Two-dimensional Clusters Research Articles

Phase transitions in normal mode spectra of two-dimensional clusters in an anisotropic power-law confining potential

We present a numerical analysis of several phase transitions which take place in the eigenmode spectrum of a two-dimensional (2D) logarithmic cluster subjected to an anisotropic power law confinement. Varying the anisotropy in a non-parabolic soft confinement drives the system to undergo structural phase transitions of first order, while for a hard wall confinement this variation affects strongly the eigenmode spectrum and breaks the symmetry of the system due to the removal of degeneracy and the coupling between some normal modes.

A new method for the determination of peak distribution across a two-dimensional separation space for the identification of optimal column combinations.

For the identification of the optimal column combinations, a comparative orthogonality study of single columns and columns coupled in series for the first dimension of a microscale two-dimensional liquid chromatographic approach was performed. In total, eight columns or column combinations were chosen. For the assessment of the optimal column combination, the orthogonality value as well as the peak distributions across the first and second dimension was used. In total, three different methods of orthogonality calculation, namely the Convex Hull, Bin Counting, and Asterisk methods, were compared. Unfortunately, the first two methods do not provide any information of peak distribution. The third method provides this important information, but is not optimal when only a limited number of components are used for method development. Therefore, a new concept for peak distribution assessment across the separation space of two-dimensional chromatographic systems and clustering detection was developed. It could be shown that the Bin Counting method in combination with additionally calculated histograms for the respective dimensions is well suited for the evaluation of orthogonality and peak clustering. The newly developed method could be used generally in the assessment of 2D separations. Graphical Abstract ᅟ.

Two-Dimensional Icy Water Clusters Between a Pair of Graphene-Like Molecules or Graphene Sheets

To understand the 2-dimensional (2D) structural evolution of water molecules intercalated into a graphene bilayer, the geometries of water clusters up to tridecamer formed between a pair of graphene sheets or between graphene-like molecules (coronene and dodecabenzocoronene) are investigated. Due to their large sizes, the self-consistent-charge density-functional tight-binding (SCC-DFTB) method expanded into the third order and supplemented with a Slater–Kirkwood dispersion term was used. In this way both hydrogen bonding and H−π/π–π interactions are calculated in a balanced manner with the right magnitude of binding energies very close to the reference values based on the most accurate ab initio results. It should be noted that conventional density functional theory (DFT) calculations underestimate the H−π/π–π interaction, while dispersion-corrected DFT calculations overestimate hydrogen bonding. The latter method is also employed for comparison and to confirm the reliability of the SCC-DFTB results. For (H2O)6, the fused bitetragonal hexamer is nearly isoenergetic to the most stable planar hexagonal ring structure, and it is more frequently found. In (H2O)10 and (H2O)13 clusters, a tetragon is the most frequent geometry followed by a pentagon, while the hexagon is less frequent. These results certainly provide evidence of the recent planar tetragonal ice structure found inside a graphene bilayer (Nature 2015, 519, 443) which is in contrast to the well-known hexagonal pattern of the bulk ice. This structural change from hexagonal to tetragonal network on the graphene surface is attributed mainly to the inherent nature of 2D water.

Chain structures and clusters of particles with the mixed dipole–quadrupole interaction in smectic freely suspended nanofilms

The formation of unusual chain structures and clusters of particles with the mixed dipole–quadrupole interaction has been found in smectic nanofilms. Unlike topological dipoles and quadrupoles, the interaction between which leads to the formation of structures with finite interparticle distances, the particles with the mixed interaction touch each other and form stable chains and two-dimensional clusters. The orientation of particles in chains is intermediate between dipole and quadrupole chains. The variation of the interparticle distance and orientation of chains is explained qualitatively on the basis of the calculation of the с-director (field lines) near particles and the mutual arrangement of particles providing the minimum distortion of field lines.

Modification of the electronic properties of magic In clusters on Si(111)7 × 7 by different environments

The charge redistribution and the electronic properties of magic In clusters on the Si(111)7 × 7 surface were investigated using scanning tunneling microscopy and spectroscopy. Thereby, special attention was directed to the influence of different environments, such as the orientation of the supporting 7 × 7 half unit cell and the beginning growth of two-dimensional cluster arrays, on the electronic properties of the clusters. It was found that clusters forming in the faulted and the unfaulted half unit cell of the 7 × 7 reconstruction as well as clusters neighboring other clusters exhibit different electronic properties. Although all clusters show a semiconducting behavior, their energy gaps vary. In addition, metal-induced gap states are observed in the tunneling spectra within the energy gap of the clusters due to the metallic states of the surrounding 7 × 7 surface that tail into the energy gap of the clusters. The larger energy gap of clusters neighboring other clusters, a situation that in principle ...

Plasmon excitations in two-dimensional atomic cluster systems

Properties of plasmon excitations in two-dimensional (2D) atomic cluster systems are theoretically studied within an extended Hubbard model. The collective oscillation equations of charge, plasmon eigen-equations and the energy-absorption spectrum formula are presented. The calculated results show that different symmetries of plasmons exist in the cluster systems, and the symmetry of charge distribution in the plasmon resonance originate from the intrinsic symmetry of the corresponding eigen-plasmon modes, but not from the symmetry of applied external fields; however, the plasmon excitation with a certain polarization direction should be excited by the field in this direction, the dipole mode of plasmons can be excited by both uniform and non-uniform fields, but multipole ones cannot be excited by an uniform field. In addition, we show that for a given electron density, plasmon spectra are red-shifted with increasing size of the systems.

Site-Specific Assembly of Fullerene Nanorings Guided by Two-Dimensional Gold Clusters

Molecules can self-assemble rather easily into straight one-dimensional wires via covalent or noncovalent bonding. To organize molecules into cyclic structures such as rings or loops where the number of molecules forming each structure is accurately controlled is a much more challenging task. Here we demonstrate the construction of fullerene nanorings on the (111) plane of gold using single-atomic-layer-high gold islands as the seeding agent. C60 molecules are trapped by the step edges of the seeding Au island leading to the formation of molecular rings. The smallest ring consists of six C60 molecules encircling 19 Au atoms. Scanning tunneling microscopy imaging reveals that the rings are formed at specific locations on the reconstructed Au(111) surface with the diameter of the ring controlled by the size of the gold island. Molecular mechanics modeling provides a detailed understanding of the relationship between the number of molecules in the ring and the number of gold atoms within the Au island.

Duality in spin systems via the SU(4) algebra

We provide several examples and an intuitive diagrammatic representation demonstrating the use of two-qubit unitary transformations for mapping coupled spin Hamiltonians to simpler ones and vice versa. The corresponding dualities may be exploited to identify phase transition points or to aid the diagonalization of such Hamiltonians. For example, our method shows that a suitable one-parameter family of coupled Hamiltonians whose ground states transform from an initially factorizing state to a final cluster state on a lattice of arbitrary dimension is dual to a family of trivial decoupled Hamiltonians containing local on-site terms only. As a consequence, the minimum energy gap (which determines the adiabatic run-time) does not scale with system size, which facilitates an efficient and simple adiabatic preparation of e.g. the two-dimensional cluster state used for measurement-based quantum computation.

Molecular Dynamics Simulation of Surface Nucleation during Growth of an Alkane Crystal

Crystal growth from the melt of n-pentacontane (C50) was studied by molecular dynamics simulation. Quenching below the melting temperature gives rise to propagation of the crystal growth front into the C50 melt from a crystalline polyethylene surface. By tracking the location of the crystal–melt interface, crystal growth rates between 0.02 and 0.05 m/s were observed, for quench depths of 10–70 K below the melting point. These growth rates compare favorably with those from a previous study by Waheed et al. [Polymer 2005, 46, 8689−8702]. Next, surface nucleation was identified with the formation of two-dimensional clusters of crystalline sites within layers parallel to the propagating growth front. Critical nucleus sizes, waiting times, and rates for surface nucleation were estimated by a mean first passage time analysis. A surface nucleation rate of ∼0.05 nm–2 ns–1 was observed, and it was nearly temperature-independent. Postcritical “spreading” of the surface nuclei to form a completely crystallized layer...

Spin dynamics and two-dimensional correlations in the fcc antiferromagneticSr2YRuO6

The face-centered-cubic (fcc) lattice of ${\mathrm{Ru}}^{5+}$ spins in the double perovskite ${\mathrm{Sr}}_{2}{\mathrm{YRuO}}_{6}$ shows a delicate, three-dimensional antiferromagnetic (AFM) ground state composed of stacked square AFM layers. Inelastic neutron scattering data taken on this state reveal a gapped low-energy excitation band emerging from [001] with spin excitations extending to 8 meV. These magnetic excitations are modeled by a simple ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ interaction scheme allowing quantitative comparisons with similar materials. At higher temperatures, the low-energy excitation spectrum is dominated by a quasielastic component associated with size fluctuations of two-dimensional AFM clusters that exhibit asymmetric correlations even at low temperatures. Thus, the fcc lattice in general and the double-perovskite structure in particular emerge as hosts of both two-dimensional and three-dimensional dynamics resulting from frustration.

Engineering microscale two-dimensional gold nanoparticle cluster arrays for advanced Raman sensing: An AFM study

We realized and tested a strategy for developing reproducible and stable two-dimensional gold nanoparticle cluster arrays arranged on silicon substrates, to be used for surface-enhanced Raman spectroscopy. We combined electron beam lithography and molecular functionalization to finely control the shape of the nanoparticle assemblies. Atomic force microscopy analysis allowed to optimize the procedure of nanoparticle cluster array fabrication in terms of electron beam dose and chemical protocol, enabling to achieve a good regularity in spacing and size (i.e. area and layer number) of the clusters. MicroRaman space resolved measurements were undertaken on large 2D arrays (100 × 100 μm2) made up of regularly microsized clusters. The high surface enhanced Raman signal measured on the structures highlights the full correspondence of the spatial and optical periodicity achieved. This standardized procedure represent the basis to realize versatile platforms for nano-optical investigation and towards an efficient high-sensitive multiplex sensing.

Electron density of states of Fe-based superconductors: Quantum trajectory Monte Carlo method

The spectral and total electron densities of states in two-dimensional FeAs clusters, which simulate iron-based superconductors, have been calculated using the generalized quantum Monte Carlo algorithm within the full two-orbital model. Spectra have been reconstructed by solving the integral equation relating the Matsubara Green’s function and spectral density by the method combining the gradient descent and Monte Carlo algorithms. The calculations have been performed for clusters with dimensions up to 10 × 10 FeAs cells. The profiles of the Fermi surface for the entire Brillouin zone have been presented in the quasiparticle approximation. Data for the total density of states near the Fermi level have been obtained. The effect of the interaction parameter, size of the cluster, and temperature on the spectrum of excitations has been studied.

Spatial distribution and source apportionment of PFASs in surface sediments from five lake regions, China.

Perfluoroalkyl substances (PFASs) have been found in environment globally. However, studies on PFAS occurrence in sediments of lakes or reservoirs remain relatively scarce. In this study, two hundred and sixty-two surface sediment samples were collected from forty-eight lakes and two reservoirs all over China. Average PFAS concentrations in surface sediments from each lake or reservoir varied from 0.086 ng/g dw to 5.79 ng/g dw with an average of 1.15 ng/g dw. Among five lake regions, average PFAS concentrations for the lakes from Eastern Plain Region were the highest. Perfluorooctanoic acid, perfluoroundecanoic acid and perfluorooctane sulfonic acid (PFOS) were the predominant PFASs in surface sediments. The significant positive correlations between PFAS concentrations and total organic carbon, total nitrogen and total phosphorus contents in sediments revealed the influences of sedimentary characteristics on PFAS occurrence. A two-dimensional hierarchical cluster analysis heat map was depicted to analyze the possible origins of sediments and individual PFAS. The food-packaging, textile, electroplating, firefighting and semiconductor industry emission sources and the precious metals and coating industry emission sources were identified as the main sources by two receptor models, with contributions of 77.7 and 22.3% to the total concentrations of C4-C14- perfluoroalkyl carboxylic acids and PFOS, respectively.

Silver- and Gold-Ordered Structures on Single-Crystal Silicon Surface After Thermal Deposition

The formation mechanisms of Ag- and Au-ordered structures on single-crystal silicon (Si) (111) and Si (110) surfaces were researched using high-resolution scanning tunneling microscopy method. It was shown that different patterns of self-assembled nanostructures with very precise and regular geometric shapes can be produced by controlling process parameters of thermal metal spraying on the substrate. The surfaces of nanorelieves at each stage of deposition were researched, and the main stages of morphological transformation were fixed.Self-ordered hexagonal pyramid-shaped nanostructures were formed at thermal deposition of gold on the Si (111), whereas only monolayer hexagonal formation could be observed on the plane Si (110). Gold monolayer flake nanostructures were obtained under certain technological parameters.Atomically smooth Ag film cannot be obtained on the Si (111) surface by means of thermal spraying at room temperature. The formation of two-dimensional (2D) clusters takes place; heating of these clusters at several hundred degrees Celsius leads to their transformation into atomically smooth covering.The weak interaction between Ag multilayer coatings and substrate was established that allows to clear crystal surface from metal with reproduction of the reconstructed Si (111) 7 × 7 surface by slight warming. The offered method can be used for single-crystal surface protection from destruction.

Extension of the two-dimensional mass channel cluster plot method to fast separations utilizing low thermal mass gas chromatography with time-of-flight mass spectrometry

Implementation of a data reduction and visualization method for use with high-speed gas chromatography and time-of-flight mass spectrometry (GC-TOFMS) is reported. The method, called the “2D m/z cluster method” facilitates analyte detection, deconvolution, and identification, by accurately measuring peak widths and retention times using a fast TOFMS sampling frequency (500 Hz). Characteristics and requirements for high speed GC are taken into consideration: fast separations with narrow peak widths and high peak capacity, rapid data collection rate, and effective peak deconvolution. Transitioning from standard GC (10–60+ minute separations) to fast GC (1–10 min separations) required consideration of how to properly analyze the data. This report validates use of the 2D m/z cluster method with newly developed GC technology that produces ultra-fast separations (∼1 min) with narrow analyte peak widths. Low thermal mass gas chromatography (LTM-GC) operated at a heating rate of 250 °C/min coupled to a LECO Pegasus III TOFMS analyzed a 115 component test mixture in 120 s with peak widths-at-base, wb (4σ), of 350 ms (average) to produce a separation with a high peak capacity, nc ∼ 340 (at unit resolution Rs = 1). The 2D m/z cluster method is shown to separate overlapped analytes to a limiting Rs ∼ 0.03, so the effective peak capacity was increased nearly 30-fold to nc ∼10,000 in the 120 s separation. The method, when coupled with LTM-GC-TOFMS, is demonstrated to provide unambiguous peak rank (i.e. the number of analytes per overlapped peak in the total ion current (TIC)), by visualizing locations of pure and chromatographically overlapped m/z. Hence, peak deconvolution and identification using MCR-ALS (multivariate curve resolution – alternating least squares) is demonstrated.

Architecture and Function of Mechanosensitive Membrane Protein Lattices.

Experiments have revealed that membrane proteins can form two-dimensional clusters with regular translational and orientational protein arrangements, which may allow cells to modulate protein function. However, the physical mechanisms yielding supramolecular organization and collective function of membrane proteins remain largely unknown. Here we show that bilayer-mediated elastic interactions between membrane proteins can yield regular and distinctive lattice architectures of protein clusters, and may provide a link between lattice architecture and lattice function. Using the mechanosensitive channel of large conductance (MscL) as a model system, we obtain relations between the shape of MscL and the supramolecular architecture of MscL lattices. We predict that the tetrameric and pentameric MscL symmetries observed in previous structural studies yield distinct lattice architectures of MscL clusters and that, in turn, these distinct MscL lattice architectures yield distinct lattice activation barriers. Our results suggest general physical mechanisms linking protein symmetry, the lattice architecture of membrane protein clusters, and the collective function of membrane protein lattices.

Non-targeted determination of 13C-labeling in the Methylobacterium extorquens AM1 metabolome using the two-dimensional mass cluster method and principal component analysis

A novel analytical workflow is presented for the analysis of time-dependent 13C-labeling of the metabolites in the methylotrophic bacterium Methylobacterium extorquens AM1 using gas chromatography time-of-flight mass spectrometry (GC-TOFMS). Using 13C-methanol as the substrate in a time course experiment, the method provides an accurate determination of the number of carbons converted to the stable isotope. The method also extracts a quantitative isotopic dilution time course profile for 13C uptake of each metabolite labeled that could in principle be used to obtain metabolic flux rates. The analytical challenges encountered require novel analytical platforms and chemometric techniques. GC-TOFMS offers advanced separation of mixtures, identification of individual components, and high data density for the application of advanced chemometrics. This workflow combines both novel and traditional chemometric techniques, including the recently reported two-dimensional mass cluster plot method (2D m/z cluster plot method) as well as principal component analysis (PCA). The 2D m/z cluster plot method effectively indexed all metabolites present in the sample and deconvoluted metabolites at ultra-low chromatographic resolution (RS≈0.04). Using the pure mass spectra extracted, two PCA models were created. Firstly, PCA was used on the first and last time points of the time course experiment to determine and quantify the extent of 13C uptake. Secondly, PCA modeled the full time course in order to quantitatively extract the time course profile for each metabolite. The 2D m/z cluster plot method found 152 analytes (metabolites and reagent peaks), with 54 pure analytes, and 98 were convoluted, with 65 of the 98 requiring mathematical deconvolution. Of the 152 analytes surveyed, 83 were metabolites determined by the PCA model to have incorporated 13C while 69 were determined to be either metabolites or reagent peaks that remained unlabeled.

Rigidity of transmembrane proteins determines their cluster shape.

Protein aggregation in cell membrane is vital for the majority of biological functions. Recent experimental results suggest that transmembrane domains of proteins such as α-helices and β-sheets have different structural rigidities. We use molecular dynamics simulation of a coarse-grained model of protein-embedded lipid membranes to investigate the mechanisms of protein clustering. For a variety of protein concentrations, our simulations under thermal equilibrium conditions reveal that the structural rigidity of transmembrane domains dramatically affects interactions and changes the shape of the cluster. We have observed stable large aggregates even in the absence of hydrophobic mismatch, which has been previously proposed as the mechanism of protein aggregation. According to our results, semiflexible proteins aggregate to form two-dimensional clusters, while rigid proteins, by contrast, form one-dimensional string-like structures. By assuming two probable scenarios for the formation of a two-dimensional triangular structure, we calculate the lipid density around protein clusters and find that the difference in lipid distribution around rigid and semiflexible proteins determines the one- or two-dimensional nature of aggregates. It is found that lipids move faster around semiflexible proteins than rigid ones. The aggregation mechanism suggested in this paper can be tested by current state-of-the-art experimental facilities.

A modified harmony search method for biclustering microarray gene expression data

Microarray experiments generate vast amounts of data, leading to new requirements and challenges for bioinformatics. The crucial step in considering gene expression data is to discover a group of genes that have similar patterns. Biclustering is a two-dimensional clustering problem where the genes and samples are grouped simultaneously. Latest research showed that biclustering has a great potential in finding marker genes that are associated with certain tissues or diseases. Here, we present an efficient biclustering algorithm called Modified Harmony Search (MHS) method. The MHS algorithm includes a step for generating the new solution by using levy flight. Levy flight increases the diversity of the solutions of harmony search (HS) algorithm and the Pitch Adjusting Rate (PAR) is changed dynamically to escape from local optima. To know the performance of the MHS, it is applied on various benchmark optimisation functions and the benchmark gene expression data sets. The experimental results show that the MHS outperforms HS in optimisation functions and biclustering problems. Also, this work determines the biological relevance of the biclusters with Gene Ontology in terms of function, process and component.

Segregation of "isotope" particles within colloidal molecules.

Clusters of spherical particles are called "colloidal molecules" because they adopt structures that resemble those of true molecules. In this analogy, the particles are the atoms, the attractive interactions between them are bonds, and the different structures that appear in equilibrium are isomers. We take this analogy a step further by doping colloidal molecules with colloidal "isotopes," particles that have the same size but different bonding energies from the other particles in the system. Our molecules are two-dimensional clusters consisting of polystyrene and silica microspheres held together by depletion interactions. Using a combination of optical microscopy and particle tracking, we examine an ensemble of 4- and 5-particle molecules at different isotope ratios. We find that the isotopes tend to segregate to particular positions in the various isomers. We explain these findings using a statistical mechanical model that accounts for the rotational entropy of the isomers and the different interaction potentials between the different types of particles. The model shows how to optimize the yield of any particular isomer, so as to put the isotopes in desired locations. Our experiments and models show that even in systems of particles with isotropic interactions, the structures of self-assembled molecules can in principle be controlled to a surprisingly high extent.