Droplet shapes on structured substrates and conformal invariance

We consider the finite-size scaling of equilibrium droplet shapes for fluid adsorption (at bulk two-phase co-existence) on heterogeneous substrates and also in wedge geometries in which only a finite domain $\Lambda_{A}$ of the substrate is completely wet. For three-dimensional systems with short-ranged forces we use renormalization group ideas to establish that both the shape of the droplet height and the height-height correlations can be understood from the conformal invariance of an appropriate operator. This allows us to predict the explicit scaling form of the droplet height for a number of different domain shapes. For systems with long-ranged forces, conformal invariance is not obeyed but the droplet shape is still shown to exhibit strong scaling behaviour. We argue that droplet formation in heterogeneous wedge geometries also shows a number of different scaling regimes depending on the range of the forces. The conformal invariance of the wedge droplet shape for short-ranged forces is shown explicitly.Comment: 20 pages, 7 figures. (Submitted to J.Phys.:Cond.Mat.

Coupled Fluctuations near Critical Wetting

Recent work on the complete wetting transition has emphasized the role played by the coupling of fluctuations of the order parameter at the wall and at the depinning fluid interface. Extending this approach to the wetting transition itself we predict a novel crossover effect associated with the decoupling of fluctuations as the temperature is lowered towards the transition temperature T_W. Using this we are able to reanalyse recent Monte-Carlo simulation studies and extract a value \omega(T_W)=0.8 at T_W=0.9T_C in very good agreement with long standing theoretical predictions.Comment: 4 pages, LaTex, 1 postscript figur

Local functional models of critical correlations in thin-films

Recent work on local functional theories of critical inhomogeneous fluids and Ising-like magnets has shown them to be a potentially exact, or near exact, description of universal finite-size effects associated with the excess free-energy and scaling of one-point functions in critical thin films. This approach is extended to predict the two-point correlation function G in critical thin-films with symmetric surface fields in arbitrary dimension d. In d=2 we show there is exact agreement with the predictions of conformal invariance for the complete spectrum of correlation lengths as well as the detailed position dependence of the asymptotic decay of G. In d=3 and d>=4 we present new numerical predictions for the universal finite-size correlation length and scaling functions determining the structure of G across the thin-film. Highly accurate analytical closed form expressions for these universal properties are derived in arbitrary dimension.Comment: 4 pages, 1 postscript figure. Submitted to Phys Rev Let

Elemental boron doping behavior in silicon molecular beam epitaxy

Boron-doped Si epilayers were grown by molecular beam epitaxy (MBE) using an elemental boron source, at levels up to 2×1020 cm−3, to elucidate profile control and electrical activation over the growth temperature range 450–900 °C. Precipitation and surface segregation effects were observed at doping levels of 2×1020 cm−3 for growth temperatures above 600 °C. At growth temperatures below 600 °C, excellent profile control was achieved with complete electrical activation at concentrations of 2×1020 cm−3, corresponding to the optimal MBE growth conditions for a range of Si/SixGe1−x heterostructures

Surely you don’t eat parsnip skins? Categorising the edibility of food waste

Food that is either wasted or lost, rather than being eaten, accounts for around a third of global food production and is linked to several environmental, economic and social issues. The reliable quantification of this wasted food is essential to monitor progress towards the United Nations’ Sustainable Development Goal 12.3, which covers food loss and waste. Currently quantification of food waste is made difficult by many differing definitions, some of which require categorisation of food items into those parts considered edible and those considered inedible. Edibility is difficult to define as it is affected by cultural and social influences. This study presents a novel, easily-replicable, questionnaire-based methodology to categorise ‘borderline’ food items thrown away from households, e.g. parsnip skin, apple cores. The methodology captures self-reported information on what people eat (self-reported consumption) and their perceptions of edibility. Our results for the United Kingdom indicate that, for a given food ‘part’, there is divergence between individuals’ responses to the survey questions: e.g. many people would ‘never’ eat carrot skins, whilst many others would ‘always’ eat them. Furthermore, there is a systematic difference between people’s self-reported consumption and their perceptions of edibility. We suggest that both need to be considered to create a balanced categorisation of edible and inedible parts; we propose a method for incorporating both elements. Within this method, a threshold needs to be applied and the resultant classification, especially of those items close to this threshold, will inevitably be contentious. Despite this, the categorisation of what is considered edible using this methodology reflects the views of the majority of the population, facilitating the quantification of food waste. In addition, we envisage this methodology can be used to compare geographical differences and track changes over time with regard to edibility

Growth studies on Si0.8Ge0.2 channel two-dimensional hole gases

We report a study of the influences of MBE conditions on the low-temperature mobilities of Si/Si0.8Ge0.2 2DHG structures. A significant dependence of 2DHG mobility on growth temperature is observed with the maximum mobility of 3640 cm2 V−1 s−1 at 5.4 K being achieved at the relatively high-growth temperature of 640 °C. This dependence is associated with a reduction in interface charge density. Studies on lower mobility samples show that Cu contamination can be reduced both by growth interruptions and by modifications to the Ge source; this reduction produces improvements in the low-temperature mobilities. We suggest that interface charge deriving from residual metal contamination is currently limiting the 4-K mobility

Effect of Gravity and Confinement on Phase Equilibria: A Density Matrix Renormalization Approach

The phase diagram of the 2D Ising model confined between two infinite walls and subject to opposing surface fields and to a bulk "gravitational" field is calculated by means of density matrix renormalization methods. In absence of gravity two phase coexistence is restricted to temperatures below the wetting temperature. We find that gravity restores the two phase coexistence up to the bulk critical temperature, in agreement with previous mean-field predictions. We calculate the exponents governing the finite size scaling in the temperature and in the gravitational field directions. The former is the exponent which describes the shift of the critical temperature in capillary condensation. The latter agrees, for large surface fields, with a scaling assumption of Van Leeuwen and Sengers. Magnetization profiles in the two phase and in the single phase region are calculated. The profiles in the single phase region, where an interface is present, agree well with magnetization profiles calculated from a simple solid-on-solid interface hamiltonian.Comment: 4 pages, RevTeX and 4 PostScript figures included. Final version as published. To appear in Phys. Rev. Let

A symmetric polymer blend confined into a film with antisymmetric surfaces: interplay between wetting behavior and phase diagram

We study the phase behavior of a symmetric binary polymer blend which is confined into a thin film. The film surfaces interact with the monomers via short range potentials. We calculate the phase behavior within the self-consistent field theory of Gaussian chains. Over a wide range of parameters we find strong first order wetting transitions for the semi-infinite system, and the interplay between the wetting/prewetting behavior and the phase diagram in confined geometry is investigated. Antisymmetric boundaries, where one surface attracts the A component with the same strength than the opposite surface attracts the B component, are applied. The phase transition does not occur close to the bulk critical temperature but in the vicinity of the wetting transition. For very thin films or weak surface fields one finds a single critical point at $\phi_c=1/2$. For thicker films or stronger surface fields the phase diagram exhibits two critical points and two concomitant coexistence regions. Only below a triple point there is a single two phase coexistence region. When we increase the film thickness the two coexistence regions become the prewetting lines of the semi-infinite system, while the triple temperature converges towards the wetting transition temperature from above. The behavior close to the tricritical point, which separates phase diagrams with one and two critical points, is studied in the framework of a Ginzburg-Landau ansatz. Two-dimensional profiles of the interface between the laterally coexisting phases are calculated, and the interfacial and line tensions analyzed. The effect of fluctuations and corrections to the self-consistent field theory are discussed.Comment: Phys.Rev.E in prin