Research on Surface Wear Characteristics and Adsorption Mechanism of Biodiesel Engine

Abstract

As a renewable fuel for diesel engines, biodiesel plays a significant role in improving the lubricating performance of low-sulfur diesel. The decline in lubricity of low-sulfur diesel can lead to increased friction and exacerbated wear on the surfaces of diesel engine friction pairs, whereas the addition of biodiesel can effectively mitigate such tribological issues. In this study, tribological performance tests of biodiesel-fueled engines were conducted, combined with molecular simulation methods. Using Materials Studio software, the adsorption behavior and dynamic processes of three typical fuel components: C₇H₁₆, C₁₁H₂₂O₂, and C₁₉H₃₆O₂, on the α-Fe (110) crystal surface were simulated. This systematically revealed the mechanism by which biodiesel improves friction and wear performance. The results indicate that biodiesel significantly enhances the lubricating properties of low-sulfur diesel. The carbonyl groups in biodiesel molecules exhibit high reactivity, demonstrating larger absolute values of adsorption energy and cohesive energy compared to alkane components, which indicates stronger surface adsorption capacity. This facilitates the formation of a stable and continuous lubricating film on metal surfaces, thereby providing anti-wear and friction-reducing effects, ultimately improving the wear resistance of key components in diesel engines.

1. Introduction

The content limits for certain elements in automotive fuels are becoming increasingly stringent, particularly for sulfur. To meet standards, diesel requires desulfurization. During this process, some natural lubricating components are removed. However, it will lead to more wear in certain diesel engine components that rely on diesel for lubrication [1,2]. Consequently, diesel lubricity improvers (or anti-wear additives) need to be added to enhance diesel’s lubricating performance and reduce wear on diesel engine components [3]. Commonly used diesel anti-wear agents are mainly fatty acids and their ester derivatives of two categories [4,5]. Biodiesel, primarily composed of large-molecule fatty acid methyl esters (FAME), belongs to the ester derivatives category and can function as a fuel lubricity improver. Furthermore, biodiesel serves as an alternative fuel for diesel engines. Its application not only significantly reduces soot and its precursors in emission pollutants [6,7], but also contributes to alleviating the energy crisis while simultaneously reducing pollutant emissions.

Aiming at the wear of diesel engine burning biodiesel parts and components, domestic and foreign scholars have carried out a lot of research work. Reddy et al. [8] carried out a 250 h durability test on a diesel engine and considered that the wear of biodiesel in the fuel system on the plunger coupling, needle valve coupling, and outlet valve coupling in the injection system was less than that of mineral diesel. In addition to the fuel system moving parts, Gupta et al. [9] recognized normal wear on the crank linkage mechanism of a biodiesel-fired engine. Msna et al. [10] added mixtures of biodiesel and diesel fuel from different sources to the lubricating oil, respectively, and simulated the frictional wear of the parts after the lubricating oil was contaminated in a four-ball testing machine, and the results showed that the wear of the parts from different sources of biodiesel was varied. Li, Xu, and Li et al. [11,12,13] concluded that biodiesel composition has a significant effect on its wear performance. Zhou et al. [14] found that oxidation of biodiesel for a short period of time helps to improve the lubricity of the lubricant, but prolonged oxidation leads to a high acid value, which reduces its lubricity.

The molecular structures of biodiesel derived from different sources significantly influence its lubricating and tribological performance. However, conventional approaches cannot adequately explain interfacial phenomena such as microscopic adsorption and friction. Recent advances in quantum chemical calculations and molecular dynamics simulations provide crucial technical support for revealing fuel molecular characteristics, including chemical structures, reaction activity, and surface adsorption features at the molecular level. Quantum chemical calculations, based on molecular electronic structures, can predict critical parameters of diesel and biodiesel molecules: electronic configurations, molecular reactivity, electrostatic potentials, and adsorption stability. Meanwhile, molecular dynamics simulations elucidate the dynamic adsorption processes of fuel systems on metal surfaces and the stability of adsorption films, thereby clarifying their impact on lubrication performance. These methodologies offer significant insights for investigating the interaction mechanisms between biodiesel molecular reactivity and metal surfaces in this field.

Mei et al. [15] studied the autoxidation product model of biodiesel molecules adsorbed on aluminum and stainless steel surfaces using density flooding theory. The results showed that the adsorption capacity of oxygenated organic compounds was stronger than that of anaerobic organic compounds and oxygen-free organic compounds. Mei et al. [16] concluded that the molecular adsorption capacity depends on their molecular weight, with increased molecular weight leading to enhanced adsorption capacity and improved lubricating properties.

Li et al. [17] believed that increasing the carbon chain length could significantly enhance the adsorption energy of molecules on the iron surface and strengthen the van der Waals interactions within the adsorption film, thereby improving both the stability and compactness of the adsorbed film. Canterelli et al. [18] proposed that the adsorption performance of saturated esters on iron surfaces is predominantly governed by rigid adsorption energy, with the hydrogen atoms in FAME containing –OH polar groups exhibiting significantly enhanced rigid adsorption energy on iron surfaces.

Domestic and international scholars mentioned above have conducted research on the tribological performance of moving parts in fuel systems and diesel engines under biodiesel conditions, as well as biodiesel from different feedstocks. These studies have confirmed that biodiesel composition affects engine component wear differently compared to conventional diesel, which is attributed to biodiesel’s feedstock sources and molecular structures. However, the exact mechanisms of how biodiesel’s varied structures and components influence friction and wear remain unclear. Based on this foundation, and considering that the use of ultra-low sulfur diesel (ULSD) in diesel engines may exacerbate wear, the research team added biodiesel to ULSD and conducted engine wear tests with biodiesel blends. The study investigates the wear mechanisms of biodiesel on engine tribo-pairs from the perspective of molecular structures and intermolecular forces, aiming to establish a theoretical framework for understanding how alternative fuels affect friction and wear in critical engine metal components.

2. Experimental Methods and Materials

The engine was operated with DB5 and 0# diesel. BD5 is a blended fuel composed of 5% biodiesel and 95% #0 petroleum diesel, where the biodiesel is derived from waste cooking oil, and the #0 diesel (which contains no FAME) is commercially available diesel. The schematic of the experimental setup used for performing the engine experiments is shown in Figure 1, with engine specifications provided in

Table 1. Test engine specifications.

Engine Type	4-Stroke, Turbocharged, Inter-Cooled Diesel
Number of Cylinders	4
Cylinder Diameter	94 mm
Cubic Capacity	2770 cc
Max. Power Output	92@3000 (kW, rpm)
Maximum Torque	285@1800 (Nm, rpm)
Compression ratio	18.5:1

. The diesel engine’s cooling system utilizes an external radiator for coolant circulation, with the following temperature controls: engine coolant outlet temperature maintained at 85–90 °C, radiator coolant temperature regulated to 55–65 °C, and lubricating oil temperature controlled within 90–120 °C. Prior to tribological testing, the diesel engine underwent a 50 h run-in operation under rated conditions. Following initial performance evaluation, the engine was disassembled for dimensional inspection of critical tribo-pair components. After reassembly, wear tests were conducted using both DB5 and #0 diesel fuels. After 1000 h of continuous operation under test conditions, the engine’s primary moving components were remeasured. The complete durability test protocol is detailed in Figure 2. The lubricity measurement of the fuels was primarily conducted using a high-frequency reciprocating friction wear tester.

3. Molecular Structure Characteristics and Molecular Surface Adsorption Simulation of Fuel Systems

3.1. Molecular Structure Characteristics

Biodiesel is a mixture composed of various FAMEs. The molecular structure is characterized by the RCOOCH₃ group, representing long-chain macromolecules. Their FAMEs vary in both carbon chain length and degree of saturation.

Since both diesel and biodiesel are mixtures, in molecular dynamics calculations, diesel has a cetane number of approximately 50 and a C/H ratio of 0.54, while n-heptane has a cetane number of approximately 56 and a C/H ratio of 0.44. N-heptane and diesel share similar properties. Scholars both domestically and internationally have conducted extensive research on n-heptane as a surrogate fuel for diesel [19,20]. This paper uses n-heptane (C₇H₁₆) as a model molecule for diesel fuel.

Methyl decanoate and methyl oleate do not possess the actual high molecular weight of biodiesel, but they share the same carbon, hydrogen, and oxygen composition as biodiesel, as well as the fundamental chemical structure of methyl esters –RCOOCH₃, where a methyl ester group is attached to a long-chain alkyl or alkenyl group. Therefore, methyl decanoate (with zero C=C double bonds in the molecule) and methyl oleate (with one C=C double bond in the molecule) were selected as model molecules for biodiesel. Comparative analyses with n-heptane, representing diesel, were conducted using molecular dynamics simulations to evaluate aspects such as molecular reactivity and adsorption stability [21,22].

Figure 3 further compares the infrared spectra of diesel and biodiesel. Compared with diesel FTIR, biodiesel FTIR shows additional absorption peaks at wavenumbers 1742 cm⁻¹ and 1462 cm⁻¹, respectively. The peak at 1742 cm⁻¹ corresponds to the C=O stretching vibration characteristic peak, exhibiting a very strong absorption effect. The peak at 1462 cm⁻¹ is attributed to the asymmetric bending vibration absorption of –OCH₃. Other wavenumbers are generally similar.

Molecular geometry optimization was performed on ball-and-stick models of three compounds using the Forcite module in Materials Studio software to achieve energetically minimized configurations. Figure 4 displays the optimized structures at their round states: Figure 4a n-heptane exhibits complete symmetry with non-polar characteristics and unform CCC bond angles of 109°; Figure 4b methyl decanoate shows slight angular distortion (108°) near the carbonyl group, introducing weak polarity; Figure 4c methyl oleate demonstrates more pronounced structural deformation with varying bond angles (108–110°) and consequently stronger polar.

3.2. Molecular Surface Adsorption Simulation in Fuel System

The study employed combined Amorphous Cell and Forcite modules to develop adsorption kinetic models for three representative fuel components (C₇H₁₆, C₁₁H₂₂O₂, and C₁₉H₃₆O₂) on α-Fe (110) surfaces. Following system energy optimization, interfacial adsorption models were constructed to investigate both molecular adsorption characteristics and underlying friction-wear mechanisms through molecular dynamics simulations.

The molecular dynamics simulations were performed using the Forcite module. The simulations were carried out in the NVT ensemble (constant number of particles, volume, and temperature). The system temperature was maintained at 298 K by the Andersen thermostat. The integration time step was set to 1.0 fs with a total simulation duration of 500 ps. These molecular dynamics simulations were conducted to investigate the dynamic adsorption processes, equilibrium configurations, and interfacial interaction characteristics of three fuel molecules on the α-Fe (110) surface (representative adsorption configurations are shown in Figure 5a).

After establishing the adsorption dynamics simulation, a surface model of α-Fe (110) with periodic boundary conditions was constructed as the adsorption substrate. Based on the experimental densities of the components (C₇H₁₆, 0.683 g/cm³; C₁₁H₂₂O₂, 0.872 g/cm³; C₁₉H₃₆O₂, 0.874 g/cm³), the initial amorphous liquid-phase configurations of the corresponding fuel molecules were built (a typical configuration is shown in Figure 5b). Preliminary geometry optimization and energy minimization were performed on each independent fuel molecular system to ensure structural stability.

The solid–liquid interfacial model was constructed by placing the optimized fuel molecular system between two parallel layers of α-Fe (110) crystalline surfaces using the Build Layers tool. The interlayer spacing of iron was set to 15 Å to accommodate the fuel molecular layer and form a well-defined interfacial region (the initial configuration schematic, using methyl decanoate as an example, is shown in Figure 5c). This spacing was designed to simulate the gap environment of friction pairs. The assembled iron-fuel interface system subsequently underwent further geometry optimization and energy minimization to eliminate unreasonable atomic overlaps and high-energy configurations, thereby obtaining a stable initial adsorption configuration.

4. Results and Discussion

4.1. Tribological Properties

In diesel engines, the operating conditions of moving friction pairs (especially those in the crankshaft-connecting rod mechanism and valve train) are particularly severe, enduring significant pressure, thermal loads, and impact loads. These harsh conditions make it difficult to maintain a continuous lubricating film on friction surfaces, resulting in accelerated wear, particularly in low-sulfur environments. Friction and wear tests were performed with DB5 biodiesel and conventional #0 diesel. After running for 1000 h, wear measurements were conducted on key engine components, piston pin outer diameter, compression ring end gap, and major friction pairs of the crankshaft and camshaft.

In the friction and wear tests, the emission performance of the diesel engine was investigated at a speed of 1800 rpm, as illustrated in Figure 6. An increase in engine load leads to a rise in the in-cylinder average temperature and higher fuel injection quantities, resulting in an upward trend in soot emissions for both DB5 and conventional diesel. However, due to the oxygenated molecular structure of DB5, which promotes the oxidation of soot precursors, its soot emissions remain consistently lower than those of pure diesel. CO and HC emissions exhibit a non-monotonic trend with increasing load: at low to medium loads, elevated combustion temperatures enhance oxidation reactions, gradually reducing emissions; at high loads, a decrease in the excess air ratio causes localized oxygen deficiency, intensifying incomplete combustion and leading to a subsequent increase in emissions. The oxygen content in DB5 effectively improves local oxygen distribution within the air–fuel mixture, resulting in overall lower CO and HC emissions compared to diesel. Notably, NOx emissions from DB5 are generally higher than those from diesel, primarily attributable to the elevated peak in-cylinder temperatures induced by oxygen-enriched combustion, which amplifies the formation of thermal NOx under high-temperature and oxygen-abundant conditions.

The influence of different fuels on the wear characteristics of the diesel engine was investigated, as shown in Figure 7. From Figure 7, it can be observed that when fueled with either biodiesel or diesel, wear occurred in various friction pairs across all cylinders of the engine. For both fuels, the maximum wear was identified at the following locations: the outer diameter of the piston pin in the fourth cylinder, the closed gap of the gas ring in the first cylinder, the second main journal, and the fifth camshaft journal. Statistical analysis of the maximum wear values revealed that, for the biodiesel-fueled engine, the maximum wear of the piston pin outer diameter was reduced by 33%, 47%, 35%, and 13%, respectively, compared to that of the diesel engine. Similarly, the maximum wear of the main crankshaft journals decreased by 10%, 19%, 25%, and 50%, respectively. These results demonstrate that, under high-speed operating conditions, the biodiesel-fueled engine exhibits superior anti-wear performance compared to the diesel engine. Under identical operating conditions, this improvement can be largely attributed to the molecular interactions involving oxygen-containing carbonyl groups in biodiesel molecules.

Figure 8 presents the variation curves of friction force and friction coefficient over time for the two fuels during high-frequency reciprocating friction tests. As shown in Figure 8, significant fluctuations in the reciprocating stroke occurred during the initial period, primarily due to random vibrations during machine startup. Subsequently, the stroke fluctuations diminished and remained within the permissible experimental error range.

Figure 8 also indicates that the friction force and friction coefficient of biodiesel were consistently not greater than those of diesel. The average friction forces for biodiesel and diesel were 0.431 N and 0.435 N, respectively, while the average friction coefficients were 0.2197 and 0.2219, respectively. This demonstrates that biodiesel exhibits superior friction-reducing performance. Further observation reveals that the friction coefficient of biodiesel remained relatively stable during the friction process, whereas diesel showed some fluctuations. This may be attributed to the tendency of fine diesel droplets to break apart and deposit on the friction surface, leading to variations in the friction coefficient.

The maximum wear of each group, such as the diameter of piston skirt (DPS), the diameter of connecting rod big end hole (DCRH), the valve sinking amount (VSA), and the valve clearance (VC), was statistically analyzed, as shown in Figure 9. When the diesel engine was fueled with BD5, the maximum wear of key components did not exceed the allowable limits. The addition of a small proportion of biodiesel to conventional diesel significantly improved the wear condition of moving friction pairs in all three assemblies (piston, crankshaft, and valve train), demonstrating biodiesel’s effective mitigation of wear caused by low-sulfur diesel.

4.2. Friction Morphology and Mechanism Analysis

The SEM of the cylinder liner surface before and after the friction and wear test was analyzed, as shown in Figure 10. As can be seen from Figure 10, the biodiesel engine cylinder liner exhibits relatively shallow wear scratches on the surface, with localized plastic deformation. These characteristics are primarily caused by fatigue wear resulting from reciprocating motion. In contrast, the diesel engine cylinder liner shows pits, furrows, and micropores in certain areas on the surface; the degree of plastic deformation is more severe, and spherical particles are also observed on the friction surface. The aforementioned SEM observations are consistent with the friction and wear test data: the surface damage of the biodiesel engine cylinder liner (shallow scratches and localized plastic deformation) is relatively milder compared to that of the diesel engine cylinder liner (pits, furrows, severe plastic deformation, and spherical particles). This indicates that adding biodiesel to diesel fuel helps improve the lubrication performance of the friction pairs in diesel engines.

The varying carbon chain lengths, number of double bonds, and molecular chain bending configurations in biodiesel molecules result in differences in intermolecular polar forces and van der Waals forces. These variations affect the physical adsorption capacity on metal surfaces, leading to differences in the thickness of the formed adsorption films.

Biodiesel is a macromolecular substance with one end being –RCOOCH₃, which exhibits polar forces. The polar groups firmly adsorb onto the metal surface through intermolecular polar forces, forming a multi-molecular layer adsorption film with layered and oriented arrangements.

When biodiesel is present between moving friction pairs, its adsorption film separates the two metal surfaces, providing an interface with low shear resistance. This reduces the friction coefficient and prevents surface adhesion. The friction generated under these conditions is primarily external friction between the adsorption film layers, constituting physical adsorption lubrication. When the temperature of the metal surface increases, polar molecules react with the metal surface to form metal soaps. These metal soaps are firmly adsorbed onto the metal surface via chemical bonds, forming a more stable chemical adsorption layer.

Figure 11 illustrates the wear mechanisms of biodiesel and diesel in diesel engines. Figure 11a depicts the lubrication condition between the piston ring and cylinder wall during the reciprocating motion of the piston. The yellow represents lubricating oil, and the oil film forms between the cylinder wall and piston ring, as shown within the green ellipse in Figure 11a. A magnified view of the oil film between the cylinder wall and piston ring is provided in Figure 11b. If the sulfur content is high, it rapidly undergoes a chemical reaction with the metal surface, generating a chemical reaction film with a thickness of d₁ (as shown in Figure 11b). However, low-sulfur diesel weakens the ability to form chemical reaction films, significantly reducing the film thickness to d₂ (as shown in Figure 11c). This thinning diminishes the protective effect of the reaction film, exacerbating wear on engine components.

Adding biodiesel to diesel enhances the physical and chemical adsorption capacities of carbonyl molecules in biodiesel with the metal surface, promoting the formation of a thicker reaction film (with a thickness increased to d₃, as shown in Figure 11d). This reaction film bonds firmly to the metal surface. During friction, even if parts of the reaction film are worn away, the addition of biodiesel effectively increases the reaction film thickness from d₂ to d₃, forming a more stable lubricating film. This effectively mitigates the increased wear of engine components caused by diesel desulfurization.

An increase in the number of carbon atoms, molecular weight, and carbon chain length in biodiesel molecules leads to a thicker adsorption film, which in turn reduces the friction coefficient and enhances lubrication effectiveness. Therefore, adding biodiesel to diesel effectively reduces wear, as confirmed by 1000 h friction and wear tests.

4.3. Molecular Reactivity

To elucidate the mechanism of biodiesel in improving friction and wear performance, we analyzed the effect of molecular reactivity on adsorbed oil film formation from a molecular dynamics perspective. Density functional theory (DFT) calculations were employed to evaluate the chemical reactivity of molecules, with the highest occupied molecular orbital energy (E_HOMO, eV) and lowest unoccupied molecular orbital energy (E_LUMO, eV) serving as key parameters for assessing electron-donating and electron-accepting capabilities [23,24]. Specifically, higher E_HOMO values indicate stronger electron-donating ability, while lower E_LUMO values suggest greater capacity for accepting electrons from metal surfaces.

The energy gap ΔE (ΔE = E_LUMO − E_HOMO, in eV), along with key chemical reactivity descriptors including chemical potential (μ, in eV), global hardness (η, in eV), softness (σ, in eV⁻¹), and electrophilicity index (ω, in eV), serves as fundamental indicators for evaluating the chemical reactivity of organic molecules. The quantitative parameters can be derived from Equations (1)–(5), where ν represents the local external potential (in eV).

$$\Delta E=E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}-E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}}$$

(1)

$$\mu ={\displaystyle \frac{1}{2}}\left(E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}+E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}}\right)$$

(2)

$$\eta ={\displaystyle \frac{1}{2}}\left(E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}-E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}}\right)$$

(3)

$$\sigma ={\displaystyle \frac{1}{\eta }}=\left({\displaystyle \frac{\partial \mu }{\partial N}}\right)\nu$$

(4)

$$\omega ={\displaystyle \frac{{\mu }^2}{2\eta }}$$

(5)

Table 2. Molecular front orbital parameters calculated by density functional theory.

Molecule	EHOMO/eV	ELUMO/eV	ΔE/eV	μ/eV	η/eV	σ/eV−1	ω/eV
C7H16	−7.088	1.511	8.600	−2.788	4.300	0.232	0.904
C11H22O2	−6.103	0.755	6.859	−2.673	3.429	0.291	1.042
C19H36O2	−5.429	0.736	6.166	−2.346	3.083	0.324	0.893

shows the calculation results on the front orbital parameters of three molecules (C₇H₁₆, C₁₁H₂₂O₂, and C₁₉H₃₆O₂) calculated by density flood theory. Obviously, C₇H₁₆ has the smallest E_HOMO and the largest E_LUMO, indicating that C₇H₁₆ is weak in giving electrons and strong in accepting electrons, and on the contrary, C₁₉H₃₆O₂ has the largest E_HOMO and the smallest E_LUMO (out of the three), suggesting that it is strong in giving electrons and weak in accepting electrons.

The energy level difference ΔE = 6.166 eV of C₁₉H₃₆O₂ is the smallest among the three compounds, indicating its highest reactivity, as electrons are more easily excited to participate in reactions. Additionally, C₁₉H₃₆O₂ has a relatively small η (hardness) and a relatively large softness (σ). The reactivity order of the three compounds is C₁₉H₃₆O₂ > C₁₁H₂₂O₂ > C₇H₁₆. It can be concluded that higher reactivity (especially in C₁₉H₃₆O₂) means the molecules can more readily form strong chemical adsorption bonds on metal surfaces. This robust chemical adsorption facilitates the formation of a more stable and continuous lubricating film, thereby delivering superior anti-wear and friction-reducing effects during friction processes.

According to the frontier orbital distribution shown in Figure 12, the HOMO of the three oils is distributed on the main chain of the molecule, indicating that the nucleophilic reaction center is located on the main chain. LUMO distributions are significantly different, and the LUMO of C₇H₁₆ is distributed in the middle region of the carbon chain. HOMO and LUMO of C₁₁H₂₂O₂ are concentrated near the carbonyl structure at the end of the carbon chain, indicating that the nucleophilic and electrophilic reaction centers are located at the carbonyl group at the end of the molecular chain. The HOMO of C₁₉H₃₆O₂ is distributed in the unsaturated carbon chain, while the LUMO is distributed in the carbonyl structure at the end of the carbon chain. This LUMO distribution at the end (observed in C₁₁H₂₂O₂ and C₁₉H₃₆O₂) can effectively reduce the steric hindrance of organic molecules in the adsorption process on the metal surface, thus promoting the adsorption of biodiesel molecules on metal surface, which can form a more regular, dense, and stable molecular film on metal surface, and significantly improve the anti-wear and antifriction properties of biodiesel.

Furthermore, molecular local reactivity serves as a crucial indicator for evaluating adsorption reactions, typically characterized by Fukui indices. The Fukui indices include f_k⁺, f_k⁰, and f_k⁻, where f_k⁺ represents the ability of a reactant molecule to accept electrons, f_k⁰ reflects the capacity to form shared electron pairs between molecules in radical reactions, and f_k⁻ denotes the ability of a reactant molecule to donate electrons. Figure 13 presents the Fukui index distributions for C₇H₁₆, C₁₁H₂₂O₂, and C₁₉H₃₆O₂.

As shown in Figure 13a, the three Fukui indices (f_k⁺, f_k⁰, and f_k⁻) of C₇H₁₆ reveal symmetric distributions in the molecule: C₁ and C₇, C₂ and C₆, as well as C₃ and C₅ are symmetrically positioned about C₄, with hydrogen atoms following identical patterns.

Figure 13b demonstrates that the reactive sites of C₁₁H₂₂O₂ are primarily located at the C and O atoms of the terminal carbonyl group and their bonded H atoms, indicating that both electrophilic and nucleophilic reactions readily occur near this carbonyl moiety.

In Figure 13c, C₁₉H₃₆O₂ exhibits two distinct reactive sites: the first at the unsaturated C=C bond region, and the second at the terminal carbonyl group’s C/O atoms and their attached H atoms.

Notably, the maximum Fukui index values of both C₁₁H₂₂O₂ and C₁₉H₃₆O₂ surpass those of C₇H₁₆, confirming their superior chemical reactivity. This enhanced reactivity facilitates stronger adsorption interactions with metal surfaces.

4.4. Adsorption Stability

To more intuitively explain the adsorption behavior of fuel molecules on the α-Fe (110) surface more intuitively, the adsorption processes of C₇H₁₆, C₁₁H₂₂O₂, and C₁₉H₃₆O₂ molecules were analyzed based on Figure 5, as shown in Figure 14. As the molecular dynamics simulation progressed, all three fuel molecules exhibited progressive adsorption onto the α-Fe (110) surface. Upon reaching equilibrium, each fuel species formed a densely packed adsorption film on the α-Fe (110) substrate. With further progression of the simulation, an increasing number of C₁₁H₂₂O₂ and C₁₉H₃₆O₂ molecules accumulated on the α-Fe (110) surface, forming a more densely packed oil film with greater thickness compared to C₇H₁₆. Meanwhile, the interfacial region between the two α-Fe (110) surfaces exhibited relatively sparse molecular distribution.

Following molecular dynamics simulations, the intermolecular interactions were evaluated through adsorption energy and cohesive energy. Adsorption energy, a thermodynamic parameter characterizing the heat released during molecular adsorption onto surfaces, serves as an indicator of system stability. Greater heat release corresponds to stronger adsorption and higher stability. Cohesive energy represents the average energy required to completely separate all molecules to infinite distances. A higher cohesive energy denotes greater energy input needed for molecular separation, thus reflecting enhanced system stability.

According to thermodynamic principles, the exothermic nature of the adsorption process leads to a reduction in the system’s free energy. The adsorption energy E_adsorption of molecules on the α-Fe (110) surface can be calculated using Equations (6) and (7) [25,26].

$$E_{\mathrm{interaction}}=E_{\mathrm{total}}-\left(E_{\mathrm{surface}}+E_{\mathrm{fuel}}\right)$$

(6)

$$E_{\mathrm{absorption}}=-E_{\mathrm{interaction}}$$

(7)

where E_interaction is the interaction energy of the entire adsorption system (negative value), E_total is the total energy of the fuel system, and α-Fe(110) surface (kcal·mol⁻¹), E_surface is the total energy of the adsorption surface (kcal·mol⁻¹), E_fuel is the total energy of the fuel system (kcal·mol⁻¹), and E_adsorption is the adsorption energy between fuel molecules and the Fe(110) surface (kcal·mo⁻¹).

E_total, E_surface, and E_fuel were calculated using the Forcite Tools module. Based on Equations (6) and (7), the adsorption energy and cohesive energy of C₇H₁₆, C₁₁H₂₂O₂, and C₁₉H₃₆O₂ on the iron surface are summarized in

Table 3. Adsorption energy and cohesive energy of different fuel molecular systems on α-Fe (110) surface.

System	Adsorption Energy/kJ·mol−1	Cohesive Energy/kJ·mol−1
C7H16	−2862.3	−1570.7
C11H22O2	−3193.5	−2286.4
C19H36O2	−3150.1	−2104.8

.

Table 3 shows the adsorption and cohesion energies of C₇H₁₆, C₁₁H₂₂O_2, and C₁₉H₃₆O₂ on the iron surface. From Table 3, it can be seen that the adsorption of the three molecular systems on the iron surface is an exothermic reaction and can proceed spontaneously. The C₁₁H₂₂O₂ molecule exhibits a higher absolute value of adsorption energy, indicating that it is more likely to adsorb on the surface. Meanwhile, the cohesive energy is related to the stability of the formed molecular film. The greater the absolute value of the cohesive energy, the more stable the molecular film becomes, and the less prone it is to rupture. According to the cohesive energy data of fuel molecules in Table 3, the cohesive energies of C₁₁H₂₂O₂ and C₁₉H₃₆O₂ are close in value, and their absolute values are both higher than that of C₇H₁₆. This indicates that the molecular films formed by these two compounds exhibit similar stability, which is greater than that of C₇H₁₆. Therefore, on the friction pair surfaces of diesel engines, biodiesel can form an oil film with stronger adsorption capacity and better stability compared to conventional diesel. This conclusion is consistent with the experimental results shown in Figure 8.

5. Conclusions

This study conducted tribological performance testing on biodiesel engines, which focused on the molecular structure and kinetic characteristics of biodiesel. Simulation with Materials Studio software was used to further explore the friction and wear mechanisms. The results show the following:

(1)

During and after the 1000 h endurance test, no significant abnormalities were observed in the main friction pair. Wear amounts were within allowable limits. The results show that biodiesel addition reduces wear in low-sulfur diesel engine components.

(2)

Materials Studio simulation results revealed that on the α-Fe (110) crystal plane, the reactivity of C₁₉H₃₆O₂, C₁₁H₂₂O₂, and C₇H₁₆ decreased sequentially (based on density functional theory and Fukui index analysis). Frontier orbital analysis demonstrated that the LUMOs of C₁₁H₂₂O₂ and C₁₉H₃₆O₂ were localized at their terminal carbonyl groups, which significantly reduced steric hindrance for adsorption. This promoted their effective adsorption on the metal surface, facilitating the formation of more ordered, compact, and stable molecular films. Consequently, higher adsorption energy and absolute cohesive energy values were achieved, ultimately enhancing the anti-wear and friction-reduction performance of biodiesel at friction pair interfaces.

(3)

The addition of biodiesel to low-sulfur diesel systems effectively enhances the lubrication performance of diesel engine friction pairs. This improvement primarily originates from the unsaturated bonds and carbonyl functional groups in biodiesel molecules, which significantly strengthen the chemical adsorption capacity of biodiesel components on metal surfaces. Compared to low-sulfur diesel, this stronger adsorption not only promotes the formation of a thicker tribochemical reaction film but also establishes more robust bonding between the film and the metal surface, thereby improving adsorption stability. This firmly bonded thick tribochemical reaction film can form a stable lubricating layer on friction pair surfaces, consequently effectively reducing wear.