| Counterion behavior controls interactions between charged surfaces in aqueous environments, and can cause attraction between like charged objects. Mean field approaches to describing counterion behavior, such as the Poisson-Boltzmann formalism and Manning condensation theory, predict that charged surfaces are renormalized by a surrounding counterion cloud or condensed counterion layer, but such mean field approaches never predict an attraction. However, a large number of theoretical studies have shown that by accounting for counterion correlations, attractive forces between like charged objects can be predicted. In this work we present the first observations of counterion correlations in charged polymer systems. At the ∼60 A scale, we used small angle x-ray scattering to observe that the counterions in F-actin bundles adopt a periodic distribution, forming a one-dimensional charge density wave. At the ∼5 A scale, we used high-resolution inelastic x-ray scattering to observe inter-ion correlations. From the dissipative dynamics of an unexpected acoustic phonon-mode associated with the counterions, we show that the counterions behave as a dense hard-sphere fluid and obtain an inter-ion distance which can be controlled by changing ion number density within the bundles. Finally, we show how counterion behavior impinges on bundles of specifically linked protein filaments, and observe an architectural polymorphism which can be controlled by monovalent salt concentration. |
