title: Ion multivalence and like-charge polyelectrolyte attraction.
abstract: It is known empirically that multivalent ions generate attractions between like-charged polyelectrolytes, with different valence requirements for different systems. How multivalent must an ion be before it can condense a given polyelectrolyte? Using charge-tunable M13 virus rods and a family of artificial homologous "dumbbell" divalent ions of different sizes, we have constructed a multivalent ion-polyelectrolyte phase diagram, and find an experimentally motivated general criterion for like-charged attraction based on the ion valence, ion size, and the Gouy-Chapman length.
authors.affiliation: Department of Materials Science & Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
authors.forename: John C
authors.initials: JC
authors.lastname: Butler
authors.forename: Thomas
authors.initials: T
authors.lastname: Angelini
authors.forename: Jay X
authors.initials: JX
authors.lastname: Tang
authors.forename: Gerard C L
authors.initials: GC
authors.lastname: Wong
mesh_terms: D000838:Anions / Q000737:chemistry; D017104:Bacteriophage M13 / Q000737:chemistry*; D002413:Cations, Divalent / Q000737:chemistry; D004573:Electrolytes / Q000737:chemistry*; D006863:Hydrogen-Ion Concentration; D012542:Scattering, Radiation; D055672:Static Electricity; D014961:X-Ray Diffraction; D014965:X-Rays
chemical_list: D000838:Anions; D002413:Cations, Divalent; D004573:Electrolytes