Various computational methods are applied to investigate structural and dynamical properties of ionomers of PEMFC. The simulation methods differ in their purposes, accuracy, system size, and time scales.
Classical MD simulations with empirical potentials have been em- ployed, for example, to study morphological changes of ionomers with water content [171, 33, 34], water cluster formation [203, 32], and for eval- uation of structural models of ionomers [38, 101, 169, 128]. It has been shown, for example, that the formation of narrow necked water channels is possible and that in the vicinity of the percolation threshold proton transfer occurs most likely through these narrow pores [203]. Most of the classical MD simulations of PEM have utilized the classical hydronium cation models (or light cations Na+or K+), in which proton hopping by the Grotthuss mechanism was not allowed.
Simulations, which are based on empirical valence bond (EVB) interac- tion potentials [98, 176, 28, 175, 158, 157], reactive force fields [197, 81] and stochastic hopping algorithms [173, 172] are not hindered by this limitation and can include transport of protons via the Grotthuss mechanism. The transition state for proton transfer obtained usually from ab initio calcula- tions is used to define the reaction pathways. However, the main disad- vantage is that these methods only allow predefined reaction pathways. Therefore, the contribution of unpredicted chemical reactions to dynami- cal and structural properties can not be taken into account. Furthermore, these methods can not provide reliable answers at very low water content,
2.5 Computational research on ionomers
where protons interact strongly [86].
Computational studies based on First Principle methods do not suffer from these difficulties and can provide reliable answers even at low water content, since any molecular structure is allowed and the Grotthuss mecha- nism is inherently included. One needs to take into account, however, that the number of atoms is limited due to the computational expense. There- fore, this approach requires modeling of pores. In the following chapter, ab initio molecular dynamics is elaborated.
It has been employed, for example, to find out the optimized structure of hydrophilic side chain models (i.e. CF3SO3H+(H2O)λ) with respect to
changing hydration level [147, 149, 148, 150, 206]. It has been found that protons start dissociating from the sulfonic acid group when the number of water molecules per sulfonate group is three.
Various models based on sulfonate groups were investigated by ab initio density functional theory. For example, in order to address the questions regarding the optimum sulfur-sulfur distance for the proton dissociation step, a periodic surface layer of CF3-SO3H and CF3-O-CF2-CF2-SO3H enti-
ties has been used [166, 141, 165]. This distance was found to be between 6 and 7 Å and depends somewhat on the length of the chain.
Another example for an ionomer pore model, which has been inves- tigated by ab initio methods, is based on a sulfonated carbon nanotube containing small amounts of water [70, 71]. It was observed that fluorina- tion of the nanotube (hydrophobicity) affects the fraction of the observed proton complexes. As stated before, ab initio MD studies have predicted the formation of stable triflate ion-hydronium ion complexes and shown
that such formation causes low diffusion and possibly hinders the onset of the proton transfer at low water content [182].
Chapter 3
Various experimental techniques are applied to investigate the structure and the proton transfer in polymer electrolyte membrane, among them small-angle X-ray scattering (SAXS), nuclear magnetic resonance, neutron scattering, infrared spectroscopy etc. Despite of the fact that many of these techniques can provide information for a wide range of length and time scales down to molecular resolution, an atomistic level description of the system, which is necessary for proton transfer in narrow pores of ionomers, is missing.
At the atomic scale, molecular dynamics (MD) is an indispensable tool to provide microscopic information. MD is one of the most widely used techniques to sample the phase space of a system of particles and provides necessary information about structural and dynamic processes. In general, molecular dynamics describes the time-dependent behavior of a system of particles. The coordinates of individual atoms are determined according to the equations of motion, which are the governed by their interactions.
The traditional way of using molecular dynamics is the "classical MD" approach which makes use of pre-defined interaction potentials. These interactions are represented by analytical functional forms. This simplifi- cation makes the classical MD an appropriate tool to study systems con- taining up to millions of atoms for thousands of nanoseconds of simulation time (depending on the computational resources). Compared to ab initio MD, the number of atoms and the simulation time achievable by classi- cal MD simulations are both larger and longer than those achievable by ab initio MD, using the same computational resources. Therefore, within PEMFC research, the classical MD is usually preferred for investigating
the morphology of ionomers [101, 128].
However, the inherent nature of the proton transfer (Grotthuss mech- anism), where the bonds are broken and re-formed, limits the classical molecular dynamics approaches. A number of reactive force field schemes, where some sort of prior knowledge about the process being studied is re- quired, have proven to be successful for describing aqueous proton transfer processes [171]. Coarse-graining methods, where a group of molecules is treated as a single particle, can be applied together with smoothed reactive force fields. This combination prolongs the length and time scale of the simulations related to proton transfer in PEMFC [97].
Another way to overcome the limitation of the classical approach is to use ab initio molecular dynamics (AIMD), in which the electronic structure of the system is calculated. No prior knowledge about chemical reactions in the system is required. There are various ways to solve the electronic structure problem in the context of MD simulations. The most popular among them are the Born-Oppenheimer MD and the Car-Parrinello MD. The CPMD and CP2K program packages are used for Car-Parrinello and Born-Oppenheimer molecular dynamics, respectively [30, 121, 120].
In the following, the theoretical methods relevant for the MD simula- tions discussed in this work are briefly explained. Basics and techniques of molecular dynamics are well documented in many textbooks and lecture notes [4, 132, 133, 31, 194, 195, 188, 161, 59].