Chains Of Spheres Research Articles

Ultrasonic propagation in finite-length granular chains

A narrowband ultrasound source has been used to generate solitary wave impulses in finite-length chains of spheres. Once the input signal is of sufficient amplitude, both harmonics and sub-harmonics of the input frequency can be generated as non-linear normal modes of the system, allowing a train of impulses to be established from a sinusoidal input. The characteristics of the response have been studied as a function of the physical properties of the chain, the input waveform and the level of static pre-compression. The results agree with the predictions of a theoretical model, based on a set of discrete dynamic equations for the spheres for finite-length chains. Impulses are only created for very small pre-compression forces of the order of 0.01N, where strongly non-linear behaviour is expected.

Problems and Perspectives of Formation of Agricultural Clusters for Increasing Food Security of Developing Countries

1. Introduction The global financial crisis, apart from negative influence on the economy and social conditions in many countries, caused the aggravation of the whole range of global problems of development, among which the most important is the threat for food security in developing countries and regions. As a result, there is a complex of economic and social factors in developing countries which emerged under the influence of the crisis. Thus, the reasons for emergence of the complex of food security problems became the growth of global prices for food and reduction of offer for food products in sales market with inability to satisfy the demand of net importers of food. Implementation of limitations for export of agricultural products by some countries showed the existing disproportions in the global food system, which leads to many food net importers' dependence on several countries-exporters. This causes the necessity for corresponding measures for prevention of food crisis in case of instability in countries-exporters. For this purpose, the authors offer to create agricultural clusters for increasing the competitiveness of domestic agricultural producers and providing food security of developing countries. 2. Materials and Methods The existing separate provisions of methodological nature are related to development of criterion of selecting the spheres (types of activity) for clustering, while the algorithm of agricultural cluster formation is poorly substantiated and poorly elaborated in methodological aspect; there is no clear instrumentarium of sequence and interdependence of various types of activity and production spheres in a cluster. That's why this study develops the proprietary methodology of integral approach to formation of projects and programs of socio-economic development, which allows differentiating the sub-system of previously viewed indicators as to the level of users' demands. For this purpose, they are differentiated in the projects for bodies of state (municipal) power, for bodies of executive power, and for specific economic subjects (Garthwaite et al., 2015). Based on the results of evaluation of territories' capabilities for sustainable economic and ecological development, the algorithm of their further ranking according to the principles of cluster analysis is formed. On the basis of the analysis and generalization of materials in this research, the principles of cluster formation are allocated: informational openness, diversification of demand, and geographical proximity. The sense of the offered methodology consists in the agricultural cluster creation technology's division into several independent stages: selection of the goal and of contextual element of cluster and elaboration of the chain of spheres and types of activities which enter (comprise) a cluster. Comparison of given stages and tasks, which form them, points at the fact that the latter task in creation of sectorial cluster is the most important, at the same time being the least developed, contradictive, and short of methodological level. The model of organizational & economic mechanism of managing agricultural cluster includes totality of methods of influence for the purpose of achievement of desired level of efficiency of activities and functions of management (analytical, organizational & coordinating, accounting & controlling, and stimulating). Methodological base for managing socio-economic development of agricultural cluster includes: technological support, regulatory support, informational support, marketing support, and organizational & economic support (He, 2015). Another group of problems is related to development of conceptual model of the system of indicators of agricultural cluster strategic development. Taking competitiveness of agricultural cluster as a possibility to rationally use the current potential for manifesting competitive advantages, it is possible to state that competitiveness is a result of the level of managing agricultural cluster for achieving its sustainable development. …

Self-organization of magnetic moments in dipolar chains with restricted degrees of freedom.

Equilibrium behavior of a single chain of dipolar spheres is investigated by the method of molecular dynamics in a wide range of the dipolar coupling constant λ. Two cases are considered: rodlike and flexible chains. In the first case, particle centers are immovably fixed on one axis, but their magnetic moments retain absolute orientational freedom. It has been found that at λ≳1.5 particle moments are chiefly aligned parallel to the chain axis, but the total moment of the chain continuously changes its sign with some mean frequency, which exponentially decreases with the growth of λ. Such behavior of the rodlike chain is analogous to the Néel relaxation of a superparamagnetic particle with a finite energy of magnetic anisotropy. In the flexible chain particles are able to move in the three-dimensional space, but the distance between centers of the first-nearest neighbors never exceeds a given limiting value r(max). If r(max)≃d (d is the particle diameter) then the most probable shape of the chain of five or more particles at λ≳6 is that of a ring. The behavior of chains with r(max)≥2d is qualitatively different: At λ≃4 long chains collapse into dense quasispherical globules and at λ≳8 these globules take toroidal configuration with a spontaneous azimuthal ordering of magnetic dipoles. With the increase of r(max) to larger values (r(max)>10d) globules expand and break down to form separate rings.

Attenuation of short strongly nonlinear stress pulses in dissipative granular chains.

Attenuation of short, strongly nonlinear stress pulses in chains of spheres and cylinders was investigated experimentally and numerically for two ratios of their masses keeping their contacts identical. The chain with mass ratio 0.98 supports solitary waves and another one (with mass ratio 0.55) supports nonstationary pulses, which preserve their identity only on relatively short distances, but attenuate on longer distances because of radiation of small amplitude tails generated by oscillating small mass particles. Pulse attenuation in experiments in the chain with mass ratio 0.55 was faster at the same number of the particles from the entrance than in the chain with mass ratio 0.98. It is in quantitative agreement with results of numerical calculations with effective damping coefficient 6 kg/s. This level of damping was critical for eliminating the gap openings between particles in the system with mass ratio 0.55 present at lower or no damping. With increase of dissipation numerical results show that the chain with mass ratio 0.98 provides faster attenuation than the chain with mass ratio 0.55 due to the fact that the former system supports the narrower pulse with the larger difference between velocities of neighboring particles. The investigated chains demonstrated similar behavior at large damping coefficient 100 kg/s.

Methane Adsorption in a Series of IRMOFs Studied by PHSC and Sanchez–Lacombe Equations of State

In this study, the methane adsorption on several kinds of isoreticular metal organic frameworks (IRMOF) has been modeled by applying perturbed hard sphere chain (PHSC) and Sanchez–Lacombe (SL) equation of state. PHSC and SL equation of state have three characteristic parameters calculated using group contribution method. In this study, the methane adsorption on absorbents, namely, IRMOF-6, IRMOF-8, IRMOF-10, IRMOF-14 has been obtained at temperature 298 K and various pressures up to 10 MPa. Finally, results have been compared with the simulated adsorption data points to show the precision of PHSC and SL equation of state in predicting the methane sorption trend.

A perturbed hard sphere chain equation of state for refrigerants

The present work shows a successful extension of a recently developed modified perturbed hard sphere equation of state to liquid refrigerants. Our objective is the prediction of a reliable model to describe the volumetric properties of refrigerants. In this regard, we have applied our previously developed equation of state to R12, R13, R13b1, R22, R23, R32, R123, R124, R134a, R141b, R142b, R143a, R170, R218, R227ea, R290, R1150 and R1270. Two temperature dependent parameters which are universal functions of the reduced temperature and just one adjustable parameter that can be calculated by fitting to a few experimental data exist in this equation of state. Boiling point constants are utilized as scaling factors. In order to evaluate the model, we compared the predicted densities to the literature data. This led to very encouraging results. The results of four other equations of state are presented for comparison. Our results seem to be promising in view of application to mixtures of refrigerants and long-chain hydrocarbons. In this respect the paper can be regarded as a necessary step towards the prediction of the mixture behavior of refrigerants and the effect of the presence of the lubricant oil in the mixture.

Propagation of Collective Surface Plasmons in Linear Periodic Ionic Structures: Plasmon Polariton Mechanism of Saltatory Conduction in Axons

The propagation of collective surface plasmons, called plasmon polaritons, in infinite equidistant electrolyte sphere chains is analyzed. The quenching of radiative losses of these ionic excitations in the chain is demonstrated by the inclusion of the retarded near-, medium-, and far-field components of the dipole interaction between the spheres in the chain in analogy to metallic nanochains. It is shown that the damping of the plasmon polariton self-modes in the wide region of the domain is reduced to only residual Ohmic losses that are much lower than the radiation losses for the separate electrolyte sphere. The self-frequencies and group velocities of plasmon polaritons for longitudinal and transversal (with respect to the chain orientation) polarization are determined and assessed for various ion and electrolyte parameters. It is proved that there exist weakly damped self-modes of plasmon polaritons in the chain for which the propagation range is limited only by relatively small Ohmic losses. Complete...

Plastic waves in one-dimensional heterogeneous granular chains under impact loading: Single intruders and dimer chains

Elastic granular dimer chains (defined as arrays of repeating dissimilar material granule pairs) have shown promise for wave mitigation applications since it has been observed that for certain dimer mass ratios significant force attenuation can occur along the chain during dynamic wave propagation (Jayaprakash et al., 2013). However in many applications, applied forces are likely to be such that the elastic assumption would be violated at locations of high stress concentration – the granule contact points. In this work we seek to investigate the force transmitted through dimer chains and chains with a single intruder (i.e., differing granule from the surroundings), subjected to dynamic loading in the plastic regime. A split Hopkinson pressure bar was used to dynamically load one-dimensional metallic dimer chains and homogeneous chains of metallic spheres with single intruders. Loading magnitudes ranging from 10kN to 35kN were applied to these chains, producing significant plasticity in the beads. The results in each case were quantified by the ratio of the output to incident force from the granular chain. Transmitted force results were compared to those in elastic dimer chains for which force attenuation was controlled by the mass ratio of the dimer pair. In the plastic case, however, the propagating pulse was found to have a strong dependence on the yielding material, not on the dimer mass ratio. Although output force was significantly reduced over input force, the reduction was driven by plastic dissipation and not elastic attenuation mechanisms. Chains with a single intruder were also seen to behave differently when the intruder was relatively softer or harder than the remainder of the chain. For a softer intruder the transmitted force decreased as the intruder location moved further down the chain, while for a harder intruder the output force did not depend on intruder location and was roughly the same as that of a homogeneous chain, i.e., the harder intruder did not affect wave transmission.

Generation of Impulses from Single Frequency Inputs Using Non-linear Propagation in Spherical Chains

This paper investigates the use of chains of spheres to produce impulses. An ultrasonic horn is used to generate high amplitude sinusoidal signals. These are then input into chains of spheres, held together using a minimal force. The result is a non-linear, dispersive system, within which solitary waves can exist. The authors have discovered that resonances can be created, caused by the multiple reflection of solitary waves within the chain. The multiply-reflecting impulses can have a wide bandwidth, due to the inherent nonlinearity of the contact between spheres. It is found that the effect only occurs for certain numbers of spheres in the chain for a given input frequency, a result of the creation of a nonlinear normal mode of resonance. The resulting impulses have many applications, potentially creating high amplitude impulses with adjustable properties, depending on both the nature and number of spheres in the chain, and the frequency and amplitude of excitation.

Thermal instabilities and Rayleigh breakup of ultrathin silver nanowires grown in helium nanodroplets.

Ag nanowires with diameters below 6 nm are grown within vortex containing superfluid helium nanodroplets and deposited onto a heatable substrate at cryogenic temperatures. The experimental setup allows an unbiased investigation of the inherent stability of pristine silver nanowires, which is virtually impossible with other methods due to chemical processes or templates involved in standard production routes. We demonstrate by experiment and by adaption of a theoretical model that initially continuous wires disintegrate into chains of spheres. This phenomenon is well described by a Rayleigh-like breakup mechanism when the substrate is heated to room temperature. Our findings clarify the recent discussions on the cause of the observed segmented patterns, where a breakup during deposition [Gomez et al., Phys. Rev. Lett., 2012, 108, 155302] or mechanisms intrinsic to the helium droplet mediated growth process [Spence et al., Phys. Chem. Chem. Phys., 2014, 16, 6903] have been proposed. The experimental setup confirms the validity of previous suggestions derived from bulk superfluid helium experiments [Gordon et al., Phys. Chem. Chem. Phys., 2014, 16, 25229] for the helium droplet system, and further allows a much more accurate determination of the breakup temperature.

The role of bond tangency and bond gap in hard sphere crystallization of chains

We report results from Monte Carlo simulations on dense packings of linear, freely-jointed chains of hard spheres of uniform size. In contrast to our past studies where bonded spheres along the chain backbone were tangent, in the present work a finite tolerance in the bond is allowed. Bond lengths are allowed to fluctuate in the interval [σ, σ + dl], where σ is the sphere diameter. We find that bond tolerance affects the phase behaviour of hard-sphere chains, especially in the close vicinity of the melting transition. First, a critical dl(crit) exists marking the threshold for crystallization, whose value decreases with increasing volume fraction. Second, bond gaps enhance the onset of phase transition by accelerating crystal nucleation and growth. Finally, bond tolerance has an effect on crystal morphologies: in the tangent limit the majority of structures correspond to stack-faulted random hexagonal close packing (rhcp). However, as bond tolerance increases a wealth of diverse structures can be observed: from single fcc (or hcp) crystallites to random hcp/fcc stackings with multiple directions. By extending the simulations over trillions of MC steps (10(12)) we are able to observe crystal-crystal transitions and perfection even for entangled polymer chains in accordance to the Ostwald's rule of stages in crystal polymorphism. Through simple geometric arguments we explain how the presence of rigid or flexible constraints affects crystallization in general atomic and particulate systems. Based on the present results, it can be concluded that proper tuning of bond gaps and of the connectivity network can be a controlling factor for the phase behaviour of model, polymer-based colloidal and granular systems.

Polymer segregation under confinement: free energy calculations and segregation dynamics simulations.

Monte Carlo simulations are used to study the behavior of two polymers under confinement in a cylindrical tube. Each polymer is modeled as a chain of hard spheres. We measure the free energy of the system, F, as a function of the distance between the centers of mass of the polymers, λ, and examine the effects on the free energy functions of varying the channel diameter D and length L, as well as the polymer length N and bending rigidity κ. For infinitely long cylinders, F is a maximum at λ = 0, and decreases with λ until the polymers are no longer in contact. For flexible chains (κ = 0), the polymers overlap along the cylinder for low λ, while above some critical value of λ they are longitudinally compressed and non-overlapping while still in contact. We find that the free energy barrier height, ΔF ≡ F(0) - F(∞), scales as ΔF/k(B)T ∼ ND(-1.93 ± 0.01), for N ⩽ 200 and D ⩽ 9σ, where σ is the monomer diameter. In addition, the overlap free energy appears to scale as F/k(B)T = Nf(λ/N; D) for sufficiently large N, where f is a function parameterized by the cylinder diameter D. For channels of finite length, the free energy barrier height increases with increasing confinement aspect ratio L/D at fixed volume fraction ϕ, and it decreases with increasing ϕ at fixed L/D. Increasing the polymer bending rigidity κ monotonically reduces the overlap free energy. For strongly confined systems, where the chain persistence length P satisfies D ≪ P, F varies linearly with λ with a slope that scales as F'(λ) ∼ -k(B)TD(-β)P(-α), where β ≈ 2 and α ≈ 0.37 for N = 200 chains. These exponent values deviate slightly from those predicted using a simple model, possibly due to insufficiently satisfying the conditions defining the Odijk regime. Finally, we use Monte Carlo dynamics simulations to examine polymer segregation dynamics for fully flexible chains and observe segregation rates that decrease with decreasing entropic force magnitude, f ≡ |dF/dλ|. For both infinite-length and finite-length channels, the polymers are not conformationally relaxed at later times during segregation.

Wave tailoring by precompression in confined granular systems.

We present a granular system whose response under an impact load can be varied from rapidly decaying to almost constant amplitude waves by an external regulator. The system consists of a granular chain of larger spheres surrounded by small spheres, confined in a hollow cylindrical tube and supporting wave propagation along the axis of the cylinder. We demonstrate using numerical simulations that the response can be controlled by applying radial precompression. These observations are then complemented by an asymptotic analysis, which shows that the decay in the leading wave is due to energy leakage to the oscillating small beads in the tail of the wave. This system has potential applications in systems requiring tuning of elastic waves.

Self‐Organization of Anisotropic and Binary Colloids in Thermo‐Switchable 1D Microconfinement

Anisotropic and binary colloids self‐assemble into a variety of novel supracolloidal structures within the thermo‐switchable confinement of molecular microtubes, achieving structuring at multiple length scales and dimensionalities. The multistage self‐assembly strategy involving hard colloidal particles and a soft supramolecular template is generic for colloids with different geometries and materials as well as their binary mixtures. The colloidal architectures can be controlled by colloid shape, size, and concentration. Colloidal cubes align in chains with face‐to‐face arrangement, whereas rod‐like colloids predominantly self‐organize in end‐to‐end configurations with their long axis parallel with the long axis of the microtubes. The 1D microconfinement imposed on binary mixtures of anisotropic and isotropic colloids further increases the diversity of colloid‐in‐tube structures. In cube–sphere mixtures, cubes may act as additional confiners, locking in colloidal sphere chains, while a “colloidal Morse code” is generated where rods and spheres alternate in the case of rod–sphere mixtures. The versatile confined colloidal superstructures including their thermoresponsive assembly and disassembly are relevant for the development of stimulus–responsive materials where controlled release and encapsulation are desired.

Twinning of Polymer Crystals Suppressed by Entropy

We propose an entropic argument as partial explanation of the observed scarcity of twinned structures in crystalline samples of synthetic organic polymeric materials. Polymeric molecules possess a much larger number of conformational degrees of freedom than low molecular weight substances. The preferred conformations of polymer chains in the bulk of a single crystal are often incompatible with the conformations imposed by the symmetry of a growth twin, both at the composition surfaces and in the twin axis. We calculate the differences in conformational entropy between chains in single crystals and chains in twinned crystals, and find that the reduction in chain conformational entropy in the twin is sufficient to make the single crystal the stable thermodynamic phase. The formation of cyclic twins in molecular dynamics simulations of chains of hard spheres must thus be attributed to kinetic factors. In more realistic polymers this entropic contribution to the free energy can be canceled or dominated by nonbonded and torsional energetics.

Sorption of methane in a series of Zn-based MOFs studied by PHSC equation of state

Adsorption and storage of gaseous methane as a clean fuel for cars has always attracted the attention of researchers. One of the most famous porous absorbents which has been used for separation and storage of several gases is called metal organic framework (MOF). These kinds of absorbents have been intensely studied in recent years. In this study, the experimental data related to methane adsorption on and desorption from five absorbents, namely, MOF-5, MOF-177, MOF-200, MOF-205 and MOF-210 have been adopted. Then, the methane sorption has been modeled by applying Perturbed Hard Sphere Chain Equation of State (PHSC EoS). PHSC equation of state has three molecular-based parameters, r, σ and ɛ; which are the number of segments per molecule, the hard-sphere diameter and the non-bonded interaction energy, respectively. These three parameters have been calculated using the group contribution (GC) method. The amount of methane uptake in the adsorbents has been obtained through gas-absorbents phase equilibrium calculations at temperature 298K and various pressures up to 90×105Pa. Finally, results have been compared with the experimental data to show the precision of PHSC equation of state in predicting the methane sorption trend.

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

We review the main results from extensive Monte Carlo (MC) simulations on athermal polymer packings in the bulk and under confinement. By employing the simplest possible model of excluded volume, macromolecules are represented as freely-jointed chains of hard spheres of uniform size. Simulations are carried out in a wide concentration range: from very dilute up to very high volume fractions, reaching the maximally random jammed (MRJ) state. We study how factors like chain length, volume fraction and flexibility of bond lengths affect the structure, shape and size of polymers, their packing efficiency and their phase behaviour (disorder–order transition). In addition, we observe how these properties are affected by confinement realized by flat, impenetrable walls in one dimension. Finally, by mapping the parent polymer chains to primitive paths through direct geometrical algorithms, we analyse the characteristics of the entanglement network as a function of packing density.

Capability of PHSC equation of state for thermodynamic modeling of aqueous amino acid and peptide solutions

The Perturbed Hard Sphere Chain (PHSC) equation of state (EoS) has been utilized for thermodynamic modeling of aqueous amino acid and peptide solutions. For this purpose, the parameters of amino acids and peptides have been adjusted to activity coefficient, liquid density and solubility of amino acids and peptides in water. Furthermore, water activity, osmotic coefficient and vapor pressure of aqueous amino acid solution have been predicted. Finally the solubility of amino acid mixtures in water has been calculated using additional adjustable parameters. The results of PHSC EoS were in good agreement with experimental data. Average deviations in estimation of activity coefficients, liquid densities, water activity and osmotic coefficient are 1.44%, 0.38%, 0.067% and 2.6%, respectively. In addition the solubility of mixed aqueous amino acids has been calculated to show the ability of mentioned model.

Hydrogen storage in a series of Zn-based MOFs studied by PHSC equation of state

One of the most famous porous adsorbents used for separation and storage of several gases is metal organic framework (MOF). In this study, the experimental data related to hydrogen adsorption on and desorption from five adsorbents including MOF-5, MOF-177, MOF-200, MOF-205 and MOF-210 is adopted. Then, the hydrogen sorption is modeled by applying Perturbed Hard Sphere Chain Equation of State (PHSC EoS). PHSC equation of state has three molecular-based parameters, namely, the number of segments per molecule, the hard-sphere diameter and the non-bonded interaction energy, respectively. The amount of hydrogen uptake in the adsorbents is obtained through gas-adsorbents phase equilibrium calculations at temperature 77 K and various pressures up to 80 × 105 Pa. Finally, the result is compared with the experimental data to show the precision of PHSC equation of state in predicting the hydrogen sorption trend.

Vapor–liquid and liquid–liquid equilibrium calculations in mixtures containing non-ionic glycol ether surfactant using PHSC equation of state

In this study, vapor–liquid and liquid–liquid equilibrium in mixtures containing glycol ether surfactant, non-polar and polar compounds are calculated using Perturbed Hard Sphere Chain (PHSC) equation of state (EoS). Pure liquid density and vapor pressure of surfactants are used for parameter estimation of glycol ether surfactants. The PHSC parameters are calculated for both ethylene glycol ether and propylene glycol ether surfactants. Glycol ether surfactant molecules are modeled as associating components by considering two association sites for each molecule. The results show that the PHSC model is capable of correlating thermodynamic behavior of binary (polar+surfactant) and (non-polar+surfactant) systems. Upper critical solution temperature (UCST) for hydrocarbon+surfactant and lower critical solution temperature (LCST) for water+surfactant systems are accurately calculated. The critical temperatures and the extent of immiscibility are in good agreement with the available experimental data.