Mooney curves

The experimental error range is of great importance. A 1% error in the determination of X has a tremendous effect on the Mooney curve when 1/a > 0.9 this part of the curve is therefore highly imreliable (156). 

Figure 6.1 Typical Mooney curves very different viscoelastic properties for the same...

These data for typical properties of EP polymers are either as measured or as advertised by respective manufacturers. This table is not intended to be definitive either in terms of the total grade slate or the specific data reported for each producer. Note that the molecular weight distribution data are based on a qualitative comparison of GPC curves. Mooney viscosities are repotted for final product form (i.e.. in the case of oil-extended rubbers, the viscosity is that of the EP plus oil. 

Number-average molecular weights are Mn = 660 and 18,500 g/ mol, respectively (15,). Measurements were carried out on the unswollen networks, in elongation at 25°C. Data plotted as suggested by Mooney-Rivlin representation of reduced stress or modulus (Eq. 2). Short extensions of the linear portions of the isotherms locate the values of a at which upturn in [/ ] first becomes discernible. Linear portions of the isotherms were located by least-squares analysis. Each curve is labelled with mol percent of short chains in network structure. Vertical dotted lines indicate rupture points. Key O, results obtained using a series of increasing values of elongation 0, results obtained out of sequence to test for reversibility. 

A development of plasticity determination by means of the Mooney viscometer. The same instrument is used but the temperature of operation is higher and the test is continued until the sample vulcanises. A curve of Mooney reading against time is drawn, from which the scorch and cure characteristics are estimated (BS 903-A58). 

When data are available in the form of the flow rate-pressure gradient relationship obtained in a small diameter tube, direct scale-up for flow in larger pipes can be done. It is not necessary to determine the r-y curve with the true value of y calculated from the Rabinowitsch-Mooney equation (equation 3.20). 

When trying to determine the flow behaviour of a material suspected of exhibiting wall slip, the procedure is first to establish whether slip occurs and how significant it is. The magnitude of slip is then determined and by subtracting the flow due to slip from the measured flow rate, the genuine flow rate can be determined. The standard Rabinowitsch-Mooney equation can then be used with the corrected flow rates to determine the tw-jw curve. Alternatively, the results can be presented as a plot of tw against the corrected flow characteristic, where the latter is calculated from the corrected value of the flow rate. 

Figure 28 41 depicts the isochronal Mooney-Rivlin plots for SBR-1, where the extrapolated values of bW/bli and X lbW/bI2 are represented by solid lines and the sum of them by broken lines. As above, these sums are equivalent to the Mooney-Rivlin plot of uniaxial data. We again find that the slope of the sum curves depends mainly on the Xj dependence of bW/dli and therefore the slope is not equal to... 

These values were estimated from biaxial data in same manner as in Fig. 27. Sum curves are equivalent to Mooney-Rivlin plot, and C1 and C2 may be determined. Note that C is apparently independent of time t, while actual values of bWjbly are not... 

Even when the above complications are negligible or properly accounted for and when strain-induced crystallization is absent, the stress-strain curves for networks seldom conform to Eq. (7.3). The ratio //(a — 1/a2) generally decreases with elongation. An empirical extension of Eq. (7. IX the Mooney-Rivlin equation, has been used extensively to correlate experimental results ... 

In unfilled rubbers, which are not capable of strain-induced crystallization, the upturns on Mooney-Rivlin curves have shown to be absent 92 95). They disappear also in crystallizable rubbers at elevated temperatures and in the presence of solvents. On the other hand, the upturns do not appear for butadiene, nitrile and polyurethane rubbers if the limited chain extensibility function is introduced in the Mooney-Rivlin expression 97). Mark 92) has concluded that in the absence of selfreinforcement due to strain-induced crystallization or domains the rupture of the networks occurs long before the limited chain extensibility can be reached. 

Fig. 22, The same data as in Fig. 21 plotted as force versus deformation ratio. If one identifies the compression modulus with the Gaussian constant 3 (A vk T/Lt) (( >o) the experimental curve in extension lies below the Gaussian curve. The C part of the Mooney-Rivlin curve in extension lies again below the experimental curve...

Fig. 23. Mooney-Rivlin plots of extended natural rubber vulcanizates. The upswing at small A 1 values, i.e. large strains, is due to finite extensibility [Mullins (72S)]. At high crosslinking densities (upper curves) the upswing occurs at a smaller strain...

Fig. 24. Mooney-Rivlin plots of extended and swollen rubbers. The upswing is again due to finite extensibility, which comes into play at an earlier stage the higher the swelling (lower curves) [Mullins 128)1...

The most common method of measurement is to run the compound in the mooney viscometer until the viscosity shows a 5 point rise above the minimum. The viscosity of the compounded rubber at the processing temperatures can also be obtained from the minimum of the curve. The values normally taken from the cure curve are ... 

In all the above methods, it is necessary to cure specimens of test samples for each of a series of curing times and then perform the desired test on the vulcanizate. However, in the test for continuous measurement of vulcanization complete information could be obtained with saving in time. The mooney viscometer test approaches this objective. However a weakness of the mooney viscometer test is that the test is completed before a measurable modulus value after the scorch point has been obtained. This is because the test sample is destroyed after the induction period is passed due to tearing by continuous rotation of the rotor whether small or large. To overcome this deficiency and to provide a total cure curve for the entire vulcanization cycle, a series of instruments called cure meters was developed. In each of these instruments the stiffness or modulus of the compound was chosen as parameters for vulcanization continuously. The Vulkameter developed by Bayers, Germany was the first of the cure meters developed. 

Choosing the correct flow period is a very important aspect in the forming and shaping process. Mooney cure curves give good data on the flow period. The flow period also depends on the flow distances in the cavities of the mould and the viscosity of the rubber stock and the repeat pressure application cycles, called "bumping" cycles on the shop floor. 

For gum rubbers and lightly filled compounds, the Mooney-Rivlin equation often models the tensile stress-strain curve well up to extensions of 150% or more. However, for more highly filled compounds (and almost always for commercially important compounds) this simple function only works well up to about 50% strain. A much better fit over an extended strain range can be obtained by taking the next logical term in the infinite series of the general expression. Using ... 

The stress-strain curve for unfilled NR exhibits a large increase in stress at higher deformations. NR displays, due to its uniform microstructure, a very unique important characteristic, that is, the ability to crystallise under strain, a phenomenon known as strain-induced crystallization. This phenomenon is responsible for the large and abrupt increase in the reduced stress observed at higher deformation corresponding, in fact, to a self-toughening of the elastomer because the crystallites act as additional cross-links in the network. This process can be better visualized by using a Mooney-Rivlin representation, based on the so-called Mooney-Rivlin equation ... 

GAP-DEPENDENT APPARENT SHEAR RATE. Indirect evidence of slip, as well as a measurement of its magnitude, can be extracted from the flow curve (shear stress versus shear rate) measured at different rheometer gaps (Mooney 1931). If slip occurs, one expects the slip velocity V (a) to depend on the shear stress a, but not on the gap h. Thus, if a fluid is sheared in a plane Couette device with one plate moving and one stationary, and the gap h is varied with the shear stress a held fixed, there will be a velocity jump of magnitude Vs(ct) at the interfaces between the fluid and each of the two plates. There will also be a velocity gradient >(a) in the bulk of the fluid thus the velocity of the moving surface will be y = 2V,(a) + y (a)/i. The apparent shear rate V/h will therefore be... 

Stress-strain curves for the various models are plotted in the Mooney-Rivlin fashion in Fig. 9. 

The viscosity data of Figure 5 can be reduced to a single curve by replotting nr as a function of /o indicating that the relative viscosity at zero shear rate is a unique function of /0 A relation between dispersion viscosity and

0, derived by Mooney (5) and modified, by Krieger and Dougherty (6), gives... 

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