Mooney-type equations

Eq. (IV-26a) can be confronted with birefringence-strain data, which can also be written in a Mooney-Rivlin type equation. Remembering that the measured birefringence refers to the strained cross-section, the classical result for the Gaussian part is (171)... 

Mooney [97] proposed that at very high concentrations an Arrhenius type equation (with the addition of crowding factor (1 — a )) of the following form could be used ... 

As can be seen, Q does not depend on the type and level of CB, contrary to C2. In fact, the C2 term in the Mooney-Rivlin equation somewhat expresses the deviation with respect to the ideal elastic network (as readily seen when comparing Equations 5.17 and 5.18). When using this equation... 

Effect of Carbon Black Type and Level on Cj and C2 Constants in Mooney-Rivlin Equation... 

Figure 11 shows plots according to equation(lO) of stress-strain data for triol-based polyester networks formed from the same reactants at three initial dilutions (0% solvent(bulk), 30% solvent and 65% solvent). Only the network from the most dilute reactions system has a strictly Gaussian stress-strain plot (C2 = 0), and the deviations from Gaussian behaviour shown by the other networks are not of the Mooney-Rivlin type. As indicated previously, they are more sensibly interpreted in terms of departures of the distribution of end-to-end vectors from Gaussian form. 

Equation 3.29 is helpful in showing how the value of the correction factor in the Rabinowitsch-Mooney equation corresponds to different types of flow behaviour. For a Newtonian fluid, n = 1 and therefore the correction factor has the value unity. Shear thinning behaviour corresponds to < 1 and consequently the correction factor has values greater than unity, showing that the wall shear rate yw is of greater magnitude than the value for Newtonian flow. Similarly, for shear thickening behaviour, yw is of a... 

A rather complete survey of the entire field of viscometry, including the mathematical relationships applicable to various types of instruments, has been made by Philippoff (P4). The problem of slip at the walls of rotational viscometers has been discussed by Mooney (M15) and Reiner (R4). Mori and Ototake (M17) presented the equations for calculation of the physical constants of Bingham-plastic materials from the relationship between an applied force and the rate of elongation of a rod of such a fluid. ... 

The type of chosen polymer and additives most strongly influences the rheological and processing properties of plastisols. Plastisols are normally prepared from emulsion and suspension PVC which differ by their molecular masses (by the Fickentcher constant), dimensions and porosity of particles. Dimensions and shape of particles are important not only due to the well-known properties of dispersed systems (given by the formulas of Einstein, Mooney, Kronecker, etc.), but also due to the fact that these factors (in view of the small viscosity of plasticizer as a composite matrix ) influence strongly the sedimental stability of the system. The joint solution of the equations of sedimentation (precipitation) of particles by the action of gravity and of thermal motion according to Einstein and Smoluchowski leads 37,39) to the expression for the radius of the particles, r, which can not be precipitated in the dispersed system of an ideal plastisol. This expression has the form ... 

In [31] a correlation is foimd between the Mooney viscosity and the apparent viscosity, obtained by means of a capillary viscometer. The investigations were carried out on both rheometers with 6 types of rubbers, namely NR crepe sheets (natural mbber), SMR-20 (Standard Malaysian Rubber, i.e., type natural rubber), SBR (styrene-butadiene rubber), NBR (acrylonitrile-butadiene rubber), MQ (silicone rubber), HR 268 R (butyl rubber) and their compounds. The following equation was obtained ... 

A correlation was discovered [34] between the Mooney viscosity ML and the torque Mb on a Plasticorder and the corresponding equations for this dependency were derived for rubber compounds based on SBR (styrene-butadiene rubber) containing different types of carbon black and for compounds with one and the same type of carbon black but of different level of filling. 

We add to these set of equations the constitutive equations that relate stresses to strains. One form of constitutive equations for isotropic highly deformable materials is of the generalized Mooney-Rivlin type [2] in which the strain energy density W is expressed in terms of the strain invariants ... 

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