Simulation-based molecular force on the surface of gallium-based liquid metals

Abstract

Owing to their excellent properties, gallium-based liquid metal materials have been continuously discovered and innovated for various applications, but the self-confined oxide products formed on their surfaces have always been the key to elucidating their nature. In order to study the nature of the reaction and reveal its mechanism, we utilized sophisticated molecular dynamics simulations to meticulously examine their behaviors in an aqueous setting, focusing on four gallium oxide derivatives—two types of gallium oxide (Ga₂O₃, GA1, trigonal-shaped; Ga₂O₃, GA2, linear-shaped), gallium oxide hydroxide (GaOOH, GA3), and gallium hydroxide (Ga(OH)₃, GA4). Based on previous studies, as a proof of concept, the intricate dynamics of gallium derivatives and their interactions with azo dye (Ponceau S) under variable solution conditions are pivotal for developing advanced material applications. A key aspect of our study is that we explored the temperature sensitivity of these interactions, revealing that although van der Waals and electrostatic forces between the gallium species and Ponceau S decrease with increasing temperature, the dye continues to aggregate at the heart of these clusters. Of particular note are the distinct preferences in the binding hierarchy among the gallium derivatives to Ponceau S, with GA2 emerging as the most dominant due to its strong polar interactions, closely followed by GA4, which engages through hydrogen bonding. Conversely, GA1 and GA3 display limited involvement in clustering, suggesting a lack of strong affinity for the dye. Additionally, we discovered the critical role of ions in mediating these interactions, especially the unexpected attraction of GA4 and GA1 towards sodium ions (Na⁺), challenging traditional assumptions and potentially reconfiguring gallium species distribution and aggregate stability. Chloride ions (Cl⁻) showed no such selectivity, reinforcing the need for careful consideration of ionic environments to understand the clustering phenomena. In conclusion, our findings emphasize the temperature-dependent and ion-influenced nature of gallium derivative interactions with Ponceau S, underscoring the importance of environmental factors in the design and performance prediction of gallium-based materials. This study is of great significance for revealing the force of interface reactions on liquid metal surfaces, setting the stage for future inquiries into other physicochemical aspects and opening avenues for exploiting controlled aggregation pathways in liquid environments for innovative material synthesis.

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1 Introduction

Similar to aluminum, gallium exhibits a well-known propensity to spontaneously form a surface layer of gallium oxide (Ga₂O₃), which acts as a passivating shield against further oxidation, penetrating the bulk metal, and as a specific interface reaction platform.^1–3 Typically, an ultrathin oxide layer (∼2 nm) formed at the gallium-based liquid metal-ambient interface under the action of oxygen and water (the oxygen content reaches the ppm level) acts as a natural barrier against further oxidation.^4,5 The surface oxide layer spontaneously passivates due to the diffusion barrier of Ga₂O₃ and the accompanying decay of the interfacial electric field. The introduction of electrical, chemical, electrochemical, mechanical, or ultrasonic stimuli, along with changes in reaction parameters, such as composition, temperature, and time, can accelerate oxide formation.^6–8 Studies have shown that the presence of oxides is a double-edged sword. For example, to deliberately tailor fundamental physicochemical properties, previous studies have shown that precise control of liquid metal (LM) oxidation endows the material with distinctive interfacial features, adjustable surface tension, controllable wettability, enhanced mechanical strength, catalytic activity, and selective adsorption, which are vital for meeting specific application demands.^1,9,10 Therefore, investigating the formation and properties of LM oxidation is essential for a deeper understanding of its effects on the composition, structure, and characteristics of gallium-based liquid metals. This inherent property is essential for the material's resistance to corrosion and the preservation of its desirable characteristics in various applications.^11–15 When exposed to different environmental conditions or subjected to specific chemical treatments, gallium can yield various derivative compounds: gallium oxide (Ga₂O₃, GA1, and trigonal-shaped), gallium oxide (Ga₂O₃, GA2, and linear-shaped), gallium oxide hydroxide (GaOOH and GA3), and gallium hydroxide (Ga(OH)₃ and GA4).^16,17 The selection of these four gallium derivatives allows for a comprehensive investigation into the diverse behaviors and potential applications of gallium-based materials under varying solution conditions, providing valuable insights into the complex interplay between gallium derivatives and specific molecules, such as Ponceau S (PS).¹⁸ However, the reaction mechanism is not well understood, which is valuable for functional design applied in various areas.

The molecular species under investigation, GA1, GA2, GA3, and GA4 (Scheme 1), are predominantly insoluble in water.¹⁹ This characteristic implies that when introduced into an aqueous environment at substantial concentrations, these gallium derivatives tend to separate from the solvent and aggregate, ultimately leading to precipitation. This insolubility is likely due to the strong ionic or covalent bonding within the gallium compounds, which hinders their dissolution into the polar water matrix and prevents the formation of stable hydration shells around individual particles. Based on previous studies, as a proof of concept, Ponceau S (PS), a soluble red compound with many functional groups commonly used as a staining solution, was mixed with a liquid metal; consequently, the red color disappeared. This indicates that it readily dissolves in water, forming a homogenous solution in which the dye molecules are dispersed at the molecular level and are extensively hydrated. The interaction between the insoluble gallium derivatives and soluble Ponceau S presents an intriguing system in which the behavior of these two chemically distinct components becomes intertwined. When mixed, the gallium compounds are expected to precipitate, while Ponceau S remains in the solution. However, the presence of gallium derivatives can potentially influence the solubility of Ponceau S, either by interacting with the gallium derivatives or by altering the local solvation environment around the gallium species, thereby affecting their aggregation kinetics.

Scheme 1 Molecular configuration and force field of four gallium oxide derivatives (GA1/GA2/GA3/GA4).

This study specifically aims to elucidate the nature of the interactions between gallium derivatives and azo molecules, such as Ponceau S, recognizing the importance of understanding such complex interactions. To achieve this goal, molecular dynamics simulations were employed. This computational technique enables the exploration of atom-level details and the temporal evolution of the system, providing insights into the microscopic forces driving the association or dissociation of the components, the conformational changes in the PS upon interaction with the gallium derivatives, and the possible rearrangement of water molecules in the vicinity of the interacting species. By simulating the dynamics of the system over time, we can observe how the initially dissolved PS molecules interact with nascent or growing gallium precipitates, revealing the preferred binding sites, binding energies, and the effect of these interactions on the overall stability and organization of the gallium phases. Additionally, simulations can shed light on the role of solvent molecules in mediating these interactions, such as through hydrogen bonding, electrostatic effects, or steric hindrance. This study is meaningful for discovering the nature of liquid metal surface interface reactions and promoting environmental control and optimization in the applications of gallium-based liquid metals in fields such as biomedical engineering, flexible detection or environmental engineering.

2 Results and discussion

2.1 Behavior of the oxide layer on the surface of liquid gallium

The formation and behavior of the oxide layer on the surface of liquid gallium in water were simulated using a three-dimensional periodic box measuring 10 nm on each side. The simulation method through GROMACS is consistent with previous studies.^20–22 The initial setup of the simulation involved positioning four distinct gallium derivatives, including GA1, GA2, GA3, and GA4, within the box in a manner that approximated a thin oxide layer formed on the liquid gallium surface (Fig. 1 and Movie S1). These derivatives were arranged to occupy a central region of the box, mimicking their organization as an interfacial layer in the actual liquid-gallium-oxide system. However, upon commencement of the simulation, this initially structured layer rapidly disintegrated, with the gallium derivatives dispersing uniformly throughout the entire simulation volume over a relatively short timescale.

Fig. 1 GA1, GA2, GA3 and GA4 in solution. GA1s are red, GA2s are green, GA3s are blue, and GA4s are yellow, and water molecules are gray. GA1, GA2, GA3 and GA4 have 800 molecules each. (a) t = 0 ns of the oxidization layer simulation. (b) t = 1000 ns of the oxidization layer simulation. (c) t = 0 ns of the self-assembly simulation. (d) t = 1000 ns of self-assembly simulation.

To ensure that the observed distribution of the derivatives was not influenced by any inherent self-assembling tendencies or preferential interactions among them, additional simulations were conducted with the four derivatives randomly distributed within the same 10 nm cubic box. These randomized simulations served as control experiments, allowing investigators to assess whether the observed even distribution of the gallium derivatives was a result of their inherent properties or simply a consequence of the imposed initial configuration.

In these randomized simulations, no significant clustering or aggregation of the gallium derivatives was detected. This finding suggests that under the simulated conditions and within the timeframe of the simulations, the individual gallium oxide species do not exhibit strong tendencies to self-assemble or associate with one another beyond what would be expected from random encounters driven by thermal motion. Instead, they behave as relatively independent entities, diffusing freely and uniformly throughout the simulation space. They indicate that, under the conditions studied, the oxide layer is not maintained as a coherent, structured entity but rather exists as a collection of dispersed, individual gallium oxide species that are prone to rapid redistribution and do not exhibit pronounced self-assembly behavior.

2.2 Ponceau S on the surface under different pressures

The PS dye was incorporated into the simulation system alongside the previously described gallium derivatives (GA1, GA2, GA3, and GA4) to investigate their mutual interactions under varying pressure and temperature conditions. GAFF2 was used to describe the fore field between GAs and PS molecules, which is commonly used to simulate the force field of organic–inorganic hybrid molecules.^23–26 The inclusion of PS allowed for the examination of both van der Waals and electrostatic forces acting between the dye molecules and the gallium derivatives, which are fundamental in dictating the overall behavior and stability of the resulting aggregates.

Simulations were performed across a range of pressures (0.1 bar, 1 bar, and 10 bar). As shown in Fig. 2 and Movie S2–S4, it was observed that the nature of the interactions between the gallium derivatives and Ponceau S remained largely unchanged despite the variation in external pressure. This suggests that the relative strengths and orientations of the van der Waals force and the electrostatic forces were not significantly affected by the applied pressure variations. Notably, the simulations revealed the occurrence of significant clustering events, with the Ponceau S molecules consistently occupying the central positions within these clusters. This central localization of PS within the aggregates indicates a strong affinity between the dye and some of the gallium derivatives, likely driven by a combination of favorable van der Waals contacts and electrostatic complementarity between the respective molecular structures.

Fig. 2 10 × 10 × 10 nm box interaction energy between GAs and PS at different pressures; the RDF for GA1, GA2, GA3, and GA4 around the PS molecules with respect to different pressures. (a) Electrostatic interaction between GAs and PS at different pressures. (b) van der Waals interaction between GAs and PS at different pressures. (c) Total interaction (electrostatic interaction plus van der Waals interaction) between GAs and PS at different pressures. (d) RDF for GAs around PS molecules when the pressure is 0.1 bar. (e) RDF for GAs around PS molecules when the pressure is at 1.0 bar. (f) RDF for GAs around PS molecules when the pressure is 10.0 bar.

In addition to the qualitative observation of clustering behavior, the radial distribution function (rdf/RDF) was calculated to quantitatively assess the spatial distribution of the dye molecules and gallium derivatives within the simulation box. RDF is used to measure how particle density varies with distance from a reference species to provide critical insights into ion-specific interactions.²⁷ The results showed that the rdf patterns remained relatively constant under the different pressure conditions studied, indicating that the overall arrangement and spatial correlations between the Ponceau S dye and the gallium derivatives were not appreciably altered by changes in pressure.

In summary, the simulations demonstrated that the interactions between the gallium derivatives and PS dye were robust against variations in pressure, maintaining consistent van der Waals and electrostatic contributions. The dye consistently exhibited a strong propensity to cluster, occupying central positions within the aggregates, and this clustering behavior, along with the overall spatial organization of the system, as captured by the rdf, remained largely invariant under the tested pressure conditions.

2.3 Ponceau S on the surface at different temperatures

Contrary to the insensitivity of the gallium derivative-Ponceau S interactions to changes in pressure, the influence of temperature on these interactions was substantial. As the simulation temperature increased, a discernible decline in the strength and significance of both van der Waals and electrostatic interactions between the gallium derivatives and the Ponceau S dye was observed (Fig. 3 and Movie S5–S8). This attenuation of intermolecular forces can be attributed to the increased kinetic energy of the particles at elevated temperatures, leading to more frequent and energetic collisions, disrupting the stable arrangements and weakening the attractive interactions between the dye and the gallium compounds.

Fig. 3 10 × 10 × 10 nm box interaction energy between GAs and PS at different temperatures; the RDF for GA1, GA2, GA3, and GA4 around the PS molecules with respect to different temperatures. (a) Electrostatic interaction between GAs and PS at different temperatures. (b) van der Waals interaction between GAs and PS at different temperatures. (c) Total interaction (electrostatic interaction plus van der Waals interaction) between GAs and PS at different temperatures. (d) RDF for GAs around PS molecules when the temperature is 297 K. (e) RDF for GAs around PS molecules when the temperature is 310 K. (f) RDF for GAs around PS molecules when the temperature is 323 K. (g) RDF for GAs around PS molecules when the temperature is 336 K.

Despite the reduction in overall interaction strength, the simulations still revealed the presence of significant clustering, with Ponceau S molecules consistently occupying central positions within these aggregates. This persistent clustering behavior, even under increasingly unfavorable thermodynamic conditions, implies that the dye maintains a certain degree of specificity and selectivity in its interactions with gallium derivatives, allowing it to act as a nucleation point or core for the formation of these clusters, which could be used in molecular weaving techniques.²⁸ The central localization of PS within the aggregates suggests that, although weakened, the remaining van der Waals and electrostatic interactions are still sufficient to drive the assembly of the dye and gallium species into clustered structures, consistent with the experimental results.¹⁸

In line with the qualitative observation of clustering and the weakening of intermolecular forces, the rdf calculated for the system showed a decreasing trend as the temperature increased, reflecting the decreased ordering and structuring in the system owing to the elevated temperature. This decrease in the rdf further confirms the quantitative diminution of the spatial correlations and organization between the dye and the gallium compounds as the temperature increases.

In summary, although the interactions between the gallium derivatives and Ponceau S dye were found to be insensitive to changes in pressure, they exhibited a marked sensitivity to temperature variations. As the temperature increased, both van der Waals and electrostatic interactions between the dye and the gallium species weakened, but the dye still retained a strong tendency to cluster, occupying central positions within the aggregates. This clustering behavior, as well as the overall spatial organization of the system, as quantified by the decreasing rdf, diminished as the temperature increased, highlighting the temperature-dependent nature of the interactions and aggregate structures formed between Ponceau S and the gallium derivatives.

2.4 Interactions of PS on the surface of liquid gallium

As depicted in Fig. 4 and S1, and Movie S9, GA2 was found to exhibit the highest propensity to associate with PS, significantly outnumbering the occurrences of the other gallium species (GA1, GA3 and GA4) in proximity to the dye molecule. This preferential interaction of GA2 with PS is attributed to the strong polar interactions that occur between them. GA2's molecular structure appears to be particularly conducive to forming multiple polar interactions with Ponceau S owing to its unique length. Specifically, a single GA2 molecule can engage in two simultaneous polar interactions with two sulfuric groups present on the same PS dye molecule. This dual interaction capability likely contributes to the high observed frequency of GA2 molecules in close association with Ponceau S, making GA2 the dominant species in the clustering process involving the dye. It is noteworthy that the study deliberately focuses on a physiologically/biologically relevant temperature range (297–336 K), which is far below the thermal transition thresholds for gallium oxide derivatives (∼1273.2 K). Within this regime, classical non-reactive force fields (GAFF2/AMBER) are fully justified: covalent bond dissociation, which these models cannot simulate, is negligible, as the temperatures are far below gallium oxide decomposition thresholds, ensuring the maintained structural integrity of all gallium derivatives.

Fig. 4 Interaction energy changes with temperature with respect to each of the GAs to PS molecules and how they differ in the simulation. (a) Different GAs interact differently with PS molecules with variations in temperature. (b) GA1's distribution within the GAs and PS mixture simulation system at t = 0 ns (left) and t = 1000 ns (right). (c) GA4's distribution within the GAs and PS mixture simulation system at t = 0 ns (left) and t = 1000 ns (right).

GA4, although not as prevalent as GA2 in terms of its association with PS, occupies the second position in terms of its distribution around the dye. The primary mode of interaction between GA4 and PS is through hydrogen bonding, which occurs primarily with the sulfuric groups and the imine moiety of the dye molecule. These hydrogen bonds between GA4 and PS, although less numerous than the polar interactions observed for GA2, still contribute significantly to the overall clustering of gallium derivatives (GA1, GA2 and GA3) with Ponceau S.

In contrast to GA2 and GA4, GA1 plays a relatively minor role in the clustering process. Although GA1 interacts with the PS dye to some extent, its contribution to the formation of aggregates is evidently less substantial. This reduced involvement of GA1 in the clustering may be due to its molecular characteristics, which may not facilitate strong or multiple interactions with the functional groups present in the Ponceau S dye. Finally, GA3 demonstrates almost negligible participation in the clustering with the PS dye. Simulation data show that GA3 molecules are essentially randomly distributed throughout the system, indicating a lack of specific affinity or a strong interaction with the dye.

In summary, the simulation results reveal a clear hierarchy in the clustering behavior of the gallium derivatives (GA1–4) with Ponceau S. GA2 exhibits the strongest and most abundant interactions, followed by GA4, while GA1 plays a lesser role, and GA3 is virtually absent from the clustering process. The nature of these interactions varies, with GA2 engaging in multiple polar interactions, GA4 forming hydrogen bonds, GA1 participating to a lesser extent through less effective interactions, and GA3 displaying virtually no specific affinity for the dye.

2.4.1 Ion influence. The role of ions in the clustering behavior of the gallium derivatives and Ponceau S dye is highlighted as a crucial factor in the simulation results (Fig. 5). Specifically, the presence and distribution of sodium (Na⁺) and chloride (Cl⁻) ions were found to significantly impact the organization and interactions within the system. All simulations contained both Na⁺ and Cl⁻ ions (0.15 M NaCl). The rdf for Na⁺ and Cl⁻ ions exhibits stark differences, indicating their distinct influence on the clustering of the gallium species. For Na⁺, sharp RDF peaks at ∼2 Å from GA1 and GA4 revealed preferential coordination with their polar oxygen atoms, driving spatial redistribution of these gallium species toward Na⁺ rich zones and directly facilitating their incorporation into dye-mediated clusters. In stark contrast, Cl⁻ exhibited no significant RDF peaks near any gallium derivative, with a near–uniform profile indicating passive dispersion as a nonspecific counterion. Thus, although Cl⁻ is uniformly dispersed to screen electrostatic interactions, Na⁺ is selectively accumulated near GA1 and GA4 via coordination with polar oxygen sites. Unexpectedly, Na⁺ ions, being positively charged, were observed to exert a strong attractive effect on GA4 and GA1, accumulating substantial numbers of these gallium derivatives in their immediate vicinity. This phenomenon may be attributed to the polar oxygen atoms present in the molecular structures of GA4 and GA1, which form favorable electrostatic interactions with the positively charged sodium ions, leading to the preferential localization of GA4 and GA1 near these cations. This demonstrates that Na⁺ specificity dominates over Cl⁻ in modulating gallium derivative distribution, even in a complete ionic environment.

Fig. 5 RDF with respect to sodium ions (Na⁺) and chlorine ions (Cl⁻), and the sodium ions interact with GAs and PS molecules. GAs and PS molecules are in a stick model; sodium ions are purple balls, and the yellow dashed line indicates polar interactions between those atoms. (a) RDF for GAs and PS molecules with respect to sodium ions. (b) RDF for GAs and PS molecules with respect to chlorine ions. (c) GA1 and GA4 interact with sodium ions and have relatively close coordination. (d) Sodium ions interact with sulfate and hydroxy groups on the PS molecule. (e) Sodium ions interact with the sulfate group on the PS molecule only. (f) Sodium ions interact with the benzene ring on the PS molecule.

The ability of Na⁺ to selectively attract GA4 and GA1 suggests a complex interplay between the ionic environment and the polar oxygen within gallium derivatives. This selective interaction could potentially modulate the overall clustering dynamics, as the presence of Na⁺ ions effectively redistributes GA4 and GA1 in the system, potentially altering their relative proximity to the Ponceau S dye and influencing the overall aggregate structures formed (Fig. 6).

Fig. 6 Sodium ions (Na⁺) play a role in clustering. Na⁺ ions are purple balls, and PS molecules are represented by a stick model. (a) Na⁺ distribution when t = 0 ns of the mixture simulation. (b) Na⁺ distribution when t = 1000 ns of the mixture simulation. (c) Na⁺ in conjunction with the PS molecule distribution when t = 1000 ns of the mixture simulation.

In contrast to Na⁺, the Cl⁻ ions, being negatively charged, do not display a similar preferential association with any particular gallium derivative. Their rdf profiles do not show marked accumulation of GA1, GA2, GA3, or GA4, suggesting a more uniform distribution or weaker specific interactions with these species. This difference in behavior between Na⁺ and Cl⁻ ions underscores the importance of considering the ionic environment and the specific ion–species interactions when examining the clustering behavior of the gallium derivatives and Ponceau S dye. Furthermore, this dichotomy—Na⁺ acting as a selective aggregator through electrostatic complementarity with gallium oxides, while Cl⁻ merely screening bulk charges—underscores the pivotal yet distinct roles of cations versus anions in modulating liquid metal interfacial behavior, which is essential for rational ionic environment design.

In summary, ions, particularly Na⁺ ions, play a pivotal role in shaping the clustering of gallium derivatives and their interactions with the Ponceau S dye (Fig. 7). The positive Na⁺ ions demonstrate a surprising capacity to attract GA4 and GA1 through electrostatic interactions with their polar oxygen atoms, leading to a non-uniform distribution of these gallium species and potentially influencing the overall aggregation patterns. This highlights the complex interplay between ionic forces, polar interactions, and the specific molecular structures of gallium derivatives in determining clustering behavior in the presence of Ponceau S dye and an ionic environment. Furthermore, to eliminate the influence of spatial factors, we compared the intermolecular forces in a 5 × 5 × 5 nm box and 10 × 10 × 10 nm box (Fig. S2–S4). The simulation results indicate that the spatial distance had almost no impact on the interaction forces between the oxide layer and the molecules.

Fig. 7 PS molecules interact with GA2s. Both sodium and PS molecules are represented by the stick model. (a) GA2 interacts with the sulfate group on the PS molecule. (b) GA2 interacts with the sulfate and imine groups on the PS molecules. (c) One GA2 interacts with two sulfate groups on the same PS molecule. (d) GA2 interplays with two PS molecules, which intertwine together.

3 Discussion

The selected gallium compounds, including gallium oxide (Ga₂O₃) in trigonal (GA1) and linear (GA2) forms, gallium oxide hydroxide (GaOOH, GA3), and gallium hydroxide (Ga(OH)₃, GA4), exhibit a common insensitivity to pressure changes while demonstrating a marked sensitivity to temperature fluctuations. Molecular dynamics simulations have been instrumental in unraveling the nature of these interactions, offering atomic-scale insights into the underlying mechanisms and the role of solvent molecules in mediating these processes.

3.1 Temperature–dependent interactions

A key finding of our investigation is the profound influence of temperature on the interactions between gallium derivatives and Ponceau S. As the temperature increases, both van der Waals and electrostatic forces between the dye and gallium species weaken, but the dye persists in clustering behavior, occupying central positions within the aggregates. The radial distribution function (rdf) revealed a decreasing trend with increasing temperature, signifying a decline in the spatial organization and correlation between the dye and gallium compounds. This temperature sensitivity highlights the dynamic nature of the aggregate structures formed, with higher temperatures promoting a more disordered arrangement.

3.2 Preferential binding and interaction hierarchies

The study identified distinct preferences and hierarchies in the binding of gallium derivatives to Ponceau S. GA2 emerged as the dominant species in dye clustering, exhibiting the highest propensity for association owing to its strong polar interactions with the dye. Its unique molecular structure, particularly its length, allows for simultaneous engagement with multiple sulfuric groups on the dye molecule, contributing to its pronounced frequency of occurrence near the dye. GA4, although less abundant than GA2, occupied the second position in terms of its distribution around Ponceau S. Its primary mode of interaction involves hydrogen bonding with the dye's sulfuric groups and imine moiety, which, although fewer in number compared to GA2's polar interactions, still significantly contribute to the overall clustering process.

GA1, in contrast, played a relatively minor role in the clustering, suggesting that its molecular characteristics might not favor strong or multiple interactions with the dye's functional groups. Finally, GA3 demonstrated a nearly negligible involvement in the clustering, with its molecules being randomly distributed in the system, indicating a lack of specific affinity for Ponceau S.

3.3 Ions are influential

A key point of interest is the differential impact of Na⁺ and Cl⁻ ions. The attraction of GA4 and GA1 gallium derivatives toward Na⁺ ions challenges conventional expectations based solely on charge, revealing a more nuanced mechanism driven by the electrostatic affinity between the positively charged ions and the polar oxygen atoms in GA4 and GA1. This selective aggregation mediated by Na⁺ potentially alters the spatial arrangement of gallium species, which could have implications for the formation and stability of aggregates and their interaction dynamics with Ponceau S dye. Cl⁻ ions do not exhibit discernible preferences for any specific gallium derivative, displaying a more uniform distribution or engaging in weaker interactions. This disparity between the behaviors of Na⁺ and Cl⁻ ions accentuates the necessity of meticulous consideration of the ionic milieu and specific ion–molecule interactions in understanding and predicting clustering phenomena.

It is noteworthy that although bulk gallium oxide adopts crystalline structures, our simulations focus on nanoscale derivatives (GA1–GA4) in aqueous environments, where they behave as discrete molecular entities. This approach captures the dominant local interactions governing dye adsorption and aggregation. Nevertheless, future studies modeling extended crystalline surfaces could provide additional insights into epitaxial growth or lattice-directed assembly.

Moreover, the simulations model gallium oxide derivatives (GA1–GA4) as discrete species in water, representing the dynamic oxide layer shed from liquid gallium surfaces. Although this approach captures the dominant interactions governing dye aggregation, it does not explicitly include the liquid gallium substrate without considering the effect of liquid gallium. The existence of a liquid gallium substrate may enhance the specific interaction when liquid gallium produces more oxide/delivering Ga ions after oxides are depleted by connecting with PS. This simplification without a liquid gallium substrate is justified because (i) experimental evidence confirms that oxide layers mediate gallium–dye interactions¹¹ and (ii) the simulation of high mobility of liquid gallium atoms requires quantum-mechanical methods or specialized force fields, which are infeasible for system sizes and timescales needed to study aggregation under aqueous conditions. Thus, future studies should explore coupled Ga/Ga-oxide models to assess substrate-induced oxide restructuring.

4 Conclusion and future perspectives

In conclusion, this study investigated the temperature-sensitive interactions between gallium derivatives and azo dye molecules (Ponceau S), revealing preferential binding hierarchies and the distinct roles of individual gallium species in the clustering process. The pronounced influence of temperature on these interactions underscores the importance of considering environmental conditions when designing or predicting the performance of gallium-based materials in applications involving Ponceau S or similar dyes. Future studies could explore the effects of other physicochemical factors, such as pH, ionic strength, or the presence of additional ligands, on the interactions between gallium derivatives and Ponceau S. In the future, we will extend the simulation time scales or employ alternative computational methods or extend the crystalline surface of gallium oxide on liquid metal to provide deeper insights into the long-term behavior and potential self-assembly pathways of the gallium oxide species in liquid environments. This study is of great significance for revealing the force of interface reactions on liquid metal surfaces, setting the stage for future inquiries into other physicochemical aspects and opening avenues for exploiting controlled aggregation pathways in liquid environments for innovative material synthesis. It is hoped that this study will promote environmental control and optimization in the applications of gallium-based liquid metals in fields such as biomedical engineering, flexible detection or environmental engineering.

5 Methods

5.1 Molecular dynamics (MD) simulation and analysis

The GAs and PS molecules were solvated by a TIP3P solvent with 0.15 M Na⁺/Cl⁻ ions. Ions and TIP3P water were described by the AMBER FF14SB force field,²⁹ while the force field between GAs and PS molecules was described using GAFF2,²⁶ which was constructed by GaussView6;³⁰ the geometry was optimized by Gaussian09W,³¹ and the charge distribution was replaced by the RESP charge after Gaussian09W optimization. The initial structure of the oxidation layer simulation system was constructed by PACKMOL,³² and all other systems were constructed using GROMACS. All MD simulations were performed using GROMACS-2020.1.³³ Energy minimization was performed for 5000 steps by applying the steepest descent algorithm, with a van der Waals radius of 0.9 nm and a coulomb radius of 0.9 nm. The H-bond was constrained by the LINCS algorithm. Equilibration was performed with a 0.125 ns NVT simulation at different temperatures: 297 K, 310 K, 323 K, and 336 K. For the different temperature simulations, the NVT temperature was at 297 K, and for the different pressure simulations, the NVT temperature was at 297 K. The cutoff scheme used Verlet and the Nosé–Hoover Langevin thermostat for temperature coupling. Finally, the production NPT simulations were performed at different temperatures and pressures for 1000 ns with a timestep of 0.002 ps using the Nosé–Hoover Langevin thermostat and the Parrinello-Rahman barostat with a cutoff of 0.9 nm for van der Waals and short-range electrostatic interactions. The particle mesh Ewald algorithm was used to treat long-range electrostatic interactions. The covalent bonds containing hydrogen atoms were constrained using the LINCS algorithm. Data analysis, including radial distribution function (RDF), root mean square deviation (RMSD), radius of gyration (Rg), and energy interaction, was carried out using GROMACS and MDTraj.³⁴

Note

Simulation framework and force fields

1. MD (Molecular Dynamics): Core computational method simulating atom movements over time.

2. TIP3P: Rigid 3-site water model used for solvation (AMBER/GROMACS compatible).

3. AMBER FF14SB: Protein/nucleic acid force field for ions and solvent (Standard AMBER parametrization).

4. GAFF2 (General AMBER Force Field 2): Force field for organic molecules (GA/PS parametrization).

5. RESP charge (Restrained ElectroStatic Potential): Quantum chemistry-derived atomic charges (Gaussian09 → AMBER workflow).

Software tools

1. GaussView6: Molecular structure builder (pre-simulation design).

2. Gaussian09W: Quantum chemistry software for geometry optimization/charge calculation (pre-processing).

3. PACKMOL: Initial system packing tool (oxidation layer construction).

4. GROMACS: Primary MD engine for simulation/analysis (energy minimization → production run).

5. MDTraj: Trajectory analysis library (RDF/RMSD/Rg calculations).

Simulation algorithms and parameters

1. Steepest descent: Energy minimization algorithm (GROMACS implementation).

2. LINCS (Linear Constraint Solver): Bond constraint algorithm for H-bonds (enables a 2 fs timestep in GROMACS).

3. Verlet cutoff: Neighbor-search scheme for efficient non-bonded interactions (GROMACS default).

4. Nosé–Hoover Langevin thermostat: Hybrid temperature control method (NVT/NPT ensembles in GROMACS).

5. Parrinello–Rahman barostat: Pressure coupling algorithm (NPT ensemble in GROMACS).

6. PME (Particle Mesh Ewald): Long-range electrostatics solver (cutoff = 0.9 nm; GROMACS/AMBER standard).

Simulation ensembles

1. NVT (Canonical ensemble): Constant Number-Volume-Temperature (equilibration phase).

2. NPT (Isothermal-isobaric ensemble): Constant Number-Pressure-Temperature (production phase).

Analysis metrics

1. RDF (Radial Distribution Function): Spatial correlation analysis (e.g., solvation shells).

2. RMSD (Root Mean Square Deviation): Structural stability metric (backbone atom drift).

3. Rg (Radius of Gyration): Molecular compactness measure (folding/unfolding analysis).

4. Energy interaction: Non-bonded energy calculations (van der Waals/electrostatics).

Author contributions

X. Wang and J. Liu conceived the idea, designed and executed the experiments, analyzed the data, and wrote the article. G. Li, Z. Wang and Y. Zhou provide useful platform and resources. Z. Liu, Y. Guo and Y. Fan assisted in the analysis and reviewed the article. All authors discussed the experiments and gave consent for this publication.

Conflicts of interest

The authors declare no conflict of interest.

Data availability

The data supporting this article have been included as part of the SI. Supplementary information is available. See DOI: https://doi.org/10.1039/d5ta03843j.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 52405315), Shandong Provincial Natural Science Foundation (ZR2024QE197), the Research Start-up Funds for Recruited Talents of University of Health and Rehabilitation Sciences (KWXZ 2023026) and Funded with the Marine Natural Products R&D Laboratory, Qingdao Key Laboratory (QDSHYTRCWYJKF 2024-01). The authors would like to extend their heartfelt thanks for the guidance by Dr Jing Liu, professor at Tsinghua University, for the revision of the article.

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Footnote

† Co-first authors.

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