Phase Separation Driven by a Fluctuating Two-Dimensional Self-Affine Potential Field

We study phase separation in a system of hard-core particles driven by a fluctuating two-dimensional self-affine potential landscape which evolves through Kardar–Parisi–Zhang (KPZ) dynamics. We find that particles tend to cluster together on a length scale which grows in time. The final phase-separated steady state is characterized by an unusual cusp singularity in the scaled correlation function and a broad distribution for the order parameter. Unlike the one-dimensional case studied earlier, the cluster-size distribution is asymmetric between particles and holes, reflecting the broken reflection symmetry of the KPZ dynamics, and has a contribution from an infinite cluster in addition to a power law part. A study of the surface in terms of coarse-grained depth variables helps understand many of these features.     

Effect of disorder on relaxation in the one-dimensional Glauber model

We study the long-time relaxation of magnetization in a disordered linear chain of Ising spins from an initially aligned state. The coupling constants are ferromagnetic and nearest-neighbor only, taking valuesJ ₀ andJ ₁ with probabilitiesp and 1–p, respectively. The time evolution of the system is governed by the Glauber master equation. It is shown that for large timest, the magnetizationM(t) varies as [exp(–₀ t](t), where ₀ is a function of the stronger bond strengthJ ₀ only, and (t) decreases slower than an exponential. For very long times, we find that ln (t) varies as –t ^1/3. For low enough temperatures, there is an intermediate time regime when ln (t) varies as –t ^1/2. The results can be extended to more general probability distributions of ferromagnetic coupling constants, assuming thatM(t) can only increase if any bond in the chain is strengthened. If the coupling constants have a continuous distribution in which the probability density varies as a power law near some maximum valueJ ₀, we find that ln (t) varies as –t ^1/3(lnt)^2/3 for large times.     

Dimethylthiocarbamate (DMTC): an alcohol protecting group

Dimethylthiocarbamates (DMTCs), prepared from the corresponding alcohols using commercial dimethylthiocarbamoyl chloride, are spectrally simple, achiral, and nonpolar. DMTCs are moderately to highly stable to a wide range of reagents and conditions including metal hydrides, hydroboration, ylides, NaOH, HCl, organolithiums, Grignards, DDQ, PCC, Swern, n-Bu(4)NF, CrCl(2), heat, and Lewis acids. They are readily removed by NaIO(4) or H(2)O(2) in the presence of other common alcohol protecting groups. [structure: see text]     

Strong phase separation in a model of sedimenting lattices

We study the steady state resulting from instabilities in crystals driven through a dissipative medium, for instance, a colloidal crystal which is steadily sedimenting through a viscous fluid. The problem involves two coupled fields, the density and the tilt; the latter describes the orientation of the mass tensor with respect to the driving field. We map the problem to a one-dimensional lattice model with two coupled species of spins evolving through conserved dynamics. In the steady state of this model each of the two species shows macroscopic phase separation. This phase separation is robust and survives at all temperatures or noise levels- hence the term strong phase separation. This sort of phase separation can be understood in terms of barriers to remixing which grow with system size and result in a logarithmically slow approach to the steady state. In a particular symmetric limit, it is shown that the condition of detailed balance holds with a Hamiltonian which has infinite-ranged interactions, even though the initial model has only local dynamics. The long-ranged character of the interactions is responsible for phase separation, and for the fact that it persists at all temperatures. Possible experimental tests of the phenomenon are discussed.     

Modulated phases in the Falicov-Kimball model

The arrangement of localized f electrons in the ground state of the Falicov-Kimball model is studied as a function of the energy of the f-level. For the half-filled case in one dimension, perturbation theory in the d-electron bandwidth together with numerical results reveals a sequence of transitions between long-period modulated arrangements of the f electrons. Results suggest the existence of a multiphase point at zero d-band-width and f energy, and a complete devil's staircase for the variation of f occupation as the energy of the f-level is changed when the d-bandwidth is nonzero.     

Deposition and evaporation ofk-mers: Dynamics of a many-state system

When the dynamics of a system partitions the phase space of configurations into very many disjoint sectors, we are faced with an assignment problem: Given a configuration, how can we tell which sector it belongs to? We study this problem in connection with the dynamics of deposition and evaporation ofk particles at a time, from a lattice substrate. Fork ≥ 3, the system shows complex behaviour: (a) The number of disjoint sectors in phase space grows exponentially with the size. (b) The asymptotic time dependence of the autocorrelation function shows slow decays, with power laws which depend on the sector. Both (a) and (b) are explained in terms of a nonlocal construct known as the irreducible string (IS), formed from a particle configuration by applying a deletion algorithm. The IS provides a label for sectors; the multiplicity of possible IS’s accounts for (a), and let us determine sector numbers and sizes. The elements of the IS are conserved; thus their motion is responsible for the slow modes of the system, and accounts for (b) as well.     

Fe(0)-mediated synthesis of tri- and tetra-substituted olefins from carbonyls: an environmentally friendly alternative to Cr(II)

Fe(0) was investigated as a cost-effective, environmentally friendly alternative to Cr(II) for the olefination of carbonyls by activated polyhalides. In many instances, Fe(0) was equivalent or superior to Cr(II). Notably, Fe(0), but not Cr(II), proved compatible with a wide range of functionality, inter alia, unprotected phenol, aryl nitro, carboxylic acid, and alkyl nitrile. A surprising reversal of stereoselectivity for aldehydes versus ketones was observed using both metals. The resultant alpha-halo-alpha,beta-unsaturated or alpha,beta-unsaturated carboxylic acids, esters, and nitriles are common structural elements in numerous compounds of interest as well as key intermediates in the preparation of other functionality.