Non-equilibrium self-assembly of block copolymers offers a pathway to engineer nanostructures with tailored morphologies that deviate from equilibrium states. This approach leverages kinetic control during processing to achieve metastable or kinetically trapped configurations, enabling the fabrication of materials with unique properties. Key factors influencing non-equilibrium assembly include flow-induced alignment, rapid quenching, and the formation of kinetically trapped structures. Understanding these mechanisms is critical for designing functional materials for applications ranging from nanolithography to advanced coatings.

Flow-induced alignment is a powerful tool for directing the orientation of block copolymer microdomains. Under shear or extensional flow, the chains experience forces that promote alignment along the flow direction. For example, polystyrene-block-polyisoprene copolymers subjected to steady shear flow exhibit lamellar domains oriented parallel to the flow direction at low shear rates, while perpendicular alignment dominates at higher rates. The degree of alignment depends on the interplay between the applied shear rate and the relaxation time of the polymer chains. Flow fields can also induce transitions between morphologies, such as from spherical to cylindrical micelles, when the imposed deformation overcomes the energy barriers associated with equilibrium phase transitions. Microfluidic confinement further enhances alignment by coupling shear effects with geometric constraints, yielding highly ordered nanostructures over large areas.

Rapid quenching from a disordered state is another strategy to access non-equilibrium morphologies. When a block copolymer melt or solution is cooled abruptly below the order-disorder transition temperature, the system lacks sufficient time to reach equilibrium, resulting in metastable structures. For instance, rapid cooling of polystyrene-block-polybutadiene can produce a disordered bicontinuous network instead of the equilibrium lamellar phase. The quenching rate must exceed the characteristic relaxation time of the copolymer to suppress equilibrium ordering. Solvent evaporation rate plays a similar role in solution casting; fast evaporation kinetically traps non-equilibrium configurations, such as perforated lamellae or disordered micellar aggregates. The final morphology depends on the competition between the rate of solvent removal and the chain mobility required for reorganization.

Kinetically trapped structures arise when intermediate states during self-assembly become frozen due to energy barriers or vitrification. In block copolymers with high glass transition temperatures, such as polystyrene-block-poly(methyl methacrylate), the mobility of one block may be severely restricted upon cooling, preventing the system from reaching equilibrium. This leads to structures like distorted cylinders or partially ordered grains. External fields, such as electric or magnetic fields, can also guide the assembly process toward non-equilibrium states by selectively aligning one block while kinetically trapping defects. The stability of these structures depends on the energy landscape; some may relax over time, while others remain indefinitely trapped if the energy barrier to reorganization is too high.

Processing-structure relationships in non-equilibrium assembly are governed by several parameters. Molecular weight and block asymmetry influence the kinetic pathways by altering chain entanglement and segregation strength. High molecular weight copolymers exhibit slower dynamics, making them more susceptible to kinetic trapping. The choice of solvent in solution processing affects the assembly kinetics; selective solvents for one block can stabilize non-equilibrium micellar shapes, such as ellipsoids or worms, instead of equilibrium spheres. Processing temperature is equally critical, as it determines the chain mobility and the rate of structure evolution. For example, annealing near the glass transition temperature of one block can lock in intermediate morphologies by vitrifying that block while allowing the other to reorganize.

Applications of non-equilibrium assembled block copolymers exploit their unique structural features. Perpendicularly oriented lamellae achieved through flow alignment are useful for nanotemplates in lithography, enabling high-resolution patterning. Kinetically trapped micelles with anisotropic shapes serve as building blocks for responsive gels or drug delivery carriers, where morphology impacts release kinetics. Disordered bicontinuous networks formed by rapid quenching provide high interfacial area for membrane applications or conductive composites. The ability to tailor nanostructures through processing conditions expands the design space beyond equilibrium limitations, offering access to materials with tunable mechanical, optical, and transport properties.

Challenges remain in predicting and controlling non-equilibrium outcomes due to the complexity of kinetic pathways. Multiscale modeling combining coarse-grained simulations with experimental validation is advancing the understanding of how processing parameters influence final morphologies. In-situ characterization techniques, such as time-resolved X-ray scattering, provide insights into the dynamic evolution of nanostructures during processing. Future directions include exploiting feedback loops between processing and characterization to achieve real-time control over non-equilibrium assembly, paving the way for on-demand fabrication of functional nanomaterials.

The study of non-equilibrium self-assembly in block copolymers bridges fundamental kinetics with practical materials design. By manipulating flow, quenching rates, and kinetic traps, researchers can access a rich array of nanostructures that defy equilibrium thermodynamics. This approach not only expands the library of available morphologies but also enables the integration of block copolymers into advanced manufacturing processes where non-equilibrium conditions are inherent. Continued progress in this field promises to unlock new functionalities for nanotechnology applications.