Forward-flux sampling with jumpy order parameters

Bridging classical nucleation theory and molecular dynamics simulation for homogeneous ice nucleation

Water freezing, initiated by ice nucleation, occurs widely in nature, ranging from cellular to global phenomena. Ice nucleation has been experimentally proven to require the formation of a critical ice nucleus, consistent with classical nucleation theory (CNT). However, the accuracy of CNT quantitative predictions of critical cluster sizes and nucleation rates has never been verified experimentally. In this study, we circumvent this difficulty by using molecular dynamics (MD) simulation. The physical properties of water/ice for CNT predictions, including density, chemical potential difference, and diffusion coefficient, are independently obtained using MD simulation, whereas the calculation of interfacial free energy is based on thermodynamic assumptions of CNT, including capillarity approximation among others. The CNT predictions are compared to the MD evaluations of brute-force simulations and forward flux sampling methods. We find that the CNT and MD predicted critical cluster sizes are consistent, and the CNT predicted nucleation rates are higher than the MD predicted values within three orders of magnitude. We also find that the ice crystallized from supercooled water is stacking-disordered ice with a stacking of cubic and hexagonal ices in four representative types of stacking. The prediction discrepancies in nucleation rate mainly arise from the stacking-disordered ice structure, the asphericity of ice cluster, the uncertainty of ice-water interfacial free energy, and the kinetic attachment rate. Our study establishes a relation between CNT and MD to predict homogeneous ice nucleation.

Comparing brute force to transition path sampling for gas hydrate nucleation with a flat interface: comments on time reversal symmetry

Fluid to solid nucleation is often investigated with the rare event method transition path sampling (TPS). I claim that the inherent irreversibility of solid nucleation, even at stationary conditions, calls into question TPS's applicability for determining solid nucleation mechanisms, especially for pre-critical behavior. Even when applied to a phenomenon which displays time reversal asymmetry like solid nucleation, TPS is a good means of exploring phase space and giving trends in post-critical structure, and its ability to facilitate nucleation rate and free energy calculations remains outstanding. Forward-only splitting and ratcheting methods such as forward flux sampling are more attractive for understanding nucleation mechanisms as they do not require time reversal symmetry, but at low driving forces may suffer from the same limitations as brute force: they may never make it to the first ratchet. Here I briefly summarize the TPS method and gas hydrate nucleation simulation literature, focusing on topics within both to facilitate a comparison of brute force hydrate nucleation to transition path sampling of hydrate nucleation. Perhaps anecdotally, the brute force technique results in more crystalline trajectories despite having higher driving forces than TPS. I maintain this difference is because of the inherent irreversibility of hydrate nucleation, meaning its pre-critical behavior cannot accurately be determined by the melting trajectories that comprise approximately half of the configurations in TPS's path ensemble.

Divergence among Local Structure, Dynamics, and Nucleation Outcome in Heterogeneous Nucleation of Close-Packed Crystals

Heterogeneous crystal nucleation is the dominant mechanism of crystallization in most systems, yet its underlying physics remains an enigma. While emergent interfacial crystalline order precedes heterogeneous nucleation, its importance in the nucleation mechanism is unclear. Here, we use path sampling simulations of two model systems to demonstrate that crystalline order in its traditional sense is not predictive of the outcome of the heterogeneous nucleation of close-packed crystals. Consequently, structure-based collective variables (CVs) that reliably describe homogeneous nucleation can be poor descriptors of heterogeneous nucleation. This divergence between structure and nucleation outcome is accompanied by an intriguing dynamical anomaly, wherein low-coordinated crystalline particles outpace their liquid-like counterparts. We use committor analysis, high-throughput screening, and machine learning to devise CV optimization strategies and present suitable structural heuristics within the metastable fluid for CV prescreening. Employing such optimized CVs is pivotal for properly characterizing the mechanism of heterogeneous nucleation in metallic and colloidal systems.

Correlations in Charged Multipore Systems: Implications for Enhancing Selectivity and Permeability in Nanoporous Membranes

Nanoporous membranes have emerged as powerful tools for diverse applications, including gas separation and water desalination. Achieving high permeability for desired molecules alongside exceptional rejection of other species presents a significant design challenge. One potential strategy involves optimizing the chemistry and geometry of isolated nanopores to enhance permeability and selectivity while maximizing their density within a membrane. However, the impact of the pore proximity on membrane performance remains an open question. Through path sampling simulations of model graphitic membranes with multiple subnanometer pores, we reveal that nanoscale proximity between pores detrimentally affects water permeability and salt rejection. Specifically, counterion transport is decelerated, while co-ion transport is accelerated, due to direct interactions among water molecules, salt ions, and the dipoles within neighboring pores. Notably, the observed ionic transport time scales significantly deviate from established theories such as the access resistance model but are well explained using the simple phenomenological model that we develop in this work. We use this model to prescreen and optimize pore arrangements that elicit minimal correlations at a target pore density. These findings deepen our understanding of multipore systems, informing the rational design of nanoporous membranes for enhanced separation processes such as water desalination. They also shed light on the physiology of biological cells that employ ion channel proteins to modulate ion transport and reversal potentials.

Ideal conductor/dielectric model (ICDM): A generalized technique to correct for finite-size effects in molecular simulations of hindered ion transport

Molecular simulations serve as indispensable tools for investigating the kinetics and elucidating the mechanism of hindered ion transport across nanoporous membranes. In particular, recent advancements in advanced sampling techniques have made it possible to access translocation timescales spanning several orders of magnitude. In our prior study [Shoemaker et al., J. Chem. Theory Comput. 18, 7142 (2022)], we identified significant finite size artifacts in simulations of pressure-driven hindered ion transport through nanoporous graphitic membranes. We introduced the ideal conductor model, which effectively corrects for such artifacts by assuming the feed to be an ideal conductor. In the present work, we introduce the ideal conductor dielectric model (Icdm), a generalization of our earlier model, which accounts for the dielectric properties of both the membrane and the filtrate. Using the Icdm model substantially enhances the agreement among corrected free energy profiles obtained from systems of varying sizes, with notable improvements observed in regions proximate to the pore exit. Moreover, the model has the capability to consider secondary ion passage events, including the transport of a co-ion subsequent to the traversal of a counter-ion, a feature that is absent in our original model. We also investigate the sensitivity of the new model to various implementation details. The Icdm model offers a universally applicable framework for addressing finite size artifacts in molecular simulations of ion transport. It stands as a significant advancement in our quest to use molecular simulations to comprehensively understand and manipulate ion transport processes through nanoporous membranes.

Brute-force nucleation rates of hard spheres compared with rare-event methods and classical nucleation theory

We determine nucleation rates of hard spheres using brute-force molecular dynamics simulations. We overcome nucleation barriers of up to 28 kBT, leading to a rigorous test of nucleation rates obtained from rare-event methods and classical nucleation theory. Our brute-force nucleation rates show excellent agreement with umbrella sampling simulations by Filion et al. [J. Chem. Phys. 133, 244115 (2010)] and seeding simulations by Espinosa et al. [J. Chem. Phys. 144, 034501 (2016)].

Interplay of multiple clusters and initial interface positioning for forward flux sampling simulations of crystal nucleation

Forward flux sampling (FFS) is a path sampling technique widely used in computer simulations of crystal nucleation from the melt. In such studies, the order parameter underpinning the progress of the FFS algorithm is often the size of the largest crystalline nucleus. In this work, we investigate the effects of two computational aspects of FFS simulations, using the prototypical Lennard-Jones liquid as our computational test bed. First, we quantify the impact of the positioning of the liquid basin and first interface in the space of the order parameter. In particular, we demonstrate that these choices are key to ensuring the consistency of the FFS results. Second, we focus on the frequently encountered scenario where the population of crystalline nuclei is such that there are multiple clusters of size comparable to the largest one. We demonstrate the contribution of clusters other than the largest cluster to the initial flux; however, we also show that they can be safely ignored for the purposes of converging a full FFS calculation. We also investigate the impact of different clusters merging, a process that appears to be facilitated by substantial spatial correlations-at least at the supercooling considered here. Importantly, all of our results have been obtained as a function of system size, thus contributing to the ongoing discussion on the impact of finite size effects on simulations of crystal nucleation. Overall, this work either provides or justifies several practical guidelines for performing FFS simulations that can also be applied to more complex and/or computationally expensive models.

Kinetic reconstruction of free energies as a function of multiple order parameters

A vast array of phenomena, ranging from chemical reactions to phase transformations, are analyzed in terms of a free energy surface defined with respect to a single or multiple order parameters. Enhanced sampling methods are typically used, especially in the presence of large free energy barriers, to estimate free energies using biasing protocols and sampling of transition paths. Kinetic reconstructions of free energy barriers of intermediate height have been performed, with respect to a single order parameter, employing the steady state properties of unconstrained simulation trajectories when barrier crossing is achievable with reasonable computational effort. Considering such cases, we describe a method to estimate free energy surfaces with respect to multiple order parameters from a steady state ensemble of trajectories. The approach applies to cases where the transition rates between pairs of order parameter values considered is not affected by the presence of an absorbing boundary, whereas the macroscopic fluxes and sampling probabilities are. We demonstrate the applicability of our prescription on different test cases of random walkers executing Brownian motion in order parameter space with an underlying (free) energy landscape and discuss strategies to improve numerical estimates of the fluxes and sampling. We next use this approach to reconstruct the free energy surface for supercooled liquid silicon with respect to the degree of crystallinity and density, from unconstrained molecular dynamics simulations, and obtain results quantitatively consistent with earlier results from umbrella sampling.

Exponential increase of transition rates in metastable systems driven by non-Gaussian noise

Noise-induced escape from metastable states governs a plethora of transition phenomena in physics, chemistry, and biology. While the escape problem in the presence of thermal Gaussian noise has been well understood since the seminal works of Arrhenius and Kramers, many systems, in particular living ones, are effectively driven by non-Gaussian noise for which the conventional theory does not apply. Here we present a theoretical framework based on path integrals that allows the calculation of both escape rates and optimal escape paths for a generic class of non-Gaussian noises. We find that non-Gaussian noise always leads to more efficient escape and can enhance escape rates by many orders of magnitude compared with thermal noise, highlighting that away from equilibrium escape rates cannot be reliably modelled based on the traditional Arrhenius-Kramers result. Our analysis also identifies a new universality class of non-Gaussian noises, for which escape paths are dominated by large jumps.

Enhanced path sampling using subtrajectory Monte Carlo moves

Path sampling allows the study of rare events, such as chemical reactions, nucleation, and protein folding, via a Monte Carlo (MC) exploration in path space. Instead of configuration points, this method samples short molecular dynamics (MD) trajectories with specific start- and end-conditions. As in configuration MC, its efficiency highly depends on the types of MC moves. Since the last two decades, the central MC move for path sampling has been the so-called shooting move in which a perturbed phase point of the old path is propagated backward and forward in time to generate a new path. Recently, we proposed the subtrajectory moves, stone-skipping (SS) and web-throwing, that are demonstrably more efficient. However, the one-step crossing requirement makes them somewhat more difficult to implement in combination with external MD programs or when the order parameter determination is expensive. In this article, we present strategies to address the issue. The most generic solution is a new member of subtrajectory moves, wire fencing (WF), that is less thrifty than the SS but more versatile. This makes it easier to link path sampling codes with external MD packages and provides a practical solution for cases where the calculation of the order parameter is expensive or not a simple function of geometry. We demonstrate the WF move in a double-well Langevin model, a thin film breaking transition based on classical force fields, and a smaller ruthenium redox reaction at the ab initio level in which the order parameter explicitly depends on the electron density.

Ideal Conductor Model: An Analytical Finite-Size Correction for Nonequilibrium Molecular Dynamics Simulations of Ion Transport through Nanoporous Membranes

Modulating ion transport through nanoporous membranes is critical to many important chemical and biological separation processes. The corresponding transport timescales, however, are often too long to capture accurately using conventional molecular dynamics (MD). Recently, path sampling techniques, such as forward-flux sampling (FFS), have emerged as attractive alternatives for efficiently and accurately estimating arbitrarily long ionic passage times. Here, we use non-equilibrium MD and FFS to explore how the kinetics and mechanisms of pressure-driven chloride transport through a nanoporous graphitic membrane are affected by its lateral dimensions. We not only find ionic passage times and free energy barriers to decrease dramatically upon increasing the membrane surface area but also observe an abrupt and discontinuous change in the locus of the transition state. These strong finite size effects arise due to the cumulative effect of the periodic images of the leading ion entering the pore on the distribution of the induced excess charge at the membrane surface in the feed. By assuming that the feed is an ideal conductor, we analytically derive a finite size correction term that can be computed from the information obtained from a single simulation and successfully use it to obtain corrected free energy profiles with no dependence on the system size. We then estimate ionic passage times in the thermodynamic limit by assuming an Eyring-type dependence of rates on barriers with a size-independent prefactor. This approach constitutes a universal framework for removing finite size artifacts in molecular simulations of ion transport through nanoporous membranes and biological channel proteins.

Extending and validating bubble nucleation rate predictions in a Lennard-Jones fluid with enhanced sampling methods and transition state theory

We calculate bubble nucleation rates in a Lennard-Jones fluid through explicit molecular dynamics simulations. Our approach—based on a recent free energy method (dubbed reweighted Jarzynski sampling), transition state theory, and a simple recrossing correction—allows us to probe a fairly wide range of rates in several superheated and cavitation regimes in a consistent manner. Rate predictions from this approach bridge disparate independent literature studies on the same model system. As such, we find that rate predictions based on classical nucleation theory, direct brute force molecular dynamics simulations, and seeding are consistent with our approach and one another. Published rates derived from forward flux sampling simulations are, however, found to be outliers. This study serves two purposes: First, we validate the reliability of common modeling techniques and extrapolation approaches on a paradigmatic problem in materials science and chemical physics. Second, we further test our highly generic recipe for rate calculations, and establish its applicability to nucleation processes.

Homogeneous ice nucleation rates for mW and TIP4P/ICE models through Lattice Mold calculations

Water freezing is the most common liquid-to-crystal phase transition on Earth, however, despite its critical implications on climate change and cryopreservation among other disciplines, its characterization through experimental and computational techniques remains elusive. In this work, we make use of computer simulations to measure the nucleation rate (J) of water at normal pressure under different supercooling conditions, ranging from 215 to 240K. We employ two different water models, mW, a coarse-grained potential for water, and TIP4P/ICE, an atomistic non-polarizable water model that provides one of the most accurate representations of the different ice phases. To evaluate J, we apply the Lattice Mold technique, a computational method based on the use of molds to induce the nucleus formation from the metastable liquid under conditions at which observing spontaneous nucleation would be unfeasible. With this method, we obtain estimates of the nucleation rate for ice Ih, Ic and a stacking mixture of ice Ih/Ic; reaching consensus with most of the previously reported rates, although differing with some others. Furthermore, we confirm that the predicted nucleation rates by the TIP4P/ICE model are in better agreement with experimental data than those obtained through the mW potential. Taken together, our study provides a reliable methodology to measure nucleation rates in a simple and computationally efficient manner which contributes to benchmarking the freezing behaviour of two popular water models.

Practical guide to replica exchange transition interface sampling and forward flux sampling

Path sampling approaches have become invaluable tools to explore the mechanisms and dynamics of the so-called rare events that are characterized by transitions between metastable states separated by sizable free energy barriers. Their practical application, in particular to ever more complex molecular systems, is, however, not entirely trivial. Focusing on replica exchange transition interface sampling (RETIS) and forward flux sampling (FFS), we discuss a range of analysis tools that can be used to assess the quality and convergence of such simulations, which is crucial to obtain reliable results. The basic ideas of a step-wise evaluation are exemplified for the study of nucleation in several systems with different complexities, providing a general guide for the critical assessment of RETIS and FFS simulations.

Can molecular simulations reliably compare homogeneous and heterogeneous ice nucleation?

In principle, the answer to the posed titular question is undoubtedly "yes." But in practice, requisite reference data for homogeneous systems have been obtained with a treatment of intermolecular interactions that is different from that typically employed for heterogeneous systems. In this article, we assess the impact of the choice of truncation scheme when comparing water in homogeneous and inhomogeneous environments. Specifically, we use explicit free energy calculations and a simple mean field analysis to demonstrate that using the "cut-and-shift" version of the Lennard-Jones potential (common to most simple point charge models of water) results in a systematic increase in the melting temperature of ice I_h. In addition, by drawing an analogy between a change in cutoff and a change in pressure, we use existing literature data for homogeneous ice nucleation at negative pressures to suggest that enhancements due to heterogeneous nucleation may have been overestimated by several orders of magnitude.

Signatures of sluggish dynamics and local structural ordering during ice nucleation

We investigate the microscopic pathway of spontaneous crystallization in the ST2 model of water under deeply supercooled conditions via unbiased classical molecular dynamics simulations. After quenching below the liquid–liquid critical point, the ST2 model spontaneously separates into low-density liquid (LDL) and high-density liquid phases, respectively. The LDL phase, which is characterized by lower molecular mobility and enhanced structural order, fosters the formation of a sub-critical ice nucleus that, after a stabilization time, develops into the critical nucleus and grows. Polymorphic selection coincides with the development of the sub-critical nucleus and favors the formation of cubic (Ic) over hexagonal (Ih) ice. We rationalize polymorphic selection in terms of geometric arguments based on differences in the symmetry of second neighbor shells of ice Ic and Ih, which are posited to favor formation of the former. The rapidly growing critical nucleus absorbs both Ic and Ih crystallites dispersed in the liquid phase, a crystal with stacking faults. Our results are consistent with, and expand upon, recent observations of non-classical nucleation pathways in several systems.

Homogeneous nucleation of NaCl in supersaturated solutions

The seeding method is an approximate approach to investigate nucleation that combines molecular dynamics simulations with classical nucleation theory. Recently, this technique has been successfully implemented in a broad range of nucleation studies. However, its accuracy is subject to the arbitrary choice of the order parameter threshold used to distinguish liquid-like from solid-like molecules. We revisit here the crystallization of NaCl from a supersaturated brine solution and show that consistency between seeding and rigorous methods, like Forward Flux Sampling (from previous work) or spontaneous crystallization (from this work), is achieved by following a mislabelling criterion to select such threshold (i.e. equaling the fraction of the mislabelled particles in the bulk parent and nucleating phases). This work supports the use of seeding to obtain fast and reasonably accurate nucleation rate estimates and the mislabelling criterion as one giving the relevant cluster size for classical nucleation theory in crystallization studies.

Thermodynamics and kinetics of crystallization in deeply supercooled Stillinger-Weber silicon

We study the kinetics of crystallization in deeply supercooled liquid silicon employing computer simulations and the Stillinger-Weber three-body potential. The free energy barriers to crystallization are computed using umbrella sampling Monte Carlo simulations and from unconstrained molecular dynamics simulations using a mean first passage time formulation. We focus on state points that have been described in earlier work [S. Sastry and C. A. Angell, Nat. Mater. 2, 739 (2003)] as straddling a liquid-liquid phase transition (LLPT) between two metastable liquid states. It was argued subsequently [Ricci et al., Mol. Phys. 117, 3254 (2019)] that the apparent transition is due to the loss of metastability of the liquid state with respect to the crystalline state. The presence of a barrier to crystallization for these state points is therefore of importance to ascertain, which we investigate, with due attention to ambiguities that may arise from the choice of order parameters. We find a well-defined free energy barrier to crystallization and demonstrate that both umbrella sampling and mean first passage time methods yield results that agree quantitatively. Our results thus provide strong evidence against the possibility that the liquids at state points close to the reported LLPT exhibit slow, spontaneous crystallization, but they do not address the existence of a LLPT (or lack thereof). We also compute the free energy barriers to crystallization at other state points over a broad range of temperatures and pressures and discuss the effect of changes in the microscopic structure of the metastable liquid on the free energy barrier heights.

Enthalpic and Entropic Selectivity of Water and Small Ions in Polyamide Membranes

While polyamide reverse osmosis and nanofiltration membranes have been extensively utilized in water purification and desalination processes, the molecular details governing water and solute permeation in these membranes are not fully understood. In this study, we apply transition-state theory for transmembrane permeation to systematically break down the intrinsic permeabilities of water and small ions in loose and tight polyamide nanofiltration membranes into enthalpic and entropic components using an Eyring-type equation. We analyze trends in these components to elucidate molecular phenomena that induce water-salt, monovalent-divalent, and monovalent-monovalent selectivity at different pH values. Our results suggest that in pores that are either too small or contain an electrostatically repelling mouth, the thermal activation of ions in the form of ion dehydration is less likely, promoting entropically driven selectivity with steric exclusion of hydrated ions. Instead, larger uncharged pores enable ion dehydration, inducing enthalpic selectivity that is driven by differences in the ion hydration properties. We also demonstrate that electrostatic interactions between cations and intrapore carboxyl groups hinder salt permeability, increasing the enthalpic barrier of the transport. Last, permeation tests of monovalent cations in the loose and tight polyamide membranes expose opposite rejection trends that further support the phenomenon of ion dehydration in large subnanopores.

Role of Nanoscale Interfacial Proximity in Contact Freezing in Water

Contact freezing is a mode of atmospheric ice nucleation in which a collision between a dry ice nucleating particle (INP) and a water droplet results in considerably faster heterogeneous nucleation. The molecular mechanism of such an enhancement is, however, still a mystery. While earlier studies had attributed it to collision-induced transient perturbations, recent experiments point to the pivotal role of nanoscale proximity of the INP and the free interface. By simulating the heterogeneous nucleation of ice within INP-supported nanofilms of two model water-like tetrahedral liquids, we demonstrate that such nanoscale proximity is sufficient for inducing rate increases commensurate with those observed in contact freezing experiments, but only if the free interface has a tendency to enhance homogeneous nucleation. Water is suspected of possessing this latter property, known as surface freezing propensity. Our findings therefore establish a connection between the surface freezing propensity and kinetic enhancement during contact nucleation. We also observe that faster nucleation proceeds through a mechanism markedly distinct from classical heterogeneous nucleation, involving the formation of hourglass-shaped crystalline nuclei that conceive at either interface and that have a lower free energy of formation due to the nanoscale proximity of the interfaces and the modulation of the free interfacial structure by the INP. In addition to providing valuable insights into the physics of contact nucleation, our findings can assist in improving the accuracy of heterogeneous nucleation rate measurements in experiments and in advancing our understanding of ice nucleation on nonuniform surfaces such as organic, polymeric, and biological materials.

Parasitic crystallization of colloidal electrolytes: growing a metastable crystal from the nucleus of a stable phase

Colloidal particles have been extensively used to comprehend the main principles governing liquid-crystal nucleation. Multiple mechanisms and frameworks have been proposed, through either experiments or computational approaches, to rationalise the ubiquitous formation of colloidal crystals. In this work, we elucidate the nucleation scenario behind the crystallization of oppositely charged colloids. By performing molecular dynamics simulations of colloidal electrolytes in combination with the Seeding technique, we evaluate the fundamental factors, such as the nucleation rate, free energy barrier, surface tension and kinetic pre-factor, that determine the liquid-to-solid transition of several crystalline polymorphs. Our results show that at a high packing fraction, there is a cross-over between the nucleation of the CsCl structure and that of a substitutionally disordered fcc phase, despite the CuAu crystal being the most stable phase. We demonstrate that the crucial factor in determining which phase nucleates the fastest is the free energy cost of the cluster formation rather than their kinetic ability to grow from the liquid. While at a low packing fraction, the stable phase, CsCl, is the one that nucleates and subsequently grows, we show how at moderate and high packing fractions, a disordered fcc phase subsequently grows regardless of the nature of the nucleating phase, termed parasitic crystallization. Taken together, our results provide a panoramic perspective of the complex nucleation scenario of oppositely charged colloids at moderate temperature and rationalise the different thermodynamic and kinetic aspects behind it.

Rate Prediction for Homogeneous Nucleation of Methane Hydrate at Moderate Supersaturation Using Transition Interface Sampling

The crystallization of methane hydrates via homogeneous nucleation under natural, moderate conditions is of both industrial and scientific relevance, yet still poorly understood. Predicting the nucleation rates at such conditions is notoriously difficult due to high nucleation barriers, and requires, besides an accurate molecular model, enhanced sampling. Here, we apply the transition interface sampling technique, which efficiently computes the exact rate of nucleation by generating ensembles of unbiased dynamical trajectories crossing predefined interfaces located between the stable states. Using an accurate atomistic force field and focusing on specific conditions of 280 K and 500 bar, we compute for nucleation directly into the sI crystal phase at a rate of ∼10^-17 nuclei per nanosecond per simulation volume or ∼10² nuclei per second per cm³, in agreement with consensus estimates for nearby conditions. As this is most likely fortuitous, we discuss the causes of the large differences between our results and previous simulation studies. Our work shows that it is now possible to compute rates for methane hydrates at moderate supersaturation, without relying on any assumptions other than the force field.

Towards single-species selectivity of membranes with subnanometre pores

Synthetic membranes with pores at the subnanometre scale are at the core of processes for separating solutes from water, such as water purification and desalination. While these membrane processes have achieved substantial industrial success, the capability of state-of-the-art membranes to selectively separate a single solute from a mixture of solutes is limited. Such high-precision separation would enable fit-for-purpose treatment, improving the sustainability of current water-treatment processes and opening doors for new applications of membrane technologies. Herein, we introduce the challenges of state-of-the-art membranes with subnanometre pores to achieve high selectivity between solutes. We then analyse experimental and theoretical literature to discuss the molecular-level mechanisms that contribute to energy barriers for solute transport through subnanometre pores. We conclude by providing principles and guidelines for designing next-generation single-species selective membranes that are inspired by ion-selective biological channels.

Thermodynamically driven assemblies and liquid-liquid phase separations in biology

The sustenance of life depends on the high degree of organization that prevails through different levels of living organisms, from subcellular structures such as biomolecular complexes and organelles to tissues and organs. The physical origin of such organization is not fully understood, and even though it is clear that cells and organisms cannot maintain their integrity without consuming energy, there is growing evidence that individual assembly processes can be thermodynamically driven and occur spontaneously due to changes in thermodynamic variables such as intermolecular interactions and concentration. Understanding the phase separation in vivo requires a multidisciplinary approach, integrating the theory and physics of phase separation with experimental and computational techniques. This paper aims at providing a brief overview of the physics of phase separation and its biological implications, with a particular focus on the assembly of membraneless organelles. We discuss the underlying physical principles of phase separation from its thermodynamics to its kinetics. We also overview the wide range of methods utilized for experimental verification and characterization of phase separation of membraneless organelles, as well as the utility of molecular simulations rooted in thermodynamics and statistical physics in understanding the governing principles of thermodynamically driven biological self-assembly processes.

Does Local Structure Bias How a Crystal Nucleus Evolves?

The broad scientific and technological importance of crystallization has led to significant research probing and rationalizing crystal nucleation processes. Previous work has generally neglected the possibility of the molecular-level dynamics of individual crystal nuclei coupling to local structures. However, recent experimental work has conjectured that this can occur. Therefore, to address a deficiency in scientific understanding of crystallization, we have probed the nucleation of prototypical single and multicomponent crystals (specifically, ice and mixed gas hydrates). We establish that local structures can bias the evolution of nascent crystal phases on a nanosecond time scale by, for example, promoting the appearance or disappearance of specific crystal motifs and thus reveal a new facet of crystallization behavior. Moreover, we demonstrate structural biases are likely present during crystallization processes beyond ice and gas hydrate formation. Structurally biased dynamics are a lens for understanding existing computational and experimental results while pointing to future opportunities.

Calculation of critical nucleation rates by the persistent embryo method: application to quasi hard sphere models

We study the crystal nucleation of the Weeks-Chandler-Andersen (WCA) model, using the recently introduced persistent embryo method (PEM). The method provides detailed characterization of pre-critical, critical and post-critical nuclei, as well as nucleation rates that compare favorably with those obtained using other methods (umbrella sampling, forward flux sampling or seeding). We further map our results to a hard sphere model allowing comparison with other existing predictions. Implications for experiments are also discussed.

Unravelling the origins of ice nucleation on organic crystals

Organic molecules such as steroids or amino acids form crystals that can facilitate the formation of ice - arguably the most important phase transition on earth. However, the origin of the ice nucleating ability of organic crystals is still largely unknown. Here, we combine experiments and simulations to unravel the microscopic details of ice formation on cholesterol, a prototypical organic crystal widely used in cryopreservation. We find that cholesterol - which is also a substantial component of cell membranes - is an ice nucleating agent more potent than many inorganic substrates, including the mineral feldspar (one of the most active ice nucleating materials in the atmosphere). Scanning electron microscopy measurements reveal a variety of morphological features on the surfaces of cholesterol crystals: this suggests that the topography of the surface is key to the broad range of ice nucleating activity observed (from -4 to -20 °C). In addition, we show via molecular simulations that cholesterol crystals aid the formation of ice nuclei in a unconventional fashion. Rather than providing a template for a flat ice-like contact layer (as found in the case of many inorganic substrates), the flexibility of the cholesterol surface and its low density of hydrophilic functional groups leads to the formation of molecular cages involving both water molecules and terminal hydroxyl groups of the cholesterol surface. These cages are made of 6- and, surprisingly, 5-membered hydrogen bonded rings of water and hydroxyl groups that favour the nucleation of hexagonal as well as cubic ice (a rare occurrence). We argue that the phenomenal ice nucleating activity of steroids such as cholesterol (and potentially of many other organic crystals) is due to (i) the ability of flexible hydrophilic surfaces to form unconventional ice-templating structures and (ii) the different nucleation sites offered by the diverse topography of the crystalline surfaces. These findings clarify how exactly organic crystals promote the formation of ice, thus paving the way toward deeper understanding of ice formation in soft and biological matter - with obvious reverberations on atmospheric science and cryobiology.