Rapid Quench Structure Formation: Fabrication of periodic network morphologies and their stabilization via crosslinking in diblock copolymers

• Applicant: Professor Dr. Marcus Müller
• Subject Area: Experimental and Theoretical Physics of Polymers ; Polymer Materials ; Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics ; Theoretical Chemistry: Molecules, Materials, Surfaces
• Term: from 2013 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 244599224

• Final Report Year: 2018

Final Report Abstract

Novel, periodic morphologies of block copolymers have attracted abiding interest because of their beneficial mechanical properties and high interface-to-volume ratio. However, they are often only metastable, and traditional strategies aim at increasing their thermodynamic stability by augmenting the complexity of the molecular architecture or mitigating packing frustration via polydispersity or blending. In this project we have demonstrated by large-scale computer simulations as well as self-consistent field theory that one can reproducibly fabricate a wealth of novel, metastable mesostructures (inter alia Schoen’s I-WP and F-RD morphologies, as well as positionally and orientationally ordered ellipsoid domains) by processdirected self-assembly. Our strategy relies on the time scale separation between (i) the rapid change of thermodynamic state (quench), (ii) the thermodynamically driven, spontaneous structure formation from the highly unstable morphology after the quench to the metastable mesostructure, and (iii) the escape from the metastable mesostructure to equilibrium via thermally activated nucleation. Three prototypical processes have been applied to equilibrium mesophases in order to induce a transformation into a different, metastable mesostructure: a rapid pressure of a compressible AB-diblock copolymer system, where the components are characterized by different compressibilities; a transformation where a portion of the molecular contour rapidly changes its chemo-physical properties; a mechanical step-strain deformation. The systematic exploration of the processing parameters highlights the following general findings that may serve as a guide to devise processing protocols for fabricating specific mesostructures: The transformation path does not simply follow the steepest descent on the free-energy landscape but, instead, the local conservation of the densities have to be duly accounted for. We have generalized the string method such that it not only correctly identifies saddle-points and metastable minima but also the path between them in particle-based simulations. Since the spontaneous relaxation from the process-generated unstable state to the metastable free-energy minimum occurs on a similar time scale as the relaxation of the molecular conformations (provided that the change of the morphology occurs within a unit cell of the spatially periodic structure), the chain conformations cannot be assumed to be in equilibrium with the instantaneous density distribution – an assumption inherent in dynamic self-consistent field theory. Instead, our studies suggest that the variance of the first Rouse mode is an appropriate, additional, slow variable that quantifies the non-equilibrium of the molecular conformations. Processing often does not result in a transition between free-energy basins but, instead, the change of the thermodynamic control parameters alters the free-energy landscape and thereby the concomitant morphology that corresponds to the minimum of the basin. Thus, the variation of the morphology with process parameters (e.g., pressure or composition of the diblock copolymer) qualitatively differs from the equilibrium phase behavior. These findings illustrate the usefulness of process-directed self-assembly and identify challenges for a development of field-theoretic approaches that account for (i) the non-equilibrium molecular conformations and (ii) the interplay between the single-chain dynamics and the collective dynamics of the morphology.

Publications

• Directing the self-assembly of block copolymers into a metastable complex network phase via a deep and rapid quench, Phys. Rev. Lett. 111, 267801 (2013)
  M. Müller and D.-W. Sun
  
• Living polymer systems at a solid substrate: Computer simulation of a soft, coarse-grained model and self-consistent field theory, Macromolecules 48, 6016 (2015)
  D.-W. Sun and M. Müller
  
• Process-directed self-assembly of block copolymers: A computer simulation study, J. Phys.: Condens. Matter 27, 194101 (2015)
  M. Müller and D.-W. Sun
  
• Process-accessible states of block copolymers, Phys. Rev. Lett. 118, 067801 (2017)
  D.-W. Sun and M. Müller
  
• Fabrication of ellipsoidal mesostructures in block copolymers via a step-shear deformation, Macromolecules 51, 275 (2018)
  D.-W. Sun and M. Müller