attributed to the increase of aromatic nonpolar functional groups on carbon black surfaces [11]. While, an interesting result is obtained in the case of BCB, resulting from the increase of γSL after basic chemical modification. This seems to be a consequence of improving the surface roughness (or increasing the specific surface area) and the chemical erosion of the carbon blacks. 3.2. Cure kinetics Fig. 1 shows the cure behavior of carbon black/SBR composites at 145 ◦ C, depending on the type of surface modifications, and the main cure properties are listed in Table 4. In previous studies [11–13], the cure behaviors of surface modified carbon blacks/rubber (butadiene rubber) composites were found. The basic surface modification of carbon blacks caused an increase in the vulcanization reaction of the composites, resulting from the improvement of the dispersive force of carbon blacks in the rubber matrix resins. In the present work, the vulcanization reaction is found to be considerably accelerated in the cases of basic and nonpolar surface modifications in the results of t2 and t90 , but considerably higher in view of torques than those of virgin carbon blacks, VCB. These results are dependent on the changes of surface functional groups and the surface free energies of the carbon blacks studied [11–13].
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Fig. 1. Rheocurves of the carbon black/SBR composites, measured at 145 ◦ C.
Fig. 2. Conversion ratio of the carbon black/SBR composites.
Table 4 Cure properties of the carbon black/SBR composites Specimen MH (J/m2 )a ML (J/m2 )a M (J/m2 )b t2 (min)c t90 (min)c VCB BCB NCB
5.0 5.0 5.7
1.2 1.2 1.3
3.8 3.8 4.4
13.8 13.2 12.1
45.9 37.9 44.2
a Maximum and minimum torque, respectively. b Difference between maximum and minimum torque. c Times for rubber compound to be vulcanized 2 and 90%, respectively,
based on the torque.
To compare the cure rates in more detail, the conversion ratio, χt , at a given time t is defined by the following equation based on the rheocurves, as shown in Fig. 1 [25], M t − ML , (2) MH − ML where MH and ML represent the minimum and maximum torque, respectively, and Mt the torque at a given time t. Fig. 2 shows the conversion of carbon black/SBR composites for different surface modifications of carbon black surfaces as a function of cure time. The conversion of vulcanization reaction under a given condition is found to be faster in the order BCB > NCB VCB. For instance, the required time for 50% conversion is estimated to be 22 min for BCB, 29 min for NCB, and 31 min for VCB. It is well known that the reactivity in the accelerated-sulfur vulcanization reaction is increased with increasing basic surface functional groups, while it is rather decreased with increasing acidity in the rubber composites [26–28]. Table 4 shows the cure characteristics of the carbon black/SBR composites studied. As an experimental result, it can be seen that the conversion ratio of the carbon blacks treated with basic (BCB) chemical solution is similar to that of untreated carbon blacks, for which there is no significant change in conversion of vulcanization reaction. It is noted that the minimum and maximum torque, ML and MH , and the difference between them, M (= MH − ML ), are found to increase for NCB compared with VCB. The increases in
χt =
Fig. 3. Stress–strain curves for the carbon black/SBR composites.
ML and M are related to the increases in viscosity and degree of crosslinking respectively [25]. Since the same type of carbon blacks is equally loaded, the bound rubber formation depends on the secondary structure of aggregate or agglomerate, the dispersion, and the surface activity of carbon blacks [29]. In NCB, it is found that the increase in bound rubber formation results in increases of both the viscosity and the crosslinking density (the increase in ML and M), resulting in increasing London dispersive component of surface free energy or work of adhesion, as mentioned for surface energetic results. Thus, the observed increase in ML and M is explained, at least by part, by the increase of bound rubber formation. Further systematic study is necessary to confirm the observed phenomena. 3.3. Mechanical properties It is well known that the mechanical properties of carbonblack-filled rubber composites depend strongly on the degree of adhesion between the carbon black and the rubber [13]. Fig. 3 shows the results of stress–strain curves, and
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Table 5 Tensile properties of the carbon black/SBR composites Mechanical properties
VCB
BCB
NCB
Hardness (Shore A) Stress (MPa) at 50% strain at 100% strain at 200% strain at 300% strain Tensile strength (MPa) Elongation at break (%)
70
73
75
1.98 ± 0.03 3.33 ± 0.073 9.63 ± 0.15 18.9 ± 0.40 25.4 ± 2.20 377 ± 28
2.22 ± 0.04 3.97 ± 0.16 11.6 ± 0.30 21.6 ± 0.30 25.8 ± 1.0 349 ± 10
2.34 ± 0.03 4.27 ± 0.06 12.8 ± 0.20 23.4 ± 0.20 26.7 ± 1.40 342 ± 17
Fig. 5. Elastic modulus vs temperature for the carbon black/SBR composites.
Fig. 4. Dependence of tensile stress on the London dispersive component of surface free energy of the carbon blacks studied.
some main properties of the composites are summarized in Table 5. BCB- and NCB-filled SBR composites have better mechanical properties than those of VCB-filled ones. The increase of hardness, modulus, and tensile strength can possibly be explained by the improvement of the degree of adhesion at interfaces between the carbon blacks and the SBR. A similar result is found for carbon-black-filled polybutadiene (BR) compound [11–13]. In the above result on surface free energy, it is found that the London dispersive component of the surface free energy of carbon blacks is considerably increased. Also, the observed improvement is in line with the increase in torque difference, M (= MH − ML ), as seen in Table 4. Namely, the improvement in tensile properties for NCBand BCB-filled SBR composites seems to be responsible for the improved dispersion of the carbon blacks into the rubber matrix, leading to a higher bound rubber formation. To support the explanation, several essential properties are plotted in Fig. 4 as a function of the London dispersive component of surface free energy, described in Table 3. Therefore, it is recognized that the increase in the London dispersive component of surface free energy of the carbon black surfaces is important for improving the degree of adhesion between the carbon blacks and the SBR [5,11–13]. Figs. 5 and 6 show the elastic modulus, E , and tan δ determined from a dynamic mechanical analyzer under the
Fig. 6. tan δ vs temperature for the carbon black/SBR composites.
conditions of 11 Hz and 0.1% dynamic strain amplitude. These results indicate that the elastic modulus throughout the temperature ranges of the rubber composites filled with basic-treated (BCB) or nonpolar-treated (NCB) carbon black is higher than those of rubber composites filled with VCB. In the case of tan δ, the peak height at the glass transition temperature is lowered slightly, and tan δ values in the temperature range from −20 to 70 ◦ C are slightly higher for BCB and NCB than for VCB. This result indicates that BCB or NCB is effective in improving the stability of dispersion of carbon blacks, as already mentioned for the London dispersive component of surface free energy. Also, we perform normal distribution analysis to justify the significance of the obtained results of the system, as shown in Fig. 7. It can be seen from Fig. 3 that there are lines associated with the local tensile strength (σt ) of the carbon-black-filled rubber composites. The lines are of importance because they form part of any overall probabilistic failure assessment. A number of factors may produce line in measured values of mechanical properties. The conventional approach to analyzing lines is to fit the histogram of results to an assumed statistical distribution and to charac-
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W the specimen depth, and S the moment arm: S = 0.5 (Smax − Smin ).
4. Conclusions
Fig. 7. Normal distribution of the critical local fracture stresses for the carbon black/SBR composites.
terize this distribution in terms of parameters, such as the mean and standard deviation (for a normal distribution). For the present results, the first attempt is to test the hypothesis that the σt distributions are essentially single-valued, although incorporating random experimental errors. It is then of particular interest to plot the results on normal probability paper. The CDF for the σt values is plotted against the probability calculated by means of the median ranking method. The test results are arranged in an ascending order starting with the lowest value as order number 1, the second lowest as number 2, and so forth. The median rank of order number n in a total population of N , Fn , can be derived from the following close approximation [30]: Fn = (n − 0.3)/(N + 0.4).
(3)
To aid interpretation of the CDFs for the experimental data, it is necessary to assess the magnitude of the random experimental errors associated with the measurements and calculations of σt values. The ranges of the errors in the basic measurements are estimated as follows: (a) specimen breadth, B = ±0.01 mm, (b) specimen depth, W = ±0.02 mm, (c) machine load cell calibration, M = ±0.02 kN, (d) moment arm, S = ±0.5 mm, etc. It can be seen that the experimental errors arise from two main sources: dimension measurements and load measurements. The resultant errors in σt values from the load measurements can be obtained directly from the relationship between the largest maximum principal stress and the applied load, as shown in Fig. 3. The random errors resulting from dimension measurements can be estimated from the relationships to the general yield load, P = 0.63BW 2 σt /S, and then to the largest maximum principal stress in Fig. 3. The extreme situation for dimension measurements is when P = 0.63(B − 0.01)[W − 0.02]2 σt /(S + 2 × 0.5), for which the estimated error in σt value is 1.5 MPa (or −1.5 MPa if the errors are assumed to act in the opposite sense), where P in Fig. 7 is the general load, B the specimen breadth,
The effects of polar basic and nonpolar chemical surface modifications on carbon blacks has been studied in the context of surface energetics of carbon black surfaces; the resulting mechanical properties of the carbon-black-filled SBR composites, such as cure characteristics, tensile properties, and dynamic mechanical properties, were also investigated. The experimental results showed that the surface modification of carbon blacks did lead to a significant increase of the nonpolar characteristics (London dispersive component) of carbon black surfaces. The chemical modifications were also expected to improve both the stable microstructures and the surface functional groups of the nanostructured carbon black surfaces, which were correlated with the London dispersive component and the specific (or polar) component, including the electron acceptor and donor, of the surface free energy (or work of adhesion), respectively. A significant advantage of the carbon black/SBR composites was obtained by using carbon blacks modified by basic (BCB) or nonpolar (NCB) chemical solutions, resulting in improved the cure behaviors, tensile stress, and dynamic mechanical properties. Good linearity was found between the London dispersive component of surface free energy (or work of adhesion) of the carbon blacks studied and the resulting mechanical properties of the carbon black/SBR composites.
References [1] J.B. Donnet, A. Voet, Carbon Black, Dekker, New York, 1976. [2] J.L. White, Rubber Processing, Hanser, Munich, 1995. [3] P. Hajji, L. David, J.F. Gerard, J.P. Pascault, G. Vigier, J. Polym. Sci. Polym. Phys. 37 (1999) 3172. [4] S.J. Park, in: J.P. Hsu (Ed.), Interfacial Forces and Fields: Theory and Applications, Dekker, New York, 1999, ch. 9. [5] M.J. Wang, S. Wolff, in: J.B. Donnet, R.C. Bansal, M.J. Wang (Eds.), Carbon Black Science and Technology, Dekker, New York, 1993, p. 229. [6] S. Wu, J. Polym. Sci. Part C 34 (1971) 19. [7] G.J. Wang, M. Li, X.F. Chen, J. Appl. Polym. Sci. 68 (1998) 1219. [8] Z. Zhang, G. Zhang, D. Li, Z. Liu, X. Chen, J. Appl. Polym. Sci. 74 (1999) 3145. [9] C.J. van Oss, Interfacial Forces in Aqueous Media, Dekker, New York, 1994, p. 7. [10] K. Kinoshita, Carbon: Electrochemical and Physicochemical Properties, Wiley, New York, 1988, ch. 2. [11] S.J. Park, J.S. Kim, J. Colloid Interface Sci. 232 (2000) 311. [12] S.J. Park, J.S. Kim, J.R. Lee, Polymer (Korea) 23 (1999) 902. [13] S.J. Park, K.S. Cho, M. Zaborski, L. Slusarski, J. Korean Ind. Eng. Chem. 14 (2003) 23. [14] A.W. Adamson, Physical Chemistry of Surfaces, fifth ed., Wiley, New York, 1990. [15] F.M. Fowkes, J. Phys. Chem. 66 (1962) 382. [16] D.K. Owens, R.C. Wendt, J. Appl. Polym. Sci. 13 (1961) 1741. [17] D.H. Kaelble, J. Adhesion 2 (1970) 66.
S.-J. Park et al. / Journal of Colloid and Interface Science 291 (2005) 229–235
[18] C.J. van Oss, R.J. Good, M.K. Chaudhury, J. Colloid Interface Sci. 111 (1986) 397. [19] R. Tsunoda, J. Colloid Interface Sci. 188 (1997) 224. [20] E. Ruckenstein, J. Colloid Interface Sci. 196 (1997) 313. [21] W. Jia, X. Chen, J. Appl. Polym. Sci. 66 (1997) 1885. [22] M. Greiveldinger, M.E.R. Shanahan, J. Colloid Interface Sci. 215 (1999) 170. [23] G. Akovali, I. Ulken, Polymer 40 (1999) 7417.
[24] [25] [26] [27] [28] [29] [30]
235
C.M. Chan, C.L. Cheng, Polym. Eng. Sci. 37 (1997) 1135. G.R. Cotton, Rubber Chem. Technol. 45 (1972) 129. A.M. Zaper, J.L. Koenig, Rubber Chem. Technol. 60 (1987) 278. E. Morita, Rubber Chem. Technol. 57 (1984) 744. E. Morita, A.B. Sullivan, Rubber Chem. Technol. 54 (1983) 1132. E.M. Dannenberg, Rubber Chem. Technol. 59 (1986) 512. J.H. Bompas-Smith, Mechanical Survival: The Use of Reliability Data, McGraw–Hill, New York, 1973.