Scalar activity induced phase separation and liquid-solid transition in a Lennard-Jones system

Stability of the chiral crystal phase and breakdown of the cholesteric phase in mixtures of active-passive chiral rods

In this study, we aim to explore the effect of chirality on the phase behavior of active helical particles driven by two-temperature scalar activity. We first calculate the equation of state of soft helical particles of various intrinsic chiralities using molecular dynamics (MD) simulation. In equilibrium, the emergence of various liquid crystal (LC) phases such as nematic (N), cholesteric , smectic (Sm) and crystal (K) crucially depends on the presence of walls that induce planar alignment. Next, we introduce activity through the two-temperature model: keep increasing the temperature of half of the helical particles (labeled as 'hot' particles) while maintaining the temperature of the other half at a lower value (labeled as 'cold' particles). Starting from a homogeneous isotropic (I) phase, we find the emergence of 2-TIPS: two temperature-induced phase separations between the hot and cold particles. We also observe that the cold particles undergo an ordering transition to various LC phases even in the absence of a wall. This observation reveals that the hot-cold interface in the active system plays the role of a wall in the equilibrium system by inducing an alignment direction for the cold particles. However, in the case of a cholesteric phase, we observe that activity destabilizes the phase by inducing smectic ordering in the cold zone while an isotropic structure in the hot zone. The smectic ordering in the cold zone eventually transforms to a chiral crystal phase with high enough activity.

Effect of confinement and topology: 2-TIPS vs. MIPS

2-TIPS (two temperature induced phase separation) refers to the phase separation phenomenon observed in mixtures of active and passive particles which are modelled using scalar activity. The active particles are connected to a thermostat at high temperature while the passive particles are connected to the thermostat at low temperature and the relative temperature difference between "hot" and "cold" particles is taken as the measure of the activity χ of the non-equilibrium system. The study of such binary mixtures of hot and cold particles under various kinds of confinement is an important problem in many physical and biological processes. The nature and extent of phase separation are heavily influenced by the geometry of confinement, activity, and density of the non-equilibrium binary mixture. Investigating such 3D binary mixtures confined by parallel walls, we observe that the active and passive particles phase separate, but the extent of phase separation is reduced compared to bulk phase separation at high densities and enhanced at low densities. However, when the binary mixture of active and passive particles is confined inside a spherical cavity, the phase separation is radial for small radii of the confining sphere and the extent of phase separation is higher compared to their bulk counterparts. Confinement leads to interesting properties in the passive (cold) region like enhanced layering and high compression in the direction parallel to the confining wall. In 2D, both the bulk and confined systems of the binary mixture show a significant decrement in the extent of phase separation at higher densities. This observation is attributed to the trapping of active particles inside the passive cluster, which increases with density. Thus the 2D systems show structures more akin to dense-dilute phase co-existence, which is observed in motility induced phase separation in 2D active systems. The binary mixture constrained on the spherical surface also shows similar phase co-existence. Our analyses reveal that the coexistent densities observed in 2-TIPS on the spherical surface agree with the findings of previous studies on MIPS in active systems on a sphere.

Hot crystals of thermo-responsive particles with temperature dependent diameter in the presence of a temperature gradient

Structure formation under non-equilibrium steady state conditions is poorly understood. A non-equilibrium steady state can be achieved in a system by maintaining a temperature gradient. A class of cross-linked microgel particles, such as poly-N-iso-propylacrylamide, is reported to increase in size due to the adsorption of water as the temperature decreases. Here, we study thermo-responsive particles with a temperature sensitive diameter in the presence of a temperature gradient, using molecular dynamics simulations with the Langevin thermostat. We find long-ranged structural order using bond order parameters in both cold and hot regions of the system beyond a certain diameter ratio of the cold and hot particles. This is due to an increase in packing and pressure in both regions. Our observations might be useful in understanding ordered structures under extreme conditions of a non-equilibrium steady state.

Phase behavior of active and passive dumbbells

We report phase separation in a mixture of "hot" and "cold" three-dimensional dumbbells which interact by Lennard-Jones potential. We also have studied the effect of asymmetry of dumbbells and the variation of ratio of "hot" and "cold" dumbbells on their phase separation. The ratio of the temperature difference between hot and cold dumbbells to the temperature of cold dumbbells is a measure of the activity χ of the system. From constant density simulations of symmetric dumbbells, we observe that the "hot" and "cold" dumbbells phase separate at higher activity ratio (χ>5.80) compared to that of a mixture of hot and cold Lennard-Jones monomers (χ>3.44). We find that, in the phase-separated system, the hot dumbbells have high effective volume and hence high entropy which is calculated by two-phase thermodynamic method. The high kinetic pressure of hot dumbbells forces the cold dumbbells to form dense clusters such that at the interface the high kinetic pressure of hot dumbbells is balanced by the virial pressure of cold dumbbells. We find that phase separation pushes the cluster of cold dumbbells to have solidlike ordering. Bond orientation order parameters reveal that the cold dumbbells form solidlike ordering consisting of predominantly face-centered cubic and hexagonal-close packing packing, but the individual dumbbells have random orientations. The simulation of the nonequilibrium system of symmetric dumbbells at different ratios of number of hot dumbbells to cold dumbbells reveals that the critical activity of phase separation decreases with increase in fraction of hot dumbbells. The simulation of equal mixture of hot and cold asymmetric dumbbells revealed that the critical activity of phase separation was independent of the asymmetry of dumbbells. We also observed that the clusters of cold asymmetric dumbbells showed both crystalline and noncrystalline order depending on the asymmetry of dumbbells.

Two-temperature activity induces liquid-crystal phases inaccessible in equilibrium

In equilibrium hard-rod fluids, and in effective hard-rod descriptions of anisotropic soft-particle systems, the transition from the isotropic (I) phase to the nematic phase (N) is observed above the rod aspect ratio L/D=3.70 as predicted by Onsager. We examine the fate of this criterion in a molecular dynamics study of a system of soft repulsive spherocylinders rendered active by coupling half the particles to a heat bath at a higher temperature than that imposed on the other half. We show that the system phase-separates and self-organizes into various liquid-crystalline phases that are not observed in equilibrium for the respective aspect ratios. In particular, we find a nematic phase for L/D=3 and a smectic phase for L/D=2 above a critical activity.

Modeling the viscoelastic relaxation dynamics of soft particles via molecular dynamics simulation-informed multi-dimensional transition-state theory

Viscoelastic soft colloidal particles have been widely explored in mechanical, chemical, pharmaceutical and other engineering applications due to their unique combination of viscosity and elasticity. The characteristic viscoelastic relaxation time shows an Arrhenius-type (or super-Arrhenius due to temperature-dependent transition attempts) thermally-activated behavior, but a holistic explanation from the relevant transition-state theory remains elusive. In this paper, the viscoelastic relaxation times of Lennard-Jones soft colloidal particle systems, including a single particle type system and a binary particle mixture based on the Kob-Andersen model, are determined using molecular dynamics (MD) simulations as the benchmark. First, the particle systems show a non-Maxwellian behavior after comparing the MD-predicted viscoelastic relaxation time and dynamic moduli (storage and loss modulus) to the classic Maxwell viscoelastic model and the recent particle local connectivity theory. Surprisingly, neither the Maxwell relaxation time τ_Maxwell (obtained from the static shear viscosity η and the high-frequency shear modulus G_∞) nor the particle local connectivity lifetime τ_LC can capture the super-Arrhenius temperature-dependent behavior in the MD-predicted relaxation time τ_MD. Then, the particle dissociation and association transition kinetics, fractal dimensions of the particle systems, and neighbor particle structure (obtained from the radial distribution functions) are shown to collectively determine the viscoelastic relaxation time. These factors are embedded into a new multi-dimensional transition kinetics model to directly estimate the viscoelastic relaxation time τ_Model, which is found to agree with the MD-predicted τ_MD remarkably well. This work highlights the microscopic origin of viscoelastic relaxation dynamics of soft colloidal particles, and theoretically connects rheological dynamics and transition kinetics in soft matters.

Gas-liquid interface of a Lennard-Jones binary mixture controlled by differential activity: phase transition and interfacial stability

We perform molecular dynamics simulations of a two-dimensional binary mixture of Lennard-Jones particles, characterized by some degree of "activity" inside. Starting from a base state that features a gas-liquid interface and a completely segregated system at thermodynamic equilibrium, we introduce differential scalar activity between the two species by prescribing two different effective temperatures. The differential activity is measured as the ratio of the two temperatures. Previous studies showed segregation in a homogeneously mixed system induced by high activity. In this study, we investigate the effect of activity on a pre-existing gas-liquid interface between two separated species. Whereas a high activity ratio induces the formation of new interfaces, we show that a low activity ratio destabilizes existing ones. Moreover, the combination of a pre-existent interface with differential activity leads to partial crystallization and thus to triple phase coexistence (solid, liquid and gas), which is observed over a wide range of moderate differential activities. Findings from this idealized system can guide our understanding of interfacial behaviors in certain biological systems.

Phase Separation and Correlated Motions in Motorized Genome

The human genome is arranged in the cell nucleus nonrandomly, and phase separation has been proposed as an important driving force for genome organization. However, the cell nucleus is an active system, and the contribution of nonequilibrium activities to phase separation and genome structure and dynamics remains to be explored. We simulated the genome using an energy function parametrized with chromosome conformation capture (Hi-C) data with the presence of active, nondirectional forces that break the detailed balance. We found that active forces that may arise from transcription and chromatin remodeling can dramatically impact the spatial localization of heterochromatin. When applied to euchromatin, active forces can drive heterochromatin to the nuclear envelope and compete with passive interactions among heterochromatin that tend to pull them in opposite directions. Furthermore, active forces induce long-range spatial correlations among genomic loci beyond single chromosome territories. We further showed that the impact of active forces could be understood from the effective temperature defined as the fluctuation-dissipation ratio. Our study suggests that nonequilibrium activities can significantly impact genome structure and dynamics, producing unexpected collective phenomena.

A long-range order in a thermally driven system with temperature-dependent interactions

Aggregation of macro-molecules under an external force is far from being understood. An important driving situation is achieved by temperature difference. Inter-particle interactions in metallic nanoparticles with ligand capping are reported to be sensitive to temperature and the zeta potential of the particles being reduced in the cold region. Such particles form aggregates in the cold region of the system in the presence of temperature difference. Here we study the aggregation of particles in the presence of temperature difference with temperature-dependent interaction parameters using Brownian dynamics simulation. The particle interaction and particle diffusion are considered to be sensitive to the local temperature. We identify a long-range structural order in the cold region of the system using the Avrami equation for crystal growth kinetics. Our observations might be useful in designing ordered structures with macro-molecules under non-equilibrium steady-state conditions.

Depletion Induced Demixing and Crystallization in Binary Colloids Subjected to an External Potential Barrier

Depletion interaction plays an important role in determining the structural and dynamical properties of binary colloidal mixtures. We have investigated the effect of the attractive depletion interaction between an external potential barrier and larger species in the binary mixture on the phase behavior of a binary colloidal mixture using canonical-isokinetic ensemble molecular dynamics simulations. The demixing of the binary mixture due to this depletion interaction increases as the volume fraction increases, and a pure phase of larger particles forms in the region of the potential barrier. The local density of this pure phase is high enough that a face centered cubic crystalline domain is formed at this region. This crystalline phase diffuses perpendicular to the external potential barrier, indicating that moving crystals can be obtained in an equilibrium system. The temperature dependence of diffusivity of larger particles is non-Arrhenius and changes from sub-Arrhenius to super-Arrhenius as the volume fraction increases. This crossover from sub-Arrhenius to super-Arrhenius diffusion coincides with the crystalline formation near the potential barrier.

Heating leads to liquid-crystal and crystalline order in a two-temperature active fluid of rods

We report phase separation and liquid-crystal ordering induced by scalar activity in a system of soft repulsive spherocylinders (SRSs) of shape anisotropy L/D=5 using molecular dynamics (MD) simulations. Activity is introduced by increasing the temperature of half of the SRSs (labeled hot) while maintaining the temperature of the other half constant at a lower value (labeled cold). The difference between the two temperatures scaled by the lower temperature provides a measure of the activity. Starting from different equilibrium initial phases, we find that activity leads to segregation of the hot and cold particles. Activity also drives the cold particles through a phase transition to a more ordered state and the hot particles to a state of less order compared to the initial equilibrium state. The cold components of a homogeneous isotropic structure acquire nematic and, at higher activity, crystalline order. Similarly, the cold zone of a nematic initial state undergoes smectic and crystal ordering above a critical value of activity while the hot component turns isotropic. We find that the hot particles occupy a larger volume and exert an extra kinetic pressure, confining, compressing, and provoking an ordering transition of the cold-particle domains.

Two Faces of the Two-Phase Thermodynamic Model

The quantum harmonic model and the two-phase thermodynamic method (2PT) are widely used to obtain quantum-corrected properties such as isobaric heat capacities or molar entropies. 2PT heat capacities were calculated inconsistently in the literature. For water, the classical heat capacity was also considered, but for organic liquids, it was omitted. We reanalyzed the performance of different quantum corrections on the heat capacities of common organic solvents against experimental data. We have pointed out serious flaws in previous 2PT studies. The vibrational density of states was calculated incorrectly causing a 39% relative error in diffusion coefficients and 45% error in the 2PT heat capacities. The wrong conversion of isobaric and isochoric heat capacities also caused about 40% error but in the other direction. We have introduced the concept of anharmonic correction (AC), which is simply the deviation of the classical heat capacity from that of the harmonic oscillator model. This anharmonic contribution is around +30 to 40 J/(mol K) for water depending on the water model and −8 to −10 J/(mol K) for hydrocarbons and halocarbons. AC is unrealistically large, +40 J/(K mol) for alcohols and amines, indicating some deficiency of the OPLS force field. The accuracy of the computations was also assessed with the determination of the self-diffusion coefficients.

Nonequilibrium phase transition in an Ising model without detailed balance

We study a two-dimensional ferromagnetic Ising model in which spins are updated using modified versions of the Metropolis and Glauber algorithms. These update rules do not obey the detailed balance condition. The steady-state behavior of the model is studied using molecular field theory and Monte Carlo simulations. This model is found to exhibit a nonequilibrium phase transition from a "paramagnetic" state with zero magnetization to a "ferromagnetic" state with nonzero magnetization as the variable that plays the role of temperature in the spin updates is decreased. From detailed Monte Carlo simulations using the modified Metropolis algorithm, we demonstrate explicitly the nonequilibrium nature of the transition and show that it cannot be described as an equilibrium transition with an effective temperature different from the temperature used in the spin updates. The critical exponents that characterize the singular behavior near this continuous phase transition are calculated from finite size scaling of specific heat, magnetization, susceptibility, and correlation length. We find that the values of these exponents are the same (within error bars) as those of the equilibrium Ising model in two dimensions.

Translational and rotational dynamics of a self-propelled Janus probe in crowded environments

We computationally investigate the dynamics of a self-propelled Janus probe in crowded environments. The crowding is caused by the presence of viscoelastic polymers or non-viscoelastic disconnected monomers. Our simulations show that the translational as well as rotational mean square displacements have a distinctive three-step growth for fixed values of self-propulsion force, and steadily increase with self-propulsion, irrespective of the nature of the crowder. On the other hand, in the absence of crowders, the rotational dynamics of the Janus probe is independent of self-propulsion force. On replacing the repulsive polymers with sticky ones, translational and rotational mean square displacements of the Janus probe show a sharp drop. Since different faces of a Janus particle interact differently with the environment, we show that the direction of self-propulsion also affects its dynamics. The ratio of long-time translational and rotational diffusivities of the self-propelled probe with a fixed self-propulsion, when plotted against the area fraction of the crowders, passes through a minimum and at higher area fraction merges to its value in the absence of the crowder. This points towards the decoupling of the translational and rotational dynamics of the self-propelled probe at an intermediate area fraction of the crowders. However, such translational-rotational decoupling is absent for passive probes.

Escape of a passive particle from an activity-induced energy landscape: emergence of slow and fast effective diffusion

Spontaneous persistent motions driven by active processes play a central role in maintaining living cells far from equilibrium. In the majority of research studies, the steady state dynamics of an active system has been described in terms of an effective temperature. By contrast, we have examined a prototype model for diffusion in an activity-induced rugged energy landscape to describe the slow dynamics of a tagged particle in a dense active environment. The expression for the mean escape time from the activity-induced rugged energy landscape holds only in the limit of low activity and the mean escape time from the rugged energy landscape increases with activity. The precise form of the active correlation will determine whether the mean escape time will depend on the persistence time or not. The activity-induced rugged energy landscape approach also allows an estimate of the non-equilibrium effective diffusivity characterizing the slow diffusive motion of the tagged particle due to activity. On the other hand, in a dilute environment, high activity augments the diffusion of the tagged particle. The enhanced diffusion can be attributed to an effective temperature higher than the ambient temperature and this is used to calculate the Kramers' mean escape time, which decreases with activity. Our results have direct relevance to recent experiments on tagged particle diffusion in condensed phases.

Phase separation in a two-dimensional binary colloidal mixture by quorum sensing activity

We present results from Langevin dynamics simulations of a glassy active-passive mixture of soft-repulsive binary colloidal disks. Activity on the smaller particles is applied according to the quorum sensing scheme, in which a smaller particle will be active for a persistence time if its local nearest neighbors are equal to or greater than a certain threshold value. We start with a passive glassy state of the system and apply activity to the smaller particles, which shows a nonmonotonous glassy character of the active particles with the persistence time of the active force, from its passive limit (zero activity). On the other hand, passive particles of the active-passive mixture phase separate at the intermediate persistence time of the active force, resulting in the hexatic-liquid and solid-liquid phases. Thus, our system shows three regimes as active glass, phase separation, and active liquid, as the persistence time increases from its smaller values. We show that the solidlike and hexatic phases consisting of passive large particles are stable due to the smaller momentum transfer from active to passive particles, compared to the higher persistence time where the positional and orientational ordering vanishes. Our model is relevant to active biological systems, where glassy dynamics is present, e.g., bacterial cytoplasm, biological tissues, dense quorum sensing bacteria, and synthetic smart amorphous glasses.

Approach to equilibrium and nonequilibrium stationary distributions of interacting many-particle systems that are coupled to different heat baths

A Hamiltonian-based model of many harmonically interacting massive particles that are subject to linear friction and coupled to heat baths at different temperatures is used to study the dynamic approach to equilibrium and nonequilibrium stationary states. An equilibrium system is here defined as a system whose stationary distribution equals the Boltzmann distribution, the relation of this definition to the conditions of detailed balance and vanishing probability current is discussed both for underdamped as well as for overdamped systems. Based on the exactly calculated dynamic approach to the stationary distribution, the functional that governs this approach, which is called the free entropy S_{free}(t), is constructed. For the stationary distribution S_{free}(t) becomes maximal and its time derivative, the free entropy production S[over ̇]_{free}(t), is minimal and vanishes. Thus, S_{free}(t) characterizes equilibrium as well as nonequilibrium stationary distributions by their extremal and stability properties. For an equilibrium system, i.e., if all heat baths have the same temperature, the free entropy equals the negative free energy divided by temperature and thus corresponds to the Massieu function which was previously introduced in an alternative formulation of statistical mechanics. Using a systematic perturbative scheme for calculating velocity and position correlations in the overdamped massless limit, explicit results for few particles are presented: For two particles localization in position and momentum space is demonstrated in the nonequilibrium stationary state, indicative of a tendency to phase separate. For three elastically interacting particles heat flows from a particle coupled to a cold reservoir to a particle coupled to a warm reservoir if the third reservoir is sufficiently hot. This does not constitute a violation of the second law of thermodynamics, but rather demonstrates that a particle in such a nonequilibrium system is not characterized by an effective temperature which equals the temperature of the heat bath it is coupled to. Active particle models can be described in the same general framework, which thereby allows us to characterize their entropy production not only in the stationary state but also in the approach to the stationary nonequilibrium state. Finally, the connection to nonequilibrium thermodynamics formulations that include the reservoir entropy production is discussed.