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Thermodiffusion in Polymer Solutions
Jutta Luettmer-StrathmannDepartment of Physics, The University of Akron, Akron, OH 44325-4001, USA
• Thermodiffusion
• Polyethylene oxide in ethanol-water mixtures
• Lattice model for polymer in a compressible mixed solvent
• Results and discussion TB
TA
APS March Meeting, Austin, Texas, March 3-7, 2003
Thermodiffusion — Ludwig-Soret Effect
side warm theto
side cold theto
migrates 2component
negative is
positive is
2component of
:2component offraction mass theis
and re temperatu theis where
)1(
1:2component oft coefficienSoret
T
2211
22
T
S
mNmN
mNcc
T
T
c
ccS
1 2
Fluid mixture with uniform temperature T
under a temperature gradient
• There is no microscopic theory that (reliably) predicts the sign of the Soret coefficient.
• Typically, the heavier component migrates to the cold sideThot Tcold
Thermodiffusion in polymer solutions
J. Rauch and W. Köhler, Phys. Rev. Lett. 88, 185901 (2002)
Dilute solutions:
Soret coefficient is independent of concentration, increases with chain length (ST ~ M0.53)
Concentrated solutions:
ST is independent of chain length, decreases with concentration (ST ~ (c/c*)-0.73)
PEO in ethanol/water mixturesResults from TDFRS
Mass fraction of water
0.0 0.2 0.4 0.6 0.8 1.0
ST (
K-1
)
-0.2
-0.1
0.0
0.1
0.2
PEO moves tocold side
PEO movesto warm side
In solution, the polymer migrates almost always to the cold side, with only two known exceptions
poly(vinyl alcohol) in water, Giglio and Vendramini, Phys. Rev. Lett. 38, 26 (1977)
poly(ethylene oxide) (PEO) in ethanol/water mixtures with low water content,B.-J. de Gans et al, to be published
The Soret coefficient of PEO changes sign!
Poly (ethyleneoxide) in ethanol/water Poly (ethyleneoxide) in ethanol/water
H O CH2 CH2 OHn
E.E. Dormidontova, Macromolecules, 35 (2002), 987
H2O
Ethanol:not a good solvent at room-temperature
Lattice model for PEO in ethanol/water
simple cubic lattice
Nc = number of contiguous sites for polymer
Ns = number of solvent sites
Nw = number of water sites
Nv = number of void sites
Interaction energies:
pp , ss , ww from pure component PVT propertiesws geometric mean approximationps PEO/ethanol, poor solvent (chain dimensions)pw,n pw,s PEO/water, non-specific, poor solvent (pw,n = ps )
specific, very attractive (chain dimensions)
Canonical Partition Function
rspwnpwpsspp
w
Ewnm
s s
wpnn
w
pn
m w
nwN
sN
wNNnN
s
n
wN
NnN
w
nmcNZ
eee5e
)(6)(
,,)(
][][
ionapproximat mixing randomin nsinteractiosolvent -solvent todueenergy
ethanol
waterby occupied sitesneighbor nearest ofnumber
chain theof sitesneighbor nearest available ofnumber 224
r
pn
E
s
w
mNn
2
0,,
0
contactspolymer -polymer with
on conformatichain afor y probabilit
summations Partial
site latticeper volume,ln
from Pressure
gm
NNN
Rm
p
vN
ZPv
cws
T = 293 K
P 0.1 MPa
5g/L of PEO
Nc = 17
Chain dimensions from lattice model:
Note: thermodynamic properties of the pure components and solvent quality of the solution are used to determine the system-dependent parameters.
Chamber A, temperature TA Chamber B, temperature TB
Chambers are non-interacting ZAZB = partition function for given configuration
Set T = 10-4 K and NA = NB = N/2
Q
Q
wspiQQQQNNZNZQ
A
BABAAii
B
N
Ai
A
Ai
0
00in polymer in polymer ][
A)(chamber chamber hot in thepolymer thefind y toProbabilit
},,{,})({})({
:states of Sum
Lattice model results for the probability to find the polymer in the warmer/colder chamber
properties onalconformation basedt coefficienSoret for estimate
)1(
1 p
ppLatticeT,
T
c
ccS
Mass fraction of water
0.0 0.2 0.4 0.6 0.8 1.0
( Q
0A/Q
- 1
/2 )
/ T
-0.10
0.00
0.10
0.20
0.30
PEO movesto warm side
PEO movesto cold side
cw0.0 0.2 0.4 0.6 0.8 1.0
ST,Lattice ( K-1)
-0.5
0.0
0.5
T = 293 K
P 0.1 MPa
5g/L of PEO
Nc = 17
Mass fraction of water
0.0 0.2 0.4 0.6 0.8 1.0
ST (
K-1
)
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6PEO 5.0 g/LPEO 5.0 g/LPEO 0.5 g/Llattice model
PEO moves to warm side
Comparison with experiment
T = 293 K
P 0.1 MPa
5g/L of PEO
Nc = 17
Lattice model results
Temperature (K)
290 300 310 320 330S
T (
K-1
) -0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
cw = 0.801
cw = 0.501
cw = 0.202
Temperature dependence of PEO Soret coefficient in mixed solvent
Discussion• Lattice model for dilute solutions of PEO in ethanol/water
• chain with 17 beads corresponds to about 27 repeat units of PEO, Mw~1187 g/mol
• interactions with polymer treated explicitly, solvent-solvent interactions in random mixing approximation
• specific interactions between water and polymer taken into account
• chain dimensions at given temperature, pressure, composition as indicator for solvent quality
• Thermodiffusion
• In general, the better the solvent quality, the larger the Soret coefficient
• PEO moves to the cold(hot) side in ethanol/water with high(low) water content
• PVA moves to the hot side in water (Giglio and Vendramini, 1977)
• In model calculations, this trend is reversed for very attractive pp
• The Soret coefficient may change sign as a result of temperature variation
• In future work, take specific interactions between solvent molecules into account
Acknowledgements:The authors would like to thank Mark Taylor and Simone Wiegand for many helpful discussions. Financial support through the National Science Foundation (DMR-013704), the Ohio Board of Regents, the Research Corporation (CC5228), and the Petroleum Research Fund (#36559 GB7) is gratefully acknowledged.