A commercially viable solution process to control long-chain branching in polyethylene.

In polyolefins, long-chain branching is introduced through an energy-intensive, high-pressure radical process to form low-density polyethylene (LDPE). In the current work, we demonstrated a ladder-like polyethylene architecture through solution polymerization of ethylene and less than 1 mole % of α,ω-dienes, using a dual-chain catalyst. The ladder-branching mechanism requires catalysts with two growing polymer chains on the same metal center, thus enchaining the diene without the requirement of a steady-state concentration of pendant vinyl groups. Molecular weight distributions lacking a high-molecular weight tail, distinctive Mark-Houwink signatures, nuclear magnetic resonance characterization, and shear and extensional rheology consistent with highly branched polyethylene architectures are described. This approach represents an industrially viable solution-polymerization process capable of producing controlled long-chain branched polyethylene with rheological properties comparable to those of LDPE or its blends with linear low-density polyethylene (LLDPE).

Extended Ensemble Approach to Transferable Potentials for Low-Resolution Coarse-Grained Models of Ionomers.

We develop an extended ensemble method for constructing transferable, low-resolution coarse-grained (CG) models of polyethylene-oxide (PEO)-based ionomer chains with varying composition at multiple temperatures. In particular, we consider ionomer chains consisting of 4 isophthalate groups, which may be neutral or sulfonated, that are linked by 13 PEO repeat units. The CG models represent each isophthalate group with a single CG site and also explicitly represent the diffusing sodium counterions but do not explicitly represent the PEO backbone. We define the extended ensemble as a collection of equilibrium ensembles that are obtained from united atom (UA) simulations at 2 different temperatures for 7 chemically distinct ionomers with varying degrees of sulfonation. We employ a global force-matching method to determine the set of interaction potentials that, when appropriately combined, provide an optimal approximation to the many-body potential of mean force for each system in the extended ensemble. This optimized xn force field employs long-ranged Coulomb potentials with system-specific dielectric constants that systematically decrease with increasing sulfonation and temperature. An empirical exponential model reasonably describes the sensitivity of the dielectric to sulfonation, but we find it more challenging to model the temperature-dependence of the dielectrics. Nevertheless, given appropriate dielectric constants, the transferable xn force field reasonably describes the ion pairing that is observed in the UA simulations as a function of sulfonation and temperature. Remarkably, despite eliminating any explicit description of the PEO backbone, the CG model predicts string-like ion aggregates that appear qualitatively consistent with the ionomer peak observed in X-ray scattering experiments and, moreover, with the temperature dependence of this peak.

Depletion attraction of sheet-like ion aggregates in low-dielectric ionomer melts.

Ionomers are polymers in which an ionic group is covalently bonded to the polymer backbone. Ion aggregates in ionomers have morphologies that allow for the packing of the attached polymer backbone. Using ion-only coarse-grained molecular dynamics, we observe that string-like ion aggregates become flat and sheet-like at lower dielectric constants. A consequence of the changing morphology is that the sheet-like aggregates self-assemble to form ordered, lamellar structures. We use a simple thermodynamic model to demonstrate that depletion attraction mediated by small aggregates can explain the observed order. Our results suggest that depletion attraction can drive ions to form structures that have the size scale suggested by direct visualization, produce the commonly observed experimental correlation peak from X-ray and neutron scattering, and satisfy chain-packing constraints that have been demonstrated to be important in simulations.

Ion-mediated charge transport in ionomeric electrolytes.

Ionomers, or single-ion conductors, serve as a model system to study ion transport in polymeric systems. Conductivity is a system property that depends on the net charge transport in the system. The mechanism through which ions are transported can dramatically change the contribution of an ion's self-motion (i.e. diffusion coefficient) to the conductivity of the system. For example, positive and negative ions diffusing as a pair have no net contribution to conductivity. In a coarse-grained molecular dynamics simulation of sodium-neutralized poly(PEO-co-sulfoisophthalate), we show that ion transport is mediated through consecutive coordination with ion pairs and higher order clusters due to the high density of ions. This transport mechanism is highly efficient and shows evidence of cation relaying. We show that larger ion aggregates can serve as ion-conducting paths for positive charges, and demonstrate how a highly ordered ion aggregate network can improve conductivity by enhancing correlated ion transport.

Scaling behavior and local structure of ion aggregates in single-ion conductors.

Single-ion conductors are attractive electrolyte materials because of their inherent safety and ease of processing. Most ions in a sodium-neutralized PEO sulfonated-isophthalate ionomer electrolyte exist as one dimensional chains, restricted in dimensionality by the steric hindrance of the attached polymer. Because the ions are slow to reconfigure, atomistic MD simulations of this material are unable to adequately sample equilibrium ion structures. We apply a novel coarse-graining scheme using a generalized-YBG procedure in which the polymer backbone is completely removed and implicitly represented by the effective potentials of the remaining ions. The ion-only coarse-grained simulation allows for substantial sampling of equilibrium aggregate configurations. We extend the wormlike micelle theory to model ion chain equilibrium. Our aggregates are random walks which become more positively charged with increasing size. Defects occur on the string-like structure in the form of "dust" and "knots," which form due to cation coordination with open sites along the string. The presence of these defects suggest that cation hopping along open third-coordination sites could be an important mechanism of charge transport using ion aggregates.