1.  Phase behavior of polymer solutions and polymer blends in confinement Juan C. Burgos Juan C. Burgos Texas A&M University College Station, TX 2011 1

2. Phase behavior of polymers 1. Thermodynamic of polymer solutions Lattice model regular solution theory Entropy of mixing Total number of possible configurations m1m1 m2m2 Enthalpy of mixing 2

3. Flory-Huggins theory N = degree of polymerization χ = interaction parameter χ > 0.5 bad solvent χ < 0.5 good solvent χ = 0.5 theta solvent 3

4.  Phase behavior At critical pointAt spinodal 4

5.  Polymer blends Polymer blends use to exhibit LCST due to the small increases in entropy and specific molecular interactions 5 BATES, F. S. (1991). Science 251, 898

6.  Liquid–liquid demixing for the Asakura–Oosawa (AO) model (bulk) Colloid particle RCRC RPRP  Colloid particles are hard spheres  Polymer chains are soft spheres U pp (r) = 0  Reservoir packing fraction 6 Binder, K., J. Horbach, et al. (2008).Soft Matter 4(8), 1555

7. Polymer mixes in confinement  Polymer-colloid mix  Polymer blend Some important considerations:  Interplay must be expected between surface effects on the fluid due to the confining walls, such as adsorption, and formation of wetting (or drying) layers, due to the finite width of the capillary.  Unlike small molecules in confinement, effects due to the atomistic corrugation of the walls, are much less important in mesoscopic scale of polymer mixtures 7

8.  Size effects on the polymer-colloid mixtures L L L 8 Binder, K., J. Horbach, et al. (2008).Soft Matter 4(8), 1555

9.  Confinement by symmetric walls: evidence for capillary-condensation-like behavior L L D 9 Binder, K., J. Horbach, et al. (2008).Soft Matter 4(8), 1555

10.  Determining the critical point by cummulant analysis D = 5.0 10

11. Critical amplitude  Phase behavior in confinement for ε = 0 Order parameter ( Δ = M C ) Order parameter Relative distance Effective exponent 11

12.  Structure of the coexisting phases o For ε = 0, colloidal particles are enriched at the walls in the vapor-like phase o For ε = 2, colloidal particles are enriched at the walls in the liquid-like phase D = 10 12 Binder, K., J. Horbach, et al. (2008).Soft Matter 4(8), 1555

13.  Density profiles across the thin film o The colloid density in the liquid phase near the walls shows a pronounced layering effect o polymer density in the vapor-like phase lacks the corresponding behavior  Polymer chains are soft spheres U pp (r) = 0 13 Binder, K., J. Horbach, et al. (2008).Soft Matter 4(8), 1555

14.  Confinement by asymmetric walls: evidence for an interface localization transition o One wall attracts predominantly colloids, whereas the other attracts polymers μ is small (μ coex – μ) is large η r p > η r p,critic (D)  first order η r p = η r p,critic (D)  first order η r p < η r p,critic (D)  second order 14 Binder, K., J. Horbach, et al. (2008).Soft Matter 4(8), 1555

15.  Snapshot picture of the polymer-rich phase 15 Binder, K., J. Horbach, et al. (2008).Soft Matter 4(8), 1555

16.  Density profiles along the thin film phase B I B IIA B IIB a)η r p < η r p,critic (one phase) b)η r p,critic < η r p < η r p,critic (D) c)η r p > η r p,criti (D) d)η r p > η r p,criti (D) 16 Binder, K., J. Horbach, et al. (2008).Soft Matter 4(8), 1555

17.  Phase Diagrams ε ∞ μ Critical point is shifted upwards as ε increases and D decreases As ε increases, thin films coexistence curve move closer to that of bulk 17

18. Polymer blends in confinement  Laterally segregated binary films  If the AB interface tension is comparable to the liquid/vapour tension, it ‘drags’ the film surface towards the substrate so as to reduce the length of the AB interface  If the liquid/vapour tension exceeds the AB interface tension by about two orders of magnitude, however, the surface is almost flat 18

19.  Probability distribution of the composition  Two phases are separated by a large free energy barrier, which corresponds to the free energy cost of two interfaces between the coexisting phases of size L 2  Around φ = 1/2 the typical configuration consists of two domains separated by two AB interfaces of size L 2  The model correspond to confined geometry  MC simulations were performed  Repulsion between molecules were repsesented by: 19

20.  Wetting transition (self consistent field calculations)  The fact that curves intersect under a finite angle indicates that the wetting transitions are of first order  As the monomer– surface attraction is reduced the wetting transition shifts to higher temperatures (k B T/ε) and becomes weaker 20 Muller, M. and K. Binder (2005). Journal of Physics: Condensed Matter 17(9): S333.

21.  Phase diagrams in terms of composition and temperature  the critical point is shifted to lower temperatures and larger composition of the species attracted by the surfaces  The spinodals in a film do not converge towards their bulk counterparts Δ as → ∞, as binodals does  The phase diagram for anti-symmetric wall contains two critical points and a triple line 21 Muller, M. and K. Binder (2005). Journal of Physics: Condensed Matter 17(9): S333.

22.  Effective interface potential in a film with antisymmetric surfaces.  AB interface becomes bound to one of the surfaces. In the case of a first order interface localization/delocalization transition this corresponds to a triple point: an A-rich phase, a B-rich phase and a phase with symmetric composition coexist.  g(l) describes the interaction between AB interface and a surface T Triple point 22

23.  Dependence of the phase diagram on the film thickness  The central peak of the probability distribution of the order parameter m is a factor 1.2 higher than the outer peaks  In the case of r Δ > Δ tri, the transition is of first order, and the estimate tends towards the triple temperature 23

24.  Crossover from capillary condensation to interface localization/delocalization  For symmetric surfaces (capillary condensation) the critical point is shifted towards lower temperatures  As the preference of the top surface for species B is reduced, the critical point and the critical composition tend towards their bulk values (φ = 0.5, 1/χN = 0.5)  Upon making the top surface attracting the other component, B, we gradually change the character of the phase transition towards an interface localization/delocalization transition 24

25. Confinement-induced miscibility in polymer blends  Effect of confinement on micelle formation  Large changes in the c.m.c. only happen at high degrees of confinement. Initially, at small degrees of confinement, the micelle reacts by undergoing a slight decrease in its size  Confinement further, the micelle gets smaller and the entropic losses that occur with the packing of linear diblock copolymers into smaller spheres starts increasing rapidly  The length scale at which confinement changes the behavior of the system is approximately twice the radius of the bulk micelle 25 Zhu, S., Y. Liu, et al. (1999) Nature 400(6739): 49

26.  scanning force microscopy (SFM) images of the bilayer samples t PS is 1000 Å t PS is 800 Å t PS is 500 Å a)Undissolved micelles remaining on the PMMA layer surface. b)Coexisting micelles and microemulsion structures are observed. c)Only a microemulsion is seen 26 Zhu, S., Y. Liu, et al. (1999) Nature 400(6739): 49

27. Summary  Confinement effects for polymer-colloid mixtures and polymer blends phase behavior were analyzed  For the case of polymer-colloid mixtures two kinds of phase transition are observed. Capillary condensation for symmetric walls, and interface localization transition for asymmetric walls  Reducing distance between the surfaces enhance the miscibility of polymer blends and polymer-colloids mixtures  For first order interface localization transition for polymer blends a triple point is observed, where an A-rich phase, a B-rich phase and a phase with symmetric composition coexist. 27