David Limmer

Princeton University, Princeton Center for Theoretical Sciences, Post-Doc

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I am currently an independent research fellow at the Princeton Center for Theoretical Science. My general research interests involve understanding the structure and dynamics of complex, condensed phase systems. Specific themes in my work include theories of phase transitions in and out of equilibrium, highly correlated dynamics such as in glassy materials, and the importance of collective effects in condensed phase catalysis. Below are recent areas of research
Supervisors: David Chandler

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Papers by David Limmer

The electric double layer has a life of its own

Using molecular dynamics simulations with recently developed importance sampling methods, we show... more Using molecular dynamics simulations with recently developed importance sampling methods, we show that the differential capacitance of a model ionic liquid based double-layer capacitor exhibits an anomalous dependence on the applied electrical potential. Such behavior is qualitatively incompatible with standard mean-field theories of the electrical double layer, but is consistent with observations made in experiment. The anomalous response results from structural changes induced in the interfacial region of the ionic liquid as it develops a charge density to screen the charge induced on the electrode surface. These structural changes are strongly influenced by the out-of-plane layering of the electrolyte and are multifaceted, including an abrupt local ordering of the ions adsorbed in the plane of the electrode surface, reorientation of molecular ions, and the spontaneous exchange of ions between different layers of the electrolyte close to the electrode surface. The local ordering exhibits signatures of a first-order phase transition, which would indicate a singular charge-density transition in a macroscopic limit.

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The length and time scales of water's glass transitions

Using a model for the equilibrium dynamics of supercooled water, I derive the average length and ... more Using a model for the equilibrium dynamics of supercooled water, I derive the average length and time scales that govern the nonequilibrium relaxation behavior of amorphous ice prepared by rapid cooling. Upon cooling, water falls out of equilibrium whereby the temperature dependence of water's relaxation time is shown to change from super-Arrhenius to Arrhenius. A consequence of this crossover is that the location of water's glass transition temperature depends logarithmically on cooling rate. Accompanying the change in temperature dependence is the emergence of a dynamical length-scale, the size of which depends on the cooling rate and varies between angstroms and 10s of nanometers. Elucidating this protocol dependence on the properties of amorphous ice clarifies a number of previous experimental observations.

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Theory of amorphous ices

We derive a phase diagram for amorphous solids and liquid supercooled water and explain why the a... more We derive a phase diagram for amorphous solids and liquid supercooled water and explain why the amorphous solids of water exist in several different forms. Application of large-deviation theory allows us to prepare such phases in computer simulations. Along with nonequilibrium transitions between the ergodic liquid and two distinct amorphous solids, we establish coexistence between these two amorphous solids. The phase diagram we predict includes a nonequilibrium triple point where two amorphous phases and the liquid coexist. While the amorphous solids are long-lived and slowlyaging glasses, their melting can lead quickly to the formation of crystalline ice. Further, melting of the higher density amorphous solid at low pressures takes place in steps, transitioning to the lower density glass before accessing a nonequilibrium liquid from which ice coarsens.

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On the fluctuations that order and frustrate liquid water

At ambient conditions, water sits close to phase coexistence with its crystal. More so than in ma... more At ambient conditions, water sits close to phase coexistence with its crystal. More so than in many other materials, this fact is manifested in the fluctuations that maintain a large degree of local order in the liquid. These fluctuations and how they result in long-ranged order, or its absence, are emergent features of many interacting molecules. Their study therefore requires using the tools of statistical mechanics for their systematic understanding. In this dissertation we develop such an understanding. In particular, we focus on collective behavior that emerges in liquid and solid water. At room temperatures, the thermophysical properties of water are quantified and rationalized with simple molecular models. A key feature of these models is the correct characterization of the competition between entropic forces of packing and the energetic preference for tetrahedral order. At cold temperatures, the properties of ice surfaces are studied with statistical field theory. The theory we develop for the long wavelength features of ice interfaces allows us to explain the existence of a premelting layer on the surface of ice and the stability of ice in confinement. In between these extremes, the dynamics of supercooled water are considered. A detailed theory for the early stages of coarsening is developed and used to explain the peculiar observation of a transient second liquid state of water. When coarsening dynamics are arrested, the result is the formation of a glassy states of water. We show that out-of-equilibrium the phase diagram for supercooled water exhibits a rich amount of structure, including a triple point between two glass phases of water and the liquid. At the end, we explore possible technological implications for the interplay between ordering and frustration in studies of water at metal interfaces.

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Nature of the anomalies in the supercooled liquid state of the mW model of water

Characterizing heterogeneous dynamics at hydrated electrode surfaces

The putative liquid-liquid transition is a liquid-solid transition in atomistic models of water. II

Corresponding states for mesostructure and dynamics of supercooled water

Charge fluctuations in nanoscale capacitors

Gas transport in ethylene–propylene–diene (EPDM) elastomer: Molecular simulation and experimental study

Time lag permeation measurements with ethylene–propylene–diene (EPDM) elastomer have been underta... more Time lag permeation measurements with ethylene–propylene–diene (EPDM) elastomer have been undertaken in an effort to characterize the gas transport properties of this barrier material. The derived solubility and diffusivity of a series of probe gases including helium, hydrogen, neon, argon, krypton, oxygen, nitrogen, carbon dioxide and methane were measured and compared with molecular simulation predictions.

Solvation at Aqueous Metal Electrodes

We have applied molecular dynamics and methods of importance sampling to study structure and dyna... more We have applied molecular dynamics and methods of importance sampling to study structure and dynamics of liquid water in contact with metal surfaces. The specific surfaces considered resemble the 100 and 111 faces of platinum. Several results emerge that should apply generally, not just to platinum. These results are generic consequences of water molecules binding strongly to surfaces that are incommensurate with favorable hydrogen-bonding patterns. We show that adlayers of water under these conditions have frustrated structures that interact unfavorably with adjacent liquid water. We elucidate dynamical processes of water in these cases that extend over a broad range of timescales, from less than picoseconds to more than nanoseconds. Associated spatial correlations extend over nanometers. We show that adlayer reorganization occurs intermittently, and each reorganization event correlates motions of several molecules. We show that soft liquid interfaces form adjacent to the adlayer, as is generally characteristic of liquid water adjacent to a hydrophobic surface. The infrequent adlayer reorganization produces a hydrophobic heterogeneity that we characterize by studying the degrees by which different regions of the adlayers attract small hydrophobic particles. Consequences for electrochemistry are discussed in the context of hydronium ions being attracted from the liquid to the metal-adlayer surface. E xtended metal interfaces play a fundamental role in aqueous electrochemistry, a field of principal importance in the advancement of renewable, clean energy sources (1, 2). In many processes that occur at metal interfaces, such as electrolysis, corrosion, and electrocatalysis, water is ubiquitous, often acting as both solvent and reactant (3). Although many studies exist that detail the behavior of water across small length scales and timescales (4-7) and at low temperatures (8-10), at present there is little understanding of the large length scale correlations and emergent behavior of water on metal surfaces, even though such effects are likely to influence function in important ways . Here, we address this gap in knowledge with a theoretical model of the interactions between water and a metal surface. Specifically we illustrate how a metal surface can impose geometrical constraints within the adlayer of water, leading to a composite metal-water interface that is hydrophobic on large length scales. We further show how defects within the hydrogen-bonding patterns of the adlayer create transient regions of hydrophobic behavior that exist on small length scales and over long timescales. These results offer a microscopic explanation and generalization of previous experimental observations that have inferred hydrophobicity of a platinum surface at low temperatures .

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Phase diagram of supercooled water confined to hydrophilic nanopores

We present a phase diagram for water confined to cylindrical silica nanopores in terms of pressur... more We present a phase diagram for water confined to cylindrical silica nanopores in terms of pressure, temperature and pore radius. The confining cylindrical wall is hydrophilic and disordered, which has a destabilizing effect on ordered water structure. The phase diagram for this class of systems is derived from general arguments, with parameters taken from experimental observations and computer simulations and with assumptions tested by computer simulation. Phase space divides into three regions: a single liquid, a crystal-like solid, and glass. For large pores, radii exceeding 1 nm, water exhibits liquid and crystal-like behaviors, with abrupt crossovers between these regimes. For small pore radii, crystal-like behavior is unstable and water remains amorphous for all non-zero temperatures. At low enough temperatures, these states are glasses. Several experimental results for supercooled water can be understood in terms of the phase diagram we present.

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Evaluating the Liquid Liquid Phase Transition Hypothesis of Supercoooled Water

To explain the anomalous behavior of supercooled water it has been conjectured that buried within... more To explain the anomalous behavior of supercooled water it has been conjectured that buried within an experimentally inaccessible region of liquid water's phase diagram there exists a second critical point, which is the terminus of a first order transition line between two distinct liquid phases. The so-called liquid-liquid phase transition (LLPT) has since generated much study, though to date there is no consensus on its existence. In this talk, we will discuss our efforts to systematically study the metastable phase diagram of supercooled water through computer simulation. By employing importance-sampling techniques, we have calculated free energies as a function of the density and long-range order to determine unambiguously if two distinct liquid phases exist. We will argue that, contrary to the LLPT hypothesis, the observed phenomenology can be understood as a consequence of the limit of stability of the liquid far away from coexistence. Our results suggest that homogeneous nucleation is the cause of the increased fluctuations present upon supercooling. Further we will show how this understanding can be extended to explain experimental observations of hysteresis in confined supercooled water systems.

Rheological complexity in simple chain models

Chemical Physics, 2008

Dynamical properties of short freely jointed and freely rotating chains are studied using molecul... more Dynamical properties of short freely jointed and freely rotating chains are studied using molecular dynamics simulations. These results are combined with those of previous studies, and the degree of rheological complexity of the two models is assessed. New results are based on an improved analysis procedure of the rotational relaxation of the second Legendre polynomials of the end-to-end vector in terms of the Kohlrausch-Williams-Watts (KWW) function. Increased accuracy permits the variation of the KWW stretching exponent β to be tracked over a wide range of state points. The smoothness of β as a function of packing fraction ɛ is a testimony both to the accuracy of the analytical methods and the appropriateness of (ɛ0-ɛ) as a measure of the distance to the ideal glass transition at ɛ0. Relatively direct comparison is made with experiment by viewing β as a function of the KWW relaxation time τKWW. The simulation results are found to be typical of small molecular glass formers. Several manifestations of rheological complexity are considered. First, the proportionality of α-relaxation times is explored by the comparison of translational to rotational motion (i.e., the Debye-Stokes-Einstein relation), of motion on different length scales (i.e., the Stokes-Einstein relation), and of rotational motion at intermediate times to that at long time. Second, the range of time-temperature superposition master curve behavior is assessed. Third, the variation of β across state points is tracked. Although no particulate model of a liquid is rigorously rheologically simple, we find freely jointed chains closely approximated this idealization, while freely rotating chains display distinctly complex dynamical features.

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The putative liquid-liquid transition is a liquid-solid transition in atomistic models of water

Hydration of metal surfaces can be dynamically heterogeneous and hydrophobic

David Limmer

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