Curtiss-Bird theory

The reptation theory of viscoelasticity developed by Doi Edvards has paractically predetermined the appearance of Curtiss-Bird s reptation theory55). The latter is constructed on the basis of general kinetic theory of polymer fluids in phase space. According to the Curtiss-Bird theory, the longitudinal viscosity may increase only by a factor of two compared to the initial value. Note that a more significant increase in longitudinal viscosity was observed in experiments. 

The Curtiss-Bird theory for concentrated systems is structured quite differently, taking as the starting point the general phase-space formalism as shown in Figure 8. The polymer molecule is modeled throughout as a Kramers chain, and the restricted motion of the molecule is described by means of an anisotropic Stokes law expression for the links and an anisotropic Brownian motion. Despite the great differences between the Doi-Edwards and Curtiss-Bird theories, some of the key results are very similar. For example, both theories lead to a diffusion equation for a segment of the polymer chain as follows ... 

Figure 14 Data on rjiy) and 1(7) for 7% solutions of poly(a-methylstyrene) in Kanechlor (by H. Endo, T. Fujimoto and M. Nagasawa, J. Polym. Sci. Part 1971,2, 345) and Curtiss-Bird theory curves computed by H. H. Saab (see ref. 152). The values of rjQ (in Pa s), /, and N are shown and e= provides a good fit for the data...

The Curtiss-Bird theory has been extended to include polydispersity effects extensive data comparisons for the steady-state shear compliance and various nonlinear rheological properties further support the inclusion of the link-tension coefficient in the theory. 

In addition to the Curtiss-Bird theory for Kramers bead-rod chains, a simpler theory for FENE dumbbells has also been worked out and compared with experimental data. The simplicity of this model enables one to see the structure of the theory without the mathematical complications. 

Hirschfelder, Curtis Bird (1954) J.O. Hirschfelder, C.F. Curtis R.B. Bird, "Molecular Theory of Gases and Liquids , Wiley, NY (1954)... 

J. O. Hirschfelder, C. F. Curtis, and R. B. Bird, Molecular Theory of Gases and Eiquids,]ohxi Wiley Sons, Inc., New York, 1954. 

Hirschfelder, J. G., Curtis, C. F. and Bird, R. B., Molecular Theory of Gases and Liquids, John Wiley Sons, New York, (1954). 

Maryott, A. A., and Buckley, E, U. S. National Bureau of Standards Circular No. 537, 1953. A tabulation of dipole moments, dielectric constants, and molar refractions measured between 1910 and 1952, and used here to determine polarizabilities if no more recent result exists. The polarizability is 3/(4ttA/ ) times the molar polarization or molar refraction, where is Avogadros number. The value 3/(4tiA/ ) = 0.3964308 x 10 cm was used for this conversion. A dagger (t) following the reference number in the tables indicates that the polarizability was derived from the molar refraction and hence may not include some low-frequency contributions to the static polarizability these static polarizabilities are therefore low by 1 to 30%. Hirschfelder, J. O., Curtis, C. E, and Bird, R. B., Molecular Theory of Gases and Liquids, Wiley, New York, 1954, p. 950. Fundamental information on molecular polarizabilities. 

Hirschfelder, J.O. Curtis, C.F. Bird, R.B. Molecular Theory of Gases and Liquids John Wiley New York, 1954 1126-1127. 

Hirschfelder,J.O., Curtis,C.R., Bird,R.B. Molecular theory of gases and liquids. New York Wiley 1954. 

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