Dynamics of Circular Macromolecules: Evidence of Rubber-like Behavior at High Z-numbers*

It is "known" that macromolecular rings of modest molecular weight show no rubbery plateau.  It is also known that addition of relatively small amounts of linear chain can lead to the development of a rubbery plateau, but one that is lower than that of the linear counterpart.  In the present work, we explore this phenomenon in two series of experiments.  First we examine solutions of mixtures of circular DNA with the linear analog to investigate the rubbery plateau and viscosity behavior.  In this case, while the DNA is a very large molecule, the value of Z_w varies from 2.6 to 8.4.  We find that the rubbery plateau G_N⁰ varies with linear chain content in a fashion similar to that reported in the synthetic polymer literature.  At the same time, we also find a very large viscosity enhancement relative to the pure linear material for blends of 15% and 50% linear chains in the rings, the enhancements being greater than found in synthetic polymer investigations, thus suggesting that linear chain threading has a different impact on the rubbery response and the dynamics themselves.  Second, we examine the behavior of circular poly(3,6-dioxa-1,8-octanedithiol) (polyDODT) synthesized by reversible radical recombination polymerization (R3P) that has molecular weights M_w from approximately 43 kg/mol to over 550 kg/mol, which corresponds to an entanglement number Z_w from approximately 23 to over 300 if the chains were linear.  We find that these systems exhibit a G_N⁰ that is the same as that of the linear counterpart.  However, upon diluting the systems to control the value of Z_w, that G_N⁰ scales similarly to the linear polymer except that the plateau disappears for Z_w<15, i.e., a much higher nominal entanglement number.  We also find that the circular macromolecules, below a critical value of Z_w follow the same linear dependence of viscosity on Z_w as do Rouse-like linear chains, but to much higher values of Z_w. Furthermore, when the value of Z_w exceeds 15 in the rings, the viscosity follows Z_w^5.8 whereas in the linear chains the viscosity turns to a Z_w^3.4 power dependence at approximately Z_w=2.