1. 1 Thermodiffusion in Polymer Solutions Jutta Luettmer-Strathmann Department of Physics, The University of Akron, Akron, OH 44325-4001, USA 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 TBTB TATA Condensed Matter Colloquium, Physics Department, Ohio University, September 12, 2002

2. 2 Thanks to Mike Boiwka for performing Monte Carlo simulations

3. 3 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.

4. 4 Thermodiffusion — Ludwig-Soret Effect 12 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 side T hot T cold

5. 5 Heat of Transfer The heat of transfer Q a *, introduced by Eastman and Wagner (1926, 1930) T’, P’, V, N a -1, N b T, P, V, N a, N b Qa*Qa* T, P, V’, N a -1, N b Wirtz (1943) and Denbigh (1951) estimate Q a * - Q b * 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

6. 6 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 (S T ~ M 0.53 ) Concentrated solutions: S T is independent of chain length, decreases with concentration (S T ~ (c/c * ) -0.73 )

7. 7 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!

8. 8 Single chain on a simple cubic lattice - exact enumerations pair contact with interaction energy  For a chain of N p beads, ( N p -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.

9. 9 Single chain in an incompressible solvent  ss  pp  ps

10. 10 Rg2()Rg2() 

11. 11  ss  pp  ps  ss Chamber A, temperature T A Chamber B, temperature T B

12. 12

13. 13 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, U nop T, U pol T A > T B TBTB

14. 14

15. 15 Poly (ethyleneoxide) in ethanol/water E.E. Dormidontova, Macromolecules, 35 (2002), 987 H2OH2O Ethanol: ? not a good solvent at room- temperature

16. 16 0.00.20.40.60.81.0 -0.5 0.0 0.5 1.0 1.5 2.0 S T / K weight fraction water PEO in ethanol/water PEO moves to hot side PEO moves to cold side TDFRS results

17. 17 light scattering results The addition of water expands the chains 510152025 22 24 26 28 30 32 34 36 R G 2 weight fraction of water aggregation guide for the eye

18. 18 Observations regarding PEO in ethanol/water ethanol/waterhighly miscible PEO in ethanolimmiscible at room temperature, chains collapsed UCST phase diagram PEO in watermiscible at room temperature, chains highly extended LCST phase diagram specific interactions pressure dependence PEO in ethanol/water solubility increases (chains expand) with water content for low water concentrations, ethanol is preferentially adsorbed at a water concentration of 19% by weight, a transition to preferential adsorption of water takes sets in

19. 19 Lattice model for PEO in ethanol/water simple cubic lattice N p = number of contiguous sites for polymer N s = number of solvent sites N w = number of water sites N v = 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)

20. 20 Canonical Partition Function

21. 21 T = 293 K P  0.1 Mpa 5g/L of PEO N p = 17 Lattice model calculations reproduce: Chains expand with increasing water content. Preferential adsorption changes from ethanol to water at 19 % water wt Note: thermodynamic properties of the pure components, solvent quality of the solution, and preferential adsorption are used to determine the system-dependent parameters.

22. 22 Chamber A, temperature T A Chamber B, temperature T B Chambers are non-interacting  Z A Z B = partition function for given configuration Set  T = 10 -3 K and N A = N B = N/2

23. 23 Lattice model results for the probability to find the polymer in the warmer/colder chamber

24. 24 Comparison with experiment

25. 25 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 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.

26. 26