The radial distribution function of worm-like chains

Thermal conformations of semiflexible macromolecules are generically described by the worm-like chain model. The end-to-end distance distribution, a fundamental quantity of the model, is not yet known in closed form. We provide a solution to the practical problem of choosing an appropriate approximation. First, a comprehensive review of existing approximations and exact limiting results is given. We then propose an explicit expression which interpolates between all relevant limiting cases. We show that it accurately reproduces, at no computational cost, high-precision Monte Carlo data, covering a wide range from stiff to flexible chains and from looped to fully stretched configurations. Using this result we quantify the enhancement of short worm-like loop formation by (protein) bridges.     

On the number of intersections of self-repelling polymer chains

We give a detailed analysis of the intersection properties of polymers. Using the renormalization group we provide a full crossover function for the dependence of the number of intersections in a single polymer on chain length and excluded volume strength. We compare our results with Monte-Carlo data and with exact calculations for a random walk, finding good agreement in all respects. Restricting to the vicinity of the eight ternary fixed points we also calculate the number of intersections between two chains placed at a fixed distance, including the two halves of a block-copolymer. The analysis of these systems confirms the interpretation of the different contributions to the number of intersections in a single chain. Due to the highly nontrivial character of the correlations in a polymer chain the correction exponents in both cases however are different. None of the results can be extracted from any Flory-type estimate. Received: 1 April 1997 / Revised: 24 October 1997 / Accepted: 29 January 1998     

Adsorption of polymer chains by disordered traps

We study the adsorption cross-over of ideal polymer chains in an environment of disordered traps. Starting from the assumption of an optimal cluster size of traps (optimal fluctuation method) we derive a general scaling form of the free energy function for arbitrary spatial dimensions. For small concentrations of traps we find a cross-over from localized (adsorbed) behavior to delocalized behavior depending on the chain's length and on the depth of the traps; this is connected with the non-monotonic behavior of the chain's extension. In terms of the free energy of the chain this cross-over resembles a first order transition scenario, the chain gets localized at many traps at once. Received 18 November 1998     

Anomalous adhesion in adsorbed polymer layers

Anomalous adhesion behaviour observed in the polydimethylsiloxane/heptane/silica system is reported. This behaviour is characterised by the infrequent appearance of one or more elastic minima which occur in addition to the ever-present primary adhesion. The resulting elastic force is attributed to loops connecting the tip to the substrate and can be described by two models; a worm-like chain, and a freely jointed chain. Both models give similar values for the characteristic segment length of around 0.24 nm and indicate that the chains have been extended by between 90 to 95% of their chain contour length before desorption. In some cases multiple adhesions were observed between tip and substrate and have been used to suggest a method for determining the distribution of adsorbed polymer loops. Received: 12 November 1997 / Accepted: 6 March 1998     

Modeling impurity-assisted chain creation in noble-metal break junctions

In this work we present the generalization of the model for chain formation in break junctions, introduced by Thiess et al (2008 Nano Lett. 8 2144), to zigzag transition-metal chains with s and p impurities. We apply this extended model to study the producibility trends for noble-metal chains with impurities, often present in break junction experiments, namely, Cu, Ag and Au chains with H, C, O and N adatoms. Providing the material-specific parameters for our model from systematic full-potential linearized augmented plane-wave first-principles calculations, we find that the presence of such impurities crucially affects the binding properties of the noble-metal chains. We reveal that both the impurity-induced bond strengthening and the formation of zigzag bonds can lead to a significantly enhanced probability for chain formation in break junctions.     

Binary N-step Markov chains and long-range correlated systems

A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In our model, the conditional probability that the ith symbol in the chain equals zero (or unity) is a linear function of the number of unities among the preceding N symbols. The correlation and distribution functions as well as the variance of number of symbols in the words of arbitrary length L are obtained analytically and numerically. If the persistent correlations are not extremely strong, the variance is shown to be nonlinearly dependent on L. A self-similarity of the studied stochastic process is revealed. The applicability of the developed theory to the coarse-grained written and DNA texts is discussed.     

On the probability of ferromagnetic strings in antiferromagnetic spin chains

We study the probability of formation of ferromagnetic string in the antiferromagnetic spin-1/2 XXZ chain. We show that in the limit of long strings with weak magnetization per site the bosonization technique can be used to address the problem. At zero temperature the obtained probability is Gaussian as a function of the length of the string. At finite but low temperature there is a crossover from the Gaussian behavior at intermediate lengths of strings to the exponential decay for very long strings. Although the weak magnetization per site is a necessary small parameter justifying our results, the extrapolation of obtained results to the case of maximally ferromagnetic strings is in qualitative agreement with known numerics and exact results. The effect of an external magnetic field on the probability of formation of ferromagnetic strings is also studied.     

Vortex flux channeling in magnetic nanoparticle chains

A detailed understanding of the formation of magnetic vortices in closely spaced ferromagnetic nanoparticles is important for the design of ultra-high-density magnetic devices. Here, we use electron holography and micromagnetic simulations to characterize three-dimensional magnetic vortices in chains of FeNi nanoparticles. We show that the diameters of the vortex cores depend sensitively on their orientation with respect to the chain axis and that vortex formation can be controlled by the presence of smaller particles in the chains.     

Closed-form solutions for continuous time random walks on finite chains

Continuous time random walks (CTRWs) on finite arbitrarily inhomogeneous chains are studied. By introducing a technique of counting all possible trajectories, we derive closed-form solutions in Laplace space for the Green's function (propagator) and for the first passage time probability density function (PDF) for nearest neighbor CTRWs in terms of the input waiting time PDFs. These solutions are also the Laplace space solutions of the generalized master equation. Moreover, based on our counting technique, we introduce the adaptor function for expressing higher order propagators (joint PDFs of time-position variables) for CTRWs in terms of Green's functions. Using the derived formula, an escape problem from a biased chain is considered.     

Electro-optical properties of excitons in polydiacetylene chains

We show how to compute the optical functions (reflectivity, transmission, and absorption) of polydiacetylene chains diluted in their monomer matrix exposed to a uniform electric field in the chain direction, in the excitonic energy region. Adopting a model electron-hole potential, we derived an analytical expression for the effective chain susceptibility, which gives the optical functions. The resulting absorption shows excitonic peaks below the gap and Franz-Keldysh oscillations above the gap. The method has been applied for a 3BCMU polydiacetylene chain, showing a good agreement with experimental spectra. Received 5 November 1998 and Received in final form 23 February 1999     

Conformation of poly(L-lysine)-graft-poly(ethylene glycol) molecular brushes in aqueous solution studied by small-angle neutron scattering

Small-angle neutron scattering (SANS) has been employed for the analysis of conformations of poly(L-lysine)-graft-poly(ethylene glycol) (PLL-g -PEG) molecular bottle brushes in aqueous solutions. The degree of polymerisation of the PEG chains was systematically varied in order to unravel dependence of the conformational properties of the bottle brushes on the molecular weight of the grafted chains. The grafting density was kept constant and high enough to ensure strong overlap of the PEG chains. The scattering spectra were fitted on the basis of the model of an effective worm-like chain with the account of average radial distribution and local fluctuations of the PEG density in the bottle brush. The results of the fits indicate that molecular brushes retain weakly bent configuration on the length scale of the order of (or larger than) the brush thickness. This finding is in agreement with earlier simulation and recent theoretical results.     

Strain stiffening in random packings of entangled granular chains

Random packings of granular chains are presented as a model system to investigate the contribution of entanglements to strain stiffening. The chain packings are sheared in uniaxial compression experiments. For short chain lengths, these packings yield when the shear stress exceeds the scale of the confining pressure, similar to granular packings of unconnected particles. In contrast, packings of chains which are long enough to form loops exhibit strain stiffening, in which the effective stiffness of the material increases with strain, similar to many polymer materials. The latter packings can sustain stresses orders-of-magnitude greater than the confining pressure, and do not yield until the chain links break. X-ray tomography measurements reveal that the strain-stiffening packings contain system-spanning clusters of entangled chains.     

Ag原子链的结构稳定性和磁性

采用第一性原理方法研究了Ag原子链的结构稳定性和磁学性质.在结构稳定性方面,计算了线性链、平面之字型、梯型和三条线性原子链组成的T型等链式结构.结果表明,线性原子链的结合能最小,结构最不稳定性;T型结构的结合能最大,结构最稳定.所有这些一维结构的原子间键长都小于Ag体材料的键长,表明一维下原子间的成键比体材料时更强.对Ag线性原子链的磁性计算表明,线性Ag原子链在平衡状态下并不表现出磁性,但是当原子链的原子键长被压缩了约52%时,体系可表现出铁磁性.通过Stoner判据和原子轨道相互作用图像,解释了这种磁性出现的原因. 关键词： Ag原子链 结构稳定性 磁性 从头计算     

Effect of hydrogen on the formation of the atomic structure of linear carbon chains: An ab initio approach

An ab initio study of the features of the formation of the atomic structure of carbon chains, which are structural parts of films of linear carbon chains, has been performed using the electron density functional theory. It has been shown that the formation and stabilization of experimentally observed kinks of carbon chains require the presence of hydrogen impurities in the chamber during the synthesis of linear carbon chains. The kinks of a carbon chain are formed in the process of the adsorption of hydrogen atoms on a chain. The optimal kink angle of carbon chains has been determined. The stability of kinks of carbon chains has been estimated as a function of the length of linear fragments. An additional mechanism has been proposed for the formation of kinks in carbon chains owing to the joining of short carbon chains with hydrogen ends.     

Anomalous conductance oscillations and half-metallicity in atomic Ag-O chains

Using spin density functional theory, we study the electronic and magnetic properties of atomically thin, suspended chains containing silver and oxygen atoms in an alternating sequence. Chains longer than 4 atoms develop a half-metallic ground state implying fully spin-polarized charge carriers. The conductances of the chains exhibit weak even-odd oscillations around an anomalously low value of 0.1G0 (G0=2e2/h) which coincide with the averaged experimental conductance in the long chain limit. The unusual conductance properties are explained in terms of a resonating-chain model, which takes the reflection probability and phase shift of a single bulk-chain interface as the only input. The model also explains the conductance oscillations for other metallic chains.     

A study of atom zigzag chains on the surface of Tungsten

Nishigaki and Nakamura have observed zigzag chains on the central (011) face of tungsten after field evaporation at T #62; 140 K. In this paper, a study of the formation, disappearance and structure of such chains is described. Tungsten tips of small radii down to 60 Å were used. Chains of 3 to 9 spots, that are clearly visible, are found even at 90 K. Four different structure models of the zigzag chains are discussed, including the multibranch model proposed by the Japanese authors. The interpretation of our experimental results shows fairly clearly that the real zigzag chain structure is a special non-dense structure. It must be formed by a local displacement of the tungsten adatoms in the field. Without the field, a zigzag chain is transformed into a two-dimensional cluster of the nearest neighbour atom by a small increase in temperature. If the field is reintroduced, the cluster can revert to the initial zigzag structure. The zigzag structure is interpreted as being caused by forces of repulsion between the atom dipoles.     

Impact of receptor-ligand distance on adhesion cluster stability

Cells in multicellular organisms adhere to the extracellular matrix through two-dimensional clusters spanning a size range from very few to thousands of adhesion bonds. For many common receptor-ligand systems, the ligands are tethered to a surface via polymeric spacers with finite binding range, thus adhesion cluster stability crucially depends on receptor-ligand distance. We introduce a one-step master equation which incorporates the effect of cooperative binding through a finite number of polymeric ligand tethers. We also derive Fokker-Planck and mean field equations as continuum limits of the master equation. Polymers are modeled either as harmonic springs or as worm-like chains. In both cases, we find bistability between bound and unbound states for intermediate values of receptor-ligand distance and calculate the corresponding switching times. For small cluster sizes, stochastic effects destabilize the clusters at large separation, as shown by a detailed analysis of the stochastic potential resulting from the Fokker-Planck equation.     

Magnetism of Mg atomic chains on the NaCl(100) surface

Based on the first-principles calculations within the density-functional theory, we have investigated the magnetism of 1D Mg nanowires, both unsupported and supported by the NaCl(100) surface. It is shown that Mg can exhibit magnetism in both the geometry of linear and zigzag chains. The freestanding Mg linear chain shows magnetization when the bonds are compressed. For an Mg zigzag chain, however, ferromagnetism is predicted at the equilibrium bond length. It is found that the magnetism of Mg chains can be maintained when deposited on the NaCl(100) surface. We have also analyzed the results by using the Stoner theory and the calculated electronic band structures.     

Structure of resonances and formation of stationary points in symmetrical chains of bilinear oscillators

Dynamics of strongly nonlinear systems can in many cases be modelled by bilinear oscillators, which are the oscillators whose springs have different stiffnesses in compression and tension. This underpins the analysis of a wide range of phenomena, from oscillations of fragmented structures, connections and mooring lines to deformation of geological media. Single bilinear oscillators were studied previously and the presence of multiple resonances both super- and sub-harmonic was found. Less attention was paid to systems of multiple bilinear oscillators that describe many natural and engineering processes such as for example the behaviour of fragmented solids. Here we fill this gap concentrating on the simplest case – 1D symmetrical chains of bilinear oscillators. We show that the presence and structure of resonances in a symmetric chain of bilinear oscillators with fixed ends depends upon the number of oscillating masses. Two elementary chains act as the basic ones: a single mass bilinear chain (a mass connected to the fixed points by two bilinear springs) that behaves as a linear oscillator with a single resonance and a two mass chain that is a coupled bilinear oscillator (two masses connected by three bilinear springs). The latter has multiple resonances. We demonstrate that longer chains either do not have resonances or get decomposed, in the resonance, into either the single mass or two mass elementary chains with stationary masses in between. The resonance frequencies are inherited from the basic chains of decomposition. We show that if the number of masses is odd the chain can be decomposed into the single mass bilinear chains separated by stationary masses. It then inherits the resonances of the single mass bilinear chain. The chains with the number of masses minus 2 divisible by 3 can be decomposed into the two mass bilinear chains separated by stationary masses and inherit the resonances of the two mass chains. The chains whose lengths satisfy both criteria (such as chains with 5, 11, 17 … masses) allow both types of resonances.     

Landau-Zener transition of a two-level system driven by spin chains near their critical points

The Landau-Zener (LZ) transition of a two-level system coupling to spin chains near their critical points is studied in this paper. Two kinds of spin chains, the Ising spin chain and XY spin chain, are considered. We calculate and analyze the effects of system-chain coupling on the LZ transition. A relation between the LZ transition and the critical points of the spin chain is established. These results suggest that LZ transitions may serve as the witnesses of criticality of the spin chain. This may provide a new way to study quantum phase transitions as well as LZ transitions.