Fluctuating Bond Model Research Articles

Magnetotransport properties and pseudogap phase diagram of superconducting EuBa2Cu3Oy thin films: the influence of Eu substitution

This research explores and debates magnetotransport properties and the pseudogap phase diagram of high-temperature superconducting EuBa2Cu3Oy (EBCO) films through ρxx(T) and ρxy(T) measurements. The mixed state transport properties of samples with higher doped levels show a power-law field-dependence of activation energy U, U ∝ H−α with α = 0.52 ± 0.05, while the slightly doped samples reveal a logarithmic field-dependence of U. In addition, for the first time, all samples in the underdoped region display an unusual power-law behavior of U ∝ pγ with γ = −5.90 ± 0.28, which is qualitatively explained. A sign reversal of transverse resistivity in the mixed state is also present in the nearly optimum-doped samples, which have strong pinning energies. In the normal state, the cotangent of the Hall angle shows a wide range quadratic temperature dependence for all the samples, which can be described by Anderson’s theory. The values of spin excitation bandwidth W are coincident between two results obtained from the hidden Fermi-liquid theory and from the Hall angle for the slightly overdoped sample. Moreover, the phase diagram of EBCO, containing the superconducting transition temperatures, the T* and T** temperatures in the pseudogap (PG) phase, and the antiferromagnetic transition temperatures θN, in the whole underdoped region has been completed and compared with those for YBa2Cu3Oy (YBCO). The findings demonstrate that EBCO has lower T* and T** values, versus those of YBCO in the same doping region. The observed smaller magnitude of PG for EBCO is explained by considering the oxygen vibrational amplitudes in Cu−O−Cu bonds, which agrees with the inference based on the fluctuating bond model. The influence of Eu substitution is examined and discussed.

Ab initiotheory of the pseudogap in cuprate superconductors driven byC4 symmetry breaking

Understanding the origin of the pseudogap is an essential step toward elucidating the pairing mechanism in the cuprate superconductors. Recently there has been strong experimental evidence showing that $C$4 symmetry breaking occurs on the formation of the pseudogap. This form of symmetry breaking was predicted by the fluctuating bond model (FBM), an empirical model based on a strong, local coupling of electrons to the square of the planar oxygen vibrator amplitudes. In this paper we approach the FBM theory from a new direction, starting from ab initio molecular dynamics simulations. The simulations demonstrate a doping-dependent instability of the in-plane oxygens toward displacement off the Cu-O-Cu bond axis. From these results and perturbation theory we derive an improved and quantitative form of the FBM. A mean-field solution of the FBM leads to $C$4 symmetry breaking in the oxygen vibrational amplitudes and to a $d$-type pseudogap in the electronic spectrum, the features linked by recent experimental data. The phase diagram of the pseudogap derived from mean-field theory, its doping and temperature dependences, including the phase boundary ${T}^{*}$, agree well with experimental data. We extend the theory to include the long-range Coulomb interaction on the same basis as the FBM interaction. When the long-range Coulomb interaction is included in the FBM, a charge density wave (CDW) instability in the charge channel is predicted, which explains the nanoscale, rather than spatially uniform, behavior of the $C$4 symmetry breaking. Taking the CDW into account, with the theoretical $k$ dependence of the pseudogap, enables the Fermi surface arc phenomenon to be understood.

Fluctuating bond model of high temperature superconductivity in cuprates

Despite extensive experimental and theoretical work, there is currently no consensus theory for the pairing mechanism in High Temperature Superconductors or for their other anomalous properties. We present a new theory based on a strong, local, nonlinear coupling between the electronic bond strength and oxygen motion in the Cu-O-Cu bond. This model is able to explain a wide range of properties involving superconductivity and symmetry breaking in these materials.

Polymer translocation through a nanopore under an applied external field

We investigate the dynamics of polymer translocation through a nanopore under an externally applied field using the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. We concentrate on the influence of the field strength E, length of the chain N, and length of the pore L on forced translocation. As our main result, we find a crossover scaling for the translocation time tau with the chain length from tau approximately N2nu for relatively short polymers to tau approximately N1+nu for longer chains, where nu is the Flory exponent. We demonstrate that this crossover is due to the change in the dependence of the translocation velocity v on the chain length. For relatively short chains v approximately N-nu, which crosses over to v approximately N(-1) for long polymers. The reason for this is that with increasing N there is a high density of segments near the exit of the pore, which slows down the translocation process due to slow relaxation of the chain. For the case of a long nanopore for which R parallel, the radius of gyration Rg along the pore, is smaller than the pore length, we find no clear scaling of the translocation time with the chain length. For large N, however, the asymptotic scaling tau approximately N1+nu is recovered. In this regime, tau is almost independent of L. We have previously found that for a polymer, which is initially placed in the middle of the pore, there is a minimum in the escape time for R parallel approximately L. We show here that this minimum persists for weak fields E such that EL is less than some critical value, but vanishes for large values of EL.

Polymer translocation through a nanopore: A two-dimensional Monte Carlo study

We investigate the problem of polymer translocation through a nanopore in the absence of an external driving force. To this end, we use the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. To overcome the entropic barrier without artificial restrictions, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau required for the polymer to completely exit the pore on either end. We find numerically that tau scales with the chain length N as tau approximately N(1+2nu), where nu is the Flory exponent. This is the same scaling as predicted for the translocation time of a polymer which passes through the nanopore in one direction only. We examine the interplay between the pore length L and the radius of gyration R(g). For L<<R(g), we numerically verify that asymptotically tau approximately N(1+2nu). For L>>R(g), we find tau approximately N. In addition, we numerically find the scaling function describing crossover between short and long pores. We also show that tau has a minimum as a function of L for longer chains when the radius of gyration along the pore direction R( parallel) approximately L. Finally, we demonstrate that the stiffness of the polymer does not change the scaling behavior of translocation dynamics for single-segment dynamics.

Diffusion of end-grafted chain-like molecules on surfaces

We have studied the diffusion of short end-grafted chain-like molecules on smooth surfaces using the fluctuating bond model and Monte Carlo simulations. In our simulations, one end of each chain is restricted to lie on the surface, where it can move in a diffusive manner. The other segments of the chains can fluctuate freely above the surface. We study the behavior of the collective diffusion coefficient, D C( θ), as a function of the coverage, θ. Through simulations, we demonstrate that with relatively short end-grafted chains, D C( θ) first increases as a function of θ but then eventually approaches zero for θ→1. This is caused by an entropy-induced repulsive interaction in analogy to the case of purely 2D diffusion of polymers.

Surface diffusion of long chainlike molecules: The role of memory effects and stiffness on effective diffusion barriers

We study the coverage dependence of surface diffusion for chainlike molecules by the fluctuating-bond model with a Monte Carlo dynamics. The model includes short-ranged excluded volume interactions between different chains as well as an intrachain bond angle potential to describe the chain stiffness. Our primary aim is to consider the role played by chain stiffness and the resulting memory effects in tracer diffusion, and in particular their role in the effective tracer diffusion barrier EAT extracted from the well-known Arrhenius form. We show that the memory effects in tracer diffusion become more pronounced at an increasing coverage as a result of packing requirements. Increasing the chain flexibility furthermore has the same overall effect as increasing the chain length, namely, they both increase EAT. We then analyze the influence of memory effects on EAT and find that, for a single diffusing chain, about 20% of EAT arises from temperature variations in the memory effects, while only the remaining part comes from thermally activated chain segment movements. At a finite coverage, the memory contribution in EAT is even larger and is typically about 20%–40%. Further studies with chains of different lengths lead to a conclusion that, for a single diffusing chain, the memory contribution in EAT decreases along with an increasing chain length and is almost negligible in the case of very long chains. Finally, we close this work by discussing our results in light of recent experimental work as regards surface diffusion of long DNA molecules on a biological interface.

Diffusive spreading of chainlike molecules on surfaces.

We study the diffusion and submonolayer spreading of chainlike molecules on surfaces. Using the fluctuating bond model we extract the collective and tracer diffusion coefficients D_c and D_t with a variety of methods. We show that D_c(theta) has unusual behavior as a function of the coverage theta. It first increases but after a maximum goes to zero as theta go to one. We show that the increase is due to entropic repulsion that leads to steep density profiles for spreading droplets seen in experiments. We also develop an analytic model for D_c(theta) which agrees well with the simulations.

Local structure of model polymeric fluids: Hard-sphere chains and the three-dimensional fluctuating bond model

Monte Carlo simulations are performed for athermal polymers in the three-dimensional fluctuating bond lattice model. Polymer molecules composed of 20 and 50 freely-jointed beads are studied at volume fractions ranging from 0.2 to 0.35. Chain dimensions, intramolecular correlation functions, and intermolecular correlation functions are compared to results of off-lattice simulations for a similar freely-jointed chain model. It is found that the intramolecular correlation functions are qualitatively similar both on and off the lattice; there are quantitative differences which arise because of the larger persistence lengths of the off-lattice chains. At low densities the intermolecular correlation functions are similar in the two models, but significant differences appear at higher densities because of the limited extent of packing in the lattice fluid. We conclude that the lattice model adequately describes the effect of configurational entropy on fluid structure, but is inadequate to address packing effects which are important in the study of polymer melts. The volumetric behavior of the two model fluids is also discussed.

New simulation method for grafted polymeric brushes

We present the first Monte Carlo simulation method for determining the force between two surfaces due to the interaction of end-grafted polymers. The method is an elaboration of recently devised techniques for measuring the pressure by introducing hard or repulsive walls. The approach is applied to the usual self-avoiding-walk lattice model, as well as to the fluctuating bond model devised by Carmesin and Kremer. The latter is found to offer very significant computational advantages. Our results are in qualitative agreement with recent theoretical predictions.

Fluctuating bond model of DNA gel electrophoresis

We present a Monte Carlo algorithm that allows a small length scale numerical study of DNA gel electrophoresis in high electric fields, similar to the fluctuating bond model for dynamical properties of polymeric systems. This approach combines advantages of lattice Monte Carlo methods with those from continuous Brownian dynamics algorithms, and also takes into account the persistence length of DNA, as well as the random nature of the gel. The initial orientation and acceleration of a random-walk DNA conformation shows a number of features that can be related to experimental results. The detailed description of DNA motion provided by this approach may lead to a first realistic computer study of the process of DNA sequencing.

Equation of state for athermal lattice chains in a 3d fluctuating bond model

A generalization of the well-known Flory and Flory–Huggins mean-field approximations to the equation of state is derived for a three-dimensional lattice model in which a monomer occupies an entire unit cell, and many bond lengths and bond angles are possible. By measuring the probability for particles to be in contact with the walls of the system, the pressure is determined via computer simulation over the full density range from dilute solution to dense melt. The results are used to test the mean-field predictions. Comparing the equation of state of the present model to those of conventional lattice models and of hard-sphere chains in continuous space, it is seen that our method approximates the continuum limit far better than single site lattice models. Also the large n des Cloizeaux scaling behavior is approached more rapidly.