10. Block Copolymers

Transcription

1 10. Block Copolymers 10.1 Definitions Block copolymers comprise two or more homopolymer subunits linked by covalent bonds many different types: diblock copolymers: two different homopolymers A and B are linked via a covalent bond (A-A-A-A---A-A-A-A-A-A) m -(B-B-B-B-B-B----B-B-B-B) n name: Poly(A-block-B) or short P(A-b-B) and not PA-b-PB triblock copolymers: three different homopolymers A, B and C are linked via a covalent bond (A-A-A-A---A-A-A-A) m -(B-B-B-B----B-B-B-B) n -(C-C-C-C----C-C-C-C) p name: Poly(A-block-B-block-C) or short P(A-b-B-b-C) and not PA-b-PB-b-PC Important parameters: N degree of polymerization f composition (block ratio) χ Flory-Huggins parameter in comparison to a polymer mixture of A and B is χ A-b-B χ A+B caused by a slight change of the entropic contribution to the polymer-polymer interaction parameter 10.2 Micro-phase separation A and B are incompatible: in polymer blend phase separation into macro domains, is replaced in block copolymers by micro-phase separation due to the covalent bond between both size of domains is given by the chain length (degree of polymerization) Example: Lamella princeton.edu Chapter10 1

2 Reversible transition between ordered and disordered state: - common for the blocks to spontaneously self-assemble ("order") into a diversity of meso-phases - intermix freely at sufficiently high temperature, or when sufficiently diluted with solvent, generating the "disordered" structure a) symmetric, monodisperse diblock copolymers (f=0.5): mean-field theory (Bates 1990) χn<<10.5: homogeneous melt chains are not stretched and described by Gaussian distribution with R g N 0.5 χn<10.5: χn 10.5: fluctuations are present in the disordered melt 15% deviation of the center of mass from a Gaussian chains with R g N 0.72 WSL (weak segregation limit): weak demixing repulsion between the blocks is that large that phase separation occurs sinusoidal shape of concentration profile phase transition of 2. order at the micro-phase separation temperature T MST periodicity at T MST : D= 3.2 R g N 0.5 with chain length dependence χn= n -1/3 with N Ginzburg-parameter which is as well proportional to M w χn>>10.5: SSL (strong segregation limit): strong demixing increased immiscibility results in reduced interface between blocks stretching of chains is increased Rectangular shpe of concentration profile periodicity at T MST : D bn 2/3 χ 1/6 structure: lamella (f=0.5) else other geometries comparison of concentration profiles in SSL-WSL (1d cuts through the volume) for given chemical composition of block copolymer it depends on the degree of polymerization Chapter10 2

3 Example: P(S-b-pMS) with χ=a+b/t and A= and B=6.8K at T=300K ΣM w χn Regime 42k 4.4 disordered 84k 8.8 disordered 123k 12.8 WSL 230k 24.0 SSL 346k 36.1 SSL critical value for symmetric diblock copolymer is (χn) c =10.5 b) asymmetric, monodisperse diblock copolymers (f 0.5): mean-field theory (Bates 1990) in case the length of a block is not sufficient to be space filling in a lamella geometry, other geometries are installed (spheres, cylinders, gyroid) spheres of B in a matrix of A (body centered cubic lattice) cylinders of B in a matrix of A (hexagonal lattice) dual labyrinths of B in a matrix of A (double gyroid) alternating sheets (lamellae) of A and B dual labyrinths of A in a matrix of B msri.org phase diagram in χn(f) space cylinders of A in a matrix of B spheres of A in a matrix of B 10.3 Phase diagram Weak segregation limit (WSL) theories for order and disorder in diblock copolymers: (a) mean-field theory and (b) fluctuation theory Chapter10 3

4 a) mean-field theory (Leibler, 1980) 1. only at f=0.5 direct transition from disordered into lamella phase 2. critical point at (χn) c = calculated 3. for f 0.5 always intermediate phases b) fluctuation theory (Fredrickson and Helfhand, 1987) 1. for finite degree of polymerization the disordered regime is extended to larger values of χn 2. direct transition from disordered into lamella phase in a broad range around f=0.5 2 [ ] critical point at χ N ) = ( ρ ) ( c R g c because χ 1/T phase transition happens at lower temperature T c) self-consistent field theory: far more Fourier terms are used to represent the segment profiles; good matching with experimental results Comparison of different theoretical approaches: 1/ 3 commonly temperature T is changed to probe phase diagram Chapter10 4

5 P(A-b-B) self-assembly: Selection of topology by used block-ratio A/B Matsen and Bates; Macromolecules 29, 1091 (1996) calculated phase diagram is symmetric Measured phase diagram: not existing for many block copolymers, but a few examples only Example: P(S-b-I) in dependence of ratio of PI block A. K. Khandpur, S. Forster, F. S. Bates, I. W. Hamley, A. J. Ryan, W. Bras, K. Almdal, K. Mortensen, Macromolecules 28, 8796 (1995) asymmetric very complex structures ordered phases shifted to higher values of χn = disordered phase extended transitions between different phases possible Chapter10 5

6 microstructure of the copolymer from SAXS/SANS and TEM Triblock copolymer: significantly increase complexity more stable phases depending on the type of A,B, C blocks F.S. Bates, G.H. Fredrickson, Phys Today, 52, 32 (1999) Rod-coil copolymer: significantly increase complexity A B Chapter10 6

7 10.4 Phase transitions Transition from order to disorder and between different ordered phases which differ in the micro-structure ODT: order-disorder transition OOT: order-order transition determined by either rheology or small-angle X-ray (or neutron) scattering (SAXS or SANS): abrupt increase in dynamic shear modulus (G ) or change in the positions of higher order peaks in SAXS profiles with increasing temperature Rheology: ODT = disorder-to-order transition (DOT) at P(S-b-I-b-S) using differential scanning calorimetry (DSC): Schematic of the enthalpy change near the OOT between HEX and BCC microdomains Kim et al.; Macromolecules 1998, 31, is an exothermic process due to the undulated cylinders formed during the transition alternative: influence of pressure p change example glass transition temperature increases with pressure: T g p P(S-b-pMS) T g = *Δp/kbar The dynamic slows down at higher pressures inverse to the temperature. Vilgis (2000) χ p Chapter10 7

8 Pressure experiments: Stamm (1999) Pressure jumps with subsequent relaxation: Stamm (1999) OOT transitions explained within the Kolmogorov model n t intensity I( t) = I 1 exp τ with grain dimension d = n-1 and time constant τ Chapter10 8

9 10.5 Block copolymer films When confined to a thin film, the orientation of block copolymer domains with respect to the substrate surface is crucial for many applications. two different interfaces: substrate and air (A) Lamellae lying parallel to the substrate, (B) lamellae aligned perpendicular, (C) cylinders lying parallel, (D) cylinders perpendicular, and (E) spheres. R. A. Segalman; Materials Science and Engineering R 48 (2005) In contrast to the films confined between two hard walls, the period of the parallel lamellae in the free-surface film can reach its equilibrium value. Assumptions: strong segregation theory, symmetric diblock copolymer lamellar orientation in thin, free-surface films: Phase diagram Igor I. Potemkin; Macromolecules, 2004, 37, 3505 Phase diagram of a supported, lamellar diblock copolymer film in variables x A = S A /[γ ĀB (n + 1)] and x B = S B /[γ ĀB (n + 1)], where S A and S B are the spreading parameters of polymers A and B, γ ĀB is the dimensionless surface tension coefficient of A B interfaces, and n is the total number of internal A and B layers of the film, each with the thickness d/2. The interaction with the interfaces determines the resulting orientation. Typically this interaction gives rise to high degree of orientation. direct result of surface and interfacial energy minimization new morphologies can result Chapter10 9

10 Block Copolymer thick films: Whereas in the bulk block copolymers undergo a well defined order-disorder transition, in thick films the interaction with the interfaces introduces order at temperatures well above this temperature. Example: P(S-b-D-MMA) (523.2 nm) probed with neutron reflectivity at different temperatures (1) reflectivity drops markedly above a critical momentum (2) first-order reflection observed position no significant T dependence broadens and diminishes in intensity at higher T (3) higher-order reflection observed at ~0.038 Å -1 and ~0.056 Å -1 at 135 C more narrow and intense with increasing film thickness (4) higher-order reflection gradually lost only a ridge is seen ridge is less pronounced with increasing T and film thickness A. Menelle, et.al., Phys. Rev. Lett. 68 (1992) Minimization of free energy density: Surface induced ordering above the T ODT (Fredrickson, 1987) φ + / z 2πz φ A ( z) = φ A + exp cos + δ cosδ ξ D the component with the higher surface affinity enriches at the interfaces in the disordered phase (volume is disordered) due to the chemical bonds between both blocks a zone with enrichment of the other block follows a sin-shaped modulation with the periodicity D results with increasing distance from the interface the amplitude of the modulation is decaying correlation length ξ δ additional phase shift of modulation possible Chapter10 10

11 It follows: D=4πR g (Nχ-Nχ S +8 3) -1/2 ξ=-2r g (Nχ-Nχ S ) -1/2 δ=arctan(d/2πξ) and at T ODT is χ=χ S with D ODT =3.38 R g surface-induced ordering: decay length ξ: damping of the concentration oscillation from air or substrate interface ξ undergoes abrupt change at T,t transition from partially to fully ordered at T,t A. Menelle, et.al., Phys. Rev. Lett. 68 (1992) transition temperature of partially to fully ordered state depends strongly on film thickness A. Menelle, et.al., Phys. Rev. Lett. 68 (1992) Block Copolymer thin films: phenomenological free energy model with assumptions 1) system confined between infinite, parallel plates 2) A and B block have equal number of segments 3) A and B block present same preference to surface 2m F ( ) h = λ + + 2Γ + δ Fn 3 λ mλ 2 with normalized period λ=l/l 0 and the normalized surface tensions Γ=γ AS /γ AB and δ=(γ BS -γ AS )/γ AB Chapter10 11

12 horizontal asymmetric is never favored D. G. Walton, et.al., Macromolecules 27 (1994) The wetting behavior can be tuned by the use of polymer brushes. a) horizontal symmetric (both sides are PS) b) horizontal asymmetric (bottom PMMA, top PS) c) mixed lamellar vertical (bottom) horizontal (top) d) vertical E. Huang, et.al., Macromolecules 32 (1999) Film has two interfaces: substrate-polymer and polymer-air superposition of two surface-induced waves 2/3 lamella with periodicity D M w Example: P(S-b-pMS) with M w =230k results in D=45 nm M w =84k D=23 nm a) one block has preferred interaction with both walls enhanced structure formation if l=nd b) each block prefers another wall enhanced structure formation if l=(n+0.5)d Problem: film thickness does not match these conditions of optimum enthalpy formation of islands or holes depending on the amount of excess material, placed on a homogeneous film with film thickness D formation of large domains on micrometer scale Alamgir Karim, NIST Chapter10 12

13 Block Copolymer ultra-thin films: The self-assembly of block copolymers is fundamentally influenced by the boundary conditions including film thickness. A. Knoll, et al., Phys. Rev. Lett (2002) Parts (a) and (b) are phase SPM images of a thin poly(styrene-b-butadiene-bstyrene) triblock copolymer which reconstructs as a function of film thickness. Part (c) is a schematic height profile of the phase images shown above, while part (d) is a simulation of the same block copolymer. Comparison of film thickness l with intrinsic properties of polymer such as the radius of gyration R g and the volume periodicity D Ultra-thin defined via D l no longer sufficient space to develop full lamella with periodicity D a) D l: build-up of lamella with reduced periodicity L<D right after preparation via spin-coating an ordered structured has evolved in case of P(S-b-pMS) but not for P(S-b-MMA), due to differences in the surface energies γ PS > γ PpMS but γ PS γ PMMA films typically stable against dewetting although thin and additional effects such as correlated roughness possible b) D >> l and R g >l: confined (ultra-)thin films depending on substrate a perpendicular lamella more favored film can show instability: dewetting possible Chapter10 13

14 Example: P(S-b-pMS) on Si-SiOx advantage of slow process due to selected temperature Müller-Buchbaum et al.; Macromolecules 35, 2017 (2002) Ordered block Copolymer films: Micro-phase separation structure typically lacks long-ranged order this imposes a challenge for the creation of highly ordered block copolymer films. The orientation ranges from random (left) when the zone is broad and fast to highly oriented (right). Alamgir Karim, NIST In recent years several different approaches have been developed. They can be summarized as directed self-assembly (DSA) of block copolymers (= topographically or chemically patterned templates to guide the orientation and placement of block copolymer micro-domains over macro size areas). Chapter10 14

15 a) Kramer and co-workers pioneered the concept of graphoepitaxy of block copolymer films on topographically patterned substrates R. A. Segalman, et al., Adv. Mater. 2001, 13, b) Kim and co-workers demonstrated the fabrication of gratings by a corrugation-directed self-assembly process H. C. Kim, et al., Nanotechnology 2008, 19, c) Kim and co-workers reported the soft graphoepitaxy of block copolymer assembly with disposable photoresist confinement S.-J. Jeong, et al., Nano Lett. 2009, 9, d) Ross and co-workers described the templated self-assembly of block copolymers in trenches, photo lithographically placed on a surface and also showed a controlled self-assembly of block copolymers using the width of modulated topographical templates J. Y. Cheng, et al., Nat. Mater. 2004, 3, d) Russell and co-workers investigated the chemically heterogeneous surfaces to control the ordering and orientation of block copolymer microdomains L. Rockford, et al., Phys. Rev. Lett. 1999, 82, Chapter10 15

16 e) Nealey and co-workers studied the epitaxial behavior of block copolymers on chemically patterned substrates S. O. Kim, et al., Nature 2003, 424, f) Russell and co-workers demonstrated the use of shallow trenches to overcome the limitation of the grain size of block copolymers due to the width of trenches S. W. Hong, et al., ACS Nano 2011, 5, g) Russell and co-workers used faceted surfaces of commercially available sapphire wafers to guide the self-assembly of block copolymer microdomains into oriented arrays with quasi long-range crystalline order over arbitrarily large wafer surfaces (C) Smooth PS-b-PEO (M n = 43.0 kg/mol) thin films were spincoated onto these surfaces that, upon annealing in o-xylene vapors (D), produced highly ordered cylindrical micro-domains oriented normal to the film surface. S. Park, et al., Science, 2009, 323, Chapter10 16