Cooperative Chain Dynamics of Tracer Chains in Highly Entangled Polyethylene Melts.

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}.

A practical method to account for random phase approximation effects on the dynamic scattering of multi-component polymer systems.

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.

Scaling analysis of the viscoelastic response of linear polymers.

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.

Effect of nanoconfinement on polymer dynamics: surface layers and interphases.

We present neutron spin echo experiments that address the much debated topic of dynamic phenomena in polymer melts that are induced by interacting with a confining surface. We find an anchored surface layer that internally is highly mobile and not glassy as heavily promoted in the literature. The polymer dynamics in confinement is, rather, determined by two phases, one fully equal to the bulk polymer and another that is partly anchored at the surface. By strong topological interaction, this phase confines further chains with no direct contact to the surface. These form the often invoked interphase, where the full chain relaxation is impeded through the interaction with the anchored chains.

Ultrasoft colloid-polymer mixtures: structure and phase diagram.

Binary mixtures of ultrasoft colloids and linear polymer chains were investigated by small-angle neutron scattering and liquid state theory. We show that experimental data can be described by employing recently developed effective interactions between the colloid and the polymer chains, in which both components are modeled as point particles in a coarse-grained approach, in which the monomers have been traced out. Quantitative, parameter-free agreement between experiment and theory for the pair correlations, the phase behavior and the concentration dependence of the interaction length is achieved.

Cooperative dynamics in homopolymer melts: a comparison of theoretical predictions with neutron spin echo experiments.

We present a comparison between theoretical predictions of the generalized Langevin equation for cooperative dynamics (CDGLE) and neutron spin echo data of dynamic structure factors for polyethylene melts. Experiments cover an extended range of length and time scales, providing a compelling test for the theoretical approach. Samples investigated include chains with increasing molecular weights undergoing dynamics across the unentangled to entangled transition. Measured center-of-mass (com) mean-square displacements display a crossover from subdiffusive to diffusive dynamics. The generalized Langevin equation for cooperative dynamics relates this anomalous diffusion to the presence of the interpolymer potential, which correlates the dynamics of a group of slowly diffusing molecules in a dynamically heterogeneous liquid. Theoretical predictions of the subdiffusive behavior, of its crossover to free diffusion, and of the number of macromolecules undergoing cooperative motion are in quantitative agreement with experiments.

Asymmetric poly(ethylene-alt-propylene)-poly(ethylene oxide) micelles: a system with starlike morphology and interactions.

We report on an experimental study of single particle properties and interactions of poly(ethylene-alt-propylene)-poly(ethylene oxide) (PEP-PEO) starlike micelles. The starlike regime is achieved by an extremely asymmetric block ratio (1:20) and the number of arms (functionality) is changed by varying the composition of the solvent (the interfacial tension). Small angle neutron scattering (SANS) data in the dilute regime can be modeled by assuming a constant density profile in the micellar core (compact core) and a starlike density profile in the corona (starlike shell). The starlike morphology of the corona is confirmed by a direct comparison with SANS measurements of dilute poly butadiene star solutions. Comparison of structure factors obtained by SANS measurements in the concentrated regime shows in addition that the interactions in the two systems are equivalent. Micellar structure factors at several packing fractions can be modeled by using the ultrasoft potential recently proposed for star polymers [Likos, Phys. Rev. Lett. 80, 4450 (1998)]. The experimental phase diagram of PEP-PEO micelles is quantitatively compared to theoretical expectations, finding good agreement for the location of the liquid-solid boundary and excellent agreement for the critical packing fraction where the liquid-to-bcc crystal transition takes place for f<70. The functionality, i.e., the coronal density, strongly influences the nature of the solid phase: for f<70 the system crystallizes into a bcc phase, high f>70 formation of amorphous arrested states prevents crystallization.

Perspectives of Deuteron Field-Cycling NMR Relaxometry for Probing Molecular Dynamics in Soft Matter.

Due to the single-particle character of the quadrupolar interaction in molecular systems, (2)H NMR poses a unique method for probing reorientational dynamics. Spin-lattice relaxation gives access to the spectral density, and its frequency dependency can be monitored by field-cycling (FC) techniques. However, most FC NMR studies employ (1)H; the use of (2)H is still rare. We report on the application of (2)H FC NMR for investigating the dynamics in molecular liquids and polymers. Commercial as well as home-built relaxometers are employed accessing a frequency range from 30 Hz to 6 MHz. Due to low gyromagnetic ratio, high coupling constants, and finite FC switching times, current (2)H FC NMR does not reach the dispersion region in liquids (toluene and glycerol), yet good agreement with the results from conventional high-field (HF) relaxation studies is demonstrated. The pronounced difference at low frequencies between (2)H and (1)H FC NMR data shows the relevance of intermolecular relaxation in the case of (1)H NMR. In the case of the polymers polybutadiene and poly(ethylene-alt-propylene), very similar relaxation dispersion is observed and attributed to Rouse and entanglement dynamics. Combination with HF (2)H relaxation data via applying frequency-temperature superposition allows the reconstruction of the full spectral density reflecting both polymer as well as glassy dynamics. Transformation into the time domain yields the reorientational correlation function C2(t) extending over nine decades in time with a long-time power law, C2(t) ∝ t(-0.45±0.05), which does not conform to the prediction of the tube-reptation model, for which ∝ t(-0.25) is expected. Entanglement sets in below C2(t = τe) ≅ S(2) = 0.001, where τe is the entanglement time and S the corresponding order parameter. Finally, we discuss the future prospects of the (2)H FC NMR technique.

Dynamics of poly(ethylene oxide) in a blend with poly(methyl methacrylate): a quasielastic neutron scattering and molecular dynamics simulations study.

In this paper, we have addressed the question of the dynamic miscibility in a blend characterized by very different glass-transition temperatures, Tg, for the components: poly(ethylene oxide) and poly(methyl methacrylate) (PEO/PMMA). The combination of quasielastic neutron scattering with isotopic labeling and fully atomistic molecular dynamics simulations has allowed us to selectively investigate the dynamics of the two components in the picosecond-10 nanoseconds scale at temperatures close and above the Tg of the blend. The main focus was on the PEO component, i.e., that of the lowest Tg, but first we have characterized the dynamics of the other component in the blend and of the pure PEO homopolymer as reference. In the region investigated, the dynamics of PMMA in the blend is strongly affected by the alpha-methyl rotation; an additional process detected in the experimental window 65 K above the blend-Tg can be identified as the merged alphabeta process of this component that shows strong deviations from Gaussian behavior. On the other hand, pure PEO displays entropy driven dynamics up to very large momentum transfers. Such kind of motion seems to freeze when the PEO chains are in the blend. There, we have directly observed a very heterogeneous and moreover confined dynamics for the PEO component. The presence of the hardly moving PMMA matrix leads to the creation of little pockets of mobility where PEO can move. The characteristic size of such confined islands of mobility might be estimated to be of approximately 1 nm. These findings are corroborated by the simulation study, which has been an essential support and guide in our data analysis procedure.

Origin of dynamic heterogeneities in miscible polymer blends: A quasielastic neutron scattering study

In order to investigate the origin of the often invoked nanoheterogeneities in miscible polymer blends, we have performed quasielastic neutron scattering experiments on the component dynamics within the miscible polymer blend polyisoprene/polyvinyl ether including the pure components as a reference. We find that the apparent local heterogeneities observed by spectroscopic techniques originate from the chain specific crossover properties between entropy driven and local chain dynamics and are, thus, a purely dynamical phenomenon.

Local structure and glass transition of polybutadiene up to 4 GPa.

This communication presents a determination of the glass transition of polybutadiene under very high pressure, and raises the problem of the determination of the relative effects of temperature and density on the glass transition, depending on the pressure and temperature conditions. Local structure and slow dynamics were studied, by neutron scattering and calorimetry. To the best of our knowledge in neutron diffraction on soft matter such a high pressure, up to 4 GPa, was achieved.

Influence of density and temperature on the microscopic structure and the segmental relaxation of polybutadiene.

We investigate the influence of temperature and density on the local structure and the dynamics of polybutadiene by controlling both hydrostatic pressure and temperature in polarized neutron diffraction experiments on deuterated polybutadiene and in inelastic incoherent scattering experiments on protonated polybutadiene. We observe that the static structure factor S(Q) does not change along macroscopic isochores. This behavior is contrary to the relaxations observed on the nanosecond and picosecond time scales and viewed by the dynamic incoherent scattering law S(Q,omega), which differ strongly along the same thermodynamic path. We conclude that the static behavior, i.e., S(Q), is dominated by macroscopic density changes, similar to the vibrational excitations in the meV range. However, the relaxation dynamics is more sensitive to thermal energy changes. This is confirmed by the finding that lines of identical relaxation behavior (in time, shape, and Q dependence), isochrones on the 10(-9) sec time scale, clearly cross the constant density lines in the (P,T) plane. Concerning S(Q), we can reasonably relate the variation of the main-peak position to the average neighbor chain distance and deduce crude microscopic thermal expansion and compressibility coefficients. In the low-Q regime, the observed pressure and temperature variation of S(Q) exceeds the compressibility contribution and suggests the existence of additional scattering, which might originate from structural correlations arising at higher temperature and low pressure.

Advanced rheological characterization of soft colloidal model systems.

The complex flow behavior of polymer-based soft colloidal model systems was investigated using steady and oscillatory shear to prove new concepts for advanced rheological characterization. In the very dilute regime we investigated high molecular weight polybutadiene star polymers to quantify the internal relaxation time arising from the polymeric nature of these ultra-soft colloids. The observed shear-induced brush deformation is interpreted in terms of the internal Zimm time τ(z). The observed dependence of τ(z) on matrix viscosity can be explained by shrinkage of the star polymer due to an increasing incompatibility with increasing matrix molecular weight. The influence of the polymeric nature on the characteristic structural relaxation time in the concentrated regime was investigated using non-linear rheology following Wyss et al (SRFS) (2007 Phys. Rev. Lett. 98 238303). Here we used star-like block copolymer micelles to systematically tune the 'softness' of the colloids by variation of the block ratio. A master curve with proper scaling parameters could be generated independent of the degree of colloidal 'softness'. However, the obtained strain-rate independent structural relaxation time τ(0) was not observed in the linear regime. In addition, a high frequency discrepancy was clearly found in all our experimental data. Both reflect the shortcomings of the SRFS approach.

Molecular observation of constraint release in polymer melts.

The dynamics of binary polymer blends of few labeled long chains in successively shorter matrix chains has been investigated by neutron spin echo (NSE) spectroscopy. For the first time the effect of constraint release on the chain relaxation has been directly observed on a microscopic scale. Decreasing the matrix chain length reduces the topological confinement until unconfined Rouse motion is observed, when the matrix chains are too short to confine the long chain in a tube. Whereas an analytical description of the effect is not yet available, a new simulation based on the slip-link model shows perfect agreement with the NSE data over the full range of matrix molecular weights.

Starlike micelles with starlike interactions: a quantitative evaluation of structure factors and phase diagram.

Starlike PEP-PEO block copolymer micelles offer the possibility to investigate the phase behavior and interactions of regular star polymers (ultrasoft colloids). Micellar functionality f can be smoothly varied by changing solvent composition (interfacial tension). Structure factors obtained by small-angle neutron-scattering can be quantitatively described in terms of an effective potential for star polymers. The experimental phase diagram reproduces to a high level of accuracy the predicted liquid-solid transition. Whereas for intermediate f a bcc phase is observed, for high f the formation of a fcc phase is preempted by glass formation.

An in situ study of the t-butyllithium initiated polymerization of butadiene in d-heptane via small angle neutron scattering and 1H-NMR.

We present a combined 1H-NMR and small angle neutron scattering in situ study of the anionic polymerization of butadiene using t-butyllithium as the initiator. Both initiation and propagation phases were explored. This combined approach allows the structural and kinetic characteristics to be accessed and cross compared. The use of the D22 instrument (ILL Grenoble) permits the attainment of Q approximately equal to 2 x 10(-3) A. This, in turn, led to the identification of coexisting large-scale and smaller aggregates during all stages of the polymerization. The smaller aggregates contain most of the reacted monomers. Their structure changes from high functionality wormlike chains at early stages of the reaction to starlike aggregates where the crossover occurs at a degree of polymerization of approximately equal to 40. The initiation event involved these small, high functionality (approximately equal to 120) aggregates that apparently consisted of cross-associated t-butyllithium with the newly formed allylic-lithium head groups. As the initiation event progressed the initiation rate increased while the functionality of these small aggregates decreased and their size increased. Propagation, in the absence of initiation, was found to have a rate constant that was molecular weight dependent. At approximately 11 kg/mol the measured polymerization rate was found to increase while no further structural changes were seen.

Direct observation of the transition from free to constrained single-segment motion in entangled polymer melts.

We report a direct determination of the time dependent mean-squared segment displacement of a polymer chain in the melt covering the transition from free to constraint Rouse relaxation along the virtual tube of the reptation model. This has been achieved by a neutron spin-echo (NSE) measurement of the segmental self-correlation function as conveyed by the spin-incoherent scattering from two fully protonated polymer melts, polyethylene and polyethylene propylene. Within the scenario of de Gennes reptation model a transition of the time dependence of segmental mean-squared displacements from proportional, variant t(1/2) to proportional, variant t(1/4) is expected and clearly corroborated by the incoherent NSE results.