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 (C6H5N═NC6H5) 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 Ti–N 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 (2√3×3)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)(2√3×3)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 diffraction—exploiting 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 information—was 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)(√3 × √3)R30°–CH3S 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 S–Au bondlength of 2.42 ± 0.02 Å, 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)-(√3×√3)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