Ab Initio Modeling of Proton Transfer in Phosphoric Acid Clusters




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Ab Initio Modeling of Proton Transfer in Phosphoric Acid Clusters
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Proton transfer is of vital importance in many chemical and
biological systems and processes.1 The conduction of protons
plays a central role in the function of many devices, including
polymer electrolyte membrane (PEM) fuel cells.2 Recently, the
ability of fuel cells to generate electric power with no
greenhouse gas emissions and at high efficiency has generated
tremendous interest from various research and industrial communities.
The search for novel high-performance electrolytes
suitable for low- and intermediate-temperature operation where
no exte
al humidification is required has spurred efforts
including synthesis and characterization of a wide range of
materials suitable as the separator. The development of new
materials requires a fundamental understanding of the protonconduction
process at the atomic level, and an Edisonian
approach for synthesizing new membrane materials is insufficient.
3
Proton transfer involves bond-breaking and -forming processes
and the transfer of H+ between two entities accompanied
by a local redistribution of electron density.4 Despite the
diversity of proton-conducting electrolyte materials,5,6 the
protonic defects in these materials are solvated by very few
species,7 water, oxide ions, heterocycles, and oxo acids and
anions. These species are typically responsible for the intrinsic
generation of charge carriers, but a molecular description of
the mechanism of proton transfer has only been secured for an
excess proton in water.8 A complete understanding of the
solvation structure and dynamics of an excess proton in water,
however, remains elusive.9 It is widely recognized that hydrogen
bonding is a key feature in all systems exhibiting proton
transport. Of relevance for understanding proton conduction in
PEMs is the consideration of ingredients that encompass
complexity, connectivity, and cooperativity.10,11 Investigation of
hydrogen bonding from structural as well as dynamical aspects
is warranted in order to understand the phenomena at a
molecular level. There are few experimental techniques capable
of probing the effects accompanying the hydrogen-bond formation
or breaking at this scale, and therefore, various simulation
methods have been utilized for describing these processes.
Proton mobility in liquid water surpasses the hydrodynamic
limit by a factor of more than 4.5 and is approximately five
times higher than that of Li+ in water.12 The first hypothesis in
trying to explain this behavior comes with a picture of highly
correlated charge-transfer events along the hydrogen-bonded
chains, also known as structure diffusion or Grotthuss hopping.13
However, a process involving only proton-transfer events
between water molecules along the chains leads to a local
polarization of the network and no net conduction. Thus, a
successive reorientation of the molecules in the outer hydration
shell is necessary in order to depolarize the network and yield
a new configuration permitting the next proton-transfer event.
The first mechanistic picture for the overall excess protontransfer
mechanism in water was determined from NMR data
interpreted by Agmon4 and confirmed by Tuckerman et al.14,15
with Car-Parrinello ab initio molecular dynamics (AIMD)
simulations.16 The region containing the excess proton corresponds
to either a hydrated hydronium ion (i.e., H9O4
+ or Eigen
cation17,18) or a dimeric form sharing the excess charge between
two water molecules (i.e., a H5O2
+ or Zundel cation19). The
proton-transfer mechanism in water proceeds via a series of
structural rearrangements between these patte
s; in this manner,
an Eigen ion is transformed into a Zundel ion, which itself is
converted to an Eigen ion (i.e., EZE mechanism8). The main
qualitative features complemented with some significant quantitative
corrections of the above-described mechanism were later
* To whom correspondence should be addressed. E-mail: spaddison@
utk.edu.
† Max-Planck-Institut fu¨r Festko¨rperforschung.
‡ University of Tennessee.
J. Phys. Chem. A XXXX, xxx, 000 A
10.1021/jp903005r CCC: $40.75  XXXX American Chemical Society
Downloaded by AUSTRIA CONSORTIA on July 6, 2009
Published on July 1, 2009 on http://pubs.acs.org | doi: 10.1021/jp903005r
confirmed by more sophisticated techniques involving nuclear
quantum effects.20-24
The structure of neat liquid phosphoric acid (H3PO4) consists
of an extended intermolecular network of hydrogen bonds and
exhibits high proton conductivity, making it of particular interest
for use in fuel cells. Phosphoric acid fuel cells (PAFCs), in
contrast to PEM fuel cells, use phosphoric acid (instead of a
solid polymer) as the electrolyte, do not require water for
operation, and operate at higher temperature (150-200 °C).
Although PAFCs dominate the stationary fuel cell market, there
are some serious drawbacks due to low efficiency and a much
lower power to size ratio when compared to those for other
fuel cells.25
Recently, phosphoric acid has become an important constituent
of alte
ative proton-conducting membranes, particularly in
complexes with basic polymers, such as poly(benzimidazole)
for use as the electrolyte in PEM and direct methanol fuel cells.26
Despite the fact that the PBI/PA composite has a very low
conductivity (∼2 × 10-3 S/cm), it has extraordinary thermomechanical
and chemical stabilities, which are crucial for fuel
cell applications.27,28 Drawbacks in these systems indicate the
fact that H3PO4 is not strongly bound to the polymer and
therefore leaches out by water during fuel cell operation and
also that the proton conductivity dramatically decreases with
decreasing concentration of PA. The latter is a common feature
in both phosphoric and phosphonic acid systems.29 Obviously,
proton conduction in phosphoric acid is very sensitive toward
perturbations, but it is not clear to what extent these perturbations
are the consequences of chemical interaction or just the
confinement in the diverse matrixes. Of course, such questions
can only be addressed in a meaningful way on the basis of a
better understanding of proton dynamics in pure bulk phosphoric
acid.
The H3PO4 molecule has three proton-donor sites and one
proton-acceptor site. As a liquid, it is able not only to solvate
the excess charge but also generate the charge carriers through
self-dissociation (∼7.4%) along with some condensation, mainly
yielding pyrophosphoric acid (H4P2O7).30 The acid has a low
diffusion coefficient of phosphate “blocks” but an extremely
high proton mobility, which presumably proceeds via proton
transfer between phosphate species and is facilitated by structural
rearrangement. The contribution of Grotthuss-type hopping is
∼98%, with the remaining 2% coming from hydrodynamic
diffusion of charged species.31,32 Greenwood and Thompson33,34
were the first to suggest a mechanism for proton conduction in
phosphoric acid by introducing Grotthuss chains and a mechanism
where the proton hops between neighboring phosphate
species. The observation of almost negligible changes in the
mobility with an exchange of H with D suggests that the transfer
of the proton between phosphate units occurs with very small
barriers, and quantum effects might be excluded from the
description of the structural mechanism. Most of the previous
simulation work aimed at modeling the structure of liquid and
solid states was performed using empirical interatomic potentials,
which are unable to describe bond-breaking and -forming
processes in such a complex system as phosphoric acid.35 A
more recent AIMD study36 was unable to provide insight into
the mechanism of proton transfer in this system in part due to
the short time of the simulations.
The aim of this study is to investigate the hydrogen-bonding
and proton-transfer energetics in phosphoric acid clusters with
ab initio electronic structure calculations. Clusters of up to six
molecules are investigated using density functional theory and
a moderate size basis set in order to probe collective effects on
the proton-transfer potentials and the critical number of molecules
necessary for an effective proton-transfer event. Previous
studies of similar scope and employing the same computational
protocol performed on phosphonic acid, sulfonic acid, and
imidazole systems have proved to yield results which were in
good agreement with experimental data.37 The paper is organized
as follows; the first section contains a short description of the
computational methods used to determine the structures and
energetics for all molecular systems. This methods section is
followed by a discussion section describing the structures and
binding energies for each of the phosphoric acid clusters.

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