M. Fátima Vaz

Grain size distribution: The lognormal and the gamma distribution functions

Summary The distribution of grain sizes (volume, intersected area or intercept length) in a polycrystal is usually fitted to a lognormal distribution. An alternative distribution function that can be used is the gamma function. The experimental data available in the literature seem to indicate that the latter distribution may be more adequate, since it gives log plots which are not symmetrical. The two distributions (lognormal and gamma) are in fact fairly similar, as we have shown, and the experimental results may not be precise enough to favour one or the other. There is, however, a good argument in favour of the gamma distribution. This is the fact that the cell model leads to a distribution of cell sizes which is very well described by gamma functions, with α values (Table 2) that depend on the definition of size used. The values of α in Table 2 for the 3D partition indicate that the distribution of cell volume is narrower than the distributions of intercept length and area. The adequacy of gamma functions in relation to the cell model is not entirely surprising, considering that the statistics of the cell model is essentially the Poisson statistics. Of course, the cell model may not be an adequate model for a polycrystal. Other models, which admit, for example, a sequential, rather than simultaneous, nucleation have been considered (13), including the Johnson-Mehl model (7,9), but the data available is not sufficient for an analysis of the type undertaken here for the cell model. There is indication, however, that the grain size distributions become broader (smaller values of α, if gamma functions are still appropriate) as the time delay in the nucleation of successive grains increases (e.g.the Johnson-Mehl distribution is broader than the cell distribution). Grain growth is also expected to broaden the distribution of grain sizes (e.g.ref.4).

The transition from two-dimensional to three-dimensional foam structures

Abstract:Small cells in an experimental sample of two-dimensional foam, such as that which is contained between two glass plates, may undergo a transition to a three-dimensional form, becoming detached from one boundary. We present the first detailed observations of this phenomenon, together with computer simulations. The transition is attributed to an instability of the Rayleigh-Plateau type. A theoretical analysis is given which shows that an individual cell is susceptible to this instability only if it has less than six sides.

Minimal perimeter for N identical bubbles in two dimensions: Calculations and simulations

The minimal perimeter enclosing N planar regions, each being simply connected and of the same area, is an open problem, solved only for a few values of N . The problems of how to construct the configuration with the smallest possible perimeter E ( N ) and how to estimate the value of E ( N ) are considered. Defect-free configurations are classified and we start with the naïve approximation that the configuration is close to a circular portion of a honeycomb lattice. Numerical simulations and analysis that show excellent agreement to within one free parameter are presented; this significantly extends the range of values of N for which good candidates for the minimal perimeter have been found. We provide some intuitive insight into this problem in the hope that it will help the improvement in future numerical simulations and the derivation of exact results.

Experiments on defect spreading in hexagonal foams

Defects were introduced in a hexagonal liquid foam prepared by a novel technique and their coarsening was observed. Both isolated defect clusters, with and without dislocation character, and grain boundaries were produced. As the defects coarsen, a gradient of cell size develops along the direction of growth. Differences in the growth characteristics of isolated defects were found, depending on whether the average size of the cells in the defect clusters is larger (type I) or smaller (type II) than the size of the surrounding honeycomb cells. Clusters of type I show an approximately linear increase of diameter with time, while clusters of type II have an initial contraction. The evolution to the scaling regime of a honeycomb containing a distribution of type I clusters is discussed.

Friction properties of cork

The friction coefficient, μ, of cork sliding on another material (glass and steel in most experiments and also cork) was measured for various compressive stresses and sliding velocities. There is a strong effect of stress and a negligible effect of velocity on the friction coefficient. Values of μ are in the range 0.4 to 1.2. The effect of moisture content of cork was also evaluated. For dry cork (6% moisture content) there is anisotropy of the friction coefficient related to the orientation of the sliding plane of cork, with larger values for sliding in the tangential plane (compression in the radial direction) as compared to sliding in planes perpendicular to this. At larger moisture contents, the anisotropy of μ decreases. No in-plane of sliding anisotropy was detected. The friction coefficients for sliding on glass and on steel are comparable, but an effect of roughness was detected. The friction coefficients for sliding on glass and on steel are comparable, but an effect of roughness was detected. The friction against cork is large, with μ close to unity. The interplay between the friction coefficient and the compression properties of cork is discussed.

The contact mechanics of cellular solids

A model for the contact of a cellular solid with a compact counter-surface is developed. The cell walls and edges at the surface of the cellular solid deform elastically by compression and bending and, at larger forces, collapse. For open cell materials, a simple general equation is derived relating the fraction f of cell edges in contact to the applied compressive stress σ. The ratio σ/f is proportional to an average strain of the cell struts in contact, which is calculated in particular cases. A geometrical construction is described with which the fraction f can be obtained as a function of the applied stress σ. The analysis of the contact of closed cell materials is also undertaken, leading to relations between the applied stress and the fractions of edges and walls in contact.

Characterisation of ceramic pastes of portuguese ancient tiles

Portuguese ceramic tiles of different origins from XVIth century to XXth century were studied. In this work we describe microstructural, mechanical and mineralogical characterisation and water absorption studies. Microstructural features (pore size) were determined using Scanning Electron Microscope (SEM) photographs. Mechanical tests (four point bending) were performed and the bending strength was determined from the fracture loads. From water absorption essays the absorption coefficient and the total amount of water retained were obtained and the open porosity was estimated. The maximum water absorbed tends to decrease from XVIth century until XXth century, showing a more pronounced drop for the tiles of the XIXth and XXth centuries. This evolution is also observed in the open porosity values. From image analysis data we also observed that porosity decreases progressively with time and an important drop is observed for XXth century tiles. The bending resistance of tiles from XVIIth to XXth century is almost constant and higher than that of XVIth century samples. This evolution does not correlate with porosity. Advances in ceramic processing, such as higher firing temperatures may lead to the appearance of quartz as almost the only crystalline phase. We consider that an increase in the bending strength is due to a more effective vitrification and a lower porosity.

Initiation and propagation of cell collapse in dynamic compression of cellular materials

Abstract A one-dimensional model of a cellular material is used to simulate deformation in compression at constant velocity. Each cell has a characteristic load-strain curve with a saddle transition to simulate cell collapse. Different cells may have different collapse forces. A damping term is included in the dynamic equations of motion, which are numerically integrated. Particular attention is given to the initiation of collapse and to its propagation, either to adjacent cells (band propagation) or in a random fashion. The actual behaviour depends on the imposed velocity and on the parameters of the characteristic equations. Low velocities tend to favour random propagation while high velocities originate a band that initiates at the moving end. At intermediate velocities two bands form. Equations are derived for the force for propagation of collapse under quasi-static and dynamic conditions. When there is a weaker element, collapse tends to initiate in it and may propagate to adjacent elements, under an approximately constant force which is affected by damping. When there are large differences among the collapse forces of the various elements, collapse occurs under an increasing load.

Antifungal activity of dental resins containing amphotericin B-conjugated nanoparticles.

OBJECTIVES To evaluate the antifungal activity, biocompatibility and mechanical properties of dental resins containing silica nanoparticles functionalized with amphotericin B (SNP-DexOxAmB) against five species of Candida. METHODS Dental resin composites (Spectrum, Dentsply DeTrey, GmbH, Germany) having 2% (w/w) of SNP-DexOxAmB (SNPs of 5 and 80nm, denoted as SNP5 and SNP80) were aged for 10, 20 and 30 days at 37°C, in phosphate buffer saline buffer pH 7.4 (PBS). At different time, the antifungal activity was evaluated by a direct contact assay against 1×10(4)cells of Candida. The biocompatibility of the resins was tested against human fibroblasts, endothelial cells and red blood cells. RESULTS Dental resins containing SNP5-DexOxAmB have high (1×10(4)cells killed in 5h by ∼70mg of dental resin composite containing 2% (w/w) of SNP-DexOxAmB) and durable (for at least 1 month) antifungal activity against five strains of Candida. The incorporation of the nanoparticles (NPs) had no significant change in the mechanical properties of the resin, specifically the flexural strength and modulus. Our results further show that the antifungal activity is mainly mediated by direct contact and not by leaching of NPs from the resin. Resins incorporating SNP5-DexOxAmB have longer-term antifungal activity than SNP80-DexOxAmB. The antimicrobial activity of resins with SNP5-DexOxAmB persists after 4 cycles of re-use and it is superior to the activity obtained for dental resins containing silver NPs. In addition, dental resins incorporating SNP5-DexOxAmB are non-cytotoxic against human skin fibroblasts and human umbilical vein endothelial cells, and non-hemolytic against human red blood cells. SIGNIFICANCE The incorporation of SNP5-DexOxAmB in dental resins resulted in a non-cytotoxic composite with high and durable antifungal activity.

Pressures inside bubbles in planar clusters

We provide theoretical estimates and undertake Surface Evolver experiments on the pressures inside bubbles in planar clusters. The equation of equilibrium implies that as the number, N, of unit bubbles become large, the average normalized pressure in an energy-minimizing cluster approaches 2−1/231/4 ≈ 0.9306. An equation is derived for the rigorous theoretical upper and lower bounds on the average pressure in terms of N. Surface Evolver experiments agree with these estimates.