The structure and relaxation behavior of thermoreversible gels made with poly(methyl methacrylate)-poly(n-butyl acrylate)-poly(methyl methacrylate) [PMMA-PnBA-PMMA] triblock copolymers in 2-ethylhexanol, a midblock selective solvent, were studied by small-angle X-ray scattering (SAXS) and rheology. Effects of endblock length, endblock fraction, and gel concentration on the gel properties were investigated. A dramatic decrease in SAXS intensity was observed over a 20 °C interval where the gel transitions smoothly from elastic to viscous behavior. SAXS patterns were fit with a Percus-Yevick disordered hard-sphere model from which aggregation number and average domain spacing were calculated. Aggregation number increases with increasing gel concentration and endblock length. Increasing the endblock length from 9K to 25K increases the relaxation time of a gel with a polymer volume fraction of 0.15 by a factor of 10 6 . For a given triblock endblock fraction and molecular weight, the micelle aggregation number is strongly correlated to the gel relaxation time. Arrhenius behavior with an effective activation energy of ∼550 kJ/mol was observed for all triblocks and concentrations. This very high effective energy barrier describes gels relaxation behavior over a 40 °C temperature range, where the relaxation times vary by a factor of 10 10 .

We perform a comprehensive set of coarse-grained molecular dynamics simulations of ionomer melts with varying polymer architectures and compare the results to experiments in order to understand ionic aggregation on a molecular level. The model ionomers contain periodically or randomly spaced charged beads, placed either within or pendant to the polymer backbone, with the counterions treated explicitly. The ionic aggregate structure was determined as a function of the spacing of charged beads and also depends on whether the charged beads are in the polymer backbone or pendant to the backbone. The low wavevector ionomer peak in the counterion scattering is observed for all systems, and it is sharpest for ionomers with periodically spaced pendant charged beads with a large spacing between charged beads. Changing to a random or a shorter spacing moves the peak to lower wavevector. We present new experimental X-ray scattering data on Na(+)-neutralized poly(ethylene-co-acrylic acid) ionomers that show the same two trends in the ionomer peak, for similarly structured ionomers. The order within and between aggregates, and how this relates to various models used to fit the ionomer peak, is quantified and discussed.

The morphology of a series of linear poly(ethylene-co-acrylic acid) zinc-neutralized ionomers with either precisely or randomly spaced acid groups was investigated using X-ray scattering, differential scanning calorimetry (DSC), and scanning transmission electron microscopy (STEM). Scattering from semicrystalline, precise ionomers has contributions from acid layers associated with the crystallites and ionic aggregates dispersed in the amorphous phase. The precisely controlled acid spacing in these ionomers reduces the polydispersity in the aggregate correlation length and yields more intense, well-defined scattering peaks. Remarkably, the ionic aggregates in an amorphous, precise ionomer with 22 mol % acid and 66% neutralization adopt a cubic lattice; this is the first report of ionic aggregate self-assembly onto a lattice in an ionomer with an all-carbon backbone. Aggregate size is insensitive to acid content or neutralization level. As the acid content increases from 9.5 to 22 mol % at approximately 75% neutralization, the number density of aggregates increases by approximately 5 times, suggesting that the ionic aggregates become less ionic with increasing acid content.

Macromolecular motion is reduced in crowded polymer nanocomposites. Tracer diffusion is measured for deuterated polystyrene (dPS) into a polystyrene (PS):silica nanoparticle (NP) matrix using elastic recoil detection. This nanocomposite is ideal for studying diffusion in a crowded system because the interparticle distance (ID) that defines confinement can be varied from much greater than to much less than the size of the dPS chain, which is described by 2R g, the radius of gyration, and varies from 10 to 40 nm in this study. Diffusion is observed to be significantly slower than that predicted by the Maxwell model. The tracer diffusion coefficient of dPS in the nanocomposite relative to the pure PS matrix (D/D 0) plotted against the NP separation relative to probe size (i.e., ID/2R g) falls on a master curve, indicating that crowding is a property of both the dPS size and confinement in the nanocomposite. Moreover, the normalized diffusion coefficient decreases more rapidly when ID/2R g is less than ∼1, suggesting strong confinement conditions. The scaling of the diffusion coefficient with chain length is in excellent agreement with the entropic barrier model that accounts for the slowing down associated with the loss of chain entropy due to constrictive bottlenecks.

International audienceThe rate dependence of fracture has been studied in a series of physically associating triblock copolymer gels that have a well-defined molecular structure. Compressive experiments were performed to develop a strain energy function that accurately captures the strain hardening behavior of these materials. This same strain energy function was utilized in a finite element model of the crack tip stresses, which become highly anisotropic at stress values below the failure strength of the gels. The rate dependence of the energy release rate, G, is independent of the gel concentration when G is normalized by the small strain Young's modulus, E. The gels exhibit a transition from rough, slow crack propagation to smooth, fast crack propagation for a well-defined value of the characteristic length, G/E

Designing acid-and ion-containing polymers for optimal proton, ion, or water transport would benefit profoundly from predictive models or theories that relate polymer structures with ionomer morphologies. Recently, atomistic molecular dynamics (MD) simulations were performed to study the morphologies of precise poly-(ethylene-co-acrylic acid) copolymer and ionomer melts.Here, we present the first direct comparisons between scattering profiles, I(q), calculated from these atomistic MD simulations and experimental X-ray data for 11 materials. This set of precise polymers has spacers of exactly 9, 15, or 21 carbons between acid groups and has been partially neutralized with Li, Na, Cs, or Zn. In these polymers, the simulations at 120 °C reveal ionic aggregates with a range of morphologies, from compact, isolated aggregates (type 1) to branched, stringy aggregates (type 2) to branched, stringy aggregates that percolate through the simulation box (type 3). Excellent agreement is found between the simulated and experimental scattering peak positions across all polymer types and aggregate morphologies. The shape of the amorphous halo in the simulated I(q) profile is in excellent agreement with experimental I(q). The modified hard-sphere scattering model fits both the simulation and experimental I(q) data for type 1 aggregate morphologies, and the aggregate sizes and separations are in agreement. Given the stringy structure in types 2 and 3, we develop a scattering model based on cylindrical aggregates. Both the spherical and cylindrical scattering models fit I(q) data from the polymers with type 2 and 3 aggregates equally well, and the extracted aggregate radii and inter-and intra-aggregate spacings are in agreement between simulation and experiment. Furthermore, these dimensions are consistent with real-space analyses of the atomistic MD simulations. By combining simulations and experiments, the ionomer scattering peak can be associated with the average distance between branches of type 2 or 3 aggregates. This direct comparison of X-ray scattering data to the atomistic MD simulations is a substantive step toward providing a comprehensive, predictive model for ionomer morphology, gives substantial support for this atomistic MD model, and provides new credibility to the presence of stringy, branched, and percolated ionic aggregates in precise ionomer melts.

The origin of the frequency-dependent Mott–Schottky behavior observed in a wide range of ZnO-Bi2O3 varistor systems has been investigated. Lumped parameter/complex plane analysis of two-probe ac electrical data indicates that several trapping relaxations contribute to the measured MOV grain-boundary admittance in the frequency range, 10−2 Hz≤f≤107 Hz. Furthermore, this approach allows the development of an equivalent circuit representation which incorporates these trapping phenomena in a systematic manner.

The effect of polymer concentration on mechanical response and micelle morphology of ABA and AB copolymers in B-selective solvents has been systematically studied. Micelle morphology was determined using a combination of small-angle X-ray scattering, shear, and birefringence while mechanical response at low and high strains was determined using indentation techniques. Self-consistent field theory calculations were used to determine micelle volume fraction profiles and to construct an equilibrium phase map. The transition from spherical to cylindrical micelles increases the triblock gel modulus and energy dissipation. Combining knowledge of gel relaxation time, which determines the rate at which the gel can equilibrate its micelle structure, with the equilibrium phase map allows estimation of the experimental temperatures and time scales over which kinetic trapping will arrest micelle structure evolution. Kinetic trapping enables cylindrical morphologies to be obtained at significantly lower polymer fractions than is possible in equilibrated systems.