4,323 research outputs found
Renormalisation-theoretic analysis of non-equilibrium phase transitions II: The effect of perturbations on rate coefficients in the Becker-Doring equations
We study in detail the application of renormalisation theory to models of
cluster aggregation and fragmentation of relevance to nucleation and growth
processes. In particular, we investigate the Becker-Doring (BD) equations,
originally formulated to describe and analyse non-equilibrium phase
transitions, but more recently generalised to describe a wide range of
physicochemical problems. We consider here rate coefficients which depend on
the cluster size in a power-law fashion, but now perturbed by small amplitude
random noise. Power-law rate coefficients arise naturally in the theory of
surface-controlled nucleation and growth processes. The noisy perturbations on
these rates reflect the effect of microscopic variations in such mean-field
coefficients, thermal fluctuations and/or experimental uncertainties. In the
present paper we generalise our earlier work that identified the nine classes
into which all dynamical behaviour must fall by investigating how random
perturbations of the rate coefficients influence the steady-state and kinetic
behaviour of the coarse-grained, renormalised system. We are hence able to
confirm the existence of a set of up to nine universality classes for such BD
systems.Comment: 30 pages, to appear in J Phys A Math Ge
Identifying the Azobenzene/Aniline reaction intermediate on TiO2-(110) : a DFT Study
Density functional theory (DFT) calculations, both with and without dispersion corrections, have been performed to investigate the nature of the common surface reaction intermediate that has been shown to exist on TiO2(110) as a result of exposure to either azobenzene (C6H5NâNC6H5) or aniline (C6H5NH2). Our results confirm the results of a previous DFT study that dissociation of azobenzene into two adsorbed phenyl imide (C6H5N) fragments, as was originally proposed, is not energetically favorable. We also find that deprotonation of aniline to produce this surface species is even more strongly energetically disfavored. A range of alternative surface species has been considered, and while dissociation of azobenzene to form surface C6H4NH species is energetically favored, the same surface species cannot form from adsorbed aniline. On the contrary, adsorbed aniline is much the most stable surface species. Comparisons with experimental determinations of the local adsorption site, the TiâN bond length, the molecular orientation, and the associated C 1s and N 1s photoelectron core level shifts are all consistent with the DFT results for adsorbed aniline and are inconsistent with other adsorbed species considered. Possible mechanisms for the hydrogenation of azobenzene required to produce this surface species are discussed
The (2â3Ă3)rect. phase of alkylthiolate self-assembled monolayers on Au(111): a symmetry-constrained structural solution
Low-energy electron-diffraction (LEED) patterns of the Au(111)(2â3Ă3)rect.-butylthiolate surface phase (a structure also seen in longer alkane chain thiolate self-assembled monolayers) show missing diffracted beams characteristic of glide symmetry, but do not show the larger set of missing beams found in surface x-ray diffraction (SXRD). The difference can be attributed to the greatly enhanced role of multiple scattering in LEED, but the combination of symmetry constraints placed on possible structural models by the observed SXRD and LEED beam extinctions greatly reduces the number of possible structural models. Only three such models are identified, one of which is clearly incompatible with other published experimental data. The relative merits of the remaining models, both involving Au adatom-thiolate moieties, are discussed in the light of the results of previous experimental studies
Photoelectron diffraction: from phenomenological demonstration to practical tool
The potential of photoelectron diffractionâexploiting the coherent interference of directly-emitted and elastically scattered components of the photoelectron wavefield emitted from a core level of a surface atom to obtain structural informationâwas first appreciated in the 1970s. The first demonstrations of the effect were published towards the end of that decade, but the method has now entered the mainstream armoury of surface structure determination. This short review has two objectives: First, to outline the way that the idea emerged and the way this evolved in my own collaboration with Neville Smith and his colleagues at Bell Labs in the early years: Second, to provide some insight into the current state-of-the art in application of (scanned-energy mode) photoelectron diffraction to address two key issue in quantitative surface structure determination, namely, complexity and precision. In this regard a particularly powerful aspect of photoelectron diffraction is its elemental and chemical-state specificity
Renormalisation-theoretic analysis of non-equilibrium phase transitions I: The Becker-Doring equations with power law rate coefficients
We study in detail the application of renormalisation theory to models of
cluster aggregation and fragmentation of relevance to nucleation and growth
processes. We investigate the Becker-Dorging equations, originally formulated
to describe and analyse non-equilibrium phase transitions, and more recently
generalised to describe a wide range of physicochemical problems. In the
present paper we analyse how the systematic coarse-graining renormalisation of
the \BD system of equations affects the aggregation and fragmentation rate
coefficients. We consider the case of power-law size-dependent cluster rate
coefficients which we show lead to only three classes of system that require
analysis: coagulation-dominated systems, fragmentation-dominated systems and
those where coagulation and fragmentation are exactly balanced. We analyse the
late-time asymptotics associated with each class.Comment: 18 pages, to appear in J Phys A Math Ge
The local adsorption site of methylthiolate on Au(1 1 1): Bridge or atop?
Measurements of the local adsorption geometry of the S head-group atom in the Au(1 1 1)(â3 Ă â3)R30°âCH3S surface have been made using normal incidence X-ray standing waves (NIXSW) and S 1s scanned-energy mode photoelectron diffraction on the same surface preparations. The results confirm that the local adsorption site is atop an Au atom in a bulk-continuation site with a SâAu bondlength of 2.42 ± 0.02 Ă
, and that there can be no significant fraction of coadsorbed bridging species as recently proposed in a combined molecular dynamics/experimental study by Mazzarello et al. [R. Mazzarello, A. Cossaro, A. Verdini, R. Rousseau, L. Casalis, M.F. Danisman, L. Floreano, S. Scandolo, A. Morgante, G. Scoles, Phys. Rev. Lett. 98 (2007) 016102]. The results do not, however, clearly distinguish the different local reconstruction (adatom) models proposed for this surface
Local methylthiolate adsorption geometry on Au(111) from photoemission core-level shifts
The local adsorption structure of methylthiolate in the ordered Au(111)-(â3Ăâ3)R30° phase has been investigated using core-level-shift measurements of the surface and bulk components of the Au 4f7/2 photoelectron binding energy. The amplitude ratio of the core-level-shift components associated with surface Au atoms that are, and are not, bonded to the thiolate is found to be compatible only with the previously proposed Au-adatom-monothiolate moiety in which the thiolate is bonded atop Au adatoms in hollow sites, and not on an unreconstructed surface, or in Au-adatom-dithiolate species
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