Self-assembly of polymers with crystallizable blocks may lead to micelles with ordered, gel-like or crystalline cores. Here we investigate binary mixtures of n-alkyl-poly(ethylene oxide), Cn-PEOx (n = 28, x = 3-20 kDa) and study their self-assembly to gain insight into the effect of confinement on the core-crystallization and micellar structure. By employing identical core block length but varying corona block lengths, the size of the core can be tuned by variation of the block ratios. The micelles were characterized by small-angle X-ray scattering (SAXS) to gain insight into the overall and internal structure, including aggregation number, core size, and density distribution of the corona. SAXS curves from examined samples showed a characteristic pattern of spherical core-shell micelles but with broader corona distribution in the binary mixtures as compared to the neat samples. The structural parameters of the micelles were extracted from the SAXS data by employing a spherical core-shell model with dual density profiles in the core. We found that the aggregation number decreases as PEO length increases following a power law predicted in the literature. Furthermore, the melting point and melting enthalpy of crystalline alkyl cores were closely inspected by densitometry and differential scanning calorimetry (DSC). Correlating the core radius obtained from SAXS, we found that the melting point depression caused by the self-confinement in the micellar core can be described by the Gibbs-Thomson equation. These results show that the micellar structure and phase transition of the semicrystalline core can be easily tuned through blending diblock copolymers with different corona block lengths.

Disentangled ultrahigh molecular weight polyethylene exhibits a time-dependent increase in rheology modulus when molten. This originates from its kinetically evolving heterogeneous microstructure consisting of disentangled and entangled regions. We report a quantitative analysis of this microstructure using X-rays and neutrons that capture the signatures of these regions. We analyze the absolute intensities to obtain the volume fraction and size distribution of the disentangled domains in the melt. Employing neutrons, we follow the changes in these parameters with time. The trends are qualitatively similar to those of the previous rheological observations. Our methodology also provides an experimental verification of the theoretical report by McLeish, T. C. B. Soft Matter 2007, 3 (1), 83-87, which predicts the presence of high density disentangled domains in a low density entangled matrix. The analysis presented here is a useful instrument for unveiling the origin of differences in the properties of polymers obtained through different processing routes.

The development of self-healing materials, which are capable of reforming into their original structure following rupture and damage, represents a fascinating and important area of research, with a wide range of potential applications. Telechelic polymers, defined as polymers with functional chain ends such as hydrophobically end-modified polymers, serve as prime examples of systems capable of forming hydrogel networks with transient bonding structures. In this study, we investigate the internal chain dynamics and self-diffusion of hydrogel networks made from telechelic polymers, employing selective contrast variation for small-angle neutron scattering and neutron spin echo spectroscopy. We show that the chain dynamics in the gel follow regular Zimm dynamics without any apparent evidence of restricted motion due to chain connectivity, possibly because the lifetime of the bonds is short. On the other hand, the micellar cores show slow relaxation, reflecting the restricted motion due to the connectivity and crowdedness of the system. The study highlights the decoupling between the slow dynamics of the micellar cores, which play a critical role in the rheological response, and the fast, relatively unconstrained chain dynamics that contribute to their "self-healing" properties. The results provide detailed insight into the multiscale dynamics in hydrogels with transient bonds useful for applications of these types of materials, natural or synthetic.

We investigate surface charged "starlike" micelles in aqueous solution formed by carboxy terminated n-octacosyl-poly(ethylene oxide) block copolymers, C-28-PEO5-COOH with 5 the PEO molar mass in kg/mol, by small angle neutron scattering (SANS), zeta-potential measurements, and rheology. The -COOH end group was introduced by selective oxidation of the -CH2-OH end group of a C-28-PEO5-OH precursor using Bobbitt's salt. Micellar solutions of different concentrations in the dilute and semidilute range were investigated at pH 2, 6, and 12 to vary ionic strength and the number of effective surface charges Z(eff). Z(eff) was further varied by using mixtures of C-28-PEO5-COOH and C-28-PEO5-OH at different mixing ratios. SANS measurements reveal that the intramicellar form factor P(Q) is identical at the different pH values, which implies that the individual micellar structure is unaffected by the number of surface charges. On the contrary, the intermicellar structure factor S(Q) and the phase behavior show a strong dependence on Z(eff). In particular, we observe a distinct shift of the liquid-fcc crystal phase boundary. A quantitative analysis in terms of a screened Hard Sphere Yukawa potential reveals very good agreement between experiment and theory. Because of this consistency and of the tunability of the n-alkyl-PEO starlike micelles, we consider this system to be an excellent model for further studies on the interplay between steric and electrostatic interactions in soft colloids.

Often nanostructures formed by self-assembly of small molecules based on hydrophobic interactions are rather unstable, causing morphological changes or even dissolution when exposed to changes in aqueous media. In contrast, peptides offer precise control of the nanostructure through a range of molecular interactions where physical stability can be engineered in and, to a certain extent, decoupled from size via rational design. Here, we investigate a family of peptides that form beta-sheet nanofibers and demonstrate a remarkable physical stability even after attachment of poly(ethylene glycol). We employed small-angle neutron/X-ray scattering, circular dichroism spectroscopy, and molecular dynamics simulation techniques to investigate the detailed nanostructure, stability, and molecular exchange. The results for the most stable sequence did not reveal any structural alterations or unimer exchange for temperatures up to 85 °C in the biologically relevant pH range. Only under severe mechanical perturbation (i.e., tip sonication) would the fibers break up, which is reflected in a very high activation barrier for unimer exchange of ∼320 kJ/mol extracted from simulations. The results give important insight into the relation between molecular structure and stability of peptide nanostructure that is important for, e.g., biomedical applications.

By neutron spin echo spectroscopy, we have studied the center of mass motion of short tracer chains on the molecular length scale within a highly entangled polymer matrix. The center of mass mean square displacements of the tracers independent of their molecular weight is subdiffusive at short times until it has reached the size of the tube d; then, a crossover to Fickian diffusion takes place. This observation cannot be understood within the tube model of reptation, but is rationalized as a result of important interchain couplings that lead to cooperative chain motion within the entanglement volume ∼d^{3}. Thus, the cooperative tracer chain motions are limited by the tube size d. If the center of mass displacement exceeds this size, uncorrelated Fickian diffusion takes over. Compared to the prediction of the Rouse model we observe a significantly reduced contribution of the tracer's internal modes to the spectra corroborating the finding of cooperative rather than Rouse dynamics within d^{3}.

We investigated the influence of an n-alkyl-PEO polymer on the structure and dynamics of phospholipid vesicles. Multilayer formation and about a 9% increase in the size in vesicles were observed by cryogenic transmission electron microscopy (cryo-TEM), dynamic light scattering (DLS), and small-angle neutron/X-ray scattering (SANS/SAXS). The results indicate a change in the lamellar structure of the vesicles by a partial disruption caused by polymer chains, which seems to correlate with about a 30% reduction in bending rigidity per unit bilayer, as revealed by neutron spin echo (NSE) spectroscopy. Also, a strong change in lipid tail relaxation was observed. Our results point to opportunities using synthetic polymers to control the structure and dynamics of membranes, with possible applications in technical materials and also in drug and nutraceutical delivery.

Investigations of polymer systems that rely on the interpretation of dynamical scattering results as, e.g., the structure factor S(Q, t) of single chains or chain sections may require the inclusion of effects, as described within the framework of the random phase approximation (RPA) for polymers. To do this in practice for the dynamic part of S(Q, t) beyond the initial slope is a challenge. Here, we present a method (and software) that allows a straightforward assessment of dynamical RPA effects and inclusion of these in the process/procedures of model fitting. Examples of applications to the interpretation of neutron spin-echo data multi-component polymer melts are shown.

Self-assembly of amphiphilic polymers into micelles is an archetypical example of a "self-confined" system due to the formation of micellar cores with dimensions of a few nanometers. In this work, we investigate the chain packing and resulting shape of Cn-PEOx micelles with semicrystalline cores using small/wide-angle X-ray scattering (SAXS/WAXS), contrast-variation small-angle neutron scattering (SANS), and nuclear magnetic resonance spectroscopy (NMR). Interestingly, the n-alkyl chains adopt a rotator-like conformation and pack into prolate ellipses (axial ratio ϵ ≈ 0.5) in the "crystalline" region and abruptly arrange into a more spheroidal shape (ϵ ≈ 0.7) above the melting point. We attribute the distorted spherical shape above the melting point to thermal fluctuations and intrinsic rigidity of the n-alkyl blocks. We also find evidence for a thin dehydrated PEO layer (≤1 nm) close to the micellar core. The results provide substantial insight into the interplay between crystallinity and molecular packing in confinement and the resulting overall micellar shape.

Telechelic polymers contain two chain ends that are able to promote self-assembly into "flowerlike" or interconnected micellar structures. Here, we investigate the molecular exchange kinetics of such micelles using time-resolved small-angle neutron scattering. We show that the activation energies of monofunctional and telechelic chain exchange are identical. This demonstrates that the two chain ends are not simultaneously released in a single event. Instead, the results show that, contrary to regular micelles, the kinetics occurs in a multistep process involving a collision-induced single-molecule exchange mechanism where the exchange rate is directly proportional to the polymer concentration. We show that this novel mechanism can be quantitatively explained by a simple kinetic model.

Mixtures of amphiphilic polymers and surfactants are used in a wide range of applications, e.g., pharmaceuticals, detergents, cosmetics, and drug delivery systems. Still, many questions remain on how the structure and, in particular, the kinetics of block copolymer micelles are affected in the presence of surfactants and what controls the solubilization kinetics. In this work, we have studied the stability and solubilization kinetics of block copolymer micelles upon the addition of the surfactant sodium dodecyl sulfate (SDS) using small-angle X-ray/neutron scattering. The ability of the surfactant to dissolve polymer micelles or form mixed micelles has been investigated using two types of amphiphilic polymers, poly(ethylene-alt-propylene)–poly(ethylene oxide) (PEP1-PEO20) and n-alkyl-functionalized PEO (C28-PEO5). The exchange kinetics of C28-PEO5 micelles are in the order of hours, while PEP1-PEO20 micelles are known to be frozen on a practical timescale. In this work, we show that the addition of SDS to PEP1-PEO20 provides virtually no solubilization, even after an extended period of time. However, upon adding SDS to C28-PEO5 micelles, we observe micellar dissolution and formation of mixed micelles occurring on the timescale of hours. Using a coexistence model of mixed and neat micelles, the SAXS data were analyzed to provide detailed structural parameters over time. First, we observe a fast fragmentation/fission step followed by a slow reorganization process. The latter process is essentially independent of concentration at low volume fraction but is greatly accelerated at larger concentrations. This might indicate a crossover from a predominance of molecular exchange to fusion/fission processes.

We investigate micelles formed by mixtures of n-alkyl-poly(ethylene oxide) block copolymers, Cn-PEO, with different alkyl block lengths in aqueous solution. This model system has previously been used to shed light on the interplay between exchange kinetics and crystallinity in self-assembling systems [König et al., Phys. Rev. Lett., 2019, 122, 078001]. Now we report on the structure and thermodynamics of these micelles by combining results from small-angle X-ray scattering, differential scanning calorimetry and volumetric measurements. We show that mixed micelles are formed despite the fact that length-mismatched n-alkanes of similar weights in bulk tend to demix below the crystallization temperature. Instead, the system exhibits similar properties as single-component micelles but with a modulated melting region. Interestingly, the melting point depression due to self-confinement within the micellar core can be approximately described by a generalized Gibbs-Thomson equation, similar to single-component micelles [Zinn et al. Phys. Rev. Lett., 2014, 113, 238305]. Furthermore, we find a novel scaling law for these micelles where, at least for larger n, the aggregation number scales with the third power of the length of the hydrophobic block, Nagg ∝ n3. Possibly, there might be a cross-over from the conventional Nagg ∝ n2 behaviour around n ≈ 19. However, the reason for such a transition as well as the strong n dependence remains a challenge and requires more theoretical work.

Molecular exchange processes are important equilibration and transport mechanisms in both synthetic and biological self-assembled systems such as micelles, vesicles, and membranes. Still, these processes are not entirely understood, in particular the effect of crystallinity and the interplay between cooperative melting processes and chain exchange. Here we focus on a set of simple polymer micelles formed by binary mixtures of poly(ethylene oxide)-mono-n-alkyl-ethers (C_{n}-PEO5) which allows the melting point to be tuned over a wide range. We show that the melting transition is cooperative in the confined 4-5 nm micellar core, whereas the exchange process is widely decoupled and unimeric in nature. As confirmed by differential scanning calorimetry, the total activation energy for ejecting a molecule out of the micellar core below the melting point is the sum of the enthalpy of fusion and the corresponding activation energy in the melt state. This suggests that a "local, single-chain melting process" preludes the molecular diffusion out of the micelle during chain exchange.

Proton multiple-quantum time-domain NMR combined with time-temperature superposition is a powerful method to study entangled chain dynamics. Overcoming the previous limitation to regimes II-IV of the tube model, this study extends the method to regime I (localized Rouse motions) by use of a pulse sequence adapted to shorter times, thus covering all relevant regimes for the model case of poly(butadiene) with molecular weights (M) between 10 and 200 kDa. We determine a value for the entanglement time that is consistent with current rheological results and confirm a value below 1 for the time scaling exponent of the segmental orientation autocorrelation function (OACF) in regime I previously observed by other NMR techniques. The origins of deviations from tube-model predictions are assessed by focusing on the dynamics of the chain centers in end-chain deuterated triblock samples and by dilution of probe chains to 15% in a deuterated matrix with M of 2 MDa. The study is complemented by self-diffusion coefficients measured by pulsed-gradient NMR. Our OACF-based results for the terminal time reinforce the current consensus that below a chain length of 30-50 entanglements matrix effects cannot explain the nonideal M-scaling exponent of 3.4 but are responsible for an M-independent slowdown. The protracted approach of the pure local-reptation scaling in regime II is found to be only somewhat reduced for both chain centers and chains in a long matrix, confirming its generic intrachain origin. These microscopic insights could be compared with results from large-scale computer simulations and provide a gauge for theoretical approaches such as those dealing with constraint release and contour-length fluctuations.

Viscoelastic response in terms of the complex shear modulus G*(ω) of the linear polymers poly(ethylene-alt-propylene), poly(isoprene), and poly(butadiene) is studied for molar masses (M) from 3k up to 1000k and over a wide temperature range starting from the glass transition temperature Tg (174 K–373 K). Master curves G′(ωτα) and G″(ωτα) are constructed for the polymer-specific relaxation. Segmental relaxation occurring close to Tg is independently addressed by single spectra. Altogether, viscoelastic response is effectively studied over 14 decades in frequency. The structural relaxation time τα used for scaling is taken from dielectric spectra. We suggest a derivative method for identifying the different power-law regimes and their exponents along G″(ωτα) ∝ ωε″. The exponent ε″ = ε″(ωτα) ≡ d ln G″(ωτα)/d ln(ωτα) reveals more details compared to conventional analyses and displays high similarity among the polymers. Within a simple scaling model, the original tube-reptation model is extended to include contour length fluctuations (CLFs). The model reproduces all signatures of the quantitative theory by Likhtman and McLeish. The characteristic times and power-law exponents are rediscovered in ε″(ωτα). The high-frequency flank of the terminal relaxation closely follows the prediction for CLF (ε″ = −0.25), i.e., G″(ω) ∝ ω−0.21±0.02. At lower frequencies, a second regime with lower exponent ε″ is observed signaling the crossover to coherent reptation. Application of the full Likhtman-McLeish calculation provides a quantitative interpolation of ε″(ωτα) at frequencies below those of the Rouse regime. The derivative method also allows identifying the entanglement time τe. However, as the exponent in the Rouse regime (ωτe > 1) varies along εeRouse = 0.66 ± 0.04 (off the Rouse prediction εRouse = 0.5) and that at ωτe < 1 is similar, only a weak manifestation of the crossover at τe is found at highest M. Yet, calculating τe/τα= (M/Mo)2, we find good agreement among the polymers when discussing ε″(ωτe). The terminal relaxation time τt is directly read off from ε″(ωτα). Plotting τt/τe as a function of Z = M/Me, we find universal behavior as predicted by the TR model. The M dependence crosses over from an exponent significantly larger than 3.0 at intermediate M to an exponent approaching 3.0 at highest M in agreement with previous reports. The frequency of the minimum in G″(ωτα) scales as τmin ∝ M1.0±0.1. An M-independent frequency marks the crossover to glassy relaxation at the highest frequencies. Independent of the amplitude of G″(ω), which may be related to sample-to-sample differences, the derivative method is a versatile tool to provide a detailed phenomenological analysis of the viscoelastic response of complex liquids.

We investigate the effect of the number of arms (functionality f) on the mobility of the branch point in symmetric star polymers. For this purpose we carry out large-scale molecular dynamics simulations of simple bead–spring stars and neutron spin echo (NSE) spectroscopy experiments on center labeled polyethylene stars. This labeling scheme unique to neutron scattering allows us to directly observe the branch point motion on the molecular scale by measuring the dynamic structure factor. We investigate the cases of different functionalities f = 3, 4, and 5 for different arm lengths. The analysis of the branch point fluctuations reveals a stronger localization with increasing functionality, following 2/f scaling. The dynamic structure factors of the branch point are analyzed in terms of a modified version, incorporating dynamic tube dilution (DTD), of the Vilgis–Boue model for cross-linked networks [J. Polym. Sci., Part B 1988, 26, 2291−2302]. In DTD the tube parameters are renormalized with the tube surviv...