1. Effect of Shear Flow on Polymer Demixing- the unanswered questions H. GERARD, J. T. CABRAL, J. S. HIGGINS Department of Chemical Engineering Imperial College, London

2. Thermodynamics Flory-Huggins lattice theory Combinatorial entropy Enthalpy Polymer miscibility 1

3. Phase separation 2 Concentration fluctuations oo ++ -  Metastable: nucleation & growth Unstable: spinodal decomposition

4. Free Energy of mixing Composition C 0 B' B'' T0T0 Spinodal decomposition 3 EARLY LATER FINAL distance C0C0 B' B'' 80  m Optical microscopy

5. 4 Cahn-Hilliard Cahn-Hilliard linearised theory equation of motion concentration fluctuations -D app M: diffusional mobility f(D 1,D 2 ) & q c Growth rate of Fourier components t-indep diffusion Sharp interfaces Qm Qc R (s -1 ) growth relaxation Q (nm -1 ) 0

6. Scattering photodiode array Heating block He-Ne 5mW laser  m : characteristic length of phase separation ~ 1m (LS) Structure factor solid angle: d  S(Q,) LS schematic 7

7. Time (s) 030060090012001500 Intensity (au) 0 5 10 15 20 25 30 q=0.00124 A deep quench shallow quench LS 0 2000 1000 time (s) q (nm -1 ) I (au) Light scattering 8 TMPC/PS 50:50 T jump =240.6 o C

8. TMPC/PSd 70:30 MM 254 o C Q (A ) 0.0020.0040.0060.0080.010 Intensity (cm) -1 0 50 100 150 200 250 300 350 180 s x 15 s TMPC/PSd70:30 258 o C Time (s) 0200400600 Intensity (au) 0 2 4 6 8 LS: Q=0.00152 A Light scattering Q (A ) 0.0000.0040.0080.0120.016 R (s -1 ) 0.00 0.01 0.02 0.03 TMPC/PSd 70:30 MM 254 o C Q C Q M Time (s) 0100200300 Intensity e 1 e 2 e 3 e 4 Q=4.9x10 -3 A TMPC/PSd 70:30 T=252 o C Early stages (SANS) 11

12. §In 1996 we had observed apparent SID at temperatures well below the quiescent LCST for a number of amorphous blends. §Shifts in LCST ranged from 40K to less than 5K and seemed to correlate with differences in the component rheological behaviour. §We had not followed the kinetics of SID, and there was no theoretical development to describe such kinetics §We believed that observing the kinetics might answer the question of SID (ie a true thermodynamic phase separation) v enhanced concentration fluctuations

13. Theoretical Approaches Wolf Add a stored energy term to the Gibbs free energy: with  May dramatically influence  2  G m /  2   Good qualitative description of the shear behaviour of PS/PVME, SMA/PMMA and SAN/PMMA blends. But uno description of the anisotropy u equilibrium thermodynamics applied to such a case? Clarke & McLeish They use, following Doi and Onuki, the two- fluid model considering the visco-elastic behaviour of both components.  For low shear rates, in the y,z plane:   quiescent part shear part where  =((  A ’/  A )-(  B ’/  B ))/(  A ’ +  B ’),  i ’ being the frictional drag per monomeric volume associated with component i, related to the monomeric friction coefficient per volume by:  i ’=  i (N i /N ei )  0i ’

14. Shear Light Scattering Experiments 1D LS Shear Experiments: samples sheared in plate-plate geometry, the scattered light (He-Ne Laser, =632.8 nm, incident beam // to the velocity gradient direction) being collected along the vorticity direction For blends 1 and 2 (critical composition) and for a shear rate, scattered intensity increases with time after a delay time  d : Diode array I(q)=I(q,  d )exp(2R(q)(t-  d )) “early stage” R(q) Velocity Gradient Vorticity Characteristics of the three 30/70% w/w PS/PVME blends studied .

16. Clarke and McLeish:   extracted from shear LS experiments Decent fit for low shear rates: LS Results and Theoretical Predictions D app0 May also be obtained from “remixing” quiescent LS experiments:  Influence of molecular deformation on blends thermodynamics?  Estimation of shear rate?  Did we miss the “early stage”?

17. §Small Angle Neutron Scattering – the aim is to look at much smaller size scale and “catch” the early stages §One component is deuterated to give contrast - this may shift the LCST. §We had no shear cell for SANS and had to use quenched samples. §The neutron beam is much larger than the laser beam so we were averaging over a range of shear rates

18. M w (kg/mol.) M w /M n T g (ºC)blend T g (ºC) spinodal temperature (T s ) (ºC) PVME892.5-32 PS12704.7106.6-15.5 ± 4.101.8 ±.5 PS22831.35108.7-19.4 ±.5101.5 ±.4 PS3 (d-PS) 3031.6108.6-19.2 ±.5141.5 ± 1. PS410201.15110.6-18.4 ± 3.90.2 ± 2.

19. shear-quenched SANS (highest shear rate)

20. Conclusions Our first SANS results seem to partially confirm what was first observed through light scattering in similar (from a rheological point of view) protonated blends.  For low q : the rise of S(q) for high shear rates may be due to an enhancement of concentration fluctuations in accordance with our LS results  For high q : higher shear rates seem to reduce concentration fluctuations, a feature not explained by two-fluid models inspired approaches such as Clarke & McLeish’s one. Might explain the discrepancy between the apparent diffusion coefficients obtained from quiescent experiment and deduced from Due to the effect of molecular deformation on the thermodynamics of the system?

21. The Unanswered Questions §Is the D from SID really different from the D obtained in re-mixing experiments?-experiments first and if confirmed theory needs some thought. §Would a more sophisticated statistical mechanics description of the free energy help? We have been having considerable success in quiescent systems using a version of BGY which includes compressibility and non-random mixing. §What happens in the early stages of SID? – can we find a system where deuteration does not have such a large effect on LCST? – or can we use another technique, eg AFM on quenched samples? §All these Qs aimed at the “big” one –is this SID or just enhanced concentration fluctuations?

23. Parameters which characterize the pure fluid  ii   r i v strength of nearest-neighbour interaction number of contiguous lattice sites per molecule volume per mole of lattice sites …and the mixture g =  ij /(  ii  jj ) 1/2 characterizes the deviation from the geometric mean approximation Lattice Born-Green-Yvon (BGY) theory links the microscopic character of a polymer/blend to its thermodynamic properties Macromolecules 36, 2977 (2003)

24. Formal definition of p(i,j), pair distribution function approximations non-randomly mixed local connectivity compressible A few remarks about the theory Sum over lattice of pair contributions to internal energy E (T,  ii,  ij,  i ) internal energy Various partial derivatives lead successively to … A (T,  ii,  ij,  i, V) P (T,  ii,  ij,  i, V)  (T, P,  ii,  ij,  i ) Helmholtz equation of state chemical potential

25. g exp =   exp /(       When (g exp -1) is negative/positive the geometric mean is over/underestimating the strength of the 1-2 interaction

27. Ornstein Zernicke Formulae

31. Blend Rheology Rheological Experiments: The Clarke & McLeish approach has been developed for the weak shear regime (  < 1 where  is the longest relaxation time of the blend). It also assumes that both components present different relaxation times in the blend. Rheological experiments were performed on a Paar Physica UDS 200 Rheometer to check both assumptions: Relaxation time and for blend 1  weak shear regime if we assume that  corresponds to the intercept of G’ and G’’.  in our frequency range, only one relaxation time may be detected in the blend. Critical time = -1

32. Concentration Fluctuations in Polymer Blends Effect of shear flow: shear (dispersed phase) droplet break-up (Taylor) influence on thermodynamics (Wolf) stress/concentration fluctuations coupling (Doi, Onuki) T  one phase D app < 0 two-phase (unstable) D app > 0 spinodal T s Binodal D app < 0 glass transition T g Concentration fluctuations enhancement (for the early stage inside the spinodal line) and decays (for the “late stage” in the one phase region) may be described Cahn-Hilliard theory, giving an expression for their growth rate R(q): with the apparent diffusion coefficient

33. Small Angle Neutron Scattering Ornstein-Zernike at high q: S(0) -1   ( from 100 to  Å  Structure Factor S(q) for blend 3 sheared at T=86.6ºC then quenched in liquid N 2 Beam centre shear rate These features are not described by the available theoretical models

34. Enhancement of Concentration Fluctuations in the (x,z) Plane q (  m -1 ) 0 5 10 2D LS patterns for blend 1 at T=84.6ºC a) before shear and b) after 26.5 min. of shearing with = 5 s -1 a) b) Optical micrograph of the bulk of a quenched sample after 25 min. shear at  T = -17.2 K and = 1.4 s -1 for two different magnifications. 10  m 100  m flow vorticity

35. Small Angle Neutron Scattering Blend 3: deuterated PS/PVME blend sheared at T = 86.6ºC (  T = - 54 K) Two samples with  maximal (2.1 and 5.2 s -1 ) but similar maximal strain (   Rheological steady state is reached with no change in LS patterns The shearing is then stopped and the sample quenched in liquid N 2 SANS (on D22 under cryostat at the ILL, Grenoble):  No obvious anisotropy in our q range (7. 10 -3 to 1.1 10 -1 Å -1 )  High q (> 4 10 -2 Å -1 ): S(q)  with  reduction of small wavelength concentration fluctuations with shear S(0) -1 obtained from high q fits is increasing with  “Shear Induced Mixing”  Low q (< 4 10 -2 Å -1 ): S(q)  then  with intermediate scale structure growing (as seen in PS/DOP)?  “Shear Induced Demixing”? But similar low q high scattering for unsheared blend! Effect of quench? But we are scanning  local flow directions: incident beam