Microswimmers under the spotlight: interplay between agents with different levels of activity.

The ability of active matter to assemble into reconfigurable nonequilibrium structures has drawn considerable interest in recent years. We investigate how active fluids respond to spatial light patterns through simulations and experiments on light-activated self-propelled colloidal particles. We examine the processes of inverse templated assembly, which involves creating a region without active particles through a bright pattern, and templated assembly, which promotes the formation of dense particle regions through a dark pattern. We identify scaling relations for the characteristic times for both processes that quantify the interplay between the dimension of the applied pattern and the intrinsic properties of the active fluid. We also explore the assembly mechanism and dynamics of large clusters and show how assembly and inverse assembly can be combined to create any arbitrarily complex template. In addition to providing protocols for templated assembly via light patterning, our results demonstrate how the local packing fraction can be fine-tuned by modulation of the light intensity. The protocol so obtained exceeds the capabilities of conventional assembly strategies, in which packing fraction is dictated by thermodynamics, and opens the door to arbitrarily precise and programmable nonequilibrium assembly strategies in active matter.

Entropy determination for mixtures in the adiabatic grand-isobaric ensemble.

The entropy change that occurs upon mixing two fluids has remained an intriguing topic since the dawn of statistical mechanics. In this work, we generalize the grand-isobaric ensemble to mixtures and develop a Monte Carlo algorithm for the rapid determination of entropy in these systems. A key advantage of adiabatic ensembles is the direct connection they provide with entropy. Here, we show how the entropy of a binary mixture A-B can be readily obtained in the adiabatic grand-isobaric (µA, µB, P, R) ensemble, in which µA and µB denote the chemical potential of components A and B, respectively, P is the pressure, and R is the heat (Ray) function, that corresponds to the total energy of the system. This, in turn, allows for the evaluation of the entropy of mixing and the Gibbs free energy of mixing. We also demonstrate that our approach performs very well both on systems modeled with simple potentials and with complex many-body force fields. Finally, this approach provides a direct route to the determination of the thermodynamic properties of mixing and allows for the efficient detection of departures from ideal behavior in mixtures.

Machine-Learned Free Energy Surfaces for Capillary Condensation and Evaporation in Mesopores.

Using molecular simulations, we study the processes of capillary condensation and capillary evaporation in model mesopores. To determine the phase transition pathway, as well as the corresponding free energy profile, we carry out enhanced sampling molecular simulations using entropy as a reaction coordinate to map the onset of order during the condensation process and of disorder during the evaporation process. The structural analysis shows the role played by intermediate states, characterized by the onset of capillary liquid bridges and bubbles. We also analyze the dependence of the free energy barrier on the pore width. Furthermore, we propose a method to build a machine learning model for the prediction of the free energy surfaces underlying capillary phase transition processes in mesopores.

Entropy scaling close to criticality: From simple to metallic systems.

Entropy has recently drawn considerable interest both as a marker to detect the onset of phase transitions and as a reaction coordinate, or collective variable, to span phase transition pathways. We focus here on the behavior of entropy along the vapor-liquid phase coexistence and identify how the difference in entropy between the two coexisting phases vary in ideal and metallic systems along the coexistence curve. Using flat-histogram simulations, we determine the thermodynamic conditions of coexistence, critical parameters, including the critical entropy, and entropies along the binodal. We then apply our analysis to a series of systems that increasingly depart from ideality and adopt a metal-like character, through the gradual onset of the Friedel oscillation in an effective pair potential, and for a series of transition metals modeled with a many-body embedded-atoms force field. Projections of the phase boundary on the entropy-pressure and entropy-temperature planes exhibit two qualitatively different behaviors. While all systems modeled with an effective pair potential lead to an ideal-like behavior, the onset of many-body effects results in a departure from ideality and a markedly greater exponent for the variation of the entropy of vaporization with temperature away from the critical temperature.

Entropy production in model colloidal suspensions under shear via the fluctuation theorem.

Dissipative systems often exhibit novel and unexpected properties. This is, for instance, the case of simple liquids, which, when subjected to shear and after reaching a steady state, can exhibit a negative entropy production over finite length scales and timescales. This result, among others, is captured by nonequilibrium relations known as fluctuation theorems. Using nonequilibrium molecular dynamics simulations, we examine how, by fine-tuning the properties of the components of a complex fluid, we can steer the nonequilibrium response of the fluid. More specifically, we show how we control the nonequilibrium probability distribution for the shear stress and, in turn, how often states with a negative entropy production can occur. To achieve this, we start by characterizing how the size for the liquid matrix impacts the probability of observing negative entropy states, as well as the timescale over which these can be observed. We then measure how the addition of larger particles to this liquid matrix, i.e., simulating a model colloidal suspension, results in an increase in the occurrence of such states. This suggests how modifications in the composition of the mixture and in the properties of its components lead to an increase in the probability of observing states of negative entropy production and, thus, for the system to run in reverse.

Entropy in Molecular Fluids: Interplay between Interaction Complexity and Criticality.

Using flat-histogram simulations, we calculate the entropy of molecular fluids along the vapor-liquid phase boundary. Our simulation approach is based on the evaluation of the canonical and grand-canonical partition functions, which, in turn, provide access to entropy through the statistical mechanics formalism. The results allow us to determine the critical entropy of molecular fluids and to uncover that the transition occurs symmetrically from an entropic standpoint. This can best be seen through the patterns exhibited by the thermodynamic variables temperature and pressure when plotted against the entropy of the coexisting phases. This behavior is found to hold for apolar, quadrupolar, and dipolar fluids. Finally, we identify functional forms that characterize the relation between thermodynamic variables and entropy along the coexistence curve up to the critical point.

The central role of entropy in adiabatic ensembles and its application to phase transitions in the grand-isobaric adiabatic ensemble.

Entropy has become increasingly central to characterize, understand, and even guide assembly, self-organization, and phase transition processes. In this work, we build on the analogous role of partition functions (or free energies) in isothermal ensembles and that of entropy in adiabatic ensembles. In particular, we show that the grand-isobaric adiabatic (µ, P, R) ensemble, or Ray ensemble, provides a direct route to determine the entropy. This allows us to follow the variations of entropy with the thermodynamic conditions and thus explore phase transitions. We test this approach by carrying out Monte Carlo simulations on argon and copper in bulk phases and at phase boundaries. We assess the reliability and accuracy of the method through comparisons with the results from flat-histogram simulations in isothermal ensembles and with the experimental data. Advantages of the approach are multifold and include the direct determination of the µ-P relation, without any evaluation of pressure via the virial expression, the precise control of the system size (number of atoms) via the input value of R, and the straightforward computation of enthalpy differences for isentropic processes, which are key quantities to determine the efficiency of thermodynamic cycles. A new insight brought by these simulations is the highly symmetric pattern exhibited by both systems along the transition, as shown by scaled temperature-entropy and pressure-entropy plots.

Unraveling liquid polymorphism in silicon driven out-of-equilibrium.

Using nonequilibrium molecular dynamics simulations, we study the properties of supercooled liquids of Si under shear at T = 1060 K over a range of densities encompassing the low-density liquid (LDL) and high-density liquid (HDL) forms. This enables us to generate nonequilibrium steady-states of the LDL and HDL polymorphs that remain stabilized in their liquid forms for as long as the shear is applied. This is unlike the LDL and HDL forms at rest, which are metastable under those conditions and, when at rest, rapidly undergo a transition toward the crystal, i.e., the thermodynamically stable equilibrium phase. In particular, through a detailed analysis of the structural and energetic features of the liquids under shear, we identify the range of densities, as well as the range of shear rates, which give rise to the two forms. We also show how the competition between shear and tetrahedral order impacts the two-body entropy in steady-states of Si under shear. These results open the door to new ways of utilizing shear to stabilize forms that are metastable at rest and can exhibit unique properties, since, for instance, experiments on Si have shown that HDL is metallic with no bandgap, while LDL is semimetallic with a pseudogap.

Nucleation of Capillary Bridges and Bubbles in Nanoconfined CO2.

Using molecular simulation, we examine the capillary condensation and the capillary evaporation of CO2 in cylindrical nanopores. More specifically, we employ the recently developed µV T-S method to determine the microscopic mechanism associated with these processes and the corresponding free energy profiles. We calculate the free energy barrier for capillary condensation and identify that the key step consists in the nucleation of a liquid bridge of a critical size. Similarly, the free energy maximum found for the capillary evaporation process is found to correspond to the nucleation of a vapor bubble of a critical size. In addition, we assess the impact of the strength of the wall-fluid on the height of the free energy barrier and on the critical size of liquid bridges (condensation process) and vapor bubbles (evaporation process). We observe that the height of the free energy barrier increases with the strength of the wall-fluid interactions. Finally, we build a theoretical model, based on capillary theory, to rationalize our findings. In particular, the simulation results reveal a linear scaling of the free energy barrier with the critical size, in excellent agreement with the theoretical predictions.

Can Ordered Precursors Promote the Nucleation of Solid Solutions?

Crystallization often proceeds through successive stages that lead to a gradual increase in organization. Using molecular simulation, we determine the nucleation pathway for solid solutions of copper and gold. We identify a new nucleation mechanism (liquid→L1_{2} precursor→solid solution) involving a chemically ordered intermediate that is more organized than the end product. This nucleation pathway arises from the low formation energy of L1_{2} clusters which, in turn, promote crystal nucleation. We also show that this mechanism is composition dependent since the high formation energy of other ordered phases precludes them from acting as precursors.

Communication: Existence and control of liquid polymorphism in methanol under shear.

The liquid-liquid hypothesis, which states that a pure substance can exhibit two liquid forms (or polymorphs), has drawn considerable interest in recent years. The appeal of this theory is that it provides the basis for a deeper understanding of the properties of supercooled liquids. However, the study of this phenomenon is extremely challenging and a complete understanding of its impact on fluid properties has remained elusive so far, since the low-temperature liquid form is generally not stable and undergoes rapid crystallization. Using a coarse-grained model for methanol, we show that methanol under shear can exhibit, in the steady state, two liquid forms that respond differently to the applied shear. Using molecular simulations, we show that the difference in dynamical response is correlated with structural differences between the two liquid forms. This establishes the existence of liquid polymorphism for systems driven out-of-equilibrium. Our findings also show how, by varying the pressure or the shear stress applied to the system, liquid-liquid transitions can be triggered and how a control of liquid polymorphism can be achieved. The resulting solid-liquid-liquid nonequilibrium phase diagram leads us to identify new ways for the stabilization and study of liquid polymorphism.

Prediction of the phase equilibria for island-type asphaltenes via HMC-WL simulations.

Recent force microscopy experiments have shed light on new possible molecular structures for asphaltenes, which are key compounds for the oil industry. These studies have revealed the significance of asphaltenes with an island molecular architecture, i.e., composed of a large polycyclic aromatic hydrocarbon (PAH) core and alkyl side chains. In this work, we carry out molecular simulations based on a Wang-Landau sampling of the isothermal-isobaric ensemble to determine the thermodynamic properties of island-type asphaltenes at the vapor-liquid coexistence. We first parameterize a coarse-grained force field for these systems, focusing on compounds with a PAH core containing fluorene, fluoranthene, and dibenzothiophene motifs. Then, using this coarse-grained force field, we predict the entire phase envelope, including the boiling points and the critical parameters for a series of island-type asphaltenes.

A new approach for the prediction of partition functions using machine learning techniques.

Using machine learning (ML), we predict the partition functions and, thus, all thermodynamic properties of atomic and molecular fluids over a wide range of temperatures and pressures. Our approach is based on training neural networks using, as a reference, the results of a few flat-histogram simulations. The neural network weights so obtained are then used to predict fluid properties that are shown to be in excellent agreement with the experiment and with simulation results previously obtained on argon, carbon dioxide, and water. In particular, the ML predictions for the Gibbs free energy, Helmholtz free energy, and entropy are shown to be highly accurate over a wide range of conditions and states for bulk phases as well as for the conditions of phase coexistence. Our ML approach thus provides access instantly to G, A, and S, thereby eliminating the need to carry out any additional simulations to explore the dependence of the fluid properties on the conditions of temperature and pressure. This is of particular interest, for e.g., the screening of new materials, as well as in the parameterization of force fields, for which this ML approach provides a rapid way to assess the impact of new sets of parameters on the system properties.

Non-monotonic variations of the nucleation free energy in a glass-forming ultra-soft particles fluid.

Using molecular dynamics simulation, we study the impact of the degree of supercooling on the crystal nucleation of ultra-soft particles, modeled with the Gaussian core potential. Focusing on systems with a high number density, our simulations reveal dramatically different behaviors as the degree of supercooling is varied. In the moderate supercooling regime, crystal nucleation proceeds as expected from classical nucleation theory, with a decrease in the free energy of nucleation, as well as in the size of the critical nucleus, as supercooling is increased. On the other hand, in the large supercooling regime, we observe an unusual reversal of behavior with an increase in the free energy of nucleation and in the critical size, as supercooling is increased. This unexpected result is analyzed in terms of the interplay between the glass transition and the crystal nucleation process. Specifically, medium range order crystal-like domains, with structural features different from that of the crystal nucleus, are found to form throughout the system when the supercooling is very large. These, in turn, play a pivotal role in the increase in the free energy of nucleation, as well as in the critical size, as the temperature gets closer to the glass transition.

Modeling antigen-antibody nanoparticle bioconjugates and their polymorphs.

The integration of nanomaterials with biomolecules has recently led to the development of new ways of designing biosensors, and through their assembly, to new hybrid structures for novel and exciting applications. In this work, we develop a coarse-grained model for nanoparticles grafted with antibody molecules and their binding with antigens. In particular, we isolate two possible states for antigen-antibody pairs during the binding process, termed as recognition and anchoring states. Using molecular simulation, we calculate the thermodynamic and structural features of three possible crystal structures or polymorphs, the body-centered cubic, simple cubic, and face-centered cubic phases, and of the melt. This leads us to determine the domain of stability of the three solid phases. In particular, the role played by the switching process between anchoring and recognition states during melting is identified, shedding light on the complex microscopic mechanisms in these systems.

Unusual Crystallization Behavior Close to the Glass Transition.

Using molecular simulations, we shed light on the mechanism underlying crystal nucleation in metal alloys and unravel the interplay between crystal nucleation and glass transition, as the conditions of crystallization lie close to this transition. While decreasing the temperature of crystallization usually results in a lower free energy barrier, we find an unexpected reversal of behavior for glass-forming alloys as the temperature of crystallization approaches the glass transition. For this purpose, we simulate the crystallization process in two glass-forming Copper alloys, Ag_{6}Cu_{4}, which has a positive heat of mixing, and CuZr, characterized by a large negative heat of mixing. Our results allow us to identify this unusual behavior as directly correlated with a nonmonotonic temperature dependence for the formation energy of connected icosahedral structures, which are incompatible with crystalline order and impede the development of the crystal nucleus, leading to an unexpectedly larger free energy barrier at low temperature. This, in turn, promotes the formation of a predominantly closed-packed critical nucleus, with fewer defects, thereby suggesting a new way to control the structure of the crystal nucleus, which is of key importance in catalysis.

Free Energy of Nucleation and Interplay between Size and Composition in CuNi Systems.

Using molecular simulation, we shed light on the crystal nucleation process in systems of Cu, Ni, and their nanoalloy. For each system, we simulate the formation of the crystal nucleus along the entire nucleation pathway and determine the free energy barrier overcome by the system to form a critical nucleus. Comparing the results obtained for the pure metals to those for the nanoalloy, we analyze the impact of alloying on the free energy of nucleation, as well as on the size and structure of the crystal nucleus. Specifically, we relate the greater free energy of nucleation, and bigger critical nuclei, obtained for the nanoalloy, to the difference in size and cohesive energy between the two metals. Furthermore, we characterize the dependence of the local composition of the incipient crystal cluster on its size, which is of key significance for the applications of bimetallic nanoparticles in catalysis.

Free energy calculations along entropic pathways. II. Droplet nucleation in binary mixtures.

Using molecular simulation, we study the nucleation of liquid droplets from binary mixtures and determine the free energy of nucleation along entropic pathways. To this aim, we develop the µ1µ2VT-S method, based on the grand-canonical ensemble modeling the binary mixture, and use the entropy of the system S as the reaction coordinate to drive the formation of the liquid droplet. This approach builds on the advantages of the grand-canonical ensemble, which allows for the direct calculation of the entropy of the system and lets the composition of the system free to vary throughout the nucleation process. Starting from a metastable supersaturated vapor, we are able to form a liquid droplet by gradually decreasing the value of S, through a series of umbrella sampling simulations, until a liquid droplet of a critical size has formed. The µ1µ2VT-S method also allows us to calculate the free energy barrier associated with the nucleation process, to shed light on the relation between supersaturation and free energy of nucleation, and to analyze the interplay between the size of the droplet and its composition during the nucleation process.

Free energy calculations along entropic pathways. I. Homogeneous vapor-liquid nucleation for atomic and molecular systems.

Using the entropy S as a reaction coordinate, we determine the free energy barrier associated with the formation of a liquid droplet from a supersaturated vapor for atomic and molecular fluids. For this purpose, we develop the µVT-S simulation method that combines the advantages of the grand-canonical ensemble, that allows for a direct evaluation of the entropy, and of the umbrella sampling method, that is well suited to the study of an activated process like nucleation. Applying this approach to an atomic system such as Ar allows us to test the method. The results show that the µVT-S method gives the correct dependence on supersaturation of the height of the free energy barrier and of the size of the critical droplet, when compared to predictions from the classical nucleation theory and to previous simulation results. In addition, it provides insight into the relation between the entropy and droplet formation throughout this process. An additional advantage of the µVT-S approach is its direct transferability to molecular systems, since it uses the entropy of the system as the reaction coordinate. Applications of the µVT-S simulation method to N2 and CO2 are presented and discussed in this work, showing the versatility of the µVT-S approach.

Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. V. Impact of an electric field on the thermodynamic properties and ideality contours of water.

Using molecular simulation, we assess the impact of an electric field on the properties of water, modeled with the SPC/E potential, over a wide range of states and conditions. Electric fields of the order of 0.1 V/Å and beyond are found to have a significant impact on the grand-canonical partition function of water, resulting in shifts in the chemical potential at the vapor-liquid coexistence of up to 20%. This, in turn, leads to an increase in the critical temperatures by close to 7% for a field of 0.2 V/Å, to lower vapor pressures, and to much larger entropies of vaporization (by up to 35%). We interpret these results in terms of the greater density change at the transition and of the increased structural order resulting from the applied field. The thermodynamics of compressed liquids and of supercritical water are also analyzed over a wide range of pressures, leading to the determination of the Zeno line and of the curve of ideal enthalpy that span the supercritical region of the phase diagram. Rescaling the phase diagrams obtained for the different field strengths by their respective critical properties allows us to draw a correspondence between these systems for fields of up to 0.2 V/Å.