Universal Scaling for the Exit Dynamics of Block Copolymers from Micelles at Short and Long Time Scales

Effect of chain architecture on the structure, dynamics, and rheology of thermoresponsive poloxamer hydrogels and associated blends

Poloxamers, ABA triblock polymers composed of a poly(propylene oxide) (PPO) midblock (B) and poly(ethylene oxide) (PEO) endblocks (A), are widely studied for biomedical applications. Aqueous poloxamer 407 (P407; also referred to as F127) undergoes a solution-to-gel transition with increasing temperature, driven by the formation and ordering of micelles onto periodic lattices; however, the gel temperature and resulting modulus has limited tunability. Here, reverse P407 (RP407), a BAB polymer of the same composition and molar mass but the inverted architecture, is synthesized via anionic polymerization. The micellization and gelation temperatures of RP407 are higher than that of P407 and the PPO endblocks allow for intermicelle bridging; however, both single-component solutions favor body-centered cubic (BCC) packings. Further, aqueous RP407 displays a "soft gel" region with interesting rheological behavior, including viscoelastic aging and thermal hysteresis. Combining P407 and RP407 yields solutions with intermediate transition temperatures and alters the size and micelle packing. While the single-component solutions produce BCC packings, the blends form close-packed structures and larger micelles of higher aggregation numbers. Blends of P407 with an analogous AB diblock (E111P32) display similar behavior, whereas RP407/diblock blends form intermediate-sized BCC-packed micelles. These differences in packing and aggregation alter the local environments within the gels, which could have implications for applications such as drug delivery and protein stabilization.

Dynamics and Equilibration Mechanisms in Block Copolymer Particles

Self-assembly of block copolymers into interesting and useful nanostructures, in both solution and bulk, is a vibrant research arena. While much attention has been paid to characterization and prediction of equilibrium phases, the associated dynamic processes are far from fully understood. Here, we explore what is known and not known about the equilibration of particle phases in the bulk, and spherical micelles in solution. The presumed primary equilibration mechanisms are chain exchange, fusion, and fragmentation. These processes have been extensively studied in surfactants and lipids, where they occur on subsecond time scales. In contrast, increased chain lengths in block copolymers create much larger barriers, and time scales can become prohibitively slow. In practice, equilibration of block copolymers is achievable only in proximity to the critical micelle temperature (in solution) or the order-disorder transition (in the bulk). Detailed theories for these processes in block copolymers are few. In the bulk, the rate of chain exchange can be quantified by tracer diffusion measurements. Often the rate of equilibration, in terms of number density and aggregation number of particles, is much slower than chain exchange, and consequently observed particle phases are often metastable. This is particularly true in regions of the phase diagram where Frank-Kasper phases occur. Chain exchange in solution has been explored quantitatively by time-resolved SANS, but the results are not well captured by theory. Computer simulations, particularly via dissipative particle dynamics, are beginning to shed light on the chain escape mechanism at the molecular level. The rate of fragmentation has been quantified in a few experimental systems, and TEM images support a mechanism akin to the anaphase stage of mitosis in cells, via a thin neck that pinches off to produce two smaller micelles. Direct measurements of micelle fusion are quite rare. Suggestions for future theoretical, computational, and experimental efforts are offered.

Perspective: New directions in dynamical density functional theory

Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In particular, there has been a remarkable growth in the amount of work related to chemistry. Moreover, DDFT has stimulated research on other theories such as phase field crystal models and power functional theory. In this perspective, we summarize the latest developments in the field of DDFT and discuss a variety of possible directions for future research.