Chains Of Spheres Research Articles

The Generation and Analysis of Waves with Varying Nonlinearity through a One-Dimensional Chain of Spheres

Abstract Many waves formed in nature are primarily linear and have a property called dispersion causing different waveforms to separate and lose amplitude. Solitons can retain their pulse form as they propagate and cancel out that dispersion, making nonlinear waves useful for transferring energy. Waves traveling through a chain of spheres would display nonlinear behaviors when struck with enough force causing separation in the chain; the sound would not reflect back through the system disrupting the wave. Also in a chain of spheres, the waves traveling within would display nonlinear behaviors; the stress from the spheres' masses would cause deformation in the chain and waves traveling through them become nonlinear. The first trials tested wave behaviors with different amounts of striking force. A test sphere was placed atop the chain and struck with various forces. The second trials tested wave behaviors with a consistent force, changing the location of a test sphere in the chain. The third trials tested ...

About the correlation between the mobility of a polyion and that of its counterions

In this paper, we propose a new approach in order to interpret the variation of the conductibility of the PSS polyion with the nature and the concentration of the alkaline counter-ions Li+, Na+ and K+, and the hydrophobic cations Et4N+ and Bu4N+. This approach is based on a recent model in which the stretched polyion is represented by a chain of successive charged spheres, partially condensed by the counter-ions. We have found that the moderate variation of the hydrodynamic friction on the polyion with the size RM of condensed counter-ions, cannot completely explain the important decrease (of about 35% from K+ to Bu4N+) of the conductibility (lPSS,M ) of the PSS polyion with the nature of the counter-ions. Consequently, we have proposed a supplementary explanation by taking into account of the translational dielectric friction on the moving polyion. Formal analysis of this friction shows that it is very sensitive to the local structure of water surrounding the polyions. As this local structure depends in its turn, on the nature of the condensed counter-ions; we suggested that this specific sensitivity could explain the high dependence of the mobility of the polyion with the nature of its counter-ions.

A general strategy for one-step fabrication of one-dimensional magnetic nanoparticle chains based on laser ablation in liquid

Assembly of one-dimensional (1D) magnetic nanoparticle (NP) chains is attractive due to considerable technical demand in new materials and devices. Conventional assemblies are usually divided into two steps: one is the synthesis of NPs and the other is the fabrication of 1D NP chains. Here, we demonstrate a general strategy for fabricating 1D magnetic NP chains within one step, i.e. the magnetic field assisted laser ablation in liquid (MF-LAL), which combines NPs’ synthesis and 1D chains’ fabrication within one step. This is a green and facile LAL-based approach. Using this technique, we assemble 1D chains of submicron cobalt carbide spheres, which are ferromagnetic with anomalous giant magnetizations of 232 emu g−1 at room temperature, the highest reported so far for cobalt-based magnetic nanomaterials. The blocking temperature of the chains is more than 300 K, which is ascribed to the anisotropy of the configuration. We establish a theoretical model to pursue the fabrication of 1D magnetic NP chains, in which the basic physics and chemistry involved in the MF-LAL fabrication are discussed. These findings can guide researchers choosing interesting target and liquid for the assembly of 1D magnetic NP chains for the purpose of fundamental research and potential applications.

The Scattering of Acoustic Wave by a Chain of Elastic Spheres in Liquid

The scattering of acoustic waves by a chain of elastic spheres in liquid is studied. The incident wave, the scattering wave in the host, and the transmitted waves (including longitudinal and transverse wave modes) in the elastic spheres are all expanded in the form of a series of spherical wave functions. The total waves are obtained by the addition of all scattered waves from individual elastic sphere. The addition theorem of spherical wave function is used to perform the coordinates transform for the scattering waves from different spheres. The expansion coefficients of scattering waves are determined by the interface condition between the elastic spheres and the liquid host. The scattering cross section and the scattering amplitude in far field are computed as numerical examples. Two cases, steel spheres and lead spheres embedded in water, are considered in the numerical examples.

Detachable microsphere scalpel tips for potential use in ophthalmic surgery with the erbium:YAG laser

Vitreoretinal surgery is performed using mechanical dissection that sometimes results in iatrogenic complications, including vitreous hemorrhage, retinal breaks, incomplete membrane delamination, retinal distortion, microscopic damage, etc. An ultraprecise laser probe would be an ideal tool for cutting away pathologic membranes; however, the depth of surgery should be precisely controlled to protect the sensitive underlying retina. The ultraprecise surgical microprobe formed by chains of dielectric spheres for use with the erbium:YAG laser source (λ=2940 nm), with extremely short optical penetration depth in tissue, was optimized. Numerical modeling demonstrated a potential advantage of five-sphere focusing chains of sapphire spheres with index n=1.71 for ablating the tissue with self-limited depth around 10 to 20 μm. Novel detachable microsphere scalpel tips formed by chains of 300 μm sapphire (or ruby) spheres were tested on ophthalmic tissues, ex vivo. Detachable scalpel tips could allow for reusability of expensive mid-infrared trunk fibers between procedures, and offer more surgical customization by interchanging various scalpel tip configurations. An innovative method for aiming beam integration into the microsphere scalpel to improve the illumination of the surgical site was also shown. Single Er:YAG pulses of 0.2 mJ and 75-μs duration produced ablation craters in cornea epithelium for one, three, and five sphere structures with the latter generating the smallest crater depth (10 μm) with the least amount of thermal damage depth (30 μm). Detachable microsphere laser scalpel tips may allow surgeons better precision and safety compared to mechanical scalpels when operating on delicate or sensitive areas like the retina.

Experimental realization of a nonlinear acoustic lens with a tunable focus

We realize a nonlinear acoustic lens composed of a two-dimensional array of sphere chains interfaced with water. The chains are able to support solitary waves which, when interfaced with a linear medium, transmit compact pulses with minimal oscillations. When focused, the lens is able to produce compact pressure pulses of high amplitude, the “sound bullets.” We demonstrate that the focal point can be controlled via pre-compression of the individual chains, as this changes the wave speed within them. The experimental results agree well both spatially and temporally with analytical predictions over a range of focus locations.

Translational Dielectric Friction on a Chain of Charged Spheres

We have proved in details that the dielectric friction remains the principal frictional effect for a stretched polyion modeled as a chain of charged spheres, whereas, in the case of Manning's model (infinite thread with a continuous distribution of charge), this friction effect is nonexistent. According to this chain model, it is therefore possible to detect by conductivity measurements any transition from a coiled configuration (ellipsoidal model) to a stretched configuration during dilution process. We have also underlined the important interdependence between the dielectric friction and the ionic condensation of the counterions, in order to distinguish between the Ostwald regime and the Manning regime for which the degree of condensation is practically constant in a large range of concentrations.

Plasmon focusing in short gold sphere nanochains for surface-enhanced Raman scattering.

Power-flow focusing in metal nanostructures is attracting growing attention to design efficient and tunable substrates for surface-enhanced Raman spectroscopy (SERS), and to propose a more reliable alternative to random surfaces for single-molecule sensing. In this paper, finite-difference time-domain simulations were used to explore the near-field amplification features of short chains of gold (Au) nanospheres. Short chains of gold spheres were found to induce stronger field enhancements than infinite chains due to a more efficient trapping and focusing of the incident energy. In addition, interaction with a suitably tuned SiO2/Au double-layer substrate was demonstrated to widen the resonance's bandwidth, meeting another practical need for SERS.

Partial cationic inversion-induced magnetic hardening of densely packed 23-nm-sized nanocrystallite-interacting nickel ferrite electrospun nanowires

Although the average crystallite size (23 nm) is very close to a critical radius of superparamagnetism, a magnetic hardening (coercive field and saturation magnetization) was observed in interacting single-domain nanogranular nickel ferrite electrospun nanowires as compared with the bulk. The phenomena can be attributed to a small change in the cation occupancy on the spinel sites from (Fe3+)A(Ni2+Fe3+)BO4 to [F1−δ3+Niδ2+] A[Ni1−δ2+Fe1+δ3+] BO4 (δ = 3.67%), and an additive interaction of the “chain of spheres” type. The larger shape anisotropy contribution (Keff = 8.24 × 104 erg/cm3) is also as a factor leading to enhanced coercive field.

Intra-particle dynamics and the impact response of granular chains

Low-frequency waves generated by an impact on an isostatic granular medium with vanishing confinement pressure are theorized to depend on rigid-particle collisions. According to this model, an impact generates a solitary wave spanning several particle diameters. High-frequency waves with wavelengths smaller than a typical granule size behave differently, and their propagation can be modeled as diffusive. In this paper, experiments and simulations based on a one-dimensional chain of spheres are performed to measure surface and bulk waves in individual granules. Results show that an impact also generates high-frequency waves, due to the dynamic behavior of the individual granules, appearing simultaneously with the solitary wave. Intra-particle Rayleigh waves play a key role in generating and transmitting macroscopic wave modes. The exchange energy between intra-particle wave modes also influences the decay of the solitary wave.

Formation of polarized beams in chains of dielectric spheres and cylinders

Using numerical modeling, it is shown that chains of dielectric spheres and cylinders act as polarizers. The mechanism is based on gradual filtering of periodically focused modes with a certain polarization propagating with minimal losses due to Brewster angles conditions, whereas orthogonally polarized modes are strongly attenuated. It is shown that chains of cylinders filter linearly polarized beams, whereas chains of spheres filter radially polarized beams. In the geometrical optics limit, we show that in a range of sphere refractive indices 1.68-1.80 a degree of radial polarization in excess of 0.9 can be obtained in 10-sphere-long chains.

Sorption of CO2, C2H2 and C2H4 in HOF-1a studied by PHSC equation of state

Acetylene is a byproduct of modern ethylene production by cracking of hydrocarbons. There are extensive research efforts to exchange solvent extraction and hydrogenation methods for removing acetylene from ethylene with cost-effective membrane separation technology. Recently, the first Hydrogen-bonded Organic Framework (HOF) has been established to examine its capacity for acetylene uptake. In this study, Perturbed Hard Sphere Chain equation of state (PHSC) has been selected to obtain volumetric data for CO2, C2H2 and C2H4 sorption on HOF-1a system. Three molecular-based parameters including hard-sphere diameter (σ), the non-bonded interaction energy (ɛ) and number of segments per molecule (r) have been employed as scaling constants and calculated using group contribution (GC) method. High capacity of HOF-1a has been demonstrated for C2H2/C2H4 separation. C2H2 and C2H4 coupling effects in the mixed gas sorbed in HOF-1a, have been extracted from PHSC EoS for mixture sorption. The sorption of acetylene decreases in the presence of ethylene while sorption of ethylene increases in the presence of acetylene. HOF-1a has high capacity to sorb C2H2 as an impurity in industrial gas separation, but its low selectivity causes the loss of ethylene which makes it economically detrimental.

What is the most efficient way to reach the canonical MP2 basis set limit?

Various ways of reaching the complete basis set limit at the second-order Møller–Plesset perturbation theory (MP2) level are compared with respect to their cost-to-accuracy ratio. These include: (1) traditional MP2 calculations with correlation consistent basis sets of increasing size, with and without the resolution of identity for Coulomb and exchange (RIJK) or the combined RIJ and ‘chain of spheres’ (RIJCOSX) approximations; (2) basis set extrapolation obtained with the same MP2 variants; and (3) explicitly correlated F12-MP2 methods. The time required to solve the Hartree–Fock equations is part of the evaluation because the overall efficiency is of central interest in this work. Results were obtained for the ISO34, DC9 and S66 test sets and were analysed in terms of efficiency and accuracy for total energies, reaction energies and their effect on the basis set superposition error. Among the methods studied, the RIJK-MP2-F12 and RIJK-MP2-EP1 (where EP1 stands for ‘Extrapolation Protocol 1’ as explained in the text) methods perform outstandingly well. Although extrapolation is, in general, slightly faster than explicit correlation, it is found that for reaction energies, RIJK-MP2-F12 performs systematically better. This holds especially in combination with a triple zeta basis set, in which case it even outperforms the much more costly extrapolation involving quadruple- and quintuple-zeta correlation consistent basis sets.

Absorption and scattering by long and randomly oriented linear chains of spheres

This paper demonstrates that the scattering cross section per unit length of randomly oriented linear chains of optically soft spheres asymptotically converges toward those of randomly oriented and infinitely long cylinders with volume-equivalent diameter as the number of spheres increases. The critical number of spheres necessary to approximate the linear chains of spheres as infinitely long cylinders decreased rapidly as the size parameter of an individual sphere increased from 0.01 to 10. On the other hand, their absorption cross section per unit length was identical to that of an infinitely long volume-equivalent cylinder for any number of spheres. However, this approximation does not apply to the angle-dependent normalized Stokes scattering matrix element ratios.

Development of plastic nonlinear waves in one-dimensional ductile granular chains under impact loading

A modified split Hopkinson pressure bar (SHPB) was used to load one-dimensional granular chains of metallic spheres under impact loading rates. These homogeneous chains, comprised of brass spherical beads ranging from a single sphere to a chain of sixteen, are of interest because of their unique wave propagation characteristics. In the elastic range, for loads around 10s of N, nonlinear elastic solitary waves have been observed to form. In this work, loading magnitudes spanning from 9kN to 40kN – considerably higher than most previous works on these systems which have been conducted in the elastic regime – cause the granular chains to severely deform plastically. The aim of this study is to identify whether a nonlinear solitary-type wave will be generated under such high load levels, and if so, under what conditions (e.g., chain length, load level, etc.) it will do so. The propagating pulse was found to assume a distinctive shape after travelling through five beads, similar to the elastic case where solitary waves are realized with a traveling wavelength of five bead diameters. The wave speed of the plastic pulses observed here was seen to depend on maximum force, indicating that indeed it is a nonlinear wave in nature and is comparable to the elastic solitary wave. Locally, the plastic dissipation at every contact point through the chains was studied by measuring the residual plastic contact area. It was found that after the formation of the plastic nonlinear solitary wave had occurred there is also decreasing plastic deformation along the chain length except at the end beads in contact with the SHPB, which rebound into the SHPB bar causing larger plastic dissipation locally. To our knowledge this research is the first effort to investigate in detail the development and evolution of solitary-like waves in the plastic regime and will form the basis of future work in this area.

Calculation of the Density and Activity of Water in ATPS Systems for Separation of Biomolecules

In this study, the perturbed hard sphere chain equation of state is utilized to calculate the activity of water in binary and ternary solutions of polyethylene glycol (PEG), salt and water. The liquid density of the binary and ternary solutions is also predicted. To estimate the water activity in PEG–water binary systems, a linear correlation is obtained for the binary interaction parameter between water and PEG. Then, using this correlation and without introducing any additional binary parameters, the water activities are predicted in ternary solutions of water, salt and PEG with different molecular weights (MW). Our results show that the mean absolute average relative deviation (AARD %) of water activity for binary PEG–water solutions in 298 K is 0.73 %. In addition, the water activity in ternary solutions of water and two PEGs with different MW is predicted within 0.31 % AARD %. Furthermore, the AARD % for prediction of water activities in binary PEG–water solutions over the temperature range 308–338 K is 0.41 %. Also, the water activities of aqueous two-phase systems are predicted with AARD % = 0.64 %. In this regard, no adjustable parameters were correlated between salt and PEG. Finally, liquid densities were predicted in binary solutions of water–PEG and ternary solutions of water–PEG–salt.

Liquid-vapor equilibrium and surface properties of short rigid chains with one long range attractive potential

Liquid-vapor coexistence and interfacial properties of short lineal rigid vibrating chains with three tangent monomers in two and three dimensions are calculated. The effect of the range and position of a long ranged square well attractive potential is studied. Orthobaric densities, vapor pressures, surface tensions, and interfacial widths are reported. Two types of molecules are studied. Chains of three tangent hard sphere monomers and chains of three and five tangent hard sphere monomers interacting with a square well attractive potential with λ(∗) = λ∕σ = 1.5 in units of the hard core diameter σ. The results are reported in two and three dimensions. For both types of chains, a long ranged square well attractive potential is located at various positions in the chain to investigate its effect in the properties of the corresponding systems. Results for hard sphere chains are presented for a series of different sizes of λ(∗) between 2.5 and 5. For square well chains the position in the chain of the long ranged potential has no influence in the coexistence and interfacial properties. Critical temperatures increase monotonically with respect to λ(∗) and critical densities decrease systematically for both types of chains. When the long ranged potential is located in the middle monomer of the hard sphere chains no critical point is found for λ(∗) < 2.4. No critical point is found when the long ranged potential is located in one of the extremes of the hard sphere chains.

Jamming and crystallization in athermal polymer packings

Dense packings of chains of hard spheres possess characteristic features that do not have a counterpart in corresponding packings of monomeric spheres especially near the maximally random jammed (MRJ) state. From the modelling perspective the additional requirement that spheres keep their connectivity while maximizing the occupied volume fraction imposes severe constraints on generation algorithms of dense chain configurations. The extremely sluggish dynamics imposed by the uncrossability of chains precludes the use of deterministic or stochastic dynamics to generate all but dilute polymer packings. As a viable alternative, especially tailored chain-connectivity-altering Monte Carlo (MC) algorithms have been developed that bypass this kinetic hindrance and have actually been able to produce packings of hard-sphere chains in a volume fraction range spanning from infinite dilution up to the MRJ state. Such very dense athermal polymer packings share a number of structural features with packings of monomeric hard spheres, but also display unique characteristics due to the constraints imposed by connectivity. We give an overview of the most relevant results of our recent modeling work on packings of freely-jointed chains of tangent hard spheres about the MRJ state, local structure, chain dimensions and their scaling with density, topological constraints in the form of entanglements and knots, contact network at jamming, and entropically driven crystallization.

Dynamics of two-dimensional and quasi-two-dimensional polymers

The dynamic properties of dense two-dimensional (2D) polymer melts are studied using discontinuous molecular dynamics simulations. Both strictly 2D and quasi-2D systems are investigated. The strictly 2D model system consists of a fluid of freely jointed tangent hard disc chains. The translational diffusion coefficient, D, is strongly system size dependent with D ∼ ln L where L is the linear dimension of the square simulation cell. The rotational correlation time, τrot, is, however, independent of system size. The dynamics is consistent with Rouse behavior with D∕ln L ∼ N(-1) and τrot ∼ N(2) for all area fractions. Analysis of the intermediate scattering function, Fs(k, t), shows that the dynamics becomes slow for N = 256 and the area fraction of 0.454 and that there might be a glass transition for long polymers at sufficiently high area fractions. The polymer mobility is not correlated with the conformation of the molecules. In the quasi-2D system hard sphere chains are confined between corrugated surfaces so that chains cannot go over each other or into the surfaces. The conformational properties are identical to the 2D case, but D and τrot are independent of system size. The scaling of D and τrot with N is similar to that of strictly 2D systems. The simulations suggest that 2D polymers are never entangled and follow Rouse dynamics at all densities.

Scaled Particle Theory for the Coil–Globule Transition of an Isolated Polymer Chain

We have developed a scaled particle theory for the coil–globule transition (CGT) of a chain of attractive hard spheres in an attractive hard sphere solvent. The model predicts a lower critical solution temperature (LCST) related CGT that merges with a high temperature upper critical solution temperature (UCST) related CGT at a high pressure hypercritical point. The predicted hypercritical point is in good agreement with simulations of a bead–spring polymer chain in a symmetric solvent, without the use of any adjustable parameters. The model predicts that increasing bulkiness of monomers relative to solvent molecules, decreasing polymer cohesive energy relative to solvent cohesive energy, and reduced chain length stabilize the expanded coil state, in qualitative agreement with simulations. These trends in the UCST-CGT and LCST-CGT are found to emerge from incompressible-solvent effects and equation-of-state effects, respectively, consistent with the enthalpic origin of the UCST and the entropic origin of t...