Application of density functional theory to analysis of energetic heterogeneity and pore size distribution of activated carbons

A new approach based on the nonlocal density functional theory to determine pore size distribution (PSD) of activated carbons and energetic heterogeneity of the pore wall is proposed. The energetic heterogeneity is modeled with an energy distribution function (EDF), describing the distribution of solid-fluid potential well depth (this distribution is a Dirac delta function for an energetic homogeneous surface). The approach allows simultaneous determining of the PSD (assuming slit shape) and EDF from nitrogen or argon isotherms at their respective boiling points by using a set of local isotherms calculated for a range of pore widths and solid-fluid potential well depths. It is found that the structure of the pore wall surface significantly differs from that of graphitized carbon black. This could be attributed to defects in the crystalline structure of the surface, active oxide centers, finite size of the pore walls (in either wall thickness or pore length), and so forth. Those factors depend on the precursor and the process of carbonization and activation and hence provide a fingerprint for each adsorbent. The approach allows very accurate correlation of the experimental adsorption isotherm and leads to PSDs that are simpler and more realistic than those obtained with the original nonlocal density functional theory.

Influence of charge size distribution on net-power draw of tumbling mill based on DEM modelling

Modelling and optimization of the power draw of large SAG/AG mills is important due to the large power draw which modern mills require (5-10 MW). The cost of grinding is the single biggest cost within the entire process of mineral extraction. Traditionally, modelling of the mill power draw has been done using empirical models. Although these models are reliable, they cannot model mills and operating conditions which are not within the model database boundaries. Also, due to its static nature, the impact of the changing conditions within the mill on the power draw cannot be determined using such models. Despite advances in computing power, discrete element method (DEM) modelling of large mills with many thousands of particles could be a time consuming task. The speed of computation is determined principally by two parameters: number of particles involved and material properties. The computational time step is determined by the size of the smallest particle present in the model and material properties (stiffness). In the case of small particles, the computational time step will be short, whilst in the case of large particles; the computation time step will be larger. Hence, from the point of view of time required for modelling (which usually corresponds to time required for 3-4 mill revolutions), it will be advantageous that the smallest particles in the model are not unnecessarily too small. The objective of this work is to compare the net power draw of the mill whose charge is characterised by different size distributions, while preserving the constant mass of the charge and mill speed. (C) 2004 Elsevier Ltd. All rights reserved.

Rotary atomizer drop size distribution database

Wind tunnel measurements of drop Size distributions from Micronair A U4000 and A U5000 rotary atomizers were collected to develop a database for model use. The measurements varied tank mix, flow rate, air speed, and blade angle conditions, which were correlated by multiple regressions (average R-2 = 0.995 for A U4000 and 0.988 for AU5000). This database replaces an outdated set of rotary atomizer data measured in the 1980s by the USDA Forest Service and fills in a gap in data measured in the 1990s by the Spray Drift Task Force. Since current USDA Forest Service spray projects rely on rotary atomizers, the creation of the database (and its multiple regression interpolation) satisfies a need seen for ten years.

Adsorption in slit pores and pore-size distribution: A molecular layer structure theory

A new approach is developed to analyze the thermodynamic properties of a sub-critical fluid adsorbed in a slit pore of activated carbon. The approach is based on a representation that an adsorbed fluid forms an ordered structure close to a smoothed solid surface. This ordered structure is modelled as a collection of parallel molecular layers. Such a structure allows us to express the Helmholtz free energy of a molecular layer as the sum of the intrinsic Helmholtz free energy specific to that layer and the potential energy of interaction of that layer with all other layers and the solid surface. The intrinsic Helmholtz free energy of a molecular layer is a function (at given temperature) of its two-dimensional density and it can be readily obtained from bulk-phase properties, while the interlayer potential energy interaction is determined by using the 10-4 Lennard-Jones potential. The positions of all layers close to the graphite surface or in a slit pore are considered to correspond to the minimum of the potential energy of the system. This model has led to accurate predictions of nitrogen and argon adsorption on carbon black at their normal boiling points. In the case of adsorption in slit pores, local isotherms are determined from the minimization of the grand potential. The model provides a reasonable description of the 0-1 monolayer transition, phase transition and packing effect. The adsorption of nitrogen at 77.35 K and argon at 87.29 K on activated carbons is analyzed to illustrate the potential of this theory, and the derived pore-size distribution is compared favourably with that obtained by the Density Functional Theory (DFT). The model is less time-consuming than methods such as the DFT and Monte-Carlo simulation, and most importantly it can be readily extended to the adsorption of mixtures and capillary condensation phenomena.

Pore size distribution analysis of activated carbons: Application of density functional theory using nongraphitized carbon black as a reference system

The application of nonlocal density functional theory (NLDFT) to determine pore size distribution (PSD) of activated carbons using a nongraphitized carbon black, instead of graphitized thermal carbon black, as a reference system is explored. We show that in this case nitrogen and argon adsorption isotherms in activated carbons are precisely correlated by the theory, and such an excellent correlation would never be possible if the pore wall surface was assumed to be identical to that of graphitized carbon black. It suggests that pore wall surfaces of activated carbon are closer to that of amorphous solids because of defects of crystalline lattice, finite pore length, and the presence of active centers.. etc. Application of the NLDFT adapted to amorphous solids resulted in quantitative description of N-2 and Ar adsorption isotherms on nongraphitized carbon black BP280 at their respective boiling points. In the present paper we determined solid-fluid potentials from experimental adsorption isotherms on nongraphitized carbon black and subsequently used those potentials to model adsorption in slit pores and generate a corresponding set of local isotherms, which we used to determine the PSD functions of different activated carbons. (c) 2005 Elsevier Ltd. All rights reserved.

Size distribution curves of senile plaques in patients with Alzheimer’s disease: do plaques grow according to the log-normal model?

The size frequency distributions of diffuse, primitive and cored senile plaques (SP) were studied in single sections of the temporal lobe from 10 patients with Alzheimer’s disease (AD). The size distribution curves were unimodal and positively skewed. The size distribution curve of the diffuse plaques was shifted towards larger plaques while those of the neuritic and cored plaques were shifted towards smaller plaques. The neuritic/diffuse plaque ratio was maximal in the 11 – 30 micron size class and the cored/ diffuse plaque ratio in the 21 – 30 micron size class. The size distribution curves of the three types of plaque deviated significantly from a log-normal distribution. Distributions expressed on a logarithmic scale were ‘leptokurtic’, i.e. with excess of observations near the mean. These results suggest that SP in AD grow to within a more restricted size range than predicted from a log-normal model. In addition, there appear to be differences in the patterns of growth of diffuse, primitive and cored plaques. If neuritic and cored plaques develop from earlier diffuse plaques, then smaller diffuse plaques are more likely to be converted to mature plaques.

Pd/C catalysts based on synthetic carbons with bi- and tri-modal pore-size distribution:applications in flow chemistry

Two new types of phenolic resin-derived synthetic carbons with bi-modal and tri-modal pore-size distributions were used as supports for Pd catalysts. The catalysts were tested in chemoselective hydrogenation and hydrodehalogenation reactions in a compact multichannel flow reactor. Bi-modal and tri-modal micro-mesoporous structures of the synthetic carbons were characterised by N2 adsorption. HR-TEM, PXRD and XPS analyses were performed for characterising the synthesised catalysts. N2 adsorption revealed that tri-modal synthetic carbon possesses a well-developed hierarchical mesoporous structure (with 6.5 nm and 42 nm pores), contributing to a larger mesopore volume than the bi-modal carbon (1.57 cm3 g-1versus 1.23 cm3 g-1). It was found that the tri-modal carbon promotes a better size distribution of Pd nanoparticles than the bi-modal carbon due to presence of hierarchical mesopore limitting the growth of Pd nanoparticles. For all the model reactions investigated, the Pd catalyst based on tri-modal synthetic carbon (Pd/triC) show high activity as well as high stability and reproducibility. The trend in reactivities of different functional groups over the Pd/triC catalyst follows a general order alkyne ≫ nitro > bromo ≫ aldehyde.

Essays on city size distribution and real estate bubbles

This is a dissertation about urban systems; within this broad subject I tackle three issues, one that focuses on an observed inter-city relationship and two that focus on an intra-city phenomenon. In Chapter II I adapt a model of random emergence of economic opportunities from the firm growth literature to the urban dynamics situation and present several predictions for urban system dynamics. One of these predictions is that the older the city the larger and more diversified it is going to be on average, which I proceed to verify empirically using two distinct datasets. In Chapter III I analyze the Residential Real Estate Bubble that took place in Miami-Dade County from 1999 to 2006. I adopt a Spatial-Economic model developed for the Paris Bubble episode of 1984–1993 and formulate an innovative test of the results in terms of speculative intensity on the basis of proxies of investor activity available in my dataset. My results support the idea that the best or more expensive areas are also where the greatest speculative activity takes place and where the rapid increase in prices begins. The most significant departure from previous studies that emerges in my results is the absence of a wider gap between high priced areas and low priced areas in the peak year. I develop a measure of dispersion in value among areas and contrast the Miami-Dade and Paris episodes. In Chapter IV I analyze the impact on tax equity of a Florida tax-limiting legislation known as Save Our Homes. I first compare homesteaded and non-homesteaded properties, and second, look within the subset of homesteaded properties. I find that non-homesteaded properties increase their share of taxes paid relative to homesteaded properties during an up market, but that this is reversed during a down market. For the subset of homesteaded properties I find that the impact on tax equity of SOH will depend on differential growth rates among higher and lower valued homes, but during times of rapid home price appreciation, in a scenario of no differential growth rates in property values, SOH increases progressivity relative to the prior system.

Modelling the size distribution of cosmic voids

The Standard Cosmological Model is generally accepted by the scientific community, there are still an amount of unresolved issues. From the observable characteristics of the structures in the Universe,it should be possible to impose constraints on the cosmological parameters. Cosmic Voids (CV) are a major component of the LSS and have been shown to possess great potential for constraining DE and testing theories of gravity. But a gap between CV observations and theory still persists. A theoretical model for void statistical distribution as a function of size exists (SvdW) However, the SvdW model has been unsuccesful in reproducing the results obtained from cosmological simulations. This undermines the possibility of using voids as cosmological probes. The goal of our thesis work is to cover the gap between theoretical predictions and measured distributions of cosmic voids. We develop an algorithm to identify voids in simulations,consistently with theory. We inspecting the possibilities offered by a recently proposed refinement of the SvdW (the Vdn model, Jennings et al., 2013). Comparing void catalogues to theory, we validate the Vdn model, finding that it is reliable over a large range of radii, at all the redshifts considered and for all the cosmological models inspected. We have then searched for a size function model for voids identified in a distribution of biased tracers. We find that, naively applying the same procedure used for the unbiased tracers to a halo mock distribution does not provide success- full results, suggesting that the Vdn model requires to be reconsidered when dealing with biased samples. Thus, we test two alternative exten- sions of the model and find that two scaling relations exist: both the Dark Matter void radii and the underlying Dark Matter density contrast scale with the halo-defined void radii. We use these findings to develop a semi-analytical model which gives promising results.

Fig. 2. Lithology, water and total carbon content, cumulative grain-size distribution, and quartz, feldspar, and mica contents of core sequence Lz1013 from south-western Beaver Lake

A 100 cm long sediment sequence was recovered from Beaver Lake in Amery Oasis, East Antarctica, using gravity and piston corers. Sedimentological and mineralogical analyses and the absence of micro and macrofossils indicate that the sediments at the base of the sequence formed under glacial conditions, probably prior to c. 12 500 cal. yr BP. The sediments between c. 81 and 31 cm depth probably formed under subaerial conditions, indicating that isostatic uplift since deglaciation has been substantially less than eustatic sea-level rise and that large areas of the present-day floor of Beaver Lake must have been subaerially exposed following deglaciation. The upper 31 cm of the sediment sequence were deposited under glaciomarine conditions similar to those of today, supporting geomorphic observations that the Holocene was a period of relative sea-level highstand in Amery Oasis.