Linear Chains Of Particles Research Articles

Survival condition for low-frequency quasi-one-dimensional breathers in a two-dimensional strongly anisotropic crystal

We investigate a two-dimensional s2Dd strongly anisotropic crystal s2D SACd on substrate: 2D system of coupled linear chains of particles with strong intrachain and weak interchain interactions, each chain being subjected to the sine background potential. Nonlinear dynamics of one of these chains when the rest of them are fixed is reduced to the well known Frenkel-KontorovasFKd model. Depending on strengh of the substrate, the 2D SAC models a variety of physical systems: polymer crystals with identical chains having light side groups, an array of inductively coupled long Josephson junctions, anisotropic crystals having light and heavy sublattices. Continuum limit of the FK model, the sine-Gordon ssGd equation, allows two types of soliton solutions: topological solitons and breathers. It is known that the quasi-one-dimensional topological solitons can propagate also in a chain of 2D system of coupled chains and even in a helix chain in a three-dimensional model of polymer crystal. In contrast to this, numerical simulation shows that the long-living breathers inherent to the FK model do not exist in the 2D SAC with weak background potential. The effect changes scenario of kink-antikink collision with small relative velocity: at weak background potential the collision always results only in intensive phonon radiation while kink-antikink recombination in the FK model results in long-living low-frequency sG breather creation. We found the survival condition for breathers in the 2D SAC on substrate depending on breather frequency and strength of the background potential. The survival condition bears no relation to resonances between breather frequency and frequencies of phonon band—contrary to the case of the FK model.

Nonlinear Fano resonance and bistable wave transmission

We consider a discrete model that describes a linear chain of particles coupled to a single-site defect with instantaneous Kerr nonlinearity. We show that this model can be regarded as a nonlinear generalization of the familiar Fano-Anderson model and it can generate amplitude-dependent bistable resonant transmission or reflection. We identify these effects as the nonlinear Fano resonance and study its properties for continuous waves and pulses.

Nested self-similar wrinkling patterns in skins

Stiff thin films on soft substrates are both ancient and commonplace in nature; for instance, animal skin comprises a stiff epidermis attached to a soft dermis. Although more recent and rare, artificial skins are increasingly used in a broad range of applications, including flexible electronics, tunable diffraction gratings, force spectroscopy in cells, modern metrology methods, and other devices. Here we show that model elastomeric artificial skins wrinkle in a hierarchical pattern consisting of self-similar buckles extending over five orders of magnitude in length scale, ranging from a few nanometres to a few millimetres. We provide a mechanism for the formation of this hierarchical wrinkling pattern, and quantify our experimental findings with both computations and a simple scaling theory. This allows us to harness the substrates for applications. In particular, we show how to use the multigeneration-wrinkled substrate for separating particles based on their size, while simultaneously forming linear chains of monodisperse particles.

Lithographically directed deposition of silica nanoparticles using spin coating

Directed self-assembly is an important direction for the extension of patterning to the nanoscale regime and below. Here, examples are given of both individual particle placement and composite structure formation involving assemblies of many nanometer scale particles, both on patterned surfaces and on planar surfaces where the photoresist is used as a sacrificial layer to define the pattern and is subsequently removed. The underlying technologies employed in these experiments include interferometric lithography to define large-area, nanometer-scale patterns and directed self-assembly by spin coating to control particle placement. Three sizes of silica nanoparticles (mean diameters: 78, 50, and 15nm) were employed for spin-coating processes. Single linear silica particle chain patterns and isolated two-dimensional particle patterns were easily formed on patterned surfaces. Silica particle rows, cross networks, and isolated posts with controllable thickness could be formed on flat surfaces using this approach. Directed self-assembly using nanoscale lithography and spin coating is a facile approach to the extension of lithographic techniques to the nanoscale.

Consistency of thermal activation model based on the stochastic Landau–Lifshitz equation and classical spin-wave description

Numerical studies of magnetisation fluctuations in a linear chain of spherical particles are carried out using the Langevin dynamic (LD) approach, and compared directly to the predictions of spin-wave theory. The results enable the identification of the magnetisation fluctuations in terms of exchange and magnetostatic spin-wave modes. Excellent quantitative agreement between the numerical and analytical results is obtained, suggesting that the LD approach correctly excites the normal modes (spin waves) of the chain.

Direct observation of dipolar chains in ferrofluids in zero field using cryogenicelectron microscopy

The particle structure of ferrofluids is studied in situ, by cryogenic electronmicroscopy, on vitrified films of iron and magnetite dispersions. By means ofsynthesis of iron colloids with controlled particle size and different types ofsurfactant, dipolar particle interactions can be varied over a broad range, whichsignificantly influences the ferrofluid particle structure. Our experiments on irondispersions (in contrast to magnetite dispersions) for the first time demonstrate,in ferrofluids in zero field, a transition with increasing particle size from separateparticles to linear chains of particles (Butter K, Bomans P H, Frederik P M,Vroege G J and Philipse A P 2003 Nature Mater. 2 88). These chains, alreadypredicted theoretically by de Gennes and Pincus (de Gennes P G and Pincus P A1970 Phys. Kondens. Mater. 11 189), very much resemble the fluctuatingchains found in simulations of dipolar fluids (Weis J J 1998 Mol. Phys. 93361, Chantrell R W, Bradbury A, Popplewell J and Charles S W 1982 J.Appl. Phys. 53 2742). Decreasing the range of steric repulsion betweenparticles by employing a thinner surfactant layer is found to change particlestructures as well. The dipolar nature of the aggregation is confirmedby the alignment of existing chains and individual particles in the fielddirection upon vitrification of dispersions in a saturating magnetic field.Frequency-dependent susceptibility measurements indicate that particle structuresin truly three-dimensional ferrofluids are qualitatively similar to those in liquidfilms.

Dynamic interaction of a semi-infinite linear chain of coupled oscillators with a strongly nonlinear end attachment

We study the dynamics of a semi-infinite linear chain of particles that is weakly coupled to a strongly nonlinear oscillator at its free end. We analyze families of localized standing waves situated inside the lower or upper attenuation zones of the linear chain, corresponding to energy predominantly confined in the nonlinear oscillator. These families of standing waves are generated due to resonant interactions between the chain and the nonlinear attachment. In addition, we estimate the energy radiated from the nonlinear oscillator back to the chain, when the oscillator is excited under nonresonant conditions by wavepackets with dominant frequencies inside the propagation zone of the chain. We conclude that the system is capable of energy pumping, i.e., of one-way, irreversible energy transfer from the semi-infinite chain to the nonlinear oscillator. Such energy transfer closely depends on the excitation by the external forcing of a localized standing wave of the type studied in this work. A scenario for the realization of energy pumping phenomena in the system under consideration is discussed, and is confirmed by direct numerical simulations of the chain–attachment dynamic interaction.

Direct observation of dipolar chains in iron ferrofluids by cryogenic electron microscopy

A key issue in research on ferrofluids (dispersions of magnetic colloids) is the effect of dipolar interactions on their structure and phase behaviour, which is not only important for practical applications but gives fundamental insight in dipolar fluids in general. In 1970, de Gennes and Pincus predicted a Van der Waals-like phase diagram and the presence of linear chains of particles in ferrofluids in zero magnetic field. Despite many experimental studies, no direct evidence of the existence of linear chains of dipoles has been reported in the absence of magnetic field, although simulations clearly show the presence of chain-like structures. Here, we show in situ linear dipolar structures in ferrofluids in zero field, visualized on the particle level by electron cryo-microscopy on thin, vitrified films of organic dispersions of monodisperse metallic iron particles. On systematically increasing the particle size, we find an abrupt transition from separate particles to randomly oriented linear aggregates and branched chains or networks. When vitrified in a permanent magnetic field, these chains align and form thick elongated structures, indicating lateral attraction between parallel dipole chains. These findings show that the experimental model used is well suited to study the structural properties of dipolar particle systems.

A Hands-On Introduction to Molecular Dynamics

We present an introduction to the chemical and computational aspects of the molecular dynamics (MD) simulation technique. Using just a few elementary ideas from classical mechanics and numerical analysis, and linear chains of identical particles as example systems, we take the reader through the steps required for the design and analysis of a simple molecular dynamics experiment. We employ the Hooke's law model for the interactions between the particles since its visualization in terms of masses and springs provides a natural model for chemical bonds. We derive the classical equations of motion in detail for the three-particle chain. We then introduce two simple methods for numerically integrating the equations of motion, one based on Euler's method for differential equations, and the other a more accurate algorithm developed by Verlet. We analyze the dynamics of the three-particle system in terms of its normal modes of vibration. Finally, exploiting the closed-form solution admitted by the Hooke's law po...

Electrostatic field and force calculation for a chain of identical dielectric spheres aligned parallel to uniformly applied electric field

We apply the re-expansion method proposed by Washizu to a linear particle chain aligned in the direction of a uniform electric field. The calculated results show that the potential distribution around the particles becomes very complicated and the electric field is highly concentrated near the contact points of particles. The pearl-chain forming force rapidly increases with increasing number of particles and reaches a saturation value for chains consisting of some tens of particles. The force at a contact point in a particle chain is reduced near both the ends of the chain but is still much stronger than the interaction force of the two particles. The present method can be extended to cases of coated particles. One example of the application is a new model for the surface roughness of electro-rheological (ER) particles. A layered particle model, in which the surface roughness is replaced with an equivalent surface layer, provides a more reasonable method for the force calculation, because the existing gap model is too sensitive to the fictitious interstice representing the roughness. Another example is the effect of surface coating to reduce the electric field at the contact points. Such a coating will be preferable for ER particles to prevent electrical breakdown in the fluid.

Theory of the Lesage-Jeans instability in a linear chain of dust particles in plasma

The dynamics of the Lesage-Jeans instability in a linear infinite periodic chain of dust particles in plasma is studied theoretically by deriving and numerically solving the nonlinear wave equation.

Laser-excited waves in a plasma crystal

The radiation pressure of a chopped laser beam is used to excite low-frequency (f = 0.4-5 Hz) waves in plasma crystals. The first system studied is a linear chain of spherical plastic particles of m diameter. The second system is a single-layer crystal with hexagonal structure made of the same kind of particles. The measured dispersion and damping of longitudinal compressional waves is compared with a model for dust lattice waves in a system of particles interacting by Yukawa-type potentials. From the best fit the shielding factor is determined. The finding that the measured shielding length is comparable with the interparticle distance is supported by Monte Carlo simulations.

Brownian electrorheological fluids as a model for flocculated dispersions

The rheological behavior of Brownian electrorheological (ER) fluids is studied as a model for flocculated colloidal dispersions. The ER fluid has the advantages that the interparticle potential energy can be varied by simply changing the applied field strength, and the microstructure consists of essentially linear chains of particles aligned with the field direction. Under simple shear flow, the suspension has a high‐shear‐rate Newtonian viscosity and a shear thinning viscosity at lower shear rates. For moderate attractive potential well depths, Umin/kT, the suspension has a low‐shear viscosity that scales as exp(Umin/kT). Furthermore, the low‐shear limiting behavior is seen at shear rates that scale as exp(−Umin/kT). A theory is proposed that makes use of the time scale of diffusion for aggregated particles out of their mutual potential well, τ∼(a2/D)(kT/Umin)exp(Umin/kT), much in the spirit of the Eyring theory. Here a is the particle radius and D is the diffusivity of an isolated particle. When the she...

Shear stresses in magnetorheological fluids: Role of magnetic saturation

The interparticle forces and resulting shear stresses in a magnetorheological fluid are calculated. The field due to a linear chain of particles in a fixed average magnetic induction Bave is determined from a finite element analysis in which the nonlinearity and saturation of the particle magnetization are incorporated. The shear stresses are then computed from the field using Maxwell’s stress tensor. The stresses obtained for all but the lowest magnetic inductions are controlled by the saturation of the magnetization in the contact regions of each particle. Identifying the maximum shear stress as a function of shear strain with the yield stress gives values in agreement with results reported for typical fluids. For high magnetic inductions the yield stress plateaus due to the complete saturation of the particle magnetization; the stress scales as the square of the saturation magnetization in this regime.

A study of the electrical current passing through water-activated electro-rheological fluids

Current leakage is a serious problem in electro-rheological fluids. In this study, the electrical current leaking through water-activated electro-rheological fluids has been investigated as a function of particle volume fraction, water content, electric field strength and temperature by both static and dynamic experiments. The effect of electric field strength on current leakage is presented in terms of a power-law relation between current density and applied field strength. The nonlinear characteristic of the I-V behaviour of water-activated electro-rheological fluids is a consequence of the nonlinearity of the resistance of the fluid. The exponent in the relation between current density and applied electric field strength was found to depend strongly on the water content but only weakly on the particle volume fraction. The electrolysis of water molecules under the applied electric field is proposed to explain this nonlinearity in electrical resistance of the electro-rheological materials. We note that the temperature-dependency of current density through our electro-rheological fluids is similar to that observed for semiconducting materials, that is the conductivity increases with increasing temperature. The Arrhenius-type activation energy of water-activated electro-rheological fluids was also estimated to be about 3 J mol-1 a similar value to that of pure water. An increase in thermal motion of water in the particles (silica in this case) may be a reason for this behaviour. Furthermore, an equilibrium structure consisting of linear chains of particles with branches has been determined from the power-law relation between electrical current and volume fraction of dispersed particles. The electrical current was also measured as the suspension was being subjected to shear. The current decreased as the shear rate increased, implying that the particle chains, formed by the applied electric field, were destroyed by the shear field.

Raman scattering by high-density dispersions. III. Calculation of Raman intensities for molecules physisorbed on linear chains of spherical particles

In parts I and II of this series, the dominant role of ‘‘primary’’ Raman moments of degree greater than one, to Raman intensities for molecules forming a uniform coating on pairs of spherical particles in close proximity, is demonstrated. In this paper, the effect of chain length, coverage, particle size, and separation, and the location of the particle in the chain on the intensity are explored for linear chains of coated particles. Intensity enhancements calculated for visible excitation are up to 30 times those for two particles, being ∼4×106 for infinite chains of silver particles of radius 25–50 Å separated by the thickness of a layer of CO ∼105 for platinum and ∼104 for germanium chains. Furthermore, the enhancement for chains falls off appreciably more slowly with particle separation. Graphs of intensity vs coverage vary greatly in shape depending on particle size, molecular size, and polarizability.

Systematics of alpha-chain states in 4 N-nuclei

Recently a six-alpha chain state has been discovered in 24Mg. The Bloch-Brink cranked cluster model shows that linear chains of alpha particles are associated with stable minima in the potential-energy surface for all 4 N-nuclei. Experimental candidates in 8Be, 12C and 16O have already been identified. Using a Brink-Boeker effective interaction, and allowing free variation of all parameters, we calculate the geometric arrangements and energies of the lowest alpha-chain states. These configurations are then cranked to predict the maximum angular momenta and the excitation energies that they can sustain. We conclude that states similar to that in 24Mg should also be accessible to experimental investigation in other nuclei.

Evidence for alpha-particle chain configurations in 24Mg.

Many theoretical models have been employed to described the structure of the nucleus {sup 24}Mg. Among these are the Cranked Shell model (CSM), the Cranked Cluster Model (CCM), and calculations have also been performed using the Hartree-Fock formalism. One very striking prediction of these calculations is that in this nucleus there exist very unusual configurations, with structures reminiscent of linear chains of alpha particles. In the CSM, for instance, such a configuration is identified with a pronounced minimum in the potential energy energy at very large prolate deformation. In the CCM, several very different alpha-particle duster configurations are identified, many having rather large deformations. These cluster configurations can be associated with the different potential-energy minima obtained in the CSM results. In the case of the CCM, a 6{alpha} chain-like configuration is predicted to occur at excitation energies between 40 and 50 MeV, with predicted rotational spacing given by {Dirac h}{sup 2}/2I=22 keV. At this excitation energy, such a chain configuration would lie well above the threshold for the decay of {sup 24}Mg into 6 alpha particles, and its identification poses a difficult experimental challenge. This report discusses this challenge.

WAXS- and SAXS-investigations of structure formation in alcoholic SiO 2 solutions

Small- and wide-angle X-ray scattering (SAXS and WAXS, respectively) were used to examine in situ formation and evolution of SiO 2-structures in alcoholic solutions of tetra-alkoxysilanes (TAOS) as a function of chemical conditions. In acid-catalyzed reactions with a molar ratio of ⩽ r w ⩽ 51 forH 2O against TAOS primary particles with a diameter of ∼ 1 nm were always found. These particles aggregated to form secondary clusters. The resulting aggregated clusters can be described by means of the fractal concept, diffusion-limited or chemical-limited cluster-cluster aggregations being the dominant mechanisms of formation. When using an under-stoichiometric water content ( r w = 1) the formation of smaller primary particles with a diameter of ∼ 0.5 nm is observed; these particles preferably aggregated to form linear particle chains. In alkaline-catalyzed reactions the SiO 2-particles grew beyond the visual field of the measurement ( r max = 20 nm) and featured nearly smooth surfaces. As a result of WAXS examinations, it was found that the internal structure of the condensates is characterized by a well-defined topology (polyhedrons). The liquid environment exerts a force on the SiO 2-particles and the polyhedron size varies with the composition of the solution.

Dynamic simulation of hydrodynamically interacting particles

A general method for computing the hydrodynamic interactions among N suspended particles, under the condition of vanishingly small particle Reynolds number, is presented. The method accounts for both near-field lubrication effects and the dominant many-body interactions. The many-body hydrodynamic interactions reproduce the screening characteristic of porous media and the ‘effective viscosity’ of free suspensions. The method is accurate and computationally efficient, permitting the dynamic simulation of arbitrarily configured many-particle systems. The hydrodynamic interactions calculated are shown to agree well with available exact calculations for small numbers of particles and to reproduce slender-body theory for linear chains of particles. The method can be used to determine static (i.e. configuration specific) and dynamic properties of suspended particles that interact through both hydrodynamic and non-hydrodynamic forces, where the latter may be any type of Brownian. colloidal, interparticle or external force. The method is also readily extended to dynamically simulate both unbounded and bounded suspensions.