The Configuration and Dynamics of Self-Attractive Flexible and Semi-Flexible Polymers

We study ``bead-rod'' chains containing stiff Fraenkel springs with nearly fixed Kuhn length, but with varying numbers of rods representing each Kuhn length, N$_{\mathrm{r,K}}$, modeled by incorporating a bending potential between consecutive rods. We find converged results as we increase the number of rods per Kuhn step. We find that at high $\varepsilon ^{\mathrm{\ast }}$N$_{\mathrm{r,K}}$, where $\varepsilon^{\mathrm{\ast }}$ is the attractive interaction strength per bead normalized by kT, collapsed globules are produced at moderate dimensionless chain diameter $\sigma^{\mathrm{\ast }}=$1/4, while for $\sigma^{\mathrm{\ast }}=$1, helices are formed, and for $\sigma^{\mathrm{\ast }}=$1/16, tori, folded bundles, and finally globules, are formed as $\varepsilon ^{\mathrm{\ast }}$N$_{\mathrm{r,K}}$ increases. Under shear, a universal tumbling state is found where chain width in the shear gradient direction is independent of chain length and proportion to shear rate to the fourth power.