Molecular dynamics simulation of heterogeneous nucleation at a structureless solid surface

Heterogeneous Condensation on Simplified Viral Envelope Protein Structures

Elucidating the mechanisms of heterogeneous condensation on viral and bacterial envelopes is crucial for understanding biothreat transport phenomena and optimizing capture efficiency in condensation-based detection devices. We investigate the impact of viral envelope geometric parameters [e.g., surface structure pitch-to-diameter ratio (p/d)] due to protruding glycoproteins and surface wettability [via liquid-solid interaction intensity (f)] on heterogeneous condensation using molecular dynamics simulations. Complex glycoprotein structures were modeled as cylindrical pillars to analyze condensation rates and active surface areas across a range of p/d ratios (1.0, 1.2, 1.3, 1.7, 2.0, and ∞) and contact angles (θ = 15°, 75°, and 105°, corresponding to f = 3.0, 2.0, and 1.5) to address envelope geometries for a wide variety of viruses. The results indicate that initial condensation rates on surfaces with intermediate p/d ratios (e.g., 1.2-1.3) are significantly higher due to increased active surface area and droplet cluster formations. The rapid initial condensation fills up the gap between the pillars, reducing the active surface area and leading to a gradual decrease and a plateau in the condensation rate. The increased peak condensation rates are not observed as p/d increased to and above 1.7, as the exhibited behavior is like condensation on the unstructured surface. An increase in surface hydrophilicity (θ = 15°, f = 3.0) leads to faster nucleation and higher peak condensation rates compared to hydrophobic surfaces (θ = 105°, f = 1.5). The influence of viral envelope geometries and surface wettability on the heterogeneous condensation mechanisms offers foundational insights required to understand airborne biothreat transmission, which is particularly important in the atmosphere and respiratory tract, and improve biothreat detection methods utilizing condensation-based capture devices.

Mechanism of Charged Graphene Substrate Effects on the Stability of Interfacial Nanobubbles: Molecular Dynamics Simulations

Charged solid substrates play a crucial role in influencing the behavior of interfacial nanobubbles, although the underlying mechanisms are not yet fully understood. To explore this process in greater depth, we employed molecular dynamics (MD) simulations to systematically examine the effects of charged graphene on the morphological evolution, solid interface structure, and stability of interfacial nanobubbles, thereby revealing the intrinsic mechanisms. Our findings indicate that as surface charge density increases, the gas-solid interactions gradually diminish while the liquid-solid interactions significantly intensify. This results in a progressive reduction in both the contact angle and radius of the nanobubbles, eventually causing their detachment from the substrate and transformation to bulk-phase nanobubbles. Moreover, the enhanced gas accumulation effect at the solid interface leads to a reduction in the internal pressure of the bubbles, thus improving the stability of the interfacial nanobubbles. Additionally, the increase in the surface charge density elevates the water molecule density at the solid interface, which in turn strengthens the hydrogen bond network of interfacial water molecules, further stabilizing the liquid-solid interface structure. In summary, this study highlights the critical role of surface charge in regulating interfacial nanobubble behavior, providing new theoretical guidance for optimizing electrode materials and controlling bubble behavior in electrochemical systems.

Size-Dependent Wetting Contact Angles at the Nanoscale Defined by Equimolar Surfaces and Surfaces of Tension

The wetting characteristics of fluids play a crucial role in various fields of interface and surface science. Contact angle serves as a fundamental indicator of wetting behavior. However, accurate quantification of wetting phenomena even at the macroscale often poses challenges, particularly due to the hysteresis between receding and advancing contact angles. The complexity increases further at the nanoscale, where the significant volume of the interphase region causes ambiguity in defining the "dividing surface." In this study, we use molecular dynamics simulations to investigate the wetting dynamics of a "cylindrical nanodroplet" and an argon nanofilm. Through analysis of microscopic density distribution maps and tension tensor distributions within the Gibbs framework, we identified equimolar and tension surfaces at both liquid-gas and liquid-solid interfaces. Our results show over 10% discrepancies between equilibrium contact angles calculated for equimolar surfaces and those based on tension surfaces in the case of the cylindrical nanodroplet. We observed a clear dependence of wetting contact angles on the cross-sectional radius of cylindrical droplets with a straight three-phase contact line. As the radius decreases, the differences between contact angles at equimolar and tension surfaces increase, while for larger droplets, these differences diminish and become negligible.

Formation of Liquid Film in Heterogeneous Condensation of Water Vapor: Effects of Solid-Fluid Interaction and Sulfuric Acid Component

Understanding the phenomenon of filmwise condensation on solid surfaces is vital for industrial processes such as air pollutant control and desalination. In this work, we study the formation of condensed liquid films via molecular dynamics simulations, and the effects of solid-fluid interactions and the sulfuric acid component are given major attention. Water is chosen as the fluid, while the solid-fluid interaction is modified to characterize different solid surfaces. The results show that as the solid-fluid interaction decreases, the solid surface transforms from a completely wetting surface to a partially wetting surface, and the film formation process shows significant differences. The condensed liquid on the completely wetting surface forms small liquid films, which merge to form a complete film covering the surface. With the enhancement of solid-fluid interaction, the condensation rate increases first and then remains virtually invariant, resulting in a film formation time that decreases first and then maintains constant. The condensed liquid on the partially wetting surfaces appears as nanodroplets, and the coalescence between nanodroplets leads to the formation of the liquid film. It is found that the stronger the solid-fluid interaction, the more the coalesced droplets tend to be pinned at nucleation sites, the easier it is to form a liquid film, and the shorter the time required for droplet merging. The sulfuric acid component accelerates liquid film formation on both completely wetting and partially wetting surfaces, but the effect of sulfuric acid is more significant on partially wetting surfaces. The 5% molar fraction of sulfuric acid reduces the nucleation time by 72% and increases the condensation rate by 137% under partial wetting, while the same amount of sulfuric acid only increases the nucleation rate by 6% on the completely wetting surface.

Molecular insights on NaCl crystal formation approaching PVDF membranes functionalized with graphene

Atomistic simulations of graphene–PVDF membranes speeding up NaCl crystal nucleation and growth in comparison to the pristine PVDF membranes.

The Impact of the Electric Field on Surface Condensation of Water Vapor: Insight from Molecular Dynamics Simulation

In this study, molecular dynamics simulations were carried out to study the coupling effect of electric field strength and surface wettability on the condensation process of water vapor. Our results show that an electric field can rotate water molecules upward and restrict condensation. Formed clusters are stretched to become columns above the threshold strength of the field, causing the condensation rate to drop quickly. The enhancement of surface attraction force boosts the rearrangement of water molecules adjacent to the surface and exaggerates the threshold value for shape transformation. In addition, the contact area between clusters and the surface increases with increasing amounts of surface attraction force, which raises the condensation efficiency. Thus, the condensation rate of water vapor on a surface under an electric field is determined by competition between intermolecular forces from the electric field and the surface.

Thermodynamic formulation of the barrier for heterogeneous pinned nucleation: Implication to the crossover scenarios associated with barrierless and homogeneous nucleation

The effect of contact line pinning on nucleation is reported using continuum thermodynamics. Based on the principle of the free-energy maximization, closed-form expressions in the dimensionless form for the free-energy of the three-phase metastable system and the thermodynamic barrier are formulated with respect to the system geometry and the substrate wettability. The condition of maximality limits the dynamic contact angle within the cluster-phase-phobic regime. The dimensionless nucleation barrier or the potency factor can be divided into two components related to the system geometry and the pinning effect. Depending on the relative value of the equilibrium and the critical dynamic contact angle, the contact line pinning can either have favorable or adverse effects. Associated pinning-depinning transition can also lead to the crossovers related to barrierless and homogeneous nucleation. Contact line tension is found to have a considerable effect during these transitional scenarios. Complete wetting transition associated with barrierless nucleation can take place due to the presence of tensile (negative) line tension. On the other hand, complete drying transition related to homogeneous nucleation can occur when line tension is compressive (positive) in nature. The pinning has a favorable effect only when the substrate wettability is within the cluster-phase-philic regime. There can be favorable, adverse, or no pinning effects when the substrate wettability is within the cluster-phase-phobic regime. Although the contact line is pinned, the minimum value of the potency factor is obtained when equilibrium and dynamic contact angles are equal.

On the onset of surface condensation: formation and transition mechanisms of condensation mode

Molecular dynamics simulations have been carried out to investigate the onset of surface condensation. On surfaces with different wettability, we snapshot different condensation modes (no-condensation, dropwise condensation and filmwise condensation) and quantitatively analyze their characteristics by temporal profiles of surface clusters. Two different types of formation of nanoscale droplets are identified, i.e. the formations with and without film-like condensate. We exhibit the effect of surface tensions on the formations of nanoscale droplets and film. We reveal the formation mechanisms of different condensation modes at nanoscale based on our simulation results and classical nucleation theory, which supplements the 'classical hypotheses' of the onset of dropwise condensation. We also reveal the transition mechanism between different condensation modes based on the competition between surface tensions and reveal that dropwise condensation represents the transition states from no-condensation to filmwise condensation.

Effect of nano structures on the nucleus wetting modes during water vapour condensation: from individual groove to nano-array surface

The geometrical structures of surfaces are important to the formation and growth of nuclei during water vapour condensation. Nucleus wetting modes on grooved surfaces are determined by the intrinsic contact angle and the cross sectional angle.

Effect of surface free energies on the heterogeneous nucleation of water droplet: a molecular dynamics simulation approach

Heterogeneous nucleation of water droplet on surfaces with different solid-liquid interaction intensities is investigated by molecular dynamics simulation. The interaction potentials between surface atoms and vapor molecules are adjusted to obtain various surface free energies, and the nucleation process and wetting state of nuclei on surfaces are investigated. The results indicate that near-constant contact angles are already established for nano-scale nuclei on various surfaces, with the contact angle decreasing with solid-liquid interaction intensities linearly. Meanwhile, noticeable fluctuation of vapor-liquid interfaces can be observed for the nuclei that deposited on surfaces, which is caused by the asymmetric forces from vapor molecules. The formation and growth rate of nuclei are increasing with the solid-liquid interaction intensities. For low energy surface, the attraction of surface atoms to water molecules is comparably weak, and the pre-existing clusters can depart from the surface and enter into the bulk vapor phase. The distribution of clusters within the bulk vapor phase becomes competitive as compared with that absorbed on surface. For moderate energy surfaces, heterogeneous nucleation predominates and the formation of clusters within bulk vapor phase is suppressed. The effect of high energy particles that embedded in low energy surface is also discussed under the same simulation system. The nucleation preferably initiates on the high energy particles, and the clusters that formed on the heterogeneous particles are trapped around their original positions instead of migrating around as that observed on smooth surfaces. This feature makes it possible for the heterogeneous particles to act as fixed nucleation sites, and simulation results also suggest that the number of nuclei increases monotonously with the number of high energy particles. The growth of nuclei on high energy particles can be divided into three sub-stages, beginning with the formation of a wet-spot, increase of contact angle with near-constant contact line, and finally growth with constant contact angle. The growth rate of nuclei also increases with the size of high energy particles.

Heterogeneous crystal nucleation: the effect of lattice mismatch

A simple dynamical density functional theory is used to investigate freezing of an undercooled liquid in the presence of a crystalline substrate. We find that the adsorption of the crystalline phase on the substrate, the contact angle, and the height of the nucleation barrier are nonmonotonic functions of the lattice constant of the substrate. We show that the free-growth-limited model of particle-induced freezing by Greer et al. [Acta Mater. 48, 2823 (2000)] is valid for larger nanoparticles and a small anisotropy of the interface free energy. Faceting due to the small size of the foreign particle or a high anisotropy decouples free growth from the critical size of homogeneous nuclei.

Binding affinity of a small molecule to an amorphous polymer in a solvent. Part 1: free energy of binding to a binding site

Crystallization is commonly used in a separation and purification process in the production of a wide range of materials in various industries. In industry, crystallization usually starts with heterogeneous nucleation on a foreign surface. The complicated mechanism of heterogeneous nucleation is not well understood; however, we hypothesize that there might be a possible correlation between binding affinity to a surface and enhancement of nucleation. Recent studies show that amorphous polymers can be used to control crystallization, selectively produce pharmaceutical polymorphs, and discover novel pharmaceutical polymorphs. To investigate the possible correlation between the binding affinity of one molecule to key binding sites (local binding) and heterogeneous nucleation activity as well as the possibility of using this binding affinity to help guide the selection of polymers that promote heterogeneous nucleation, we computed the free energy of binding of aspirin to four nonporous cross-linked polymers in an ethanol-water 38 v% mixture. These cross-linked polymers are poly(4-acryloylmorpholine) (PAM), poly(2-carboxyethyl acrylate) (PCEA), poly(4-hydroxylbutyl acrylate) (PHBA), and polystyrene (PS); all of them were cross-linked with divinylbenzene (DVB). These systems were used because their heterogeneous nucleation activities are available in literature, and the ranking is PAM > PCEA > PHBA ≈ PS. We generated three independent surfaces for each polymer and computed the free energy of binding of aspirin to the best binding site that we found on each surface. The average free energies of binding to the best sites of PAM, PCEA, PHBA, and PS are -20.4 ± 1.0, -16.7 ± 1.0, -14.4 ± 1.1, and -13.6 ± 1.1 kcal/mol, respectively. We found that the trend of the magnitudes of the average free energies of binding to the best sites is PAM > PCEA > PHBA ≈ PS. This trend is very similar to that of heterogeneous nucleation activity. Our results suggest the importance of the free energy of binding to key sites (local binding) and the possibility of using this quantity to help guide the selection of polymers that promote heterogeneous nucleation.

Binding affinity of a small molecule to an amorphous polymer in a solvent. Part 2: preferential binding to local sites on a surface

Crystallization, a separation and purification process, is commonly used to produce a wide range of materials in various industries, and it usually begins with heterogeneous nucleation on a foreign surface in industrial practice and most other circumstances. Recent studies show that amorphous polymeric substrates are useful in controlling crystallization and selectively producing pharmaceutical polymorphs. In our previous publication, we investigated the possible correlation of the binding affinity of one molecule to key binding sites (local binding), and the possibility of using this binding affinity to guide the selection of polymers promoting heterogeneous nucleation. The studied systems were aspirin binding to four nonporous cross-linked polymers in ethanol-water 38 v% mixture. Cross-linked with divinylbenzene (DVB), these polymers were poly(4-acryloylmorpholine) (PAM), poly(2-carboxyethyl acrylate) (PCEA), poly(4-hydroxylbutyl acrylate) (PHBA), and polystyrene (PS). We discovered that the trend of the magnitudes of the average free energies of binding to the best sites is very similar to that of heterogeneous nucleation activities. This Article aims to investigate whether or not local binding to key sites is the important variable to describe heterogeneous nucleation as opposed to the overall/average binding affinity of molecules to a surface, and to investigate the possibility of using the overall binding affinity to guide the selection of polymers. We used the polymer surfaces generated from our previous study to calculate the overall binding affinity of aspirin molecules to the surface as measured by the preferential interaction coefficients of aspirin (1 m) to these polymers. We discovered that the trend of the average preferential interaction coefficients does not correlate as well to that of heterogeneous nucleation activities as the free energies of binding to the best sites. We also computed the average numbers of aspirin molecules associated with the areas of the surfaces' best binding sites and found that they correlate better to heterogeneous nucleation activities than the average preferential interaction coefficients. These results further support that local binding is indicative of heterogeneous nucleation. Moreover, we found a weak trend of the distance order parameters of the aspirin molecules to be similar that of heterogeneous nucleation activities. Our results from the two-part study suggest the importance of local binding to heterogeneous nucleation as well as the possibility of using the binding affinity to the local area (the free energy of binding to the best site and the number of nucleating molecules associated with the area of the best binding site) and the distance order parameters to guide the selection of polymers.

Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2D and 3D

We apply a simple dynamical density functional theory, the phase-field crystal (PFC) model of overdamped conservative dynamics, to address polymorphism, crystal nucleation, and crystal growth in the diffusion-controlled limit. We refine the phase diagram for 3D, and determine the line free energy in 2D and the height of the nucleation barrier in 2D and 3D for homogeneous and heterogeneous nucleation by solving the respective Euler-Lagrange (EL) equations. We demonstrate that, in the PFC model, the body-centered cubic (bcc), the face-centered cubic (fcc), and the hexagonal close-packed structures (hcp) compete, while the simple cubic structure is unstable, and that phase preference can be tuned by changing the model parameters: close to the critical point the bcc structure is stable, while far from the critical point the fcc prevails, with an hcp stability domain in between. We note that with increasing distance from the critical point the equilibrium shapes vary from the sphere to specific faceted shapes: rhombic dodecahedron (bcc), truncated octahedron (fcc), and hexagonal prism (hcp). Solving the equation of motion of the PFC model supplied with conserved noise, solidification starts with the nucleation of an amorphous precursor phase, into which the stable crystalline phase nucleates. The growth rate is found to be time dependent and anisotropic; this anisotropy depends on the driving force. We show that due to the diffusion-controlled growth mechanism, which is especially relevant for crystal aggregation in colloidal systems, dendritic growth structures evolve in large-scale isothermal single-component PFC simulations. An oscillatory effective pair potential resembling those for model glass formers has been evaluated from structural data of the amorphous phase obtained by instantaneous quenching. Finally, we present results for eutectic solidification in a binary PFC model.

Nucleation of fluids confined between parallel walls: a lattice Monte Carlo study

Nucleation phenomena in lattice gas models of simple and chain molecules confined in slitlike pores are studied using Monte Carlo methods. Finite-size scaling is used to investigate the nature of phase transitions accompanying the formation of layers at the pore walls. It is demonstrated that nucleation leads to the symmetry breaking and the formation of nuclei at one wall only.

Homogeneous and heterogeneous nucleation of Lennard-Jones liquids

The homogeneous and heterogeneous nucleation of a Lennard-Jones liquid is investigated using the umbrella sampling method. The free energy cost of forming a nucleating droplet is determined as a function of the quench depth, and the saddle point nature of the droplets is verified using an intervention technique. The structure and symmetry of the nucleating droplets are found for a range of temperatures. We find that for deep quenches the nucleating droplets become more anisotropic and diffuse with no well-defined core or surface. The environment of the nucleating droplets forms randomly stacked hexagonal planes. This behavior is consistent with a spinodal nucleation interpretation. We also find that the free energy barrier for heterogeneous nucleation is a minimum when the lattice spacing of the impurity equals the lattice spacing of the equilibrium crystalline phase. If the lattice spacing of the impurity is different, the crystal grows into the bulk instead of wetting the impurity.

Heterogeneous and homogeneous nucleation compared: rapid nucleation on microscopic impurities

We use computer simulation to calculate the rates of both homogeneous nucleation and heterogeneous nucleation on microscopic impurities. We do so in perhaps the simplest model of fluids and magnets: the two-dimensional Ising model. We expect our results to be qualitatively applicable to many simple and complex fluids. We find that heterogeneous nucleation on an impurity that is not only microscopic but also as small as possible, that is, a single fixed spin, is more than four orders of magnitude faster than homogeneous nucleation. The rate of heterogeneous nucleation then increases by a factor of approximately five for each additional fixed spin in the impurity. These results suggest that impurities as small as single molecules can result in homogeneous nucleation being irrelevant due to heterogeneous nucleation on these microscopic impurities being much faster.

Computer simulation of nucleation in a gas-saturated liquid

Molecular dynamics methods have been used to investigate the kinetics of the liquid-gas phase transition in a two-component Lennard-Jones system at negative pressures and elastic stretches of the liquid to values close to spinodal ones. The molecular dynamics system consists of 2048 interacting particles with parameters of the Lennard-Jones potential for argon and neon. Density dependences of pressure and internal energy have been calculated for stable and metastable states of the mixture at a temperature T* approximately 0.7+/-0.01 and three values of the concentration. The location of mechanical and the diffusion spinodals has been determined. It has been established that a gas-saturated mixture retains its stability against finite variations of state variables up to stretches close to the values near the diffusion spinodal. The statistic laws of the process of destruction of the metastable state have been investigated. The lifetimes of the metastable phase have been determined. It is shown that owing to the small height of the potential barrier that separates the microheterogeneous from the homogeneous state a system of finite size has a possibility to make the reverse transition from the microheterogeneous into the homogeneous state. The lifetimes of the system in the microheterogeneous state, as well as the expectation times of the occurrence of a critical nucleus, are described by Poissonian distributions.

Formation of a metastable phase due to the presence of impurities

Phase transitions into a new phase that is itself metastable are common; instead of the equilibrium phase nucleating, a metastable phase does so. When this occurs the system is sometimes said to be obeying Ostwald's rule. We show how this can happen when there are impurities present that reduce the barrier to heterogeneous nucleation of the metastable phase. We do so by studying a Potts lattice model using Monte Carlo simulation. Thus, which phase forms depends not only on the properties of the different phases but also on the impurities present. Understanding why systems obey Ostwald's rule may therefore require a study of the impurities present.

Aspects of prewetting at nonplanar surfaces

We employ Monte Carlo simulations in the grand canonical ensemble (GCEMC) to investigate the impact of nonplanarity of a solid substrate on the locus of the prewetting phase transition. The substrate is modelled as a periodic sequence of furrows of depth D and periodicity sx in the x direction; the furrows are infinitely long in the y direction. Our results indicate that a necessary prerequisite for a prewetting transition is the formation of a(n approximately) planar interface between molecularly thin films and an adjacent (bulk) gas. Thus, in general the prewetting transition is shifted to larger chemical potentials because the formation of a planar film-gas interface is more difficult next to a nonplanar compared with a planar solid surface. However, this shift turns out to be nonmonotonic depending on D on account of subtle packing effects manifested in the deviation of the local density Deltarho(x,Deltaz;D) at the nonplanar solid surface from that at a planar substrate. If D becomes sufficiently large prewetting as a discontinuous phase transition is suppressed because inside the furrow a highly ordered film forms that prevents a planar film-gas interface from forming.