Normal Modes of Branched Polymers. I. Simple Ring and Star-Shaped Molecules

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Abstract
A molecular theory is developed to calculate the viscoelastic properties of free‐draining branched or cyclic macromolecules in concentrated solution or in bulk. The approach taken is that of the normal‐coordinate method of Rouse, together with a procedure which involves transformation of crosslinked chains into mechanically equivalent decoupled chains. This method simplifies the calculation of relaxation times. Application of the decoupling procedure to symmetric star‐shaped, irregular star‐shaped, and cyclic macromolecules permits a rigorous calculation of the viscoelastic properties. Examples of the viscoelastic behavior are given in the form of the steady‐state zero shear rate viscosity, the steady‐state shear compliance, and the viscoelastic spectra. The excellent agreement between the results obtained presently and those obtained by other methods confirms the validity of the decoupling process for the general case.

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