Effect of finite number of segments on flow birefringence extinction angle and the determination of internal viscosity and chain relaxation time

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The effect of restriction to a finite number of segments in modeling a flexible macromolecule by a linear Gaussian chain is considered. This model with an internal viscosity included has been used byCerf to develop the behavior of the extinction angle in flow birefringence. The consequences of restriction to a finite number of segments together with variable internal hydrodynamic interaction are determined with respect to the behavior of the extinction angle at low flow gradients and the characteristic chain relaxation times. The theoretical behavior of the extinction angle is shown to depend uniquely on the product of the longest characteristic relaxation time and the flowgradient. The relations between both extinction angle and intrinsic viscosity and the longest relaxation time is dependent upon both number of segments and hydrodynamic interaction. Also the relation given byCerf between gradient dependence of extinction angle and internal viscosity is dependent on both number of segments and hydrodynamic interaction. Results are given for a number of segments ranging from 1 to 1000 and for hydrodynamic interaction ranging from the free draining condition to an extreme nonfree draining condition.