Effect of Internal Viscosity on the Deformation of a Linear Macromolecule in a Sheared Solution

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Abstract
The deformation of macromolecules in a solution subjected to time‐dependent shear flow is described by means of a modified Rouse model. Into every segment of this model an internal viscosity force is introduced which is proportional to the rate at which the end‐to‐end distance of the segment is changed, and acts in the direction of the tie line between the end points. No a priori assumptions have been made on the motion of the segments themselves. An analytical solution for the distribution function of the segment lengths can now no longer be derived. At low values of the internal viscosity, an approximate solution can be obtained by means of a perturbation calculus. The effect of internal viscosity on the moments of the distribution function and, hence, on the average dimensions of the macromolecules, can be calculated. It appears that with constant shear flow at high rates of shear, as well as with oscillatory shear at high frequencies, an increase of the internal viscosity results in a decrease of the average deformation of the molecules. The flow birefringence at high shear rates decreases as the internal viscosity increases, whereas the optical extinction angle is hardly influenced by it. In the literature there is no unanimity on the relation between the deformation of the molecules and the shear stress; in the present study we use the formula of Kirkwood and Riseman. In the case of constant shear flow, the apparent viscosity of the solution decreases with increasing rates of shear. With oscillatory shear flow the internal viscosity leads to a finite limiting value of the dynamic viscosity at high frequencies, and this value should increase when a constant shear rate is superimposed on the oscillatory shear rate. This theoretical prediction conflicts with experimental data.