Polymer Synthesis CHEM 421 Block Copolymers Block Copolymer Basics Polymer Synthesis CHEM 421 • MOST polymers DO NOT mix (like oil and water). Polymer A Polymer B Let’s consider the fundamentals of mixing… Mixing Thermodynamics Polymer Synthesis CHEM 421 Consider a binary mixture : mixing VA VB Volume occupied by species A Volume occupied by species B VTOT = VA + VB Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003. Mixing Thermodynamics Volume Fractions: VA A VA VB Polymer Synthesis CHEM 421 B 1 A NA = Number of lattice sites occupied by each molecule of species A NB = Number of sites occupied by B molecules v0 = lattice site volume Lattice Volume molecularvolumeof species A A 0 N A molecularvolumeof species B B 0 N B Regular solutionsare mixturesof low molar mass species with NA NB 1 Polymer solutions are mixtures of macromolecules ( NA N 1) with low molar mass species ( NB 1) Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003. Polymer Synthesis CHEM 421 Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003. Mixing Thermodynamics Polymer Synthesis CHEM 421 Three cases of interest: NA Small Molecule Solutions 1 Polymer Solutions N Polymer Blends NA NB 1 1 NB • VTOT = VA + VB occupy n sites: n VA VB 0 • All molecules of A occupy: VA n A 0 Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003. Mixing Thermodynamics Polymer Synthesis CHEM 421 Consider a solution of polymer A (species B is the solvent) T heentropyS is theproduct of the Boltsmanconstantk and thenaturallogarithmof thenumber of ways (ln ) to arrange moleculeson thelattice S k ln A nA AB n For a homogeneous mixture of A and B, each molecule has ΩAB possible states where n is the total # of lattice sites S A k ln AB k ln A k ln AB A S A k ln A Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003. Mixing Thermodynamics Polymer Synthesis CHEM 421 • To calculate the total entropy of mixing, sum entropy contributions from each molecule: Smix nA SA nB SB k nA ln A nB ln B • The number of molecules of A and B are: nA n A NA nB nB NB Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003. Mixing Thermodynamics Polymer Synthesis CHEM 421 • Entropy of mixing: Smix B A k ln A ln B NB NA • For a regular solution, NA = NB = 1 Smix k A ln A B ln B A large entropy of mixing for small molecule solutions! Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003. Mixing Thermodynamics Polymer Synthesis CHEM 421 • Entropy of mixing for polymer solutions, NA = N and NB = 1 Smix A k ln A B ln B NA • Enormous differences in the entropy of mixing for polymer solutions versus regular solutions versus polymer blends! ΔSmix, polymer < ΔSmix, small molecule Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003. Mixing Thermodynamics Polymer Synthesis CHEM 421 • Entropy of mixing for polymers, NA = N and NB = N Smix B A k ln A ln B NB NA • Is even worse!! Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003. Polymer Synthesis CHEM 421 Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003. Block Copolymer Basics Polymer Synthesis CHEM 421 • MOST polymers DO NOT mix (like oil and water). Polymer A Polymer B Let’s consider the fundamentals of mixing… Microphase Separation • Most polymers are immiscible Polymer Synthesis CHEM 421 Block Copolymer Basics Polymer Synthesis CHEM 421 The chemically different segments of a block copolymer cannot completely phase separate, because they are covalently bound (“frustrated” separation). The propensity of two different polymers to phase separate can lead to interesting solid-state and solution morphologies. Let’s consider the parameters affecting phase separation in diblock copolymers … Polymer Synthesis CHEM 421 Diblock Morphologies (TEM) Polymer Synthesis CHEM 421 • Spheres PS-b-PI fPS = 0.16 100 nm Han, C. D.; Vaidya, N. Y.; Kim, D.; Shin, G.; Yamaguchi, D.; Hashimoto, T.; Macromolecules 2000, 33(10), 3767-3780. Polymer Synthesis CHEM 421 Diblock Morphologies (TEM) Cylinders (Dendritic Benzyl Ether)-b-PS Stained w/ RuO4 Pochan, D. J.; Pakstis, L.; Huang, E.; Hawker, C.; Vestberg, R.; Pople, J.; Macromolecules 2002, 35(24), 9239-9242. 200 nm Polymer Synthesis CHEM 421 Diblock Morphologies (TEM) Polymer Synthesis CHEM 421 Lamellae PS-b-PI fPS = fPI Stained with OsO4 Bailey, T.S.; Pham, H. D.; Bates, F. S. Macromolecules 2001, 34, 6994-7008. 50 nm PS-b-PI Same magnification Same volume fraction… Left: MW = 104 Right: MW = 105 Polymer Synthesis CHEM 421 Polymer Synthesis CHEM 421 • PS-b-PI • 45% PS • Differences in TEMs? discrete block copolymer tapered block copolymer Copolymerization Kinetics Polymer Synthesis CHEM 421 Homo-propagation Cross-propagation Cross-propagation Homo-propagation Styrene = M1 Bd = M2 r1 = k11 / k12 = 0.04 r2 = k22 / k21 = 26 For free radical r2 >>1 and r1 < 1 gives….? For living polymerization r2 >>1 and r1 < 1 gives….? Mixing Thermodynamics • Free Energy of mixing for polymers, ΔG = ΔH - T ΔS Smix B A k ln A ln B NB NA • ln of a fraction is negative! Polymer Synthesis CHEM 421 Block Copolymer Uses • Unique properties of triblocks Polymer Synthesis CHEM 421 Polymer Synthesis CHEM 421 Triblock Morphologies Polymer Synthesis CHEM 421 Bates, F.S., 1999 MSRI Lecture notes: http://www.msri.org/publications/ln/msri/1999/materials/fbates/1/banner/03.htm, accessed 9/2003. Polymer Synthesis CHEM 421 TEM of PI-b-PS-b-PDMS Polymer Synthesis CHEM 421 Bates, F.S., 1999 MSRI Lecture notes: http://www.msri.org/publications/ln/msri/1999/materials/fbates/1/banner/03.htm, accessed 9/2003. Phase Separation in PS-b-(PE-co-PB)-b-PMMA 0.5μm Breiner, U.; Krappe, U.; Thomas, E. L.; Stadler, R. Macromolecules 1998, 31, 134-141. Polymer Synthesis CHEM 421