On the coupling between slow diffusion transport and barrier crossing in nucleation

Microwave-assisted synthesis of polyoxometalate-Dy2O3 monolayer nanosheets and nanotubes

Two-dimensional (2D) materials have shown unique chemical and physical properties; however, their synthesis is highly dependent on the layered structure of building blocks. Herein, we developed monolayer Dy2O3-phosphomolybdic acid (PMA) nanosheets and nanotubes based on microwave synthesis. Microwave-assisted synthesis with high-energy input gives a faster and dynamically driven growth of nanomaterials, resulting in high-purity nanostructures with a narrow size distribution. The reaction times of the nanosheets and nanotubes under microwave synthesis are significantly reduced compared with oven-synthesis. Dy2O3-PMA nanosheets and nanotubes exhibit enhanced activity and stability in photoconductance, with higher sensitivities (0.308 μA cm-2 for nanosheets and 0.271 μA cm-2 for nanotubes) compared to the individual PMA (0.12 μA cm-2) and Dy2O3 (0.025 μA cm-2) building blocks. This work demonstrates the promising application potential of microwave-synthesized 2D heterostructures in superconductors and photoelectronic devices.

Stochastic Monte Carlo Model for Simulating the Dynamic Liquid-Liquid Phase Separation in Bacterial Cells

There is growing evidence showing that many critical biological processes are driven by biomolecule condensates through liquid-liquid phase separation (LLPS). Although the qualitative observation and description of LLPS have been well documented, quantitative simulations of the time-dependent progression of LLPS in live cells are generally lacking. In this work, we build a stochastic Monte Carlo model to simulate the dynamic LLPS process during the formation of bacterial aggresomes. We demonstrate that the size distribution of the protein condensates evolves from an exponential-like to a bimodal-like pattern, and the number of condensates increases at the beginning and then decreases after reaching a maximum. Incorporating diffusion and collision, our simplified model recapitulates the two-step LLPS process in which many smaller condensates are formed in the first step and then merged into a few larger ones. We further reveal that the condensation speed, which can be defined by the condensates formed in unit time during the first step, is mainly determined by both the collision energy barrier and the initial protein density, while the number of condensates at the equilibrium is mainly associated with the dissociation energy barrier. Moreover, the LLPS process is not sensitive to temperature changes ranging around physiological conditions. Additionally, we consider the effect of the nucleation energy barrier on LLPS. We find that a higher nucleation energy barrier brings a slower condensation speed. Overall, we simulate the spatiotemporal dynamics of the LLPS process and provide qualitative guidance for understanding the dynamics of LLPS in bacterial cells, which can faithfully recapitulate experimental observations and facilitate the design of future experimental tests.

Nonisothermal nucleation in the gas phase is driven by cool subcritical clusters

Nucleation of clusters from the gas phase is a widely encountered phenomenon, yet rather little is understood about the underlying out-of-equilibrium dynamics of this process. The classical view of nucleation assumes isothermal conditions where the nucleating clusters are in thermal equilibrium with their surroundings. However, in all first-order phase transitions, latent heat is released, potentially heating the clusters and suppressing the nucleation. The question of how the released energy affects cluster temperatures during nucleation as well as the growth rate remains controversial. To investigate the nonisothermal dynamics and energetics of homogeneous nucleation, we have performed molecular dynamics simulations of a supersaturated vapor in the presence of thermalizing carrier gas. The results obtained from these simulations are compared against kinetic modeling of isothermal nucleation and classical nonisothermal theory. For the studied systems, we find that nucleation rates are suppressed by two orders of magnitude at most, despite substantial release of latent heat. Our analyses further reveal that while the temperatures of the entire cluster size populations are elevated, the temperatures of the specific clusters driving the nucleation flux evolve from cold to hot when growing from subcritical to supercritical sizes and resolve the apparent contradictions regarding cluster temperatures. Our findings provide unprecedented insight into realistic nucleation events and allow us to directly assess earlier theoretical considerations of nonisothermal nucleation.

A review of the microwave-assisted synthesis of carbon nanomaterials, metal oxides/hydroxides and their composites for energy storage applications

Currently, nanomaterials are considered to be the backbone of modern civilization. Especially in the energy sector, nanomaterials (mainly, carbon- and metal oxide/hydroxide-based nanomaterials) have contributed significantly. Among the various green approaches for the synthesis of these nanomaterials, the microwave-assisted approach has attracted significant research interest worldwide. In this context, it is noteworthy to mention that because of their enhanced surface area, high conducting nature, and excellent electrical and electrochemical properties, carbon nanomaterials are being extensively utilized as efficient electrode materials for both supercapacitors and secondary batteries. In this review article, we briefly demonstrate the characteristics of microwave-synthesized nanomaterials for next-generation energy storage devices. Starting with the basics of microwave heating, herein, we illustrate the past and present status of microwave chemistry for energy-related applications, and finally present a brief outlook and concluding remarks. We hope that this review article will positively convey new insights for the microwave synthesis of nanomaterials for energy storage applications.

Long-wavelength density fluctuations as nucleation precursors

Recent theories of nucleation that go beyond classical nucleation theory predict that diffusion-limited nucleation of both liquid droplets and of crystals from a low-density vapor (or weak solution) begins with long-wavelength density fluctuations. This means that in the early stages of nucleation, "clusters" can have low density but large spatial extent, which is at odds with the classical picture of arbitrarily small clusters of the condensed phase. We present the results of kinetic Monte Carlo simulations using forward flux sampling to show that these predictions are confirmed, namely, that on average, nucleation begins in the presence of low-amplitude, but spatially extended density fluctuations thus confirming a significant prediction of the nonclassical theory.

Reaction coordinates and rate constants for liquid droplet nucleation: Quantifying the interplay between driving force and memory

In this work, we revisit the classic problem of homogeneous nucleation of a liquid droplet in a supersaturated vapor phase. We consider this at different extents of the driving force, or equivalently the supersaturation, and calculate a reaction coordinate (RC) for nucleation as the driving force is varied. The RC is constructed as a linear combination of three order parameters, where one accounts for the number of liquidlike atoms and the other two for local density fluctuations. The RC is calculated from biased and unbiased molecular dynamics (MD) simulations using the spectral gap optimization approach "SGOOP" [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)]. Our key finding is that as the supersaturation decreases, the RC ceases to simply be the number of liquidlike atoms, and instead, it becomes important to explicitly consider local density fluctuations that correlate with shape and density variations in the nucleus. All three order parameters are found to have similar barriers in their respective potentials of mean force; however, as the supersaturation decreases, the density fluctuations decorrelate slower and thus carry longer memory. Thus, at lower supersaturations, density fluctuations are non-Markovian and cannot be simply ignored from the RC by virtue of being noise. Finally, we use this optimized RC to calculate nucleation rates in the infrequent metadynamics framework and show that it leads to a more accurate estimate of the nucleation rate with four orders of magnitude acceleration relative to unbiased MD.

Nucleation and growth of a core-shell composite nucleus by diffusion

The critical radius of a core-shell-type nucleus grown by diffusion in a phase-separated solution is studied. A kinetic critical radius rather than the thermodynamic critical radius of standard classical nucleation theory can be defined from the diffusional growth equations. It is shown that there exist two kinetic critical radii for the core-shell-type nucleus, for which both the inner-core radius and the outer-shell radius will be stationary. Therefore, these two critical radii correspond to a single critical point of the nucleation path with a single energy barrier even though the nucleation looks like a two-step process. The two radii are given by formulas similar to that of classical nucleation theory if the Ostwald-Freundlich boundary condition is imposed at the surface of the inner nucleus and that of the outer shell. The subsequent growth of a core-shell-type postcritical nucleus follows the classical picture of Ostwald's step rule. Our result is consistent with some of the experimental and numerical results which suggest the core-shell-type critical nucleus.

Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations

The nucleation of crystals in liquids is one of nature's most ubiquitous phenomena, playing an important role in areas such as climate change and the production of drugs. As the early stages of nucleation involve exceedingly small time and length scales, atomistic computer simulations can provide unique insights into the microscopic aspects of crystallization. In this review, we take stock of the numerous molecular dynamics simulations that, in the past few decades, have unraveled crucial aspects of crystal nucleation in liquids. We put into context the theoretical framework of classical nucleation theory and the state-of-the-art computational methods by reviewing simulations of such processes as ice nucleation and the crystallization of molecules in solutions. We shall see that molecular dynamics simulations have provided key insights into diverse nucleation scenarios, ranging from colloidal particles to natural gas hydrates, and that, as a result, the general applicability of classical nucleation theory has been repeatedly called into question. We have attempted to identify the most pressing open questions in the field. We believe that, by improving (i) existing interatomic potentials and (ii) currently available enhanced sampling methods, the community can move toward accurate investigations of realistic systems of practical interest, thus bringing simulations a step closer to experiments.

Classical nucleation theory for solute precipitation amended with diffusion and reaction processes near the interface

During the processes of nucleation and growth of a precipitate cluster from a supersaturated solution, the diffusion flux between the cluster and the solution changes the solute concentration near the cluster-solution interface from its average bulk value. This feature affects the rates of attachment and detachment of solute atoms at the interface, and, therefore, the entire nucleation-growth kinetics is altered. Unless quite obvious, this effect has been ignored in classical nucleation theory. To illustrate the results of this approach, for the case of homogeneous nucleation, we calculate the total solubility and the nucleation rate as functions of two parameters of the model (the reduced interface energy and the inverse second Damköhler number), and we compare these results to the classical ones. One can conclude that discrepancies with classical nucleation theory are great in the diffusion-limited regime, when the rate of bulk diffusion is small compared to the rate of interface reactions, while in the opposite interface-limited case they vanish.

Salting out the polar polymorph: analysis by alchemical solvent transformation

We computationally examine how adding NaCl to an aqueous solution with α- and γ-glycine nuclei alters the structure and interfacial energy of the nuclei. The polar γ-glycine nucleus in pure aqueous solution develops a melted layer of amorphous glycine around the nucleus. When NaCl is added, a double layer is formed that stabilizes the polar glycine polymorph and eliminates the surface melted layer. In contrast, the non-polar α-glycine nucleus is largely unaffected by the addition of NaCl. To quantify the stabilizing effect of NaCl on γ-glycine nuclei, we alchemically transform the aqueous glycine solution into a brine solution of glycine. The alchemical transformation is performed both with and without a nucleus in solution and for nuclei of α-glycine and γ-glycine polymorphs. The calculations show that adding 80 mg/ml NaCl reduces the interfacial free energy of a γ-glycine nucleus by 7.7 mJ/m(2) and increases the interfacial free energy of an α-glycine nucleus by 3.1 mJ/m(2). Both results are consistent with experimental reports on nucleation rates which suggest: J(α, brine) < J(γ, brine) < J(α, water). For γ-glycine nuclei, Debye-Hückel theory qualitatively, but not quantitatively, captures the effect of salt addition. Only the alchemical solvent transformation approach can predict the results for both polar and non-polar polymorphs. The results suggest a general "salting out" strategy for obtaining polar polymorphs and also a general approach to computationally estimate the effects of solvent additives on interfacial free energies for nucleation.

Nucleation and growth by diffusion under Ostwald-Freundlich boundary condition

The critical radius of a nucleus grown by diffusion in a solution is studied thermodynamically as well as kinetically. The thermodynamic growth equation called Zeldovich equation of classical nucleation theory and the kinetic diffusional growth equation combined with the Ostwald-Freundlich boundary condition lead to the same critical radius. However, it should be pointed out that the diffusional equation may lead to a kinetic critical radius that is different from the thermodynamic critical radius, thus indicating the possibility of kinetically controlling the critical radius of a nucleus.

Self-assembly of multicomponent structures in and out of equilibrium

Theories of phase change and self-assembly often invoke the idea of a "quasiequilibrium," a regime in which the nonequilibrium association of building blocks results nonetheless in a structure whose properties are determined solely by an underlying free energy landscape. Here we study a prototypical example of multicomponent self-assembly, a one-dimensional fiber grown from red and blue blocks. We find that if the equilibrium structure possesses compositional correlations different from those characteristic of random mixing, then it cannot be generated without error at any finite growth rate: there is no quasiequilibrium regime. However, by exploiting dynamic scaling, structures characteristic of equilibrium at one point in phase space can be generated, without error, arbitrarily far from equilibrium. Our results, supported by mean-field theory in higher dimensions, thus suggest a "nonperturbative" strategy for multicomponent self-assembly in which the target structure is, by design, not the equilibrium one.