First Mooney constant

Figure 4.16 shows the detailed experimental data on the depression of the sttess. The extrapolation to a oo gives the first Mooney constant 1C, which turns out to be independent of the polymer volume fraction 4>. In contrast, the slope of the lines decreases... 

In many cases it is reasonable to take the initial value of [f ]ph = 2Ci, where 2Ci is the first Mooney-Rivlin constant. An alternative possibility is to estimate [f ]ph from the stoichiometry of the chemical reaction using Eqs. (29.12)-(29.14) and (29.41). 

Considerably better agreement with the observed stress-strain relationships has been obtained through the use of empirical equations first proposed by Mooney and subsequently generalized by Rivlin. The latter showed, solely on the basis of required symmetry conditions and independently of any hypothesis as to the nature of the elastic body, that the stored energy associated with a deformation described by ax ay, az at constant volume (i.e., with axayaz l) must be a function of two quantities (q +q +q ) and (l/a +l/ay+l/ag). The simplest acceptable function of these two quantities can be written... 

This is Mooney s equation for the stored elastic energy per unit volume. The constant Ci corresponds to the kTvel V of the statistical theory i.e., the first term in Eq. (49) is of the same form as the theoretical elastic free energy per unit volume AF =—TAiS/F where AaS is given by Eq. (41) with axayaz l. The second term in Eq. (49) contains the parameter whose significance from the point of view of the structure of the elastic body remains unknown at present. For simple extension, ax = a, ay — az—X/a, and the retractive force r per unit initial cross section, given by dW/da, is... 

Evidence for wall slip was suggested over thirty years ago [9,32,63]. One of the first attempts at a slip mechanism was the performance of a Mooney analysis by Blyler and Hart [32]. Working in the condition of constant pressure, they explicitly pointed out melt slip at or near the wall of the capillary as the cause of flow discontinuity. On the other hand, they continued to insist that bulk elastic properties of the polymer melt are responsible for the flow breakdown on the basis that the critical stress for the flow discontinuity transition was found to be quite insensitive to molecular weight. Lack of an explicit interfacial mechanism for slip prevented Blyler and Hart from generating a satisfactory explanation for the flow oscillation observed under a constant piston speed. 

Rouse chains. The fundamental feature here is the appearance of cooperative interchain motions due to cross-linking. First approaches to evaluating the dynamical properties of such networks started from the intrachain relaxation, and accounted for the connectivity between chains only in simplified, effective ways. For instance, the dynamics of Rouse chains that have fixed (constant) end-to-end distances were studied [60]. Alternatively, Mooney considered Rouse chains with fixed (immobile) ends as a model for a polymer network [3,61]. In particular, he found that the relaxation modulus of such a chain coincides with that of a Rouse chain with free ends, except for a constant contribution, which can be considered as being the nonvanishing, equilibrium modulus of the network However, the idea of the GGS formalism is to take the connectivity exactly into account, see Eqs. 1 and 2. In order to gradually increase the complexity of the networks, one can start by first considering chains cross-linked into regular spatial structures. This is the subject of the present section. 

It is usually possible to correct this apparent wall slip and determine the true viscosity of the sample by extrapolating to infinite diameter. Apparent wall shear rates measured at constant extrusion pressure (i.e., constant Tw) for a constant L/R are plotted against l/R according to the relation first developed by Mooney (1931)... 

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