Searcharxiv⌕ Search

arXiv subjects

Rakesh S. Singh

Publications and source records attributed to Rakesh S. Singh.

At least 19 recordsLinked to original sources
arXiv2026

Liquid-Liquid Phase Separation in a Minimal Explicit-Solvent Lattice Model Mimicking Protein Solutions

Biomolecular condensates play essential roles in cellular processes, and recent efforts have focused on understanding their assembly and rational design principles. In this study, we have employed an explicit-solvent minimal statistical mechanical model based on the lattice-gas Hamiltonian with quenched disorder -- which mimics crowders -- to investigate how protein-solvent and protein-crowder interactions influence condensate phase behavior and morphology. The computed phase diagrams reveal rich behavior, including upper critical solution temperature (UCST), closed-loop, and reentrant type transitions under varying protein-solvent interactions at both equilibrium and out-of-equilibrium conditions. We elucidated the origin of these phase behavior changes and examined the role of protein-crowder interactions in modulating condensed phase morphology and stability. We further extended this model to binary protein mixtures where we studied the phase behavior in the presence and absence of quenched disorder. Without disorder, the system exhibits diverse phase-separated morphologies -- partially wetted, fully wetted, segregative, and associative -- with phase boundaries delicately sensitive protein-solvent interactions. The introduction of quenched disorder (or crowder) leads to a broader spectrum of complex morphologies, dictated by the interplay among protein-protein, protein-solvent, and protein-crowder interaction parameters. In general, this work underscores that protein-solvent and protein-crowder interactions, together with protein-protein interactions, can act as key regulatory parameters for modulating condensate morphology. These insights may guide future computational and experimental studies of liquid-liquid phase separation in biomolecular systems aimed at designing stimuli-responsive condensates.

cond-mat.soft↗
arXiv2025

From Fresh to Salty: How Ions Modulate Solvent-Mediated Interactions between Grafted Silica Nanoparticles in Water

Nanoparticles (NPs) are fundamental building blocks for engineering functional soft materials, where precise control over the solvent-mediated inter-particle effective interaction (Ueff) is essential for tailoring bulk structure and properties. These solvent-mediated interactions are strongly influenced by NP's surface chemistry, solvent properties, and thermodynamic conditions such as temperature (T) and pressure (P). However, despite considerable progress, a general predictive framework for tuning Ueff and guiding self-assembly remains lacking. In this work, using all-atom molecular dynamics simulations, we investigated the alteration of Ueff between silica nanoparticles (Si-NPs) functionalized with polyethylene (PE) and polyethylene glycol (PEG) by salt (sodium chloride) across a range of thermodynamic conditions. At ambient thermodynamic conditions, bare (not functionalized) Si-NPs exhibit minimal variation in Ueff even at high salt concentrations. In contrast, PE-grafted Si-NPs display strong salt-induced attractions, while PEG-grafted Si-NPs show an intermediate, more gradual response. To asses the transferability of these salt-induced effects on effective interactions, we further examined the effects of salt on Ueff under different (T,P) conditions. Our results indicate that the salt-induced modulation of Ueff between both bare and grafted Si-NPs is largely invariant across the explored (T,P) conditions. Molecular-level analysis reveals that salt promotes solvent depletion within the interparticle cavity for both hydrophobic PE and hydrophilic PEG grafts, with the strongest effect observed in the PE case. In general, this study highlights the coupled roles of surface chemistry, ion-polymer interactions, and solvent structuring in the regulation of Ueff, and provides important insights into the predictable control of interparticle interactions for soft material engineering.

cond-mat.soft↗
arXiv2025

Compositional fluctuations and polymorph selection in crystallization of model soft colloids

Understanding polymorph selection in atomic and molecular systems and its control through thermodynamic conditions and external factors (such as seed characteristics) is fundamental to the design of targeted materials and holds great significance in materials sciences. In this work, using Monte Carlo simulations on the Gaussian Core Model and Hard-Core Yukawa colloidal systems, we investigated the control of polymorph selection and explored the underlying mechanisms by tuning thermodynamic parameters. We demonstrate that by carefully modifying the free energy landscape to render the globally stable face-centered cubic (FCC) phase metastable with respect to the body-centered cubic (BCC) phase, the polymorphic identity of particles transitions from FCC-dominated to BCC-dominated via an intermediate regime where both phases nucleate -- either selectively or competitively -- giving rise to a critical-like composition fluctuation of the growing solid-like cluster during the nucleation process. We further probed the critical solid-like cluster compositions, especially in the vicinity of the triple point where the three phases coexist, and observed an interpenetrating arrangement of FCC- and BCC-like particles rather than a commonly observed non-classical core-shell-like two-step nucleation scenario. In addition, we investigated the polymorph selection signatures encoded in local structural fluctuations of the metastable fluid using a machine learning approach based on structural descriptors derived from persistent homology, a topological data analysis method. We believe that the insights gained from this work have the potential to add to the ongoing efforts to control crystallization pathways to obtain the desired functional material.

cond-mat.soft↗
arXiv2024

Manifestations of the possible thermodynamic origin of water's anomalies in non-classical vapor nucleation at negative pressures

Over the years, various scenarios -- such as the stability-limit conjecture (SLC), two critical point (TCP), critical point-free (CPF), and singularity-free (SF) -- have been proposed to explain the thermodynamic origin of supercooled waters anomalies. However, direct experimental validation is challenging due to the rapid phase transition from metastable water. In this study, we explored whether the phase transition pathways from metastable water provide insight into the thermodynamic origin of these anomalies. Using a classical density functional theory approach with realistic theoretical water models, we examined how different thermodynamic scenarios influence vapor nucleation kinetics at negative pressures. Our findings show significant variations in nucleation kinetics and mechanism during both isobaric and isochoric cooling. In the TCP scenario, the nucleation barrier increases steadily during isobaric cooling, with a slight decrease near the Widom line at lower temperatures (Ts). In contrast, the SF scenario shows a monotonic increase in the nucleation barrier. For the CPF scenario, we observed a non-classical mechanism, such as wetting-mediated nucleation (where the growing vapor nucleus is wetted by the intermediate low-density liquid phase) and the Ostwald step rule at low temperatures. Isochoric cooling pathways also revealed notable differences in T-dependent nucleation barrier trends between the TCP and CPF scenarios. Overall, this study underscores the importance of analyzing phase transition kinetics and mechanism to understand the precise thermodynamic origin of supercooled waters anomalies.

cond-mat.soft↗
arXiv2024

Effects of quenched disorder on the kinetics and pathways of phase transition in a soft colloidal system

Although impurities are unavoidable in real-world and experimental systems, most numerical studies on nucleation focus on pure (impurity-free) systems. As a result, the role of impurities in phase transitions remains poorly understood, especially for systems with complex free energy landscapes featuring one or more metastable intermediate phases. In this study, we employed Monte-Carlo simulations to investigate the effects of static impurities (quenched disorder) of varying length scales and surface morphologies on the nucleation mechanism and kinetics in the Gaussian Core Model (GCM) system, a model for soft colloidal systems. We first explored how the nucleation free energy barrier and critical cluster size are influenced by the fraction of pinned particles ($f_{\rm p}$) and the pinned cluster size ($n_{\rm p}$). Both the nucleation free energy barrier and critical cluster size increase sharply with increasing $f_{\rm p}$ but decrease as $n_{\rm p}$ grows, eventually approaching the homogeneous nucleation limit. On examining the impact of surface morphology on nucleation kinetics, we observed that the nucleation barrier significantly decreases with increasing the spherical pinned cluster (referred to as "seed") size of face-centred cubic (FCC), body-centred cubic (BCC), and simple cubic (SC) structures, with BCC showing the greatest facilitation. Interestingly, seeds with random surface roughness had little effect on nucleation kinetics. Additionally, the polymorphic identity of particles in the final crystalline phase is influenced by both seed surface morphology and system size. This study further provides crucial insights into the intricate relationship between substrate-induced local structural fluctuations and the selection of the polymorphic identity in the final crystalline phase, which is essential for understanding and controlling crystallization processes in experiments.

cond-mat.soft↗
arXiv2024

Microscopic pathways of transition from low-density to high-density amorphous phase of water

Much attention has been devoted to understanding the microscopic pathways of phase transition between two equilibrium condensed phases (such as liquids and solids). However, the microscopic pathways between non-equilibrium, non-diffusive amorphous (glassy) phases still remain poorly understood. In this work, we have employed computer simulations, persistence homology (a tool rooted in topological data analysis), and machine learning to probe the microscopic pathway of pressure-induced non-equilibrium transition between the low- and high-density amorphous (LDA and HDA, respectively) ice phases of TIP4P/2005 and ST2 water models. Using persistence homology and machine learning, we introduced a new order parameter that unambiguously identifies the LDA and HDA-like local environments. The system transitions continuously and collectively in the order parameter space via a pre-ordered intermediate phase during the compression of the LDA phase. The local order parameter susceptibilities show a maximum near the transition pressure ($P^*$) -- suggesting maximum structural heterogeneities near $P^*$. The HDA-like clusters are structurally ramified and spatially delocalized inside the LDA phase near the transition pressure. We have further investigated the (geometrical) structures and topologies of the LDA and HDA ices formed via different protocols and also studied the dependence of the microscopic pathway of phase transition in the order parameter space on the protocol followed to prepare the initial LDA phase. Finally, the method adopted here to study the microscopic pathways of transition is not restricted to the system under consideration and provides a robust way of probing phase transition pathways involving any two condensed phases at both equilibrium and out-of-equilibrium conditions.

physics.chem-ph↗
arXiv2022

Anomalous Vapor and Ice Nucleation in Water at Negative Pressures: A Classical Density Functional Theory Study

In contrast to the abundance of work on the anomalous behavior of water, the relationship between the water's thermodynamic anomalies and kinetics of phase transition from metastable water is relatively unexplored. In this work, we have employed classical density functional theory to provide a unified and coherent picture of nucleation (both vapor and ice) from metastable water, especially at negative pressure conditions. Our results suggest a peculiar non-monotonic temperature dependence of liquid-vapor surface tension at temperatures where liquid-vapor coexistence is metastable with respect to the ice phase. The vapor nucleation barrier on isochoric cooling also shows a non-monotonic temperature dependence. We further note that, for lower density isochores, the temperature of minimum vapor nucleation barrier ($T_{ΔΩ_{\rm v/min}^*}$) does not coincide with the temperature of maximum density (TMD) where metastability is maximum. The temperature difference between the $T_{ΔΩ_{\rm v/min}^*}$ and the TMD, however, decreases with increasing the density of the isochore, suggesting a strong correlation between the propensity of cavitation and metastability of the liquid water at high densities. The vapor nucleation barrier along isobaric cooling shows an interesting crossover behavior where it first increases on lowering the temperature and then shows a non-monotonic behavior in the vicinity of the Widom line on further lowering the temperature. Our results on the ice nucleation from metastable water show an anomalous retracing behavior of the ice nucleation barrier along isotherms and theoretically validate the recent findings that the reentrant ice(Ih)-liquid coexistence can induce a drastic change in the kinetics of ice nucleation. In addition, this study also provides deeper insights into the origin of the isothermal compressibility maximum on isochoric cooling.

cond-mat.soft↗
arXiv2022

Manifestations of the structural origin of supercooled water's anomalies in the heterogeneous relaxation on the potential energy landscape

Liquid water is well-known for its intriguing thermodynamic anomalies in the supercooled state. The phenomenological two-state models - based on the assumption of the existence of two types of competing local states (or, structures) in liquid water - have been extremely successful in describing water's thermodynamic anomalies. However, the precise structural features of these competing local states in liquid water still remain elusive. Here, we have employed a geometrical order parameter-free approach to unambiguously identify the two types of competing local states -- entropically and energetically-favored -- with significantly different structural and energetic features in the TIP4P/2005 liquid water. This identification is based on the heterogeneous structural relaxation of the system in the potential energy landscape (PEL) during the steepest-descent energy minimization. This heterogeneous relaxation is characterized using order parameters inspired by the spin-glass transition in frustrated magnetic systems. We have further established a direct relationship between the population fluctuation of the two states and the anomalous behavior of the heat capacity in supercooled water. The composition-dependent spatial distribution of the entropically-favored local states shows an interesting crossover from a spanning network-like single cluster to the spatially delocalized clusters in the close vicinity of the Widom line. Additionally, this study establishes a direct relationship between the topographic features of the PEL and the water's thermodynamic anomalies in the supercooled state and provides alternate markers (in addition to the locus of maxima of thermodynamic response functions) for the Widom line in the phase plane.

physics.chem-ph↗
arXiv2018

Polymorph selection during crystallization of a model colloidal fluid with a free energy landscape containing a metastable solid

The free energy landscape responsible for crystallization can be complex even for relatively simple systems like hard sphere and charged stabilized colloids. In this work, using hard-core repulsive Yukawa model, which is known to show complex phase behavior consisting of fluid, FCC and BCC phases, we studied the interplay between the free energy landscape and polymorph selection during crystallization. When the stability of the BCC phase with respect to the fluid phase is gradually increased by changing the temperature and pressure at a fixed fluid-FCC stability, the final phase formed by crystallization is found to undergo a switch from the FCC to the BCC phase, even though FCC remains thermodynamically the most stable phase. We further show that the nature of local bond-orientational order parameter fluctuations in the metastable fluid phase as well as the composition of the critical cluster depend delicately on the free energy landscape, and play a decisive role in the polymorph selection during crystallization.

cond-mat.soft↗
arXiv2017

Two-structure thermodynamics for the TIP4P/2005 model of water covering supercooled and deeply stretched regions

One of the most promising frameworks for understanding the anomalies of cold and supercooled water postulates the existence of two competing, interconvertible local structures. If the non-ideality in the Gibbs energy of mixing overcomes the ideal entropy of mixing of these two structures, a liquid-liquid phase transition, terminated at a liquid-liquid critical point, is predicted. Various versions of the "two-structure equation of state" (TSEOS) based on this concept have shown remarkable agreement with both experimental data for metastable, deeply supercooled water and simulations of molecular water models. However, existing TSEOSs were not designed to describe the negative pressure region and do not account for the stability limit of the liquid state with respect to the vapor. While experimental data on supercooled water at negative pressures may shed additional light on the source of the anomalies of water, such data are very limited. To fill this gap, we have analyzed simulation results for TIP4P/2005, one of the most accurate classical water models available. We have used recently published simulation data, and performed additional simulations, over a broad range of positive and negative pressures, from ambient temperature to deeply supercooled conditions. We show that, by explicitly incorporating the liquid-vapor spinodal into a TSEOS, we are able to match the simulation data for TIP4P/2005 with remarkable accuracy. In particular, this equation of state quantitatively reproduces the lines of extrema in density, isothermal compressibility, and isobaric heat capacity. Contrary to an explanation of the thermodynamic anomalies of water based on a "retracing spinodal", the liquid-vapor spinodal in the present TSEOS continues monotonically to lower pressures upon cooling, influencing but not giving rise to density extrema and other thermodynamic anomalies.

cond-mat.stat-mech↗
arXiv2016

An Equation of State For The TIP4P/2005 Model of Water Including Negative Pressures

One of the most promising frameworks for understanding the anomalies of cold and especially supercooled water is that of two-structure thermodynamics, in which water is viewed as a non-ideal mixture of two interconvertible local structures. The non-ideality of this mixture may give rise, at very low temperatures, to a liquid-liquid phase transition (LLPT) and a liquid-liquid critical point (LLCP), at which thermodynamic response functions diverge. Various versions of the "two-structure equation of state" (TSEOS) based on this concept have shown remarkable agreement with both experimental data in real water and simulation results. However, recent experiments probing supercooled water at negative pressures reveal the inadequacy of extrapolations of equations of state developed for positive pressures, and have begun to shed additional light on the source of the anomalies of supercooled water. We have analyzed simulation results for the TIP4P/2005 model over a broad range of positive and negative pressures from ambient temperature to deep supercooling. We find that by explicitly incorporating a liquid-vapor spinodal into a two-structure equation of state, we are able to match the simulation data in TIP4P/2005 with striking accuracy. In particular, our equation of state reproduces the observed lines of minima and maxima in the density, isothermal compressibility, and isobaric heat capacity. Contrary to scenarios in which a retracing spinodal accounts for the thermodynamic anomalies of water, we find that the liquid-vapor spinodal in this model continues monotonically to lower pressures as temperature is decreased, influencing but not giving rise to the locus of density maxima and other thermodynamic anomalies. We explain the behavior of TIP4P/2005 in terms of two phenomena: the competition between two local structures and a monotonic liquid-vapor spinodal.

cond-mat.stat-mech↗
arXiv2016

Two-State Thermodynamics and the Possibility of a Liquid-Liquid Phase Transition in Supercooled TIP4P/2005 Water

Water shows intriguing thermodynamic and dynamic anomalies in the supercooled liquid state. One possible explanation of the origin of these anomalies lies in the existence of a metastable liquid-liquid phase transition (LLPT) between two (high and low density) forms of water. While the anomalies are observed in experiments on bulk and confined water and by computer simulation studies of water-like models, the existence of a LLPT in water is still debated. Unambiguous experimental proof of the existence of a LLPT in bulk supercooled water is hampered by fast ice nucleation which is a precursor of the hypothesized LLPT. Moreover, the hypothesized LLPT, being metastable, in principle cannot exist in the thermodynamic limit (infinite size, infinite time). Therefore, computer simulations of water models are crucial for exploring the possibility of the metastable LLPT and the nature of the anomalies. In this work, we present new simulation results in the NVT ensemble for one of the most accurate classical molecular models of water, TIP4P/2005. To describe the computed properties and explore the possibility of a LLPT we have applied two-structure thermodynamics, viewing water as a non-ideal mixture of two interconvertible local structures ("states"). The results suggest the presence of a liquid-liquid critical point and a LLPT in this model for the simulated length and time scales. We have compared the behavior of TIP4P/2005 with other popular water-like models, namely mW and ST2, and with real water, all of which are well described by two-state thermodynamics. In view of the current debate involving different studies of TIP4P/2005, we discuss consequences of metastability and finite size in observing the liquid-liquid separation. We also address the relationship between the phenomenological order parameter of two-structure thermodynamics and the microscopic nature of the low-density structure.

cond-mat.stat-mech↗
arXiv2016

Density and bond-orientational relaxations in supercooled water

Recent computational studies have reported evidence of a metastable liquid-liquid phase transition (LLPT) in molecular models of water under deeply supercooled conditions. A competing hypothesis suggests, however, that non-equilibrium artifacts associated with coarsening of the stable crystal phase have been mistaken for an LLPT in these models. Such artifacts are posited to arise due to a separation of time scales in which density fluctuations in the supercooled liquid relax orders of magnitude faster than those associated with bond-orientational order. Here, we use molecular simulation to investigate the relaxation of density and bond-orientational fluctuations in three molecular models of water (ST2, TIP5P and TIP4P/2005) in the vicinity of their reported LLPT. For each model, we find that density is the slowly relaxing variable under such conditions. We also observe similar behavior in the coarse-grained mW model of water. Our findings therefore challenge the key physical assumption underlying the competing hypothesis.e find that density relaxes significantly faster than bond-orientational order, as incorrectly predicted by this competing hypothesis.

cond-mat.stat-mech↗
arXiv2015

Orientational order as the origin of the long-range hydrophobic effect

The long range attractive force between two hydrophobic surfaces immersed in water is observed to decrease exponentially with their separation -- this distance-dependence of effective force is known as the hydrophobic force law (HFL). We explore the microscopic origin of HFL by studying distance-dependent attraction between two parallel rods immersed in 2D Mercedes Benz model of water. This model is found to exhibit a well-defined HFL. Although the phenomenon is conventionally explained by density-dependent theories, we identify orientation, rather than density, as the relevant order parameter. The range of density variation is noticeably shorter than that of orientational heterogeneity. The latter is comparable to the observed distances of hydrophobic force. At large separation, attraction between the rods arises primarily from a destructive interference among the inwardly propagating oppositely oriented heterogeneity generated in water by the two rods. As the rods are brought closer, the interference increases leading to a decrease in heterogeneity and concomitant decrease in free energy of the system, giving rise to the effective attraction. We notice formation of hexagonal ice-like structures at the onset of attractive region which suggests that metastable free energy minimum may play a role in the origin of HFL.

cond-mat.soft↗
arXiv2014

Correlation between thermodynamic anomalies and pathways of ice nucleation in supercooled water

The well-known classical nucleation theory (CNT) for the free energy barrier towards formation of a nucleus of critical size of the new stable phase within the parent metastable phase fails to take into account the influence of other metastable phases having density/order intermediate between the parent metastable phase and the final stable phase. This lacuna can be more serious than capillary approximation or spherical shape assumption made in CNT. This issue is particularly significant in ice nucleation because liquid water shows rich phase diagram consisting of two (high and low density) liquid phases in supercooled state. The explanations of thermodynamic and dynamic anomalies of supercooled water often invoke the possible influence of a liquid-liquid transition between two metastable liquid phases. To investigate both the role of thermodynamic anomalies and presence of distinct metastable liquid phases in supercooled water on ice nucleation, we employ density functional theoretical approach to find nucleation free energy barrier in different regions of phase diagram. The theory makes a number of striking predictions, such as a dramatic lowering of nucleation barrier due to presence of a metastable intermediate phase and crossover in the dependence of free energy barrier on temperature near liquid-liquid critical point. These predictions can be tested by computer simulations as well as by controlled experiments.

cond-mat.stat-mech↗
arXiv2013

Solid-solid collapse transition in a two dimensional model molecular system

Solid-solid collapse transition in open framework structures is ubiquitous in nature. The real difficulty in understanding detailed microscopic aspects of such transitions in molecular systems arises from the interplay between different energy and length scales involved in molecular systems, often mediated through a solvent. In this work we employ Monte Carlo (MC) simulations to study the collapse transition in a model molecular system interacting via both isotropic as well as anisotropic interactions having different length and energy scales. The model we use is known as Mercedes-Benz (MB) which for a specific set of parameters sustains three solid phases: honeycomb, oblique and triangular. In order to study the temperature induced collapse transition, we start with a metastable honeycomb solid and induce transition by heating. High density oblique solid so formed has two characteristic length scales corresponding to isotropic and anisotropic parts of interaction potential. Contrary to the common believe and classical nucleation theory, interestingly, we find linear strip-like nucleating clusters having significantly different order and average coordination number than the bulk stable phase. In the early stage of growth, the cluster grows as linear strip followed by branched and ring-like strips. The geometry of growing cluster is a consequence of the delicate balance between two types of interactions which enables the dominance of stabilizing energy over the destabilizing surface energy. The nuclei of stable oblique phase are wetted by intermediate order particles which minimizes the surface free energy. We observe different pathways for pressure and temperature induced transitions.

cond-mat.soft↗
arXiv2013

Nucleation of a stable solid from melt in the presence of multiple metastable intermediate phases: Wetting, Ostwald step rule and vanishing polymorphs

In many systems, nucleation of a stable solid may occur in the presence of other (often more than one) metastable phases. These may be polymorphic solids or even liquid phases. In such cases, nucleation of the solid phase from the melt may be facilitated by the metastable phase because the latter can "wet" the interface between the parent and the daughter phases, even though there may be no signature of the existence of metastable phase in the thermodynamic properties of the parent liquid and the stable solid phase. Straightforward application of classical nucleation theory (CNT) is flawed here as it overestimates the nucleation barrier since surface tension is overestimated (by neglecting the metastable phases of intermediate order) while the thermodynamic free energy gap between daughter and parent phases remains unchanged. In this work we discuss a density functional theory (DFT) based statistical mechanical approach to explore and quantify such facilitation. We construct a simple order parameter dependent free energy surface that we then use in DFT to calculate (i) the order parameter profile, (ii) the overall nucleation free energy barrier and (iii) the surface tension between the parent liquid and the metastable solid and also parent liquid and stable solid phases. The theory indeed finds that the nucleation free energy barrier can decrease significantly in the presence of wetting. This approach can provide a microscopic explanation of Ostwald step rule and the well-known phenomenon of "disappearing polymorphs" that depends on temperature and other thermodynamic conditions. Theory reveals a diverse scenario for phase transformation kinetics some of which may be explored via modern nanoscopic synthetic methods.

cond-mat.mtrl-sci↗