Dynamical heterogeneity in active glasses is inherently different from its equilibrium behavior.

Activity-driven glassy dynamics, while ubiquitous in collective cell migration, intracellular transport, dynamics in bacterial and ant colonies, etc., also extends the scope and extent of the as-yet mysterious physics of glass transition. Active glasses are hitherto assumed to be qualitatively similar to their equilibrium counterparts at an effective temperature, [Formula: see text]. Here, we combine large-scale simulations and an analytical mode-coupling theory (MCT) for such systems and show that, in fact, an active glass is inherently different from an equilibrium glass. Although the relaxation dynamics can be equilibrium-like at a [Formula: see text], effects of activity on the dynamic heterogeneity (DH), which is a hallmark of glassy dynamics, are quite nontrivial and complex. With no preexisting data, we employ four distinct methods for reliable estimates of the DH length scales. Our work shows that active glasses exhibit dramatic growth of DH and systems with similar relaxation times, and thus, [Formula: see text] can have widely varying DH. To theoretically study DH, we extend active MCT and find good qualitative agreement between the theory and simulation results. Our results pave avenues for understanding the role of DH in glassy dynamics and can have fundamental significance even in equilibrium.

Dependence of the Glass Transition and Jamming Densities on Spatial Dimension.

We investigate the dynamics of soft sphere liquids through computer simulations for spatial dimensions from d=3 to 8, over a wide range of temperatures and densities. Employing a scaling of density-temperature-dependent relaxation times, we precisely identify the density ϕ_{0}, which marks the ideal glass transition in the hard sphere limit, and a crossover from sub- to super-Arrhenius temperature dependence. The difference between ϕ_{0} and the athermal jamming density ϕ_{J}, small in 3 and 4 dimensions, increases with dimension, with ϕ_{0}>ϕ_{J} for d>4. We compare our results with recent theoretical calculations.

Relaxation time scales of interfacial water upon fluid to ripple to gel phase transitions of bilayers.

The slow relaxation of interface water (IW) across three primary phases of membranes is relevant to understand the influence of IW on membrane functions at supercooled conditions. To this objective, a total of ∼16.26µs all-atom molecular dynamics simulations of 1,2-dimyristoyl-sn-glycerol-3-phosphocholine lipid membranes are carried out. A supercooling-driven drastic slow-down in heterogeneity time scales of the IW is found at the fluid to the ripple to the gel phase transitions of the membranes. At both fluid-to-ripple-to-gel phase transitions, the IW undergoes two dynamic crossovers in Arrhenius behavior with the highest activation energy at the gel phase due to the highest number of hydrogen bonds. Interestingly, the Stokes-Einstein (SE) relation is conserved for the IW near all three phases of the membranes for the time scales derived from the diffusion exponents and the non-Gaussian parameters. However, the SE relation breaks for the time scale obtained from the self-intermediate scattering functions. The behavioral difference in different time scales is universal and found to be an intrinsic property of glass. The first dynamical transition in the α relaxation time of the IW is associated with an increase in the Gibbs energy of activation of hydrogen bond breaking with locally distorted tetrahedral structures, unlike the bulk water. Thus, our analyses unveil the nature of the relaxation time scales of the IW across membrane phase transitions in comparison with the bulk water. The results will be useful to understand the activities and survival of complex biomembranes under supercooled conditions in the future.

Quantifying dynamical heterogeneity length scales of interface water across model membrane phase transitions.

All-atom molecular dynamics simulations of 1,2-dimyristoyl-sn-glycero-3-phosphocholine lipid membranes reveal a drastic growth in the heterogeneity length scales of interface water (IW) across fluid to ripple to gel phase transitions. It acts as an alternate probe to capture the ripple size of the membrane and follows an activated dynamical scaling with the relaxation time scale solely within the gel phase. The results quantify the mostly unknown correlations between the spatiotemporal scales of the IW and membranes at various phases under physiological and supercooled conditions.

Athermal quasistatic cavitation in amorphous solids: Effect of random pinning.

Amorphous solids are known to fail catastrophically via fracture, and cavitation at nano-metric scales is known to play a significant role in such a failure process. Micro-alloying via inclusions is often used as a means to increase the fracture toughness of amorphous solids. Modeling such inclusions as randomly pinned particles that only move affinely and do not participate in plastic relaxations, we study how the pinning influences the process of cavitation-driven fracture in an amorphous solid. Using extensive numerical simulations and probing in the athermal quasistatic limit, we show that just by pinning a very small fraction of particles, the tensile strength is increased, and also the cavitation is delayed. Furthermore, the cavitation that is expected to be spatially heterogeneous becomes spatially homogeneous by forming a large number of small cavities instead of a dominant cavity. The observed behavior is rationalized in terms of screening of plastic activity via the pinning centers, characterized by a screening length extracted from the plastic-eigenmodes.

Universal non-Debye low-frequency vibrations in sheared amorphous solids.

We study energy minimised configurations of amorphous solids with a simple shear degree of freedom. We show that the low-frequency regime of the vibrational density of states of structural glass formers is crucially sensitive to the macroscopic stress of the sampled configurations. In both two and three dimensions, shear-stabilised configurations display a D(ωmin) ∼ ω5min regime, as opposed to the ω4min regime observed under unstrained conditions. In order to isolate the source of these deviations from crystalline behaviour, we also study configurations of two dimensional, strained amorphous solids close to a plastic event. We show that the minimum eigenvalue distribution at a strain 'γ' near the plastic event occurring at 'γP' assumes a universal form that displays a collapse when scaled by , and with the number of particles as N-0.22. Notably, at low frequencies, this scaled distribution displays a robust D(ωmin) ∼ ω6min power-law regime, which survives in the large N limit. Finally, we probe the properties of these configurations through a characterisation of the second and third eigenvalues of the Hessian matrix near a plastic event.

Enhanced short time peak in four-point dynamic susceptibility in dense active glass-forming liquids.

Active glassy systems are simple model systems that imitate complex biological processes. Sometimes, it becomes crucial to estimate the amount of activity present in such biological systems, such as predicting the progression rate of the cancer cells or the healing time of the wound, etc. In this work, we study a model active glassy system to quantify the degree of activity from the collective, long-wavelength fluctuations in the system. These long-wavelength fluctuations present themselves as an additional peak in the four-point dynamic susceptibility (χ4(t)) apart from the usual peak at structural relaxation time. We then show how the degree of the activity at such a small timescale can be obtained by measuring the variation in χ4(t) due to changing activity. A Detailed finite size analysis of the peak height of χ4(t) suggests the existence of an intrinsic dynamic length scale that grows with increasing activity. Finally, we show that this peak height is a unique function of effective activity across all system sizes, serving as a possible parameter for characterizing the degree of activity in a system.

Thermodynamics and its correlation with dynamics in a mean-field model and pinned systems: A comparative study using two different methods of entropy calculation.

A recent study introduced a novel mean-field model system where each particle over and above the interaction with its regular neighbors interacts with k extra pseudo-neighbors. Here, we present an extensive study of thermodynamics and its correlation with the dynamics of this system. We surprisingly find that the well-known thermodynamic integration (TI) method of calculating the entropy provides unphysical results. It predicts vanishing of the configurational entropy at temperatures close to the onset temperature of the system and negative values of the configurational entropy at lower temperatures. Interestingly, well below the temperature at which the configurational entropy vanishes, both the collective and the single-particle dynamics of the system show complete relaxation. Negative values of the configurational entropy are unphysical, and complete relaxation when the configurational entropy is zero violates the prediction of the random first-order transition theory (RFOT). However, the entropy calculated using the two-phase thermodynamics (2PT) method remains positive at all temperatures for which we can equilibrate the system, and its values are consistent with RFOT predictions. We find that with an increase in k, the difference in the entropy computed using the two methods increases. A similar effect is also observed for a system where a randomly selected fraction of the particles are pinned in their positions in the equilibrated liquid. We show that the difference in entropy calculated via the 2PT and TI methods increases with pinning density.

Translational dynamics of a rod-like probe in supercooled liquids: an experimentally realizable method to study Stokes-Einstein breakdown, dynamic heterogeneity, and amorphous order.

The use of probe molecules to extract the local dynamical and structural properties of complex dynamical systems is an age-old technique both in simulations and in experiments. A lot of important information which is not immediately accessible from bulk measurements can be accessed via these local measurements. Still, a detailed understanding of how a probe particle dynamics is affected by the surrounding liquid medium is lacking, especially in the supercooled temperature regime. This work shows how the translational dynamics of a rod-like particle immersed in a supercooled liquid can give us information on the growth of the correlation length scales associated with dynamical heterogeneity and the multi-body static correlations in the medium. This work also provides an understanding of the breakdown of Stokes-Einstein and Stokes-Einstein-Debye relations in supercooled liquids along with a unified scaling theory that rationalizes all the observed results. Finally, this work proposes a novel yet simple method accessible in experiments to measure the growth of these important length scales in molecular glass-forming liquids.

On the existence of thermodynamically stable rigid solids.

Customarily, crystalline solids are defined to be rigid since they resist changes of shape determined by their boundaries. However, rigid solids cannot exist in the thermodynamic limit where boundaries become irrelevant. Particles in the solid may rearrange to adjust to shape changes eliminating stress without destroying crystalline order. Rigidity is therefore valid only in the metastable state that emerges because these particle rearrangements in response to a deformation, or strain, are associated with slow collective processes. Here, we show that a thermodynamic collective variable may be used to quantify particle rearrangements that occur as a solid is deformed at zero strain rate. Advanced Monte Carlo simulation techniques are then used to obtain the equilibrium free energy as a function of this variable. Our results lead to a unique view on rigidity: While at zero strain a rigid crystal coexists with one that responds to infinitesimal strain by rearranging particles and expelling stress, at finite strain the rigid crystal is metastable, associated with a free energy barrier that decreases with increasing strain. The rigid phase becomes thermodynamically stable when an external field, which penalizes particle rearrangements, is switched on. This produces a line of first-order phase transitions in the field-strain plane that intersects the origin. Failure of a solid once strained beyond its elastic limit is associated with kinetic decay processes of the metastable rigid crystal deformed with a finite strain rate. These processes can be understood in quantitative detail using our computed phase diagram as reference.

Dynamic coupling of a hydration layer to a fluid phospholipid membrane: intermittency and multiple time-scale relaxations.

Understanding the coupling of a hydration layer and a lipid membrane is crucial to gaining access to membrane dynamics and understanding its functionality towards various biological processes. To find out how significant the mutual influence of the hydration layer and bilayer dynamics is, a fully hydrated 1,2-dimyristoyl-sn-glycero-3-phosphorylcholine (DMPC) lipid bilayer is simulated atomistically in the presence of the TIP4P/2005 water model at 308 K. Interface water (IW) molecules are classified based on their continuous physical proximity or ability to form hydrogen bonds with different moieties of lipid heads. A gradient in retardation of translational mean square displacements is found to operate coherently for both IW and lipid components across the bilayer normal. Deviations from Gaussianity in van Hove correlation functions increase for the lipids and decrease for the IW from the tails to the heads. The IW molecules exhibit Fickian but intermittent dynamics due to coupled vibrations in the local cage formed by the hydrogen bonds with the lipid heads followed by decoupled translational jumps. Importantly, the differences in regional dynamics of lipid heads are clearly reflected in the dynamics of spatially resolved IW molecules physically close to the lipid heads, but not to the dynamics of the hydrogen bonded IW molecules far from the lipid heads. These analyses imply that spatially resolved interface water dynamics can act as a sensitive reflector of regional membrane dynamics occurring at sub ps to hundreds of ps time-scales for several important biological functions at physiological temperature in the future.

Effect of Pinning on the Yielding Transition of Amorphous Solids.

Using numerical simulations, we have studied the yielding response, in the athermal quasistatic limit, of a model amorphous material having inclusions in the form of randomly pinned particles. We show that, with increasing pinning concentration, the plastic activity becomes more spatially localized, resulting in smaller stress drops, and a corresponding increase in the magnitude of strain where yielding occurs. We demonstrate that, unlike the spatially heterogeneous and avalanche led yielding in the case of the unpinned glass, for the case of large pinning concentration, yielding takes place via a spatially homogeneous proliferation of localized events.

Quantification of spatio-temporal scales of dynamical heterogeneity of water near lipid membranes above supercooling.

A hydrated 1,2-dimyristoyl-sn-glycero-3-phosphorylcholine (DMPC) lipid membrane is investigated using an all atom molecular dynamics simulation at 308 K to determine the physical sources of universal slow relaxations of hydration layers and length-scale of the spatially heterogeneous dynamics. Continuously residing interface water (IW) molecules hydrogen bonded to different moieties of lipid heads in the membrane are identified. The non-Gaussian parameters of all classes of IW molecules show a cross-over from cage vibration to translational diffusion. A significant non-Gaussianity is observed for the IW molecules exhibiting large length correlations in translational van Hove functions. Two time-scales for the ballistic motions and hopping transitions are obtained from the self intermediate scattering functions of the IW molecules with an additional long relaxation, which disappears for bulk water. The long relaxation time-scales for the IW molecules obtained from the self intermediate scattering functions are in good accordance with the hydrogen bond relaxation time-scales irrespective of the nature of the chemical confinement and the confinement lifetime. Employing a block analysis approach, the length-scale of dynamical heterogeneities is captured from a transition from non-Gaussianity to Gaussianity in van Hove correlation functions of the IW molecules. The heterogeneity length-scale is comparable to the wave-length of the small and weak undulations of the membrane calculated by Fourier transforms of lipid tilts. This opens up a new avenue towards a possible correlation between heterogeneity length-scale and membrane curvature more significant for rippled membranes. Thus, our analyses provide a measure towards the spatio-temporal scale of dynamical heterogeneity of confined water near membranes.

Role of α and ß relaxations in collapsing dynamics of a polymer chain in supercooled glass-forming liquid.

Understanding the effect of glassy dynamics on the stability of bio-macromolecules and investigating the underlying relaxation processes governing degradation processes of these macromolecules are of immense importance in the context of bio-preservation. In this work, we have studied the stability of a model polymer chain in a supercooled glass-forming liquid at different amounts of supercooling in order to understand how dynamics of supercooled liquids influence the collapse behavior of the polymer. Our systematic computer simulation studies find that, apart from long time relaxation processes (α relaxation), short time dynamics of the supercooled liquid, known as ß relaxation, is also correlated with the stability of the model polymer. We also show that anti-plasticizing effect found in this context can be rationalized using the ß-relaxation process and how it is modified due to changes in the specific interactions between the biomolecules and the solvent molecules or changes in the local packing around the biomolecules. Our results corroborate with other recent results which suggest that it is important to take in to account both the α and ß relaxation times while choosing appropriate bio-preservatives. We believe that our results will have implications in understanding the primary factors in protein stabilization in the context of bio-preservation.

Glass Transition in Supercooled Liquids with Medium-Range Crystalline Order.

The origin of the rapid dynamical slowdown in glass forming liquids in the growth of static length scales, possibly associated with identifiable structural ordering, is a much debated issue. Growth of medium range crystalline order (MRCO) has been observed in various model systems to be associated with glassy behavior. Such observations raise the question of whether molecular mechanisms for the glass transition in liquids with and without MRCO are the same. In this study we perform extensive molecular dynamics simulations of a number of glass forming liquids and show that the static and dynamic properties of glasses with MRCO are different from those of other glass forming liquids with no predominant local order. We also resolve an important issue regarding the so-called point-to-set method for determining static length scales, and demonstrate it to be a robust method for determining static correlation lengths in glass formers.

Possible universal relation between short time ß-relaxation and long time α-relaxation in glass-forming liquids.

Relaxation processes in supercooled liquids are known to exhibit interesting complex behavior. One of the hallmarks of this relaxation process observed in the measured auto correlation function is the occurrence of multiple steps of relaxations. The shorter time relaxation is known as the ß-relaxation which is believed to be due to the motion of particles in the cage formed by their neighbors. The longer time relaxation is called the α-relaxation. The time scales of these two relaxations processes dramatically separate out with supercooling. In spite of decades of research, it is still not clearly known how these relaxation processes are related to each other. In this work, we show that there is a possible universal relation between short time ß-relaxation and long time α-relaxation. We also show that the proposed relation can be rationalized within random first order transition theory of glass transition if power law relation is assumed between static and dynamic length scales.

Plastic deformation of a permanently bonded network: Stress relaxation by pleats.

We show that a flat two dimensional network of connected vertices, when stretched, may deform plastically by producing "pleats", system spanning linear structures with width comparable to the lattice spacing, where the network overlaps on itself. To understand the pleating process, we introduce an external field that couples to local non-affine displacements, i.e., those displacements of neighbouring vertices that cannot be represented as a local affine strain. We obtain both zero and finite temperature phase diagrams in the strain-field plane. Pleats occur here as a result of an equilibrium first-order transition from the homogeneous network to a heterogeneous phase where stress is localised within pleats and eliminated elsewhere. We show that in the thermodynamic limit, the un-pleated state is always metastable at vanishing field for infinitesimal strain. Plastic deformation of the initially homogeneous network is akin to the decay of a metastable phase via a dynamical transition. We make predictions concerning local stress distributions and thermal effects associated with pleats which may be observable in suitable experimental systems.

Block Analysis for the Calculation of Dynamic and Static Length Scales in Glass-Forming Liquids.

We present block analysis, an efficient method of performing finite-size scaling for obtaining the length scale of dynamic heterogeneity and the point-to-set length scale for generic glass-forming liquids. This method involves considering blocks of varying sizes embedded in a system of a fixed (large) size. The length scale associated with dynamic heterogeneity is obtained from a finite-size scaling analysis of the dependence of the four-point dynamic susceptibility on the block size. The block size dependence of the variance of the α relaxation time yields the static point-to-set length scale. The values of the obtained length scales agree quantitatively with those obtained from other conventional methods. This method provides an efficient experimental tool for studying the growth of length scales in systems such as colloidal glasses for which performing finite-size scaling by carrying out experiments for varying system sizes may not be feasible.

Pinning susceptibility: a novel method to study growth of amorphous order in glass-forming liquids.

The existence and growth of amorphous order in supercooled liquids approaching glass transition is a subject of intense research. Even after decades of work, there is still no clear consensus on the molecular mechanisms that lead to a rapid slowing down of liquid dynamics approaching this putative transition. The existence of a correlation length associated with amorphous order has recently been postulated and has also been estimated using multi-point correlation functions which cannot be calculated easily in experiments. Thus the study of growing amorphous order remains mostly restricted to systems like colloidal glasses and simulations of model glass-forming liquids. In this work, we propose an experimentally realizable yet simple susceptibility to study the growth of amorphous order. We then demonstrate the validity of this approach for a few well-studied model supercooled liquids and obtain results which are consistent with other conventional methods.

Equilibrium and dynamic pleating of a crystalline bonded network.

We describe a phase transition that gives rise to structurally non-trivial states in a two-dimensional ordered network of particles connected by harmonic bonds. Monte Carlo simulations reveal that the network supports, apart from the homogeneous phase, a number of heterogeneous "pleated" phases, which can be stabilised by an external field. This field is conjugate to a global collective variable quantifying "non-affineness," i.e., the deviation of local particle displacements from local affine deformation. In the pleated phase, stress is localised in ordered rows of pleats and eliminated from the rest of the lattice. The kinetics of the phase transition is unobservably slow in molecular dynamics simulation near coexistence, due to very large free energy barriers. When the external field is increased further to lower these barriers, the network exhibits rich dynamic behaviour: it transforms into a metastable phase with the stress now localised in a disordered arrangement of pleats. The pattern of pleats shows ageing dynamics and slow relaxation to equilibrium. Our predictions may be checked by experiments on tethered colloidal solids in dynamic laser traps.