Spontaneous breaking of one-dimensional chains investigated with scanning tunneling microscopy

Landau (1937) [1] had an argument that one-dimensional long chains are not stable at finite temperature, and will break into short sections due to thermal fluctuation. However, until recently, fragmentation of one-dimensional chains by formation of thermal vacancies was first discovered in Bagatskii et al. (2014) [6] for the Xenon that physically adsorbed in the grooves of single-walled carbon nanotube bundles. In this work, scanning tunneling microscopy (STM) was first used to observe the influence of thermal fluctuations on the length of one-dimensional chains of the amino acids systems chemically adsorbed on metal surfaces. One-dimensional chains of amino acids formed on noble metal surfaces are spontaneously broken into chain segments with an average length of ～46 Å at room temperature. Very amazingly, the chain phase shows a unique self-adaptability in that it can always keep the length of chain segments unchanged at a fixed value, which is fulfilled through their flexible orientations, even though there is space limitation. While thermal fluctuation is a stochastic process, breaking of chains does not occur randomly along the chains. Breaking points are equidistantly distributed along the chain with a density (i.e., ratio of breaking points to adsorbates in a chain) of ～1/9 at room temperature. After heated to 400 K, the chain segments are shortened to ～31 Å. And thus, the breaking point density is increased to ～1/6. The activation energy for forming a breaking point is ～0.04 eV, being within the range of energy for a common hydrogen bond, implying that the amino acid chain is formed by intermolecular hydrogen bonds between adsorbates. The stable spatial distribution of broken points in a chain is resulted from the loss of one-dimensional translational symmetry at the two ends of a chain. This research experimentally first time substantiated both Landau's argument as well as prediction in some recent theoretical simulations.     

Scaling behavior of one-dimensional weakly disordered models

The density of states and various characteristic lengths of one-dimensional tight-binding models and disordered harmonic chains are calculated in the limit of weak disorder at the band edge of the ordered system. The density of states and a localization length of the one-dimensional Anderson model were already calculated by Derrida and Gardner; we recover their results. For the tight-binding models with off-diagonal disorder our results are in agreement with numerical calculations of Krey.     

Surface nanocrystallization of an ionic liquid

Surface crystallization at the vapor-liquid interface of the ionic liquid (1-butyl-3-methylimidazolium hexafluorophosphate) is observed in synchrotron x-ray diffraction studies. Sharp Bragg reflections emerge in grazing-angle x-ray diffraction patterns 37?°C above the bulk melting temperature, indicating the presence of a long-range ordered phase at the surface in coexistence with the bulk parent liquid. The unique structure of the vapor-liquid interface where butyl chains attached to the cations are expelled to the vapor side facilitates interionic electrostatic interactions that lead to the crystallization. Our results demonstrate the complexity of ionic-liquid structure with their tendency to spontaneously phase separate into nanodomains with finite correlation lengths in coexistence with the liquid phase. By virtue of interfacial boundary conditions, these nanodomains grow laterally to form quasi-two-dimensional crystals.     

Finite-sized Heisenberg chains and magnetism of one-dimensional metal systems

We present a combined experimental and theoretical study of the magnetization of one-dimensional atomic cobalt chains deposited on a platinum surface. We discuss the intrinsic magnetization parameters derived by X-ray magnetic circular dichroism measurements and the observation of ferromagnetic order in one dimension in connection with the presence of strong, dimensionality-dependent anisotropy energy barriers of magnetocrystalline origin. An explicit transfer matrix formalism is developed to treat atomic chains of finite length within the anisotropic Heisenberg model. This model allows us to fit the experimental magnetization curves of cobalt monatomic chains, measured parallel to the easy and hard axes, and provides values of the exchange coupling parameter and the magnetic anisotropy energy consistent with those reported in the literature. The analysis of the spin–spin correlation as a function of temperature provides further insight into the tendency to magnetic order in finite-sized one-dimensional systems. PACS 57.10.Pq; 75.30.-m; 75.30.Gw; 78.70.Dm     

Systematic study of the effect of disorder on nanotribology of self-assembled monolayers

The adhesion and friction between pairs of ordered and disordered self-assembled monolayers on SiO2 are studied using molecular dynamics. The disorder is introduced by randomly removing chains from a well ordered crystalline substrate and by attaching chains to an amorphous substrate. The adhesion force between monolayers at a given separation increases monotonically with chain length at full coverage and with coverage for fixed chain length. Friction simulations are performed at shear velocities between 0.02-2 m/s at constant applied pressures between 200 and 600 MPa. Stick-slip motion is observed at full coverage but disappears with disorder. With random defects, the friction becomes insensitive to chain length, defect density, and substrate.     

The use of biopolymer templates to fabricate low-dimensional gold particle structures

We report the current–voltage characteristics of gold nanoparticle–biopolymer networks at room temperature. The characteristics have features that are indicative of single-electron charging in ordered, one-dimensional chains of nanoparticles. From capacitance estimates and numerical simulations, we argue that the observed electrical behavior is related to the low size dispersion of the nanoparticles and the uniformity of the biopolymer lengths imbedded within the network.     

Asymptotic behavior of fluctuations for the 1D Ising model in zero-temperature limit

Fluctuation of the average spin for one-dimensional Ising spins with nearest neighbor interactions are studied. The distribution function for the average spin is calculated for a finite volume, finite temperature, and finite magnetic field. As the volume increases and the temperature diminishes at zero magnetic field, there are two limits in which the probability distribution shows quite different behaviors: in the thermodynamic limit as the volume goes to infinity for finite temperature, small deviations of the fluctuations are described by a Gaussian distribution, and in the limit as the temperature vanishes for a finite volume, the ground states are realized with probability one. The crossover between these limits is analyzed via a ratio of the correlation length to the volume. The helix-coil transition in a polypeptide is discussed as an application.     

Influence of the polydispersity of side chains on the phase behavior of multigraft copolymers

Weak segregation theory is applied to studying the phase behavior of a melt of a binary multigraft copolymer with polydisperse side chains regularly spaced along the backbone. The resulting phase diagrams of the melt show an increase of the temperature of transition to an ordered state with increasing coefficient of polydispersity of side chains. The effects of the average length of the side chains and the distance between the points of their grafting on the phase diagram of the melt are examined.     

Simple model for a quantum wire III. Transmission in finite samples with correlated disorder

The effect of a continuous model of correlations upon one-dimensional finite disordered quantum wires modeled by an array of delta-potentials, is analyzed. Although the model proposed is not able to include new truly extended states in the spectrum, the transport properties of a finite sample are noticeably improved due to the existence of states whose localization length is larger than the system size. This enhancement of transmission is maximized for relatively short chains.     

Extended acoustic waves in diluted random systems

In this paper we study the propagation of acoustic waves in an one-dimensional diluted random media which is composed of two interpenetrating chains with pure and random elasticity. We considered a discrete one-dimensional version of the wave equation where the elasticity distribution appears as an effective spring constant. By using a matrix recursive reformulation we compute the localization length within the band of allowed frequencies. In addition, we apply a second-order finite difference method for both time and spatial variables, and study the nature of the waves that propagate in the chain. We numerically demonstrate that the diluted random elasticity distribution promotes extended acoustic modes at high-frequencies.     

Excitation chains at the glass transition

The excitation-chain theory of the glass transition, proposed in an earlier publication, predicts diverging, super-Arrhenius relaxation times and, via a similarly diverging length scale, suggests a way of understanding the relations between dynamic and thermodynamic properties of glass-forming liquids. I argue here that critically large excitation chains play a role roughly analogous to that played by critical clusters in the droplet model of vapor condensation. Unlike a first-order condensation point in a vapor, the glass transition is not a conventional phase transformation, and may not be a thermodynamic transition at all.     

Calculation of the Binding Energy in the One-Dimensional Hubbard Model by the VMC Method

Using variational Monte-Carlo method and choosing an antiferromagnetic trial wave function,we have calculated the binding energies just off half-filling in one-dimensional Hubbard chains. We found the binding for the lattice length N being less than 40 in the degenerate case, but no binding at aU in the non-degenerate case. However, with lattice length increasing gradually, difference between the two cases becomes smaller and smaller. Finally, there is no binding at all no matter whether or not the chains have a degeneracy at the Fermi level in the non-interacting (U=0) limit. It may bean in,dication of the independence of the final calculation results on the boundary conajtions for the large enough system or in thermodynamic limit.     

Equilibration and universal heat conduction in fermi-pasta-ulam chains

It is shown numerically that for Fermi-Pasta-Ulam (FPU) chains with alternating masses and heat baths at slightly different temperatures at the ends, the local temperature (LT) on small scales behaves paradoxically in steady state. This expands the long established problem of equilibration of FPU chains. A well-behaved LT appears to be achieved for equal mass chains; the thermal conductivity is shown to diverge with chain length N as N(1/3), relevant for the much debated question of the universality of one-dimensional heat conduction. The reason why earlier simulations have obtained systematically higher exponents is explained.     

Self-assembling of gold nanoparticles in one, two, and three dimensions

In the present work, we report the growth of ordered arrays of gold nanoparticles passivated with n-alkylthiol molecules using crystallization in toluene vapor. We kept constant the average particle size and the length of the passivating molecule (1-dodecanethiol). The temperature and time of growth were varied. We show that in the initial stages of the growth, nano-chains of particles are produced. These nano-chains aggregate to form two-dimensional arrays. In the initial stages the nano-chains form a two-dimensional square lattice which then relaxes to a close-packed structure. In latter stages of growth a three-dimensional supercrystal is produced. It is found that the packing of nanoparticles corresponds to an average FCC lattice. However, large variations on the local parameters of the lattice are observed. Near the edges of the supercrystal the anomalous packing reported by Zanchet et al. [20] and Fink et al. [21] was observed. The energy of the observed structures is analyzed using molecular dynamics simulation. It is concluded that using the vapor growth method, it is possible to produce controlled ordered structures from one to three dimensions. Received: 24 February 2000 / Accepted: 28 March 2000 / Published online: 13 July 2000     

Lattice bosons in a quasi-disordered environment

In this paper, we study non-interacting bosons in a quasi-disordered one-dimensional optical lattice in a harmonic potential. We consider the case of deterministic quasi-disorder produced by an Aubry–André potential. Using exact diagonalization, we investigate both the zero temperature and the finite temperature properties. We investigate the localization properties by using an entanglement measure. We find that the extreme sensitivity of the localization properties to the number of lattice sites in finite size closed chains disappear in open chains. This feature continues to be present in the presence of a harmonic confining potential. The quasi-disorder is found to strongly reduce the Bose–Einstein condensation temperature and the condensate fraction in open chains. The low temperature thermal depletion rate of the condensate fraction increases considerably with increasing quasi-disorder strength. We also find that the critical quasi-disorder strength required for localization increases with increasing strength of the harmonic potential. Further, we find that the low temperature condensate fraction undergoes a sharp drop to 0.5 in the localization transition region. The temperature dependence of the specific heat is found to be only marginally affected by the quasi-disorder.     

The bulk dynamics of a compositionally asymmetric diblock copolymer studied using dynamic light scattering

We have studied the bulk dynamics of a compositionally asymmetric poly(ethylene propylene)-poly(dimethylsiloxane) (PEP-PDMS) diblock copolymer in a large temperature range both in the ordered and in the disordered state. The volume fraction of the PEP block is 0.22. Apart from the disordered state, the sample shows three ordered morphologies. Using dynamic light scattering, we have investigated the dynamics in all four phases and combined these results with those obtained using pulsed field gradient NMR. In the disordered state, we find--apart from the slow cluster mode--the heterogeneity mode related to the self-diffusion of single chains. The relaxation time of this mode, reduced by temperature and the zero-shear viscosity , , increases with temperature. In the cubic phase right below the ODT temperature, we observe two diffusive processes, and we attribute the faster one to the mutual diffusion of micelles and block copolymers not bound to micelles (“free chains”) through the PDMS matrix. The slower mode may either be due to the mutual diffusion of free chains and chains bound to PEP micelles or to the cooperative diffusion of micellar aggregates. In the non-cubic ordered state at intermediate temperatures, an additional weak diffusive mode is observed. The low-temperature ordered state is body-centered cubic, and here, only the mutual diffusion of micelles and free chains lies in our experimental time window. Received 19 March 1999 and Received in final form 25 August 1999     

The effect of spin dilution on magnetism of the linear chain system β-Cu2?xZnxV2O7

We have measured the magnetic susceptibility (χ) and heat capacity (C _p) of β-Cu_2−x Zn _x V₂O₇ (x = 0, 0.05, 0.1, 0.15, 0.2, 0.3, 2) in the temperature range 2–300 K. A one-dimensional alternating exchange Heisenberg antiferromagnetism (HAF) is observed in all compositions with chains of infinite length. The intra-chain exchange remains uniform and decreases marginally with dilution of the magnetic state. A cooperative ordering is seen in the magnetic chains for all Zn concentrations (x ≤ 0.3). The temperature of occurrence of this transition decreases with increasing Zn concentration. Though the conventional spin-wave theory has been used here to describe the properties of the ordered phase, the presence of some contributions like the lattice heat capacity in C _p and the Curie-Weiss term in susceptibility introduces some uncertainties in the estimation of the proportions contributed by the spin system. Therefore, the nature of the ordered phase could not be ascertained unambiguously.     

On diffusion mixing of vapor and gas

A self-similar solution is obtained for a one-dimensional problem of diffusion mixing of vapor and gas, which is followed by condensation process. Two limiting cases of mixing are considered: in the first one, the vapor and gas occupy in their initial states the volumes of semi-infinite extension, in the second case, the vapor has a semi-infinite extension, and constant values of temperature and gas concentration are maintained at its boundary. The peculiarities of the temperature and concentration fields are analysed versus the vapor and gas temperatures, and the temperature values are found, at which the mixing occurs with the condensate formation.     

Electronic effects in the length distribution of atom chains

Gold deposited on Si(553) leads to self-assembly of atomic chains, which are broken into finite segments by defects. Scanning tunneling microscopy is used to investigate the distribution of chain lengths and the correlation between defects separating the chains. The length distribution reveals oscillations that indicate changes in the cohesive energy as a function of chain length. We present a possible interpretation in terms of the electronic scattering vectors at the Fermi surface of the surface states. The pairwise correlation function between defects shows long-range correlations that extend beyond nearest-neighbor defects, indicating coupling between chains.     

A mathematical method for the analysis of heat capacity and thermal conductivity measurements by the heat pulse technique

We present a new mathematical method for the analysis of heat capacity and thermal conductivity measurements by the heat pulse technique for the case of samples of finite length with a one-dimensional heat flow. In these experiments a heat pulse is produced by a heater, and the temperature is measured as a function of time at a different location on the sample. Finite length effects are taken care of in a natural way, and the thermal conductivity is obtained very simply. In addition, this method is capable of separating the heat capacities of the sample, of the heater and of the thermometer, which may be of practical importance for the case of thin samples with a small heat capacity. The mathematical analysis is based on Laplace transform techniques similar to those used for electrical transmission lines. The analysis of the experimental data is performed by calculating several moments of the temperature rise in the thermometer as a function of time. The method is particularly suitable for on-line computer experiments.