Atomistic Mechanism of Ion Solution Evaporation: Insights from Molecular Dynamics

Abstract

The study of ion solution evaporation is of paramount importance to the environment as it pertains to numerous critical domains in our lives. This research employs molecular dynamics methods to systematically investigate the influence of ion species, concentration, temperature, and the surface area-to-volume ratio on the ion solution evaporation process. Firstly, we introduce the process of molecular dynamics modeling of ion solutions, encompassing the selection of simulation parameters, the definition of potential energy functions, and the adjustment of time steps. Subsequently, we analyze the molecular dynamics simulation results from various aspects, such as atomic motion and ion concentration distribution, to elucidate the mechanisms underlying the ion solution evaporation. Finally, we summarize the significance of this study, emphasizing its potential applications in industrial production, water resource management, and ecological preservation, thereby providing a robust theoretical foundation for environmental protection and sustainable development.

1. Introduction

Ionic solution refers to liquids in which ions (charged molecules or ionized compounds) are dissolved in water or other solvents. This type of liquid finds wide applications, including energy technologies [1], ecosystem health [2], and material synthesis [3]. The evaporation of ion solution is a critical step in the synthesis of nanomaterials and the fabrication of thin films. The precise control of the evaporation process can influence the morphology, composition, and properties of the resulting materials, which are essential for electronics, optics, and other applications [4]. In energy storage and conversion technologies, including batteries and fuel cells, the evaporation of ion solutions can affect the manufacturing processes and the performance of these devices [5]. Understanding these processes can lead to more efficient and durable energy solutions. Therefore, a thorough exploration of the mechanisms and impacts in this field is crucial for better environmental protection and the advancement of nanomaterial synthesis, as well as more efficient and durable energy solutions.

Experimental studies on the evaporation of ionic solutions typically involve a range of methods and techniques to monitor and analyze the behavior of ions in the evaporation process. Wang introduced a pioneering approach using calcium-based metal-organic frameworks for seawater-evaporation-induced electricity generation, highlighting experiments and simulations that uncovered selective sodium ion transport as the driving force behind the technology [6]. Zhu et al. presented a computational design for a Vapor-Cooled Shield (VCS) for liquid hydrogen storage tanks, demonstrating significant improvements in thermal insulation and reduction of heat intrusion by optimizing the VCS tube diameter, number of tubes, and insulation thermal conductivity [7]. Liu presented a novel and simple solution for an evaporation process combined with methylammonium iodide (MAI) solution immersion to prepare high-quality perovskite films for solar cells. The method significantly improved the power conversion efficiency (PCE) by 30% compared to traditional sequential deposition, offering a more practical approach for large-scale production of perovskite solar cells [8]. These methodologies have contributed to a comprehensive understanding of the dynamics of ionic solution evaporation, providing valuable insights into the concentration changes of ions throughout the process.

However, despite the valuable information that these experimental methods can provide regarding the evaporation process of ionic solutions, they still have some limitations, particularly in revealing the underlying mechanisms. Most experimental methods lack sufficient spatial resolution to determine the distribution of ions at the microscopic scale. This makes it challenging to study the local concentration changes of ions during the evaporation process. In addition, some experimental methods have limited temporal resolution when studying the dynamics of the evaporation process, making it difficult to capture instantaneous changes. Further, the surface effects of experimental containers may also impact the evaporation process, and these effects are often challenging to completely eliminate.

Therefore, in elucidating the mechanisms of ionic solution evaporation, researchers often resort to numerical simulations and theoretical models to complement the shortcomings of experimental approaches. Molecular dynamics (MD) is a computational method used to simulate the motion and interactions of particles in molecular systems, offering numerous advantages in studying the evaporation process of ionic solutions. MD allows for the simulation of the motion and interactions of each particle (molecule or ion) in a solution at the microscopic scale. This enables the acquisition of detailed information about ions in the solution, including their positions, velocities, energies, and interactions. Molecular dynamics methods exhibit significant advantages in the study of ionic solution evaporation by offering detailed information about the distribution, density, and local concentration of ions during the evaporation process. Yu and Wang employed molecular dynamics simulations to investigate the microscale mechanisms of extremely thin liquid evaporation, yielding insights into the evaporation process [9]. Zhakohovskii and Anisimov utilized molecular dynamics to study the dynamic behavior during the evaporation of solution, unraveling the mechanisms underlying liquid evaporation [10]. The research by Loche et al. provided a detailed molecular dynamics study of the chloride ion’s evaporation energetics and kinetics from liquid water. The findings highlight the significant role of ion hydration in lowering the evaporation energy barrier and enhancing chloride diffusivity, offering valuable insights into atmospheric processes and gas-phase catalysis [11].

Current molecular dynamics studies on ion solution evaporation face several limitations, primarily due to insufficient exploration of how variables such as temperature, specific surface area, and ion types influence the evaporation process. This paper aims to address these gaps by examining the impacts of these crucial factors on the evaporation dynamics of ion solutions, providing a more comprehensive understanding of the underlying mechanisms. Firstly, the molecular dynamics modeling process for ionic solutions in this study is introduced. Subsequently, the results of molecular dynamics simulations are analyzed from various perspectives, including atomic motion and ion concentration distribution. Finally, the mechanism of ionic solution evaporation is elucidated. The findings of this research will contribute to a microscopic understanding of ionic solution evaporation. This, in turn, will establish a solid theoretical foundation for improving industrial production, water resource management, and ecosystem health.

2. Materials and Methods

Molecular dynamics (MD) simulations are a powerful computational technique used to study the physical movements and interactions of atoms and molecules in a system. The fundamental idea behind MD is to solve Newton’s equations of motion for a system of particles over discrete time steps, allowing for the calculation of trajectories and the observation of how the system evolves over time. By modeling the interactions between atoms using empirical or semi-empirical potential functions, MD can predict the behavior of complex systems with high accuracy. MD simulations provide a detailed atomic-level view of processes, offering insights into dynamic properties, such as diffusion, thermodynamics, and phase transitions, that are difficult to measure experimentally. In this study, we employ MD to investigate the evaporation dynamics of ionic solutions, a process that involves complex interactions between solvent molecules and ions. Unlike traditional experimental methods, which may lack the spatial and temporal resolution to observe such detailed molecular behavior, MD allows us to simulate the evaporation process at the atomic scale, capturing the essential mechanisms driving the evaporation, ion distribution, and clustering phenomena.

One of the main advantages of MD simulations is the ability to control and vary parameters such as temperature, ion concentration, and the size of the system, which are critical factors in understanding the evaporation behavior of ionic solutions. Moreover, MD offers the unique ability to track the motion of individual particles, revealing local phenomena, such as ion–solvent interactions, that cannot be captured through macroscopic measurements alone. In our study, this capability is key to understanding the role of ionic interactions in the evaporation process, allowing us to explore how ion concentration and temperature influence the rate and uniformity of evaporation.

2.1. Potential Function

The TIP3P water molecule model is one of the commonly utilized models in molecular dynamics simulations to describe the interactions of water molecules [12,13]. TIP3P stands for “Transferable Intermolecular Potential with 3 Points”, and its potential function is employed to simulate the intermolecular interactions of water molecules. The TIP3P model comprises three atoms: one oxygen atom (O) and two hydrogen atoms (H), which together constitute an H₂O water molecule. In the TIP3P model, the hydrogen atoms are covalently bonded to the oxygen atom, forming the fundamental structure of a water molecule. The potential function of the TIP3P water molecule model includes the bond energy, angle energy, and van der Waals potential. The summation of these energy components constitutes the potential energy of the water molecule. The potential function of the TIP3P water molecule model is represented as follows:

• Bond energy:

In the TIP3P model, the internal energy of the hydrogen–oxygen bonds within a water molecule can be represented by a harmonic oscillator potential. The formula for the bond energy is as follows:

$$E_{bond}(r_{\mathrm{OH}})={\displaystyle \frac{1}{2}}{k}_{\mathrm{OH}}{(r_{\mathrm{OH}}-r_0)}^2$$

(1)

where r_OH is the length of the hydrogen–oxygen bond, k_OH is the bond force constant, and r₀ is the equilibrium bond length.

• Angle energy:

The energy term related to the angle between the hydrogen–oxygen–hydrogen atoms is represented by a harmonic oscillator potential as well. The formula for the angle energy is as follows:

$$E_{angle}({\theta }_{\mathrm{HOH}})={\displaystyle \frac{1}{2}}{k}_{\mathrm{HOH}}{({\theta }_{\mathrm{HOH}}-{\theta }_0)}^2$$

(2)

where θ_HOH is the angle of the hydrogen–oxygen–hydrogen bond, k_HOH is the angle force constant, and θ₀ is the equilibrium angle.

• Van der Waals Potential:

In the TIP3P model, the van der Waals potential energy term describes the attractions and repulsions between molecules [14]. It is typically represented by the Lennard-Jones potential. However, in the TIP3P model, the van der Waals potential primarily functions to maintain the intermolecular distances between water molecules. This van der Waals potential does not include the hard sphere diameter parameter because the TIP3P model simulates only the intermolecular interactions of water, without involving the hard sphere diameter.

The potential energy function of the TIP3P water molecule model integrates the above three energy terms. These parameters are adjusted and optimized to enable the model to accurately describe the properties and interactions of water molecules. This model is widely used in many molecular dynamics simulations because it can simulate the properties of water, such as density, solubility, and phase transition behaviors, with a high degree of accuracy. As for the potential for Na, Cu, and Cl, we implement CHARMM potential function to describe the interactions between them, which is widely applied in much of the research [15,16,17,18].

2.2. Modeling of Ion Solution Evaporation

We use Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS, version: stable_29 August 2024) to investigate the impact of various conditions on the evaporation of ionic solutions, this study established multiple molecular dynamics simulations under different conditions, as detailed in

Table 1. Molecular Dynamics Simulation Settings for the Evaporation of Ionic Solutions.

Model	Initial Concentration [mol/L]	Heating Temperature [K]
Dilute NaCl Solution	0.527	700
Dense NaCl Solution	5.27	700
Dilute CuCl2 Solution	0.527	700
Dense CuCl2 Solution	5.27	700
High-Temperature Dense NaCl Solution	5.27	700
Low-Temperature Dense NaCl Solution	5.27	400
Dense NaCl Small Droplet	5.27	700
Dense NaCl Large Droplet	5.27	700

:

In terms of preparation, we first set up the solvent system by determining the number of solvent molecules required for the simulation. This calculation is based on the desired volume of the system and the concentration of solute molecules we aim to achieve. Once the solvent system was prepared, the appropriate number of solute molecules was added to the system to achieve the desired concentration. After this, the system was equilibrated under high temperature at 1000 K. During this initial stage, we employed the NPT ensemble. The NPT ensemble refers to a simulation condition where the N is the number of particles, P is the pressure, and T is the temperature. In this ensemble, both the temperature and pressure are controlled, allowing the volume of the system to fluctuate to reach a stable state while maintaining constant temperature and pressure conditions. This helps the system relax, and ensures the uniform distribution of solute molecules within the solvent.

Once the system was equilibrated at high temperature, it was gradually cooled down to room temperature to mimic typical experimental conditions. The cooling step ensures that the system transitions to a more stable state appropriate for molecular dynamics simulations at standard conditions. During the actual simulation, we used the NVT ensemble. In the NVT ensemble, N refers to the number of particles, V is the volume, and T is the temperature, with the volume of the system held constant. This ensemble maintains a constant temperature throughout the simulation by using a thermostat, which allows us to study the system’s behavior under constant volume and temperature conditions. This is particularly useful for simulating the system at room temperature while studying the effects of temperature on the evaporation dynamics of ionic solutions.

3. Results and Discussion

3.1. Influence of Temperature on Evaporation of Ionic Solutions

The molecular dynamics simulations represented in Figure 1 offer a detailed visual account of the evaporation process of an ionic solution under two distinct thermal conditions. The temperature effect on the evaporation is evident when comparing the series of simulation snapshots at 400 K (left) and 700 K (right). At the lower temperature of 400 K, the sequence of images illustrates a relatively steady configuration of the solution with marginal reductions in volume as the simulation progresses. The snapshots from the initial to the final stages reveal a gradual decrease in the number of liquid molecules, corresponding to a measured rate of evaporation. This observation is consistent with the lower kinetic energy available to the molecules at 400 K, which only permits a fraction of molecules, those with sufficient energy, to escape the liquid phase.

Conversely, the simulation conducted at 700 K (right in Figure 1) presents a starkly different scenario. Early in the sequence, there is a noticeable increase in the activity within the vapor phase, indicative of a heightened rate of molecular evaporated from the liquid surface. As time progresses, there is a clear and significant reduction in the liquid bulk, emphasizing the accelerated rate of evaporation at this elevated temperature. The increased kinetic energy at 700 K facilitates a larger proportion of molecules to acquire the requisite energy to overcome intermolecular attractions and transition into the gas phase.

The effect of temperature on the evaporation process can be further dissected by examining the density and distribution of molecules in the gas phase. At 400 K, the vapor above the liquid surface remains sparsely populated throughout the simulation, suggesting a balance between the evaporation and condensation processes. However, at 700 K, there is a dense and progressively expanding collection of molecules in the vapor phase, signifying a dominant evaporation process with reduced condensation, consistent with the Clausius–Clapeyron relation, which describes the exponential increase of vapor pressure with temperature.

Furthermore, a detailed analysis of the simulation at 700 K reveals the onset of a rapid depletion of the liquid phase, accompanied by the formation of a non-uniform concentration of ions in the residual liquid. This non-uniformity may be indicative of complex interactions between the evaporating solvent and the solute, which can lead to a heterogeneous distribution of ions and potentially the initiation of nucleation sites for crystal formation.

Figure 2 provides a density contour plot which represents the density evolution of an ionic solution during the evaporation process over time, with the horizontal axis marking time in picoseconds (ps), and the vertical axis representing the height of the solution (angstroms). The color gradient indicates the density of the solution normalized to the maximum of the solution density, ranging from low density (blue) to high density (red).

At the start of the evaporation process (left side of the plot), the density is uniformly high across the solution height, as indicated by the consistent warm colors. This uniformity suggests that, initially, the solution is in a stable state with a homogenous distribution of ions and solvent molecules. As time progresses to the right, we observe a gradient forming from top (blue) to bottom (red), which indicates that the density at the top of the solution decreases, while it remains higher at the bottom. The transition from warm to cool colors in the upper portion of the contour plot illustrates the reduction in density as the solvent molecules evaporate. This effect creates a density gradient due to the loss of the more volatile components, presumably the solvent, from the surface of the solution.

The gradual shift in color towards the middle section of the contour from a uniform warm color to a stratified pattern of warm and cool colors indicates a continuous evaporation process, with the solution becoming less dense at the top due to the solvent molecules leaving the liquid phase. The persistence of high density at the bottom suggests that the ions and possibly some solvent molecules remain, potentially leading to a supersaturated region or the formation of a concentrated solution or even precipitate. Towards the end of the simulation (far right), the density at the top has significantly decreased, as indicated by the broad blue region, which suggests that the rate of solvent loss is high and that a substantial amount of solvent has evaporated. The warm colors confined to the bottom of the plot indicate that a small, highly dense portion of the solution remains, possibly a brine or saturated solution, where no further evaporation can occur without the removal of solute or an increase in temperature or other conditions to re-initiate the evaporation.

Figure 3 illustrates the effect of temperature on the evaporation rate (measured in ${\displaystyle \frac{\mu \mathrm{L}}{\mathrm{s}}}\times {\mathrm{m}\mathrm{m}}^2$). The evaporation rate increases with the rising temperature, as depicted by the bar chart. At lower temperatures (400 K and 500 K), the evaporation rate is negligible, but at 600 K, it begins to rise significantly. By 700 K, the evaporation rate shows a marked increase, indicating a rapid rise as the temperature escalates. As the temperature increases, the exponential dependence of the equation predicts a rapid increase in vapor pressure. Since the evaporation rate is directly influenced by the vapor pressure (higher vapor pressure leads to faster evaporation), the steep rise in the evaporation rate at higher temperatures (600 K to 700 K) aligns with this principle. The graph illustrates the non-linear nature of this relationship, as predicted by the Clausius–Clapeyron equation.

The above simulations provide compelling visual evidence for the substantial influence of temperature on the evaporation dynamics of ion solutions. At the elevated temperature of 700 K, the process is markedly more vigorous, resulting in a faster transition of the solution to the gaseous phase. These results underscore the importance of temperature as a pivotal factor in the evaporation process.

3.2. Effect of Concentration on Evaporation

The relationship between the solute concentration and the evaporation rate in the saline solution is critical in understanding the behavior of such systems, particularly when considering the formation of solid residues post-evaporation and the efficiency of processes such as crystal growth and material drying.

Figure 4 provides a visual representation of the evaporation process at different CuCl₂ concentrations. In the dilute CuCl₂ solution (Figure 4, left side), ions are uniformly dispersed, allowing the evaporation process to proceed evenly, resulting in a uniformly distributed residue. By contrast, the denser CuCl₂ solution (Figure 4, right side) exhibits significant ion clustering as the solvent evaporates, leading to the formation of distinct ion-rich regions. These clusters suggest that interactions between the ions become more pronounced at higher concentrations, which not only affects the rate of evaporation but leads to an uneven distribution of the remaining solid residue. The formation of ion clusters and a concentrated layer at the air–solution interface may also hinder further solvent transport and evaporation, as evidenced by the snapshots that show the evolution of these clusters over time.

The clustering observed in denser solutions may also lead to the formation of a concentrated layer at the air–solution interface, which could act as a barrier to evaporation and solvent transport. This barrier effect becomes more evident in the snapshots from the dense solution, where the formation of large clusters and the resulting crust can be seen as the process progresses. These observations highlight the complexity of the evaporation process in ionic solutions, where factors such as ion concentration not only influence the rate of evaporation but dictate the distribution and morphology of the salt residue. Such an understanding has significant implications for the optimization of industrial drying processes and the manufacturing of materials where the control of crystal size and morphology is essential.

The results from Figure 4 underscore the importance of controlling solution conditions to achieve desired outcomes in evaporation processes. They also suggest that, beyond a certain concentration threshold, the evaporation rate is hampered, which is crucial information for industries where drying and crystallization processes are fundamental, such as in the production of pharmaceuticals or desalination technologies. Further research is necessary to quantitatively describe these observations and to incorporate them into predictive models for the evaporation of ionic solutions.

The results in Figure 5 reveal a clear inverse relationship between the NaCl concentration and the evaporation rate. At low concentrations, the evaporation rate is highest. However, as the concentration increases, the evaporation rate decreases significantly. This trend highlights how higher NaCl concentrations hinder water evaporation. This behavior is explained by the vapor pressure lowering, a colligative property. Dissolved NaCl ions interact with water molecules, forming hydration shells that reduce the number of free water molecules available for evaporation. As the concentration increases, these ion–water interactions intensify, further suppressing evaporation. The nonlinear nature of the decline, particularly at higher concentrations, reflects the cumulative effects of hydration and the increasing density of the dissolved ions. The temperature and concentration effect on the evaporation is close to the experimental study [19].

3.3. Effects of Ions on Solution Evaporation

The evaporation of ionic solutions is a critical phenomenon with profound implications for various scientific and industrial processes. The molecular dynamics simulations depicted in the provided figures serve as a cornerstone for examining the impact of ionic species on the evaporation process. Figure 6 offers a sequential view of the evaporation progression for both salts at a consistent temperature of 700 K.

The evaporation process captured in Figure 6 elucidates the dynamic behavior of these ionic solutions under thermal stress. Initially, both solutions present a homogeneous mixture of ions and solvent. As the temperature sustains at 700 K, solvent molecules progressively vacate the system, leaving behind an increasing concentration of ions. The snapshots distinctly show that CuCl₂ experiences a more dramatic structural evolution during evaporation than NaCl. This can be attributed to the stronger hydration shells formed around the Cu²⁺ ions, which require more substantial energy input to disassemble, slowing down the rate of evaporation and leading to a higher propensity for the formation of clusters.

The intricacies of these clusters reveal much about the non-uniform distribution of ions in the evaporating CuCl₂ solution, suggesting a departure from the ideal solution behavior expected in dilute conditions. Such deviations have considerable ramifications for the understanding of nucleation and crystal growth processes, particularly in industrial settings where the purity and form of crystalline products are paramount.

In assessing the final products after evaporation, as shown in Figure 7, it is apparent that the nature of the ions involved profoundly influences the morphology of the resulting structures. The NaCl structure displays a relatively open and regular lattice, reflecting the simplistic and symmetric ionic interactions characteristic of monovalent ions. Conversely, the CuCl₂ structure exhibits a more compact and disordered arrangement, likely due to the increased Coulombic interactions associated with divalent Cu²⁺ ions. These interactions not only lead to a denser ion pack but may result in a more complex crystal lattice, as ions navigate a landscape of potential energy that is substantially altered by the presence of a multivalent cation.

The investigation of the evaporation behavior of ionic solutions through MD simulations provides valuable perspectives on the role of ionic species in dictating the kinetics and morphology of crystal formation. The ability to predict and control such processes is instrumental in advancing both theoretical understanding and practical applications in materials science and environmental technology. The academic significance of these findings lies in their potential to refine the theoretical framework that describes the evaporation of ionic solutions. In practice, the insights gained from these molecular dynamics simulations can inform the optimization of processes like the fabrication of nanomaterials and thin films, where control over the evaporation stage is crucial to achieving the desired material properties. Additionally, these results highlight the necessity of considering the individual characteristics of ions in environmental models, where the evaporation of saline waters can influence ecosystem dynamics.

3.4. Shape Effect on the Solution Evaporation

The shape of nanostructures significantly impacts boiling by enhancing the heat transfer, thereby controlling the bubble dynamics. They also influence nucleation, promoting stable bubble formation and reducing dry-out risks. These effects are crucial for improving boiling efficiency and stability in advanced thermal systems, making shape-engineered nanostructures vital for applications like heat exchangers, electronics cooling, and energy systems. In this subsection, we investigate the shape effects of nanostructures on the evaporation, as shown in Figure 8.

The molecular dynamics simulation results depicted in Figure 8 illustrate the thin-film boiling process on a nanostructured surface, shedding light on the atomistic mechanisms of bubble nucleation, growth, and vapor formation. At the initial stage, as shown in Figure 8a, the liquid layer, rendered as transparent, remains stable atop the nanostructured substrate (orange). At this point, the system is in equilibrium, and thermal energy has not yet overcome the intermolecular forces binding the liquid molecules, resulting in negligible vapor formation. The nanostructured surface begins to exert its influence by enhancing localized thermal gradients and providing preferential sites for nucleation due to its increased surface area and irregular geometry.

As the simulation progresses to Figure 8b, the influence of the nanostructured substrate becomes evident as thermal energy input initiates bubble nucleation near the solid–liquid interface. Atoms in close proximity to the nanostructures experience higher localized temperatures due to the efficient transfer of heat from the substrate. The atomistic mechanism involves the weakening of intermolecular forces between the liquid molecules, particularly at high-energy contact points with the nanostructure, where nanoscale cavities and peaks act as nucleation sites. These irregularities lower the energy barrier for phase transition, allowing vapor cavities to form in the liquid.

By Figure 8c,d, bubble growth becomes increasingly pronounced as the vapor phase expands. The nanostructure promotes rapid heat transfer, accelerating the evaporation process. The cavities and peaks enhance the surface wettability and capillary forces, facilitating liquid replenishment and sustaining nucleation sites. At the molecular level, atoms in the liquid near the substrate gain sufficient kinetic energy to overcome cohesive forces and escape into the vapor phase. This leads to a rapid phase transition and the formation of interconnected vapor pathways, as observed in the simulations. The nanostructured geometry supports the separation of bubbles and minimizes the coalescence of vapor pockets, ensuring a more uniform vapor distribution.

At the later stages, depicted in Figure 8e,f, the vapor phase dominates the liquid film as boiling intensifies. The nanostructure’s role in enhancing boiling efficiency becomes clear: its geometric features not only provide abundant nucleation sites but sustain efficient heat transfer due to the intimate contact between the solid and liquid phases. The formation of a vapor layer near the nanostructure reduces thermal resistance, allowing heat to propagate rapidly into the liquid film. Simultaneously, the nanostructure’s surface texture aids in disrupting the formation of insulating vapor layers, thereby maintaining high heat flux.

The atomistic mechanism underlying this process is closely tied to the thermal motion of atoms and their interactions at the solid–liquid interface. Nanostructures amplify localized heating effects, reducing the activation energy required for evaporation. The snapshots in Figure 8 demonstrate the progressive destabilization of the liquid film, where vapor continuously replaces liquid molecules in the high-energy zones. The combined effects of nanostructure-enhanced nucleation, the rapid vapor phase propagation, and the efficient heat transfer account for the observed boiling behavior.

In summary, the results highlight the critical role of nanostructures in thin-film boiling. Their ability to lower nucleation barriers, enhance heat transfer, and sustain liquid replenishment creates an ideal environment for efficient boiling. This study provides valuable insights into the atomistic mechanisms governing phase transitions and underscores the potential of nanostructured surfaces for thermal management applications, such as heat exchangers and electronic cooling systems.

The density contour plot in Figure 9 provides a detailed visualization of the thin-film boiling process on a nanostructured surface over time, illustrating the atomistic dynamics of phase transition and vapor–liquid interactions. The vertical axis represents the density distribution within the system, while the horizontal axis captures the time evolution of the boiling process. The color gradient, ranging from red (high density, liquid phase) to blue (low density, vapor phase), highlights the progressive evaporation of the thin liquid film and the formation of a vapor region as boiling evolves.

At the initial stages of the simulation, the density profile remains relatively uniform and high near the nanostructured surface (bottom red region), indicative of a stable liquid layer. However, as the time progresses beyond approximately 20 ps, a clear density gradient begins to form at the liquid–vapor interface. This gradient, transitioning from red to yellow and green regions, signifies the onset of vaporization driven by localized heating. The nanostructures facilitate this phase change by enhancing thermal conduction and creating localized hotspots where liquid molecules gain sufficient kinetic energy to escape into the vapor phase.

The upper region of the contour plot (blue) represents the vapor phase, which gradually expands over time, particularly after 40 ps. This expansion reflects the sustained and accelerated evaporation of the liquid film. The formation of a distinct liquid–vapor boundary, evident from the gradual color transition, underscores the role of the nanostructured surface in promoting efficient heat transfer. The nanoscale cavities and protrusions act as nucleation sites, reducing the energy barrier for bubble formation and ensuring continuous vapor release. Furthermore, the high surface area-to-volume ratio of the nanostructure enhances the contact area between the liquid and solid, further improving thermal energy distribution.

As the boiling process advances, the vapor phase becomes increasingly prominent, as seen in the upper portion of Figure 9 where the density drops to near-zero values (blue region). This trend correlates with the depletion of the liquid phase near the surface, evidenced by the thinning of the red region over time. The persistence of intermediate density regions (yellow to green) suggests the presence of transient vapor clusters or bubbles undergoing dynamic coalescence and detachment. These regions also reflect the non-uniformity of vapor generation caused by the nanostructures, where localized hotspots drive heterogeneous evaporation.

The plot reveals that the nanostructured surface not only enhances the rate of evaporation but maintains a stable liquid–vapor interface, preventing the formation of insulating vapor layers that could otherwise impede heat transfer. The continued liquid replenishment near the surface, facilitated by capillary effects induced by the nanostructure, supports sustained nucleation and evaporation. This is particularly critical in thin-film boiling, where maintaining an efficient heat exchange is paramount to avoid thermal runaway or dry-out conditions.

3.5. Size Effect on the Ion Solution Droplet

The impact of droplet size on the evaporation process of the CuCl₂ solution droplets is a subject of interest due to its implications for material science and industrial applications. Figure 10 showcases the CuCl₂ solution droplets of varying sizes, providing a visual representation of the evaporation progression. The CuCl₂ droplet evaporation rate is close to the experiment research [20]. In smaller droplets, the evaporation appears to be faster, likely due to the increased surface area-to-volume ratio, which facilitates a higher rate of solvent molecule escape. Conversely, larger droplets exhibit a slower evaporation process, as the proportion of surface area to volume is smaller, reducing the number of solvent molecules that can escape per unit time.

As the evaporation proceeds in these larger droplets, a transition occurs from a state of uniform distribution of ions to one where clustering and aggregation are evident. This aggregation is indicative of the increasing influence of interionic forces as the solvent evaporates, which can lead to diverse morphologies in the resultant solid, depending on the droplet size. The concentration gradient within the droplets also plays a critical role. As the solvent evaporates, the solute concentration near the droplet surface increases, potentially leading to the formation of a crust of solute that may further inhibit the evaporation process. This crust formation is more pronounced in larger droplets due to the longer diffusion path for solute molecules to reach the surface.

Our simulations show that smaller droplets exhibit a faster evaporation rate compared to larger droplets. This is primarily due to the higher surface area-to-volume ratio in smaller droplets, which facilitates a greater rate of solvent molecule escape. In smaller droplets, the larger surface area allows for more solvent molecules to escape per unit of time, leading to a faster overall evaporation process. As the solvent evaporates, ions become more concentrated near the surface, potentially forming a concentrated layer or crust that can affect the rate of evaporation in the later stages.

By contrast, larger droplets experience a slower evaporation rate. The smaller surface area-to-volume ratio in larger droplets means fewer solvent molecules are available at the interface for evaporation at any given time. Additionally, as the solvent evaporates, the concentration of ions in the droplet increases, and the formation of ion clusters may occur more gradually, affecting the overall evaporation process. These clusters can further slowdown the evaporation rate by forming barriers that hinder solvent diffusion to the surface.

Furthermore, the concentration gradient within the droplet becomes more pronounced in larger droplets, leading to a more substantial build-up of ions near the surface, which may eventually result in a solid crust forming, further impeding evaporation. In smaller droplets, the crust forms more quickly due to the more immediate concentration of solute, but the faster evaporation rate minimizes the impact on the overall process. These findings underline the importance of droplet size in controlling the evaporation dynamics of ionic solutions and offer valuable insights into the optimization of drying processes, particularly in industrial applications such as thin-film fabrication and material synthesis.

4. Conclusions

Based on the comprehensive analysis and findings presented in this research, it is evident that the evaporation of ion solutions is a complex process influenced by multiple factors, including temperature, ion concentration, the nature of the ions involved, and the surface area-to-volume ratio of the solution. Molecular dynamics simulations have provided profound insights into the atomic and molecular interactions that govern the evaporation process, offering a detailed understanding that surpasses the limitations of traditional experimental methods.

The influence of temperature on the evaporation rate is significant, with higher temperatures accelerating the process due to increased kinetic energy, which facilitates a greater proportion of molecules to transition into the gas phase. The concentration of the ion solution also plays a crucial role, where higher concentrations lead to ion clustering and affect the uniformity of the evaporation process. Furthermore, the type of ions present influences the evaporation dynamics and the morphology of the residual crystal structures, with divalent ions, such as Cu²⁺, demonstrating more complex interactions compared to monovalent ions, like Na⁺. Lastly, the droplet size effect, illustrated through the CuCl₂ solution droplets, highlights how the surface area-to-volume ratio impacts evaporation rates, with smaller droplets evaporating faster due to a higher ratio facilitating solvent escape.

This study not only enhances our understanding of the molecular dynamics of ion solution evaporation but establishes a robust theoretical foundation for future research and practical applications in fields such as industrial production, water resource management, and ecological preservation. The insights gained from this research have the potential to inform the optimization of processes in nanomaterial synthesis, the manufacturing of thin films, and environmental management practices, thereby contributing to the advancement of environmental protection and sustainable development. The findings underscore the necessity of a multidimensional approach to studying ion solution evaporation, emphasizing the importance of considering the intricate interplay between various factors that influence the process.