Lutz Willner

Dynamics of polybutadienes with different microstructures. 2. Dielectric response and comparisons with rheological behavior

A series of 1,2-1,4-polybutadienes with varying 1,2 vinyl content was investigated using time-domain dielectric spectroscopy. The time range was 10 Ϫ5-300 s, which can be converted by Laplace transform to a frequency range of 10 Ϫ3-6000 Hz. The samples were the same as those used in a previous rheological study from these laboratories. Therefore, a direct comparison of dielectric and mechanical responses was possible. Within experimental uncertainty, the ␣ relaxation observed by both methods shows the same temperature dependence but there is an offset between the characteristic times of both methods, which increases with increasing vinyl content. This result can be qualitatively understood from the difference of the size of the dipolar groups, viz. cis and vinyl monomeric units, in the context of the DiMarzio-Bishop model. In addition, the question of time-temperature superposition was studied using the dielectric data. In the cases of a vinyl content у0.53 no deviations from time-temperature superposition were detected. Only for the sample with the lowest vinyl content 0.07 does the attempt to construct a master curve from the dielectric loss data fail. In this case a fit with a combination of a Havriliak-Negami and a Cole-Cole functions suggests that this deviation from time-temperature superposition is an intrinsic feature of the ␣ relaxation rather than an effect of its merging with the ␤ relaxation. The absence of indications for such a deviation in the rheological study can be explained by the smaller frequency range of the latter. This stresses the necessity of a large dynamic range in experiments aimed at the examination of the time-temperature superposition principle.

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.

Equilibrium exchange kinetics in n-alkyl–PEO polymeric micelles: single exponential relaxation and chain length dependence

In this communication we present first results on the chain exchange kinetics of n-alkyl–PEO polymeric micelles by time-resolved small angle neutron scattering. We found that the rate strongly depends on the alkyl-chain length and that the relaxation function almost perfectly follows the single exponential decay predicted by theory. The key achievement of this study is the experimental verification that core block polydispersity accounts for the almost logarithmic time decay in block copolymer micelles as recently suggested by Choi et al. The results thus directly show that unimer exchange is the main mechanism for molecular exchange in block copolymer micelles.

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.

Kinetics of Block Copolymer Micelles Studied by Small-Angle Scattering Methods

This article reviews recent progress in studying the kinetics of block copolymer micellar systems by time-resolved small angle scattering techniques. The review includes an overview of the theoretical background concerning block copolymer micellar structure and kinetics, with a clear distinction between equilibrium and non-equilibrium processes. Basic principles of both static and time-resolved small-angle X-ray and neutron scattering (TR-SAXS and TR-SANS) techniques are summarized, with a special emphasis on the characterization of block copolymer micellar systems. In particular, the principle of SANS in combination with hydrogen/deuterium (H/D) contrast variation for the determination of chain exchange under equilibrium conditions is highlighted. In the experimental part, we first review results on equilibrium kinetics obtained within the last decade by the TR-SANS/H/D labeling technique. In general, the experimental results strongly indicate that the component exchange between different micelles proceeds via the exchange of single unimers. In agreement with the theoretical prediction, chain expulsion is the rate-determining step. The corresponding activation energy is mainly governed by the interfacial tension and the length of the insoluble block, which determine the exchange rate with a double exponential dependence. Thus, due to this extremely strong dependence, even synthetic polymers with modest chain length distribution show a logarithmic time dependence instead of the theoretically expected single exponential decay. In the second part, the kinetic results obtained under non-equilibrium conditions, i.e., relaxation processes obtained after perturbations from equilibrium, are reviewed. This part covers formation kinetics as well as reorganization and morphological transition kinetics. We present, as a special highlight, TR-SAXS measurements with millisecond resolution on the formation of star-like micelles after stopped-flow mixing of molecularly dissolved block copolymers with a selective solvent. The micellization process could be modelled as a nucleation & growth process with unimer exchange as the elemental mechanism. The resulting scenario could be described as a three step process that includes a fast nucleation event, a region of micellar growth, and a final equilibration to thermodynamically stable micelles. In summary, this review demonstrates the importance of small angle scattering techniques for studying fundamental aspects of kinetics in block copolymer micelles and in soft matter materials in general.

Ordering Phenomena of Star Polymers in Solution by SANS

In this paper we present the experimental evidence of incipient ordering of star polymers in solution near the overlap concentration * as predicted by scaling laws. We have studied 8- and 18-arm polyisoprene stars in the dilute and semi-dilute regime. A peak in the interparticle structure factor S(Q) due to a liquidlike ordering of spheres was found by small-angle neutron scattering. A shift of the peak position to higher Q was observed with increasing concentration. The corresponding mean particle distance 2π/Qmax scales with -1/4 for both stars. Our results, in accordance with predictions, follows the general scaling behavior.

Dynamic response of block copolymer wormlike micelles to shear flow

The linear and nonlinear dynamic response to an oscillatory shear flow of giant wormlike micelles consisting of Pb–Peo block copolymers is studied by means of Fourier transform rheology. Experiments are performed in the vicinity of the isotropic–nematic phase transition concentration, where the location of isotropic–nematic phase transition lines is determined independently. Strong shear-thinning behaviour is observed due to critical slowing down of orientational diffusion as a result of the vicinity of the isotropic–nematic spinodal. This severe shear-thinning behaviour is shown to result in gradient shear banding. Time-resolved small-angle neutron scattering experiments are used to obtain an insight into the microscopic phenomena that underlie the observed rheological response. An equation of motion for the order parameter tensor and an expression of the stress tensor in terms of the order parameter tensor are used to interpret the experimental data, both in the linear and nonlinear regimes. Scaling of the dynamic behaviour of the orientational order parameter and the stress is found when critical slowing down due to the vicinity of the isotropic–nematic spinodal is accounted for.

Unraveling the equilibrium chain exchange kinetics of polymeric micelles using small-angle neutron scattering – architectural and topological effects

In this paper, we present a study of micellar structures formed by poly(styrene)-poly(butadiene) (PS10-PB10; the numbers indicate the molecular weight in kg mol−1) diblock copolymers and PB10-PS20-PB10 triblock copolymers in different n-alkane solvents. Particular emphasis is placed on the dynamic properties of these micelles under equilibrium which are studied using a novel time-resolved small-angle neutron scattering technique. The results show that the structures of the micelles are very similar for both the diblock and triblock copolymers, which allows a direct comparison of the dynamic properties. A novel logarithmic relaxation is found for both the triblock and the diblock micelles which is not consistent with theoretical expectations. However, for the diblock micelles, the relaxation kinetics seem to approach the rate and the single exponential decay predicted by Halperin & Alexander [Macromolecules, (1989), 22, 2403–2412] when the micellar cores are strongly swollen with solvent. For the triblock micelles a logarithmic relaxation is found for all cases as an effect of additional topological knots present even in highly swollen micellar cores. This behavior is assigned to an increased coupling of chain motion within the dense confined core – an effect which seems to vanish in diblock micelles when the core is sufficiently swollen.

Polymer dynamics under soft confinement in a self-assembled system

Block copolymers that self-assemble into nano-structured melts provide an interesting template for soft confinement. An important question that arises is how the chain dynamics is affected in such self-assembled systems. Here we consider a system composed of poly(isoprene)-b-poly(dimethyl siloxane) (PI6-PDMS30, where the numbers indicate the molecular weight in kg mole−1) having a large asymmetry where the minor PI component block constitutes 19% of the total molecular weight. As shown by small angle neutron scattering (SANS), the system forms hexagonally ordered cylindrical structures composed of a PI phase (with a cylinder radius of about 6.4 nm) in a continuous PDMS matrix. Here we demonstrate using neutron spin-echo spectroscopy and careful H/D contrast matching schemes how the dynamics of single polymer chains (single chain contrast) and the interfacial dynamics of the domains can be resolved independently. This is achieved in the former “single chain contrast” case by matching out the net domain scattering leaving only the intra chain coherent structure factor visible. In the latter “bulk contrast” case, the protonated (h) PI and deuterated (d) PDMS domains are visible and most of the contrast comes from the small interfacial layer where h-PI/d-PDMS segments are intermixed and give rise to a significant contrast by which the fluctuations can be observed. Combining the results from the two contrast conditions, we show that the dynamics can be consistently described in terms of Rouse motion modified by the surface fluctuation and laterally restricted to 2D surface diffusion. Surprisingly, the fluctuations of the interface significantly contribute to the dynamics and the interfacial tension drives the fluctuations of a sizeable portion of the polymer chains while the dynamics is similar to Rouse motion.

Anomalous chain diffusion in unentangled model polymer nanocomposites

We studied unentangled poly(ethylene-alt-propylene) (PEP) in a composite with hydrophobic silica particles as a function of the filler concentration. Our neutron spin echo (NSE) experiments cover both the internal dynamics as well as the center of mass diffusion beyond the Rouse time. The key experimental results are (i) all of the chains are equally mobile, (ii) the basic segmental (Rouse) relaxation rate is unaffected even at highest filler concentrations, and (iii) apparently the obstacles reduce significantly the translational center of mass motion. This happens, even in the case when the particles do not significantly confine the polymer. (iv) A transition from regular to anomalous diffusion in the Rouse regime at the highest particle fractions is clearly evidenced. In order to understand the microscopic mechanisms underlying the experimental observations, we performed coarse grained simulations. We demonstrate that the geometrical confinement only affects the dynamics at a long time scale outside the experimental window and therefore it is not able to explain the results found in the NSE experiments. The consideration of inter-chain interactions, however, results in a significant influence even at shorter times and a quantitative agreement between the experiments and simulations was found. The simulations clearly demonstrate that the interfaces cause a deceleration of the chains in their close vicinity. Then the inter-chain interactions carry this slowing down to the other chains at a time-scale of the Rouse relaxation time. Hence, in the experimental datasets an overall slowing down is observed.