Schematic of free energy vs composition for systems of limited solubility This graph can be used to evaluate the number of phases present at a certain composition: At any composition less than B 1 and greater than B 2 a single phase (given by the solid curve) has a lower free energy then any 2 phase system with the same overall composition. i.e. at these compositions only one phase will exist. For compositions in between, the system will consist of two phases of composition B 1 and B 2. GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 1
Polymer-polymer solutions In order to for 2 substances to form a solution the Gibbs free energy of mixing must be negative and at its lowest possible value: ΔG M = ΔH ΔH M is usually positive and ΔS M depends on the number of ways that the chain units can be arranged in space In a polymer polymer mixture the number of possible arrangements is much smaller than in a polymer solvent system Additionally the contribution of the volume of mixing to the free energy of mixing becomes significant This results in limited solubility in many cases and some unique solubility behaviour such as phase separation at high temperatures and dissolution at lower temperatures GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 2 M TΔS M
Illustration of combinatorial entropy of mixing 2 small molecule substances Polymer solvent system Polymer polymer system: the entropy of mixing is reduced because the units of the two chains are restricted to particular arrangements defined by the covalent bonds between subsequent mers. GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 3
Phase diagram for a polymer polymer mixture Lower critical solution temperature Upper critical solution temperature GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 4
Flory equation of state for homopolymers and miscible polymer blends: ~ 2 ~ P T ~ 1 ~ 1 ~ 1 ρ + ρ ρ 3 = y~ = y ( ) 0 Where the reduced variables are defined relative to the close packed condition (the condition of zero free volume) y* In order for 2 polymers to be miscible their T* values must be similar. Also if T* 1 >T* 2 then P* 1 must be > P* 2 and the polymers must have similar values of coefficient of thermal expansion. GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 5
Example of criteria for miscibility The Flory EOS can be used to compute the volume of mixing and combined with the heat of mixing and combinatorial entropy term to determine the free energy of mixing.this allows us to evaluate miscilibility. Examples: For 2 polymers with M = 10 5 having T* values of 6900 K and P* values of about 450 J/cm 3 a difference in P* of 10 J/cm 3 is sufficient to give immiscibility with a critical temperature (UCST) near room temperature A difference in T* values of 250 K is sufficient to give immiscibility with a critical temperature (LCST) near room temperature A difference of about 8 J/cm 3 in P* and 190 K in T* is sufficient to give both LCST and UCST behavior. Lower molecular weight results in larger tolerated differences in P* and T*. Reference: Equations of state and predictions of miscibility for hyrdocarbon polymers, DJ Walsh et al, Macromolecules, 1992, 25, 5236-5240 GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 6
Kinetics of phase separation At both the lower and upper two-phase envelope there are two regimes for phase separation, the binodal and the spinodal. At the binodal conditions phase separation occurs by nucleation and growth and requires exceeding an energy barrier. At the spinodal condition, no energy barrier to phase separation exists: phase separation under this condition occurs by spinodal decomposition GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 7
Free energy diagram For compositions between B 1 and S 1 (and between S 2 and B 2 ) a single phase is metastable due to the local positive second derivative of the curve.this is equivalent to the existence of an energy barrier for phase separation: Phase separation by nucleation and growth In between S 1 and S 2 a single phase is unstable and spinodal decomposition will occur GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 8
Experimental observation of phase separation Nucleation and growth separation appears as small spherical regions of the 2 nd phase which grow over time Spinodal decomposition looks like tiny overlapping worms (i.e. the domains of each phase are interconnected). After spinodal decomposition, coarsening of the structures often occurs over time resulting in spheroid domains. Initial spinodal structure Coarsened structure GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 9
Polystyrene-poly (vinyl methyl ether) blends 〇 Phase separation by spinodal decomposition observed Phase separation by nucleation and growth observed LCST GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 10
Copolymer blends The information presented until now applies to blends of homopolymers which we have shown are mostly immiscible Blends of copolymers (or homopolymers with copolymers) sometimes have enhanced miscibility because of the repulsion between dissimilar mers on the same chain General case: Most frequent case: Example: Blends of poly (vinyl chloride) and poly(ethylenestat-vinyl acetate) are miscible while blends of poly (vinyl chloride) and polyethylene and of poly (vinyl chloride) and poly (vinyl acetate) are immiscible. GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 11
Thermodynamics of homopolymer - copolymer blends The free energy of mixing is: Where and c ij depend on the copolymer composition. For A n /(B x C 1-x ) n blends: When ΔG m is negative, miscibility is possible. GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 12
Characterization of polymer blends GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 13
Block copolymers AAAAAA ABBBBB Block copolymers are more miscible than blends of the homopolymers because of the covalent bond between blocks They can still phase separate under some conditions though leading to very interesting sets of microstructures The domains must be small enough such that one block can reside in one phase while the next block resides in the second phase Morphology changes from spheres to cylinders to lamellae depending on the relative lengths of the blocks: Spheres form in a continuous phase when one mer has short blocks while the other mer has long blocks Alternating lamellae form when the blocks are about the same length Cylinders form for intermediate cases GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 14
Idealized triblock copolymer thermoplastic elastomer morphology Each chain takes part in 2 glassy domains and the elastomeric continuous phase GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 15
PS-block-PBd-block-PS (40 % butadiene) Dark regions are the polybutadiene cylinders occurring parallel and perpendicular to the surface Perpendicular cylinders GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 16
Domain sizes The domain sizes (sphere radius, cylinder radius, lamellae half thickness) are given by: Note: Spheres form when the minor component is less than 25%, cylinders between 25 and 40% and lamellae from 40% to 50%. where K is the coefficient of proportionality between the root mean square end to end distance and the square root of the molecular weight And α is a constant which ranges between 1 and 1.5 (typical value is 1.25) Values of K for R in Angstroms of some polymers: GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 17
Example of block-copolymer phase separation PB-PS-PB triblock copolymer with M w =65-25-94 kg/mol PS makes up 13.6% of this copolymer, therefore we expect the PS blocks to form spherical domains in the PB continuous phase Tapping mode AFM image of film on silicon 25 Phase Contrast (degrees) 20 15 10 5 32 nm R theoretical = 18 nm 3 μm 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Length (μm) Reference: Measuring local viscoelastic properties of complex materials with tapping mode atomic force microscopy, Xu, Wood-Adams, Robertson, Polymer 47 (2006) 4798 4810 GCH 6101- Polymer Polymer Phase separation PM Wood-Adams 18