We demonstrate a composite medium, based on a periodic array of interspaced conducting nonmagnetic split ring resonators and continuous wires, that exhibits a frequency region in the microwave regime with simultaneously negative values of effective permeability &mgr;(eff)(omega) and permittivity varepsilon(eff)(omega). This structure forms a "left-handed" medium, for which it has been predicted that such phenomena as the Doppler effect, Cherenkov radiation, and even Snell's law are inverted. It is now possible through microwave experiments to test for these effects using this new metamaterial.

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Articles you may be interested inA self-oscillating ionic polymer-metal composite bending actuator J. Appl. Phys. 103, 084908 (2008); 10.1063/1.2903478 Modeling of electrochemomechanical response of ionic polymer-metal composites with various solvents Effect of solvents on the chemical and physical properties of ionic polymer-metal composites Comparative experimental study of ionic polymer-metal composites with different backbone ionomers and in various cation forms J. Appl. Phys. 93, 5255 (2003); 10.1063/1.1563300Electromechanical response of ionic polymer-metal composites Ionic polymer-metal composites ͑IPMCs͒ consist of a polyelectrolyte membrane ͑usually, Nafion or Flemion͒ plated on both faces by a noble metal, and is neutralized with certain counter ions that balance the electrical charge of the anions covalently fixed to the backbone membrane. In the hydrated state ͑or in the presence of other suitable solvents͒, the composite is a soft actuator and sensor. Its coupled electrical-chemical-mechanical response depends on: ͑1͒ the chemical composition and structure of the backbone ionic polymer; ͑2͒ the morphology of the metal electrodes; ͑3͒ the nature of the cations; and ͑4͒ the level of hydration ͑solvent saturation͒. A systematic experimental evaluation of the mechanical response of both metal-plated and bare Nafion and Flemion in various cation forms and various water saturation levels has been performed in the author's laboratories at the University of California, San Diego. By examining the measured stiffness of the Nafion-based composites and the corresponding bare Nafion, under a variety of conditions, I have sought to develop relations between internal forces and the resulting stiffness and deformation of this class of IPMCs. Based on these and through a comparative study of the effects of various cations on the material's stiffness and response, I have attempted to identify potential micromechanisms responsible for the observed electromechanical behavior of these materials, model them, and compare the model results with experimental data. A summary of these developments is given in the present work. First, a micromechanical model for the calculation of the Young modulus of the bare Nafion or Flemion in various ion forms and water saturation levels is given. Second, the bare-polymer model is modified to include the effect of the metal plating, and the results are applied to calculate the stiffness of the corresponding IPMCs, as a function of the solvent uptake. Finally, guided by the stiffness modeling and data, the actuation of the Nafion-based IPMCs is micromechanically modeled. Examples of the model results are presented and compared with the measured data.

An ionic polymer-metal composite (IPMC) consisting of a thin Nafion sheet, platinum plated on both faces, undergoes large bending motion when an electric field is applied across its thickness. Conversely, a voltage is produced across its faces when it is suddenly bent. A micromechanical model is developed which accounts for the coupled ion transport, electric field, and elastic deformation to predict the response of the IPMC, qualitatively and quantitatively. First, the basic three-dimensional coupled field equations are presented, and then the results are applied to predict the response of a thin sheet of an IPMC. Central to the theory is the recognition that the interaction between an imbalanced charge density and the backbone polymer can be presented by an eigenstress field (Nemat-Nasser and Hori, Micromechanics, Overall Properties of Heterogeneous Materials, 2nd Ed., Elsevier, Amsterdam, 1999). The constitutive parameter connecting the eigenstress to the charge density is calculated directly using a simple microstructural model for Nafion. The results are applied to predict the response of samples of IPMC, and good correlation with experimental data is obtained. Experiments show that the voltage induced by a sudden imposition of a curvature, is two orders of magnitude less than that required to produce the same curvature. The theory accurately predicts this result. The theory also shows the relative effects of different counter ions, e.g., sodium versus lithium, on the response of the composite to an applied voltage or a curvature.

An ionic polymer-metal composite (IPMC) consisting of a thin perfluorinated ionomer (usually, Nafion or Flemion) strip, platinum, and/or gold plated on both faces and neutralized by a certain amount of appropriate cations undergoes large bending motion when, in a hydrated state, a small electric field is applied across its thickness. When the same membrane is suddenly bent, a small voltage of the order of millivolts is produced across its surfaces. Hence IPMCs can serve as soft bending actuators and sensors. This coupled electrical-chemical-mechanical response of IPMCs depends on the structure of the backbone ionic polymer, the morphology and conductivity of the metal electrodes, the nature of the cations, and the level of hydration (or other solvent uptake). We have carried out extensive experimental studies on both Nafion-and Flemion-based IPMCs in various cation forms, seeking to understand the fundamental properties of these composites, to explore the mechanism of their actuation, and finally, to optimize their performance for various potential applications. The results of some of these tests on both Nafion-and Flemion-based IPMCs with alkali-metal or alkyl-ammonium cations are reported here. Compared with Nafion-based IPMCs, Flemion-based IPMCs with fine dendritic gold electrodes have higher ion-exchange capacity, better surface conductivity, higher hydration capacity and higher longitudinal stiffness. They also display greater bending actuation under the same applied voltage. In addition, they do not display a reverse relaxation under a sustained DC voltage, which is typical of Nafion-based IPMCs in alkali-metal form. Flemion IPMCs thus are promising composites for application as bending actuators.

Considered is a sample of cohesionless granular material, in which the individual granules are regarded rigid, and which is subjected to overall macroscopic average stresses. On the basis of the principle of virtual work, and by an examination of the manner by which adjacent granules transmit forces through their contacts, a general representation is established for the macroscopic stresses in terms of the volume average of the (tensorial) product of the contact forces and the vectors which connect the centroids of adjacent contacting granules. Then the corresponding kinematics is examined and the overall macroscopic deformation rate and spin tensors are developed in terms of the volume average of relevant microscopic kinematical variables. As an illustration of the application of the general expressions developed, two explicit macroscopic results are deduced: (1) a dilatancy equation which both qualitatively and quantitatively seems to be in accord with experimental observation, and (2) a noncoaxiality equation which seems to support the vertex plasticity model. Since the development is based on a microstructural consideration, all material coefficients entering the results have well-defined physical interpretations.

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AbstractÐThe mechanical behavior of a commercially pure titanium (CP-Ti) is systematically investigated in quasi-static (Instron, servohydraulic) and dynamic (UCSD's recovery Hopkinson) compression. Strains over 40% are achieved in these tests over a temperature range of 77±1000 K and strain rates of 10 À3 ±8000/s. At the macroscopic level, the¯ow stress of CP-Ti, within the plastic deformation regime, is strongly dependent on the temperature and strain rate, and displays complex variations with strain, strain rate, and temperature. In particular, there is a three-stage deformation pattern at a temperature range from 296 to 800 K, the speci®c range depending on the strain rate. In an e ort to understand the underlying mechanisms, a number of interrupted tests involving temperature jumps are performed, and the resulting microstructures are characterized using an optical microscope. Based on the experimental results and simple estimates, it is concluded that the three-stage pattern of deformation at temperatures from 296 to 800 K, is a result of dynamic strain aging, through the directional di usion of dislocation-core point defects with the moving dislocation at high strain rates, although the usual dynamic strain aging by point defects segregating outside the dislocation core through volume di usion is also observed at low strain rates and high temperatures. The microscopic analysis shows that there is substantial deformation twinning which cannot be neglected in modeling the plastic¯ow of CP-Ti. The density of twins increases markedly with increasing strain rate, strain, and decreasing temperature. Twin intersections occur, and become more pronounced at low temperatures or high strain rates. In sum, the true stress±true strain curves of CP-Ti show two stages of deformation pattern at low temperatures, three stages at temperatures above 296 K, and only one stage at temperatures exceeding 800 K, although all three stages may exist even at 1000 K for very high strain rates, e.g. 8000/s. While the dislocation motion is still the main deformation mechanism for plastic¯ow, the experimental results suggest that dynamic strain aging should be taken into account, as well as the e ect of deformation twinning. #