Thermodiffusion in Polymer Solutions

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Thermodiffusion in Polymer Solutions Jutta
Luettmer-StrathmannDepartment of Physics, The
University of Akron, Akron, OH 44325-4001, USA
TA

• Introduction
• Thermodiffusion in polymer solutions
• Single polymer chain in an incompressible solvent
  
• Incompressible two chamber system
• Lattice model for polymer in a compressible mixed
  solvent
• Application to poly(ethylene oxide) in
  ethanol/water mixtures
• Results for static properties and thermodiffusion
• Discussion

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Condensed Matter Colloquium, Physics Department,
Ohio University, September 12, 2002
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Thanks to Mike Boiwka for performing Monte Carlo
simulations
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Thanks to Simone Wiegand, Berend Jan de Gans, and
Rio Kita from the Max Planck Institut für
Polymerforschung in Mainz for sharing their
experimental data.
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Thermodiffusion Ludwig-Soret Effect
Fluid mixture with uniform temperature T
under a temperature gradient
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• There is no microscopic theory that (reliably)
  predicts the sign of the Soret coefficient.
• Typically, the heavier component migrates to the
  cold side

Thot
Tcold
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Heat of Transfer
The heat of transfer Qa , introduced by Eastman
and Wagner (1926, 1930)
Wirtz (1943) and Denbigh (1951) estimate Qa-
Qb from two energy contributions, the energy to
detach a molecule from its neighbors and the
energy to create a hole. Prigogine et al. (1950)
consider a free energy for detaching a molecule
to describe associated solutions
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Thermodiffusion in polymer solutions
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)
J. Rauch and W. Köhler, Phys. Rev. Lett. 88,
185901 (2002)
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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, R. Kita, and S. Wiegand
(to be published) The Soret coefficient of PEO
changes sign!
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Single chain on a simple cubic lattice - exact
enumerations
For a chain of Np beads, ( Np-1 bonds), on a
simple cubic lattice generate all conformations
so that no two beads overlap. Determine the
number c(m) of conformations with m pair
contacts. Determine the mean radius of gyration
for conformations with m pair contacts.
pair contact with interaction energy ?
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Single chain in an incompressible solvent
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Rg2(??)
??
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Chamber A, temperature TA
Chamber B, temperature TB
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Hence, the difference in internal energy between
two boxes at the same temperature, one with and
one without polymer, determines the probability
to find the polymer in the warmer of two boxes at
different temperatures ? heat of transfer
T, Unop
T, Upol
TAgt TB
TB
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Poly (ethyleneoxide) in ethanol/water
H2O

• Ethanol
• not a good solvent at room-temperature

E.E. Dormidontova, Macromolecules, 35 (2002), 987
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TDFRS results

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light scattering results
The addition of water expands the chains
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Observations regarding PEO in ethanol/water
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Lattice model for PEO in ethanol/water
simple cubic lattice Np 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 properties?ws geometric mean
approximation?ps PEO/ethanol, poor solvent
condition?pw,n ?pw,s PEO/water, non-specific
(poor solvent) specific (very attractive)
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Canonical Partition Function
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Lattice model calculations reproduce Chains
expand with increasing water content. Preferential
adsorption changes from ethanol to water at 19
water wt
T 293 K P ? 0.1 Mpa 5g/L of PEO Np 17
Note thermodynamic properties of the pure
components, solvent quality of the solution, and
preferential adsorption are used to determine the
system-dependent parameters.
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Set ?T 10-3 K and NA NB N/2
Chambers are non-interacting ? ZAZB
partition function for given configuration
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Lattice model results for the probability to find
the polymer in the warmer/colder chamber
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Comparison with experiment
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• Discussion
• In general, the better the solvent quality the
  higher the probability to find the polymer on the
  cold side.
• PEO moves to the cold side in ethanol/water with
  high water content
• PEO moves to the hot side in ethanol/water with
  low water content
• PVA moves to the hot side in water (Giglio and
  Vendramini, 1977)
• also seen in calculations of the Soret
  coefficient of PEO in pure water and ethanol
• In model calculations, the trend is reversed if
  the polymer-polymer interactions are very
  attractive
• Preferential adsorption is an important indicator
  for the behavior of the Soret coefficient

AcknowledgementsThe 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.
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