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.