Concentration Dependence of the Viscosity and Viscoelasticity of Polymer Solutions: Application of the Theory of Muthukumar and Freed

Abstract

Recently, Muthukumar and Freed have proposed a theory for the concentration dependence of several viscoelastic properties of polymer solutions. Using data taken from monodisperse solutions of T2 DNA, we have made some tests of the theory. We have found that their theory correctly predicts the concentration dependence of the primary relaxation time. The Huggins constant which can be calculated from their theory is also in good agreement with available experimental data on these solutions. If, in addition, we adopt the simple phenomenological model of Klotz and Zimm which relates creep-recovery parameters to relaxation times, we can make predictions about the concentration dependence of retardation times and recoils. Although some of these predictions are less reliable, nevertheless the corrections are all in the right direction, and the theoretically predicted slopes of the linear concentration dependences are all within a factor of 2 of the experimental values. Much previous attention has been given to relaxation times of polymer solutions. When extrapolated to zero concentration, these can be used to determine polymer molecular weights, based on the beads-springs theory of polymer dynamics.lS2 One application has been the mea- surement of molecular weights of very large DNA mole- cules from relaxation and retardation times.= Much less attention has been given to the concentration dependence, at low concentration, of these relaxation times, in part because of the formidable difficulties in dealing with the theory for a concentration-dependent hydrodynamic in- teraction. However, recently Muthukumar and Freed' have proposed such a theory (hereafter referred to as MF) of the first-order concentration dependence of the viscosity and viscoelastic parameters. Here we present a range of data, all taken on highly monodisperse solution^^^^ of DNA molecules from bacteriophage T2, which show quite good agreement with their theory. We have not done an ex- tensive test of their theory. However we show that their value of the Huggins constant is correct, as is the slope, A, of the concentration dependence of the primary relax- ation time. They predict A to be linearly dependent upon intrinsic viscosity, and we show indirect evidence which agrees with this. Combining the MF theory with a per- turbation theory of Klotz and Zimm,E which relates creep-recovery dynamics to relaxation times, we can also make predictions about the concentration dependence of creep-recovery parameters such as the retardation times and primary recoil. Relaxation Times The theory of Muthukumar and Freed' predicts that the first-order concentration dependence of the individual relaxation times will be