Strategy to design aqueous-soluble iron-oxide molecular cluster and nanostructure using polyoxometalate ligand scaffold

Profound availability of iron on earth crust and diversely accessible redox states, makes it a significant metal ion in biology as well as to design molecular catalysts and nanostructured materials. Low-oxidation potential and prone to hydrolysis in an aqueous medium, predominantly in neutral to basic pH, of the divalent iron in the active site of the catalysts, results in the formation of bulk and/or colloidal ferric-hydroxide, oxy-hydroxide, and -oxide. However, nature has developed its own strategy to preserve iron-oxide cluster core, e.g., Ferritin, without aggregation in physiological pH via designing protein scaffold as protector ligand. Although molecular iron-oxo clusters, isolated by using small organic ligands, are depicted as potent catalysts, they usually don't sustain under catalytic turnover condition. In this context, the isolation of multinuclear iron-oxo clusters soluble in water and their subsequent catalysis in the aqueous phase remains a perdurable challenge. Polyoxometalates (POM) are themselves small metal-oxo cluster anions where the metals are in the highest valent-state and a diverse POM structure can be obtained simply by varying the metal ions. Depending on the structure of the POM, the available terminal or bridging oxo groups can act as donor atoms to one or more iron centers. Consequently, a variety of iron clusters can be stabilized by using POM scaffold. Thereby, polyoxoanions, extremely aqueous-soluble and oxidatively inert under reaction conditions, behaved as versatile ligand platform to stabilize iron clusters of different nuclearity (n = 2–30) in water. Moreover, different possible structures and diversity in chemical property by varying hetero atoms or metal ions led to the isolation of a unique aqueous soluble iron-oxide and/or iron-oxy-hydroxide nanostructure where a significant number of polyoxoanions were covalently attached, making them extremely soluble nanostructures. This review summarizes the adapted synthetic strategies to isolate such molecular and nano-scopic iron clusters stabilized by POM anions and describes their stability in an aqueous medium and showcases their prospective applications in different emerging areas.     

Kinetics and mechanism of the reaction of hydroxopentaaquarhodium(III) ion with <Emphasis Type="SmallCaps">l</Emphasis>-Arginine in aqueous solution

The kinetics of the aqua ligand substitution from hydroxopentaaquarhodium(III) ion, [Rh(H₂O)₅(OH)]²⁺, by l-Arginine has been studied spectrophotometrically as a function of Arginine concentration, and temperature, at pH 4.3. The reaction proceeds via a rapid outer sphere association complex formation step followed by two consecutive steps. The first of these involves ligand-assisted anation, while the second involves chelation as the second aqua ligand is displaced. The association equilibrium constant for the outer sphere complex formation has been evaluated together with the rate constants for the two subsequent steps. The activation parameters for both steps have been evaluated using Eyring’s equation. Thermodynamic parameters calculated from the temperature dependence of the outer sphere association equilibrium constants are also consistent with an associative mode of activation. The product of the reaction has been characterized by conductivity measurement and IR spectroscopic analysis.     

Effect of solvents having different dielectric constants on reactivity: A conceptual DFT approach

Conceptual density functional theory is exploited to understand the reactivity in a medium of solvents with increasing dielectric constants. Aprotic as well as protic solvents are used for this study. It is found that the global parameters, such as chemical potential and hardness, decrease from gas phase to solvent phase with increasing dielectric constant. However, it is observed that the Fukui functions of the reactive atoms increase significantly with the dielectric constants of the aprotic solvents while for the protic solvents the variation of the reactivity indices is insignificant. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Central limit theorem for first-passage percolation time across thin cylinders

We prove that first-passage percolation times across thin cylinders of the form [0, n] × [?h _n , h _n ] ^d-1 obey Gaussian central limit theorems as long as h _n grows slower than n ^1/(d+1). It is an open question as to what is the fastest that h _n can grow so that a Gaussian CLT still holds. Under the natural but unproven assumption about existence of fluctuation and transversal exponents, and strict convexity of the limiting shape in the direction of (1, 0, . . . , 0), we prove that in dimensions 2 and 3 the CLT holds all the way up to the height of the unrestricted geodesic. We also provide some numerical evidence in support of the conjecture in dimension 2.     

Exact diffusion constant of a one-dimensional asymmetric exclusion model with open boundaries

For the 1D fully asymmetric exclusion model with open boundary conditions, we calculate exactly the fluctuations of the current of particles. The method used is an extension of a matrix technique developed recently to describe the equatime steady-state properties for open boundary conditions and the diffusion constant for particles on a ring. We show how the fluctuations of the current are related to non-equal-time correlations. In the thermodynamic limit, our results agree with recent results of Ferrari and Fontes obtained by working directly in the infinite system. We also show that the fluctuations of the current become singular when the system undergoes a phase transition with discontinuities along the first-order transition line.     

Central Limit Theorem for the Free Energy of the Random Field Ising Model

A central limit theorem is proved for the free energy of the random field Ising model with all plus or all minus boundary condition, at any temperature (including zero temperature) and any dimension. This solves a problem posed by Wehr and Aizenman (J Stat Phys 60:287–306, 1990). The proof uses a variant of Stein’s method.