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

Abstract

The correlation function for the exit of poloxamer copolymers from equilibrated micelles is found to show up to four regimes depending on the chain flexibility: an initial fast reorganization, a logarithmic intermediate regime, followed by an exponential intermediate regime, and a final exponential decay. The logarithmic intermediate regime has been observed experimentally and attributed to the polydispersity of the polymer samples. However, we present dynamic single-chain mean-field theory simulations with chains of variable flexibility which show the same logarithmic relaxation but with strictly monodisperse systems. In agreement with our previous studies, we propose that this logarithmic response arises from a degeneracy of energy states of the hydrophobic block in the micelle core. For this to occur, a sufficiently large number of degenerate conformational states are required, which depend on the polymer flexibility and therefore should not be present for rigid polymers. Experimental results for monodisperse polymeric samples claiming the absence of such a logarithmic response may also lack a sufficient number of hydrophobic blocks for the required number of configurational states for this type of response to be seen. The insight gained from analyzing the simulation results allows us to propose a modified Eyring equation capable of reproducing the observed dynamic behavior. On scaling experimental results from different sources and systems according to this equation, we find a unique master curve showing a universal nature of the intermediate regimes: the logarithmic regime together with the secondary exponential decay. The terminal exponential regime at long times proposed by the standard Halperin and Alexander model is beyond the range of the data analyzed in this article. The universality observed suggests an entropic origin of the short-time dynamic response of this class of systems rather than the polydispersity.

Dynamics and Equilibration Mechanisms in Block Copolymer Particles

“…In addition to DPD simulations, Mackie and co-workers have used a dynamical single-chain in mean-field (SCMF) simulations to model the dynamics of chain exchange in an array of micelles formed by triblock copolymers, again mimicking the TR-SANS experiment. − A remarkable outcome of their calculations is the presence of a logarithmic decay despite their simulations using a monodisperse polymer . They argue that the logarithmic behavior emerges from a degeneracy in the states available to the solvophobic midblock in the micelle core that is destroyed when that block escapes from the micelle core.…”

Unraveling Chain Exchange Kinetics in Mixed Micelles through FRET: Impact of Segment Interactions between Hydrophilic Polymers in the Corona

“…Figure a shows that the normalized FRET efficiency E ( t )/ E (∞) without the addition of PS- b -PMAA increases continuously but not logarithmically. Previous works have observed that chain exchange kinetics of diblock copolymers follow a logarithmic relaxation pattern using time-resolved small-angle neutron scattering (TR-SANS), presumably due to the hypersensitive dependence of single-chain exchange rate on the core block length. ,, However, recent work by Mackie et al has suggested that logarithmic relaxation may also be observed for block copolymers with flexible monodisperse core chains using a dynamic single-chain mean-field theory simulation method, arising from a degeneracy of energy states of the monodisperse block in the micelle core. , In contrast, for the rigid core chain, the logarithmic relaxation is absent. Therefore, the lack of logarithmic relaxation in our study could be attributed to the rigidity of the PS block despite its relatively low polydispersity index (PDI) of 1.10.…”

“…5,9,15 However, recent work by Mackie et al has suggested that logarithmic relaxation may also be observed for block copolymers with flexible monodisperse core chains using a dynamic single-chain mean-field theory simulation method, arising from a degeneracy of energy states of the monodisperse block in the micelle core. 33,34 In contrast, for the rigid core chain, the logarithmic relaxation is absent. Therefore, the lack of logarithmic relaxation in our study could be attributed to the rigidity of the PS block despite its relatively low polydispersity index (PDI) of 1.10.…”

“…These methods have been used to investigate how different variables affect the chain exchange rates of micelles formed by diblock copolymers. Experimental studies have shown that chain exchange kinetics can be appropriately altered by changing the solvent properties, ,, the length and distribution of core block, the length of corona block, , copolymer architecture, , and the morphology of the micelles. , Other theoretical and simulation approaches can also be used to study the chain exchange between micelles. ,,− Among all experimental techniques, TR-SANS has wide applications but requires access to large-scale facilities. Fluorescence resonance energy transfer (FRET) is a relatively straightforward method to characterize the chain exchange kinetics of micelles, where mixing micelles labeled with donor and acceptor dyes can lead to an increase in energy-transfer efficiency with the occurrence of chain exchange due to the decrease in the average distance between donors and acceptors. ,,, …”

Effect of Chain Architecture on the Structure, Dynamics, and Rheology of Thermoresponsive Poloxamer Hydrogels and Associated Blends

“…Similar soft gels or viscous complex fluids, loosely defined by G ′ > G ″ and 10 < G ′ < 1000 Pa, have been reported in other solutions of percolating BAB micelle clusters, ,, solutions of P407 blended with other poloxamers or RPs, ,, and over narrow temperature windows in commercial P407 solutions. , This soft gel exhibits significant viscoelastic aging with the dynamic moduli increasing over time when held at a constant temperature. Such aging is similar to that observed in colloidal glasses and attractive gels and suggests that the material is initially out-of-equilibrium but evolves over time through the breaking and reforming of attractive interparticle bonds, here involving PEO block bridging. − For RP407 in water, individual polymer bridges are expected to be able to break and reform quickly, as the process of chain exchange is very rapid for poloxamers in water (<10 ms); however, achieving an equilibrium bridge fraction will require orders of magnitude more time than the single-chain exchange mechanism. ,− Furthermore, similar to the behavior of colloidal gels, the increasing viscosity of the medium likely slows diffusion of micelles.…”