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 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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# Your search: "author:"Limmer, David""

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## Scholarly Works (13 results)

Recent Work (2019)

We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis is made possible by explicit forms for the gradients of a cost function in terms of the susceptibility of driven trajectories to changes in variational parameters. We consider probabilities of time-integrated dynamical observables as characterized by their large deviation functions and find that in many cases, the variational estimate is quantitatively accurate. Additionally, we provide expressions to exactly correct the variational estimate that can be evaluated directly. We benchmark this algorithm against the numerically exact solution of a model of a driven particle in a periodic potential, where the control force can be represented with a complete basis. We then demonstrate the utility of the algorithm in a model of repulsive particles on a line, which undergo a dynamical phase transition, resulting in singular changes to the form of the optimal control force. In both systems, we find fast convergence and are able to evaluate large deviation functions with significant increases in statistical efficiency over alternative Monte Carlo approaches.

Recent Work (2020)

We present a perspective on recent observations of the photoinduced phase separation of halides in multi-component lead-halide perovskites. The spontaneous phase separation of an initial homogeneous solid solution under steady-state illumination conditions is found experimentally to be reversible, stochastic, weakly dependent on morphology, yet strongly dependent on composition and thermodynamic state. Regions enriched in a specific halide species that form upon phase separation are self-limiting in size, pinned to specific compositions, and grow in number in proportion to the steady-state carrier concentration until saturation. These empirical observations of robustness rule out explanations based on specific defect structures and point to the local modulation of an existing miscibility phase transition in the presence of excess charge carriers. A model for rationalizing existing observations based on the coupling between composition, strain, and charge density fluctuations through the formation of polarons is reviewed.

We describe a framework to reduce the computational effort to evaluate large deviation functions of time integrated observables within nonequilibrium steady states. We do this by incorporating an auxiliary dynamics into trajectory based Monte Carlo calculations, through a transformation of the system's propagator using an approximate guiding function. This procedure importance samples the trajectories that most contribute to the large deviation function, mitigating the exponential complexity of such calculations. We illustrate the method by studying driven diffusion and interacting lattice models in one and two spatial dimensions. Our work offers an avenue to calculate large deviation functions for high dimensional systems driven far from equilibrium.

Recent Work (2019)

We present a strategy for mapping the dynamics of a fermionic quantum system to a set of classical dynamical variables. The approach is based on imposing the correspondence relation between the commutator and the Poisson bracket, preserving Heisenberg's equation of motion for one-body operators. In order to accommodate the effect of two-body terms, we further impose quantization on the spin-dependent occupation numbers in the classical equations of motion, with a parameter that is determined self-consistently. Expectation values for observables are taken with respect to an initial quasiclassical distribution that respects the original quantization of the occupation numbers. The proposed classical map becomes complete under the evolution of quadratic Hamiltonians and is extended for all even order observables. We show that the map provides an accurate description of the dynamics for an interacting quantum impurity model in the coulomb blockade regime, at both low and high temperatures. The numerical results are aided by a novel importance sampling scheme that employs a reference system to reduce significantly the sampling effort required to converge the classical calculations.

Recent Work (2020)

We derive a relationship for the electric field dependent ionic conductivity in terms of fluctuations of time integrated microscopic variables. We demonstrate this formalism with molecular dynamics simulations of solutions of differing ionic strength with implicit solvent conditions and molten salts. These calculations are aided by a novel nonequilibrium statistical reweighting scheme that allows for the conductivity to be computed as a continuous function of the applied field. In strong electrolytes, we find the fluctuations of the ionic current are Gaussian, and subsequently, the conductivity is constant with applied field. In weaker electrolytes and molten salts, we find the fluctuations of the ionic current are strongly non-Gaussian, and the conductivity increases with applied field. This nonlinear behavior, known phenomenologically for dilute electrolytes as the Onsager-Wien effect, is general and results from the suppression of ionic correlations at large applied fields, as we elucidate through both dynamic and static correlations within nonequilibrium steady states.

Recent Work (2020)

We revisit the statistical mechanics of charge fluctuations in capacitors. In constant-potential classical molecular simulations, the atomic charges of electrode atoms are treated as additional degrees of freedom which evolve in time so as to satisfy the constraint of fixed electrostatic potential for each configuration of the electrolyte. The present work clarifies the role of the overall electroneutrality constraint, as well as the link between the averages computed within the Born-Oppenheimer approximation and that of the full constant-potential ensemble. This allows us in particular to derive a complete fluctuation-dissipation relation for the differential capacitance, that includes a contribution from the charge fluctuations (around the charges satisfying the constant-potential and electroneutrality constraints) also present in the absence of an electrolyte. We provide a simple expression for this contribution from the elements of the inverse of the matrix defining the quadratic form of the fluctuating charges in the energy. We then illustrate numerically the validity of our results, and recover the expected continuum result for an empty capacitor with structureless electrodes at large inter-electrode distances. By considering a variety of liquids between graphite electrodes, we confirm that this contribution to the total differential capacitance is small compared to that induced by the thermal fluctuations of the electrolyte.

Recent Work (2018)

Photoinduced phase separation in mixed halide perovskites emerges from their electro-mechanical properties and high ionic conductivities, resulting in photoinduced I

^{-}-rich charge carrier traps that diminish photovoltaic performance. Whether photoinduced phase separation stems from the polycrystalline microstructure or is an intrinsic material property has been an open question. We investigate the nanoscale photoinduced behavior of single-crystal mixed Br^{-}/I^{-}methylammonium (MA^{+}) lead halide perovskite (MAPb(Br_{x}I_{1- x})_{3}) nanoplates, eliminating effects from extended structural defects. Even in these nanoplates, we find that phase separation occurs, resulting in I^{-}-rich clusters that are nucleated stochastically and stabilized by polarons. Upon lowering the electron-phonon coupling strength by partially exchanging MA^{+}for Cs^{+}, a phase-separated steady state is not reached, nevertheless transient I^{-}clustering still occurs. Our results, supported by multiscale modeling, demonstrate that photoinduced phase separation is an intrinsic property of mixed halide perovskites, the extent and dynamics of which depends on the electron-phonon coupling strength.Recent Work (2020)

Halide perovskites have attracted increasing research attention with regard to their potential for optoelectronic applications. Because of its low activation energy, ion migration is implicated in the long-term stability and many unusual transport behaviors of halide perovskite devices. However, direct observation and precise control of the ionic transport in halide perovskite crystals remain challenging. Here, we have designed an axial CsPbBr

_{3}-CsPbCl_{3}nanowire heterostructure, in which electric-field-induced halide ion migration was clearly visualized and quantified. We demonstrated that halide ion migration is dependent on the applied electric field and exhibits ionic rectification in this solid-state system, which is due to the nonuniform distribution of the ionic vacancies in the nanowire that results from a competition between electrical screening and their creation/destruction at the electrodes' interfaces. The asymmetric heterostructure characteristics add an additional knob to control the ion movement in the design of advanced ionic circuits with halide perovskites as building blocks.Recent Work (2017)

The distinct physical properties of hybrid organic-inorganic materials can lead to unexpected nonequilibrium phenomena that are difficult to characterize due to the broad range of length and time scales involved. For instance, mixed halide hybrid perovskites are promising materials for optoelectronics, yet bulk measurements suggest the halides reversibly phase separate upon photoexcitation. By combining nanoscale imaging and multiscale modeling, we find that the nature of halide demixing in these materials is distinct from macroscopic phase separation. We propose that the localized strain induced by a single photoexcited charge interacting with the soft, ionic lattice is sufficient to promote halide phase separation and nucleate a light-stabilized, low-bandgap, ∼8 nm iodide-rich cluster. The limited extent of this polaron is essential to promote demixing because by contrast bulk strain would simply be relaxed. Photoinduced phase separation is therefore a consequence of the unique electromechanical properties of this hybrid class of materials. Exploiting photoinduced phase separation and other nonequilibrium phenomena in hybrid materials more generally could expand applications in sensing, switching, memory, and energy storage.