Tailor‐made hybrid nanostructure of poly(ethyl acrylate)/clay by surface‐initiated atom transfer radical polymerization

Hybrid nanoarchitecture of tailor‐made Poly(ethyl acrylate)/clay was prepared by surface‐initiated atom transfer radical polymerization (SI‐ATRP), by tethering ATRP initiator on active hydroxyl group, present in surface as well as in the organic modifier of the clay used. Extensive exfoliation was facilitated by using these initiator modified clay platelets. Poly(ethyl acrylate) chains with controlled polymerization and narrow polydispersities were forced to be grown from within the clay gallery (intergallery) as well as from the outer surface (extragallery) of the clay platelets. The polymer chains attached onto clay surfaces might have the potential to provide the composites with enhanced compatibility in blends with common polymers. Attachment of the initiator on clay platelets was confirmed by Fourier transform infrared spectroscopy (FTIR), X‐ray photoelectron spectroscopy (XPS), elemental analysis, Wide‐angle X‐ray diffraction (WAXD), and microscopic analysis. Finally, end group analysis (by Matrix‐Assisted Laser Desorption Ionization Mass Spectrometry, and chain extension experiment) of the cleaved polymer and morphological study (by WAXD, Transmission Electron Microscopy), performed on the polymer grafted clays examined the effect of grafting on the efficiency of polymerization and the degree of dispersion of clay tactoids in polymer. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5014–5027, 2008     

Variable operator technique and the min-max theorem

We investigate a variation method where the trial function is generated from the application of a variable operator on a reference function. Two conditions are identified, one for obtaining a maximum and another for a minimum. Although the conditions are easy to understand, the overall formulation is somewhat unusual as each condition gives rise to a two-step variation process. As an example, projection operators are used to form the variable operator, and by this tactics one obtains the new interpretation that the pseudopotential formalism is in fact equivalent to a minimax procedure. The two-step variational process is nevertheless more flexible than the pseudopotential formalism, for it can also be used when the variable operator is not manifestly expressed in terms of projectors. This is illustrated by a comparison of the two-step method with the variational solution of Dirac’s relativistic electron equation. The same comparison leads to an alternative proof that the process of maximizing energy by varying the u–l coupling operator eliminates all negative-energy contributions from a trial spinor. The latter observation is crucial for the derivation of the min-max theorem in relativistic quantum mechanics.     

Anisotropic exchange in a tetranuclear CoII complex

Very high-frequency (50–715 GHz) electron paramagnetic resonance (EPR) studies of the tetranuclear Co^II complex [Co(hmp)(dmb)Cl]₄ (1), where dmb is 3,3-dimethyl-1-butanol and hmp^? is the monoanion of 2-hydroxy-methylpyridine, reveal the presence of significant zero-field-splitting (ZFS) within the ground state spin multiplet. Meanwhile, low-temperature hysteresis measurements of 1 (and related Co^II₄ complexes) provide evidence for slow magnetization relaxation, suggesting that it could be a single-molecule magnet (SMM). However, EPR studies of a Zn analog of 1, doped with a small quantity of Co^II, show the ground state of the Co^II ions to be an effective spin S′ = 1/2 Kramers doublet with a highly anisotropic g-tensor. The question then arises as to the origin of the ZFS within the ground state spin multiplet of 1, as well as the slow magnetization relaxation. Here, we consider the effect of anisotropic exchange interactions between the effective spin S′ = 1/2 Kramers ions within the tetranuclear complex. Such exchange anisotropy arises naturally when one treats the ground state of high-spin Co^II as a Kramers doublet. Our model provides an explanation for the ZFS in the ground state observed via EPR, and can also account for qualitative features observed through magnetic measurements.     

Evidence for covalent binding of epicocconone with proteins from synchronous fluorescence spectra and fluorescence lifetimes

Synchronous fluorescence and time-resolved fluorescence spectroscopic studies that reveal the interaction of epicocconone with human serum albumin is significantly different from its interaction with surfactant assemblies. This observation, along with steady-state fluorescence data, indicates ground-state interaction between the fluorophore epicocconone and the protein. Similarity in fluorescence properties with the adduct of the fluorophore with n-butylamine indicates that bonding occurs at the N-terminus of the protein.     

Estimation, prediction and the Stein phenomenon under divergence loss

We consider two problems: (1) estimate a normal mean under a general divergence loss introduced in [S. Amari, Differential geometry of curved exponential families — curvatures and information loss, Ann. Statist. 10 (1982) 357-387] and [N. Cressie, T.R.C. Read, Multinomial goodness-of-fit tests, J. Roy. Statist. Soc. Ser. B. 46 (1984) 440-464] and (2) find a predictive density of a new observation drawn independently of observations sampled from a normal distribution with the same mean but possibly with a different variance under the same loss. The general divergence loss includes as special cases both the Kullback-Leibler and Bhattacharyya-Hellinger losses. The sample mean, which is a Bayes estimator of the population mean under this loss and the improper uniform prior, is shown to be minimax in any arbitrary dimension. A counterpart of this result for predictive density is also proved in any arbitrary dimension. The admissibility of these rules holds in one dimension, and we conjecture that the result is true in two dimensions as well. However, the general Baranchick [A.J. Baranchick, a family of minimax estimators of the mean of a multivariate normal distribution, Ann. Math. Statist. 41 (1970) 642-645] class of estimators, which includes the James-Stein estimator and the Strawderman [W.E. Strawderman, Proper Bayes minimax estimators of the multivariate normal mean, Ann. Math. Statist. 42 (1971) 385-388] class of estimators, dominates the sample mean in three or higher dimensions for the estimation problem. An analogous class of predictive densities is defined and any member of this class is shown to dominate the predictive density corresponding to a uniform prior in three or higher dimensions. For the prediction problem, in the special case of Kullback-Leibler loss, our results complement to a certain extent some of the recent important work of Komaki [F. Komaki, A shrinkage predictive distribution for multivariate normal observations, Biometrika 88 (2001) 859-864] and George, Liang and Xu [E.I. George, F. Liang, X. Xu, Improved minimax predictive densities under Kullbak-Leibler loss, Ann. Statist. 34 (2006) 78-92]. While our proposed approach produces a general class of predictive densities (not necessarily Bayes, but not excluding Bayes predictors) dominating the predictive density under a uniform prior. We show also that various modifications of the James-Stein estimator continue to dominate the sample mean, and by the duality of estimation and predictive density results which we will show, similar results continue to hold for the prediction problem as well.