Monte-Carlo Simulation of Three Dimensional Ion Dynamics in Polymers
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MONTE-CARLO SIMULATION OF THREE DIMENSIONAL ION DYNAMICS IN POLYMERS A.Wagner, H. Kliem, Institute of Electrical Engineering Physics, Saarland University, D-66041 Saarbruecken, Germany ABSTRACT Dynamic Monte-Carlo simulations of three dimensional ion motions are carried out based on a multi-well potential model. A parallel plate capacitor is modeled with an ionic conducting polymer having two ideal blocking electrodes. Positive ions (maximum 1000) are located on a cubic lattice with a maximum size of 100x100x100 locations. A negative background charge, constant in space and time, is used to provide charge neutrality. The positive ions can perform hops between neighboring sites with a probability corresponding to distributed energy barriers. To calculate the potentials due to an interaction of the ions the method of images is used. The steady state and the dynamic properties are studied after application of a voltage step in dependence on the sample thickness, the ion concentration and the voltage. A simulation of a space charge polarization yields an explanation for the experiments in the time and in the frequency domain. INTRODUCTION Electrical relaxation processes in dielectric materials as well as in solid ionic conductors often show a dispersed behavior in a wide range. In many cases this can be expressed in a power −α of the response function in the time domain [1]. In the frequency domain we find a law j ∝ t β power law of the imaginary part of the permittivity ε’’(ω) ∝ ω respectively of the real part of β+1 the conductivity σ’(ω) ∝ ω with β = α−1 [2]. In the dielectrics this behavior can be explained with the aid of debye processes with distributed relaxation times due to an internal static energy barrier distribution. For solid polymer electrolytes several models are developed, which attribute the power law to the microscopic dynamic disorder in the material [3]. In this picture the ions can change their pathways through the electrolyte due to a rearrangement of the polymer host. For other classes of solid electrolytes similar assumption are made [4]. A model, which uses a combination of static disorder and interaction between the ions, is the counter-ion model [5]. In this model an energy distribution is caused by the coulomb interaction of counter-ions, which are fixed on lattice sites. In our model we use a constant negative background charge to provide charge neutrality. Furthermore, we introduce an intrinsic barrier energy distribution, which may be due to a disordered polymer host. Because the goal is to simulate thin structures, we have to consider the electrode effects due to image charges. The existence of blocking layers allows us to separate an injection of charges from a space charge polarization and the related accumulation of charges at the electrodes. EXPERIMENTAL Thin films (0.3 µm to 30 µm) of poly(ethylene oxide) (PEO) with molecular weights from 6 x 103 to 4 x 105 were prepared from aqueous solutions by a spin technique as Al-PEO-Al structures. Dielectric measurements (capacitance and loss
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