Breakup of Universality in the Generalized Spinodal Nucleation Theory

The problem of nucleation near spinodal is revisited. It is shown that the standard scaling argument due to Unger and Klein [Phys. Rev. B 29:2698–2708 (1984)] based on neglecting all but the first two terms of the Taylor expansion of the potential in the free energy functional is only valid below critical dimension. At critical dimension, the nucleating droplet has a bigger amplitude and a smaller spatial extent than predicted by the standard scaling argument. In this case the structure of the droplet is determined in a nontrivial fashion by the next order term in the expansion of the potential. Above critical dimension, the amplitude of the nucleating droplet turns out to be too big to justify expanding the potential in Taylor series, and no universality is to be expected in the shape and size of the droplet. Both at and above critical dimension, however, the free energy barrier remains finite, which indicates that the nucleation rate does not vanish at spinodal as predicted by the standard scaling argument.     

Precise placement of gold nanorods by capillary assembly

Capillary assembly was explored for the precise placement of 25 nm × 70 nm colloidal gold nanorods on prestructured poly(dimethylsiloxane) template surfaces. The concentration of nanorods and cationic surfactant cetyltrimethylammonium bromide (CTAB), the template wettability, and most critically the convective transport of the dispersed nanorods were tuned to study their effect on the resulting assembly yield. It is shown that gold nanorods can be placed into arrayed 120-nm diameter holes, achieving assembly yields as high as 95% when the local concentration of nanorods at the receding contact line is sufficiently high. Regular arrays of gold nanorods have several benefits over randomly deposited nanorod arrangements. Each assembled nanorod resides at a precisely defined location and can easily be found for subsequent characterization or direct utilization in a device. The former is illustrated by collecting scattering spectra from single nanorods and nanorod dimers, followed by subsequent SEM characterization without the need for intricate registration schemes.     

On an Isoperimetric Problem with a Competing Nonlocal Term I: The Planar Case

This paper is concerned with a study of the classical isoperimetric problem modified by an addition of a nonlocal repulsive term. We characterize existence, nonexistence, and radial symmetry of the minimizers as a function of mass in the situation where the nonlocal term is generated by a kernel given by an inverse power of the distance. We prove that minimizers of this problem exist for sufficiently small masses and are given by disks with prescribed mass below a certain threshold when the interfacial term in the energy is dominant. At the same time, we prove that minimizers fail to exist for sufficiently large masses due to the tendency of the low‐energy configuration to split into smaller pieces when the nonlocal term in the energy is dominant. In the latter regime, we also establish linear scaling of energy with mass, suggesting that for large masses low‐energy configurations consist of many roughly equal‐size pieces far apart. In the case of slowly decaying kernels, we give a complete characterization of the minimizers. © 2012 Wiley Periodicals, Inc.     

Non-meanfield deterministic limits in chemical reaction kinetics

A general mechanism is proposed by which small intrinsic fluctuations in a system far from equilibrium can result in nearly deterministic dynamical behaviors which are markedly distinct from those realized in the meanfield limit. The mechanism is demonstrated for the kinetic Monte Carlo version of the Schnakenberg reaction where we identified a scaling limit in which the global deterministic bifurcation picture is fundamentally altered by fluctuations. Numerical simulations of the model are found to be in quantitative agreement with theoretical predictions.     

Platinum(II) Chloride Complexes of Linear Alkyl-bridged 2,2′-Bipyridine/Catechol Ligands

Platinum(II) chloride can selectively be coordinated to the 2,2′-bipyridine moiety of the alkyl bridged sequential catechol/2,2′-bipyridine ligand 1 a-H₂ and of the related ligands 1 a/b-Me₂ and 2 . Reaction of ( 1 b-Me₂ )PtCl₂ with BBr₃ produces the platinum(II) complex ( 1 b-H₂ )PtCl₂ while ether cleavage of the uncoordinated ligand 1 b-Me₂ fails. Under basic conditions ( 1 a-H₂ )PtCl₂ forms polymeric/oligomeric species [( 1 a )Pt]_n besides traces of the dinuclear complex [( 1 a )Pt]₂.