The time-evolution equation for the time-dependent static structure factor of the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory was used to investigate the kinetics of glass-forming systems under isochoric conditions. The kinetics are studied within the framework of the fictive temperature (T_F) of the glassy structure. We solve for the kinetics of T_F(t) and the time-dependent structure factor and find that they are different but closely related by a function that depends only on temperature. Furthermore, we are able to solve for the evolution of T_F(t) in a set of temperature-jump histories referred to as the Kovacs’ signatures. We demonstrate that the NE-SCGLE theory reproduces all the Kovacs’ signatures, namely, intrinsic isotherm, asymmetry of approach, and memory effect. In addition, we extend the theory into largely unexplored, deep glassy state, regions that are below the notionally “ideal” glass temperature.

In this work, we present a first-principles theoretical framework for the description of structural and dynamical behaviors of ionic liquids. This framework applies the self-consistent generalized Langevin equation (SCGLE) theory, which predicts the dynamically arrested states of several physical systems, including charge and size asymmetric ionic liquids. In its current form, the SCGLE is a particularly useful framework for predictions of arrested and partially arrested states in both classical and room-temperature molten salts, electrolytic solutions, and superionic conductors. Some illustrative examples of the predictive power of our framework are presented in this work, showing its potential application in design and development of novel conducting materials.

In this work a systematic study over a wide number of final thermodynamic states for two gel-forming liquids was performed. Such two kind of gel formers are distinguished by their specific interparticle interaction potential. We explored several thermodynamic states determining the thermodynamic, structural and dynamic properties of both liquids after a sudden temperature change. The thermodynamic analysis allows to identify that the liquid with short range attraction and long range repulsion lacks of a stable gas–liquid phase separation liquid, in contrast with the liquid with short range attractions. Thus, although for some thermodynamic states the structural behavior, measured by the static structure factor, is similar to and characteristic of the gel phase, for the short range attractive fluid the gel phase is a consequence of a spinodal decomposition process. In contrast, gelation in the short range attraction and long range repulsion liquid is not due to a phase separation. We also analyze the similarities and differences of the dynamic behavior of both systems through the analysis of the mean square displacement, the self part of the intermediate scattering function, the diffusion coefficient and the α relaxation time. Finally, using one of the main results of the non-equilibrium self-consistent generalized Langevin equation theory (NE-SCGLE), we determine the dynamic arrest phase diagram in the volume fraction and temperature (φ vs T) plane.

We present a first-principles formalism for studying dynamical heterogeneities in glass-forming liquids. Based on the non-equilibrium self-consistent generalized Langevin equation theory, we were able to describe the time-dependent local density profile during the particle interchange among small regions of the fluid. The final form of the diffusion equation contains both the contribution of the chemical potential gradient written in terms of a coarse-grained density and a collective diffusion coefficient as well as the effect of a history-dependent mobility factor. With this diffusion equation, we captured interesting phenomena in glass-forming liquids such as the cases when a strong density gradient is accompanied by a very low mobility factor attributable to the denser part: in such circumstances, the density profile falls into an arrested state even in the presence of a density gradient. On the other hand, we also show that above a certain critical temperature, which depends on the volume fraction, any density heterogeneity relaxes to a uniform state in a finite time, known as equilibration time. We further show that such equilibration time varies little with the temperature in diluted systems but can change drastically with temperature in concentrated systems.

In the present work, the Non-Equilibrium Self-Consistent Generalized Langevin Equation (NESCGLE) theory is used to predict the final state of glass-forming liquids subjected to different cooling processes. We show that the NESCGLE theory correctly describes two essential features of the glass transition. Such features are the structural recovery and the dependence of the final state with the cooling rate. We demonstrate that below a particular temperature T_c, the system is unable to equilibrate, independently of the cooling rate. We show that the equilibrium state is only reached for the quasistatic process. Additionally, we show how, from the NESCGLE theory, it is possible to deduce a relaxation model of structural recovery, for which we obtain molecular expressions of the parameters.

In this work an artificial neural network (ANN) was used to determine the pressure and internal energy equations of state of noble gases and some molecular liquids by predicting thermodynamic state variables like density and temperature encoded in the radial distribution function. The ANN is trained to predict the thermodynamic state variables using only the structural data. Then, predicted values are used to compute equations of state of real liquids such as argon, neon, krypton and xenon as well as some molecular liquids like nitrogen, carbon dioxide, methane and ethylene. In order to assess the ANN predictions the relative percentage error with the exact values were determined, showing that its magnitude is less than 1%. Thus, the comparison between equations of state computed with the predicted variables and experimental results exhibits a very good agreement for most of the liquids studied here. Since our ANN implementation only requires the microscopic structure as an input, data incoming from experiments, theoretical frameworks or simulations are suitable to perform predictions of state variables and with that complement the thermodynamic characterisation of liquids through the determination of equations of state. Moreover, further improvements or extensions related with the microscopic structure database can be safely addressed without changing the neural network architecture presented here.