A new connection between the structure and dynamics in glass-forming liquids is presented. We show how the origin of spatially localized excitations, as defined by the dynamical facilitation (DF) theory, can be understood from a structure-based framework. This framework is constructed by associating excitation events in the DF theory to hopping events between energy minima in the potential energy landscape (PEL). By reducing the PEL to an equal energy well picture and applying a harmonic approximation, we develop a field theory to describe elastic fluctuations about inherent states, which are energy minimizing configurations of the PEL. We model an excitation as a shear transformation zone (STZ) inducing a localized pure shear deformation onto an inherent state. We connect STZs to T1 transition events that break the elastic bonds holding the local structure of an inherent state. A formula for the excitation energy barrier, denoted as Jσ, is obtained as a function of inherent-state elastic moduli and the radial distribution function. The energy barrier from the current theory is compared to the one predicted by the DF theory where good agreement is found in various two-dimensional continuous poly-disperse atomistic models of glass formers. These results strengthen the role of structure and elasticity in driving glassy dynamics through the creation and relaxation of localized excitations.

Two first-principles modeling methods were used to analyze and quantitatively predict performance characteristics of Electric DoubleLayer Capacitors (EDLCs), namely Time-Domain Current Method (TDCM) and Frequency-Domain Admittance Method (FDAM). TDCM was used to model galvanostatic discharge characteristics of capacitor while FDAM was used to model the impedance spectra. Both the methods showed excellent agreement with experimental impedance and galvanostatic discharge performance of various electrochemical capacitors made using two different commercial carbons. Details at the macroscopic (porous electrode theory) and microscopic (double layer theory) level were incorporated into the models. The methods were also able to follow changes in capacitance and resistance of the capacitor during cycling. Furthermore, FDAM was used to validate the performance of a large-scale commercial EDLC capacitor. Electrochemical capacitors are receiving considerable attention as energy storage devices that can meet the energy and power demands for electric vehicles, renewable energy storage, smart grid, and energy harvesting technologies. [1][2][3][4] Energy in these capacitors is stored either in the form of electrostatic ionic charge at electrode/electrolyte interface or through fast faradaic interactions that contribute to pseudocapacitance at the interface. [5][6][7][8][9] Transient electroanalytical techniques such as galvanostatic charge/discharge and impedance spectroscopy are the key tools that are used to assess both the EDLC's materials characteristics and device performance. Development of mathematical models that accurately describe the interfacial phenomenon and validation through experimental observation is critical to further our understanding of the complexity of electrostatic/electrochemical interaction that occurs at the electrode/electrolyte interface.The development of models for EDLCs ties very deeply with the mathematical modeling of non-faradaic phenomena at the microscopic level. In these length scales, the double layer structure is described in terms of a diffuse/Gouy-Chapman layer and compact/Helmholtz layer. The compact layer will then be further divided into inner Helmholtz plane (IHP), that contain specifically adsorbed ions, and outer Helmholtz plane, which contains solvated ions that are attracted to the electrode due to charge interactions. To apply this conceptual picture to transient electroanalytical techniques, many different variations exist based upon the mathematical details and the choice of non-faradaic effects to be included/excluded in the models, e.g. specific adsorption, diffuse layer, and compact layer.Among all non-faradaic phenomena related to the double layer structure, the diffuse layer is one of the most intensively studied. The earliest treatment came by direct incorporation of the Gouy-ChapmanStern theory for different electroanalytical techniques, with some analytical solutions in the form of hypergeometric functions given in cases where they are possible. [10][11][12][13][14][...

A central object in the computational studies of rare events is the committor function. Though costly to compute, the committor function encodes complete mechanistic information of the processes involving rare events, including reaction rates and transition-state ensembles. Under the framework of transition path theory, Rotskoff et al. [ Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference, Proceedings of Machine Learning Research (PLMR, 2022), Vol. 145, pp. 757–780] proposes an algorithm where a feedback loop couples a neural network that models the committor function with importance sampling, mainly umbrella sampling, which collects data needed for adaptive training. In this work, we show additional modifications are needed to improve the accuracy of the algorithm. The first modification adds elements of supervised learning, which allows the neural network to improve its prediction by fitting to sample-mean estimates of committor values obtained from short molecular dynamics trajectories. The second modification replaces the committor-based umbrella sampling with the finite-temperature string (FTS) method, which enables homogeneous sampling in regions where transition pathways are located. We test our modifications on low-dimensional systems with non-convex potential energy where reference solutions can be found via analytical or finite element methods, and show how combining supervised learning and the FTS method yields accurate computation of committor functions and reaction rates. We also provide an error analysis for algorithms that use the FTS method, using which reaction rates can be accurately estimated during training with a small number of samples. The methods are then applied to a molecular system in which no reference solution is known, where accurate computations of committor functions and reaction rates can still be obtained.

Lithium borate/silica composites, 40 wt% SiO 2 with x•Li 2 O + (1-x)•B 2 O 3 , x = 0.33, 0.50, were explored with the goal of achieving Li-ion conductivity enhancements across batches with different compositions and processing steps. Two batches were made for each composition, namely micron and nanoscale batches, which differ in their processing and fabrication methods. Phase and microstructural characterization showed a composite which is consisted of a conductor-rich and an insulator-rich region. Previous dispersed ionic conductors, in which conductivity is enhanced by the insulator/conductor interaction, were modeled mostly by percolation models. However, these percolation models are not compatible with conventional impedance spectroscopy circuit models and complex non-linear regression analysis. Hence, new circuit models were created based upon a

Below the onset temperature T o , the equilibrium relaxation time of most glass-forming liquids exhibits glassy dynamics characterized by a super-Arrhenius temperature dependence. In this supercooled regime, the relaxation dynamics also proceeds through localized elastic excitations corresponding to hopping events between inherent states, i.e., potential-energy-minimizing configurations of the liquid. Despite its importance in distinguishing the supercooled regime from the high-temperature regime, the microscopic origin of T o is not yet known. Here, we construct a theory for the onset temperature in two dimensions and find that an inherent-state melting transition, described by the binding–unbinding transition of dipolar elastic excitations, delineates the supercooled regime from the high-temperature regime. The corresponding melting transition temperature is in good agreement with the onset temperature found in various two-dimensional (2D) atomistic models of glass formers and an experimental binary colloidal system confined to a water–air interface. Additionally, we find the predictions for the renormalized elastic moduli to agree with the experimentally observed values for the latter 2D colloidal system. We further discuss the predictions of our theory on the displacement and density correlations at supercooled conditions, which are consistent with observations of the Mermin–Wagner fluctuations in experiments and molecular simulations.