Supporting Information for: Rapid Ordering in. Wet Brush Block Copolymer/Homopolymer

Transcription

1 Supporting Information for: Rapid Ordering in Wet Brush Block Copolymer/Homopolymer Ternary Blends Gregory S. Doerk* and Kevin G. Yager Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, United States Figure S1. SEMs of disordered or poorly ordered domain structure in thin films of ternary blends composed of lamellae forming PS-b-PMMA with ~3 kg/mol PS and PMMA homopolymers (in equal parts) annealed for 5 minutes at 250 C. The blends are: (a) The 36 kg/mol BCP with 70% (w/w) homopolymer and (b) the 74 kg/mol BCP with 90% (w/w) homopolymer. [Type text] [Type text] S1

2 Figure S2. Degree of order for a 36 kg/mol BCP blended with 50% (w/w) of ~3 kg/mol homopolymer annealed at 210 C for more than 21 hours in a vacuum oven. (a) SEM of the annealed sample. (b) Plot of correlation length (ξ) as a function of annealing time for neat and 50% blend samples at 210 C on a hot plate. The correlation length measured for the blend sample baked for > 21 hours in a vacuum oven at the same temperature is included (black triangle). The lines and equations represent fits to a power law relationship, ξ = At ν. The dashed red line is an extrapolation of the fit for the blend samples baked for a short time. [Type text] [Type text] S2

3 Figure S3. SEM of a blend of the 36 kg/mol BCP with 50% (w/w) ~3 kg/mol homopolymer baked at 250 C for 20 minutes. Figure S4. Differential scanning calorimetry traces for 3.5 kg/mol PS (bottom, red), 3 kg/mol PMMA (top, blue), and 36 kg/mol PS-b-PMMA diblock copolymer with ~50% PS by volume (middle, purple). [Type text] [Type text] S3

4 Figure S5. Plot of ξ as a function of annealing time at 220 C for a 50% (w/w) blend of the 36 kg/mol BCP with ~6 kg/mol homopolymer. The line and equation represent a fit to a power law relationship, ξ = At ν. Inset: SEM of the lamellar pattern from this blend after 1 hour of annealing (scale bar = 500 nm). Figure S6. SEMs of thin films of a 70% (w/w) blend of the 36 kg/mol BCP with ~6 kg/mol homopolymer annealed for 5 minutes at 250 C. Images (a) and (b) are from the same sample, taken at different magnifications. [Type text] [Type text] S4

5 Figure S7. SEM of a blend of the 36 kg/mol BCP with 50% (w/w) ~12 kg/mol homopolymer baked at 220 C for 20 minutes. Discussion: Estimation of Critical Homopolymer Segregation Strength Based on prior theoretical calculations, 1 the boundaries between microphase separated, macrophase separated, and disordered regions of the ternary BCP - homopolymer blend phase diagram along the symmetric isopleth plane (equal homopolymer volume fractions) are predicted to meet at the Lifshitz point, whose coordinates (ϕ H,L and χn L ) are given by: φ H,L = 1 (1 + 2α 2 ) (S1) χn L = 2(1 + 2α 2 ) α (S2) where α = N H N. The above formulas are valid for α < 1. For a direct transition from microphase separated domains to a disordered phase with increasing homopolymer volume fraction that does not pass through any larger multi-phase regions (e.g. microemulsions), as in the case of the wet-brush phase diagram (Figure 6b in the main text), χn L should be greater than χn of the BCP. Using the definition of alpha, an expression for the critical value of the homopolymer segregation strength, (χn H ) crit can be determined from equation S1: (χn H ) crit = (χn)2 (χn) (χn) (S3) [Type text] [Type text] S5

6 This expression is the solution to a quadratic equation where only the lower root is retained as the upper root implies α > 1. The condition of χn L > χn is satisfied when χn H < (χn H ) crit. Plotting the value of (χn H ) crit as a function of χn in (Figure S5) shows that it asymptotically approaches 2 for large χn and deviates to a slightly higher value of ~2.17 at the neat BCP order-disorder transition of χn The asymptotic approach of (χn H ) crit to 2 for large χn is natural, as by inspection φ H,L 1 and χn L 2 α as α 0. Note that this analysis can only provide an approximate estimation as it does not account for regions in the phase diagram with more than two phases and the impact of thin film confinement. Figure S8. Calculated values of (χn H ) crit as a function of χn using equation S3. The dashed line is a guide to the eye representing a constant value of 2. References (1) Broseta, D.; Fredrickson, G. H. Phase Equilibria in Copolymer/homopolymer Ternary Blends: Molecular Weight Effects. J. Chem. Phys. 1990, 93, [Type text] [Type text] S6