Debye-Bueche expression

Equation (2.61) predicts a 3.5-power dependence of viscosity on molecular weight, amazingly close to the observed 3.4-power dependence. In this respect the model is a success. Unfortunately, there are other mechanical properties of highly entangled molecules in which the agreement between the Bueche theory and experiment are less satisfactory. Since we have not established the basis for these other criteria, we shall not go into specific details. It is informative to recognize that Eq. (2.61) contains many of the same factors as Eq. (2.56), the Debye expression for viscosity, which we symbolize t . If we factor the Bueche expression so as to separate the Debye terms, we obtain... 

Laser fight scattering was described by one of us (2) for measuring the phase structure of an MBAS plastic as a function of graft rubber concentration. The data were analyzed with the Debye-Bueche expression (I, 2)... 

The Debye-Bueche theory, on the other hand, considers the partially draining coil as a sphere that is more or less permeable, within which a number of smaller beads is homogeneously distributed. The beads correspond to the monomeric units. The drag which one bead produces on the others is calculated, and this resistance is then expressed in terms of a length L, which corresponds to the distance from the surface of the sphere to where the flow rate of the solvent is reduced to 1 /e times what it is at the surface of this sphere. The shielding ratio, or shielding factor, is given by... 

Equation 4.130 is the usual form of the Debye-Bueche equation. This equation generally describes the scattering from a spherically symmetrical system provided a suitable expression can be found for the correlation function. For many systems, an exponential correlation... 

Debye and Bueche (1960) have employed Einstein s (1910) expression for the turbidity of a two-component solution to calculate the turbidity of a monomolecular polymer solution over the whole concentration range (c in g/cm ) (sec Equations 2.1- 32, 2.4-7,-2d)... 

The extremely simple expressions for intrinsic viscosity at zero gradient and sedimentation coefficient containing in the denominator the square root of molecular weight agree very well with experimental data of theta solutions in the whole range from fully drained to impermeable coil. They turned out to be very good approximations of the more complicated expressions derived by Kirkwood-Riseman and Debye-Bueche ° and hence were used for the calculation of intrinsic viscosity of polydisperse samples. 

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