A multiscale model applied to ionic polymer stiffness prediction
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Lisa M. Weilanda) Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, Pennsylvania 15261 (Received 25 October 2007; accepted 10 December 2007)
A multiscale modeling approach applied to the stiffness prediction of polymers with high cross-link density is discussed. The material of focus in this work is the ionic polymer Nafion威. The approach applies rotational isomeric state theory in combination with a Monte Carlo methodology to develop a simulation model for polymer chain conformation. From this a large number of end-to-end chain lengths between cross links are generated; the probability density function of these lengths is estimated with the most appropriate Johnson family method. This estimation is used in a Boltzmann statistical thermodynamics approach to the multiscale prediction of stiffness. This work addresses the importance of the simulated polymer chain length in the generation of stable predictions. The multiscale prediction is found to be physically reasonable; the approach has the potential of serving as a first-order prediction tool for properties that are experimentally difficult or impossible to measure.
I. INTRODUCTION
In parallel with rapid advances in computing power, multiscale material modeling has been receiving increasing attention. The vision is that multiscale modeling might ultimately serve as an alternate laboratory method or as a material design tool.1,2 In general, multiscale modeling is not yet mature enough for these purposes; the biggest challenges are (i) identifying appropriate methods of modeling at the atomic scale, and (ii) identifying appropriate methods to span length and time scales up to the traditional engineering scale.3–5 However, the basic tenets of multiscale modeling are not new, rather the averaging of lower-length scale effects to anticipate larger-length scale properties has historically been the basis of materials research.6 This effort adapts strategies from the earlier multiscale approaches (viz., comparatively computationally unintensive) to the goal of developing an alternate laboratory tool capable of ∼1st order accuracy. The predictions from such a model could guide more intensive studies. This work adapts rotational
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Address all correspondence to this author. e-mail [email protected] DOI: 10.1557/JMR.2008.0096 J. Mater. Res., Vol. 23, No. 3, Mar 2008
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isomeric state (RIS) theory to the creation of a multiscale stiffness prediction model appropriate to ionic polymers. Ionic polymers have recently received widespread attention for their applications in polymer electrolyte membrane fuel cells (PEM FCs) and more specifically for use in fuel cell vehicles.7–9 Recent enthusiasm aside, PEM FCs have been in existence for some time; they were first deployed in the Gemini space program in 1962.10 Moreover, PEM FCs represent only one of many applications for ionic polymers. For example, there has also been significant research activity on application of ion
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