Effect of Hydrophobic Alkyl Chain Length on the Interfacial Adhesion Performance of Emulsified Asphalt–Aggregate Systems

Abstract

To elucidate the mechanisms by which the hydrophobic hydrocarbon chain length of emulsifiers and the surface properties of aggregates influence the adhesive performance at the emulsified asphalt–aggregate interface, this study employed molecular dynamics simulations to construct interface models. Key parameters, including relative concentration, diffusion coefficients, and interfacial adhesion work, were systematically analysed to reveal the intrinsic effects of imidazoline-type emulsifier chain length and aggregate type on interfacial behaviour. The results indicate that increasing the hydrophobic chain length of the emulsifier suppresses the adsorption of emulsified asphalt at the aggregate interface. The diffusion coefficients of both emulsifier and asphalt molecules initially increase and subsequently decrease with chain length, with the non-polar asphalt components (aromatics and saturates) exhibiting greater sensitivity to chain length variations. Moderate extension of the hydrophobic chain enhances interfacial adhesion work, whereas exceeding the optimal chain length reverses this trend, weakening adhesion. Aggregate surface properties exert a significant influence on interfacial behaviour. Compared with the acidic SiO₂ (0 0 1) surface, the basic CaCO₃ (1 0 4) surface exhibits lower peak relative concentrations of emulsified asphalt, reduced sensitivity to variations in emulsifier chain length, lower molecular diffusion coefficients, and stronger interactions with asphalt molecules, resulting in superior interfacial adhesion. This study provides a molecular-level theoretical basis for the targeted design of emulsifier structures and the efficient adaptation of emulsified asphalt to different aggregate systems.

1. Introduction

Emulsified asphalt, as a low-carbon and energy-efficient material, has been widely applied in road engineering, offering both economic and environmental advantages, including ease of low-temperature construction, significant energy savings, and extended pavement service life [1,2,3,4]. It is a water-in-oil emulsion in which asphalt serves as the dispersed phase and water as the continuous phase, with emulsifiers adsorbing at the water–asphalt interface to stabilise asphalt dispersion at ambient temperature [5]. In practice, emulsified asphalt is typically mixed with mineral aggregates to produce asphalt mixtures for cold-mix, cold recycling, and surface treatment applications [6,7], with macroscopic properties such as mechanical strength, water stability, and high-temperature performance largely determined by the adhesion and coating effectiveness between the emulsified asphalt and aggregates [8].

At the microscopic level, the adhesive performance of the emulsified asphalt–aggregate interface is governed by a combination of interfacial properties and molecular interactions [9]. Among these, the role of the emulsifier at the interface is particularly critical. As a typical surfactant, the polar head group of the emulsifier interacts with water or active sites on the aggregate surface, while the hydrophobic hydrocarbon chain inserts into the asphalt phase, forming an ordered adsorption layer at the interface. This interfacial adsorption layer reduces the water–asphalt interfacial tension, facilitating asphalt wetting and spreading on the aggregate surface, while simultaneously enhancing interfacial stability through electrostatic repulsion and steric hindrance, thereby preventing detachment of the asphalt film in aqueous environments.

Beyond the emulsifier, aggregate type and its physicochemical surface properties also play a crucial role in the adhesive performance of emulsified asphalt [10,11]. Different aggregates exhibit significant variations in chemical composition, surface charge characteristics, and polar functional groups, which directly influence their interfacial interactions with emulsified asphalt [12]. Studies have shown that carbonate aggregates, such as limestone, exhibit markedly higher interfacial adhesion strength with asphalt than acidic aggregates, such as granite or quartz, which are primarily composed of SiO₂ [13,14]. Under ambient conditions, the influence of aggregate type on adhesion is notably greater than that of asphalt type [15]. Moreover, under humid or combined heat–moisture conditions, acidic aggregates are more prone to debonding and stripping than basic aggregates [16], further highlighting the significant impact of aggregate surface properties on emulsified asphalt adhesion.

Molecular dynamics (MD) simulation provides an efficient approach to investigate the dynamic evolution of materials at the molecular scale and has been widely applied in the field of road materials. This method not only enables the study of how modifiers affect asphalt viscosity, interfacial adhesion, and the interaction mechanisms between asphalt and aggregates [17,18], but also allows detailed analysis of molecular diffusion and distribution at interfaces, thereby elucidating the microscopic mechanisms underlying adhesion [19]. In recent years, numerous studies have employed MD simulations to explore interfacial behaviour in emulsified asphalt systems. Liu et al. [20] used MD to examine the adhesion mechanisms and characteristics of emulsified asphalt residue–aggregate interfaces under varying emulsifier contents. Zhu et al. [21] investigated the effect of cationic emulsifier alkyl chain length on the demulsification of cationic emulsified asphalt on CaCO₃ surfaces. Kong et al. [22,23] combined MD modelling and macroscopic experiments to study mechanisms at aggregate interfaces, quantifying the role of phenyl functional groups at the molecular level and assessing the influence of hydrocarbon chain length on adhesion between emulsified asphalt and acidic aggregates. Zhang et al. [24] employed MD simulations to examine asphalt–basalt and asphalt–steel slag interfacial adhesion. Meng et al. [25] provided atomic-scale insights into asphalt–aggregate adhesion and failure behaviour. Wang et al. [26] constructed MD models of emulsified asphalt–aggregate interfaces with varying water contents to investigate the effect of moisture on adhesion. Sun et al. [27] used MD to study molecular interactions between matrix and aged asphalt binders with silica and calcite. Collectively, these studies confirm that emulsified asphalt adhesion to aggregates is closely related to emulsifier molecular structure and aggregate surface properties, with molecular dynamics simulation serving as a critical tool for probing their relationships and underlying mechanisms at the microscopic level.

In view of the aforementioned background, this study employed molecular dynamics (MD) simulations to systematically investigate the influence of hydrophobic hydrocarbon chain length of imidazoline-type emulsifiers on the adhesion and adsorption behaviour of emulsified asphalt on CaCO₃ (1 0 4) and SiO₂ (0 0 1) surfaces. The findings provide theoretical guidance for the optimisation of emulsified asphalt systems and hold significant practical value for enhancing the quality of road engineering construction.

2. Materials and Methods

2.1. Base Asphalt Molecular Model

Asphalt is a complex multicomponent mixture composed of tens of thousands of hydrocarbons with varying molecular weights and structural characteristics [28,29]. In recent years, extensive research has been conducted both domestically and internationally to achieve precise microscopic characterisation of asphalt composition and structure. The most widely used molecular models of asphalt include the average molecular model, the three-component model, and the four-component model. In this study, based on Corbett’s SARA fractionation method, representative compounds from the four fractions—saturates, aromatics, resins, and asphaltenes—were selected as the fundamental molecular units for constructing the asphalt molecular model [30,31,32].

Using Materials Studio (MS), representative molecules of the four asphalt fractions were constructed as fundamental molecular units, and their initial geometries were optimised to verify structural plausibility. Based on this, the Construction tool in the Amorphous Cell (AC) module of MS was employed to fill the four types of molecules into a cubic simulation box with periodic boundary conditions according to the predefined component ratios (

Table 1. Number of molecules in the asphalt molecular model.

Molecular Name	Molecular Formula	Molar Mass (g/mol−1)	Number Added	Proportion (%)
Saturate	C22H46	310.61	5	7.3
Aromatics	C46H50S	634.966	7	20.8
Resin	C59H85NOS	856.395	3	12
Asphaltene	C149H177N3O2S2	2106.19	1	9.9

), thereby establishing the asphalt molecular model (Figure 1). It should be noted that the molecular model in this study was entirely constructed based on literature data and the SARA fractionation method, without direct experimental verification via microscopic imaging techniques such as AFM, SEM, or TEM. The plausibility of the model was confirmed through geometry optimization and comparison with reported molecular characteristics in the literature.

2.2. Emulsified Asphalt Molecular Model

The interfacial behaviour between emulsified asphalt and aggregates is largely governed by the action of emulsifiers. Emulsifier molecules contain both hydrophilic and lipophilic groups, which preferentially adsorb at the asphalt–water interface to form a stable interfacial adsorption layer. Under the influence of this layer, the asphalt phase is dispersed as droplets within the continuous aqueous phase, allowing the emulsified asphalt to come into contact with mineral aggregate surfaces. Upon contact, the emulsifier molecules act as a critical mediator linking the asphalt phase, aqueous phase, and aggregate surface; their interfacial configuration and molecular orientation directly influence the spreading, wetting, and adhesion of asphalt on the aggregate surface, thereby determining the interfacial interaction characteristics and adhesion stability of the emulsified asphalt–aggregate system.

Building on previous studies, this work selected long-chain aliphatic imidazoline-type emulsifiers to construct molecular models [33]. These emulsifiers are synthesised via amidation–cyclisation of tetraethylenepentamine with organic acids. Their hydrophilic groups (polar imidazoline rings) form hydrogen bonds with water molecules, enhancing interfacial compatibility, while the hydrophobic groups (long-chain alkanes) interact via van der Waals forces with the hydrophobic structures of asphalt molecules, anchoring the emulsifier at the surface of asphalt droplets. To distinguish molecular structural variations, the C_nN_m nomenclature is adopted, where n denotes the number of carbon atoms in the long alkyl chain and m the number of nitrogen atoms in the hydrophilic group; the corresponding emulsified asphalt system is referred to as the C_nN_m emulsified asphalt system. Molecular models of the long-chain aliphatic imidazoline-type emulsifiers with different alkyl chain lengths, together with water molecules, are shown in Figure 2.

Based on the aforementioned molecular models of imidazoline-type emulsifiers and water, the emulsified asphalt molecular model was constructed using the Amorphous Cell (AC) module in Materials Studio (MS). The model was configured with a molar ratio of emulsifier to water of 15:85 [34], while the molar ratio of the emulsifier–water solution to asphalt was set at 5:5. A cubic simulation box with periodic boundary conditions was generated to represent the infinite extent of the real system, ensuring that the simulation results are representative. The detailed composition of the emulsifier–water solution molecular model is listed in

Table 2. Model molecular composition of emulsifier aqueous solutions.

Composition	Molecular Name	Molecular Formula	Molar Mass (g/mol−1)	Number Added
C7N5	Emulsifier	C16H35N5	297.491	5
	Water molecule	H2O	18.015	502
C9N5	Emulsifier	C18H39N5	325.545	5
	Water molecule	H2O	18.015	502
C11N5	Emulsifier	C20H43N5	353.599	5
	Water molecule	H2O	18.015	502
C13N5	Emulsifier	C22H47N5	381.653	4
	Water molecule	H2O	18.015	502
C15N5	Emulsifier	C24H51N5	409.707	4
	Water molecule	H2O	18.015	502

.

The optimisation procedure for the emulsified asphalt molecular model and the parameters used in the molecular dynamics simulations were kept consistent with those of the asphalt molecular model, thereby enhancing the reliability and consistency of the results. The schematic diagram of the molecular model structure of C₁₁N₅ emulsified asphalt, constructed based on the number of molecules in Table 1 and Table 2, is shown in Figure 3.

2.3. Aggregate Molecular Model

In road engineering materials, mineral aggregates are complex inorganic mixtures with diverse sources, primarily composed of oxides such as SiO₂, CaO, and Fe₂O₃. Given the complexity and variability of actual aggregate mineral compositions, molecular dynamics simulations typically employ single-mineral crystal models to represent aggregates equivalently, enabling analysis of their interfacial interactions with asphalt systems. Based on existing studies and model applicability, this work selected SiO₂ and CaCO₃ as representative acidic and basic aggregates, respectively, and employed the widely used SiO₂ (0 0 1) and CaCO₃ (1 0 4) crystal planes to construct aggregate surface models for molecular dynamics analysis of emulsified asphalt–aggregate interfacial behaviour. The lattice parameters of the aggregate unit cells used are listed in

Table 3. Lattice Constants of CaCO₃ and SiO₂.

Aggregate	Lattice Constant
	a/Å	b/Å	c/Å	α/°	β/°	γ/°
CaCO3	4.99	4.99	17.061	90	90	120
SiO2	4.193	4.193	5.4052	90	90	120

.

During the construction of the aggregate models, the Cut tool in Materials Studio (MS) was used to cleave the mineral unit cells to generate specific crystal planes, with the number of layers set to control model thickness. It should be noted that cleavage of the SiO₂ crystal surface produces unsaturated atomic structures. If used directly in molecular dynamics simulations, these may undergo unrealistic interactions with water molecules or oxygen atoms, compromising the accurate representation of quartz aggregate interfacial behaviour under service conditions. Therefore, it is necessary to repair the broken bonds on the SiO₂ crystal surface to obtain a structurally stable and chemically reasonable aggregate surface model.

On this basis, the constructed crystal plane models were periodically extended in the x and y directions to achieve the model dimensions required for interfacial studies. A 30 Å vacuum layer was then introduced perpendicular to the crystal plane to mitigate the influence of periodic boundary conditions on the interface system, converting the original two-dimensional crystal plane into a three-dimensional supercell suitable for molecular dynamics simulations. The final aggregate unit cell molecular models are shown in Figure 4.

2.4. Emulsified Asphalt–Aggregate Interfacial Model

Based on the emulsified asphalt molecular models and aggregate unit cell models constructed in Section 2.1, Section 2.2 and Section 2.3, the emulsified asphalt–aggregate interface models were assembled using a “lower aggregate–upper emulsified asphalt” spatial stacking approach. To mitigate potential interference from periodic boundary conditions on interfacial microstructure and molecular dynamics behaviour, a 50 Å vacuum layer was added above the emulsified asphalt layer. A schematic of the final emulsified asphalt–aggregate interface molecular model is shown in Figure 5.

2.5. Simulation Parameters and Validation

2.5.1. Parameter Settings

Molecular simulation techniques can reveal the static structures and dynamic diffusion behaviours of substances at the microscopic scale, with atomic model construction and the choice of force field being critical [35]. The COMPASS force field, widely used in molecular simulations, accurately describes various interactions within molecular systems, making it well suited for simulating molecular aggregation and geometry optimisation during initial model construction [36]. Accordingly, the COMPASS III force field was employed throughout all simulations in this study.

It should be noted that periodic boundary conditions (PBCs) were imposed in the x, y, and z directions to minimize the boundary effects on the simulation results.

The constructed base asphalt molecular model was first subjected to geometry optimisation to eliminate unreasonable initial configurations. During geometry optimisation, the system temperature was set to 298 K, the non-bonded interaction cutoff radius was 15.5 Å, and energy minimisation was carried out using the conjugate gradient algorithm. The Coulombic electrostatic interactions and van der Waals interactions were calculated using the Ewald summation method and the Atom-Based method, respectively. After geometry optimisation, a 300 ps molecular dynamics pre-equilibration was performed to ensure the stability and reliability of the base molecular structure. The time step was set to 1 fs, and the simulation was conducted under the NPT ensemble. During the simulation, the Andersen thermostat and Berendsen barostat were employed to maintain the system temperature and pressure at 298 K and 1.0 × 10⁻⁴ GPa, respectively.

For the constructed emulsified asphalt/aggregate interface model, geometry optimisation was likewise performed using the same parameters and computational settings as those applied to the base asphalt model. Subsequently, pre-equilibration, annealing, and final equilibration were carried out in sequence. First, a 200 ps pre-equilibration was conducted under the NPT ensemble to eliminate the influence of the initial configuration. Then, the system was subjected to five heating–cooling annealing cycles between 298 K and 500 K to release internal stresses and promote structural relaxation. After annealing, a 1000 ps final equilibrium simulation was performed under the NPT ensemble to ensure that the system reached a stable state. The pre-equilibration and final equilibration processes of the emulsified asphalt/aggregate system adopted the same simulation parameters and settings as those used for the base asphalt molecular pre-equilibration.

2.5.2. Model Validation

To validate the constructed asphalt molecular model, density and glass transition temperature were selected as key evaluation indicators. Density is a critical physical parameter reflecting asphalt’s brittleness and thermal stability [37], while T_g denotes the characteristic temperature at which asphalt transitions from a glassy to a viscoelastic state, strongly correlating with its low-temperature mechanical behaviour and in-service stability, thus serving as an important criterion for assessing the reasonableness and accuracy of the molecular model [38]. Based on this approach, molecular dynamics simulations were conducted to examine the evolution of density over simulation time (Figure 6a) and to determine the model’s glass transition temperature (Figure 6b). As shown in Figure 6a, density fluctuations of the asphalt model gradually converged after 50 ps and stabilised at an equilibrium value of 1.011 g·cm⁻³, within the typical range of 1.01–1.04 g·cm⁻³ for real asphalt materials, indicating that the system had essentially reached thermodynamic equilibrium after 300 ps of dynamics. From Figure 6b, the glass transition temperature of the model was determined to be 253.3 K, falling within the temperature range of 238.15 K to 258.15 K, which is typical for asphalt transitioning from the glassy to viscoelastic state. These results demonstrate that the constructed asphalt molecular model is both reasonable and reliable, providing a robust foundation for subsequent construction of emulsified asphalt systems and simulation of interfacial interactions.

Based on the validated reliability of the asphalt molecular model through density and glass transition temperature, it is essential to further verify the thermodynamic equilibrium of the constructed emulsified asphalt–aggregate interface model to ensure the scientific validity of subsequent molecular dynamics simulations. In MD simulations, system temperature and total energy are the primary indicators of equilibrium, with their stability directly determining the credibility of interfacial behaviour analyses. Figure 7 presents the evolution of temperature and total energy of the interface model over a 1000 ps simulation. As shown, the system’s total energy converges clearly without significant drift, while the temperature fluctuates slightly around the set value. This indicates that, following 1000 ps of equilibration, the system has reached a stable thermodynamic equilibrium, confirming the model’s reliability and providing a solid foundation for quantitative analysis of interfacial adhesion, adsorption, and diffusion behaviours.

3. Results

3.1. Effect of Hydrophobic Hydrocarbon Chain Length on the Interfacial Distribution of Emulsified Asphalt–Aggregate Systems

Relative molecular concentration is an important parameter for characterising the spatial distribution of molecules within the interfacial region of the model. The position of the peak in the concentration profile quantitatively reflects the degree of molecular enrichment in that region. By analysing the number density of molecules along different spatial coordinates, this parameter provides a direct visualisation of molecular aggregation and spatial distribution at the interface, offering foundational data for further analysis of interfacial interaction mechanisms. The relative molecular concentration is calculated using Equations (1) and (2):

$$C_A={\displaystyle \frac{L_A}{D_A}}$$

(1)

$$D_A={\displaystyle \frac{M_A\times n_A}{N_a\times V}}$$

(2)

In the equations, $C_A$ denotes the relative concentration, while $D_A$, $L_A$, $M_A$, and $N_a$ represent the actual concentration, the local density, molecular weight, and number of molecules of species A, respectively. $N_a$ and $V$ correspond to Avogadro’s constant and the system volume.

In this study, molecular dynamics simulations were used to analyse the relative molecular concentration distribution of emulsified asphalt molecules along the z-axis (i.e., the vertical direction of the simulation box) in the emulsified asphalt–aggregate systems. Five time points—200 ps, 400 ps, 600 ps, 800 ps, and 1000 ps—were selected to systematically examine the spatiotemporal evolution of asphalt molecules across different interface models. Based on these results, the effects of the hydrophobic hydrocarbon chain length of imidazoline-type emulsifiers and aggregate surface properties on the distribution behaviour of emulsified asphalt molecules were further evaluated. The resulting relative molecular concentration profiles are presented in Figure 8 and Figure 9, with the boxes indicating the positions of the curve peaks.

Analysis of Figure 8 shows that the vertical coordinate range of 0–15 Å corresponds to the CaCO₃ (1 0 4) aggregate region, where the relative concentration of emulsified asphalt is zero. Within the range of hydrophobic hydrocarbon chain lengths studied, the relative concentration of emulsified asphalt molecules near the CaCO₃ (1 0 4) surface increases significantly, forming a single concentration peak. This indicates that the active structures in emulsified asphalt preferentially interact with the CaCO₃ (1 0 4) surface, resulting in adsorption and the formation of a stable monolayer. As the vertical distance from the aggregate surface increases, the relative concentration gradually stabilises, reflecting the reduced influence of aggregate surface functional groups and the transition of molecules to a freely distributed state.

Moreover, the adsorption peak of emulsified asphalt on the CaCO₃ (1 0 4) surface decreases progressively with increasing emulsifier hydrophobic chain length, indicating a negative correlation between asphalt adsorption and chain length on this basic aggregate. This behaviour arises because long-chain emulsifier molecules tend to form micellar structures through intermolecular hydrophobic interactions, reducing the effective contact probability of individual emulsifier molecules with the aggregate surface and thus lowering asphalt adsorption. Among the five emulsifier systems examined, the C₇N₅ emulsified asphalt system exhibits the highest concentration peak, reaching 5.5 at a vertical coordinate of 17.2 Å. When the hydrophobic alkyl chain length of the emulsifier increases from C₇ to C₉, the adsorption concentration peak decreases most significantly, with a reduction of approximately 9.1%. On average, for every additional two carbon atoms in the hydrophobic chain, the corresponding adsorption peak decreases by about 6.0%.

Figure 9 shows the relative concentration profiles of emulsified asphalt molecules on the SiO₂ (0 0 1) surface. As observed, the vertical coordinate range of 0–38 Å corresponds to the SiO₂ (0 0 1) aggregate region, where no asphalt molecules are present and the relative concentration is zero. For emulsified asphalt systems with different chain lengths, distinct concentration peaks appear on the SiO₂ (0 0 1) surface. Consistent with the trend observed on the CaCO₃ (1 0 4) surface, the peak relative concentration of emulsified asphalt on the SiO₂ (0 0 1) surface decreases with increasing hydrophobic chain length of the emulsifier, dropping from 7.8 for the C₇N₅ system to 5.4 for the C₁₅N₅ system. On average, the adsorption peak decreases by approximately 8.6% for every two-carbon increase in the hydrophobic chain length. These results further confirm the influence of the hydrophobic hydrocarbon chain length of imidazoline-type emulsifiers on the adsorption behaviour of emulsified asphalt at the aggregate interface, and indicate that this effect is consistent across aggregates with different surface characteristics.

By comparing the relative concentration distributions of emulsified asphalt molecules on CaCO₃ (1 0 4) and SiO₂ (0 0 1) surfaces, it is evident that, for systems with the same hydrophobic hydrocarbon chain length, both the spatial distribution patterns and adsorption intensities differ significantly between aggregates with distinct surface characteristics. Specifically, the z-axis concentration profile of asphalt on the CaCO₃ (1 0 4) surface exhibits a clearly stabilised concentration region, whereas the concentration distribution on the SiO₂ (0 0 1) surface shows more pronounced oscillatory behaviour. Quantitative analysis further indicates that the peak relative concentrations on the CaCO₃ (1 0 4) surface are considerably lower than those on SiO₂, and the average decrease in peak concentration with increasing emulsifier chain length is smaller on CaCO₃ (1 0 4) than on SiO₂.

Mechanistically, for acidic aggregates such as SiO₂ (0 0 1), van der Waals interactions are the primary force governing the adsorption of emulsified asphalt at the interface. Increasing the hydrophobic hydrocarbon chain length of the emulsifier significantly strengthens both intermolecular and molecule–aggregate van der Waals interactions, rendering the SiO₂ surface highly sensitive to changes in chain length. In contrast, CaCO₃ (1 0 4), as a basic aggregate, exhibits a more complex interaction mechanism with asphalt molecules, potentially involving a combination of electrostatic forces, hydrogen bonding, and other interactions, resulting in a comparatively moderate response to variations in emulsifier chain length. This distinction further elucidates the coupled influence of aggregate surface chemistry and emulsifier molecular structure on the adsorption behaviour at the asphalt–aggregate interface.

Upon contact with the aggregate surface, the polar head groups of emulsifier molecules interact with functional groups on the aggregate. Driven by these interfacial forces, the molecular arrangement within the emulsified asphalt system undergoes reorganisation, causing active asphalt molecules to separate from the originally stable colloidal dispersion and orientationally adsorb onto the aggregate surface, completing the asphalt demulsification process. Analysis of the relative concentration distributions of emulsified asphalt on CaCO₃ (1 0 4) and SiO₂ (0 0 1) surfaces indicates that by 800 ps, both the peak concentrations and their spatial positions have stabilised, demonstrating that the demulsification process is essentially complete [14]. By 1000 ps, asphalt demulsification is fully achieved, forming a structurally stable adsorption layer at the emulsified asphalt–aggregate interface, providing a microscopic structural basis for the subsequent enhancement of interfacial bonding strength.

Figure 10 and Figure 11 illustrate the microscopic distribution of the four asphalt components on CaCO₃ (1 0 4) and SiO₂ (0 0 1) surfaces after demulsification. The results show that all four asphalt components exhibit distinct concentration peaks on both aggregate surfaces, confirming that demulsification is complete and that the asphalt molecules have successfully adhered to the aggregates. Mechanistically, the conjugated benzene rings in the aromatic fraction can undergo π–π stacking with conjugated groups or polar sites on the aggregate surface, enabling directional adsorption. Saturates, such as small-chain alkanes, can aggregate around the hydrophobic tails of emulsifier molecules via hydrophobic interactions and migrate with the emulsifier toward the aggregate surface. Polar functional groups in resins and asphaltenes (e.g., hydroxyl and carboxyl groups) can form hydrogen bonds, electrostatic interactions, or other intermolecular forces with either the polar head groups of the emulsifier or active sites on the aggregate surface, such as hydroxyl or carbonyl groups. These mechanisms collectively allow effective adsorption of all asphalt components, though the spatial positions, intensities, and shapes of the concentration peaks differ significantly among components. Furthermore, both CaCO₃ (1 0 4) and SiO₂ (0 0 1) are hydrophilic mineral aggregates, enabling water molecules to adopt various stable conformations at the interface. This indicates that, regardless of the hydrophobic chain length of the emulsifier, water molecules readily orient and form a continuous interfacial layer on the aggregate surface. The MD simulation results (Figure 10 and Figure 11) further confirm that water molecules stably adsorb on both aggregates, with their distribution closely linked to the chemical characteristics of the aggregate surfaces.

3.2. Effect of Hydrophobic Hydrocarbon Chain Length on the Interfacial Diffusion Behaviour of Emulsified Asphalt–Aggregate Systems

The diffusion coefficient is a key parameter characterising the dynamic activity of molecules within the interfacial region and plays a crucial role in studies of interfacial mechanisms at the molecular scale. Its value is typically derived from the Einstein diffusion equation and is closely related to molecular mobility: a larger diffusion coefficient indicates higher interfacial dynamic activity and faster molecular migration. The Einstein relation describes the diffusion behavior of particles in Brownian motion. It estimates the self-diffusion coefficient through the mean square displacement of particles over time. The diffusion coefficient is calculated using the following equation:

$$D=\underset{\mathrm{t}\to \mathrm{\infty }}{\lim }{\displaystyle \frac{1}{6Nt}}<{\sum }_{i=1}^N{|r_i\left(t\right)-r_i(0\left)\right|}^2>\approx {\displaystyle \frac{k}{6}}$$

(3)

In the equation, $D$ denotes the molecular diffusion coefficient, $N$ is the number of molecules in the simulation system, $t$ represents the elapsed time, $<$⋅$>$ denotes the ensemble average (or time average), $r_i\left(t\right)$ and $r_i\left(0\right)$ are the positions of particle $i$ at times $t$ and 0, respectively, and $k$ is the slope of the mean square displacement.

In the emulsified asphalt–aggregate interfacial system, the variation in diffusion coefficients for emulsified asphalt and emulsifier molecules is shown in Figure 12. As illustrated, both types of molecules exhibit the same trend: when the emulsifier’s hydrophobic hydrocarbon chain length ranges from 7 to 13 carbon atoms, the diffusion coefficients increase with chain length; however, when the chain length reaches 15 carbon atoms, the diffusion coefficients decrease.

The hydrophobic chain length of the emulsifier is a key factor affecting its hydrophilic–lipophilic balance (HLB). As the chain length increases, the interaction between the hydrophobic segments of the emulsifier and asphalt molecules becomes stronger, which facilitates the formation of a more ordered and stable interfacial structure at the water–asphalt interface. This structural enhancement improves local molecular mobility, leading to an increase in diffusion behavior. However, when the hydrophobic chain length becomes excessively long, the molecular chains tend to undergo folding and entanglement. This strengthens the van der Waals interactions between the emulsifier and asphalt molecules or the aggregate surface, thereby increasing interfacial adsorption constraints. Consequently, molecular motion is restricted, resulting in a decrease in the diffusion coefficients of both the emulsifier and the emulsified asphalt. Additionally, the difference between the diffusion coefficients of emulsified asphalt and the emulsifier on the same aggregate surface reflects the influence of chain length on the overall mobility of asphalt molecules. Furthermore, the self-diffusion coefficients of both emulsified asphalt and the emulsifier on the CaCO₃ (1 0 4) surface are generally lower than those on SiO₂ (0 0 1), indicating more restricted molecular motion, lower migration rates, and reduced mobility on the basic aggregate surface. This phenomenon highlights the effect of aggregate surface chemistry and interfacial interaction strength on asphalt diffusion behaviour. Specifically, the CaCO₃ (1 0 4) surface contains abundant Ca²⁺ active sites, which strongly interact electrostatically and coordinatively with the polar head groups of the emulsifier and polar asphalt components, significantly enhancing interfacial binding and limiting molecular mobility. In contrast, the SiO₂ (0 0 1) surface is primarily composed of Si–OH and Si–O–Si units, with weaker surface polarity, resulting in lower interfacial interaction with emulsifier and asphalt molecules and allowing greater molecular freedom, which is reflected in higher diffusion coefficients.

Further quantitative analysis of the diffusion coefficients reveals notable differences in sensitivity to hydrophobic hydrocarbon chain length between emulsifier and emulsified asphalt molecules. When the emulsifier’s hydrophobic chain length increases from 9 to 11 carbon atoms, the diffusion coefficient of the emulsifier exhibits the most pronounced change: rising by over 100% on the CaCO₃ (1 0 4) surface and by 75.6% on the SiO₂ (0 0 1) surface. This indicates that, within this chain length range, the mobility of emulsifier molecules is particularly sensitive to chain length. For emulsified asphalt molecules, the change in diffusion coefficients is also primarily concentrated within the 9–11-carbon-atom chain length range, with increases exceeding 38% on both aggregate surfaces. These findings demonstrate that structural variations in emulsifier molecules with shorter hydrophobic chains have a more significant impact on the overall migration ability of asphalt molecules.

In summary, the hydrophobic hydrocarbon chain length of the emulsifier and the chemical characteristics of the aggregate surface have a significant influence on the molecular mobility of the individual asphalt components. To further elucidate this mechanism, a targeted analysis of the diffusion coefficients of the four asphalt components and water molecules was conducted. The variation in diffusion coefficients for the asphalt components and water molecules is presented in Figure 13.

The analysis of diffusion coefficients in Figure 13 indicates that differences in the surface characteristics of CaCO₃ (1 0 4) and SiO₂ (0 0 1) aggregates significantly affect the mobility of polar asphalt components (asphaltenes and resins), whereas the motion of non-polar components (aromatics and saturates) is primarily governed by the hydrophobic hydrocarbon chain length of the emulsifier.

Specifically, the diffusion coefficients of asphaltenes and resins on the two aggregate surfaces exhibit opposite trends, likely reflecting the contrasting chemical properties of the aggregates. In contrast, the diffusion of aromatics and saturates is relatively insensitive to the aggregate surface type but shows a non-monotonic trend with increasing emulsifier chain length, first decreasing and then increasing. This confirms that the mobility of non-polar components is mainly controlled by the emulsifier’s hydrocarbon chain length. Within a certain chain length range, longer emulsifier chains can markedly hinder the free diffusion of non-polar molecules, thereby affecting the microscopic packing density in the interfacial region. In both aggregate systems examined, the C₁₁N₅ emulsifier corresponds to an inflection point in the diffusion coefficients of saturates, aromatics, and asphaltenes, suggesting that this chain length represents a critical threshold for influencing the diffusion behaviour of non-polar and asphaltene molecules. Additionally, water molecules exhibit relatively high diffusion coefficients in both interfacial systems, indicating rapid mobility throughout the system. In comparison, emulsified asphalt and emulsifier molecules, due to their larger molecular size and stronger intermolecular interactions, experience significantly restricted free motion.

3.3. Effect of Hydrophobic Hydrocarbon Chain Length on the Interfacial Adhesion Performance of Emulsified Asphalt–Aggregate Systems

Adhesion work is a key parameter for quantitatively characterising the interfacial bonding strength between two phases. In an emulsified asphalt–aggregate system, a positive adhesion work indicates that emulsified asphalt can spontaneously adsorb onto the aggregate surface, with higher values corresponding to stronger interfacial adsorption. Conversely, a negative adhesion work implies that emulsified asphalt cannot form a stable adsorption layer on the aggregate, and spontaneous interfacial adsorption is unlikely. In this study, adhesion work was calculated according to Equation (4).

$$W_{adhesion}={\displaystyle \frac{E_{bind}}{A}}={\displaystyle \frac{-E_{inter}}{A}}={\displaystyle \frac{-[E_{total}-\left(E_A+E_B\right)]}{A}}\times K$$

(4)

In the equation, $E_{bind}$ represents the binding energy of the A–B interface; $E_{inter}$ is the interaction energy between A and B, with negative values indicating attraction and positive values indicating repulsion; $E_{total}$ denotes the total free energy of the fully relaxed A–B system; $E_A$ and $E_B$ are the free energies of the fully relaxed A and B models, respectively; K is a conversion factor, taken as 659.

Based on the above equation, the interfacial adhesion work for the CaCO₃ (1 0 4) and SiO₂ (0 0 1) surfaces was calculated, as shown in Figure 14.

Figure 14 shows that the adhesion work for both aggregate interfaces is positive, indicating that the interfacial adhesion of emulsified asphalt to the aggregates occurs spontaneously. For the CaCO₃ (1 0 4) surface, adhesion work initially increases with the emulsifier’s hydrophobic hydrocarbon chain length but decreases when the chain exceeds 13 carbon atoms. In contrast, adhesion work on the SiO₂ (0 0 1) surface continues to rise steadily with increasing hydrocarbon chain length. These results indicate that moderately extending the emulsifier’s hydrophobic chain promotes the formation of a dense, stable adsorption layer at the interface, thereby enhancing interfacial adhesion performance. Further quantitative analysis reveals that when the hydrocarbon chain length increases from 11 to 13 carbon atoms, the adhesion work reaches its maximum increase for both surfaces, at 61.0% for CaCO₃ (1 0 4) and 34.3% for SiO₂ (0 0 1). Notably, when the chain length reaches 15 carbon atoms, adhesion work on SiO₂ (0 0 1) continues to increase, but by only 1.8%, whereas that on CaCO₃ (1 0 4) decreases by 7.9%. These findings indicate that beyond 13 carbon atoms, further chain elongation contributes little to enhancing interfacial adhesion and may even reduce adhesion strength, particularly on basic aggregates. At the molecular level, short-chain emulsifiers have shorter tails, resulting in low adsorption density, limited hydrophobic interactions, and consequently low work of adhesion. In contrast, the tails of long-chain emulsifier (C₁₅) is excessively long, increasing molecular flexibility and making them prone to coiling or entanglement. This leads to a decrease in adsorption arrangement density and restricted diffusion, hindering an increase in the work of adhesion. The tail length of the C₁₃ emulsifier ensures sufficient hydrophobic contact with the surface without causing steric hindrance due to excessive length. Simultaneously, its highest diffusion coefficient enables the molecules to rapidly reach and uniformly cover the surface, thereby forming the most stable adsorption layer and minimizing the interfacial free energy. Furthermore, the hydrophilic head group of the C₁₃ emulsifier can form effective electrostatic or hydrogen-bonding interactions with both acidic and alkaline aggregate surfaces, allowing it to exhibit relatively strong adhesion under different surface chemical environments. Moreover, under identical emulsifier chain lengths, the adhesion work on CaCO₃ (1 0 4) consistently exceeds that on SiO₂ (0 0 1), demonstrating that emulsified asphalt exhibits stronger interfacial adhesion with basic aggregates, in agreement with previous studies [14].

Based on the adhesion work calculations, the contributions of electrostatic and van der Waals interactions were further decomposed, as shown in Figure 15, illustrating the relative roles and dominant mechanisms of these interactions in interfacial adhesion.

Analysis of Figure 15 indicates that, for both aggregate surfaces, the contribution of van der Waals interactions to adhesion work initially increases and then decreases as the emulsifier’s hydrophobic chain lengthens, whereas the contribution from electrostatic interactions exhibits the opposite trend. This suggests that extending the hydrophobic chain of imidazoline-type emulsifiers can enhance van der Waals interactions to a certain extent; however, beyond an optimal chain length, emulsifier molecules tend to aggregate and entangle within the asphalt phase and at the interface, preventing uniform spreading on the aggregate surface and consequently reducing the van der Waals contribution. Overall, the variation in adhesion work with hydrophobic chain length closely follows the trend of van der Waals contribution. The effect of imidazoline-type emulsifier chain length on interfacial adhesion is fundamentally mediated through modulation of van der Waals interactions: as the hydrophobic chain length increases, intermolecular van der Waals forces are strengthened, promoting the formation of a dense and stable interfacial adsorption structure and thereby enhancing interfacial adhesion performance.

Further analysis reveals that on the CaCO₃ (1 0 4) basic aggregate surface, electrostatic interactions contribute over 50% of the interfacial adhesion work, serving as the dominant force governing adhesion. In contrast, on the SiO₂ (0 0 1) acidic aggregate surface, van der Waals interactions account for more than 80% of the adhesion contribution. This observation highlights a fundamental difference in the microscopic adhesion mechanisms between these two representative aggregate crystal planes. For the basic CaCO₃ (1 0 4) surface, electrostatic forces—including ionic coordination and electrostatic adsorption—constitute the primary source of interfacial bonding strength, with van der Waals forces playing only a secondary, supportive role. Conversely, the interfacial adhesion of the acidic SiO₂ (0 0 1) surface relies predominantly on van der Waals interactions between the imidazoline-type emulsifier and the aggregate surface.

Analysis of the energy contribution proportions reveals, at a mechanistic level, the fundamental reason why basic aggregates exhibit higher adhesion work than acidic aggregates: electrostatic interactions—dominated by Coulombic forces and ionic coordination—belong to the category of strong interactions, whereas van der Waals forces are weak physical interactions. Consequently, in basic aggregate systems governed by strong electrostatic interactions, the adhesion work of emulsified asphalt is higher, and interfacial adhesion performance is superior. In conjunction with the findings on hydrophobic chain length, optimizing chain length is crucial for enhancing adhesion on van der Waals-dominated acidic aggregates, while it has limited impact on electrostatically dominated basic aggregates. Therefore, different emulsifier molecular design strategies are required for the two aggregate types to achieve optimal interfacial adhesion performance.

4. Discussion

Within the carbon chain length range from C₇ to C₁₅, the adsorption peak shows a continuous decreasing trend. This is attributed to the increase in molecular occupied area caused by the lengthening of the carbon chain, which reduces the saturated adsorption capacity per unit surface area. However, the mere decrease in adsorption capacity is insufficient to evaluate the performance of different chain lengths, and a comprehensive consideration of adsorption quality and efficiency is still required. Both the diffusion coefficient and the work of adhesion reach their maximum values at C₁₃. This synergistic peak reveals that C₁₃ achieves the optimal balance between kinetics and thermodynamics. Specifically, the largest diffusion coefficient indicates that C₁₃ molecules experience the lowest migration resistance in the bulk phase and can migrate to the interfacial region at the fastest rate. Meanwhile, the maximum work of adhesion demonstrates that the adsorption layer formed by C₁₃ at the interface is the most stable and exhibits the strongest anti-peeling ability.

The chain length of C₁₃ avoids the loose adsorption layer caused by insufficient binding force in short-chain molecules, and also overcomes the increased mass transfer resistance and reduced utilization of effective adsorption sites resulting from molecular curling and steric hindrance in overly long carbon chains. Therefore, although C₁₃ does not exhibit the highest adsorption peak, it trades moderate adsorption capacity for the optimal interfacial bonding strength and fastest adsorption rate, making it the critical chain length in this system that achieves the best synergy between efficient mass transport and strong adsorption.

This study systematically investigates the adsorption behavior, diffusion characteristics, and adhesion properties of emulsifiers with chain lengths ranging from C₇ to C₁₅ on different aggregate surfaces, elucidating the influence mechanism of imidazoline emulsifiers on the interfacial adhesion performance of emulsified asphalt/aggregate from a molecular perspective. The results reveal the critical regulatory role of emulsifier tail chain length on the emulsified asphalt/aggregate interfacial interaction, providing a theoretical basis for optimizing interfacial molecular arrangement and adhesion performance. From the perspective of road engineering applications, the adhesion performance between emulsified asphalt and aggregate is a crucial factor affecting the initial strength, interface stability, and durability of pavement structures. Based on the findings of this study, selecting emulsifiers with appropriate tail chain lengths enables the formation of highly stable adsorption layers on different types of aggregate surfaces, thereby optimizing the interfacial performance of emulsified asphalt mixtures and enhancing pavement stripping resistance and long-term service life. This research not only provides molecular-level support for an in-depth understanding of the emulsified asphalt–aggregate interface mechanism but also offers a scientific basis for the formulation design and construction process optimization of emulsified asphalt materials in road engineering.

5. Conclusions

This study, based on molecular dynamics simulations and key characterization parameters including relative concentration, diffusion coefficient, and interfacial adhesion work, systematically investigated the influence of imidazoline-type emulsifier molecular structure on the adhesion performance of the emulsified asphalt–aggregate interface, and further analyzed the effect of aggregate surface properties on the interfacial adhesion mechanism. The main conclusions are as follows:

(1)

The hydrophobic alkyl chain length of imidazoline-type emulsifiers exerts a significant regulatory effect on interfacial behavior: increasing the hydrophobic chain length suppresses the adsorption amount of emulsified asphalt at the interface. Hydrophobic chains of appropriate length enhance molecular mobility, thereby improving the interfacial adhesion performance between emulsified asphalt and aggregates. When the chain length exceeds the optimal value (C₁₃), both molecular diffusion rates and interfacial adhesion performance are weakened. In addition, the diffusion behaviors of nonpolar components (aromatics and saturates) respond noticeably to changes in alkyl chain length. Based on the combined analysis of adsorption behaviour, diffusion coefficient, and adhesion work, the interfacial performance reaches the optimum at an alkyl chain length of C₁₃.

(2)

The surface properties of aggregates significantly influence interfacial adhesion: compared with the acidic SiO₂ (0 0 1) aggregate, the CaCO₃ (1 0 4) basic aggregate exhibits overall lower relative concentration peaks of emulsified asphalt, with peak values less sensitive to variations in the hydrophobic alkyl chain length of the emulsifier. Molecular mobility is lower, adhesion work is higher, and interfacial adhesion performance is superior. These observations collectively indicate strong interactions between emulsified asphalt and the surface of basic aggregates.

(3)

The dominant energetic mechanism of interfacial adhesion depends on the type of aggregate: the adhesion of emulsified asphalt on the acidic SiO₂ (0 0 1) aggregate is primarily governed by van der Waals interactions, whereas the interfacial adhesion on the basic CaCO₃ (1 0 4) aggregate is dominated by strong electrostatic interactions.