Molecular network theory

Lodge,A.S. Constitutive equations from molecular network theories for polymer solutions. Rheol. Acta 7,379-392 (1968). 

Carreau,P.J. Rheological equations from molecular network theories. Trans. Soc. Rheol. 16,99-127 (1972). 

P. J. Carreau, Rheological Equations from Molecular Network Theories, Ph.D. thesis, University of Wisconsin, Madison, WI, 1968. 

None of the molecular network theories thus far discussed, however, is capable of predicting the course of the orientation of the crystallites which form the junction points of the network. It is only known from experiment (see p. 624) that the orientation of the crystallites runs ahead of that of the non crystalline gel component. From a large experimental material covering cellulose gels of various swelling degree and of different preparation, it was found that there seems to be a uniform relation between the optical orientation factor and that derived from X-rays holding for all cases. This relation, which may be of value, for future theoretical considerations, is shown in Fig. 102. 

Carreau, P.J. (1972) Rheological equation from molecular network theories. Thans. Soc. Rhedl., 16 (1), 99-127. 

Carreau, P. J. "Rheological Equations from Molecular Network Theories", Transactions of the Society of Rheology, 16 1, (1972), 99-127. 

For finite strains, however, several measures of strain are available, and each of these reduces to the same quantity in the limit of infinitesimal strains. The situation is therefore similar to the one encountered previously in connection with the multiplicity of time derivatives for the stress. The simplest molecular network theories o) suggest the use of the so-called Finger measure of strain, and the resulting equation is called the Lodge rubberlike liquid. Not surprisingly, one finds(9,8i) that, with the use of the Finger strain measure, Eq. (31) is mathematically the same as Eq. (26). 

An early development of the simple molecular network theory is the so-called inverse Langevin approximation for the probability distribution. The Gaussian approximation is... 

Carreau, J.P. Rheological Equations from Molecular Network Theories, Trans., Soc. of Rheology (1972) 16 1, 99-127. 

Meister, B. J., An integral constitutive equation based on molecular network theory, Trans. Soc. Rheol., 15, 63-89 (1971). 

As a matter of fact, by combining the molecular network theory and the tube model, Meister (1989) advanced an idea to predict a gradual transition from 3.4-power to 3.0-power dependence of r] on M as M/M ratio increases. Specifically, Meister obtained an expression for a 3.5-power dependence of jjq on... 

Carreau PJ (1968). Rheological Equation from Molecular Network Theory, Doctoral Dissertation, University of Wisconsin, Madison, Wisconsin. 

The film thickness for the ordinary shear-thinning response of lubricants which can be measured is now calculated. There are many generalized Newtonian fluid models that will describe the shear response displayed in Figures 1 and 2 [16]. The Ree-Eyring model utilizes a series in inverse hyperbolic sine to approximate power-law behavior at high shear rate. In others [16] the power-law exponent, , appears explicitly. Today the most widely used model outside of tribology is the Carreau equation [17] that was advanced to describe the results of molecular network theory. 

Lodge, A. S., Constitutive Equations from Molecular Network Theories for Polymer... 

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