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

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

Calculation of Critical Nucleation Rates by the Persistent Embryo Method: Application to Quasi Hard Sphere Models

We study crystal nucleation of the Weeks-Chandler-Andersen (WCA) model, using the recently introduced Persistent Embryo Method (PEM). The method provides detailed characterization of pre-critical, critical and post-critical nuclei, as well as nucleation rates that compare favorably with those obtained using other methods (umbrella sampling, forward flux sampling or seeding). We further map our results to a hard sphere model allowing to compare with other existing predictions. Implications for experiments are also discussed.Comment: 27 pages, 11 figure

Nanocrystal Programmable Assembly Beyond Hard Spheres (or Shapes) and Other (Simple) Potentials

Ligands are the key to almost any strategy in the assembly of programmable nanocrystals (or nanoparticles) and must be accurately considered in any predictive model. Hard Spheres (or Shapes) provide the simplest and yet quite successful approach to assembly, with remarkable sophisticated predictions verified in experiments. There are, however, many situations where hard spheres/shapes predictions fail. This prompts three important questions: {\em In what situations should hard spheres/shapes models be expected to work?} and when they do not work, {\em Is there a general model that successfully corrects hard sphere/shape predictions?} and given other successful models where ligands are included explicitly, and of course, numerical simulations, {\em can we unify hard sphere/shape models, explicit ligand models and all atom simulations?}. The Orbifold Topological Model (OTM) provides a positive answer to these three questions. In this paper, I give a detailed review of OTM, describing the concept of ligand vortices and how it leads to spontaneous valence and nanoparticle "eigenshapes" while providing a prediction of the lattice structure, without fitting parameters, which accounts for many body effects not captured in (two-body) potentials. I present a thorough survey of experiments and simulations and show that, to this date, they are in full agreement with the OTM predictions. I will conclude with a discussion on whether NC superlattices are equilibrium structures and some significant challenges in structure prediction.Comment: 63 pages 27 figures, Accepted to Current Opinions in Solid State and Materials Scienc

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

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

Monovalent counterion distributions at highly charged water interfaces: Proton-transfer and Poisson-Boltzmann theory

Surface sensitive synchrotron-X-ray scattering studies reveal the distributions of monovalent ions next to highly charged interfaces. A lipid phosphate (dihexadecyl hydrogen-phosphate) was spread as a monolayer at the air-water interface, containing CsI at various concentrations. Using anomalous reflectivity off and at the $L_3$ Cs$^+$ resonance, we provide, for the first time, spatial counterion distributions (Cs$^+$) next to the negatively charged interface over a wide range of ionic concentrations. We argue that at low salt concentrations and for pure water the enhanced concentration of hydroniums H$_3$O$^+$ at the interface leads to proton-transfer back to the phosphate group by a high contact-potential, whereas high salt concentrations lower the contact-potential resulting in proton-release and increased surface charge-density. The experimental ionic distributions are in excellent agreement with a renormalized-surface-charge Poisson-Boltzmann theory without fitting parameters or additional assumptions