  Conformation of single polyelectrolytes in tetravalent salt solutions is
investigated under the framework of a coarse-grained model, using Langevin
dynamics simulations. The chain size, studied by the radius of gyration, shows
three different variational behaviors with salt concentration, depending on the
chain stiffness. According to these behaviors, polyelectrolytes of fixed chain
length are classified into three categories: flexible chain, semiflexible
chain, and rigid chain. The worm-like chain model with persistence length
predicted by the Odijk-Skolnick-Fixman theory is found to be able to
qualitatively describe the end-to-end distance at low salt concentration. In a
low-salt region, a flexible polyelectrolyte extends more significantly than a
semiflexible chain, and in a high-salt region, regardless of chain stiffness, a
chain attains a dimension comparable to that of its neutral polymer. The chain
stiffness influences both the local and the global chain structures. A flexible
chain exhibits a zigzagged local structure in the presence of salt ions and the
condensed structure is a disordered, random globule. A semiflexible chain is
locally smooth, and the condensed structure is orderly packed, taking a form
such as hairpin or toroid. Moreover, the chain stiffness can also affect the
nature of the coil-globule transition. The transition is occurred in a discrete
manner for semiflexible chain, whereas in a continuous way for flexible chain.
This discrete feature is happened not only at low salt concentration when a
semiflexible chain is collapsed, but also at high salt concentration when the
collapsed chain is reexpanded. At the end, the effects of chain stiffness and
salt concentration on the conformation of single polyelectrolytes are
summarized in a schematic state diagram.
