Session P02: Non-Equilibrium and Process-Dependent Mesoscale Structures of Polymeric Compounds

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Long-lived micellar structure in the disordered state has been postulated to be the origin of complex sphere-forming phases in thermal processing of block polymers. The confirmation of this phenomenon is contingent on developing a deep understanding of the behavior of disordered micelle near the order-disorder transition. We investigated the effect of conformational asymmetry to the compositionally asymmetric disordered state in finite-length diblock copolymer using Monte Carlo Field-Theoretic Simulation (MCFTS). MCFTS includes fluctuations in the composition field which natively produces disordered micelles at sufficient segregation strength. We examined the structure of the disordered state through both real space method and its structure factor. Our calculations seek to confirm existing theoretical predictions on the effects of conformational asymmetry over different segregation strengths and provide new understanding to the behavior of the disordered phase near the order-disorder transition.   

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Block copolymer micelles have unrealized potential as model spherical particles to explore the phase states and phase transition kinetics. However, one of the current challenges is that the precise experimental characterization of block copolymer micelles as a function of thermodynamic parameters such as temperature and micelle concentration is difficult. A simple model-free inverse Fourier transform method using a modification function to characterize block copolymer micelles will be presented. By employing the model-free inverse Fourier transform method, the temperature dependence of the size of strongly-segregated micelles in water, including the corona domain, is successfully extracted.   

Live

Solution-cast films of sulfonated block copolymers (SBC) are investigated for applications in water purification, gas separations, and fuel cells. The influence of organic solvent composition on the self-assembled morphology is well known. Trace amounts of water might also play a role in the self-assembly process, as water disrupts the hydrogen bond interactions between the sulfonic acid groups, but this point has not been examined in prior studies. In this work, we examine (1) the structure of an SBC in an organic solvent mixture with varying molar ratios of water to sulfonic acid (λ); and (2) the morphology of the corresponding solvent-cast films. In solutions with λ = 0, the SBC adopts a disordered structure. The addition of trace water (λ = 3.2) to SBC solutions drives a rapid self-assembly into an ordered lamellar structure. When processed into films, trace water in the solvent has little effect on the SBC morphology, but the ambient humidity is a critical process parameter: under dry conditions, the films have a poorly developed structure, while humidity facilitates the assembly of well-defined lamellae. These outcomes demonstrate that trace water can strongly impact the self-assembly kinetics in block copolymer electrolytes.   

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Nonsolvent induced phase separation (NIPS) occurs when a polymer solution is brought into contact with a miscible nonsolvent, leading to the precipitation of a polymer-rich phase. Because of its simplicity, NIPS processes are widely used to generate a variety of microstructures in polymer materials such as membranes and micro/nanoparticles. Despite its prevalence, predicting and controlling the microstructure generated by NIPS remains a difficult challenge, owing to the complex interactions between the diffusive transport, hydrodynamics and phase-separation kinetics in the process. In our approach, we use simulations of a phase-field model of a polymer solution to examine the effect of mass transfer, hydrodynamics and geometry on the formation of microstrucure. In particular, we study the NIPS process in polymer droplets, where we examine the effect of droplet size, shape, and composition on the resulting microstucture. We also examine the impact of finite solvent/nonsolvent miscibility on the kinetics and microstructure of the phase separation.   

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The free-energy landscape of multi-component polymer systems is rough and characterized by multiple metastable minima. It depends on thermodynamic control parameters such as temperature or pressure/strain. Process-directed self-assembly refers to processes that reproducibly trap the kinetics of structure formation that ensues after a sudden change (“quench”) of the thermodynamic state into a desired, (meta)stable target state [1]. Copolymer materials are ideal model systems to explore how one can deterministically direct the assembly of multicomponent polymer systems because the lifetime of metastable structures is large and an accurate mean-field description (SCFT) for equilibrium properties is available.
The talk will discuss computational challenges for predicting the kinetics of process-directed self-assembly of copolymers by particle-based and continuum models [2-5] such as the coupling between the time evolution of the morphology and the underlying diffusive dynamics of the copolymers [4,5], and the role of nonequilibrium molecular conformations [3]. Applications to the formation of nonequilibrium morphologies with unusual periodic or helical structures in the bulk or confined geometry will be presented [5-7].

[1] M. Müller, Prog. Polym. Sci. 101, 101198 (2020)
[2] M. Müller and J.C. Orozco Rey, Mol. Syst. Des. Eng. 3, 295 (2018)
[3] M. Müller, P. Sollich, D.W. Sun, Nonequilibrium molecular conformations in polymer self-consistent field theory, preprint
[4] G. Wang, Y. Ren, and M. Müller, Macromolecules 52, 7704 (2019)
[5] J. Rottler and M. Müller, ACS Nano 10.1021/acsnano.0c06433
[6] L. Schneider, G. Lichtenberg, D. Vega, and M. Müller, Symmetric diblock copolymers in cylindrical confinement: A way to chiral morphologies? ACS Appl. Mater. Interfaces in press
[7] D.W. Sun and M. Müller, Phys. Rev. Lett. 118, 067801 (2017)   

Live

Polymer thermosets are frequently modified by the addition of a secondary polymer that phase separates during the thermoset polymerization. Generally speaking, it is challenging to control domain sizes in such materials beyond a limited range. We introduce an approach to polymerization-induced phase separation in epoxy-amine networks that enables domain sizes to be tuned over a broad range, from nanoscale to macroscale. The key element of this approach is a balance of multiple reactive species (e.g., amine curing agents) that simultaneously favor and disfavor phase separation. We demonstrate how ensuing, systematic variation of the length scale of phase separation leads to exquisite control over the curing behavior and glass transition of the resultant materials. In particular, we discuss application to rubber-toughened epoxies, where mechanical properties are critically impacted by rubber particle size. These results and insights may help guide the future design of polymer thermosets with precisely targeted microstructures and consequent thermomechanical properties.   

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Reactive blending of immiscible polymers is an important process for synthesizing polymer alloys with superior properties. Polymers with reactive end groups are processed to generate copolymer at the interface, which compatibilizes the blend. Interfaces between the reacting polymers have been observed to roughen spontaneously, resulting in a microemulsion. We quantify the onset of interfacial roughening in reactive polymer blends in a layered geometry, using a phase-field model. We study this phenomenon for different interface shapes, layer thicknesses, and reaction rates specified by a Damkohler number (Da_f), under static conditions. For a fixed Da_f, the reaction conversion and microstructure of systems with layers of same thickness evolve similarly. The conversion and the onset of roughening is slower for systems with thicker layers, and those specified by a smaller Da_f. We also show that weak thermal fluctuations accelerate the conversion, leading to a faster onset of interfacial roughening.   

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Solubility-induced phase separation techniques have arisen as popular methods for preparing porous polymeric materials, yet controlling the resulting pore size and tortuosity is difficult as it depends on heat and mass transport into the pre-cursor polymer solution. To help address the shortfalls of these and other conventional techniques, we introduce a new phase separation technique involving thermal processing of colloidal templates based on self-assembling nanoemulsions to create polymer networks with bicontinuous pore morphologies. Controlling a combination of temperature- and kinetically-dependent nanodroplet assembly with photocuring of polymer networks in one of the liquid phases produces bicontinuous structures across a range of length scales, which can be rendered porous through gentle solvent exchange to eliminate the colloidal template. We demonstrate control over the morphology and length scales of the droplet template structure by changing the temperature history and processing time during colloidal assembly and phase separation before photo-induced arrest. This control of processed structure is successfully translated to porous polymer networks, providing a new route to porous structures that is orthogonal to polymer chemistry.   

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Most soft materials are made by processing techniques that render their final properties a function of their process history and not just their equilibrium structure. One example is the bicontinuous interfacially jammed emulsion gels (bijels), a material with numerous potential applications. Bijels are formed when solid particles get jammed at the interface between two immiscible liquids undergoing a phase separation, kinetically arresting this system. In this work, we aim to quantitatively understand the surface energy of the fluid-fluid-particle interface and how these forces influence jamming. We adopt an approach that incorporates solid particles into a phase field model, similar to the Fluid Particle Dynamics method. This approach has many benefits, including transparent methods for calculating surface tension, particle-particle interactions, and hydrodynamic interactions in dense colloidal suspensions, and it avoids complicated and costly methods for tracking particle boundaries. Our preliminary results suggest that purely repulsive particles may not be stable enough at the fluid-fluid interface to jam, suggesting that attractive forces may be needed for bijel stability.   

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Understanding the kinetic pathways of self-assembly in block copolymers (BCPs) has been a long-standing challenge, mostly due to limitations of in-situ monitoring techniques. Here, we demonstrate a novel approach that uses optical birefringence, determined by spectroscopic ellipsometry (SE), as a measure of domain formation in cylinder- and lamellae- forming BCP films. The rapid experimental acquisition time in SE (ca. 1 sec) enables monitoring of the assembly/disassembly kinetics of BCP films during solvent-vapor annealing (SVA). We demonstrate that upon SVA, BCP films form ordered domains that are stable in the swollen state but disorder upon rapid drying. Surprisingly, the disassembly during drying strongly depends on the duration of solvent exposure in the swollen state, explaining previous observations of loss of order in SVA processes. SE thus allows for decoupling BCP self-assembly and disordering that occurs during solvent annealing and solvent evaporation, respectively, which is difficult to probe using other, slower techniques.   

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Water drives the self-assembly of (non)ionic diblock oligomers into spatially periodic lyotropic liquid crystals (LLCs), including lamellae, networks, hexagonally-packed cylinders (HEX), and 3D micelle packings. Beyond high symmetry body-centered cubic (BCC) and cubic close-packed micellar phases, diblock oligomers also form tetrahedrally closest-packed Frank-Kasper (FK) A15 phases. In spite of the low molecular weights of the constituent amphiphiles, we recently demonstrated that judicious thermal processing of an A15 LLC enables formation of a surprisingly long-lived, non-equilibrium state. Specifically, heating an A15 phase drives transitions to BCC and HEX phases at elevated temperatures. Quenching these LLCs unexpectedly drives formation of a remarkably well-ordered, tetragonal FK sigma phase comprising 30 quasispherical micelles per unit cell as a metastable state, which takes ~150 days of quiescent annealing at 22 °C to recover the equilibrium A15 structure. The formation and metastability of the sigma phase is contingent on sample quench rate, quench depth, and annealing temperature. These slow order-order phase transformation kinetics stem from a complex interplay of temperature-dependent phase nucleation and growth rates, which are coupled to the rates of micelle size reconfiguration by interparticle chain exchange and of spatial rearrangement of the micelles. These findings highlight the importance of processing path-dependence on the observed mesophases of self-assembled soft materials.