Anomalous Underscreening in the Restricted Primitive Model.

Underscreening is a collective term for charge correlations in electrolytes decaying slower than the Debye length. Anomalous underscreening refers to phenomenology that cannot be attributed alone to steric interactions. Experiments with concentrated electrolytes and ionic fluids report anomalous underscreening, which so far has not been observed in simulation. We present Molecular Dynamics simulation results exhibiting anomalous underscreening that can be connected to cluster formation. A theory that accounts for ion pairing confirms the trend. Our results challenge the classic understanding of dense electrolytes impacting the design of technologies for energy storage and conversion.

Exactly solvable percolation problems.

We propose a simple percolation criterion for arbitrary percolation problems. The basic idea is to decompose the system of interest into a hierarchy of neighborhoods, such that the percolation problem can be expressed as a branching process. The criterion provides the exact percolation thresholds for a large number of exactly solved percolation problems, including random graphs, small-world networks, bond percolation on two-dimensional lattices with a triangular hypergraph, and site percolation on two-dimensional lattices with a generalized triangular hypergraph, as well as specific continuum percolation problems. The fact that the range of applicability of the criterion is so large bears the remarkable implication that all the listed problems are effectively treelike. With this in mind, we transfer the exact solutions known from duality to random lattices and site-bond percolation problems and introduce a method to generate simple planar lattices with a prescribed percolation threshold.

Percolation of rigid fractal carbon black aggregates.

We examine network formation and percolation of carbon black by means of Monte Carlo simulations and experiments. In the simulation, we model carbon black by rigid aggregates of impenetrable spheres, which we obtain by diffusion-limited aggregation. To determine the input parameters for the simulation, we experimentally characterize the micro-structure and size distribution of carbon black aggregates. We then simulate suspensions of aggregates and determine the percolation threshold as a function of the aggregate size distribution. We observe a quasi-universal relation between the percolation threshold and a weighted average radius of gyration of the aggregate ensemble. Higher order moments of the size distribution do not have an effect on the percolation threshold. We conclude further that the concentration of large carbon black aggregates has a stronger influence on the percolation threshold than the concentration of small aggregates. In the experiment, we disperse the carbon black in a polymer matrix and measure the conductivity of the composite. We successfully test the hypotheses drawn from simulation by comparing composites prepared with the same type of carbon black before and after ball milling, i.e., on changing only the distribution of aggregate sizes in the composites.

Nearest-neighbor connectedness theory: A general approach to continuum percolation.

We introduce a method to estimate continuum percolation thresholds and illustrate its usefulness by investigating geometric percolation of noninteracting line segments and disks in two spatial dimensions. These examples serve as models for electrical percolation of elongated and flat nanofillers in thin film composites. While the standard contact volume argument and extensions thereof in connectedness percolation theory yield accurate predictions for slender nanofillers in three dimensions, they fail to do so in two dimensions, making our test a stringent one. In fact, neither a systematic order-by-order correction to the standard argument nor invoking the connectedness version of the Percus-Yevick approximation yield significant improvements for either type of particle. Making use of simple geometric considerations, our new method predicts a percolation threshold of ρ_{c}l^{2}≈5.83 for segments of length l, which is close to the ρ_{c}l^{2}≈5.64 found in Monte Carlo simulations. For disks of area a we find ρ_{c}a≈1.00, close to the Monte Carlo result of ρ_{c}a≈1.13. We discuss the shortcomings of the conventional approaches and explain how usage of the nearest-neighbor distribution in our method bypasses those complications.

Bayesian unsupervised learning reveals hidden structure in concentrated electrolytes.

Electrolytes play an important role in a plethora of applications ranging from energy storage to biomaterials. Notwithstanding this, the structure of concentrated electrolytes remains enigmatic. Many theoretical approaches attempt to model the concentrated electrolyte by introducing the idea of ion pairs, with ions either being tightly "paired" with a counter-ion or "free" to screen charge. In this study, we reframe the problem into the language of computational statistics and test the null hypothesis that all ions share the same local environment. Applying the framework to molecular dynamics simulations, we find that this null hypothesis is not supported by data. Our statistical technique suggests the presence of two distinct local ionic environments at intermediate concentrations, whose differences surprisingly originate in like charge correlations rather than unlike charge attraction. Through considering the effect of these "aggregated" and "non-aggregated" states on bulk properties including effective ion concentration and dielectric constant, we identify a scaling relation between the effective screening length and theoretical Debye length, which applies across different dielectric constants and ion concentrations.

Continuum percolation expressed in terms of density distributions.

We present an approach to derive the connectivity properties of pairwise interacting n-body systems in thermal equilibrium. We formulate an integral equation that relates the pair connectedness to the distribution of nearest neighbors. For one-dimensional systems with nearest-neighbor interactions, the nearest-neighbor distribution is in turn related to the pair-correlation function g through a simple integral equation. As a consequence, for those systems, we arrive at an integral equation relating g to the pair connectedness, which is readily solved even analytically if g is specified analytically. We demonstrate the procedure for a variety of pair potentials including fully penetrable spheres as well as impenetrable spheres, the only two systems for which analytical results for the pair connectedness exist. However, the approach is not limited to nearest-neighbor interactions in one dimension. Hence, we also outline the treatment of external fields and long-range interactions and we illustrate how the formalism can applied to higher-dimensional systems using the three-dimensional ideal gas as an example.

Screening Lengths in Ionic Fluids.

The decay of correlations in ionic fluids is a classical problem in soft matter physics that underpins applications ranging from controlling colloidal self-assembly to batteries and supercapacitors. The conventional wisdom, based on analyzing a solvent-free electrolyte model, suggests that all correlation functions between species decay with a common decay length in the asymptotic far field limit. Nonetheless, a solvent is present in many electrolyte systems. We show using an analytical theory and molecular dynamics simulations that multiple decay lengths can coexist in the asymptotic limit as well as at intermediate distances once a hard sphere solvent is considered. Our analysis provides an explanation for the recently observed discontinuous change in the structural force across a thin film of ionic liquid-solvent mixtures as the composition is varied, as well as reframes recent debates in the literature about the screening length in concentrated electrolytes.

Divergence of the third harmonic stress response to oscillatory strain approaching the glass transition.

The leading nonlinear stress response in a periodically strained concentrated colloidal dispersion is studied experimentally and by theory. A thermosensitive microgel dispersion serves as well-characterized glass-forming model, where the stress response at the first higher harmonic frequency (3ω for strain at frequency ω) is investigated in the limit of small amplitude. The intrinsic nonlinearity at the third harmonic exhibits a scaling behavior which has a maximum in an intermediate frequency window and diverges when approaching the glass transition. It captures the (in-) stability of the transient elastic structure. Elastic stresses in-phase with the third power of the strain dominate the scaling. Our results qualitatively differ from previously derived scaling behavior in dielectric spectroscopy of supercooled molecular liquids. This might indicate a dependence of the nonlinear response on the symmetry of the external driving under time reversal.