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Diffusivity and Solvation of Alkali &
Halide Ions in Solid and Liquid
Electrolytes
Chemistry
California State Science Fair 2016

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Introduction
The scientific process employs the use of observations, questions, and
experimentation in order to make new discoveries of the universe. These discoveries
are sometimes insightful observations which explain natural phenomena such as the
genetic code, the black hole information paradox, or the formation of wormholes. Other
times these discoveries solve practical problems in fields like materials science, human
biology, and agriculture. My science project falls in the latter category and concerns a
hot topic in tech-related research: batteries. Batteries are becoming increasingly crucial
in today’s digital-first society and are projected to form a $120 billion dollar market by
2019.1 Many critical systems today rely on batteries to provide us with various services.
Smartphones, for example, are devices upon which humans are highly dependent on
for a variety of uses. Every day we find ourselves sinking hours calling people, posting
on social media websites, and surfing the Internet. Without these services, we lose the
ability to interface with society and function normally. This problem extends to the
working world as well. Businesses would be severely handicapped if their employees
did not have the ability to use GPS, reply to emails, and work on the cloud.
Above are two graphics which show the a) widespread ‘digitization’ of society and
b) the ever-increasing amount of control that smartphones have over our lives

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These potential consequences are what make batteries essential components of
our daily lives. Today, the proliferation of batteries is widespread; they can be found
powering computers, cars, and even homes! With many of these batteries having the
same underlying technology, it becomes imperative that the core design of batteries be
as efficient, safe, and scalable as it possibly can. This ideal design mainly lies in the
choice of material for both the electrolyte and ions inside the battery.
In a typical lithium-ion battery, a liquid electrolyte is separated by two
electrodes – the cathode and the anode. The battery discharges by a movement of
positively charged cations through the electrolyte from the anode to the cathode while
electrons flow into a circuit. The battery recharges with a movement of particles in the
opposite direction, from the cathode to the anode.
Cathodes are
generally made of
lithium salts, such
as LiFePO4
Anodes are made of
carbon-based materials
such as graphite

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The electrolyte is commonly made out of inorganic liquid compounds such as
LiBF4 and LiBF6.2 While satisfactory performance-wise, liquids do not meet high safety
standards due to their volatility and flammability.3 For small-scale applications such as
smartphones, the risk of thermal runway posed by liquid electrolytes has been
dismissed as trivial.4 However, with regards to electric car and solar home batteries,
liquid electrolytes are unsuitable due to their potential risks. In fact, a popular electrical
car manufacturer recently suffered a string of battery failures after the liquid electrolyte
within their batteries caught on fire.5
Two years ago, a high-profile incident occurred in which the lithium-ion power unit of a
Boeing 787 Dreamliner aircraft caught on fire just after passengers had disembarked.6
If the fire had begun even just a few minutes earlier, it could have put the plane’s nearly
200 passengers at risk of asphyxiation and other life-threatening injuries.
In addition to this risk of flammability, liquid electrolytes can also leak, evaporate,
and decompose over time.7, 8 This problem is especially noticeable in devices such as
laptops whose capacities greatly decrease after just a few years of use.9 Besides this
non-optimal battery lifespan, the energy density of liquid electrolytes is limited because
of the need for protective canisters to hold the electrolyte fluid.8
Above on the left is an image of a burnt lithium-ion auxiliary power unit from a Boeing 787 Dreamliner aircraft
while the image on the right is of a Tesla Model S on fire due to a puncture of its power pack

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With so many notable downsides posed by liquid electrolytes, researchers have
been looking at a new class of electrolytes: polymer electrolytes. Polymers are plastics
composed of long molecular chains. Compared to liquid electrolytes, polymers neither
have the inherent flammability risk nor the tendency to decompose. This makes them a
much more appealing candidate for future batteries both safety and stability-wise.
However, as polymers are solid and far more rigid than their liquid counterparts, they
are less efficient at conducting ions at ambient temperatures.10 Thus, a continuing
challenge for polymer electrolytes is finding a polymer that demonstrates acceptable
performance in typical battery environments.
Besides the electrolyte, the selection of the metal for the ions has also been
lithium. Lithium is used for its high energy density and decent availability. However,
new materials are being studied for their potential use in batteries11, including sodium
and magnesium.
The aim of this research is to find new materials for battery electrolytes as well as
the metal ions that flow through said electrolytes. Poly(ethylene oxide) will be studied
for its feasibility as a solid polymer electrolyte (SPE). A PEO polymer was selected for
experimentation as it has been shown to conduct ions an “order of magnitude” greater
than other aliphatic polymers.12 In addition, it has also been found that ions frequently
were stuck in various polyester-based polymers for much longer times than in PEO.
This is partly because PEO is composed of a single chain with many coordination shells
which allow for the intrachain hopping of ions, a mechanism that is not found in
polymers with side-chains.

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The performance of PEO will be compared to that of a liquid electrolyte, Dimethyl
Ether. Dimethyl Ether was chosen for its intriguing properties as a single segment of
PEO.
In addition to the electrolyte material, the ion itself will be varied between lithium,
sodium, potassium, magnesium, chlorine and fluorine. These elements offer several
innate benefits compared to lithium. Sodium is advantageous because it has a greater
abundance7 (2.3%) in Earth’s crust than that of lithium (0.0017%). It is also ten times
cheaper than lithium11, making it an intriguing prospect for practical battery applications.
As an alkali-earth metal, magnesium is also a plausible candidate because it offers two
charges whereas lithium offers one.
The study itself will examine two big questions:
1) Are there alkali, alkaline earth, and halogen metals that outperform lithium in
various battery electrolytes?
2) Do solid polymer electrolytes offer significant benefits over liquid electrolytes?
This figure shows the difference between the oligomer DME and polymer PEO

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Materials and Methods
In order to study how different ions behave in various electrolytes, the use of
Molecular Dynamics (MD) simulations was employed. MD allows for the investigation of
atomic systems undergoing user-defined processes. Computer simulations are
incredibly useful for battery research because they can visualize minute details of the
battery’s internal structure and are capable of testing thousands of material candidates.
These two advantages make computer simulations more time and cost efficient than
traditional lab experimentation.
The simulations themselves were done using the Large-scale Atomic/Molecular
Massively Parallel Simulator software (LAMMPS) and analyzed with Visual Molecular
Dynamics13-14. Scripts were written using the LAMMPS standard format, Python, and
UNIX Shell. The MD simulations employed the OPLS force field and calculated motion
using the Verlet integrator over a 2 femtosecond timestep.
In essence, MD simulations calculate the forces acting on a system of atoms
through a variety of parameters, distributions, and equations. A simulation can begin
with a distribution of temperature, which is the average kinetic motion of particles in a
system. For these particular simulations, the Maxwell-Boltzmann distribution was used:

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As shown by the distribution, there tends to be an average amount of energy per
molecule. This energy can be quantified with the kinetic energy formula:
After deriving velocity from this formula, acceleration can be calculated by:
and
This acceleration can then be used to calculate force with Newton’s Second Law:
Through this set of equations, a relationship can be derived between the physical
quantities of a system of particles and the calculations used to conduct MD simulations.
In fact, this relationship can be flipped to find acceleration and velocity of different
particles from forces, such as those resulting from columbic or Lennard-Jones
interactions.
Based on the big questions established earlier, technical objectives were formed:
1) Determine the coordination effects of each electrolyte structure on various ions
2) Determine the diffusivity, or mobility, of various ions in both a polymer and liquid
electrolyte
On the left is the formula for Lennard-Jones potential, which describes the energy of attraction of two atoms at
various distances based on the strength of the attraction force (ɛ) and atomic radius (σ). On the right is
Coulomb’s Law, which gives electrostatic force based on the charges of 2 atoms and distance between them.

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In order to answer these questions, several simulations were setup with various
combinations of electrolytes and ions. Two boxes of atoms were setup: a box of
poly(ethylene oxide) and a box of dimethyl ether.
In order to test the coordination effects and diffusivity of ions in these materials,
five ions were each put into a separate version of these two boxes. It can be observed
that lithium, sodium, potassium, and magnesium are cations while chlorine and fluorine
are anions. Lastly, each ion-box group had three different coordinate configurations in
case there were any simulation anomalies.
Simulations were first conducted with fixed pressures (NPT) on the PEO box in
order to find and stabilize the system’s density. This density was calculated to be
roughly 1.16 grams per cubic centimeter.
On the left is a box of poly(ethylene oxide) and on the right is Dimethyl Ether* at 400 Kelvin.
* Note: For simulation purposes, the CH3 in Dimethyl Ether was artificially modified into a CH2
in order to free up space within the box. The density of the Dimethyl Ether was left unchanged
in order to maintain a basis for comparison with the PEO simulation.

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Afterwards, each system was minimized under a short NVT simulation (fixed
velocity) to eliminate any extraneous forces and energy potentials from the system
before beginning dynamics. This minimization step used the data output of the previous
NPT simulation to maintain the aforementioned density.
After minimization, each system was run for 100 nanoseconds on a computer
cluster with the help of a graduate student in the lab.
Density(g/cm3
)
Timesteps (fs)
Potential
Optimal Minimization Time
Extraneous Potential
Stable Potential
Average
Density
Timesteps (fs)

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Above are a snippet of the scripts and files used in the simulation. The main script defines variables,
including the timestep of the simulation, and specifies the data to be written as the simulation is running. The
settings file specifies pairwise interactions between the various atoms involved in the simulation. The data file
specifies the boundaries of the simulation, atomic masses, and coordinates of every atom in the simulation.
Using these two input files, the main script is able to produce a trajectory of the entire simulation.
Settings File – Lists coordinates (x,y,z) for every atom
Data File – Specifies atomic interactions
Main Script – Processes and Outputs data
Main Script
(LAMMPS)
Settings FileData File
Trajectory File
Simulation Hierarchy

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Results
Each simulation produced 3 GB trajectory files filled with coordinate data and metrics
such as density, kinetic energy, and pressure. Data analysis was done using the Visual
Molecular Dynamics (VMD) program along with a combination of publically available
and custom-made scripts. Firstly, the coordinate effects of both the polymer and liquid
electrolyte structures were investigated. Coordination shells in the materials consisted
of two rings which ‘trapped’ ions moving through the electrolyte.
In order to find the composition of these solvation shells, the Radial Distribution
Function (RDF) was used. This function determines the local density of any type of
atom within a certain distance from another type of atom. High local densities close to
the selected atom reveal both the presence and relative strength of a solvation shell.

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In PEO, this first solvation shell for lithium, magnesium, sodium, and potassium
was shown to be composed of oxygen. Chlorine and fluorine, on the other hand,
preferred CH2 as they are negatively charged and tend to repel the negatively charged
oxygen atoms. Interestingly, this graph indicates strong oxygen coordination with
lithium and magnesium, the two smallest ions.
In DME, the results were similar:
Potassium and sodium preferred oxygen and thus
featured it in their first solvation shell. Chlorine and
fluorine, on the other hand, preferred CH2 in their first
shell.
CH2 Solvation Structure - PEO CH2 Solvation Structure - DME

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After determining the composition of the solvation shells forming around each ion, the
number of solvation sites was quantified. This was done through a custom TCL script
which processed the trajectory file for oxygen atoms within four angstroms of each other
in a specified coordinate plane. Visualization of the resulting data provided an insight
into the number of oxygen solvation shells in each material.
On the left is a snippet of the TCL script
written to extract binding sites from the
trajectory. Above is a slice of the DME box
showing all shells with at least 5 oxygen
atoms within 4 Å of each other. Below is a
view of the same solvation shells in PEO.
DME
PEO

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The second goal of the project was to investigate the diffusivity of various ions in both
PEO and Dimethyl Ether. To accomplish this, the MSD was calculated for each ion.
MSD is the displacement that an atoms from its starting point. It is calculated by:
MSD(δt)=⟨|r⃗(δt)−r⃗(0)|2
⟩
In the equation above, δt is some timestep and r is the position vector of an atom. In
order to ascertain the diffusivity, a log-log plot was taken of MSD with respect to time in
order to observe trends in the diffusive regime.
For PEO, the results were as follows:
Surprisingly, larger ions tended to move more quickly in PEO than smaller ions.
Lithium, interestingly, was the least diffusive of all the ions.

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The same test was performed in Dimethyl Ether:
Although the bigger ions were more diffusive in DME, there were minor discrepancies.
Lithium notably also performed much better in the liquid DME than in PEO.

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Discussion:
This work has identified several interesting trends that help answer the questions posed
earlier:
1) What trends can we observe in the behavior of alkali, alkaline earth, and
halogen ions in different electrolytes?
2) Do solid polymer electrolytes offer significant benefits over liquid electrolytes?
To answer the first question, several trends were discovered that correlate the diffusivity
and solvation of various alkali, alkaline earth, and halogen ions in different electrolytes.
lithium and magnesium witnessed the formation of the dense oxygen shells at a close
proximity from their centers. While oxygen shells were also present around potassium
and sodium, they were not as dense or as close to the atoms. Chlorine and Fluorine did
not form oxygen solvation shells because their negative charge led to a greater
attraction with CH2 in PEO and in DME. The diffusivity proved to be a different case.
Fluorine happened to be the most diffusive in PEO followed by chlorine and sodium, two
of the bigger ions. Thus, the following correlation was deduced:

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Atoms that are lower on the periodic table tend to have higher ionic diffusivities yet
lower oxygen coordination. This trend intuitively makes sense because higher oxygen
coordination inhibits the movement of ions through any given material. Not only that,
but the number of solvation sites within the material seems to directly correlate with ion
diffusivity. PEO contains a greater number of binding sites that on average are denser
than their DME counterparts. This structural difference in solvation sites partly explains
PEO’s relatively high performance compared to DME.
This relationship was predicted to be flipped for the halogens due to a tendency for
certain chemical properties of alkali metals and halogens to be inverses of each other.15
The question regarding performance of ions in polymer electrolytes versus that in
liquid ones was answered by the diffusivity coefficients of the ions in both materials.
Based on the log-log plots, the slope of chlorine’s (the highest performing ion) diffusivity
curve in PEO was 0.46 compared to approximately 0.85 in DME. This performance
difference is to be expected as PEO features lower segmental mobility compared to a
liquid. It can be noted that the simulations ran at 400 Kelvin, well above the
temperature of a typical battery environment. If the temperature were to be lowered to
room temperature, (293 Kelvin) lower diffusion coefficients can be expected for PEO.
This is due to the fact that below its glass transition temperature of approximately 338
K16, PEO features a crystalline structure which does not conduct ions very well.
Dense solvation shells can impede the movement of ions through a material.
NOTE: Data from the MD simulations helped assess the validity of these theoretically sound trends. Because there is
always a measure of error in any test – experimental or theoretical - it was important to formulate results on trends in
data versus taking generated values as definite.

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Conclusions
Throughout this research, I have investigated the ionic movement in electrolytes
to find out if there was any potential for a battery featuring a solid polymer electrolyte
and an ion other than lithium. My results show promise for chlorine, magnesium, and
several other elements as candidates for further testing. I found that lithium ions, used
in almost all batteries today, performed well in liquid electrolytes. However, when
placed in a solid electrolyte, lithium performed poorly, especially compared to larger
ions such as chlorine. Therefore, I believe that a solid polymer electrolyte battery may
end up featuring an ion other than lithium.
As discussed earlier, the choice of electrolyte appreciably affected the final
results. The liquid electrolyte composed of Dimethyl Ether significantly outperformed
the PEO-based polymer electrolyte in diffusivity tests. Although it may seem that the
possibility of a PEO-based electrolyte is in jeopardy, this is not the case. First of all,
polymers don’t necessarily need to match the performance of liquids because they can
be incredibly thin, sometimes only 10% the width8 of the thinnest liquid electrolyte. In
addition, polymers are incredibly malleable and can be configured to a variety of shapes
and sizes.16 These two intrinsic characteristics allow polymers to achieve maximum
energy density without the high diffusivity of liquid electrolytes.
In the future, several re-runs of the simulations with different parameters
(temperature, pressure, volume) will be useful in determining how the results hold up in
a variety of situations. It will be especially noteworthy to see if the larger ions continue
to be more diffusive in the solid polymer electrolyte. Based on the trends identified

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earlier, certain elements – namely chlorine and fluorine - may have high diffusivities and
thin solvation shells, especially in polymer electrolytes.
Moving forward, I also plan to investigate new types of polymers for their
electrolyte potential. PEO has been shown to be remarkably better than several
polyester-based materials12, but has not offered any breakthroughs in the development
of a polymer electrolyte battery. Synthetic polymers may also be a possibility for further
research. As shown by simulation data, increased oxygen coordination corresponds to
a decrease in ion diffusivity for every ion excluding chlorine. Accordingly, a more
suitable polymer for these materials would feature less oxygen atoms and thus less
coordination.
Lastly, the use of Molecular Dynamics for simulations of atomic systems is useful
for a variety of applications, including physics, biology, and chemistry. However,
Molecular Dynamics is not just a way to model the behavior of atomic systems
(although that is incredible in its own right). It also offers huge potential as a tool for
teaching various concepts in phenomena in the aforementioned scientific subjects.
Phases of matter, thermal systems, and cellular processes are just a few examples of
what can be simulated using Molecular Dynamics. Such new teaching methodologies
can help bridge students’ understanding of core scientific concepts all while setting the
standard for education in the 21st century.
The goal of this project was to identify potential in several different materials for
Solid Polymer Electrolytes (SPEs) and battery ions. The results have shown several
promising leads for future studies in this field. They also revealed that revising our

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approach towards the development of polymer electrolytes by testing ions other than
lithium may yield noteworthy results. Such knowledge of ionic diffusivities and solvation
in solid and liquid electrolytes can contribute to the ongoing pursuit of next-generation
battery technology.

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References
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[2] "Materials for Next Generation Li-ion Batteries." Sigma-Aldrich. Sigma-Aldrich Co.,
2015. Web.
[3] Orendorff, Christopher, and Peter Roth. "How Electrolytes Influence Battery Safety."
The Electrochemical Society Interface (2012). Print.
[4] Golubkov, Andrey W., David Fuchs, Julian Wagner, Helmar Wiltsche, Christoph
Stangl, Gisela Fauler, Gernot Voitic, Alexander Thaler, and Viktor Hacker.
"Thermal-runaway Experiments on Consumer Li-ion Batteries with Metal-oxide
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[5] Baker, David. "Battery Fire Dings Tesla Stock.” SFGate. 16 May 2014. Web.
[6] Irfan, Umair. "How Lithium Ion Batteries Grounded the Dreamliner." Scientific
American Global RSS. Web.
[7] Tsai, Jenn-Kai, Wen Dung Hsu, Tian-Chiuan Wu, Jia-Song Zhou, Ji-Lin Li, Jian-Hao
Liao, and Teen-Hang Meen. "Dye-Sensitized Solar Cells with Optimal Gel
Electrolyte Using the Taguchi Design Method." International Journal of
Photoenergy (2013): 1-5. Hindawi Publishing Corporation. Web.
[8] "Solid-Polymer Electrolyte Makes Lithium-Ion Safe." Solid-Polymer Electrolyte
Makes Lithium-Ion Safe. Electronic Design, 1 Sept. 1998. Web.

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[9] "How Long Should a Laptop Battery Last?" Computer Hope. Web.
[10] Nookala, M., Kumar, B., & Rodrigues, S. (2002). Ionic conductivity and ambient
temperature Li electrode reaction in composite polymer electrolytes containing
nanosize alumina. Journal of Power Sources,111(1), 165-172.
doi:10.1016/S0378-7753(02)00303-8
[11] Kanellos, Michael. "Is Sodium the Future Formula for Energy Storage?"
Greentechgrid. Greentech Media. Web.
[12] Webb, Michael A., Yukyung Jung, Danielle M. Pesko, Brett M. Savoie, Umi
Yamamoto, Geoffrey W. Coates, Nitash P. Balsara, Zhen-Gang Wang, and
Thomas F. Miller. "Systematic Computational and Experimental Investigation of
Lithium-Ion Transport Mechanisms in Polyester-Based Polymer Electrolytes."
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[13] S. Plimpton, Fast Parallel Algorithms for Short-Range Molecular Dynamics, J
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Molec. Graphics, 1996, vol. 14, pp. 33-38.
[15] Wilterdink, Randy. "Families of Elements Comparisons." PBWorks. 1 Nov. 2014.
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[16] Sequeira, César, and Diogo Santos. Polymer Electrolytes: Fundamentals and
Applications. Cambridge: Woodhead Pub., 2010. 1-7, 48-50. Print.

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Lithium-ion battery failures are not uncommon, especially in large-scale applications. Above is a
Tesla Model S which caught on fire when its power pack was punctured by debris. Below is an
image of a 787 Dreamliner aircraft’s battery that failed midflight and forced the crew to make an
emergency landing.