molecular simulation of aqueous electrolyte solutions · laboratory of engineering thermodynamics...
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Molecular Simulation of Aqueous
Electrolyte Solutions
Stephan Deublein1, Steffen Reiser1, Jadran Vrabec2, Hans Hasse1
InMoTher Lyon, March, 19th, 2012
1 Laboratory of Engineering Thermodynamics, University of Kaiserslautern, Germany 2 Thermodynamics and Energy Technology, University of Paderborn, Germany
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
02.04.2012 2 InMoTher 2012
Electrolytes in Aqueous Solution –
Applications
Buffer solutions in pharmaceutical
and biochemical industry /
purification of proteins
CO2 -storage in saline aquifers
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Ions
1 CLJ
1 point charge
-
Simulation of aqueous electrolyte solution
02.04.2012 3
Molecular models
Water
1 CLJ
3 point charges + +
-
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Reference property:
• Density ρ
Minimize the influence of uncertainties in water model:
• Reduced density:
Electrolyte solution
Solvent
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
02.04.2012 4
Literature models NaCl
• Scattering of model parameters also for other salts
• Large deviations from experiments InMoTher 2012
Parameters Cl-:
3.5 < sCl-/ Å < 4.8
38.0 < eCl-/ K < 118.0
Parameters Na+ :
1.9 < sNa+/ Å < 4.1
0.06 < eNa+/ K <1068.8
Reduced density of NaCl solutions (T = 293 K, p = 1 bar)
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
02.04.2012 5
Adjustable parameters
• Ions: 1 CLJ with 1 point charge (±1e) – 2 parameters
Parameter optimization for alkali halides
Simulation conditions
• MC simulations at T = 293 K, p = 1 bar
• SPC/E water model
• Simulation code: extended version of ms21
1: Deublein et al.; CPC; 2011 ; http://www.ms-2.de
-
sIon, eIon
Target
• Reduced density for varying salinity
El
S
( , , , , )x
s s e e
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
02.04.2012 6
Sensitivity study
Sensitivity of simulation
results of :
• sIon dominant
• eIon negligible
Sim Sim
+ -(m) (m)
d d( , )
d dm
x x
s s
Parameter adjustment:
Sim Sim
Ions
Sim
+ -
( , )
( , , )
x
x
s
s s
m
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Reduced density of NaCl solutions (T = 293 K, p = 1 bar)
Sim
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
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Ion parameterization
Electrolyte systems:
5 cations: Li+, Na+, K+, Rb+, Cs+
4 anions: F-, Cl-, Br-, I-
20 different salts
9 parameters
Sim Sim
+ -(m) (m)
d d( , )
d dx x
s s
Exp Sim
+ -(m) (m)
!d d( , )
d dx x
s s
with s+ [1.5;4.5]
s- [2.0;4.5]
Global fitting approach:
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
02.04.2012 8 InMoTher 2012
sLi = 1.88 Å sNa = 1.89 Å sK = 2.77 Å
sRb = 3.26 Å sCs = 3.58 Å
Anions
sF = 3.66 Å
sCl = 4.41 Å
sBr = 4.54 Å
sI = 4.78 Å
Aqueous electrolyte solutions - Results
Reduced density (T = 293 K, p = 1 bar)
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Osmotic coefficient of water
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SS (n)
S
ln( )
ln( )
a
x
• Large statistical
uncertainties
• Reasonable match:
eNa = eCl = 200 K
Adjustment of the LJ energy parameters eIon to the osmotic
coefficient S of water in NaCl solutions (T = 293 K, p = 1 bar)
• Reasonable choice:
e+ = e- = 200 K
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
r1. Max / Å r1. Min / Å
Sim. Exp. Sim. Exp.
Na – O 2.2 2.3 3.0 3.0
Cl – O 3.4 3.3 3.9 4.0
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Radial distribution functions of water
Na+
Cl-
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Dilute aqueous NaCl solutions (T = 298 K, p = 1 bar)
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Self-diffusion coefficient of alkali cations
and halide anions in aqueous solution
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Predictions (T = 298K, p = 1 bar)
Water model: SPC/E
Concentration: xEL(n)= 0.018 mol/mol
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Electric conductivity of NaCl and CsCl in
aqueous solution at various salinities
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Predictions (T = 298K and p = 1 bar)
Water model: SPC/E
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Electric conductivity:
• Correlated motion of ions
in solution
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
-
Earth-alkali cations: Modeling
02.04.2012 13
1 CLJ
1 point charge
s, e
Adjustment of the cation model parameters:
• Reduced density of the aqueous earth-alkali halide
solution (T = 293 K, p = 1 bar):
El
s
Molecular model Counterion and solvent model
+ + +
- 2+
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
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Aqueous electrolyte solutions - Results
sBe = 1.69 Å
sMg = 1.77 Å
sCa = 2.58 Å
sSr = 2.69 Å
sBa = 3.12 Å
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Reduced density (T = 293 K, p = 1 bar)
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Self-diffusion coefficient of earth-alkali
cations in aqueous solution
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Predictions (T = 298K, p = 1 bar)
Water model: SPC/E
Concentration:
xEL(n)= 0.018 mol/mol
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Electric conductivity of MgCl2 and BaCl2 in
aqueous solution at various salinities
02.04.2012 16 InmoTher 2012
Water model: SPC/E
Predictions (T = 298K, p = 1 bar)
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
New atomistic force field for ions
Alkali cations: Li+, Na+, K+, Rb+, Cs+
Earth-alkali cations: Be2+, Mg2+, Ca2+, Sr2+, Ba2+
Halide anions: F-, Cl-, Br-, I-
Model adjustment
Reduced density
Osmotic coefficient
Good agreement with experimental data
Structural properties – radial distribution function
Self-diffusion coefficients
Electric conductivity
Summary
02.04.2012 17 InMoTher 2012
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
02.04.2012 18
BACKUP
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
02.04.2012 19
Alkali halides
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Self-diffusion coefficients of Na+ / Cl- in
aqueous solutions
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T = 298,15 K, p = 1 bar
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Activity of water in NaCl solution
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T = 298,15 K, p = 1 bar
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Hydration number of NaCl in solution
02.04.2012 22 InMolTher 2012
Na+
Cl-
n (xNaCl=0.09 g /g ) n (xNaCl=0.15 g /g )
Sim. Exp. Sim. Exp.
Na – O 5.5 5 – 6 5.5 5 – 6
Cl – O 7.2 7 7.6 7
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Electric conductivity
02.04.2012 23 InMolTher 2012
Time correlation function:
B
1( ) (0)
3 ot
Vk Ts
j j
Electric current flux:
Ion
1
( ) ( )N
k k
k
t q t
j v
Ion Ion Ion
2
1 1 1,
( ) (0) ( ) (0) ( ) (0)N N N
k k k k n k n
k k n n k
t q t q q t
j j v v v v
Split electric current flux:
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Electric conductivity - split
02.04.2012 24
Separation in diffusion (Z) and correlated motion of ions (D)
MgCl2
BaCl2
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Dynamic properties – Residence time
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• Definition:
• First hydration shell ends at the first
minimum in the RDF
Pairs
0( t ) ( )( t )
N
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Temperature dependence
02.04.2012 26 Stephan Deublein
Lowering of vapor pressure:
Pure solvent Electrolyte
EL Sp p pD
T / K DpSim / bar DpExp / bar
373 0.03 0.04
Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
02.04.2012 27
Earth-alkali halides
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Enthalpy of solvation
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D hsolvSim
/ kJ mol-1
D hsolvExp
/ kJ mol-1
MgCl2 2462 2683
MgBr2 2430 2615
MgI2 2378 2531
BaCl2 1972 2067
BaBr2 1940 1999
BaI2 1891 1915
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
02.04.2012 29
Complex salts
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Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse
Multicenter Lennard-Jones models –
Na2SOH4
02.04.2012 30
Sulfate - model
reproduces the reduced
density in aqueous
solution
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