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Two-Dimensional Self-assembled Patterns in Diblock Copolymers

Two-Dimensional Self-assembled Patterns in Diblock Copolymers. Peko Hosoi, Hatsopoulos Microfluids Lab. MIT Shenda Baker, Dept. Chemistry Harvey Mudd College Dmitriy Kogan (GS), CalTech. Experimental Setup. Langmuir-Blodgett trough Polystyrene-Polyethyleneoxide (PS-PEO) in Chloroform

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Two-Dimensional Self-assembled Patterns in Diblock Copolymers

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  1. Two-Dimensional Self-assembled Patterns in Diblock Copolymers Peko Hosoi, Hatsopoulos Microfluids Lab. MIT Shenda Baker, Dept. Chemistry Harvey Mudd College Dmitriy Kogan (GS), CalTech SAMSI Materials Workshop 2004

  2. Experimental Setup • Langmuir-Blodgett trough • Polystyrene-Polyethyleneoxide (PS-PEO) in Chloroform • Deposit on water • Chloroform evaporates • Lift off remaining polymer with silicon substrate • Image with atomic force microscope (AFM) SAMSI Materials Workshop 2004

  3. Continents ( > 500 nm) All features ~ 6 nm tall High Stripes (~100 nm) concentration Low Dots (70-80 nm) Photos by Shenda Baker and Caitlin Devereaux Experimental Observations SAMSI Materials Workshop 2004

  4. (CH - CH2)m - (CH2 - CH2 - O)n ……. …….. bbbbbbbbbbbhhhhh Polystyrene-Polyethyleneoxide (PS-PEO) • Diblock copolymer • Hydrophilic/hydrophobic SAMSI Materials Workshop 2004

  5. Physical Picture Marangoni Diffusion Evaporation Entanglement SAMSI Materials Workshop 2004

  6. Mathematical Model Small scales \ Low Reynols number and large damping. Approximate Velocity ~ Force (no inertia). • Diffusion - Standard linear diffusion • Evaporation - Mobility deceases as solvent evaporates. Multiply velocities by a mobility envelope that decreases monotonically with time. We choose Mobility ~ e-bt. • Marangoni - PEO acts as a surfactant thus Force = -kST c, where c is the polymer concentration. • Entanglement - Two entangled polymers are considered connected by an entropic spring (non-Hookean). Integrate over pairwise interactions … SAMSI Materials Workshop 2004

  7. Entanglement Pairwise entropic spring force between polymers1 (F ~ kT) Relaxation length ~ where l = length of one monomer and N = number of monomers Find expected value by multiplying by the probability that two polymers interact and integrating over all possible configurations. 1 e.g. Neumann, Richard M., “Ideal-Chain Collapse in Biopolymers”, http://arxiv.org/abs/physics/0011067 SAMSI Materials Workshop 2004

  8. More Entanglement Integrate pairwise interactions over all space to find the force at x0 due to the surrounding concentration: Expand c in a Taylor series about x0: where SAMSI Materials Workshop 2004

  9. Force Balance and Mass Conservation Convection Diffusion: Time rescaled; cutoff function due to “incompressibility” of PEO pancakes. SAMSI Materials Workshop 2004

  10. Numerical Evolution Experiment concentration time SAMSI Materials Workshop 2004

  11. Linear Stability PDE is stable if where c0 is the initial concentration. Fastest growing wavelength: Recall s is a function of initial concentration SAMSI Materials Workshop 2004

  12. Quantitative comparison with Experiment Triangles and squares from linear stability calculations (two different entropic force functions) Linear stability SAMSI Materials Workshop 2004

  13. Conclusions and Future Work • Patterns are a result of competition between spreading due to Marangoni stresses and entanglement • Quantitative agreement between model and experiment • Stripes are a “frozen” transient • Other systems display stripe dot transition e.g. bacteria (Betterton and Brenner 2001) and micelles (Goldstein et. al. 1996), etc. • Reduce # of approximations -- solve integro-differential equations SAMSI Materials Workshop 2004

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