Bimodality and re-entrant behaviour in the hierarchical self-assembly of polymeric nanoparticles

We show that a film of a suspension of polymer grafted nanoparticles on a liquid substrate can be employed to create two-dimensional nanostructures with a remarkable variation in the pattern length scales. The presented experiments also reveal the emergence of concentration-dependent bimodal patterns as well as re-entrant behaviour that involves length scales due to dewetting and compositional instabilities. The experimental observations are explained through a gradient dynamics model consisting of coupled evolution equations for the height of the suspension film and the concentration of polymer. Using a Flory-Huggins free energy functional for the polymer solution, we show in a linear stability analysis that the thin film undergoes dewetting and/or compositional instabilities depending on the concentration of the polymer in the solution. We argue that the formation via `hierarchical self-assembly' of various functional nanostructures observed in different systems can be explained as resulting from such an interplay of instabilities.

Delineation of homogeneous temperature regions: a two-stage clustering approach

Homogeneous temperature regions are necessary for use in hydrometeorological studies. The regions are often delineated by analysing statistics derived from time series of maximum, minimum or mean temperature, rather than attributes influencing temperature. This practice cannot yield meaningful regions in data-sparse areas. Further, independent validation of the delineated regions for homogeneity in temperature is not possible, as temperature records form the basis to arrive at the regions. To address these issues, a two-stage clustering approach is proposed in this study to delineate homogeneous temperature regions. First stage of the approach involves (1) determining correlation structure between observed temperature over the study area and possible predictors (large-scale atmospheric variables) influencing the temperature and (2) using the correlation structure as the basis to delineate sites in the study area into clusters. Second stage of the approach involves analysis on each of the clusters to (1) identify potential predictors (large-scale atmospheric variables) influencing temperature at sites in the cluster and (2) partition the cluster into homogeneous fuzzy temperature regions using the identified potential predictors. Application of the proposed approach to India yielded 28 homogeneous regions that were demonstrated to be effective when compared to an alternate set of 6 regions that were previously delineated over the study area. Intersite cross-correlations of monthly maximum and minimum temperatures in the existing regions were found to be weak and negative for several months, which is undesirable. This problem was not found in the case of regions delineated using the proposed approach. Utility of the proposed regions in arriving at estimates of potential evapotranspiration for ungauged locations in the study area is demonstrated.

Nanomechanical Mapping, Hierarchical Polymer Dynamics, and Miscibility in the Presence of Chain-End Grafted Nanoparticles

To improve the spatial distribution of nano particles in a polymeric host and to enhance the interfacial interaction with the host, the use of chain-end grafted nanoparticle has gained popularity in the field of polymeric nanocomposites. Besides changing the material properties of the host, these grafted nanoparticles strongly alter the dynamics of the polymer chain at both local and cooperative length scales (relaxations) by manipulating the enthalpic and entropic interactions. It is difficult to map the distribution of these chain-end grafted nanoparticles in the blend by conventional techniques, and herein, we attempted to characterize it by unique technique(s) like peak force quantitative nanomechanical mapping (PFQNM) through AFM (atomic force microscopy) imaging and dielectric relaxation spectroscopy (DRS). Such techniques, besides shedding light on the spatial distribution of the nanoparticles, also give critical information on the changing elasticity at smaller length scales and hierarchical polymer chain dynamics in the vicinity of the nanoparticles. The effect of one-dimensional rodlike multiwall carbon nanotubes (MWNTs), with the characteristic dimension of the order of the radius of gyration of the polymeric chain, on the phase miscibility and chain dynamics in a classical LCST mixture of polystyrene/ poly(vinyl methyl ether) (PS/PVME) was examined in detail using the above techniques. In order to tune the localization of the nanotubes, different molecular weights of PS (13, 31, and 46 kDa), synthesized using RAFT (reversible addition fragmentation chain transfer) polymerization, was grafted onto MWNTs in situ. The thermodynamic miscibility in the blends was assessed by low-amplitude isochronal temperature sweeps, the spatial distribution of MWNTs in the blends was evaluated by PFQNM, and the hierarchical polymer chain dynamics was studied by DRS. It was observed that the miscibility, concentration fluctuation, and cooperative relaxations of the PS/PVME blends are strongly governed by the spatial distribution of MWNTs in the blends. These findings should help guide theories and simulations of hierarchical chain dynamics in LCST mixtures containing rodlike nanoparticles.

Nanomechanical Mapping, Hierarchical Polymer Dynamics, and Miscibility in the Presence of Chain-End Grafted Nanoparticles

To improve the spatial distribution of nano particles in a polymeric host and to enhance the interfacial interaction with the host, the use of chain-end grafted nanoparticle has gained popularity in the field of polymeric nanocomposites. Besides changing the material properties of the host, these grafted nanoparticles strongly alter the dynamics of the polymer chain at both local and cooperative length scales (relaxations) by manipulating the enthalpic and entropic interactions. It is difficult to map the distribution of these chain-end grafted nanoparticles in the blend by conventional techniques, and herein, we attempted to characterize it by unique technique(s) like peak force quantitative nanomechanical mapping (PFQNM) through AFM (atomic force microscopy) imaging and dielectric relaxation spectroscopy (DRS). Such techniques, besides shedding light on the spatial distribution of the nanoparticles, also give critical information on the changing elasticity at smaller length scales and hierarchical polymer chain dynamics in the vicinity of the nanoparticles. The effect of one-dimensional rodlike multiwall carbon nanotubes (MWNTs), with the characteristic dimension of the order of the radius of gyration of the polymeric chain, on the phase miscibility and chain dynamics in a classical LCST mixture of polystyrene/ poly(vinyl methyl ether) (PS/PVME) was examined in detail using the above techniques. In order to tune the localization of the nanotubes, different molecular weights of PS (13, 31, and 46 kDa), synthesized using RAFT (reversible addition fragmentation chain transfer) polymerization, was grafted onto MWNTs in situ. The thermodynamic miscibility in the blends was assessed by low-amplitude isochronal temperature sweeps, the spatial distribution of MWNTs in the blends was evaluated by PFQNM, and the hierarchical polymer chain dynamics was studied by DRS. It was observed that the miscibility, concentration fluctuation, and cooperative relaxations of the PS/PVME blends are strongly governed by the spatial distribution of MWNTs in the blends. These findings should help guide theories and simulations of hierarchical chain dynamics in LCST mixtures containing rodlike nanoparticles.

Hierarchical approach to timing verification in CMOS VLSI design

This paper describes a novel hierarchical approach to timing verification. Four types of relationship existing among signal paths are distinguished, based on a classification of the degree of interdependency in the circuit. In this way, irrelevant path delays can be excluded through consideration of the interaction between critical paths and others. Furthermore, under suitable conditions, bounded delay values for large hierarchical systems can be deduced using bounded delays determined for their constituent cells. Finally, we discuss the impact on design strategy of the hierarchical delay model presented in this paper.

Does spatial clustering help explaining differences in the inequality of income distribution? : evidence from Argentina

Resumen: Este artículo analiza la relación entre la agrupación espacial de la distribución del ingreso y la desigualdad en las provincias de Argentina. El objetivo de este trabajo es usar técnicas espaciales para analizar hasta que punto la agrupación espacial de la distribución del ingreso afecta la desigualdad de la distribución del ingreso en un contexto regional de Argentina. En general, la literatura de desigualdad implícitamente considera a cada región o provincia como una entidad independiente y el potencial para la observación de la interacción a través del espacio a menudo se ha ignorado. Mientras tanto, la autocorrelación espacial ocurre cuando la distribución espacial de la variable de interés exhibe un patrón sistemático. Yo computo tres medidas de autocorrelación espacial global: La I de Moran, c de Geary, y G de Getis y Ord, como grado de CLUSTERING provincial entre 1991 y 2002. La principal conclusión del trabajo es que hay evidencia que provincias con desigualdad relativamente alta (baja) tienden a ser localizadas cerca de otras provincias con alta (baja) desigualdad más a menudo de lo esperado debido al azar. Por ende cada provincia no debería ser vista como una observación independiente, como ha sido supuesto implícitamente en estudios previos sobre la desigualdad de ingresos regional.

Effective elastic modulus of bone-like hierarchical materials

A shear-lag model is used to study the mechanical properties of bone-like hierarchical materials. The relationship between the overall effective modulus and the number of hierarchy level is obtained. The result is compared with that based on the tension-shear chain model and finite element simulation, respectively. It is shown that all three models can be used to describe the mechanical behavior of the hierarchical material when the number of hierarchy levels is small. By increasing the number of hierarchy level, the shear-lag result is consistent with the finite element result. However the tension-shear chain model leads to an opposite trend. The transition point position depends on the fraction of hard phase, aspect ratio and modulus ratio of hard phase to soft phase. Further discussion is performed on the flaw tolerance size and strength of hierarchical materials based on the shear-lag analysis.