Describing nonequilibrium soft matter with mean field game theory.

We demonstrate that combining an emerging approach to game theory with self-consistent mean field theory provides realistic treatments of diblock copolymer phase evolution. We especially examine order-order phase transformations upon quenched temperature change involving hexagonal cylinders, lamellae, and the gyroid. Our findings demonstrate that (i) the game theoretical dynamics produce realistic trajectories for the evolution of the local compositions, (ii) the predicted small-angle scattering follows experimentally observed trends, (iii) nucleation and growth is active when the system is quenched far from the critical point, and (iv) epitaxial growth is manifest. To our knowledge, the methodology presented provides the first merger of mean field game theory and statistical mechanics for soft matter systems, giving a new inroad to studying polymer dynamics.

Jammed Limit of Bijel Structure Formation.

Over the past decade, methods to control microstructure in heterogeneous mixtures by arresting spinodal decomposition via the addition of colloidal particles have led to an entirely new class of bicontinuous materials known as bijels. Herein, we present a new model for the development of these materials that yields to both numerical and analytical evaluation. This model reveals that a single dimensionless parameter that captures both chemical and environmental variables dictates the dynamics and ultimate structure formed in bijels. We demonstrate that this parameter must fall within a fixed range in order for jamming to occur during spinodal decomposition, as well as show that known experimental trends for the characteristic domain sizes and time scales for formation are recovered by this model.

Eigenvector Centrality is a Metric of Elastomer Modulus, Heterogeneity, and Damage.

We present an application of eigenvector centrality to encode the connectivity of polymer networks resolved at the micro- and meso-scopic length scales. This method captures the relative importance of different nodes within the network structure and provides a route toward the development of a statistical mechanics model that correlates connectivity with mechanical response. This scheme may be informed by analytical and semi-analytical models for the network structure, or through direct experimental examination. It may be used to predict the reduction in mechanical performance for heterogeneous materials subjected to specific modes of damage. Here, we develop the method and demonstrate that it leads to the prediction of established trends in elastomers. We also apply the model to the case of a self-healing polymer network reported in the literature, extracting insight about the fraction of bonds broken and re-formed during strain and recovery.

Highly durable fuel cell electrodes based on ionomers dispersed in glycerol.

A major, unprecedented improvement in the durability of polymer electrolyte membrane fuel cells is obtained by tuning the properties of the interface between the catalyst and the ionomer by choosing the appropriate dispersing medium. While a fuel cell cathode prepared from aqueous dispersion showed 90 mV loss at 0.8 A cm(-2) after 30,000 potential cycles (0.6-1.0 V), a fuel cell cathode prepared from glycerol dispersion exhibited only 20 mV loss after 70,000 cycles. This minimum performance loss occurs even though there was an over 80% reduction of electrochemical surface area of the Pt catalyst. These findings indicate that a proper understanding and control of the catalyst-water-ionomer (three-phase) interfaces is even more important for maintaining fuel cell durability in typical electrodes than catalyst agglomeration, and this opens up a novel path for tailoring the functional properties of electrified interfaces.

Flattening of Dendrimers from Solutions onto Charged Surfaces.

The adsorption of dendrimers onto charged surfaces plays a role in many emerging applications. Numerous studies found in the literature report that dendrimers flatten at these interfaces. Here, we provide a simple scaling theory that describes the height of the adsorbed layer, the fraction of segments within the dendrimer that touch the surface, and the total number of dendrimers adsorbed as a function of generation of growth, surface charge density, and concentration. We demonstrate that these predictions agree well with extensive molecular dynamics simulations. Combined, the simulations and scaling argument indicate that simultaneous adsorption and compression at the interface take place.