Dissolution of a solid sphere in an unbounded, stagnant liquid

An exact analytical solution is obtained for the transient dissolution of solid spheres in a diffusion-controlled environment. This result provides a useful reference point for drug testing in humans. The dimensionless solution is expressed in terms of a single parameter, which accounts for solubility, bulk flow, and stagnant fluid composition. A simple, explicit and exact expression was found to predict time-to-complete dissolution (TCD). An approximate solution was also found which tracks the exact case for low solubility conditions.

Some new examples for nonuniqueness of the evolution problem of harmonic maps

We find some new examples to show nonuniquence for the heat flow of harmonic maps where weak solutions satisfy the same monotonicity property.

Quantifying the influence of intra-aggregate concentration gradients on solute transport

The physical nonequilibrium of solute concentration resulting from preferential now of soil water has often led to models where the soil is partitioned into two regions: preferential flow paths, where solute transport occurs mainly by advection, and the remaining region, where significant solute transport occurs through diffusive exchange with the flow paths. These two-region models commonly ignore concentration gradients within the regions. Our objective was to develop a simple model to assess the influence of concentration gradients on solute transport and to compare model results with experiments conducted on structured materials. The model calculates the distribution of solutes in a single spherical aggregate surrounded by preferential now paths and subjected to alternating boundary conditions representing either an exchange of solutes between the two regions (a wet period) or no exchange but redistribution of solutes within the aggregate (a dry period). The key parameter in the model is the aggregate radius, which defines the diffusive time scales. We conducted intermittent leaching experiments on a column of packed porous spheres and on a large (300 mm long by 216 mm diameter) undisturbed field soil core to test the validity of the model and its application to field soils. Alternating wet and dry periods enhanced leaching by up to 20% for this soil, which was consistent with the model's prediction, given a fitted equivalent aggregate radius of 1.8 cm, If similar results are obtained for other soils, use of alternating wet and dry periods could improve management of solutes, for example in salinity control and in soil remediation.

Interfacial interactions and structure of organic-inorganic nanohybrids

Understanding the interfacial interactions and structure is important to better design and application of organic-inorganic nanohybrids. This paper presents our recent molecular dynamic studies on organoclays and polymer nanocomposites, including the layering behavior of organoclays, structural and dynamic properties of dioctadecyldimethyl ammoniums in organoclays, and interfacial interactions and structure of polyurethane nanocomposites. The results demonstrate that the layering behaviors of organoclays are closely related to the chain length of quaternary alkyl ammoniums and cation exchangeable capacity of clays. In addition to typical layered structures such as monolayer, bilayer and pseudo-trilayer, a pseudo-quadrilayer structure was also observed in organoclays modified with dioctadecyldimethyl ammoniums (DODDMA). In such a structure, alkyl chains do not lie flat within a single layer but interlace, and also jump to the next layer or even the next nearest layer. Moreover, the diffusion constants of nitrogen and methylene atoms increase with the temperature and methelene towards the tail groups. For polyurethane nanocomposite, the van der Waals interaction between apolar alkyl chains and soft segments of polyurethane predominates the interactions between organoclay and polyurethane. Different from most bulk polyurethane systems, there is no distinct phase-separated structure for the polyurethane.

N-methylation of diamino-substituted macrocyclic complexes: Intermolecular reactions

Two N-based isomeric copper(II) complexes of the macrocycle trans-6,13-dimethyl-6,13-bis(dimethylamino)1,4,8,11-tetraazacyclotetradecane (L(3)) have been synthesized and characterised spectroscopically and structurally: alpha-[CuL(3)(OH2)(2)]Cl-2, monoclinic, space group C2/m, a = 12.908(4), b = 12.433(2), c = 7.330(2) Angstrom, beta = 105.87(2)degrees, Z = 2; beta-[CuL(3)(OClO3)(2)]. 2H(2)O, monoclinic, space group P2(1)/c, a = 9.708(3), b = 9.686(3), c = 14.202(4) Angstrom, beta = 106.17(1)degrees, Z = 2. The two isomers exhibit very similar co-ordination spheres but significantly different visible electronic maxima. This difference is attributed to an intramolecular N ... H contact between the pendant dimethylamino group and an adjacent secondary amine H atom.

Determination of the force constant of a single-beam gradient trap by measurement of backscattered light

A single-beam gradient trap could potentially be used to hold a stylus for scanning force microscopy. With a view to development of this technique, we modeled the optical trap as a harmonic oscillator and therefore characterized it by its force constant. We measured force constants and resonant frequencies for 1-4-mu m-diameter polystyrene spheres in a single-beam gradient trap using measurements of back-scattered light. Force constants were determined with both Gaussian and doughnut laser modes, with powers of 3 and 1 mW, respectively. Typical values for spring constants were measured to be between 10(-6) and 4 x 10(-6) N/m. The resonant frequencies of trapped particles were measured to be between 1 and 10 kHz, and the rms amplitudes of oscillations were estimated to be around 40 nm. Our results confirm that the use of the doughnut mode for single-beam trapping is more efficient in the axial direction. (C) 1996 Optical Society of America.

Multi-fluorescent silica colloids for encoding large combinatorial libraries

Large chemical libraries can be synthesized on solid-support beads by the combinatorial split-and-mix method. A major challenge associated with this type of library synthesis is distinguishing between the beads and their attached compounds. A new method of encoding these solid-support beads, 'colloidal bar-coding', involves attaching fluorescent silica colloids ('reporters') to the beads as they pass through the compound synthesis, thereby creating a fluorescent bar code on each bead. In order to obtain sufficient reporter varieties to bar code extremely large libraries, many of the reporters must contain multiple fluorescent dyes. We describe here the synthesis and spectroscopic analysis of various mono- and multi-fluorescent silica particles for this purpose. It was found that by increasing the amount of a single dye introduced into the particle reaction mixture, mono- fluorescent silica particles of increasing intensities could be prepared. This increase was highly reproducible and was observed for six different fluorescent dyes. Multi-fluorescent silica particles containing up to six fluorescent dyes were also prepared. The resultant emission intensity of each dye in the multi-fluorescent particles was found to be dependent upon a number of factors; the hydrolysis rate of each silane-dye conjugate, the magnitude of the inherent emission intensity of each dye within the silica matrix, and energy transfer effects between dyes. We show that by varying the relative concentration of each silane-dye conjugate in the synthesis of multi-fluorescent particles, it is possible to change and optimize the resultant emission intensity of each dye to enable viewing in a fluorescence detection instrument.

How cracks in SiOx-coated polyester films affect gas permeation

In this paper theoretical models have been established that can account for the gas transmission through nanocomposite laminates, consisting of an oxide layer of finite permeability containing defects, on a polymer sheet of finite thickness. The defect shapes can either be in the form of long cracks or rectangular holes. The models offer a choice of exact numerical calculations or fast and intuitive analytical approximations. The experimental measurements of oxygen permeation through four different SiOx/poly (ethylene terephthalate) samples that were strained to produce distributions or cracks showed good agreement when compared with predicted results from the approximate analytic model. As a consequence of this observation, a key practical conclusion is that, because of the logarithmic dependence of transmission on the width of a crack, for a given strain it is better to have a small number of large cracks rather than a large number of small cracks. (C) 2001 Elsevier Science B.V. All rights reserved.

Freeform fabrication of aluminum metal-matrix composites

A series of metal-matrix composites were formed by extrusion freeform, fabrication of a sinterable aluminum alloy in combination with silicon carbide particles and whiskers, carbon fibers, alumina particles, and hollow flyash cenospheres. Silicon carbide particles were most successful in that the composites retained high density with up to 20 vol% of reinforcement and the strength approximately doubles over the strength of the metal matrix alone. Comparison with simple models suggests that this unexpectedly high degree of reinforcement can be attributed to the concentration of small silicon carbide particles around the larger metal powder. This fabrication method also allows composites to be formed with hollow spheres that cannot be formed by other powder or melt methods.