Effect of Corona Block Length on the Structure and Chain Exchange Kinetics of Block Copolymer Micelles

Dynamics in polymers with phase separated dynamic bonds: the case of a peculiar temperature dependence

The topic of polymers with dynamic bonds (stickers) appears as an exciting and promising area of materials science, thanks to their attractive self-healable, recyclable, extremely tough, and super extensible properties. Polymers with phase separated dynamic bonds revealed several unique properties, but mechanisms controlling their viscoelastic properties remain poorly understood. In this work, we present a dynamic analysis of a model polymer system with phase separated hydrogen bonding functionalities. The results confirm that terminal relaxation in these systems is independent of polymer segmental dynamics and is instead controlled by structural relaxations in clusters of stickers. Detailed analysis revealed a surprising result: terminal relaxation time of these systems has weaker temperature dependence than that of structural relaxation in clusters, although the former is slower than the latter. Borrowing ideas from the field of block copolymers, we ascribed this unusual result to an LCST-like behavior for the miscibility of the stickers in the polymer matrix. The presented results and ideas deepen the understanding of the viscoelasticity for polymers with dynamic bonds, enabling intelligent design of functional materials with desired macroscopic properties.

Particle topology-regulated relaxation dynamics in cluster-ordering

The granular materials of soft particles (SPs) demonstrate unique viscoelasticity distinct from general colloidal and polymer systems. Exploiting dynamic light scattering measurements, together with molecular dynamics simulations, we study the diffusive dynamics of soft particle clusters (SPCs) with spherical and cylindrical brush topologies, respectively, in the melts of SPs. A topologically constrained relaxation theory is proposed by quantitatively correlating the relaxation time to the topologies of the SPCs, through the mean free space (Va) of tethered SPs in the cluster. The tethered SPs in SPCs are crowded by SPs of the melts to form the cage zones, and the cooperative diffusion of the tether SPs in the zones is required for the diffusive motion of SPCs. The cage zone serves as an entropic barrier for the diffusion of SP clusters, while its strength is determined by Va. Three characteristic modes can be confirmed: localized non-diffusive mode around critical Va, diffusive mode with Va deviating far from the critical value, and a sub-diffusive mode as an interlude between two limits. Our studies raise attention to the emergent physical properties of materials based on SPs via a topological design while opening new avenues for the design of soft structural materials.

Stereocomplex-Driven Morphological Transition of Coil-Rod-Coil Poly(lactic acid)-Based Cylindrical Nanoparticles

The stereocomplexation of poly(lactic acid) (PLA) enantiomers opens up an avenue for the formation of new materials with enhanced performance, specifically regarding their mechanical and thermal resistance and resistance to hydrolysis. Despite these useful features, the study of the stereocomplexation between block copolymers based on PLA in solution is limited, and a comprehensive understanding of this phenomenon is urgently needed. Herein, triblock copolymers of poly(N-hydroxyethyl acrylamide) and PL(or D)LA in which PLA was midblock (PHEAAmy-b-PL(D)LAx-b-PHEAAmy) were synthesized and assembled into cylindrical micelles via crystallization-driven self-assembly . The stereocomplexation between enantiomeric micelles facilitates the morphological transition, and the transformation process was investigated in detail by varying the aging temperature, block composition, and solvent. It was found that the solubility of the copolymers played a vital role in determining the occurrence and the speed of the chain exchange between the micelles and the unimers, which thereafter has a significant impact on the shape transition. These results lead to a deeper understanding of the stereocomplex-driven morphological transition process and provide valuable guidance for further optimization of the transition under physiological conditions as a new category of stimuli-responsive systems for biomedical applications.

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.

High-χ, low-N micelles from partially perfluorinated block polymers

Kinetically trapped ("persistent") micelles enable emerging applications requiring a constant core diameter. Preserving a χN barrier to chain exchange with low-N requires a commensurately higher χ_core-solvent for micelle persistence. Low-N, high-χ micelles containing fluorophobic interactions were studied using poly(ethylene oxide-b-perfluorooctyl acrylate)s (O₄₅F_X, x = 8, 11) in methanolic solutions. DLS analysis of micelles revealed chain exchange only for O₄₅F₈ while SAXS analysis suggested elongated core block conformations commensurate with the contour lengths. Micelle chain exchange from solution perturbations were examined by characterizing their behavior as templates for inorganic materials via SAXS and SEM. In contrast to the F₈ analog, the larger χN barrier for the O₄₅F₁₁ enabled persistent micelle behavior in both thin films and bulk samples despite the low T_g micelle core. Careful measures of micelle core diameters and pore sizes revealed that the nanoparticle distribution extended through the corona and 0.52 ± 0.15 nm into the core-corona interface, highlighting thermodynamics favoring both locations simultaneously.

Energy Transfer in Stability-Optimized Perovskite Nanocrystals

Outstanding optoelectronic properties and a facile synthesis render halide perovskite nanocrystals (NCs) a promising material for nanostructure-based devices. However, the commercialization is hindered mainly by the lack of NC stability under ambient conditions and inefficient charge carrier injection. Here, we investigate solutions to both problems, employing methylammonium lead bromide (MAPbBr₃) NCs encapsulated in diblock copolymer core-shell micelles of tunable size. We confirm that the shell does not prohibit energy transfer, as FRET efficiencies between these NCs and 2D CsPbBr₃ nanoplatelets (NPLs) reach 73.6%. This value strongly correlates to the micelle size, with thicker shells displaying significantly reduced FRET efficiencies. Those high efficiencies come with a price, as the thinnest shells protect the encapsulated NCs less from environmentally induced degradation. Finding the sweet spot between efficiency and protection could lead to the realization of tailored energy funnels with enhanced carrier densities for high-power perovskite NC-based optoelectronic applications.

Unravelling the Mechanism of Viscoelasticity in Polymers with Phase-Separated Dynamic Bonds

Incorporation of dynamic (reversible) bonds within polymer structure enables properties such as self-healing, shape transformation, and recyclability. These dynamic bonds, sometimes refer as stickers, can form clusters by phase-segregation from the polymer matrix. These systems can exhibit interesting viscoelastic properties with an unusually high and extremely long rubbery plateau. Understanding how viscoelastic properties of these materials are controlled by the hierarchical structure is crucial for engineering of recyclable materials for various future applications. Here we studied such systems made from short telechelic polydimethylsiloxane chains by employing a broad range of experimental techniques. We demonstrate that formation of a percolated network of interfacial layers surrounding clusters enhances mechanical modulus in these phase-separated systems, whereas single chain hopping between the clusters results in macroscopic flow. On the basis of the results, we formulated a general scenario describing viscoelastic properties of phase-separated dynamic polymers, which will foster development of recyclable materials with tunable rheological properties.

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

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.

Computational Reverse Engineering Analysis for Scattering Experiments (CREASE) on Vesicles Assembled from Amphiphilic Macromolecular Solutions

In this paper we present the development and validation of the "Computational Reverse-Engineering Analysis for Scattering Experiments" (CREASE) method for analyzing scattering results from vesicle structures that are commonly found upon assembly of synthetic, biomimetic, or bioderived amphiphilic copolymers in solution. The two-step CREASE method takes the amphiphilic polymer chemistry and small-angle scattering intensity profile, I exp(q), as input and determines the vesicles' structural features on multiple length scales ranging from assembled vesicle wall's individual layer thicknesses to the monomer-level packing and distribution of polymer conformations. In the first step of CREASE, a genetic algorithm (GA) is used to determine the relevant vesicle dimensions from the input macromolecular solution information and I exp(q) by identifying the structure whose computed scattering profile best matches the input I exp(q). Then in the second step, the GA-determined dimensions are used for molecular reconstruction of the vesicle structure. To validate CREASE for vesicles, we test CREASE on input scattering intensity profiles generated mathematically (termed as in silico I exp(q) vs q) from a variety of vesicle sizes with known dimensions. We also test CREASE on in silico I exp(q) vs q generated from vesicles with dispersity in all relevant dimensions, resembling real experiments. After successful validation of CREASE, we compare the CREASE-determined dimensions against those obtained from the traditional approach of fitting the scattering intensity profile to relevant analytical model in SASVIEW package. We show that CREASE performs better than or as well as the core-multishell analytical model's fitting in SASVIEW in determining vesicle dimensions with dispersity. We also show that CREASE provides structural information beyond those possible from traditional scattering analysis using the core-multishell model, such as the distribution of solvophilic monomers between the vesicle wall's inner and outer layers in the vesicle wall and the chain-level packing within each vesicle layer.

Molecular Weight Dependence of Block Copolymer Micelle Fragmentation Kinetics

The effect of molecular weight (M) on the fragmentation kinetics of micelles formed by 1,2-polybutadiene-block-poly(ethylene oxide) (PB-PEO) copolymers was studied in the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide. A series of six samples, with total M ranging from 10⁴ to 10⁵ g mol^-1 and nearly constant composition (f_PEO ≈ 0.4), were examined; all six formed spherical micelles with PEO coronas. Nonequilibrium PB-PEO micelles were prepared by direct dissolution, a process that systematically produces nanoparticles with mean aggregation numbers more than twice the equilibrium values. When subjected to high temperature annealing (170 °C), the average micelle radius was found to decrease substantially, as determined by temperature-jump dynamic light scattering (T-jump DLS) and time-resolved small-angle X-ray scattering (TR-SAXS). The characteristic fragmentation times (τ) were found to increase strongly with increasing degree of polymerization N, as τ ∼ N^1.8. This result compares favorably with the prediction of a previously untested model.

Chain-Length-Dependent Photolysis of ortho-Nitrobenzyl-Centered Polymers

Herein, we demonstrate that the photochemical cleavage of linear polymers containing a midchain photocleavable moiety strongly depends on the chain length. Based on an ortho-nitrobenzyl (oNB) difunctional reversible addition-fragmentation chain-transfer agent, well-defined poly(methyl acrylate)s (M_n = 1.59-67.6 kg mol^-1, Đ = 1.3-1.4) were synthesized following a core-first approach. Photolysis at λ_max = 350 nm of the ortho-nitrobenzyl moiety led to the generation of equally sized polymer segments. The rate of oNB-driven polymer fragmentation, which can be well described by first-order kinetics, strongly increases with increasing molecular weight in a nonlinear fashion, potentially caused by entropic considerations and is compared to the ideal chain model. The current study thus demonstrates that polymer photolysis is dependent on the polymer chain length, with critical implications for photocleavable network design.

Control of Particle Size in the Self-Assembly of Amphiphilic Statistical Copolymers

A range of amphiphilic statistical copolymers is synthesized where the hydrophilic component is either methacrylic acid (MAA) or 2-(dimethylamino)ethyl methacrylate (DMAEMA) and the hydrophobic component comprises methyl, ethyl, butyl, hexyl, or 2-ethylhexyl methacrylate, which provide a broad range of partition coefficients (log P). Small-angle X-ray scattering studies confirm that these amphiphilic copolymers self-assemble to form well-defined spherical nanoparticles in an aqueous solution, with more hydrophobic copolymers forming larger nanoparticles. Varying the nature of the alkyl substituent also influenced self-assembly with more hydrophobic comonomers producing larger nanoparticles at a given copolymer composition. A model based on particle surface charge density (PSC model) is used to describe the relationship between copolymer composition and nanoparticle size. This model assumes that the hydrophilic monomer is preferentially located at the particle surface and provides a good fit to all of the experimental data. More specifically, a linear relationship is observed between the surface area fraction covered by the hydrophilic comonomer required to achieve stabilization and the log P value for the hydrophobic comonomer. Contrast variation small-angle neutron scattering is used to study the internal structure of these nanoparticles. This technique indicates partial phase separation within the nanoparticles, with about half of the available hydrophilic comonomer repeat units being located at the surface and hydrophobic comonomer-rich cores. This information enables a refined PSC model to be developed, which indicates the same relationship between the surface area fraction of the hydrophilic comonomer and the log P of the hydrophobic comonomer repeat units for the anionic (MAA) and cationic (DMAEMA) comonomer systems. This study demonstrates how nanoparticle size can be readily controlled and predicted using relatively ill-defined statistical copolymers, making such systems a viable attractive alternative to diblock copolymer nanoparticles for a range of industrial applications.

FRET-Based Determination of the Exchange Dynamics of Complex Coacervate Core Micelles

Complex coacervate core micelles (C3Ms) are nanoscopic structures formed by charge interactions between oppositely charged macroions and used to encapsulate a wide variety of charged (bio)molecules. In most cases, C3Ms are in a dynamic equilibrium with their surroundings. Understanding the dynamics of molecular exchange reactions is essential as this determines the rate at which their cargo is exposed to the environment. Here, we study the molecular exchange in C3Ms by making use of Förster resonance energy transfer (FRET) and derive an analytical model to relate the experimentally observed increase in FRET efficiency to the underlying macromolecular exchange rates. We show that equilibrated C3Ms have a broad distribution of exchange rates. The overall exchange rate can be strongly increased by increasing the salt concentration. In contrast, changing the unlabeled homopolymer length does not affect the exchange of the labeled homopolymers and an increase in the micelle concentration only affects the FRET increase rate at low micelle concentrations. Together, these results suggest that the exchange of these equilibrated C3Ms occurs mainly by expulsion and insertion, where the rate-limiting step is the breaking of ionic bonds to expel the chains from the core. These are important insights to further improve the encapsulation efficiency of C3Ms.

Determining population densities in bimodal micellar solutions using contrast-variation small angle neutron scattering

Self-assembly of amphiphilic polymers in water is of fundamental and practical importance. Significant amounts of free unimers and associated micellar aggregates often coexist over a wide range of phase regions. The thermodynamic and kinetic properties of the microphase separation are closely related to the relative population density of unimers and micelles. Although the scattering technique has been employed to identify the structure of micellar aggregates as well as their time-evolution, the determination of the population ratio of micelles to unimers remains a challenging problem due to their difference in scattering power. Here, using small-angle neutron scattering (SANS), we present a comprehensive structural study of amphiphilic n-dodecyl-PNIPAm polymers, which shows a bimodal size distribution in water. By adjusting the deuterium/hydrogen ratio of water, the intra-micellar polymer and water distributions are obtained from the SANS spectra. The micellar size and number density are further determined, and the population densities of micelles and unimers are calculated to quantitatively address the degree of micellization at different temperatures. Our method can be used to provide an in-depth insight into the solution properties of microphase separation, which are present in many amphiphilic systems.

Think Beyond the Core: Impact of the Hydrophilic Corona on Drug Solubilization Using Polymer Micelles

Polymeric micelles are typically characterized as core-shell structures. The hydrophobic core is considered as a depot for hydrophobic molecules, and the corona-forming block acts as a stabilizing and solubilizing interface between the core and aqueous milieu. Tremendous efforts have been made to tune the hydrophobic block to increase the drug loading and stability of micelles, whereas the role of hydrophilic blocks is rarely investigated in this context, with poly(ethylene glycol) (PEG) being the gold standard of hydrophilic polymers. To better understand the role of the hydrophilic corona, a small library of structurally similar A-B-A-type amphiphiles based on poly(2-oxazoline)s and poly(2-oxazine)s is investigated by varying the hydrophilic block A utilizing poly(2-methyl-2-oxazoline) (pMeOx; A) or poly(2-ethyl-2-oxazoline) (pEtOx; A*). In terms of hydrophilicity, both polymers closely resemble PEG. The more hydrophobic block B bears either a poly(2-oxazoline) and poly(2-oxazine) backbone with C3 (propyl) and C4 (butyl) side chains. Surprisingly, major differences in loading capacities from A-B-A > A*-B-A > A*-B-A* is observed for the formulation with two poorly water-soluble compounds, curcumin and paclitaxel, highlighting the importance of the hydrophilic corona of polymer micelles used for drug formulation. The formulations are also characterized by various nuclear magnetic resonance spectroscopy methods, dynamic light scattering, cryogenic transmission electron microscopy, and (micro) differential scanning calorimetry. Our findings suggest that the interaction between the hydrophilic block and the guest molecule should be considered an important, but previously largely ignored, factor for the rational design of polymeric micelles.

Direct Observation of Micelle Fragmentation via In Situ Liquid-Phase Transmission Electron Microscopy

Recently, attention has been directed toward understanding the dynamics and relaxation kinetics of block copolymer micelles, including mechanisms such as micelle fragmentation and fusion. The few prior studies on block copolymer micelle fragmentation relied on ensemble averaging techniques such as small-angle X-ray scattering and dynamic light scattering; some individual particles were imaged by ex situ transmission electron microscopy. Here we report the direct observation of fragmentation for three molecular weights of 1,2-polybutadiene-block-poly(ethylene oxide) (PB-PEO) micelles in the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide using high-temperature liquid-phase transmission electron microscopy (LP-TEM). The use of in situ LP-TEM provides unique insights into the evolution of block copolymer micelles during fragmentation. Specifically, upon heating to 170 °C, a sequence of morphological transitions from a spherical micelle to a prolate ellipsoid, then a "peanut" shape, followed by a two-spherical-compartment micelle was observed, where the last is presumed to be the transition state.

Langevin Dynamics Simulations of the Exchange of Complex Coacervate Core Micelles: The Role of Nonelectrostatic Attraction and Polyelectrolyte Length

Complex coacervate core micelles (C3Ms) are promising encapsulators for a wide variety of (bio)molecules. To protect and stabilize their cargo, it is essential to control their exchange dynamics. Yet, to date, little is known about the kinetic stability of C3Ms and the dynamic equilibrium of molecular building blocks with micellar species. Here we study the C3M exchange during the initial micellization by using Langevin dynamics simulations. In this way, we show that charge neutral heterocomplexes consisting of multiple building blocks are the primary mediator for exchange. In addition, we show that the kinetic stability of the C3Ms can be tuned not only by the electrostatic interaction but also by the nonelectrostatic attraction between the polyelectrolytes, the polyelectrolyte length ratio, and the overall polyelectrolyte length. These insights offer new rational design guides to aid the development of new C3M encapsulation strategies.