Effect of thermophoresis particle deposition and chemical ...
Thermophoresis in Liquids and its Connection to...
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Master Thesis Defense Thermophoresis in Liquids and its Connection to Equilibrium Quantities Benjamin F. Maier 23 June 2014
Transcript of Thermophoresis in Liquids and its Connection to...
Master Thesis Defense
Thermophoresis in Liquids and its Connection to Equilibrium Quantities
Benjamin F. Maier
23 June 2014
06/23/14 2
Thermophoresis
● directed movement of particles
● Induced by heat
● in gaseous or liquid systems
here: gas
● solute moves to cold
http://bit.ly/1qy7Gs7, 06/20/14
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Thermophoresis - Liquids
● Different picture for liquids
● Hot region sometimes preferred
● No coherent prediction possible
http://i.imgur.com/FKLjmUV.jpg, 06/20/14
?
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Thermophoresis – A Powerful Tool!
Powerful addition to electrophoresis
Braun, et. al. (2006)
Problem: Unpredictable!
DNA migration
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Thermophoresis in Formulae
phenomenological flux
diffusion thermal flux
Soret equilibrium
TemperatureDensityDiffusion coefficientThermal diffusive mobility
Soret coefficient
measured from Soret equilibrium density
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Soret Coefficient
● sign of dictates direction of movement
Piazza, et. al. (2008)
prefers cold region
prefers hot region
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Local Equilibrium
● assumptions
– length scale of solute-solvent interaction
– small heat flux
● Würger (2014)
● Braun/Dhont (2007)
force on solute
solvation free energy
solvation enthalpy
solvation entropy
Which one is true?
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Open Problems
● local equilibrium applicable?
● if yes, is driving force the entropy or the enthalpy?
● connection of and
● sign change of reproducible?
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Theory – Brownian Motion
● Overdamped Langevin equation (an SDE)
● interpretation: Ito or Stratonovich?
position change
external force interaction force
Gaussianstochastic process
local diffusion coefficient (not necessarily Einstein's relation)
ItoStratonovich
– friction
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Ideal Gas Soret Equilibrium Density
● ideal gas without external potential
● interpretation of
– Einstein's relation follows for spatially invariant diffusion coefficient
– may be wrong (Astumian, 2008)
– Will assume
ideal gasequation of state
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BD Simulation for 1D Ideal Gas
cold hotlinearreflective boundary conditions
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BD Simulation for 1D Ideal Gas
cold hotlinearreflective boundary conditions
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1D Ideal Gas with External Potential
cold hot
naïve Boltzmann expectation
−1.0 −0.5 0.0 0.5 1.00.0
0.2
0.4
0.6
0.8
1.0
T
−1.0 −0.5 0.0 0.5 1.00.0
0.2
0.4
0.6
0.8
1.0
T
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1D Ideal Gas with External Potential
cold hot
naïve Boltzmann expectation
−1.0 −0.5 0.0 0.5 1.00.0
0.2
0.4
0.6
0.8
1.0
T
−1.0 −0.5 0.0 0.5 1.00.0
0.2
0.4
0.6
0.8
1.0
T
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Dynamical Density Functional Theory (DDFT)
● local equilibrium assumption: use equilibrium functional
● traditional functional, dimensionless
● new scaling, adapted ideal gas functional
● interacting particles: how to scale excess functional?
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Interacting Particles – Solvent and Dilute Solute
two possibilities to scale the excess functional
solute densities
Soret coefficient
Würger, '14 Braun/Dhont, '07
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0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.0
0.2
0.4
0.6
0.8
1.0
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.0
0.2
0.4
0.6
0.8
1.0
Gaussian Solute in Ideal Gas Solvent (1D)
equilibrium from thermodynamic integration
Significant difference in predictions from enthalpy and entropyapproaches
periodic boundary conditions
fit function
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Thermophoretic BD Sim. – Gaussian Solute
hotcold
looks like the prediction from the enthalpy
−0.5 0.0 0.5
0.6
0.8
1.0
1.2
−0.5 0.0 0.5
0.6
0.8
1.0
1.2
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Thermophoretic BD Sim. – Gaussian Solute
hotcold
looks like the prediction from the enthalpy
−0.5 0.0 0.5
0.6
0.8
1.0
1.2
−0.5 0.0 0.5
0.6
0.8
1.0
1.2
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5−1.0
−0.8
−0.6
−0.4
−0.2
0.0
0.2
0.4
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5−1.0
−0.8
−0.6
−0.4
−0.2
0.0
0.2
0.4 Soret coefficient
Sign change!
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Homogeneous 1D System of Gaussian Particles
Soret equilibrium density from enthalpy connected to equation of state
hotcold
const.pressuresecond order
virial eq. of state
second virial coefficient
−0.5 0.0 0.5
20
25
30
35
40
45
−0.5 0.0 0.5
20
25
30
35
40
45
T
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Homogeneous 1D System of Gaussian Particles
Soret equilibrium density from enthalpy connected to equation of state
hotcold
const.pressuresecond order
virial eq. of state
second virial coefficient
−0.5 0.0 0.5
20
25
30
35
40
45
−0.5 0.0 0.5
20
25
30
35
40
45
T
Thermophoretic system seems to follow the equation of state!
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Summary So Far
● achieved
– local equilibrium assumption seems to be appropriate
– Soret coefficient connected to enthalpy
– sign change of reproducible
– crucial assumption:
● open
– does it describe real systems?
– choice of and its origin
MD simulations
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MD Setup
● modified SPC/E thermostats (Nosé-Hoover)
● SPC/E solvent● Lennard-Jones noble gas solute
● periodic boundary conditions in z● reflective boundary conditions in xy
● NPT equilibration● NVT runs● measuring the Soret equilibrium
density
● SPC/E: water model(extended simple point charge)
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First: Solvation Free Energy
fit function
300 350 400 450 500
T / K300 350 400 450 500
T / K
Method: Widom Insertion in thermodynamic equilibrium bulk SPC/E for Ar, Kr and Xe
example: xenon
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Thermophoretic simulations - Solvent
● 7 simulations of Ar, Xe, Kr with run times t > 200 ns in temperature range 300 K < T < 450 K● measured the Soret equilibrium density and temperature profile of solvent and solute
example: krypton solvent density
following the equation of state!
linear profile
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Thermophoretic simulations - Solute
● 7 simulations of Ar, Xe, Kr with run times t > 200 ns in temperature range 300 K < T < 450 K● measured the Soret equilibrium density and temperature profile of solvent and solute
example: krypton solute density
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Soret Coefficient from Density – Krypton
Calculate Soret coefficient as
derivative – how to model ?
Soret eq. density Soret coefficient
Kr, 300 K < T < 350 K
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Soret Coefficient from Density – Krypton
Calculate Soret coefficient as
derivative – how to model ?
Soret eq. density Soret coefficient
Kr, 300 K < T < 350 K
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Soret Coefficient from Density – Argon
Calculate Soret coefficient as
Soret eq. density Soret coefficient
Ar, 300 K < T < 350 K
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Soret Coefficient from Density – Argon
Calculate Soret coefficient as
Soret eq. density Soret coefficient
Ar, 300 K < T < 350 K
For every simulation: Soret coefficient isregion where all fits coincide
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Soret Coefficient from all Simulations
no significant agreement/results in MD simulations
no sign change
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Summary & Outlook
● theoretical derivation of Soret equilibrium density for various systems via DDFT
● connection between Soret coefficient and solvation enthalpy/equation of state found in BD simulations
● no significant agreement between Soret coefficient and solvation enthalpy in MD simulations
● agreement between Soret eq. density and eq. of state in MD simulations
● Ito/Stratonovich
● more realistic BD simulations / difference between BD and MD, extract meaningful data from MD
● connection between local diffusion coefficient and local temperature
● consideration of electrostatics and hydrodynamics
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1D Hard Rods
equation of state
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2D Ideal Gas in Harmonic Potential
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2D Ideal Gas in Harmonic Potential
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Soret Coefficient
● sign of dictates direction of movement
Piazza, et. al. (2008)
prefers cold region
prefers hot region Solute size
dependenceBraun, et. al. (2006)
Polystyrene beads
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Hypothetical Influence of Friction
Stokes' law consider SPC/E viscosityadditional factor in densityadditional term in Soret coeff.
● 8 hypotheses● sign change in
