Energy landscape, antiplasticization, and polydispersity induced crossover of heterogeneity in supercooled polydisperse liquids

NVU view on energy polydisperse Lennard-Jones systems

When energy polydispersity is introduced into the Lennard-Jones (LJ) system, there is little effect on structure and dynamics [T. S. Ingebrigtsen and J. C. Dyre, J. Phys. Chem. B 127, 2837 (2023)10.1021/acs.jpcb.3c00346]. For instance, at a given state point both the radial distribution function and the mean-square displacement as a function of time are virtually unaffected by even large energy polydispersity, which is in stark contrast to what happens when size polydispersity is introduced. We here argue-and validate by simulations of up to 30% polydispersity-that this almost invariance of structure and dynamics reflects an approximate invariance of the constant-potential-energy surface. Because NVU dynamics defined as geodesic motion at constant potential energy is equivalent to Newtonian dynamics in the thermodynamic limit, the approximate invariance of the constant-potential-energy surface implies virtually the same physics of energy polydisperse LJ systems as of the standard single-component version. In contrast, the constant-potential-energy surface is significantly affected by introducing size polydispersity.

Active-parameter polydispersity in the 2d ABP Yukawa model

In experiments and simulations of passive as well as active matter the most commonly studied kind of parameter polydispersity is that of varying particles size. This paper investigates by simulations the effects of introducing polydispersity in other parameters for two-dimensional active Brownian particles with Yukawa pair interactions. Polydispersity is studied separately in the translational and rotational diffusion coefficients, as well as in the swim velocityv0. Uniform and binary parameter distributions are considered in the homogeneous and the motility-induced phase-separation (MIPS) phases. We find only minute changes in structure and dynamics upon the introduction of parameter polydispersity, even for situations involving 50% polydispersity. The reason for this is not clear. An exception is the case ofv0polydispersity for which the average radial distribution function with changing polydispersity shows significant variations in the MIPS phase. Even in this case, however, the dynamics is only modestly affected. As a possible application of our findings, we suggest that a temporary introduction of polydispersity into a single-component active-matter model characterized by a very long equilibration time, i.e. a glass-forming active system, may be used to equilibrate the system efficiently by particle swaps.

Dynamic heterogeneity in polydisperse systems: A comparative study of the role of local structural order parameter and particle size

In polydisperse systems, describing the structure and any structural order parameter (SOP) is not trivial as it varies with the number of species we use to describe the system, M. Depending on the degree of polydispersity, there is an optimum value of M = M0 where we show that the mutual information of the system increases. However, surprisingly, the correlation between a recently proposed SOP and the dynamics is highest for M = 1. This effect increases with polydispersity. We find that the SOP at M = 1 is coupled with the particle size, σ, and this coupling increases with polydispersity and decreases with an increase in M. Careful analysis shows that at lower polydispersities, the SOP is a good predictor of the dynamics. However, at higher polydispersity, the dynamics is strongly dependent on σ. Since the coupling between the SOP and σ is higher for M = 1, it appears to be a better predictor of the dynamics. We also study the Vibrality, an order parameter independent of structural information. Compared to SOP, at high polydispersity, we find Vibrality to be a marginally better predictor of the dynamics. However, this high predictive power of Vibrality, which is not there at lower polydispersity, appears to be due to its stronger coupling with σ. Therefore, our study suggests that for systems with high polydispersity, the correlation of any order parameter and σ will affect the correlation between the order parameter and dynamics and need not project a generic predictive power of the order parameter.

Even Strong Energy Polydispersity Does Not Affect the Average Structure and Dynamics of Simple Liquids

Size-polydisperse liquids have become standard models for avoiding crystallization, thereby enabling studies of supercooled liquids and glasses formed, e.g., by colloidal systems. Purely energy-polydisperse liquids have been studied much less, but provide an interesting alternative. We here study numerically the difference in structure and dynamics obtained by introducing these two kinds of polydispersity into systems of particles interacting via the Lennard-Jones and EXP pair potentials. To a very good approximation, the average pair structure and dynamics are unchanged even for strong energy polydispersity, which is not the case for size-polydisperse systems. When the system at extreme energy polydispersity undergoes a continuous phase separation into lower and higher particle-energy regions whose structure and dynamics are different from the average, the average structure and dynamics are still virtually the same as for the monodisperse system. Our findings are consistent with the fact that the distribution of forces on the individual particles do not change when energy polydispersity is introduced, while they do change in the case of size polydispersity. A theoretical explanation remains to be found, however.

Steering self-organisation through confinement

Self-organisation is the spontaneous emergence of spatio-temporal structures and patterns from the interaction of smaller individual units. Examples are found across many scales in very different systems and scientific disciplines, from physics, materials science and robotics to biology, geophysics and astronomy. Recent research has highlighted how self-organisation can be both mediated and controlled by confinement. Confinement is an action over a system that limits its units' translational and rotational degrees of freedom, thus also influencing the system's phase space probability density; it can function as either a catalyst or inhibitor of self-organisation. Confinement can then become a means to actively steer the emergence or suppression of collective phenomena in space and time. Here, to provide a common framework and perspective for future research, we examine the role of confinement in the self-organisation of soft-matter systems and identify overarching scientific challenges that need to be addressed to harness its full scientific and technological potential in soft matter and related fields. By drawing analogies with other disciplines, this framework will accelerate a common deeper understanding of self-organisation and trigger the development of innovative strategies to steer it using confinement, with impact on, e.g., the design of smarter materials, tissue engineering for biomedicine and in guiding active matter.

Structure ordering and glass transition in size-asymmetric ternary mixtures of hard spheres: Variation from fragile to strong glasses

We investigate the structure and activated dynamics of a binary mixture of colloidal particles dispersed in a solvent of much smaller-sized particles. The solvent degrees of freedom are traced out from the grand partition function of the colloid-solvent mixture which reduces the system from ternary to effective binary mixture of colloidal particles. In the effective binary mixture colloidal particles interact via effective potential that consists of bare potential plus the solvent-induced interaction. Expressions for the effective potentials and pair correlation functions are derived. We used the result of pair correlation functions to determine the number of particles in a cooperatively reorganizing cluster (CRC) in which localized particles form "long-lived" nonchemical bonds with the central particle. For an event of relaxation to take place these bonds have to reorganize irreversibly, the energy involved in the processes is the effective activation energy of relaxation. Results are reported for hard sphere colloidal particles dispersed in a solvent of hard sphere particles. Our results show that the concentration of solvent can be used as a control parameter to fine-tune the microscopic structural ordering and the size of CRC that governs the glassy dynamics. We show that a small variation in the concentration of solvent creates a bigger change in the kinetic fragility which highlights a wide variation in behavior, ranging from fragile to strong glasses. We conclude that the CRC which is determined from the static pair correlation function and the fluctuations embedded in the system is probably the sole player in the physics of glass transition.

Effective structure of a system with continuous polydispersity

In a system of N particles, with continuous size polydispersity, there exists an N(N - 1) number of partial structure factors, making it analytically less tractable. A common practice is to treat the system as an effective one component system, which is known to exhibit an artificial softening of the structure. The aim of this study is to describe the system in terms of M pseudospecies such that we can avoid this artificial softening but, at the same time, have a value of M ≪ N. We use potential energy and pair excess entropy to estimate an optimum number of species, M₀. We then define the maximum width of polydispersity, Δσ₀, that can be treated as a monodisperse system. We show that M₀ depends on the degree and type of polydispersity and also on the nature of the interaction potential, whereas Δσ₀ weakly depends on the type of polydispersity but shows a stronger dependence on the type of interaction potential. Systems with a softer interaction potential have a higher tolerance with respect to polydispersity. Interestingly, M₀ is independent of system size, making this study more relevant for bigger systems. Our study reveals that even 1% polydispersity cannot be treated as an effective monodisperse system. Thus, while studying the role of polydispersity by using the structure of an effective one component system, care must be taken in decoupling the role of polydispersity from that of the artificial softening of the structure.

Hidden Scale Invariance in Polydisperse Mixtures of Exponential Repulsive Particles

Polydisperse systems of particles interacting by the purely repulsive exponential (EXP) pair potential are studied in regard to how structure and dynamics vary along isotherms, isochores, and isomorphs. The sizable size polydispersities of 23%, 29%, 35%, and 40%, as well as energy polydispersity 35%, were considered. For each system an isomorph was traced out covering about one decade in density. For all systems studied, the structure and dynamics vary significantly along the isotherms and isochores but are invariant to a good approximation along the isomorphs. We conclude that the single-component EXP system's hidden scale invariance (implying isomorph invariance of structure and dynamics) is maintained even when a sizable polydispersity is introduced into the system.

Apparent strength versus universality in glasses of soft compressible colloids

Microgel colloids, solvent swollen hydrogel particles of microscopic size, are in osmotic equilibrium with their surroundings. This has a profound effect on the behaviour of dense solutions of these polymeric colloids, most notably their ability to swell and deswell depending on the osmotic pressure of the system as a whole. Here we develop a minimal simulation model to treat this intrinsic volume regulation in order to explore the effects this has on the properties of dense solutions close to a liquid-solid transition. We demonstrate how the softness dependent volume regulation of particles gives rise to an apparent change in the fragility of the colloidal glass transition, which can be scaled out through the use of an adjusted volume fraction that accounts for changes in particle size. Moreover, we show how the same model can be used to explain the selective deswelling of soft microgels in a crystalline matrix of harder particles leading to robust crystals free of defects. Our results not only highlight the non-trivial effects of osmotic regulation in governing the apparent physics of microgel suspensions, but also provides a platform to efficiently account for particle deswelling in simulations.

A geometrical criterion for glass transition in soft-sphere fluids

As glass-forming fluids become colder and denser, structural rearrangements become slow and eventually cease. For hard-sphere fluids, percolation of particles unable to change neighbors (T1-inactive particles) signals the glass transition. To investigate this geometrical criterion for mobility in soft-sphere systems, we simulate monodisperse fluids interacting with a generalized Weeks-Chandler-Andersen (WCA) potential in metastable equilibrium, using our previously developed crystal-avoiding method. We find that the vanishing diffusivity as the glass transition is approached can be described by a power law below the onset temperature of super-Arrhenius behavior. By mapping the soft spheres to hard spheres based on mean collision energy, we find that the diffusivity versus effective volume fraction curves collapse onto the hard-sphere curve for all systems studied. We find that the onset of super-Arrhenius behavior and the MCT dynamic glass transition correlate well with temperature when the T1-inactive particles form clusters of two particles on average and when the T1-inactive clusters percolate the entire system, respectively. Our findings provide new insight into the structural origin of glassy dynamics.

Revealing the Link between Structural Relaxation and Dynamic Heterogeneity in Glass-Forming Liquids

Despite the use of glasses for thousands of years, the nature of the glass transition is still mysterious. On approaching the glass transition, the growth of dynamic heterogeneity has long been thought to play a key role in explaining the abrupt slowdown of structural relaxation. However, it still remains elusive whether there is an underlying link between structural relaxation and dynamic heterogeneity. Here, we unravel the link by introducing a characteristic time scale hiding behind an identical dynamic heterogeneity for various model glass-forming liquids. We find that the time scale corresponds to the kinetic fragility of liquids. Moreover, it leads to scaling collapse of both the structural relaxation time and dynamic heterogeneity for all liquids studied, together with a characteristic temperature associated with the same dynamic heterogeneity. Our findings imply that studying the glass transition from the viewpoint of dynamic heterogeneity is more informative than expected.

Effect of Size Polydispersity on the Nature of Lennard-Jones Liquids

Polydisperse fluids are encountered everywhere in biological and industrial processes. These fluids naturally show a rich phenomenology exhibiting fractionation and shifts in critical point and freezing temperatures. We study here the effect of size polydispersity on the basic nature of Lennard-Jones (LJ) liquids, which represent most molecular liquids without hydrogen bonds, via two- and three-dimensional molecular dynamics computer simulations. A single-component liquid constituting spherical particles and interacting via the LJ potential is known to exhibit strong correlations between virial and potential energy equilibrium fluctuations at constant volume. This correlation significantly simplifies the physical description of the liquid, and these liquids are now known as Roskilde-simple (RS) liquids. We show that this simple nature of the single-component LJ liquid is preserved even for very high polydispersities (above 40% polydispersity for the studied uniform distribution). We also investigate isomorphs of moderately polydisperse LJ liquids. Isomorphs are curves in the phase diagram of RS liquids along which structure, dynamics, and some thermodynamic quantities are invariant in dimensionless units. We find that isomorphs are a good approximation even for polydisperse LJ liquids. The theory of isomorphs thus extends readily to size polydisperse fluids and can be used to improve even further the understanding of these intriguing systems.

Structural evolution in the aging process of supercooled colloidal liquids

When a liquid is rapidly quenched to a temperature below the glass-transition point, it is driven out of equilibrium; it then slowly relaxes to a (quasi)equilibrium state. This slow relaxation process is called aging. By definition, any glasses are inevitably in the process of aging and actually slowly evolving with time. Thus the study of aging phenomena is of fundamental importance for understanding not only the nonequilibrium nature of the glass transition, but also the stability of glassy materials. Here we consider aging after a rather shallow quench, for which a system is still able to reach (metastable) equilibrium. By using polydisperse colloidal liquids as a model, we show the validity of dynamical scaling that there is only one relevant length scale not only for a quasiequilibrium supercooled state but also for a nonequilibrium process of aging, which is reminiscent of dynamical critical phenomena. Our finding indicates that the aging toward (metastable) equilibrium may be regarded as the growth process of critical-like fluctuations of static order associated with low-free-energy configurations, further suggesting that this ordering is the origin of cooperative slow dynamics in the systems studied. The generality of this statement for other glass-forming systems remains for a future study.

Solid-liquid transition in polydisperse Lennard-Jones systems

We study melting of a face-centered crystalline solid consisting of polydisperse Lennard-Jones spheres with Gaussian polydispersity in size. The phase diagram reproduces the existence of a nearly temperature invariant terminal polydispersity (δ(t) =/~ 0.11), with no signature of reentrant melting. The absence of reentrant melting can be attributed to the influence of the attractive part of the potential upon melting. We find that at terminal polydispersity the fractional density change approaches zero, which seems to arise from vanishingly small compressibility of the disordered phase. At constant temperature and volume fraction the system undergoes a sharp transition from crystalline solid to the disordered amorphous or fluid state with increasing polydispersity. This has been quantified by second- and third-order rotational invariant bond orientational order, as well as by the average inherent structure energy. The translational order parameter also indicates a similar sharp structural change at δ =/~ 0.09 in case of T(*) = 1.0, φ = 0.58. The free energy calculation further supports the sharp nature of the transition. The third-order rotationally invariant bond order shows that with increasing polydispersity, the local cluster favors a more icosahedral arrangement and the system loses its local crystalline symmetry. Interestingly, the value of structure factor S(k) of the amorphous phase at δ =/~ 0.10 (just beyond the solid-liquid transition density at T(*) = 1) becomes 2.75, which is below the value of 2.85 required for freezing given by the empirical Hansen-Verlet rule of crystallization, well known in the theory of freezing.

Glassy Interfacial Dynamics of Ni Nanoparticles: Part I Colored Noise, Dynamic Heterogeneity and Collective Atomic Motion

Most condensed materials exhibit a significant fraction of atoms, molecules or particles that are strongly interacting with each other, while being configured geometrically at any instant of time in an 'amorphous' state having a relatively uniform density. Recently, both simulations and experiments have revealed that the dynamics of diverse condensed amorphous materials is generally characterized by significant heterogeneity in the local mobility and by progressively increasing collective motion upon cooling that takes the form of string-like collective particle rearrangements. The direct experimental observation of this type of collective motion, which has been directly linked to the growing relaxation times of glass-forming materials, and its quantification under different thermodynamic conditions, has so far been restricted to colloidal and driven granular fluids. The present work addresses the fundamental problem of how to determine the scale of this type of collective motion in materials composed of molecules or atoms. The basic premise of our work is that large scale dynamic particle clustering in amorphous materials must give rise to large fluctuations in particle mobility so that transport properties, especially those related to particle mobility, should naturally exhibit noise related to the cooperative motion scale. In our initial exploratory study seeking a relationship of this kind, we find 1/fα or 'colored noise', in both potential energy and particle displacements fluctuations of the atoms within the glassy interfacial layer of Ni nanoparticles (NPs). A direct relation between the particle displacement (mobility) noise exponent α and the average polymerization index of the string-like collective motion L is observed for a range of NP sizes, temperatures and for surface doping of the NPs with other metal atoms (Ag, Au, Pt) to change of fragility of the glassy interfacial layer at the surface of the Ni NPs. We also introduce a successful analytic model to understand this relationship between α and L.

Dependence of the fragility of a glass former on the softness of interparticle interactions

We study the influence of the softness of the interparticle interactions on the fragility of a glass former by considering three model binary mixture glass formers. The interaction potential between particles is a modified Lennard-Jones type potential, with the repulsive part of the potential varying with an inverse power q of the interparticle distance, and the attractive part varying with an inverse power p. We consider the combinations (12,11) (model I), (12,6) (model II), and (8,5) (model III) for (q,p) such that the interaction potential becomes softer from model I to III. We evaluate the kinetic fragilities from the temperature variation of diffusion coefficients and relaxation times, and a thermodynamic fragility from the temperature variation of the configurational entropy. We find that the kinetic fragility increases with increasing softness of the potential, consistent with previous results for these model systems, but at variance with the thermodynamic fragility, which decreases with increasing softness of the interactions, as well as expectations from earlier results. We rationalize our results by considering the full form of the Adam-Gibbs relation, which requires, in addition to the temperature dependence of the configurational entropy, knowledge of the high temperature activation energies in order to determine fragility. We show that consideration of the scaling of the high temperature activation energy with the liquid density, analyzed in recent studies, provides a partial rationalization of the observed behavior.

Structural origin of dynamic heterogeneity in three-dimensional colloidal glass formers and its link to crystal nucleation

The physical understanding of glass transition remains a major challenge of physics and materials science. Among various glass-forming liquids, a colloidal liquid interacting with hard-core repulsion is now regarded as one of the most ideal model systems. Here we study the structure and dynamics of three-dimensional polydisperse colloidal liquids by Brownian dynamics simulations. We reveal that medium-range crystalline bond orientational order of the hexagonal close packed structure grows in size and lifetime with increasing packing fraction. We show that dynamic heterogeneity may be a direct consequence of this transient structural ordering, which suggests its origin is thermodynamic rather than kinetic. We also reveal that nucleation of crystals preferentially occurs in regions of high medium-range order, reflecting the low crystal-liquid interfacial energy there. These findings may shed new light not only on the fundamental nature of the glass transition, but also the mechanism of crystal nucleation.

Numerical and theoretical study of a monodisperse hard-sphere glass former

There exists a variety of theories of the glass transition and many more numerical models. But because the models need built-in complexity to prevent crystallization, comparisons with theory can be difficult. We study the dynamics of a deeply supersaturated monodisperse four-dimensional (4D) hard-sphere fluid, which has no such complexity, but whose strong intrinsic geometrical frustration inhibits crystallization, even when deeply supersaturated. As an application, we compare its behavior to the mode-coupling theory (MCT) of glass formation. We find MCT to describe this system better than any other structural glass formers in lower dimensions. The reduction in dynamical heterogeneity in 4D suggested by a milder violation of the Stokes-Einstein relation could explain the agreement. These results are consistent with a mean-field scenario of the glass transition.

Vibrational dynamics and boson peak in a supercooled polydisperse liquid

Vibrational density of states (VDOS) in a supercooled polydisperse liquid is computed by diagonalizing the Hessian matrix evaluated at the potential energy minima for systems with different values of polydispersity. An increase in polydispersity leads to an increase in the relative population of localized high-frequency modes. At low frequencies, the density of states shows an excess compared to the Debye squared-frequency law, which has been identified with the boson peak. The height of the boson peak increases with polydispersity and shows a rather narrow sensitivity to changes in temperature. While the modes comprising the boson peak appear to be largely delocalized, there is a sharp drop in the participation ratio of the modes that exist just below the boson peak indicative of the quasilocalized nature of the low-frequency vibrations. Study of the difference spectrum at two different polydispersity reveals that the increase in the height of boson peak is due to a population shift from modes with frequencies above the maximum in the VDOS to that below the maximum, indicating an increase in the fraction of the unstable modes in the system. The latter is further supported by the facilitation of the observed dynamics by polydispersity. Since the strength of the liquid increases with polydispersity, the present result provides an evidence that the intensity of boson peak correlates positively with the strength of the liquid, as observed earlier in many experimental systems.

Suppression of the rate of growth of dynamic heterogeneities and its relation to the local structure in a supercooled polydisperse liquid

The relationship between the microscopic arrangement of molecules in a supercooled liquid and its slow dynamics at low temperature near glass transition is studied by molecular dynamics simulations. A Lennard-Jones liquid with polydispersity in size and mass of constituent particles is chosen as the model system. Our studies reveal that the local structure (that varies with polydispersity) plays a crucial role both in the slowing down of dynamics and in the growth of the dynamic heterogeneities, besides determining the glass forming ability of the system. Increasing polydispersity at fixed volume fraction is found to suppress the rate of growth of dynamic correlations, as detected by the growth in the peak of the nonlinear density response function, chi4(t). The growth in dynamical correlation is manifested in a stronger than usual breakdown of Stokes-Einstein relation at lower polydispersity at low temperatures and also leads to a decrease in the fragility of the system with polydispersity. We show that the suppression of the rate of growth of the dynamic heterogeneity can be attributed to the loss of structural correlations (as measured by the structure factor and the local bond orientational order) with polydispersity. While a critical polydispersity is required to avoid crystallization, we find that a further increase in polydispersity lowers the glass forming ability.