Electrostatic correlations at the Stern layer: Physics or chemistry?

We introduce a minimal free energy describing the interaction of charged groups and counterions including both classical electrostatic and specific interactions. The predictions of the model are compared against the standard model for describing ions next to charged interfaces, consisting of Poisson–Boltzmann theory with additional constants describing ion binding, which are specific to the counterion and the interfacial charge (“chemical binding”). It is shown that the “chemical” model can be appropriately described by an underlying “physical” model over several decades in concentration, but the extracted binding constants are not uniquely defined, as they differ depending on the particular observable quantity being studied. It is also shown that electrostatic correlations for divalent (or higher valence) ions enhance the surface charge by increasing deprotonation, an effect not properly accounted within chemical models. The charged phospholipid phosphatidylserine is analyzed as a concrete example with good agreement with experimental results. We conclude with a detailed discussion on the limitations of chemical or physical models for describing the rich phenomenology of charged interfaces in aqueous media and its relevance to different systems with a particular emphasis on phospholipids

Dynamics and Instabilities of Defects in Two-Dimensional Crystals on Curved Backgrounds

Point defects are ubiquitous in two dimensional crystals and play a fundamental role in determining their mechanical and thermodynamical properties. When crystals are formed on a curved background, finite length grain boundaries (scars) are generally needed to stabilize the crystal. We provide a continuum elasticity analysis of defect dynamics in curved crystals. By exploiting the fact that any point defect can be obtained as an appropriate combination of disclinations, we provide an analytical determination of the elastic spring constants of dislocations within scars and compare them with existing experimental measurements from optical microscopy. We further show that vacancies and interstitials, which are stable defects in flat crystals, are generally unstable in curved geometries. This observation explains why vacancies or interstitials are never found in equilibrium spherical crystals. We finish with some further implications for experiments and future theoretical work.Comment: 9 pages, 11 eps figures, REVTe

The Tubular Phase of Self-Avoiding Anisotropic Crystalline Membranes

We analyze the tubular phase of self-avoiding anisotropic crystalline membranes. A careful analysis using renormalization group arguments together with symmetry requirements motivates the simplest form of the large-distance free energy describing fluctuations of tubular configurations. The non-self-avoiding limit of the model is shown to be exactly solvable. For the full self-avoiding model we compute the critical exponents using an epsilon-expansion about the upper critical embedding dimension for general internal dimension D and embedding dimension d. We then exhibit various methods for reliably extrapolating to the physical point (D=2,d=3). Our most accurate estimates are nu=0.62 for the Flory exponent and zeta=0.80 for the roughness exponent

Monte Carlo Renormalization Group calculation in λϕ34\lambda\phi^4_3

We start by discussing some theoretical issues of renormalization group transformations and Monte Carlo renormalization group technique. A method to compute the anomalous dimension is proposed and investigated. As an application, we find excellent values for critical exponents in $\lambda \phi^4_3$. Some technical questions regarding the hybrid algorithm and strong coupling expansions, used to compute the critical couplings of the canonical surface, are also briefly discussed.Comment: 3 pages, 2 PostScript files. Parallel talk given at Lattice9

New Analytical Results on Anisotropic Membranes

We report on recent progress in understanding the tubular phase of self-avoiding anisotropic membranes. After an introduction to the problem, we sketch the renormalization group arguments and symmetry considerations that lead us to the most plausible fixed point structure of the model. We then employ an epsilon-expansion about the upper critical dimension to extrapolate to the physical interesting 3-dimensional case. The results are $\nu=0.62$ for the Flory exponent and $\zeta=0.80$ for the roughness exponent. Finally we comment on the importance that numerical tests may have to test these predictions.Comment: LATTICE98(surfaces), 3 pages, 2 eps figure

Capping Ligand Vortices as “Atomic Orbitals” in Nanocrystal Self-Assembly

We present a detailed analysis of the interaction between two nanocrystals capped with ligands consisting of hydrocarbon chains by united atom molecular dynamics simulations. We show that the bonding of two nanocrystals is characterized by ligand textures in the form of vortices. These results are generalized to nanocrystals of different types (differing core and ligand sizes) where the structure of the vortices depends on the softness asymmetry. We provide rigorous calculations for the binding free energy, show that these energies are independent of the chemical composition of the cores, and derive analytical formulas for the equilibrium separation. We discuss the implications of our results for the self-assembly of single-component and binary nanoparticle superlattices. Overall, our results show that the structure of the ligands completely determines the bonding of nanocrystals, fully supporting the predictions of the recently proposed Orbifold topological model

Charge Inversion of Divalent Ionic Solutions in Silica Channels

Recent experiments (F.H.J. Van Der Heyden et al., PRL 96, 224502 (2006)) of streaming currents in silica nanochannels with divalent ions report charge inversion, i.e. interfacial charges attracting counterions in excess of their own nominal charge, in conflict with existing theoretical and simulation results. We reveal the mechanism of charge inversion by using all-atomic molecular dynamics simulations. Our results show excellent agreement with experiments, both qualitatively and quantitatively. We further discuss the implications of our study for the general problem of ionic correlations in solutions as well as in regards of the properties of silica-water interfaces.Comment: 5 pages, 5 figure

Potential of mean force for two nanocrystals: Core geometry and size, hydrocarbon unsaturation, and universality with respect to the force field

We present a detailed analysis of the interaction between two nanocrystals capped with ligands consisting of hydrocarbon chains by united atom molecular dynamics simulations. We analyze large cores (up to 10 nm in diameter) and ligands with unsaturated carbon bonds (oleic acid) and we investigate the accuracy of the computed potential of mean force by comparing different force fields. We also analyze the vortices that determine the bonding, including the case of asymmetric nanocrystals, and discuss effects related to the intrinsic anisotropy of the core. Overall our results are in agreement with the predictions of the recently proposed orbifold topological model