Two-dimensional electrochemical turbulence during the electrodissolution of metal disk electrodes: Model calculations

We present numerical studies of the spatio-temporal dynamics of disk electrodes with local limit cycle oscillations. The simulations are done with a realistic 3-D geometry of the electrochemical cell and disk-shaped working electrodes (WE). Spatio-temporal chaos is shown to exist from a critical electrode size onwards. It is analyzed by Karhunen-Loève decomposition and Hilbert transform. The former shows that the chaos becomes more complex with increasing system size, the latter allows features that generate the spatio-temporal complexity to be identified, namely, spatially extended 1-D phase defects and topological defects.     

Theory of the dielectric constant of ice

The first result of this paper is to show that the Onsager—Slater theory of the dielectric constant is consistent for some reasoable model of ice in the limit of no intrinsic defects. Accordingly, a model is presented, called the unit model, which has unit cells with no dipole moments for which the Onsager—Slater theory is exact. The second result of this paper is to show that the unit model is physically and chemically realistic. Bjerrum defects are introduced into the model and the relation between the dielectric constant and the Bjerrum defect charge found by Onsager and Dupuis for a less realistic model continues to hold and is satisfied by the experimental values. In a simple point charge approximation the charge distribution determined by the model requirements and the experimentally determined Bjerrum fault charge are found and seem reasonble. Higher order multipole interaction energies are consistent with eviations from pure 1/T dependence of the dielectric constant of real ice with intrinsic defects, can be derived in the context of the unit model. This formula interpolates between the Onsager—Slater formula in the limit of no intrinsic defects and the Kirkwood—Frohlich formula in the limit of many intrinsic defects. For the concentration of defects in real ice the interpolation formula is practically the same as the Onsager—Slater formula and differs from the Kirkwood—Frohlich formula by a factor of nearly $\text{3}\text{2}$.     

Hyperbolic Spirals as Surface Structures in Thin Layers

When thin layers of 4-chloro-3-methylphenol and a copolymer of methyl(methacrylate) and maleic acid dissolved in acetone are dried by solvent evaporation, various surface structures appear. Besides linear surface deformations that can ramify like fractals, spirals of the hyperbolic type have been found. The surface structures are due to crystallization processes and flows caused by surface tension differences. The spirals are surface elevations with grooves on both sides as shown by surface profile measurements by means of a microscope interferometer. The addition of surfactants reduces the structure formation. A large surfactant concentration prevents the structure formation. Copyright 2001 Academic Press.     

A study of the dilation of the unit cell of metallocene isotactic poly(propylenes): The monoclinic form

The lattice parameters of a series of monoclinic metallocene poly(propylenes) of constant molecular weight are measured as a function of defect content, that vary between 0.3 and 2.35 total defects per 100 monomeric units. The parameters are also measured as a function of molecular weight for a fixed defect content and as a function of the crystallization temperature. The b axis is found to increase with decreasing isothermal crystallization temperature whereas only small changes are found for samples rapidly crystallized. The a and c axis showed basically no variation with crystallization temperature. The parameters of the unit cell were essentially constant with varying defect content in the poly(propylene) chain. Lack of observed effect on the dilation of the unit cell by increasing defects is a consequence of the rapid crystallization required to ensure formation of monoclinic crystals. The unit cell parameters increased as a mild function of the molecular weight. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2511–2521, 1997     

Slip-step on polyoxymethylene crystals

Crystals of polyoxymethylene have been grown from solution in bromobenzene. In many growth features, which are similar to those for monomeric crystals, the movement of dislocation can be traced by a slip-step raised in the growth surface. Such slip-steps are associated with single spirals, two spirals of opposite senses and two spirals of the same sense. Anomalies in the growth patterns of crystals have also been observed and attributed to the movement of screw dislocation long before the cessation of growth.     

A new model for the molecular conformation in polyoxymethylene crystals

Nonintegral indices are found for the extra meridional reflections in the x-ray diffraction of drawn polyoxymethylene. The index of one of the extra reflections is estimated at 00l: l = 2.830 ± 0.003. A new model for the molecular conformation which accounts for the nonintegral indices is proposed. The new model is a helix with defects at constant intervals along the helix axis. The defect is an unwinding of the helix by 20° around the helix axis. This defect is believed to be characteristic of crystals of helical polymers. The interval between the defects is estimated as 18 monomers. The crystal structure with these defects is consistent with precise measurements of the layer line positions.     

Chaos Synchronization in the Belousov—Zhabotinsky Chemical Reaction by Adaptive Control Scheme

The adaptive synchronization sc heme proposed by John and Amritkar was employed into the Belousov-Zhabotinsky（BZ)4-varibale-Montanator model system.By the parameter adjustment,chaos synchroniztion has been obtained ,Through calculating the transient time,the optimal combination of the stiffness constant and damping constant was obtained .Furthermore,the relationships among the transient time,conditional Lyapunov exponents,the stiffiness constant and damping constant were discussed ,Also ,the BZ system with the adaptive synchronization scheme might be used for the communication purposes.     

A perturbative study of low-order resonances and chaos in the kinetically coupled two-degree-of-freedom morse system using lie transforms

The stretching dynamics of ABA triatomics is studied over a range of A/B mass ratios. The origins of global chaos found for certain ratios are discussed. Lie perturbation theory is used to construct Hamiltonians in a form ideally suited to implementing Chirikov's idea that overlapping non-linear resonances lead to chaos.     

Travelling fingers in two-frequency cholesteric liquid crystals: fragments, loops and spirals

We review the different dynamical patterns that cholesteric fingers of the first type (CF-1) and of the second type (CF-2) form in an a.c. electric field near the coexistence line with the homeotropic nematic phase. Videomicroscopy and computer image analysis were used for investigation of the patterns in polarized light. We show that CF-1s can form stable rectilinear fragments that crawl at constant velocity along their axes, whereas CF-2s form only unstable curved fragments that drift perpendicularly to their axes. Observations of CF-2 staple-shaped fragments which continuously lengthen in their centres are also reported. Finally, we describe in detail the experimental conditions in which CF-2 loops and spirals grow, collapse and destabilize.     

Travelling fingers in two-frequency cholesteric liquid crystals: fragments,loops and spirals

We review the different dynamical patterns that cholesteric fingers of the first type (CF-1) and of the second type (CF-2) form in an a.c. electric field near the coexistence line with the homeotropic nematic phase. Videomicroscopy and computer image analysis were used for investigation of the patterns in polarized light. We show that CF-1s can form stable rectilinear fragments that crawl at constant velocity along their axes, whereas CF-2s form only unstable curved fragments that drift perpendicularly to their axes. Observations of CF-2 staple-shaped fragments which continuously lengthen in their centres are also reported. Finally, we describe in detail the experimental conditions in which CF-2 loops and spirals grow, collapse and destabilize.     

Quantitative investigation of spatiotemporal chaos in the ferroin-catalyzed Belousov-Zhabotinskii reaction in a batch reactor

We have analyzed experimental data on the time dependence of the potentials of 16 platinum point-contact electrodes for spatiotemporal chaos in the Belousov-Zhabotinskii reaction. We show that the largest Lyapunov exponent is a convenient characteristic for spatiotemporal chaos. We found that in going from temporal to spatiotemporal chaos, the embedding dimension of the system increases by a factor of three. We have observed that as the largest Lyapunov exponent increases, we observe a decrease in the degree of spatial correlation of the process.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 31, No. 1, pp. 34–39, January–February, 1995.We would like to thank the Foundation for Basic Research of the State Science and Technology Committee of Ukraine for financial support of this work (Project 3.3/87).     

Delay-induced inward and outward spiral waves in oscillatory medium

Inward and outward spiral waves as well as inward target waves are induced by local delay feedback in a reaction-diffusion system exhibiting a Turing hexagon pattern spontaneously. The system gives rise to large-amplitude sinusoidal oscillations when the inward spiral waves are observed. Compared with the inward spirals, the outward spiral waves usually possess longer wavelength and exhibit larger amplitude relaxation oscillations. Varying the feedback parameters continuously, the inward spiral waves are transformed into outward spirals through a turbulent state. The dispersion analysis about the delayed system reveals that there is an unstable band on the dispersion curve, where the turbulent state arises. The dispersion curve is divided into two parts by the unstable band. The inward spiral waves exist in the left part with negative group velocity, i.e., domega/dk<0, while the outward spiral waves are stable in the right part with domega/dk>0 (omega is frequency and k wavenumber).     

Between Grocers and Physicians: Pharmacists,the new Chemistry,and Institutional Reforms in Bologna during the Napoleonic Period

Abstract

This article argues that the chemical and physiological experiments undertaken by the natural philosopher Stephen Hales (1677–1761) constituted a reformulation of providential matter theory. Hales was responding to a continuing debate about the position of chaos in the natural world between Newtonians like Samuel Clarke, who posited chaos as oppositional to immediate providential direction, and those such as John Ray and Bernard Nieuwentyt, who argued that nature was a chaos of operations, organised by divinely endowed but innate principles. Vegetable Staticks (1727) represents an attempted solution, arguing that a chaos of operations could support life only if it was concurrent with God's direction. Subsequently criticised by the Irish theologian Peter Browne for indulging frivolity, Hales responded in Haemastatics (1733) by auditing how spirituous liquor precipitated a bodily disintegration from the chaos of operations into a destructive chaos. Hales’ subsequent campaign against spirits should be read as an extension of his experimental philosophy as a moral tool.     

Period-doubling and chaotic oscillations in the ferroin-catalyzed Belousov-Zhabotinsky reaction in a CSTR

The ferroin-catalyzed Belousov-Zhabotinsky(BZ) reaction,the oxidation of malonic acid by acidic bromate,is the most commonly investigated chemical system for understanding spatial pattern forma-tion. Various oscillatory behaviors were found from such as mixed-mode and simple period-doubling oscillations and chaos on both Pt electrode and Br-ISE at high flow rates to mixed-mode oscillations on Br-ISE only at low flow rates. The complex dynamic behaviors were qualitatively reproduced with a two-cycle coupling model proposed initially by Gy?rgyi and Field. This investigation offered a proper medium for studying pattern formation under complex temporal dynamics. In addition,it also shows that complex oscillations and chaos in the BZ reaction can be extended to other bromate-driven nonlinear reaction systems with different metal catalysts.     

Eliminating chaos in the Belousov–Zhabotinsky reaction by no-delay feedback and delayed feedback

We present numerical simulations of the three-variable model of the Belousov–Zhabotinsky reaction developed by Gyorgyi and Field, where chaos can occur in the free-running system. As the rate of in-flow in the continuous-flow stirred-tank reactor is controlled by the concentration of one of the reactor species through a feedback loop, we find two simple ways to bring the chaotic behavior to periodic behavior. One is to modify the feedback strength without time delay in the feedback loop, and the other is to modify the delay time of the feedback at constant feedback strength. The possible mechanisms for the two ways are discussed.     

周期扰动位相对化学振荡的调制效应

由Rossler反应系统的理论模型出发,构造一种具有外部周期扰动的新动力学系统,并采用逆算符法和数值分析法研究该系统的振荡态在周期扰动调制下的动力学行为.结果表明,在周期扰动的调制下,系统的状态由单周期振荡态(1p)变为周期2(2p)、周期4(4p)等多周期振荡态以及混沌态.扰动位相是系统呈现上述多种演化模式的控制参数,在扰动位相不同的数值区间,系统呈现的演化模式不同,而且扰动位相数值的微小改变,还影响每种演化模式的内部结构.     

Self-assembly of the perfluoroalkyl-alkane F14H20 in ultrathin films

Scanning force microscopy on monomolecular films of eicosylperfluorotetradecane, F(CF(2))(14)(CH(2))(20)H, on mica, silicon oxide, or water revealed spontaneous organization to well-defined nanoscopic ribbon and spiral or toroidal superstructures. Whether ribbons or nanospirals were formed depended on the solvent from which the molecular monofilm was cast. Ribbons were observed when a hydrocarbon or a perfluorocarbon solvent was used, e.g., decalin or perfluorodecalin. When the compound, however, was deposited from nonselective hexafluoroxylene, the molecules assembled into spirals of defined size. The spirals/toroids transformed to ribbons when exposed either to decalin or perfluorodecalin vapor, and the ribbons transformed to toroids when exposed to hexafluoroxylene vapor. These changes could be observed in situ. Scanning force microscopy yielded an identical height and width for the bands forming the spirals and for the parallel flat ribbons. X-ray reflectivity yielded a height of 3.61 +/- 0.05 nm, again identical for both morphologies. Yet, the length of the extended F(CF(2))(14)(CH(2))(20)H molecule, i.e., 4.65 nm, exceeds the layer thickness obtained from X-ray reflectometry. It is, however, consistent with an arrangement where the fluorinated chains are oriented normal to the surface layer and where the alkyl segments are tilted with a 122 degrees angle between the two segments. Within the plane defined by the tilt, this angle allows a dense packing of the alkyl segments compensating for the larger cross-section of the fluorocarbon segment. The tilt plane defines an "easy" direction along which the monolayer structure can preserve order. In the plane perpendicular to this axis, long-range ordered dense packing of the alkyl chains is not possible. Incommensurable packing can in principle explain the finite and regular width of the ribbons and the stepwise turn in the spirals.     

Bioinspired synthesis of a hollow metallic microspiral based on a spirulina bioscaffold

Bioinspired synthesis approaches aim to take advantage of the morphology and structural features of biological materials for the development of functional micro/nanodevices. In this Letter, we report that a unicellular algae known as a Spirulina was applied as a bioscaffold for the synthesis of hollow metallic Cu microspirals with length of 200-300 μm. The electroless deposition method was employed to cover the spirulina forming the spiral. The nanomechanical properties of the spiral were investigated by using the nanoindentation technique. The results showed the hardness and elastic modulus of the spiral were 0.63-0.68 GPa and 12.35-12.63 GPa, respectively. Other metallic or alloy spirals could also be synthesized by using the spirulina as a bioscaffold with low cost and high reproducibility, and the obtained spirals could be promising materials as functional micro/nanodevices for microelectromechanical systems.     

Effect of temperature on the stress-strain behavior of a polypropylene-particulate rubber composite

Composites based on polypropylene and rubber particles were studied at different temperatures. It was found that, as the temperature is elevated, the type of defects that are formed near large filler particles changes from a crack to a diamond-shaped void and, next, to an elliptical or slit-type void. The change in the defect type predetermines the change of the composite failure mechanism at a constant particulate-filler content from brittle fracture before the yield point to fracture during neck formation or propagation and, finally, to non-uniform plastic drawing with a stable neck growth.     

Nematic ordering and defects on the surface of a sphere: a Monte Carlo simulation study

We examine the ordering of hard rods on the surface of a sphere using computer simulations. As predicted by previous theories of thin nematic shells we observe four s = + 1/2 defects. However, the predicted tetrahedral symmetry for the defects and the "baseball" director configuration is not observed. Instead the four defects are located, on average, on a great circle which splits the sphere into two hemispheres, each of which has a splay dominated director configuration. We argue that this result occurs as the bend elastic constant for hard rods is much larger than the splay elastic constant.