Thermodiffusion in Polymer Solutions Jutta Luettmer-Strathmann Department of Physics, The University of Akron, Akron, OH , USA Thermodiffusion Polyethylene oxide in ethanol-water mixtures Lattice model for polymer in a compressible mixed solvent Results and discussion TBTB TATA APS March Meeting, Austin, Texas, March 3-7, 2003

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

Thermodiffusion in polymer solutions J. Rauch and W. Köhler, Phys. Rev. Lett. 88, (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 * ) )

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 E.E. Dormidontova, Macromolecules, 35 (2002), 987 H2OH2O Ethanol: not a good solvent at room- temperature

Lattice model for PEO in ethanol/water simple cubic lattice N c = 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 (chain dimensions)  pw,n  pw,s PEO/water, non-specific, poor solvent (  pw,n =  ps ) specific, very attractive (chain dimensions)

Canonical Partition Function

T = 293 K P  0.1 MPa 5g/L of PEO N c = 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 T A Chamber B, temperature T B Chambers are non-interacting  Z A Z B = partition function for given configuration Set  T = K and N A = N B = N/2

Lattice model results for the probability to find the polymer in the warmer/colder chamber T = 293 K P  0.1 MPa 5g/L of PEO N c = 17

Comparison with experiment

T = 293 K P  0.1 MPa 5g/L of PEO N c = 17

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, M w ~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 ), the Ohio Board of Regents, the Research Corporation (CC5228), and the Petroleum Research Fund (#36559 GB7) is gratefully acknowledged.