Counterion Condensation and Fluctuation-Induced Attraction

We consider an overall neutral system consisting of two similarly charged plates and their oppositely charged counterions and analyze the electrostatic interaction between the two surfaces beyond the mean-field Poisson-Boltzmann approximation. Our physical picture is based on the fluctuation-driven counterion condensation model, in which a fraction of the counterions is allowed to ``condense'' onto the charged plates. In addition, an expression for the pressure is derived, which includes fluctuation contributions of the whole system. We find that for sufficiently high surface charges, the distance at which the attraction, arising from charge fluctuations, starts to dominate can be large compared to the Gouy-Chapmann length. We also demonstrate that depending on the valency, the system may exhibit a novel first-order binding transition at short distances.Comment: 15 pages, 8 figures, to appear in PR

Sample-to-sample torque fluctuations in a system of coaxial randomly charged surfaces

Polarizable randomly charged dielectric objects have been recently shown to exhibit long-range lateral and normal interaction forces even when they are effectively net neutral. These forces stem from an interplay between the quenched statistics of random charges and the induced dielectric image charges. This type of interaction has recently been evoked to interpret measurements of Casimir forces in vacuo, where a precise analysis of such disorder-induced effects appears to be necessary. Here we consider the torque acting on a randomly charged dielectric surface (or a sphere) mounted on a central axle next to another randomly charged surface and show that although the resultant mean torque is zero, its sample-to-sample fluctuation exhibits a long-range behavior with the separation distance between the juxtaposed surfaces and that, in particular, its root-mean-square value scales with the total area of the surfaces. Therefore, the disorder-induced torque between two randomly charged surfaces is expected to be much more pronounced than the disorder-induced lateral force and may provide an effective way to determine possible disorder effects in experiments, in a manner that is independent of the usual normal force measurement.Comment: 7 pages, 3 fig

Partially Annealed Disorder and Collapse of Like-Charged Macroions

Charged systems with partially annealed charge disorder are investigated using field-theoretic and replica methods. Charge disorder is assumed to be confined to macroion surfaces surrounded by a cloud of mobile neutralizing counterions in an aqueous solvent. A general formalism is developed by assuming that the disorder is partially annealed (with purely annealed and purely quenched disorder included as special cases), i.e., we assume in general that the disorder undergoes a slow dynamics relative to fast-relaxing counterions making it possible thus to study the stationary-state properties of the system using methods similar to those available in equilibrium statistical mechanics. By focusing on the specific case of two planar surfaces of equal mean surface charge and disorder variance, it is shown that partial annealing of the quenched disorder leads to renormalization of the mean surface charge density and thus a reduction of the inter-plate repulsion on the mean-field or weak-coupling level. In the strong-coupling limit, charge disorder induces a long-range attraction resulting in a continuous disorder-driven collapse transition for the two surfaces as the disorder variance exceeds a threshold value. Disorder annealing further enhances the attraction and, in the limit of low screening, leads to a global attractive instability in the system.Comment: 21 pages, 2 figure

Phase behavior and selectivity of DNA-linked nanoparticle assemblies

We propose a model that can account for the experimentally observed phase behavior of DNA-nanoparticle assemblies [R. Jin et al., J. Am. Chem. Soc. 125, 1643 (2003); T. A. Taton et al., Science 289, 1757 (2000)]. The binding of DNA-coated nanoparticles by dissolved DNA linkers can be described by exploiting an analogy with quantum particles obeying fractional statistics. In accordance with experimental findings, we predict that the phase-separation temperature of the nanocolloids increases with the DNA coverage of the colloidal surface. Upon the addition of salt, the demixing temperature increases logarithmically with the salt concentration. Our analysis suggests an experimental strategy to map microscopic DNA sequences onto the macroscopic phase behavior of the DNA-nanoparticle solutions. Such an approach should enhance the efficiency of methods to detect (single) mutations in specific DNA sequences

Surface and bulk dissolution properties, and selectivity of DNA-linked nanoparticle assemblies

Using a simple mean-field model, we analyze the surface and bulk dissolution properties of DNA-linked nanoparticle assemblies. We find that the dissolution temperature and the sharpness of the dissolution profiles increase with the grafting density of the single-stranded DNA "probes" on the surface of colloids. The surface grafting density is controlled by the linker occupation number, in analogy with quantum particles obeying fractional statistics. The dissolution temperature increases logarithmically with the salt concentration. This is in agreement with the experimental findings [R. Jin, G. Wu, Z. Li, C. A. Mirkin, and G. C. Schatz, J. Am. Chem. Soc. 125, 1643 (2003)]. By exploiting the unique phase behavior of DNA-coated colloids, it should be possible to detect multiple "targets" in a single experiment by essentially mapping the DNA base-pair sequence onto the phase behavior of DNA-linked nanoparticle solution

Designing ordered DNA-linked nanoparticle assemblies

We present a model study of a multi-component system that can form low-symmetry ordered phases, even though all pair interactions between the constituent particles are spherically symmetric. Using Monte Carlo simulations and a mean-field model we investigate the thermodynamic, structural, and kinetic aspects of the formation of stripe phases for a simple, multi-component lattice model. This lattice model was chosen to represent a mixture of spherically symmetric DNA-coated colloids with several species of DNA linkers. We predict that the optimal strategy to design a specific low-symmetry phase is the one which not only provides the weakest strength of competitive binding, but also leads to the 'staged' ordering of nanoparticle superstructures