Application of Monte Carlo Simulations to Hydrated Nafion Stiffness Predictions

Application of Rotational Isomeric State (RIS) theory to the prediction of Young’s modulus of a solvated ionomer is considered. RIS theory directly addresses polymer chain conformation as it relates to mechanical response trends. Successful adaptation of this methodology to the prediction of elastic moduli would thus provide a powerful tool for guiding ionomer fabrication. The Mark-Curro Monte Carlo methodology is applied to generate a statistically valid number of end-to-end chain lengths via RIS theory for a solvated Nafion case. The distribution of chain lengths is then fitted to a Probability Density Function by the Johnson Bounded distribution method. The fitting parameters, as they relate to the model predictions and physical structure of the polymer, are studied so that a means to extend RIS theory to the reliable prediction of ionomer stiffness may be identified. INTRODUCTION Ionic polymers comprise the active layer in Ionic PolymerMetal Composites (IPMCs), which were first identified just over ∗Address all correspondence to this author. a decade ago [1–5] and now constitute an emerging class of soft transducers (Fig. 1). Because they generate large strain in response to low electric field stimulation and have high gravimetric energy density, there has been considerable conjecture over the potential applications of these soft transducers [2,3,6–8] and considerable fruitful investigations towards these ends [9–11]. The high gravimetric energy density is a function of both the electromechanical transduction mechanisms of the ionic polymer layer and the global IPMC stiffness. Most models of the transduction behavior rely on the cluster morphology of the ionic polymer layer, as proposed by Hsu and Gierke [12], where the material has been solvated with water. In brief, the backbone of the ionic polymer chain is hydrophobic whereas the side chains terminate in hydrophilic ionic groups. Hsu and Geirke propose a clustering of these hydrophilic ionic side groups and the water that has been taken up by the material. The model further suggests an idealized structuring whereby the clusters are of essentially constant radius, uniformly distributed throughout the material, and interconnected by channels. Subsequently, many have sought to quantify the cluster radius and spacing as functions of polymer equivalent weight, hydration level, counterion, etc. 1 Copyright c © 2005 by ASME ~100 nm Backbone Pendant