Thermodiffusion in Polymer Solutions

1. 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 TB Condensed Matter Colloquium, Physics Department, Ohio University, September 12, 2002

2. Thanks to Mike Boiwka for performing Monte Carlo simulations

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. Thermodiffusion — Ludwig-Soret Effect Fluid mixture with uniform temperature T under a temperature gradient 1 2 • 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

5. T, P, V, Na, Nb T’, P’, V, Na-1, Nb T, P, V’, Na-1, Nb Qa* 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

6. 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)

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. 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 

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

10. Rg2() 

11. ps pp ss ss Chamber A, temperature TA Chamber B, temperature TB

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, Unop T, Upol TA> TB TB

15. Poly (ethyleneoxide) in ethanol/water H2O • Ethanol: • not a good solvent at room-temperature E.E. Dormidontova, Macromolecules, 35 (2002), 987

16. 2.0 PEO in ethanol/water 1.5 PEO moves to cold side 1.0 -1 / K 0.5 T PEO moves to hot side S 0.0 -0.5 0.0 0.2 0.4 0.6 0.8 1.0 weight fraction water TDFRS results

17. 36 34 32 30 aggregation 2 G R 28 guide for the eye 26 24 22 5 10 15 20 25 weight fraction of water light scattering results The addition of water expands the chains

18. Observations regarding PEO in ethanol/water

19. 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)

20. Canonical Partition Function

21. 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.

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

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

24. Comparison with experiment

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.