Molecular Weight Distribution of Polymers from Rheological Measurements in Dilute Solution

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Abstract
A method for obtaining the molecular weight distribution of linear polymers from rheological measurements in dilute solution is obtained through the use of the normal-coordinate theory of viscoelasticity as modified by Zimm to include hydrodynamic interactions. Equations for the frequency-dependence of viscoelastic properties in dilute solutions are shown to the form Φ (ω) = Σpλp-nf(ωλp-m), where Φ(ω) is a measurable, frequency-dependent viscoelastic property. The summation extends over the set of characteristic values λp, which accounts for the relaxation of various normal modes of motion of the molecule as perturbed by hydrodynamic interaction with the solvent; and f(ωλ1-m) is directly related to the molecular weight distribution through an integral equation λ1−nf(ωλ1−m)= ∫ 0∞K(M,ω)W(M)dM,where W(M) is the weight fraction of molecules in range dM at M and K (M, ω) is a kernel dependent upon the quantity measured. Inversion of the above summation has been accomplished for the particular case of characteristic values which obey the inequality, Σpλp-n<2λ1-n, so that f(ωλ1-m) may be obtained directly from the experimentally measured Φ(ω). W(M) is then obtained from f(ωλ1-m) through a solution of the integral equation.