Delocalization Transition in Colloidal Crystals

Sublattice melting is the loss of order of one lattice component in binary or ternary ionic crystals upon increase in temperature. A related transition has been predicted in colloidal crystals. To understand the nature of this transition, we study delocalization in self-assembled, size asymmetric binary colloidal crystals using a generalized molecular dynamics model. Focusing on BCC lattices, we observe a smooth change from localized-to-delocalized interstitial particles for a variety of interaction strengths. Thermodynamic arguments, mainly the absence of a discontinuity in the heat capacity, suggest that the passage from localization-to-delocalization is continuous and not a phase transition. This change is enhanced by lattice vibrations, and the temperature of the onset of delocalization can be tuned by the strength of the interaction between the colloid species. Therefore, the localized and delocalized regimes of the sublattice are dominated by enthalpic and entropic driving forces, respectively. This work sets the stage for future studies of sublattice melting in colloidal systems with different stoichiometries and lattice types, and it provides insights into superionic materials, which have potential for application in energy storage technologies.Comment: Hector Lopez-Rios and Ali Ehlen contributed equall

Metallization of colloidal crystals

Colloidal crystals formed by size-asymmetric binary particles co-assemble into a wide variety of colloidal compounds with lattices akin to ionic crystals. Recently, a transition from a compound phase with a sublattice of small particles to a metal-like phase in which the small particles are delocalized has been predicted computationally and observed experimentally. In this colloidal metallic phase, the small particles roam the crystal maintaining the integrity of the lattice of large particles, as electrons do in metals. A similar transition also occurs in superionic crystals, termed sublattice melting. Here, we use energetic principles and a generalized molecular dynamics model of a binary system of functionalized nanoparticles to analyze the transition to sublattice delocalization in different co-assembled crystal phases as a function of T, number of grafted chains on the small particles, and number ratio between the small and large particles $n_s$:$n_l$. We find that $n_s$:$n_l$ is the primary determinant of crystal type due to energetic interactions and interstitial site filling, while the number of grafted chains per small particle determines the stability of these crystals. We observe first-order sublattice delocalization transitions as T increases, in which the host lattice transforms from low- to high-symmetry crystal structures, including A20 to BCT to BCC, Ad to BCT to BCC, and BCC to BCC/FCC to FCC transitions and lattices. Analogous sublattice transitions driven primarily by lattice vibrations have been seen in some atomic materials exhibiting an insulator-metal transition also referred to as metallization. We also find minima in the lattice vibrations and diffusion coefficient of small particles as a function of $n_s$:$n_l$, indicating enhanced stability of certain crystal structures for $n_s$:$n_l$ values that form compounds.Comment: AE and HL-R contributed equally to this wor

Cancer nurses, are we really contributing to reduce burden via cancer prevention?

From the wisdom of experience and years, our grandparents used to say: 'Prevention is better than cure'. Nurses also want to prevent rather than cure cancer and follow that old said. Cancer is one of the leading causes of mortality in the world and the incidence is expected to keep increasing every year[1]. And while there is an improvement in cancer survival due to developments on treatments; the diagnosis, treatment and survivorship entails a high burden for patients, for communities and for health systems

On the Dirac delta as initial condition for nonlinear Schr\"odinger equations

In this article we will study the initial value problem for some Schr\"odinger equations with Diraclike initial data and therefore with infinite L2 mass, obtaining positive results for subcritical nonlinearities. In the critical case and in one dimension we prove that after some renormalization the corresponding solution has finite energy. This allows us to conclude a stability result in the defocusing setting. These problems are related to the existence of a singular dynamics for Schr\"odinger maps through the so called Hasimoto transformation.Comment: 17 pages, to appear in in AnIHP Ann Non Li