Polymer electrolytes free volume models

In polymer electrolytes (even prevailingly crystalline), most of ions are transported via the mobile amorphous regions. The ion conduction should therefore be related to viscoelastic properties of the polymeric host and described by models analogous to that for ion transport in liquids. These include either the free volume model or the configurational entropy model . The former is based on the assumption that thermal fluctuations of the polymer skeleton open occasionally free volumes into which the ionic (or other) species can migrate. For classical liquid electrolytes, the free volume per molecule, vf, is defined as ... 

The brief discussion above shows that the structure of a polymer electrolyte and the ion conduction mechanism are complex. Furthermore, the polymer is a weak electrolyte, whose ions form ion pairs, triple ions, and multidentate ions after its ionic dissociation. Currently, there are several important models that attempt to describe the ion conduction mechanisms in polymer electrolytes Arrhenius theory, the Vogel-Tammann-Fulcher (VTF) equation, the Williams-Landel-Ferry (WLF) equation, free volume model, dynamic bond percolation model (DBPM), the Meyer-Neldel (MN) law, effective medium theory (EMT), and the Nernst-Einstein equation [1]. 

The UNIFAC (Unified quasi chemical theory of liquid mixtures Functional-group Activity Coefficients) group-contribution method for the prediction of activity coefficients in non-electrolyte liquid mixtures was first introduced by Fredenslund et al. (1975). It is based on the Unified Quasi Chemical theory of liquid mixtures (UNIQUAC) (Abrams and Prausnitz, 1975), which is a statistical mechanical treatment derived from the quasi chemical lattice model (Guggenheim, 1952). UNIFAC has been extended to polymer solutions by Oishi and Prausnitz (1978) who added a free volume contribution term (UNIFAC-FV) taken from the polymer equation-of-state of Flory (1970). 

Polymers designed for use as electrolytes in batteries are used at temperatures well above Tg. In this region a different model for conduction is more applicable, namely one based on the fluctuations in the distribution of free volume that occur above Tg due to the localised movements of the polymer chain segments. It is assumed that any ion sits in a region of free volume and can move into an adjacent space only when a sufficiently large element of free volume becomes available immediately adjacent to it. 

Mohapatra SR, Thakur AK, Choudhary RNP (2009) Effect of nanoscopic confinement on improvement in ion conduction and stability properties of an intercalated polymer nanocomposite electrolyte for energy storage applications. J Power Sources 191 601-613 Napolitano S, Cangialosi D (2013) Interfacial free volume and vitrification rednctiai in Tg in proximity of an adsorbing interface explained by the free volume holes diffusitm model. Macromolecules 46 8051-8053... 

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