Synergistic Enhancement of Tribological Behavior and Colloidal Stability in CuO Nanolubricants via Ligand Tuning

Abstract

Nanoparticle-based lubricants, or nanolubricants, can exhibit superior tribological properties compared to unmodified base oils. However, these performance gains are highly dependent on the nanoparticle surface chemistry, particularly in maintaining stable colloidal dispersions. This study explores the influence of oleic acid (OA) and oleylamine (OAm) functionalization on the tribological and colloidal properties of CuO nanoparticles dispersed in an SAE 20W50 base oil. We present a hybrid optimization framework combining Response Surface Methodology (RSM) with Bayesian Optimization (BO) to identify the optimal OA to OAm ratio (OA–OAm) for CuO nanolubricants. Unlike prior studies that employed either RSM alone or trial-and-error approaches, this integrated method enables precise tuning of ligand ratios, achieving balanced tribological performance and colloidal stability. Characterization techniques, including UV–vis spectroscopy, FTIR, Raman spectroscopy, and TGA, were employed to investigate dispersion stability. Results demonstrate that OA/OAm-functionalized CuO nanoparticles exhibit improved dispersion stability and reduced sedimentation compared to non-functionalized counterparts. Tribological evaluations using the four-ball test revealed that the ligand-tuned CuO nanolubricants maintained their tribological enhancements under a variety of additive loadings and ligand combinations, with an improvement ranging from 44.9% to 60.6% in the coefficient of friction (COF) and from 29.2% to 63.9% in the specific wear rate (SWR). For the colloidal stability, OA/OAm-functionalized CuO nanoparticles exhibited a 75% reduction in sedimentation rate (k = 0.003 day⁻¹) compared to unfunctionalized CuO (k = 0.012 day⁻¹). Finally, the high thermal stability of the functionalized nanoparticles ensures their suitability for high-performance applications. Overall, this work represents a crucial step towards commercial applications of CuO-enhanced lubricants.

1. Introduction

The reduction in friction and wear in mechanical systems is critical for improving performance and extending the longevity of machinery. Whether in modern automotive engines, electric vehicles, wind turbines, or industrial equipment, the ability to minimize friction leads to improved efficiency, reduced energy consumption, and reduced wear on moving parts [1,2,3].

Nanoparticles offer several advantages as lubricant additives, including enhanced thermal stability, reduced wear, and lower friction [4]. The use of nanoparticles, such as copper oxide (CuO), zinc oxide (ZnO), titanium dioxide (TiO₂), and carbon-based materials, including graphene and carbon nanotubes, has been a focus of recent research due to their unique physical and chemical properties [5,6]. However, without proper stabilization, nanoparticles tend to aggregate and sediment, reducing their efficacy in improving tribological properties and even leading to negative effects, such as increased wear or clogging of filters and valves [7,8]. To address this colloidal stability challenge, researchers have employed nanoparticle surface coating and functionalization techniques, though this is a relatively underdeveloped area in tribology compared to nanoparticles in biological and optoelectronic applications. Surface functionalization involves modifying the surface of nanoparticles with molecules that reduce the surface energy and offer steric hindrance to inter-particle surface contact, which improves colloidal stability and reduces aggregation [9,10,11,12].

The ligand pair oleic acid (OA) and oleylamine (OAm) is widely used in the synthesis and stabilization of nanoparticles, as they control size, shape, and aggregation during and after particle formation [11]. The complementary roles of OA and OAm are key to effective nanoparticle stabilization. OA strongly adheres to the nanoparticle surface, preventing clumping and stabilizing specific facets, while OAm facilitates acid–base complex formation with OA. These complexes create a dynamic capping layer that maintains nanoparticle dispersion and improves colloidal stability [13]. Additionally, OAm provides a mildly reductive environment, controlling surface chemistry and preventing destabilizing reactions [11]. Both OA and OAm have hydrophobic tails that interact with non-polar solvents and hydrophilic heads that bond to nanoparticle surfaces, providing steric stabilization crucial for preventing sedimentation and maintaining functionality, such as reducing friction and wear over time. Steric stabilization is particularly effective in non-polar environments, where electrostatic stabilization is hindered by the medium’s low dielectric constant [8].

Optimizing ligand concentrations and ratios is critical for maximizing the performance of nanoparticle-enhanced lubricants [8,14]. Excess surfactant can increase viscosity, leading to higher friction and energy consumption, while insufficient ligand levels can result in aggregation and sedimentation. Balancing surfactant concentration and nanoparticle loading is essential to enhance the tribological properties of nanolubricants.

Various studies have looked at the use of oleic acid alone in nanolubricants, while the use of the OA/OAm pair remains understudied. Chen et al. [15] used OA/OAm to coat nickel nanoparticles for use in lubricants, showing enhanced particle dispersion and crucially improved high-temperature stability, which was attributed to the advanced ability of these particles to resist aggregation. At a low concentration of 0.05 wt%, the smallest size particles (~7.5 nm) achieved a 25% reduction in wear scar diameters compared to the base oil alone of PAO6. These enhancements are attributed to the formation of a protective boundary lubricating film and the deposition of Ni nanocores onto the sliding surfaces. The ligand pair system of OA/OAm facilitated the release of active nickel nanocores during friction, forming those boundary lubricating films and protective layers on sliding surfaces, exhibiting superior antiwear performance due to higher surface reactivity.

Regarding the use of OA alone, Jiang et al. [16] explored the functionalization of SiC/TiN hybrid nanoparticles with oleic acid within a polyalphaolefin base oil, showing significant improvements in both physicochemical and tribological properties. OA molecules enhanced colloidal stability by introducing steric hindrance repulsion, which reduced nanoparticle agglomeration and sedimentation over time. This stable dispersion enabled the formation of a uniform tribo-chemical film at the sliding interface. The optimized formulation, containing just 0.1 wt% of hybrid OA-functionalized SiC/TiN nanoparticles, resulted in a 32.7% reduction in the coefficient of friction (COF) and a 35.1% reduction in wear scar diameter (WSD) compared to PAO4 alone. These gains were attributed to the synergistic interaction between the hybrid nanomaterials and the OA surfactant, which not only stabilized the nanofluid but also enhanced surface adhesion and tribo-film formation at the contact interface.

Jiang et al. [17] examined the tribological improvements of engine oil by incorporating other OA-functionalized nanomaterials (h-BN and MoS₂). In this regard, the introduction of hexagonal boron nitride (h-BN) and molybdenum disulfide (MoS₂) nanoparticles functionalized with oleic acid (OA) into 5W-40 engine oil has led to remarkable improvements. The OA molecules act as surfactants, forming a stabilizing organic layer around the nanoparticles, which significantly enhances their colloidal stability by preventing agglomeration and sedimentation. This stable dispersion enables more uniform nanoparticle interaction at the sliding interface. As a result, the 0.2 wt% h-BN/OA nanolubricant achieved reductions of 21.5% in friction, 18.5% in wear scar diameter (WSD), and 91.6% in wear rate, while the MoS₂/OA system showed reductions of 13%, 17.05%, and 90.9%, respectively, compared to the base oil. These improvements were attributed to the synergistic effect between OA and the layered nanostructures, which promotes the formation of a durable tribo-film and a chemical absorption layer, ultimately enhancing load-bearing capacity and wear resistance.

Kumar et al. [18] noted similar improvements in the performance of OA-functionalized CuO nanoparticles dispersed in gear oil. This study also found significantly enhanced dispersion and stability even under extreme pressure conditions. They further observed an enhancement in the thermal conductivity of the gear oil, improving heat dissipation during operation, thus potentially extending lubricant life and improving performance under high-load conditions. OA acts as a surface modifier, forming a steric barrier around the nanoparticles that minimizes agglomeration and ensures stable suspension in gear oil for over 90 days, as confirmed by sedimentation and ICP analysis. This improved stability enables consistent nanoparticle interaction at contact interfaces, resulting in superior lubrication effects. At a very low concentration of just 0.005 wt%, OA-functionalized CuO nanofluids achieved up to 35.8% reduction in the coefficient of friction and 25.6% reduction in wear scar diameter (WSD) in industrial gear oil (G-2), and 18.1% and 14.9% reductions, respectively, in automotive gear oil (G-1). Additionally, the initial seizure load (ISL) and load wear index (LWI) were improved by up to 26% and 33.3%, respectively, while thermal conductivity saw an increase of up to 31.4% at 70 °C, further supporting the role of OA-CuO in reducing frictional heat and oxidative degradation.

Among various nanoparticles investigated for nanolubricant applications, CuO has emerged as one of the most effective candidates due to its favorable thermal conductivity, chemical stability, and tribological enhancement potential [14,19,20,21]. For instance, in our recent screening study [22], we systematically compared the tribological performance of three common nanoparticle additives (CuO, GO, and MoS₂) under identical operating conditions, without any surface functionalization. CuO consistently demonstrated superior friction reduction across varying loads and speeds, with COF reductions of up to 42%.

Moreover, a recent study by Hisham et al. [23] investigated the performance of CuO nanoparticles blended with cellulose nanocrystals (CNCs) in SAE 40 engine oil and revealed significant improvements in lubricant properties. The hybrid nanolubricant exhibited a 44–47% increase in viscosity index, up to 31% reduction in coefficient of friction under mixed lubrication, and notably smoother wear surfaces under ASTM G181 testing.

These points made CuO the most reliable and effective additive for further development, justifying its selection for functionalization and advanced tribological testing in this study.

In the current work, we aimed to achieve critical enhancements in the colloidal stability of a CuO nanoparticle-enhanced lubricant by application and careful tuning of the OA/OAm ligand pair. This was achieved by the application of a systematic optimization approach based on the dual use of Response Surface Methodology (RSM) and Bayesian Optimization (BO), as developed in our previous work [22]. RSM was used to explore the effects of different concentrations of nanoparticles and surfactants on the tribological performance of the nanolubricants, while BO was employed to fine-tune the optimal concentrations identified by RSM, ensuring that an optimized combination of ligand and nanoparticle concentrations was achieved. While RSM is a useful tool for experimental optimization, it can be limited by low model confidence and difficulty in identifying true optimal conditions, especially in complex systems. To overcome these challenges, combining RSM with machine learning (ML) methods like Bayesian Optimization (BO) offers a more powerful approach. This hybrid method reduces the number of required experiments while improving accuracy, making it more effective than using either RSM or ML alone [24,25,26].

The findings of this study provide valuable insights into the design and optimization of nanolubricants for high-performance applications.

2. Materials and Methods

2.1. Synthesis of Surface-Modified Nanoparticles

Oleic acid (OA), oleylamine (OAm), and CuO nanoparticles were purchased from Sigma-Aldrich (Gillingham, UK). The mineral base oil of SAE 20W50 was purchased from Halfords (Redditch, UK). All material properties are detailed as purchased in

Table 1. Material properties of nanoparticles, ligands, and base lubricant.

Substance (Purity)	Appearance		Empirical Formula	Molar Mass (g·mol−1)	Boiling Point (°C)
Copper Oxide (99.99%)	Spherical Dark Gray Particles (35 ± 5 nm)		CuO	79.55	-
Oleylamine (98%—primary amine)	Colorless to Yellow		C18H37N	267.49	348–350
Oleic acid (99.99% GC)	Very Faint Yellow		C18H34O2	282.46	194–195
Base Lubricant	Density at 15 °C (kg/m3)	Kinematic Viscosity (cSt)	Viscosity Index	Flashpoint (°C)	Pour Point (°C)
SAE 20W50	892.1	176.4 (40 °C) 19.1 (100 °C)	123	240	–24

.

Nanofluids containing modified CuO nanoparticles with 0.04–0.7 wt% were synthesized via a two-step method [13,27]. First, OA and OAm were added to about 30 mL of ethanol and stirred continuously at 100 °C for 60 min. Next the CuO nanoparticles were added and stirred for a further 60 min, before being sonicated for 30 min with a probe sonicator (Hielscher UP200St 200 W 26 kHz ultrasonic homogenizer, Hielscher Ultrasonics GmbH, Teltow, Germany). After sonication, the solution was stirred at 100 °C for another 2 h or until all the ethanol evaporated, leaving a slurry at the bottom of the beaker. This slurry was dried at 90 °C in a vacuum oven for 24 h, resulting in a functionalized fine powder of CuO nanoparticles coated with OA and OAm ligands [17]. The nanoparticle powder was then mixed into SAE 20W50 engine oil by stirring at room temperature for 6 h to ensure full dispersion. Finally, the nanolubricant was transferred into glass bottles or vials for storage and further testing.

2.2. Characterization of Functionalized CuO Nanoparticles

The size and crystalline structure of the unmodified CuO nanoparticles (NPs) were analyzed using Transmission Electron Microscopy (TEM) (JEM, JEOL, Tokyo, Japan) and X-Ray Diffraction (XRD) analysis (Empyrean, Malvern Panalytical, Malvern, UK). Fourier Transform Infrared (FTIR) spectroscopy (Nicolet iS-50, Thermo Scientific, Waltham, MA, USA), Thermogravimetric Analysis (TGA) (Mettler Toledo, Greifensee, Switzerland), UV–vis spectroscopy (UV-1800 Spectrophotometer, Shimadzu, Kyoto, Japan), and Raman spectroscopy (RMS1000, Edinburgh Instruments, Livingston, UK) were performed to characterize the functionalized NPs.

FTIR analysis was carried out at room temperature in transmission mode, spanning the spectral range of 400 to 4000 cm⁻¹ with a resolution of 4 cm⁻¹. Thermogravimetric Analysis (TGA) was performed using a Thermal Analysis System TGA/DSC 3+. A total of 30 mg of each sample was placed in an alumina crucible, and experiments were conducted under nitrogen at a flow rate of 2 mL/min. The samples were stabilized at an isothermal temperature of 30 °C, followed by a gradual increase in temperature at a rate of 10 °C/min up to 600 °C. The heating rate was then further increased until reaching 1000 °C to ensure the complete vaporization of any remaining residues.

UV–vis analysis was performed using 220 nm transparent cuvettes. The change in nanoparticle concentration in the lubricant over time was compared for CuO nanoparticles both with and without surface modification over 5 weeks. Concentration was determined by evaluating the Beer–Lambert Law ($A=\epsilon cl$, where $\epsilon$ is the molar extinction coefficient (M⁻¹·cm⁻¹), $c$ is the nanoparticle concentration (M), and $l$ is the path length (cm)). Bandgap energies were calculated using the Tauc function [28,29,30,31,32].

$$\alpha hV=A{\left(h\nu -E_g\right)}^n$$

(1)

where $A$ is the energy-independent coefficient, $E_g$ is the band gap energy, $h$ is Planck’s constant, $\alpha$ is the absorption coefficient, $n$ is a constant (1/2 for semiconductors), and $\nu$ is the photon frequency. Bandgap energy was calculated from the intercept of a plot of ($\alpha$·$E_{Phot}$)² vs. $E_{Phot}$ yielding $E_g$ for a direct transition, where $E_{Phot}=h\nu$ [29,32]. The extrapolation of the linear portion fitting of the curve to ($\alpha$·$E_{Phot}$)² = 0 is the band gap energy. The molar extinction coefficient of CuO nanoparticles was determined using the Beer–Lambert law by preparing a series of known concentrations of functionalized CuO nanolubricants and measuring their corresponding UV–vis absorbance values. The sedimentation kinetics of the nanolubricants were quantitatively analyzed by fitting the experimental concentration–time data to the exponential decay model.

$$C\left(t\right)=C_o·{\left(e\right)}^{-Kt}$$

(2)

where $C\left(t\right)$ is the nanoparticle concentration at time t, $C_o$ is the initial concentration, and K is the sedimentation rate constant. This approach has been widely employed to assess colloidal stability and nanoparticle dispersion behavior in various systems, which is commonly known from colloid science theories describing aggregation and sedimentation [33,34,35].

Raman spectroscopy was carried out using a 532 nm laser source with 100% laser power and an exposure time of 30 s.

2.3. Evaluation of the Tribological Performance

Tribological characterization was performed using the advanced ASTM D4172B-21 [36] (four-ball method) standardized test. The experiments were conducted using an MMW-1A computer-controlled vertical universal friction and wear testing machine (Jinan Liangong Ltd., Jinan, China). Balls were GCr15 steel, with a diameter of 12.7 mm and a hardness rating of HRC 63–65. The lubricating oil temperature was consistently maintained at 75 °C, and the test duration was set to 60 min. The coefficient of friction (COF) was continuously recorded by the data acquisition system with a time resolution of 300 ms.

In this test, the three lower balls were held stationary, while the upper ball was rotated at a predetermined speed using a motor. Average wear scar diameters (WSDs) on the three lower balls were measured using an optical microscope. The wear volume (V) in mm³ for the three balls post-test was estimated using the following equations [37,38].

$$V=({\displaystyle \frac{\pi h}{6}})({\displaystyle \frac{3d^2}{4}}+h^2)$$

(3)

$$h=r-\sqrt{r^2-{\displaystyle \frac{d^2}{4}}}$$

(4)

where d is the wear scar diameter and r is the radius of the ball in mm. For calculating the specific wear rate (SWR) [7,17],

$$SWR={\displaystyle \frac{V\left({mm}^3\right)}{LS(N\cdot m)}}$$

(5)

where V is the calculated wear volume of the balls, L is the normal load applied to the bottom balls, and S is the total sliding distance. All specific parameters, test conditions, and properties of the friction pair used in this study are detailed in

Table 2. Material properties of friction pair of balls, parameters, and test conditions.

Material	Density (g/cm3)	Diameter (mm)	Hardness (HRC)	Poisson’s Ratio	Elastic Modulus (GPa)
GCr15	7.8	12.7	63–65	0.3	208
Load (Kg, N)	Hertz Pressure (GPa)	Rotating Speeds (rpm)	Linear Speed (m/s)		Temperature (°C)
40 kg ± 0.2 kg, 392 N ± 2 N	892.1	1200	0.461		75 °C ± 2 °C

.

For, SEM/EDX analysis, all samples were cleaned with ethanol, dried, and then examined.

2.4. Hybrid Optimization by RSM and BO

Combined Response Surface Methodology (RSM) and Bayesian Optimization (BO) was carried out following our previously published method [22]. For RSM, the input variables were oleic acid concentration (A), oleylamine concentration (B), and CuO nanoparticle concentration (C), with the output variable being the coefficient of friction (COF) according to ASTM D4172B-21.

Input variables were assigned three levels (−1, 0, +1) as outlined in

Table 3. Levels and coded variables for the Box Behnken Design.

Factor	Code	Units	Coded Variable Levels
			–1	0	1
Oleic Acid Concentration (OA)	A	wt%	2	3.5	5
Oleylamine Concentration (OAm)	B	wt%	4	10	16
Copper Oxide Concentration (CuO)	C	wt%	0.04	0.05	0.07

. A quadratic response surface model (Equation (6)) was used, featuring twelve axial points and three to five center replicates for a three-factor model.

$${Y=\beta }_o+{\sum }_{i=1}^n{\beta }_i{X}_i+{\sum }_{i=1}^{j-1}{\sum }_{j=2}^n{B_{ij}X}_i{X}_j+{\sum }_{i=1}^n{\beta }_{ii}{X}_i^2$$

(6)

where Y is the predicted response of the prior function (objective function), $X_{i,j}$ is the output variable, ${\beta }_0$ is a constant, $B_{ij}$ is the interaction coefficient, ${\beta }_i$ is the linear coefficient, and ${\beta }_{ii}$ is the quadratic coefficient. In the BO analysis, the objective function derived from the Design of Experiments (DOEs) was modeled using a Gaussian Process (GP) as the surrogate model. This analysis was implemented in Python 3 using the GPyOpt library, which is based on Gaussian Process modeling.

The selection of OA–OAm ratios for the hybrid ligand system was guided by previous studies that demonstrated the synergistic role of this ligand pair in achieving steric stabilization of nanoparticles. According to molecular mechanics simulations [13], the co-adsorption of oleic acid (OA) and oleylamine (OAm) onto nanoparticle surfaces induces sufficient steric repulsion to reduce aggregation by modulating surface interactions and surface energy.

Additionally, as reviewed by Mourdikoudis [11], the OA/OAm pair has been widely employed in nanoparticle synthesis due to its ability to form a dynamic, packed shell around the nanoparticles, enhancing colloidal stability. Based on this literature, a series of OA–OAm ratios was selected and systematically evaluated using RSM and BO to determine the optimal balance between surface coverage and dispersion quality.

In this methodology, we employed a combination of Response Surface Methodology (RSM) and Bayesian Optimization (BO) to determine the optimal concentrations of the OA/OAm ligand pair and CuO nanoparticles. The goal was to minimize the coefficient of friction (COF), as measured by the ASTM D4172B-21 standard, while achieving optimal colloidal stability, verified through subsequent analyses.

2.5. Dispersion Stability, Physical, and Rheological Characteristics

Dispersion stability and rheological behaviors of the optimized CuO-OA/OAm nanolubricant were tested using sedimentation analysis and dynamic and high-temperature, high-shear (HTHS) viscosity analysis (Rheolab QC rheometer, Anton Paar, Graz, Austria). Flash point analysis was performed on a Koehler K13990 (Koehler, Holtsville, NY, USA), and pour point analysis was performed on a WiseCircu WCT-80 (WiseCircu, Seoul, Republic of Korea).

3. Results and Discussion

3.1. Surface Chemistry and Thermal Stability of the Modified Nanoparticles

We first conducted basic testing to ensure successful coating of the CuO nanoparticles with the OA/OAm ligand pair. The combined analytical methods enabled a detailed examination of the grafted layer on CuO nanoparticles, providing robust verification of the functionalization effects, particularly the influence of the OA/OAm ligand pair on surface properties [16,17,38,39]. The sample for this initial FTIR, Raman, TGA, and UV–vis analyses was 0.04 wt% CuO nanolubricant, selected based on our prior optimization study [22], and was examined both with and without surface modification. The ratio of the OA to OAm ligand pair for this comparative sample was set at 1:2, as recommended by [13]. Details regarding the XRD and TEM size distribution of the bare CuO NPs are provided in the Supplementary Material (Figure S1). Briefly, the TEM analysis shows a size distribution of less than 50 nm, as mentioned in the certificate of analysis, and the XRD is indexed to the cupric oxide (CuO) phase. TEM analysis (Figure S1c) revealed that the CuO nanoparticles have a mean diameter of approximately 30 nm, with a size distribution ranging from 15 nm to below 50 nm.

The FTIR spectra (Figure 1a) show a comparison of the functionalized CuO nanoparticles to the pure oleylamine, pure oleic acid, their mixture, and the base lubricant. The two sharp peaks at 2922 and 2852 cm⁻¹ are attributed to the asymmetric and symmetric stretching vibrations of the methylene (-CH₂-) groups, respectively [40]. These bands are characteristic of long-chain hydrocarbons, found in base oil and the carbon chains of the OA and OAm. For pure oleic acid, a peak around 1710 cm⁻¹ is typically associated with the C=O (carbonyl) stretching vibration of a free carboxylic acid group (-COOH) in oleic acid (head group) [13]. The absence of this 1710 cm⁻¹ peak in the functionalized CuO nanoparticles suggests complete attachment of the OA to the CuO and complexation with OAm in the OA–OAm complex. Further, the broad band observed between 1525 and 1606 cm⁻¹, which appears in both the OA/OAm sample and the functionalized CuO nanoparticles, is indicative of the carboxylate anion (COO⁻) formation, suggesting formation of the OA–OAm complex and a chemisorption process onto the surface of CuO NPs [13]. This broad band is characteristic of the asymmetric (ν_as) and symmetric (ν_s) stretching vibrations of the carboxylate group, confirming the chemical interaction between the OA and the CuO nanoparticle surface, wherein the carboxylate group binds to the copper atoms, forming a stable chemisorbed layer [13,41,42,43]. This is supported by the absence of the stretching modes of the amine group RCNH₂ of OAm (head group) at 795 cm⁻¹ in the samples of OA/OAm and the functionalized CuO NPs. This phenomenon is referred to in various studies, which refer to it as the ABC reaction and/or NP chemosorbed surface layer [40,43,44,45,46]. The characteristic peak for CuO NPs at 604 cm⁻¹ is referred to as the vibration band range of Cu-O for copper oxide, which can also be seen in the functionalized NPs and CuO nanolubricant [18].

The formation of acid–base complexes between OA and OAm during the functionalization process is a critical aspect that further stabilizes the nanoparticles. The carboxylic acid head group (RCOOH) in oleic acid forms an acid–base complex with the amine head group (RCNH₂) [13], following Equation (7).

$$RCOOH+RCN{H}_2\rightleftharpoons RCO{O}^{-}:RCN{H}_3^{+}$$

(7)

The deprotonated OA then adsorbs onto the CuO NP, overcoming the weak hydrogen bonds in the complexes. This results in a free proton that will be available in the dispersion medium to bind with the OAm, as follows:

$$RCOOH\rightleftharpoons RCO{O}^{-}+H^{+}$$

(8)

$$RCN{H}_2+H^{+}\rightleftharpoons RCN{H}_3^{+}$$

(9)

The carboxylate anion group (RCOO-) interacts with the Cu²⁺ ions on the CuO surface through coordination bonding (forming a chemisorbed ligand layer) [13,15,40,43].

With the hydrophobic alkyl chain of oleic acid projecting outward from the CuO nanoparticle surface, colloidal stability in non-polar environments like engine lubricants is promoted, along with providing steric stabilization to the particle dispersion [8,10]. A repulsive steric force originates from entropic and osmotic repulsion, with deformation of the absorbed or grafted surface layer of OA/OAm. When two particles with surface-grafted layers approach, the surface layer deforms, and the conformation of the grafted molecule changes. This leads to a change in the free energy and the repulsive force [8,47].

The Raman spectra (Figure 1b) confirmed the interaction between the OA/OAm ligands and CuO nanoparticles through a red shift in the characteristic vibrational modes of CuO, shifting from 278, 324, and 614 cm⁻¹ in the unmodified nanoparticles to 269, 317, and 608 cm⁻¹ after surface functionalization. This shift indicates a reduction in inter-particle interactions and aggregate formation, resulting from the steric stabilization provided by the surface ligands. The attachment of OA and OAm restricts nanoparticle growth and suppresses agglomeration, leading to smaller, more dispersed particles. Such effects have been observed in similar studies, where ligand-modified CuO nanoparticles and other semiconductor nanoparticles exhibit altered Raman active modes due to reduced particle size and inhibited oriented attachment after surface functionalization [48,49]. The vibration bands at 1300 and 1440 cm⁻¹ are associated with the grafting layer of the OA/OAm ligand pair [50,51]. The band at 1300 cm⁻¹ is characteristic of the C-H bending twist of the long-chain hydrocarbons -CH₂ methylene group, while the band at 1460 cm⁻¹ is CH₂ bending or scissoring motion [50], which validates the presence of the OA/OAm on the surface of CuO nanoparticles. The broad low-intensity band observed at 1656 cm⁻¹ for the functionalized CuO nanoparticles may suggest disordered carbon chains of the ligand pair [51].

In the TGA analysis (Figure 2a), both the pure OAm and OA profiles showed single degradation events at 170 °C and 238 °C, respectively. The OAm/OA mixture exhibited two degradation events, at 206 °C and 290 °C, attributed to the degradation of OAm and OA, respectively. The functionalized CuO nanoparticles exhibited a slow weight loss of 27.7% in the range of 180–287 °C, corresponding to volatilization of the adsorbed OA/OAm layer. The analysis revealed a differing amount of adsorbed OA and OAm, and that OA has a higher binding affinity to the CuO surface. Indeed, OA will preferentially bind through multiple bonding modes, while OAm can only bond through the N lone pair donation [11]. During rapid weight loss of functionalized CuO (288–338 °C), OA/OAm mass losses of 38.9% and 49.2% indicate a higher surface concentration of OA, suggesting preferential adsorption of OA onto CuO nanoparticles. Previous works have noted the same, for example, for Au surfaces [46]. This slower, extended loss profile reflects the desorption of chemisorbed OA/OAm molecules from the nanoparticle surface. Notably, the bound ligands degrade at higher temperatures compared to their pure forms. The carboxyl group of the OA is capable of forming stronger and more thermally stable bonds with the CuO surface compared to the amine group in OAm, which facilitates, on the other hand, the formation of the acid–base complex.

Overall, the ligand pair of OA/OAm has a total mass of surface coverage of 49.2%, and is totally evaporated at 472 °C, which is considered thermally stable and applicable for engine lubricant working temperatures that reach a maximum of 150 °C [52,53].

UV–vis absorption analysis (Figure 2b) showed that the comparative sample of nanolubricants prepared with the functionalized CuO nanoparticles has greater colloidal stability than those with bare CuO nanoparticles (Figure 2b) over a study period of 36 days. The sedimentation rate was insignificant for the first three days, whether the nanoparticles were grafted with OA/OAm or not. Starting from day 12 to day 36, the grafted layer of OA/OAm slowed down the sedimentation kinetics of CuO nanoparticles significantly.

The functionalized CuO nanolubricant exhibited a markedly lower sedimentation rate constant (k = 0.003 day⁻¹) compared to the unmodified CuO nanolubricant (k = 0.012 day⁻¹), indicating significantly enhanced colloidal stability. In the context of sedimentation kinetics, a lower k value corresponds to a slower rate of concentration loss over time, meaning that a larger fraction of nanoparticles remains suspended in the medium for longer durations. This improved stability can be attributed to the effective surface functionalization with OA and OAm, which form a sterically stabilizing ligand shell around the CuO nanoparticles. The surface-bound OA provides strong coordination through carboxylate groups, while OAm interacts through amine lone pair donation, resulting in a hybrid ligand architecture that inhibits agglomeration and gravitational settling. These interactions reduce inter-particle attraction, increase steric hindrance, and enhance the dispersive affinity of nanoparticles within the base oil. Therefore, the lower sedimentation rate constant quantitatively supports the conclusion that OA/OAm-functionalized CuO nanoparticles offer enhanced dispersion stability compared to their unfunctionalized counterparts.

Tauc plots showed a small increase in band gap energy between the bare (1.60 eV, Figure 3a) and functionalized (1.62 eV, Figure 3b) CuO nanoparticles, likely due to the effect of the ligands in passivating surface traps and reducing agglomeration growth. These values of band gap energies are close to the reported values of CuO nanoparticles in the size range of 20–50 nm [30,32].

3.2. Optimization Analysis

Following confirmation of improved colloidal stability using literature-derived CuO nanoparticle concentration, ligand concentrations, and ratios, we sought to optimize the preparation of our CuO nanolubricant. Specifically, we intended to improve the colloidal stability while maintaining or improving the tribological properties of the nanolubricant. Following an RSM methodology, we used Box Behnken Design (BBD) to model the coefficient of friction (COF) as a function of the concentrations of OA, OAm, and CuO as three independent variables, using three levels for each. A quadratic (second-order) model was used in the regression. This was then used as a prior function in a Bayesian Optimization (BO) routine, which was used to refine the model.

COF response values are shown in

Table 4. COF results for all conditions tested for the Box Behnken Design model.

Run	Factors			Ligand Ratio	Response (COF)
	A: Oleic Acid Concentration (OA)	B: Oleylamine Concentration (OAm)	C: Copper Oxide Concentration (CuO)	OA–OAm
1	5	10	0.07	1/2	0.0167
2	3.5	16	0.07	2/9	0.0167
3	3.5	10	0.055	1/3	0.0153
4	2	4	0.055	1/2	0.0136
5	3.5	4	0.04	7/8	0.0159
6	2	10	0.07	1/5	0.0103
7	5	4	0.055	5/4	0.0133
8	3.5	10	0.055	1/3	0.0150
9	5	16	0.055	1/3	0.0035
10	3.5	16	0.04	2/9	0.0028
11	2	16	0.055	1/8	0.0030
12	5	10	0.04	1/2	0.0038
13	3.5	10	0.055	1/3	0.0152
14	3.5	10	0.055	1/3	0.0152
15	3.5	10	0.055	1/3	0.0154
16	3.5	4	0.07	7/8	0.0151
17	2	10	0.04	1/5	0.0124

. The resultant quadratic relationship (prior function), between the independent variables (A, B, C) and the response (COF), is

$$\begin{gathered} \mathit{ln}COF=-3.31169+\left(0.320774\right)A+\left(0.155719\right)B+(-29.5575)C+(-0.0129372)AB+\left(14.1687\right) AC \\ +\left(5.47986\right)BC+(-0.155839)A^2+(-0.00902985)B^2+(-422.05) C^2 \end{gathered}$$

(10)

Each coefficient (before the individual and quadratic terms) represents the effect of this model term on the final response surface. The interaction between two factors is characterized by the coefficients before each two-factor term (Equation (10)). Thus, it can be seen that there is a high effect on the response (COF) from the concentration of OA (A), concentration of OAm (B), and the interaction between the OA with CuO concentration (AC) and OAm with CuO concentration (BC).

The results were evaluated using analysis of variance, ANOVA (Table S1), in order to verify the response model adequacy. The p-value represents the significance related to the variation of each model term, while the f-value represents its interactions with others. The model f-value (31.56) and low p-value (0.0001) revealed that this quadratic model was sufficient to predict the response (COF). The lack-of-fit for the model was not significant (p-value 0.3823). The normal probability assumption of residuals for this model was validated (Figure S2), and the quality of the model (R²) was close to unity (0.9726). Therefore, the resultant model was suitable for further analysis. The adjusted R² (0.9418) was very close to the R² (i.e., the difference between the predicted and actual model points was very low) (Table S1).

For the p-values (Table S1), it was seen that that the three linear coefficients (A, B, and C), two quadratic coefficients (A², B²), and two interaction coefficients (BC and BC) have significant correlation with the response (i.e., their p-values are <0.05, indicating a 95% confidence level). The interaction between A and B (AB) and C² did not significantly affect the final response. This means that changing the concentration only of OA and OAm, while keeping the concentration of CuO nanoparticles fixed or even squaring its value, does not affect the final tribological properties. A low coefficient of variation percentage (CV) of 3.51% revealed a low variation between predicted and experimental values. Finally, the high value of adequate precision (16.3156) signified low noise in the data (where greater than four is appropriate for BBD).

The regression model is represented by the 3D response surfaces and 2D interaction plots (Figure 4). These allowed visualization of the relationship between the experimental level of each variable and its effect on the response. At low and intermediate concentrations of CuO (0.04 and 0.055 wt%), increasing the percentage of OAm (B+) at most of the OA concentrations led to a significant reduction in the COF, compared to reducing the percentage of OAm. This is likely due to the important role of the OAm in initiating the acid–base complex reaction (ABC reaction) that provides a good environment of repulsive steric forces [11,13,45,54]. This steric stability can then decrease the attractive van der Waals force and prevent agglomeration that can adversely affect the tribological properties [8]. Under some other conditions of varying OA, OAm, and CuO, the friction properties of the lubricant are adversely affected. This can be attributed to the interaction at specific levels of ligand that can occur with nanoparticles, which leads to cross-agglomeration of nanoparticles or the interaction of ligands with lubricant molecules that can affect their viscosity, chemical, and thermal properties, and thus, the load-carrying capacity of the lubricant [53,55].

The estimated ranges that minimize the response of the objective function (from the BBD analysis) range from 1:8 to 1:2 for the OA–OAm ligand ratio, and from 0.04 to 0.05 wt% for the CuO concentration. RSM models are known to yield relatively low confidence levels for any particular condition [22]. Therefore, we sought to derive a specific solution (i.e., optimized concentrations of CuO and the OA/OAm ligand pair) that yields the greatest reduction in COF, for which we used a Bayesian Optimization (BO) approach.

In order to identify experimental conditions that yield target product properties and to identify specific regions of the search space that would allow this, we can apply BO to the prior function. An upper and lower bound of each decision variable in the prior function allowed us to define these regions. Overall, this approach allows us to conduct a relatively small number of experiments to derive a function by the DOE approach, which can then be refined using BO towards target OA/OAm ligand ratios to minimize COF.

As a test case, we selected a specific range of OA and OAm wt% (as previously in the DOE, i.e., 2–5 wt% for OA and 4–16 for OAm). We then chose a CuO wt% of 0.04 wt%, as the recommended nanoparticle concentration in our previous study that yielded the optimum tribological behavior of the non-functionalized CuO nanolubricant [22].

Through the BBD study, we observed a crucial effect of using the low concentration levels of CuO, specifically 0.04 wt% (Figure 4a,a*), in enhancing and optimizing the friction performance for CuO nanolubricants functionalized by the OA/OAm ligand pair. Therefore, we employed BO in order to refine the objective function in this region to yield a target OA/OAm ratio with a higher confidence level.

The results of the BO are shown in Figure S3. The solution yields an OA/OAm ligand pair ratio of 1:3 with the 0.04 wt% CuO that minimizes the COF. Irrespective of the number of iterations required by the model to reach the optimized solution, the results fall within the limits suggested previously by DOE for the optimization of the loss function (i.e., between 1:8 and 1:2 for the OA–OAm ligand ratio).

Bayesian Optimization (BO) is based on three main functions: the objective function (output of the BBD in our case), surrogate function, and acquisition function. The objective function refers to the real function that one wants to optimize, but is, in most cases, expensive to evaluate. To help minimize the cost of evaluation, BO uses a surrogate function (Gaussian Process in our case) to fit the objective function based on past evaluations and provide predictions with corresponding uncertainty estimates. The acquisition function operates on these predictions and uncertainties, assessing the next best point to sample by balancing exploration in uncertain regions with exploitation for potential improvements. This process is iterated, so the surrogate model becomes sequentially updated with new data from the evaluations of the objective function up to the point when an optimal solution is found or a stopping criterion is reached, doing it quickly by requiring the smallest number of expensive evaluations. Thus, this process is known as sequential model-based optimization (SMBO).

3.3. Tribological Characteristics

The tribological characteristics of the functionalized CuO nanolubricants were assessed using a four-ball tribometer under standardized testing conditions as per ASTM D4172B-21. These conditions were consistent with the previous optimization analysis of Design of Experiments (DOEs). The primary objective was to evaluate the effect of CuO nanolubricants and validate the added value provided by functionalized CuO nanoparticles. Various samples with different CuO concentrations and OA/OAm ligand ratios were selected, as shown in

Table 5. Summary of the tribological properties of the CuO nanolubricant at different conditions.

Lubricant Sample	CuO wt%	OA–OAm Ligand Pair Ratio	Specific Wear Rate—SWR (mm3/N·m) × 10−10	Percentage Reduction in SWR % vs. Base	Wear Scar Diameter—WSD (um)	AVG COF	Percentage Reduction in COF % vs. Base
Base Sample	0	0	4.583	-	443.121	0.0089	-
Optimized Sample	0.04	1:3	1.650	63.99	369.893	0.0035	60.67
Comparative Sample	0.04	1:2	0.987	78.47	364.320	0.0049	44.94
Blank Sample	0.04	0	3.244	29.22	406.467	0.0037	58.43
Sample #17	0.04	1:5	1.680	63.34	353.760	0.0124	30.34
Sample #7	0.05	5:4	6.300	−37.49% (Increase in SWR)	479.893	0.0133	−49.44 (Increase in COF)

, to be tested against the optimized sample. This was performed to examine the impact of altering CuO concentrations and ligand ratios on the final tribological behavior. This includes a base sample (as received lubricant), blank sample (CuO lubricant without ligands) with 0.04 wt% CuO suggested by our previous optimization study [22], a comparative sample with 0.04 wt% CuO loaded with OA–OAm ligand ratio of 1:2 as suggested by the literature [13], and two samples from the DOE analysis, referred to as Sample #17 and Sample #7 with different CuO wt% and ligands loadings of OA/OAm of 1:5 and 5:4, respectively, as shown in Table 5.

Figure 5a illustrates that the optimized, blank, and comparative samples demonstrated a significant reduction in the COF compared to the base oil, with an improvement ranging from 44.9% to 60.6%. These improvements were notably achieved under high-temperature conditions (75 °C) that simulate a dry friction scenario by the four-ball test. This suggests that CuO nanoparticles, whether functionalized with ligands (as in the optimized and comparative samples) or not (as in the blank sample), are effective in protecting surfaces under severe conditions by minimizing frictional energy losses.

However, the results for Samples #7 and #17, which involved varying CuO concentrations and OA/OAm ligand pair ratios, revealed a different scenario. In these cases, the tribological performance deteriorated, with COF values surpassing even those of the base oil without any nano-additives. This observation underscores the critical role of optimizing both the concentration of CuO nanoparticles and the ligand ratios to achieve desirable tribological outcomes. Inappropriate combinations can lead to increased wear and friction, conflicting with the benefits typically associated with nanolubricant formulations, as mentioned in the literature.

Continuing with the analysis, the trends observed for the specific wear rate (SWR) and wear scar diameter (WSD) are consistent with those of the COF, as presented in Table 5 and Figure 5b. Most samples demonstrated a notable enhancement in antiwear characteristics, whether the CuO nanoparticles were functionalized or not, compared to the base oil, with an improvement ranging from 44.9% to 60.6% in COF and from 29.2% to 63.9% in SWR. This indicates that CuO nanolubricants possess effective frictional and wear properties. The results further suggest that the incorporation of OA/OAm ligand pairs at specific ratios not only improves the dispersion stability of the nanoparticles but also creates a synergistic effect that significantly enhances tribological performance.

Specifically, for Sample #17, the SWR was comparable to that of the optimized sample. This can be attributed to a particular lubrication mechanism where the nanoparticles interact with the surface, potentially forming a protective film that reduces wear. However, this advantage in wear rate comes at the cost of a slight compromise in friction properties (COF), as observed in several studies of nanolubricants [56]. The wear mechanism likely involves the nanoparticles filling in surface asperities, reducing direct metal-to-metal contact and thereby decreasing the wear rate while potentially altering friction characteristics.

The microscopic examination of wear scar diameters on the three balls for each sample, shown in Figure 6, revealed severe grooves, scratches, and heterogeneous areas on the friction surfaces. These observations reflect the dry friction conditions characteristic of the four-ball test, where excessive asperity contact occurs due to lubricant thinning. While all samples exhibited some degree of surface roughness, the optimized, blank, and comparative samples (Figure 6a,b,d) displayed smoother wear scars with finer, tighter, and shallower, to some extent, abrasion marks compared to the base oil sample (Figure 6c). This suggests that, under certain conditions, the CuO nanolubricants—whether functionalized or not—can provide better surface protection and minimize abrasive damage.

Furthermore, the wear shape for Sample #17 was significantly better than that for Sample #7, likely due to the enhanced antiwear performance achieved with the specific OA/OAm ligand ratio of Sample #17. As previously discussed, while this ratio is effective in reducing wear, it does not necessarily correlate with a reduction in COF.

This highlights the complexity of optimizing tribological properties, where a balance must be struck between reducing both friction and wear simultaneously while maintaining sufficient colloidal stability.

For SEM/EDX analysis (Figure 7), the micromorphology for the lower ball for both optimized and base samples showed a relatively similar pattern of abrasion scratches, small cracks, and merging pits. However, in the case of the optimized sample, reduced scratching gave a smoother surface, in line with the friction and WSD results. The promotion in friction properties of the CuO nanolubricant is ascribed to the formation of low-resistance lubricant films (tribo-film generation), as discussed in our previous study [22]. This was confirmed through EDX surface mapping. Here, white spots on the ball surface showed signals of Cu, besides the elements of Fe, C, Cr, Mn, and V, coming from the steel balls (Figure 7a). Such tribo-films yield reduced metal–metal contact, which can be linked to the reduced COF and wear rates observed herein [16,17,57,58].

Surface roughness parameters (Ra and Rz) were thoroughly analyzed in our recent prior study [22], where the use of CuO nanolubricants led to a noticeable reduction in surface roughness, indicating a transition toward mild polishing wear and effective tribo-film formation. As the current work builds upon those findings with a focus on enhancing colloidal stability, detailed roughness measurements were not repeated here but remain relevant for interpreting the wear behavior observed.

3.4. Colloidal Stability and Rheological Properties

Characterization of other physical and chemical properties, friction, and wear is possible only if the dispersion and stability of nanofluids are achievable. The miscibility between CuO nanoparticles and SAE 20W50 oil was studied using UV–vis spectra and visual observation methods, which are reported in recent studies of nanolubricants [16,53,56].

The agglomeration tendency of the nanoparticles was assessed through two time points: one day and five weeks (36 days) after synthesis. To ensure consistency, all selected CuO colloid samples were stored under ambient conditions prior to UV–vis measurements (Figure 8). The analysis involved three distinct samples: the blank sample (no ligands), the comparative sample (OA/OAm of 1:2), and the optimized sample (OA/OAm of 1:3) (Table 5). Characteristic peaks of the absorption spectra of the CuO nanolubricant samples (Figure 8a,b)—which highly depend on the particle size, morphology, and dielectric constant of the surrounding medium [48,53,59]—are located around 600 nm and 650 nm. The first peak is correlated to the size effect of the dispersed nanoparticles, whereas the second peak reflects the oxidation state of copper and material defects, such as vacancies of O and Cu [41,48,59]. The UV–vis results suggest that the surface modification of CuO NPs by OA/OAm suppresses agglomeration (Figure 8), for both the optimized and comparative samples, where the loss of absorption is shown to be reduced with time during the five weeks of study in comparison with the non-treated CuO NPs. These results show that the presence of the ligands has a significantly positive effect on enhancing colloidal stability.

The rheological and thermophysical characterization (Figure 9) show that the addition of the OA/OAm ligand pair to CuO nanoparticles did not significantly change these properties, in contrast with the unmodified base oil. For example, in both cases of the CuO nanolubricant, there was no change in the Newtonian behavior of the base lubricant (0 wt% CuO), revealed by an unchanging dynamic viscosity with an increasing shear rate (Figure 9a). Here, there was a linear relationship in the shear stress versus shear at high temperature (100 °C) and the shear rate range of 1–5000 s⁻¹ (Figure 9b). The same scenario applies for the high-temperature, high-shear (HTHS) viscosity results (Figure 9c), where the same reduction in viscosity for both samples of CuO nanolubricants is observed at nearly 3.18 mPa.s compared with the base lubricant (3.49 mPa·s), at high temperature (150 °C) and shear rate (5.1 × 10³ s⁻¹). This reduced viscosity at elevated temperatures is a desirable trait in modern lubricant systems. It ensures lubricant flow through the small gaps under high shear, which occurs, for example, in valve trains and gear contacts. This facilitates efficient heat transfer and reduced wear [60,61].

The same scenario applies for flash and pour points analysis (Figure 9d). The CuO nanolubricant in both cases demonstrated near identical higher flash points of 264 and 262 °C, compared to 240 °C for the base lubricant, and a lower pour point of −25.5 and −25.8 °C, versus −24 °C. These characteristics indicate improved thermal stability, enabling the lubricant to function effectively at higher temperatures and offering enhanced oxidation resistance under high-temperature conditions.

The current rheological results meet with our previous optimization study of the CuO nanolubricant, emphasizing that the addition of the OA/OAm ligand pair is only significant regarding the colloidal stability and tribological behavior to some extent compared to the rheological and thermophysical properties [22].

4. Conclusions

This study demonstrated that surface functionalization of CuO nanoparticles with a hybrid ligand system of oleic acid (OA) and oleylamine (OAm) significantly enhances their colloidal and tribological performance in SAE 20W50 engine oil. FTIR, Raman, and TGA analyses confirmed successful ligand attachment via acid–base complexation, where OA provided strong chemisorption to CuO sites through its carboxyl groups, and OAm contributed steric stabilization via amine coordination. This dual-ligand approach effectively suppressed nanoparticle agglomeration, resulting in improved thermal resistance and dispersion stability, with UV–vis analysis showing minimal sedimentation for up to three weeks.

Optimization using a combined Design of Experiments (DOEs) and Bayesian Optimization (BO) approach identified the optimal formulation as 0.04 wt% CuO with an OA–OAm ratio of 1:3. Tribological testing via the ASTM four-ball method revealed substantial improvements in friction and wear performance, with the coefficient of friction reduced by up to 60.6%. SEM/EDX confirmed the formation of protective tribo-films, contributing to reduced surface damage. However, results also indicated that excessive ligand concentration may hinder tribo-film formation, emphasizing the need for a carefully balanced ligand ratio.

The key findings of our study can be summarized as follows:

• OA/OAm-functionalized CuO nanoparticles significantly enhanced dispersion stability, showing minimal sedimentation over a 5-week period.
• Tribological tests using the ASTM D4172 four-ball method revealed a reduction in the coefficient of friction (COF) by up to 39% compared to unmodified base oil.
• Optimal ligand-functionalized nanolubricants achieved up to 36.5% improvement in wear scar diameter (WSD) reduction.
• Hybrid optimization using RSM and Bayesian Optimization identified an ideal OA–OAm ratio of 1:3 and nanoparticle concentration of 0.04 wt%.
• The developed nanolubricants maintained Newtonian flow behavior and showed suitable high-temperature, high-shear viscosity performance.

Overall, these findings validate the critical role of surface chemistry in enhancing nanolubricant performance and provide a strong foundation for the design of stable, high-performance CuO-based lubricants suitable for long-term industrial use.