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WHEN DOES THE SORET COEFFICIENT SHOW A MINIMUM WITH CONCENTRATION IN AQUEOUS ALKALI HALIDE SOLUTIONS?
26.05.2020 I SHILPA MOHANAKUMAR
MOTIVATION
Page 2
Thermophoresis
Motion of solute particles induced by thermal gradient.
Sensitive tool for probing molecular interactions.
𝐷𝐷T𝐷𝐷 = −
∆𝑐𝑐𝑐𝑐 1 − 𝑐𝑐 ∆𝑇𝑇
𝑆𝑆T =𝐷𝐷T𝐷𝐷 ∝
∆𝑐𝑐∆𝑇𝑇
ȷ⃗ mass flux
c concentration
𝐷𝐷 diffusion coefficient
𝐷𝐷T thermodiffusion coefficient
𝑇𝑇 temperature
𝑆𝑆T Soret coefficient
Steady state: concentration difference/temperature difference is quantified by Soret coefficient ST.
THERMOPHORESISMonitors protein-ligand interaction
Page 3
LONGTERM GOAL: PROTEIN-LIGAND BINDINGStep 1 – Simple salts
Page 4
• Systematic study of various components:• Simple salts• Drugs• Proteins
In order to separate contributions stemming from• Ionic• Hydrophobic• Hydrogen bonds• Van der Waals force
Page 5
HOFMEISTER SERIESDifferent ions behave different…..
Y. Zhang et al., Curr. Opin. Chem. Biol., 10(2006), 658
Structure maker Structure breaker
CHOICE OF THE SYSTEMS
Page 6
KF KCl KBr KI
Is it enough to consider the charge of the salt?
Won’t the effect of hydration layer vary depending upon the salt ?
NaI LiI
Crystal radiusR. Heyrovsả, Chem. Phys. Lett., 163(1989), 207
Page 7
Temperature dependence:
𝑆𝑆𝑇𝑇(𝑇𝑇) = 𝑆𝑆𝑇𝑇∞[1 − exp 𝑇𝑇∗−𝑇𝑇𝑇𝑇0
]
Δ𝑆𝑆𝑇𝑇 = 𝑆𝑆𝑇𝑇 50 °𝐶𝐶 − 𝑆𝑆𝑇𝑇 20 °𝐶𝐶
15 20 25 30 35 40 45-0.50.00.51.01.52.02.53.0
1 M 2 M 3 M 4 M
ST
/ 10-3
K-1
Temp / o C
KCl
15 20 25 30 35 40 45-6
-4
-2
0
2
4
6
1 M 2 M 3 M 4 M
ST
/ 10-3
K-1
Temp / o C
KI
Page 8
CONCENTRATION DEPENDENCELiterature results: experiments
0.001 0.01 0.1 1-0.003-0.002-0.0010.0000.0010.0020.0030.004
c / mol/L
NaCl KCl
S T /
10-3 K
-1
Bulk water
Gaeta et al., J. Phys. Chem., 15 (1982) 2967
hydration layer
polarized area
Dominating at lowsalt content
Dominating at high salt content
( )δ
µ
µ
=∂ ∂T
1 1 1 ,/
chemical potentialp T
QSc T c
Chanu-Gaeta Model
Page 9
CONCENTRATION DEPENDENCELiterature results: experiments
0 2 4 6 8 10-8-7-6-5-4-3-2-10
LiCl
Molality / o C
ST
/ 10-3
K-1
Uses Chanu-Gaeta model
Associated with the structure breaking mechanism(Assumption!)
Colombani et al., J. Chem. Phys., 110 (1999) 8622
High amount of order exist in high concentration and high dilution
This order corresponds to 2 different structures
Page 10
CONCENTRATION DEPENDENCELiterature results: Simulations
Minimum is enhanced by … artificially decreasing the size of the Cl-
S. Di Lecce et al, Phys Chem Chem Phys, 19 (2017), 9575
Page 11
CONCENTRATION DEPENDENCELiterature results: Simulations
Higher ordering at lower temperature At the temperature corresponding to the
minimum, the co-ordination shell featuresa stronger structure
S. Di Lecce et al, Phys Chem Chem Phys, 19 (2017), 9575
Page 12
Concentration dependence:
-4
-2
0
2
-4
-2
0
2
0 1 2 3 4
KI NaI LiIS
T / 1
0-3 K
-1
Conc / M
KBr KCl
• Minimum is observed for KI, NaI and LiI.
• Minimum is absent for KCl and KBr
• All salts except NaI shows thermophilic
behavior at low concentrations
TDFRS experiments
Page 13
ATTEMPTS TO UNDERSTAND THE MINIMUMConsidering one layer of water molecule around one ion
Page 13
IonFirst layer of water molecules
𝜙𝜙𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 =𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑐𝑐𝑠𝑠𝑠𝑠𝑐𝑐𝑐𝑐𝑐𝑐 + 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑠𝑠𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑐𝑐𝑠𝑠𝑠𝑠𝑐𝑐𝑐𝑐𝑐𝑐 + 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑠𝑠𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 + (𝑁𝑁𝑐𝑐𝑠𝑠𝑠𝑠𝑐𝑐𝑐𝑐𝑐𝑐 + 𝑁𝑁𝑠𝑠𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐) ∗ 𝑉𝑉𝑉𝑉𝑉𝑉𝑤𝑤𝑠𝑠𝑠𝑠𝑤𝑤𝑤𝑤
43𝜋𝜋𝑅𝑅𝑐𝑐𝑐𝑐𝑐𝑐3 + 𝑁𝑁𝑖𝑖𝑉𝑉𝑖𝑖 ∗
43𝜋𝜋𝑅𝑅𝑤𝑤𝑠𝑠𝑠𝑠𝑤𝑤𝑤𝑤3 =
43𝜋𝜋( )𝑅𝑅𝑐𝑐𝑐𝑐𝑐𝑐 + 2𝑅𝑅𝑤𝑤𝑠𝑠𝑠𝑠𝑤𝑤𝑤𝑤 3
𝑁𝑁𝑖𝑖𝑉𝑉𝑖𝑖 is the number of water molecules surrounding the ion in first water shell
Page 14
ATTEMPTS TO UNDERSTAND THE MINIMUMConsidering one-, two-, three layers of water molecules around one ion
Page 14
Φ1- Volume fraction with one layer of water molecule surrounding the ion Φ2- Volume fraction with two layers of water molecules surrounding the ion Φ3- Volume fraction with three layers of water molecules surrounding the ion
Ki NaI LiI KCl KBr0.00
0.02
0.04
0.06
0.08 φ1
φ2
φ3
Volu
me
fract
ion(
φ sal
t)
incr
easi
ng w
ater
con
tent
Page 15Page 15
ATTEMPTS TO UNDERSTAND THE MINIMUM
Minimum for these salts was falling in between ϕ2and ϕ1
Hypothesis: Minimum occurs at the concentration in which a change in the hydration shell surrounding the ions occur.
Is this being followed for the literature data of KCl, NaCl and LiCl?
Page 16Page 16
ATTEMPTS TO UNDERSTAND THE MINIMUM
KCl, LiCl: Follows our assumption
NaCl: Deviates from our assumption (problem with the data?)
0.00 0.04 0.08 0.12 0.16
-1
0
1
2 KCl(Gaeta et al) KCl(Römer et al)
Volume fraction (φ)
ST
/ 10-3
K-1
φ1-φ with one layer of H2O
φ2-φ with two layers of H2O
0.00 0.04 0.08 0.12-3-2-10123 NaCl(Gaeta et al)
NaCl(Römer et al)
Volume fraction (φ)S
T / 1
0-3 K-1
φ1-φ with one layer of H2O
φ2-φ with two layers of H2O
0.00 0.05 0.10 0.15 0.20-8-7-6-5-4-3-2-10
LiCl(Colombani et al)
ST
/ 10-3
K-1
Volume fraction (φ)
φ1-φ with one layer of H2O
φ2-φ with two layers of H2O
Colombani et al., J. Chem. Phys., 110 (1999) 8622
Gaeta et al., J. Phys. Chem., 15 (1982) 2967Römer, et al., J. Phys. Chem. B, 117 (2013) 8209
Page 17Page 17
ASSUMPTION BASED ON THE RESULTS
ST
Concentration of salt
Water-ion interaction dominates
Ion-ion interaction dominates
Very high water content (=low salt concentration: ions sees only water
Very high salt content (=low water content) ions see ions
Moderate salt content between two and one layers of water molecules
Page 18
CONCLUSIONS
Page 18
Long term goal: Quantitative understanding of protein-ligand binding. Impact of salts
We performed systematic thermophoretic measurements of 5 Alkali halides
ST of salts KBr and KCl show the typical T- and c-dependence of non-ionic
solutes
Some salts showed a minimum of ST with concentration.
This observation is also valid for most literature systems
diluted concentration: sufficient water to form two water layers
Minimum higher concentration: only one water layer can be formed
Page 19
CONCLUSIONS
Page 19
Long term goal:Quantitative understanding of protein-ligand binding
We carried out calculations assuming that the changes in hydration layer of water
in presence of ion is the cause for the occurrence of minimum
We calculated the volume fraction corresponding to each hydration layer
Hypothesis : Minimum could be corresponding to the concentration at which a
change from second hydration shell to first shell occurs
This hypothesis was being validated for previous literature data
The first twostatements arebasicallyidentical. And personally I do not think that thisstep needs to bementioned in detail. It isincluded in thepicture.
Page 20
ACKNOWLEDGEMENT
Page 20
Simone Wiegand, Jan K.G. Dhont and the whole IBI-4
Doreen Niether, IEK-8
Thank you and Stay Healthy
Page 21
CONCENTRATION DEPENDENCELiterature results: experiments
Colombani et al., J. Chem. Phys., 110 (1999) 8622
ST
Concentration of salt
Low concentration region:• Migration of ion gives more
ordering• Results in decrease of
entropy• Results in heat liberation• Ions diffuse towards the
cold wall to contend with the heat flux due to thermal gradient(ST>0)
High concentration region:• More number of
hydrogen bonds• Results in
decrease of entropy
• ST is positive
Page 22
Temperature dependence:
15 20 25 30 35 40 45
-2
0
2
4 4 M 3 M 2 M 1 M
ST
/ 10-3
K-1
Temp / o C
NaI
Temperature dependent slope of ST increases for KI, while NaI behaves asnon-ionic solutes
15 20 25 30 35 40 45-1
0
1
2
3
4
5 1 M 2 M 3 M 4 M
ST
/ 10-3
K-1
Temp / o C
KBr
Could you please update thefigures and include all concentrations also 0.5 M
ATTEMPT TO EXPLAIN THE MINIUMUMEarly work by Gaeta – argumentation considers only entropic effects
Page 23
Bulk water
Gaeta et al., J. Phys. Chem., 15 (1982) 2967
hydration layer
polarized area
Bulk water less orderedHydrating water more ordered
Moving the ion into the area of bulkwater leads to a higher order and an entropy loss and a local heatrelease δQ > 0
Dominating at lowsalt content
Dominating at high salt content
( )δ
µ
µ
=∂ ∂T
1 1 1 ,/
chemical potentialp T
QSc T c
assuming 𝜕𝜕 ⁄𝜇𝜇1 𝜕𝜕 𝑐𝑐1 𝑝𝑝,𝑇𝑇 > 0→ 𝑆𝑆T > 0
Page 24
15 20 25 30 35 40 45
-4
-3
-2
-1 1 M 2 M 3 M 4 M
ST
/ 10-3
K-1
Temp / o C
LiIHow do the LiI data compare withColombani measurements
Page 25
0
1
2
3
1
2
3
15 20 25 30 35 40 45-30369
ST
/10-3
K-1KCl
1 M 2 M 3 M 4 M
D/1
0-5cm
2 s-1D
T/10
-8cm
2 s-1K-1
Temp / o C
Could you please update thefigures and include all concentrations
Page 26
0
2
4
1
2
3
15 20 25 30 35 40 45048
1216
ST
/10-3
K-1 KBrD
/10-5
cm2 s-1
1 M 2 M 3 M 4 M
DT/
10-8
cm2 s-1
K-1
Temp / o C
Could you please update thefigures and include all concentrations
Page 27
0
2
4
6
1
2
3
15 20 25 30 35 40 4505
101520
ST
/10-3
K-1KI
1 M 2 M 3 M 4 M
D/1
0-5cm
2 s-1D
T/10
-8cm
2 s-1K-1
Temp / o C
Could you please update thefigures and include all concentrations
EXPLANATION FOR THE SIGN CHANGE
Page 28
For energetic reasons most mixedinteraction take place on the cold side
... Minority component goes to the cold side
( ) ( )
12 1 12 2
1 2
12 11
12 22
1 2/ /kT kT
E T E T
T Te eε ε
ε εε ε
− −
∝ ∝
>>>
⇒ >
If the cross interactions are stronger than the pure interaction ...
I. Prigogine et al., Physica, 16 (1950), 851
Page 29
0 1 2 3 4
-1
0
1
2
Gaeta et al Shilpa
ST
/ 10-3
K-1
Conc / M
KCl
1. According to Chanu-Gaeta model when an ion gets solvated in water entropy decreases due to more structure formation, high number of hydrogen bonds, ion-dipole interaction etc. This leads to a liberation of heat and ion migrate towards the cold side . i.e, ST is positive
How this is explained?When free ions move through water there are 3 factors that contribute towards the heat of transporta) Local energy fluctuations associated with the interactionsb) Electrostatic interaction between ionic charges and water moleculesc) Structure making or structure breaking ability of ionHigh positive heat …….low entropyConcentration can be divide into 21)Till C* Since concentration is less water is not bound to ions and is increasingly disordered due to long range interactions2)After C* Q increases with concentration. At this point there is an ordered configuration with a polarized solvent which leads to this increase in QThe drifting particle is ion with its hydration shell. With increasing salt concentration there is a total disappearance of free water which indicates it is then e very ordered free medium.
Page 30
Polarization effect are certainly important?These structure breaking and making concepts are very vag
Region A is not affected by temperature and concentrationchanges, but is strongly dependent on the nature of the ion.
Region B and C are affected by these changes.
Remark: I expect that also regionA should be influenced byTemperature, because thenumber of hydrogen bonds will decrase with temperature
C*
ST
C
Conc is less and there are long rangeinteractions. Water is not so bound toions and highly disordered structure.Large entropy and less positive ornegative heat. ST becomes lesspositive
Conc increases. Water is bound toions and comparatively orderedstructure. Less entropy and morepositive heat. ST becomes morepositive
Disorder-order transition
Is thisargumentationin thecolombanipaper?
Page 33
CONCENTRATION DEPENDENCECross interactions
For energetic reasons most mixedinteraction take place on the cold side
... Minority component goes to the cold side
( ) ( )
12 1 12 2
1 2
12 11
12 22
1 2/ /kT kT
E T E T
T Te eε ε
ε εε ε
− −
∝ ∝
>>>
⇒ >
If the cross interactions are stronger than the pure interaction ...
[I. Prigogine et al. Physica 16 (1950) 851]
Page 34
TEMPERATURE DEPENDENCEGedankenexperiment
At low temperatures: minimization of the free energy
G = H – TSby forming hydrogen bonds (ΔU<0).
water goes to the cold side
At high temperatures: minimization of the free energy
G = H – TS by entropy production (ΔS>0).
water goes to the warm side
[Wang, Z., H
. Kriegs, andSW
J. Phys. Chem
. B, 116(2012) 7463.]
Assuming local thermodynamic equilibrium
Page 35
0 1 2 3 41.5
2.0
2.5
3.0
3.5
4.0
4.5 ST Tanner at 370 C 370 C
S T /
10-3
K-1
Concentration / M
Page 36
15 20 25 30 35 40 45
-1
0
1
2
3
KBr KCl KI NaI
ST
/ 10-3
K-1
Temp / o C
less H-bonds with temperature• ST increases• ∆ST decreases
Whichconcentration?