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Modelling of mixed electrolytes for hybrid metal-ion
batteries
Hristo Rasheeva,b *, Radostina Stoyanovab and Alia Tadjera,b
a Faculty of Chemistry and Pharmacy, University of Sofia, Sofia
1164, Bulgariab Institute of General and Inorganic Chemistry,
Bulgarian Academy of Sciences, Sofia 1113, Bulgaria
* Email: [email protected]
2+
++
2+
mailto:[email protected]
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The rationalisation of the interactions of electrolyte
components and solvent molecules in the charge-discharge process is
a
challenging task for any type of battery but this information is
critical for the design of hybrid batteries combining the
advantages
of different charge carriers. The molecular modelling allows
deeper insight into this problem. Particularly in the case of
light-metal-
ion batteries, the metal ions change continuously their
solvation status, gradually acquiring solvation shell upon leaving
one
electrode and shedding it off before intercalating in the other
electrode. All these stages can be simulated and characterised
by
means of various molecular descriptors using different
theoretical methods.
Here, the free energy of homo- and hetero-binuclear clusters
with increasing/decreasing number of explicit solvent
molecules in the gas phase and in implicit solvent is assessed
quantum-chemically and juxtaposed to the mononuclear
alternatives. The cations considered are Li+, Na+, and Mg2+ and
the solvent is ethylene carbonate (EC). The issues addressed
are:
a) the preferred coordination number of the metal ions in the
presence of a companion-cation; b) the charge transfer between
metal ions and solvation shell; c) the competition for solvent
between the cations in batteries utilizing a dual-cation
electrolyte.
The obtained findings provide insight into certain unexplained
experimental results such as the enhanced performance of
hybrid-
ion batteries compared to single ion ones.
• Gaussian 09
• B3LYP/6-31G**
• Implicit solvent model: SMD
• Charges - NBOCo
mp
uta
tio
nal
:A
bst
ract
Co
mp
on
ents
: Mep+Mq+(EC)1-10Me
p+(EC)1-8
Cation pairs
Li+
PF6-
Na+
Mg2+
Solvent:
Ethylene carbonate (EC)
Single cation
homo-nuclear hetero-nuclear
Counterion
(Simplified representation)
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Cation pairs
Single cationhomo-nuclear hetero-nuclear
Initial geometries
vacuum
&
solvent
Models
*Green spheres – generic cations; Red spheres – carbonyl oxygens
of ECs
Mep+Mq+(EC)1-10
Mep+(EC)1-8
-
Na+ coordinates two oxygens
Lower symmetry of the complexes for n>3
Confirmed coordination numbers:
Li+ - 4; Mg2+ - 6; Na+ - 5-6
as established in the literature
Cation–O distances depend on the partner
Cation–cation distances
Distances Cation-EC
Results – Structural
*
Cation–cation distances depend more
on the number of shared solvent
molecules then on the coordination
number or total number of ECs.
-
2 4 6 8-15
-10
-5
0
5
10
15
20
G
bi -
G
mo
no, kca
l/m
ol
n
Li+Li
+ Na
+Na
+ Mg
2+Mg
2+
Li+Na
+ Li
+Mg
2+ Na
+Mg
2+
Bi-
nucl
ear
pre
ferr
ed
Mo
no
-nucl
ear
pre
ferr
ed
At low degree of solvation, hetero-binuclear clusters,
particularly the
Mg2+-containing ones, are preferred to these of single ions.
𝛥𝐺𝑏𝑖 − ∆𝐺𝑚𝑜𝑛𝑜 = 𝐺(M𝑎𝑝+M𝑏𝑞+
EC n) − 𝐺 M𝑎𝑝+(𝐸𝐶)𝑛
2− 𝐺 M𝑏
𝑞+(𝐸𝐶)𝑛
2
10 9 8 7 6 5 4 3 2 1 0-10
-5
0
5
10
15
20
25
G
, kcal/m
ol
n'
Li+Li
+
Na+Na
+
Mg2+
Mg2+
Li+Na
+
Li+Mg
2+
Na+Mg
2+
10 9 8 7 6 5 4 3 2 1 0
0
20
40
60
80
100
120
140
160
180
G
, kca
l/m
ol
n'
Li+Li
+
Na+Na
+
Mg2+
Mg2+
Li+Na
+
Li+Mg
2+
Na+Mg
2+
0 1 2 3 4 5 6 7 8 9 10-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
G
, kca
l/m
ol
n
Li+Li
+
Na+Na
+
Mg2+
Mg2+
Li+Na
+
Li+Mg
2+
Na+Mg
2+
0 1 2 3 4 5 6 7 8 9 10-600
-500
-400
-300
-200
-100
0
100
G
, kca
l/m
ol
n
Li_Li
Na_Na
Mg_Mg
Li_Na
Li_Mg
Na_Mg
The curve profile of the mixed cation-pairs is closer to the
profile
of the homo-cation pair with higher charge density.
Solvation
Stepwise desolvation
M𝑎𝑝+
+ M𝑏𝑞+
+ 𝑛EC → M𝑎𝑝+M𝑏𝑞+
EC n
M𝑎𝑝+M𝑏𝑞+
EC n → M𝑎𝑝+M𝑏𝑞+
EC n−1 + EC
In vacuum the profile of the curves is monotonous while in
solvent two
stages can be discerned, related to the cation coordination
number.
𝛥𝐺𝑠𝑜𝑙𝑣 = 𝐺(M𝑎𝑝+M𝑏𝑞+
EC n) − 𝐺(M𝑎𝑝+) − 𝐺 M𝑏
𝑞+− 𝑛𝐺(EC)
𝛥𝐺𝑑𝑒𝑠𝑜𝑙𝑣 = 𝐺[M𝑎𝑝+M𝑏𝑞+
EC n−1] + 𝐺(𝐸𝐶) − 𝐺[M𝑎𝑝+M𝑏𝑞+
EC n]
*
*
Results – Energetics
Solvation:
Desolvation:
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1 2 3 4 5 6 7 8 90.5
0.6
0.7
0.8
0.9
1.0
Ch
arg
e
n
Li
Na
MgLi
a) b) c)
BGDN09/13/16.12.2016
D01-214/28.11.2018
Funding:
Results – Charges
Summary
In Mep+Meq+(EC)n: the charge of a
cation decreases with n only if thecoordination number grows
(e.g. (a) and
(b)); for same coordination – same charge,
irrespective of the partner (e.g. (a) and (c)).
• At moderate level of solvation, mixed bi-nuclear complexes are
preferred.
• EC appears to be an operable solvent for mixed Mg-containing
electrolytes.
• The coupling of Li+ or Na+ in with Mg2+ permits easier
desolvation of the
ions compared to mononuclear Li+, Na+ and Mg2+ complexes.
Medium polarity is of minor importance.
In Mep+(EC)n: the charge of the cation decreases with nuntil the
first shell is formed and stays constant thereafter.
0 1 2 3 4 5 6 7 8 9
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
Ch
arg
e lo
ss
n
Li+
Na+
Mg2+
PF6
-
