Vacuum Polarization and Dynamical Chiral Symmetry Breaking: Phase Diagram of QED with Four-Fermion Contact Interaction

We study chiral symmetry breaking for fundamental charged fermions coupled electromagnetically to photons with the inclusion of four-fermion contact self-interaction term. We employ multiplicatively renormalizable models for the photon dressing function and the electron-photon vertex which minimally ensures mass anomalous dimension = 1. Vacuum polarization screens the interaction strength. Consequently, the pattern of dynamical mass generation for fermions is characterized by a critical number of massless fermion flavors above which chiral symmetry is restored. This effect is in diametrical opposition to the existence of criticality for the minimum interaction strength necessary to break chiral symmetry dynamically. The presence of virtual fermions dictates the nature of phase transition. Miransky scaling laws for the electromagnetic interaction strength and the four-fermion coupling, observed for quenched QED, are replaced by a mean-field power law behavior corresponding to a second order phase transition. These results are derived analytically by employing the bifurcation analysis, and are later confirmed numerically by solving the original non-linearized gap equation. A three dimensional critical surface is drawn to clearly depict the interplay of the relative strengths of interactions and number of flavors to separate the two phases. We also compute the beta-function and observe that it has ultraviolet fixed point. The power law part of the momentum dependence, describing the mass function, reproduces the quenched limit trivially. We also comment on the continuum limit and the triviality of QED.Comment: 9 pages, 10 figure

The Structure of a Silica Thin Film on Oxidized Cu(111): Conservation of Honeycomb Lattice and Role of the Interlayer

There is a crucial role of the metal-oxide interface in determining the growth ofsilica thin films. However, only a few metallic substrates have been explored so far.In previous studies, metal substrates exhibiting unreconstructed surfaces under oxygenexposure have been analyzed. In this work, we study the structure of a silica thinfilm grown on Cu(111) and propose that a copper oxide film formed at the interfaceinhibits the appearance of defects and domain boundaries. Our results suggest that thesilica film structure has flexible connections with the copper oxide interlayer leadingto a lattice solely composed of six-membered rings. This honeycomb configuration iscertainly of importance in the design of well-defined two-dimensional oxide thin films onmetallic substrates as well as for catalysis applications involving metal-oxide interfaces

Crystallographic Orientation Dependence of Surface Segregation and Alloying on PdCu Catalysts for CO₂ Hydrogenation

The influence of the crystallographic orientation on surface segregation and alloy formation in model PdCu methanol synthesis catalysts was investigated in situ using near-ambient pressure X-ray photoelectron spectroscopy under CO2 hydrogenation conditions. Combined with scanning tunneling microscopy and density functional theory calculations, the study showed that submonolayers of Pd undergo spontaneous alloy formation on Cu(110) and Cu(100) surfaces in vacuum, whereas they do not form an alloy on Cu(111). Upon heating in H2, inward diffusion of Pd into the Cu lattice is favored, facilitating alloying on all Cu surfaces. Under CO2 hydrogenation reaction conditions, the alloying trend becomes stronger, promoted by the reaction intermediate HCOO*, especially on Pd/Cu(110). This work demonstrates that surface alloying may be a key factor in the enhancement of the catalytic activity of PdCu catalysts as compared to their monometallic counterparts. Furthermore, it sheds light on the hydrogen activation mechanism during catalytic hydrogenation on copper-based catalysts

Plasma-assisted Oxidation of Cu(100) and Cu(111)

Oxidized copper surfaces have attracted significant attention in recent years due to their unique catalytic properties, including their enhanced hydrocarbon selectivity during the electrochemical reduction of CO2. Although oxygen plasma has been used to create highly active copper oxide electrodes for CO2RR, how such treatment alters the copper surface is still poorly understood. Here, we study the oxidation of Cu(100) and Cu(111) surfaces by sequential exposure to a low-pressure oxygen plasma at room temperature. We used scanning tunnelling microscopy (STM), low energy electron microscopy (LEEM), X-ray photoelectron spectroscopy (XPS), near edge X-ray absorption fine structure spectroscopy (NEXAFS) and low energy electron diffraction (LEED) for the comprehensive characterization of the resulting oxide films. O2-plasma exposure initially induces the growth of 3-dimensional oxide islands surrounded by an O-covered Cu surface. With ongoing plasma exposure, the islands coalesce and form a closed oxide film. Utilizing spectroscopy, we traced the evolution of metallic Cu, Cu2O and CuO species upon oxygen plasma exposure and found a dependence of the surface structure and chemical state on the substrate's orientation. On Cu(100) the oxide islands grow with a lower rate than on the (111) surface. Furthermore, while on Cu(100) only Cu2O is formed during the initial growth phase, both Cu2O and CuO species are simultaneously generated on Cu(111). Finally, prolonged oxygen plasma exposure results in a sandwiched film structure with CuO at the surface and Cu2O at the interface to the metallic support. A stable CuO(111) surface orientation is identified in both cases, aligned to the Cu(111) support, but with two coexisting rotational domains on Cu(100). These findings illustrate the possibility of tailoring the oxidation state, structure and morphology of metallic surfaces for a wide range of applications through oxygen plasma treatments

Plasma Functionalization of Silica Bilayer Polymorphs

Ultrathin silica films are considered suitable two-dimensional model systems for the study of fundamental chemical and physical properties of all-silica zeolites and their derivatives, as well as novel supports for the stabilization of single atoms. In the present work, we report the creation of a new model catalytic support based on the surface functionalization of different silica bilayer (BL) polymorphs with well-defined atomic structures. The functionalization is carried out by means of in situ H-plasma treatments at room temperature. Low energy electron diffraction and microscopy data indicate that the atomic structure of the films remains unchanged upon treatment. Comparing the experimental results (photoemission and infrared absorption spectra) with density functional theory simulations shows that H2 is added via the heterolytic dissociation of an interlayer Si–O–Si siloxane bond and the subsequent formation of a hydroxyl and a hydride group in the top and bottom layers of the silica film, respectively. Functionalization of the silica films constitutes the first step into the development of a new type of model system of single-atom catalysts where metal atoms with different affinities for the functional groups can be anchored in the SiO2 matrix in well-established positions. In this way, synergistic and confinement effects between the active centers can be studied in a controlled manner

Time series irreversibility: a visibility graph approach

We propose a method to measure real-valued time series irreversibility which combines two differ- ent tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally effi- cient, does not require any ad hoc symbolization process, and naturally takes into account multiple scales. We find that the method correctly distinguishes between reversible and irreversible station- ary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identifiy the irreversible nature of the series.Comment: submitted for publicatio

Surface Segregation in CuNi Nanoparticle Catalysts During CO₂ Hydrogenation: The Role of CO in the Reactant Mixture

Surface segregation and restructuring in size-selected CuNi nanoparticles were investigated via near-ambient pressure X-ray photoelectron spectroscopy (NAP-XPS) at various temperatures in different gas environments. Particularly in focus were structural and morphological changes occurring under CO2 hydrogenation conditions in the presence of carbon monoxide (CO) in the reactant gas mixture. Nickel surface segregation was observed when only CO was present as adsorbate. The segregation trend is inverted in a reaction gas mixture consisting of CO2, H2, and CO, resulting in an increase of copper concentration on the surface. Density functional theory calculations attributed the inversion of the segregation trend to the formation of a stable intermediate on the nanocatalyst surface (CH3O) in the CO-containing reactant mixture, which modifies the nickel segregation energy, thus driving copper to the surface. The promoting role of CO for the synthesis of methanol was demonstrated by catalytic characterization measurements of silica-supported CuNi NPs in a fixed-bed reactor, revealing high methanol selectivity (over 85%) at moderate pressures (20 bar). The results underline the important role of intermediate reaction species in determining the surface composition of bimetallic nanocatalysts and help understand the effect of CO cofeed on the properties of CO2 hydrogenation catalysts

Thermodynamic properties of Pt nanoparticles: Size, shape, support, and adsorbate effects

This study presents a systematic investigation of the thermodynamic properties of free and γ-Al2O3-supported size-controlled Pt nanoparticles (NPs) and their evolution with decreasing NP size. A combination of in situ extended x-ray absorption fine-structure spectroscopy (EXAFS), ex situ transmission electron microscopy (TEM) measurements, and NP shape modeling revealed (i) a cross over from positive to negative thermal expansion with decreasing particle size, (ii) size- and shape-dependent changes in the mean square bond-projected bond-length fluctuations, and (iii) enhanced Debye temperatures (ΘD, relative to bulk Pt) with a bimodal size-dependence for NPs in the size range of ∼0.8–5.4 nm. For large NP sizes (diameter d >1.5 nm) ΘD was found to decrease toward ΘD of bulk Pt with increasing NP size. For NPs ≤ 1 nm, a monotonic decrease of ΘD was observed with decreasing NP size and increasing number of low-coordinated surface atoms. Our density functional theory calculations confirm the size- and shape-dependence of the vibrational properties of our smallest NPs and show how their behavior may be tuned by H desorption from the NPs. The experimental results can be partly attributed to thermally induced changes in the coverage of the adsorbate (H2) used during the EXAFS measurements, bearing in mind that the interaction of the Pt NPs with the stiff, high-melting temperature γ-Al2O3 support may also play a role. The calculations also provide good qualitative agreement with the trends in the mean square bond-projected bond-length fluctuations measured via EXAFS. Furthermore, they revealed that part of the ΘD enhancement observed experimentally for the smallest NPs (d ≤ 1 nm) might be assigned to the specific sensitivity of EXAFS, which is intrinsically limited to bond-projected bond-length fluctuations

Pattern Formation in Catalytic H₂ Oxidation on Rh: Zooming in by Correlative Microscopy

Spatio-temporal nonuniformities in H2 oxidation on individual Rh(h k l) domains of a polycrystalline Rh foil were studied in the 10–6 mbar pressure range by photoemission electron microscopy (PEEM), X-ray photoemission electron microscopy (XPEEM), and low-energy electron microscopy (LEEM). The latter two were used for in situ correlative microscopy to zoom in with significantly higher lateral resolution, allowing detection of an unusual island-mediated oxygen front propagation during kinetic transitions. The origin of the island-mediated front propagation was rationalized by model calculations based on a hybrid approach of microkinetic modeling and Monte Carlo simulations