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.

We present experimental and theoretical results for the linear rheology of melts of entangled, three-arm asymmetric polyisoprene stars. Asymmetric three-arm stars, in which two arms have the same length and the third is shorter, cross over from starlike to linear-like stress relaxation as the length of the third arm varies. We combine recent theories of stress relaxation in symmetric stars and in linear melts to predict the dynamic modulus of the asymmetric stars. For stars with short arm molecular weights of a few entanglement lengths, our theory underestimates the effective drag caused by the short arm, even when polydispersity effects are included. This unexplained discrepancy does not appear in a recent comparison of a related theory with measurements on polyisoprene H-polymers.

Ion-containing polymers have potential as single-ion conducting battery electrolyte materials. Their conductivity is often too low for such applications due to the low dielectric polymer backbone and resulting strong aggregation of ions. We simulate coarse-grained ionomer melts (with explicit counterions) of various polymer architectures to understand the effect of polymer connectivity on the dynamics. We report on the polymer and counterion dynamics as a function of periodically or randomly spaced charged groups, which can be placed in the backbone or pendant to it. The spacer length is also varied. The simulations reveal the mechanism of ion transport, the coupling between counterion and polymer dynamics, and the dependence of the ion dynamics on polymer architecture. Within the ionic aggregrates, ion dynamics is rather fluid and relatively fast. The larger scale dynamics (time and length) depends strongly on the large scale morphology of the ionomer. Systems with percolated clusters have faster counterion diffusion than systems with isolated clusters. In the systems with isolated clusters counterions diffuse through the combination, rearrangement, and separation of neighboring clusters. In this process, counterions move from one cluster to another without ever being separated from a cluster. In percolated systems, the counterions can move similarly without the need for the merging of clusters. Thus, the ion diffusion does not involve a hopping process. The dynamics also depends significantly on the details of the polymer architecture beyond the aggregate morphology. Adding randomness in spacing of the charges can either increase or decrease the ion diffusion, depending on the specific type of random sequence.

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We perform molecular dynamics simulations of coarse-grained ionomer melts with two different architectures. Regularly spaced charged beads are placed either in the polymer backbone (ionenes) or pendant to it. The ionic aggregate structure is quantified as a function of the dielectric constant. The low wave vector ionomer scattering peak is present in all cases, but is significantly more intense for pendant ions, which form compact, discrete aggregates with liquidlike interaggregate order. This is in qualitative contrast to the ionenes, which form extended aggregates.

An understanding of the dispersion of nanoparticles into polymer melts is needed in order to control material properties of polymer nanocomposites. Here we study the dispersion of polymer-grafted nanorods in homopolymer melts of the same chemistry, using both experiment and theory. The theoretical calculations are performed over the range of experimental system parameters. Polymer-grafted gold nanorods (Au NRs) were found to be dispersed when the matrix chain lengths were small relative to the brush chain lengths, and aggregated at higher matrix chain lengths. Both classical density functional theory (DFT) and self-consistent field theory (SCFT) are used to calculate the structure of a polymer brush around an isolated NR in a polymer melt. Both theories predict a gradual transition from a "wet" to a "dry" brush as the grafting density, the NR radius, and/or the ratio of matrix to brush chain lengths is increased. DFT calculations of the interaction free energy between two NRs find an attractive well at intermediate NR separations, with a repulsive barrier at closer NR separations. The strength of the attraction increases as the brushes become more dry. Including the van der Waals attractions between the NRs gives an estimate of their total interaction free energy, which can be used to predict at which values of the system parameters the NRs are dispersed or aggregated. A dispersion map shows good agreement between DFT calculations and experimental observations of dispersed and aggregated nanorods.

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 nature of ionic aggregates in ionomers remains an important open question, particularly considering its significance to their unique electrical and mechanical properties. We have carried out fully atomistic molecular dynamics simulations of melts of lithium-neutralized precise ionomers that reveal the structural features of ionic aggregates in unprecedented detail. In particular, we observe a rich variety of aggregate morphologies depending on neutralization level and ionic content, including string-like and percolated aggregates. The traditional assumption of spherical ionic aggregates with liquid-like ordering that is typically used to interpret experimental scattering data is too simplistic; a more rich and complex set of structures exist that also fit the scattering data.