Study on Nanostructure and Oxidation Reactivity of Diesel Engine Exhaust Particulates Burning Methanol/F-T Diesel

Abstract

In this study, the exhaust particulates of a diesel engine burning methanol/F-T diesel blends were collected. The nanostructure and oxidation reactivity of the particulates were explored using the Brunauer–Emmett–Teller (BET) method, high-resolution transmission electron microscope (HRTEM), and thermogravimetric analysis (TGA), and the relationship between them was assessed via the partial least squares (PLS) and variable importance in the projection (PLS-VIP). The results showed that particulates from methanol/F-T diesel combustion were aggregates composed of several primary particles, and the distribution range of particulate half pore width ($R$) was 8~76 nm. As the methanol mixture ratio increased, the mean $R$ of particulates decreased, and the particulates′ total pore volume ($V_p$), specific surface area ($S_{BET}$), and the fractal dimension ($D_f$) increased. Compared with F-T diesel, methanol/F-T diesel blends particulates showed more disordered structure with a smaller diameter ($d_p$) of primary particles, a shorter fringe length ($L_a$), a wider separation distance ($d$), and a larger tortuosity ($T_f$). With increasing the methanol mixture ratio, it was also found that the amount of soluble organic fraction (SOF) of particulates increased, while oxidation characteristic temperature and the apparent activation energy ($E_a$) reduced. The correlation coefficients of $E_a$ with $T_f$ and $D_f$ were 0.99 and 0.98, respectively, by the linear fitting, illustrating that they showed the strongest linear relationship with the reactivity among the discussed nanostructure parameters. The VIP values of $D_f$, $T_f$, $V_p$, and d, with $E_a$ obtained by the PLS and PLS-VIP, were greater than 1, indicating that they were the chief factors influencing particulate reactivity.

1. Introduction

The diesel engine is the main power source of transportation, consuming a lot of oil resources. In the background of global energy shortage and environmental protection, it has become an important issue to find high-quality alternative fuels for diesel engines. F-T diesel is a liquid fuel derived from solid coal, and has excellent properties, including extremely low sulfur and aromatic content, and high cetane number, which make it attractive as an alternative to diesel [1]. It has been demonstrated that the F-T diesel engine can significantly reduce regulated and unregulated pollutant emissions [2,3]. At present, F-T diesel has achieved commercial-scale production in China, South Africa, Malaysia, and other countries [4]. Methanol can also be produced from coal, and both it and F-T diesel can be called coal-based fuels. Methanol is a high-oxygen-content fuel, and its properties, such as low boiling point and high latent heat of vaporization, are good for the improvement of combustion characteristics, and reduce NOx and PM emissions effectively. In addition, methanol also has the advantages of mature preparation technology and low cost [5], which has been widely used in diesel engines as a promising alternative fuel. Mixing methanol with F-T diesel helps enhance fuel ignition properties and promotes more efficient coal utilization [6].

Exhaust particulates are the main pollutant of the diesel engine, and they have a negative impact on human health and the ecological environment [7,8]. They exhibit a high degree of geometric complexity and consist of spherical or approximately spherical primary particles [9]. A diesel particulate filter (DPF) has a honeycomb structure [10], which can effectively remove particulate matter (PM) from diesel exhaust ports [11] and can meet strict emission regulations. Nevertheless, prolonged operation leads to the accumulation of particulate matter in the DPF, which may impair the performance of diesel engines [12,13]. Hence, it is necessary to eliminate these deposits through either active or passive regeneration processes [14]. The oxidation reactivity of particulates is related to regeneration efficiency and is a key issue in the regeneration process of DPF.

Different alternative fuels present different combustion reaction kinetics in diesel engines, changing the formation process of particulates, resulting in exhaust particulates with different physical properties and oxidation reactivity. Many scholars have previously conducted research on the content. Zhang et al. [15] carried out a structural analysis of soot sampled from ultra-low sulfur diesel fuel (ULSD) and Fischer–Tropsch diesel fuel synthesized from coal (CFT), and reported that the soot generated by FT had a more ordered structure than ULSD soot due to the almost zero aromatic and sulfur content, high H/C ratio, low viscosity, and distillation temperature of CFT. Wang et al. [16] evaluated the nanostructure and oxidation reactivity of n-pentanol/diesel particulates, and they found that an increase in soot oxidation reactivity was observed with the increase in the n-pentanol concentration in diesel/n-pentanol mixtures. In addition, particulates of blends exhibited smaller primary particle diameter, shorter fringe length, but larger tortuosity and separation distance. Arora et al. [17] reported the difference in nanostructure of diesel/diesel-dioctyl phthalate (DOP)-blend particles. It was investigated that the presence of oxygen molecules accelerates the oxidation process of particles and inhibits the formation of initial smoke precursors, resulting in a decrease in the size of primary particles. They also found that the inclusion of the DOP fuel increases the availability of molecules of oxygen on the outermost layers of the primary particles, resulting in enhanced soot oxidation. Verma et al. [18] collected particulates from diesel engines burning fuels with different oxygen functional groups, and found that the lower fringe length, higher fringe tortuosity, and increased inter-planar spacing of fringes for particles from oxygenated fuels meant that the particles have a more disordered structure and are easier to oxidize than diesel. Wei et al. [19] discussed the physical properties and oxidation reactivity of dimethyl carbonate (DMC)/diesel blends particulates under different brake mean effective pressures (BMEPs). It was shown that with the increase in DMC blending amount, the soot particles showed more disordered nanostructure with shorter fringe lengths, wider separation distance, and greater tortuosity, and the oxidation reactivity of soot particles presented an increasing trend when the DMC blending amount increases. Du et al. [20] compared the pore structure and oxidation reactivity of different fuel particulates. It was found that biodiesel particulates have a more open pore structure and a rougher surface than diesel particulates, and the biodiesel soot exhibited higher oxidation activity. The summary of the influence of fuel on the particulate physical and chemical properties in their findings is available in

Table 1. The summary of the influence of fuel on the particulate physical and chemical properties.

Researchers	Equipment	Fuel	Main Findings
Zhang et al. [15]	A four-cylinder light-duty diesel engine	Ultra-low sulfur diesel fuel (ULSD), Fischer–Tropsch diesel fuel synthesized from coal (CFT)	Compared to ULSD soot, CFT soot exhibits more chain-like aggregates and a smaller primary particle size. The longer fringe lengths, smaller inter-fringe distances, and higher fringe tortuosity observed in CFT soot indicate a more structurally ordered arrangement. Additionally, CFT soot demonstrates lower reactivity than ULSD soot.
Wang et al. [16]	A four-cylinder, turbocharged, intercooled, high-pressure common-rail automotive diesel engine	D100 (pure diesel fuel), DP15 (15% n-pentanol and 85% diesel, v/v), DP30 (30% n-pentanol and 70% diesel, v/v)	The average $d_p$ was 21.813 nm for D100, 20.672 nm for DP15, and 20.030 nm for DP30. With increasing n-pentanol content, the mean $L_a$ decreased from 0.892 nm to 0.841 nm. The mean $T_f$ was 1.063 for D100 soot, lower than the values of 1.085 for DP15 and 1.096 for DP30. Furthermore, the proportion of fringes with $d$ greater than 0.5 nm increased from 16.39% in D100 soot to 33.80% in DP30 soot.
Arora et al. [17]	A Cummins six-cylinder diesel engine	D100DOP0 (pure ULSD), D90DOP10 (90% ULSD and 10% DOP, v/v), D80DOP20 (80% ULSD and 20% DOP fuel, v/v)	Under both transient and steady-state operating conditions, the $d_p$ was reduced when using DOP fuel blends. The incorporation of DOP into diesel fuel consistently shortened $L_a$ while increasing $T_f$ across all engine operating modes.
Verma et al. [18]	A six-cylinder turbocharged diesel engine	Diesel, D74E26 (26% eucalyptus oil and 74% diesel, v/v), D59T41 (41% tea tree oil and 59% diesel, v/v), D80B20 (20% biodiesel and 80% diesel, v/v), D59O41 (41% orange oil and 59% diesel, v/v)	Compared with diesel, the $d_p$ for D59O41 decreased by 14.4% and 26.5% at half and full load, respectively, whereas reductions of 2.8% and 4.5% were observed for D80B20. At half load, the $L_a$ was reduced by 12.8%, 8.4%, and 4.6% for D74E26, D59T41, and D80B20, respectively. At full load, the $d$ increased by 9.9%, 6.8%, and 11.2% for D74E26, D59T41, and D80B20, respectively.
Wei et al. [19]	A 4-stroke, 4-cylinder, inline water-cooled and DI diesel engine	D100 (pure diesel), DMC8.3 (8.3% DMC and 91.7% diesel, v/v), DMC15 (15% DMC and 85% diesel, v/v) and DMC25(25% DMC and 75% diesel, v/v)	The average $d_p$ is 29.98 nm for D100, 25.93 nm for DMC8.3, 23.24 nm for DMC15, and 19.82 nm for DMC25 under the 0.6 MPa BMEP. Under a BMEP of 1.2 MPa, the temperatures at which soot is completely oxidized are 694 °C, 676 °C, 674 °C, and 670 °C for D100, DMC8.3, DMC15, and DMC25, respectively.
Du et al. [20]	A high-pressure common-rail diesel engine	Diesel, soybean oil methyl ester (SME), palm oil methyl ester (PME), waste cooking oil methyl ester (WME)	Compared to diesel, the $V_p$ of SME, PME, and WME particulates increased by 6.1%, 12.2%, and 23.5%, respectively, while the average $R$ decreased by 30.2%, 39.0%, and 41.7%, and the $S_{BET}$ increased by 23.4%, 48.6%, and 68.8%. Meanwhile, the $E_a$ of SME, PME, and WME soots was reduced by 15.7%, 26.0%, and 35.4%, respectively.

.

Thus, it can be seen that the nanostructure of particulates has a great influence on their reactivity. In other studies, Chen et al. [21] theorized that particulates with a lower graphitization degree exhibit stronger oxidation reactivity, which was characterized by wider $d$, shorter $L_a$, and higher $T_f$. Wei et al. [19] specifically pointed out that among the physical properties, including the fractal dimension ($D_f$) and primary particle size, the nanostructure of primary particles was more important for the control of the oxidation reactivity. It was further suggested that, compared to the length and tortuosity of the fringe, the separation distance exhibits a stronger correlation with the oxidation reactivity of particulates among various nanostructural parameters. According to the fitting results of the linear regression method, Liang et al. [22] considered that the graphitization degree of particulates had a great relationship with oxidation reactivity, and the relationship was not completely linear due to the influence of parameters such as nanostructure and particle size. Zhang et al. [16] used the same method and found that compared with the separation distance of fringes, the fringe length and tortuosity had a clearer correlation with oxidation reactivity of particulates, which was different from the research results of Wei et al. [19].

At present, there have been many studies on the application of coal-based fuels in diesel engines [23,24], while few studies have highlighted the physicochemical properties of particulates in diesel exhaust when methanol/F-T diesel is used. Additionally, most of the current results on the relationship between the structural characteristics and oxidation reactivity of particulates are presented in a qualitative way, and qualitative analysis is still controversial, lacking quantitative evaluation of particulate oxidation reactivity. In this research, particulate matter produced by various blends of methanol and Fischer–Tropsch (F-T) diesel was collected and analyzed. The pore structure of the particulates and the nanostructure of primary particles were characterized using Brunauer–Emmett–Teller (BET) analysis and high-resolution transmission electron microscopy (HRTEM), respectively. Thermogravimetric analysis (TGA) was employed to investigate the mass loss behavior and key oxidation characteristics of the particles. Furthermore, linear regression and partial least squares (PLS) methods were applied to explore the correlation between nanostructural features and oxidative reactivity. The influence of individual nanostructure parameters on oxidation reactivity was assessed through variable importance in projection (PLS-VIP) analysis. This work aims to support the optimization of exhaust after-treatment systems and lay a foundation for the broader application of coal-based fuels.

2. Experimental Apparatus and Methods

2.1. Test Fuels

Normally, for directly mixed fuels, the maximum proportion of methanol should not exceed 15%. It is found that the diesel engine cannot run smoothly in tests when the mixture ratio of methanol is greater than 15%, which is consistent with the research results [25]. Therefore, the mixture ratio of 5%, 10% and 15% was selected in this study, which were named as FM0, FM5, FM10, and FM15, respectively. F-T diesel and methanol were provided by Inner MongoliYitai Co., Ltd. (Inner Mongoli, China) and Zhenjiang Dewei Chemicals Co., Ltd. (Zhenjiang, China), respectively. To avoid phase separation of the mixtures, 1% dodecanol was added to each mixture following the recommendations of Murayama et al. [26]. The kinematic viscosity of the test fuel was determined using a rotational viscometer (NDJ-5S) manufactured by Shanghai Changji Geological Instrument Co., Ltd. (Shanghai, China), while the fuel density was assessed with a density meter (SYD-1884) produced by Wuhan Gelaimo Testing Equipment Co., Ltd. (Wuhan, China). The cetane number and lower heating value of the fuel were estimated based on Kay’s mixing rule [27] and Mendeleev’s formula [28], respectively.

Table 2. The main properties of the test fuels.

Properties	FM0	FM5	FM10	FM15
Cetane number	78	74	71	67
Lower heating value/MJ·kg−1	47.4	46.0	44.6	43.3
Density (20 °C)/g·cm−3	0.755	0.757	0.760	0.761
Kinematic viscosity (20 °C)/mm2·s−1	2.2	2.1	2.0	1.9
Oxygen content/wt.%	0	2.6	5.2	7.8

presents the key properties of the test fuels. Compared with F-T diesel (FM0), it could be seen that the blends with different mixture ratios of methanol, such as FM5, FM10, and FM15, show a lower cetane number, lower heating value and viscosity, and higher density and oxygen content. Compared with diesel, whose cetane number is 52, F-T diesel has a higher cetane number. An excessive cetane number will cause the fuel to pyrolyze rapidly at a lower temperature, which makes it easy to produce soot. The addition of methanol to the fuel blend lowers its cetane number, leading to an extended ignition delay and enhanced combustion efficiency. Due to methanol’s high oxygen content, the concentration of oxygen-containing free radicals in the combustion chamber rises, promoting more complete combustion and reducing the formation of pollutants.

2.2. Particle Sample Collection

The diesel engine test was carried out on a single-cylinder four-stroke diesel engine model 186FA. In this study, the test was carried out at the rated speed and the full load condition (3600 r/min, 6.2 kW) of the diesel engine. The main specifications of the diesel engine are available in our prior published study [29]. The schematic diagram of the diesel engine exhaust particulate matter sampling test device is shown in Figure 1. The built test bench was equipped with an eddy current dynamometer (model CWF-25D, Shanghai Anguang Mechanical and Electrical Equipment Co., Ltd., Shanghai, China), an internal combustion engine measurement and control system (model EBT-II, Wuxi Langdi Measurement & Control Technology Co., Ltd., Wuxi, China), and a particulate matter collection device. The collection time of each particulate sample should be up to 60 min. After each collection is finished, the particulate collection device needs to be thoroughly cleaned. More details of the particulate collection device can be found elsewhere [30].

2.3. Analytical Method

2.3.1. Brunauer–Emmett–Teller (BET)

The pore structure of methanol/F-T diesel particulates is measured by the adsorption method. Since N₂ is stable and can avoid the interaction between multi-component gases, pure N₂ was selected as the adsorbent in the study. The Brunauer–Emmett–Teller (BET) model used in this study is usually used to explain the multi-layer adsorption phenomenon of porous materials. The expression of BET model is as follows [31]:

$${\displaystyle \frac{V}{V_m}}={\displaystyle \frac{C_{1}x}{\left(1-x\right)\left(1-x+C_{1}x\right)}}$$

(1)

where $x$ is the ratio of steam pressure and saturated steam pressure of N₂ at a certain temperature ($x=P/P_0$), $V_m$ is the amount of N₂ adsorbed when the monolayer is covered (cm³), $V$ is the total amount of N₂ adsorbed (cm³), and $C_1$ is the adsorption constant related to the adsorption energy and liquefaction heat.

Density functional theory (DFT) is often used to describe the adsorption behavior of heterogeneous fluids limited by porous materials, which is an effective means to extract the size distribution and half-width of pores in particulate. The expression of the DFT theoretical model is as follows [32]:

$$\mathsf{\Omega }\left[\rho \left(r\right)\right]=F\left[\rho \left(r\right)\right]+{\displaystyle \int dr}\rho \left(r\right)\left[V_{ext}\left(r\right)-{\mu }_b\right]$$

(2)

where $\rho \left(r\right)$ is the average monomer density, $V_{ext}\left(r\right)$ is the wall potential of particle pores, and ${\mu }_b$ is the chemical potential applied to the system.

The fractal dimension ($D_f$) is a characteristic parameter for evaluating surface roughness. Based on the isothermal adsorption test, the Frenkel–Halsey–Hill (FHH) model is used to calculate the $D_f$ of particulates. The expression of the FHH model is as follows [20]:

$$\ln V=k\ln [\ln ({\displaystyle \frac{1}{x}})]+C_2$$

(3)

where $C_2$ is a constant; $k$ can be obtained by formula fitting. The conversion relationship between $D_f$ and $k$ is $D_f=k+3$.

In this study, a specific surface area and pore size distribution instrument (model NOVA3000e) produced by Quantachrome company (Boynton Beach, FL, USA) was used, and the adsorption and desorption isotherms of N₂ to particulates were measured at a constant temperature of 77 K. In addition, the mass of particulate samples should exceed 100 mg to meet the requirements of instrument test accuracy. In order to remove the water (H₂O) and soluble organic fraction (SOF) from the components in the particulates, the samples shall be degassed before the test. During degassing, the process is conducted under vacuum conditions at a temperature of 300 °C for a duration of 3 h. The N₂ adsorption experiment was repeated three times for each type of particulate sample, which was performed to reduce errors arising from factors such as particulate agglomeration and uneven composition of particulates. Each time the experiment was carried out, it was ensured that the experimental conditions were as consistent as possible.

2.3.2. High-Resolution Transmission Electron Microscope (HRTEM)

The fundamental components of particulate matter primarily consist of microcrystalline fringes with varying lengths and degrees of curvature. The nanostructure characteristic parameters of the primary particles can be obtained from the TEM and HRTEM images of the particulate matter. $d$, L_a and $T_f$ reflect the distance between adjacent layer planes, the length of the fringe, and the tortuosity of the fringe, which are parameters that can be used to characterize the nanostructure of particles. L_a can be obtained by

$$L_a={\displaystyle \int dx}$$

(4)

where $dx$ is the distance between two consecutive pixels on the microcrystalline stripe $T_f$ and can be calculated by:

$$T_f=L_a/L$$

(5)

where $L$ is the linear distance between the pixels at both ends of the fringe for primary particles.

HRTEM is used to measure the nanostructure parameters of the particulate in this study, which is specifically the Tecnai G2 F30 model, manufactured by FEI Company s(Hillsboro, OR, USA). The instrument operates at an accelerating voltage of 300 kV with a point resolution of 0.2 nm. Before conducting formal observations on the samples, absolute ethanol was added to the particle samples, followed by ultrasonication for 15 min; the resulting suspension was then deposited onto a TEM grid. A similar preprocessing method has also been applied in other studies [31]. The Digital Micrograph 3.5 version was employed to measure and analyze the TEM and HRTEM images of the particulate matter obtained. For each parameter, samples were selected from multiple images captured in different areas for measurement. The samples were chosen to cover the primary particles of the particulate matter with different morphologies and positions as much as possible, and the number was no less than 200, thereby reducing the measurement error caused by factors such as changes in the sample aggregates.

2.3.3. Thermogravimetric Analysis (TGA)

The reduction in particulate mass during oxidation occurs in two phases: the evaporation of H₂O and SOF, followed by the combustion of soot. $T_i$ is the temperature associated with a 10% decrease in particulate, $T_{\max }$_x is the temperature at which particulate conversion reaches the peak, and $T_b$ refers to the temperature corresponding to 95% mass loss of particulates, which serve as indicators to assess the oxidative reactivity of particulate matter. Additionally, apparent reactive energy ($E_a$) is also a key factor to describe the oxidation process [33]. The higher the $E_a$ value, the more challenging it becomes for the particulate to participate in chemical reactions. According to Arrhenius′ theorem [34], the $E_a$ of particles can be obtained by the Coats–Redfern method. The oxidation rate equation of particles is as follows:

$${\displaystyle \frac{d\alpha }{dt}}=k\cdot f\left(\alpha \right)$$

(6)

where $\alpha$ is the reaction conversion rate, indicating the percentage of mass loss in the thermogravimetric analysis (%), $k$ is the reaction rate constant of the sample, $f\left(\alpha \right)$ is the reactionfunction related to $\alpha$, where $f\left(\alpha \right)={\left(1-\alpha \right)}^n$, and $n$ represents the reaction order. By combining the heating rate expression $\beta =dT/dt$ with Equation (6), the following relationship can be derived:

$${\displaystyle \frac{d\alpha }{dT}}={\displaystyle \frac{A}{\beta }}\cdot \exp \left({\displaystyle \frac{-E_a}{RT}}\right){\left(1-\alpha \right)}^n$$

(7)

where $A$ represents the frequency factor (s∙m∙mol⁻¹), $E_a$ denotes the activation energy of particulates (J∙mol⁻¹), $R$ is the constant of molecular gas (J∙mol⁻¹∙K⁻¹), and $T$ stands for thermodynamic temperature (K).

For diesel emissions, the reaction order value equals 1 [35]. Take the logarithm after integrating the left and right sides of Equation (7) to obtain the following equation:

$$\ln \left[-{\displaystyle \frac{\ln \left(1-\alpha \right)}{T^2}}\right]=\ln \left[{\displaystyle \frac{AR}{\beta E_a}}\left(1-{\displaystyle \frac{2RT}{E_a}}\right)\right]-{\displaystyle \frac{E_a}{RT}}$$

(8)

The thermogravimetric analyzer (TGA, model TGA/DSC1) manufactured by Mettler-Toledo company (Zurich, Switzerland) was employed to measure the thermogravimetric (TG) curves, which reflect mass loss, and the derivative thermogravimetric (DTG) curves, representing the rate of mass loss, for the particulate samples. Each sample was initially weighed to approximately 5 mg. The testing temperature was increased from 40 °C to 800 °C at a constant heating rate of 10 °C/min. Throughout the experiment, a steady flow of 50 mL/min was maintained for both the protective nitrogen gas and the reactive oxygen gas. By analyzing the obtained TG and DTG curves, the composition and key oxidation characteristic parameters of the particulates were determined. To reduce the error in thermogravimetric analysis, each particulate sample was tested three times, and the mass of the tested sample, temperature rise rate, and gas flow rate were kept consistent in each test.

3. Results and Discussion

3.1. Pore Structure of Particulates

Figure 2 presents the N₂ adsorption/desorption isotherms of methanol/F-T diesel particulates. It can be seen that the adsorption capacity of particulates increases with the increase in relative pressure. When the value of relative pressure approaches 1, the adsorption capacity increases sharply, and the isotherm has no platform. At the same relative pressure, the amount absorbed of N₂ by particulates increases with the increase in the methanol mixture ratio; that is to say, the addition of methanol enhances the adsorption capacity of particulates. According to the definition of adsorption isotherm [36] provided by the International Union of Pure and Applied Chemistry (IUPAC), particulates from the combustion of methanol/F-T diesel show the characteristics of multi-layer adsorption, belonging to type II isotherm, which is caused by capillary condensation of N₂ under certain pressure. In addition, the adsorption and desorption curves of the four particulate samples deviate, and obvious hysteresis loops appear. The shape of the adsorption hysteresis loop is related to the pore shape of the adsorbent [37]. After comparison, it is found that the isotherms in Figure 2 have H₃ hysteresis ring defined by IUPAC, indicating that methanol/F-T diesel particulates have aggregates of plant particles or contain narrow slit shaped pores. Fan et al. [38] investigated that the adsorption density of the open-side pore was greater than that of the closed-end pore. For a slit pore with a similar size, the hysteresis loop of the open-end pore is larger than that of the closed-end pore. It is not difficult to see from the figure that the hysteresis loop of the isotherm narrows with the increase in the methanol mixture ratio. Therefore, it can be inferred that F-T diesel particulates contain more through-holes with openings at both ends, while the particulates with methanol have a higher degree of agglomeration and fewer open-end pores.

Figure 3 shows the agglomerated morphology of F-T diesel (FM0) particulates. From the scanning electron microscope (SEM) image, it can be seen that the particulates have various pore shapes with different pore diameters. Figure 4 presents the TEM image of methanol/F-T diesel combustion particulates, which also shows that the pore size and shape of the particulate matter are diverse. Additionally, it is shown in the figure that as the methanol blending ratio increases, the agglomerates of particulates produced by the combustion of methanol/F-T diesel gradually transform into more compact spherical and cluster-like structures. Moreover, the overlapping areas in the TEM images are blurry, presenting more irregular shapes. This might be due to the blending of methanol, which increases the content of soluble organic matter on the surface of particulate matter. The increased soluble organic matter covers the contours of the particulate matter, making it difficult to distinguish the boundaries of multiple particles in the overlapping areas. To further analyze the physical structure characteristics of methanol/F-T diesel particulates, the BET and DFT models were used to calculate the pore structure characteristic parameters of the particulate matter.

Figure 5 shows the pore size distribution of methanol/F-T diesel particulates. The isotherm data of FM0, FM5, FM10, and FM15 particulates were fitted by the DFT method, and the fitting errors were 0.755%, 0.682%, 0.713% and 0.648%, respectively. The pore size distribution results reveal a highly developed pore structure in the particulates, characterized by a continuous multi-peak distribution pattern. And it is obvious that the proportion of pores with $R$ being less than 10 nm in diesel engine exhaust particulates increases after blending methanol. The half pore width ($R$) of particulate samples ranges from 8 nm to 67 nm, including two pore types: mesopore and macropore, which is similar to the pore size distribution characteristics of biodiesel particulates reported by Du et al. [20].

The BET equation was utilized to fit the isothermal adsorption data of N₂ on the particulates, and the specific surface area of the particulate matter from methanol/F-T diesel combustion was obtained. Then, the total pore volume and mean half pore width of the particulates were calculated by fitting the adsorption isotherm curve with the DFT model. The BET equation and DFT model are listed in Section 2.3.1. Figure 6 and

Table 3. Characteristic parameters of the pore structure of methanol/F-T diesel blends particulates.

Characteristic Parameter	FM0	FM5	FM10	FM15
Total pore volume/cm3·g−1	0.103	0.109	0.115	0.122
Mean half pore width/nm	14.483	12.986	10.532	8.440
Specific surface area/m2·g−1	62.206	68.792	78.813	93.617

show the total pore volume ($V_p$), mean half pore width ($R$), and specific surface area ($S_{BET}$) of methanol/F-T diesel particulates. It can be obtained with the increase in the methanol volume ratio; the mean $V_p$ and mean $S_{BET}$ of particulates increase, and the respective mean $R$ decreases. The mean value of $V_p$ in F-T diesel particulates was 0.103 cm³·g⁻¹. Compared with FM0 particulates, the mean $V_p$ of FM5 particulates, FM10, and FM15 particulates increased by 5.8%, 11.7% and 18.4%. The increase in $V_p$ value may be attributed to the higher disorder degree of primary particles formed by the combustion of oxygenated fuel, which is more prone to oxidation reaction, and the formation of more pore structures in the aggregate. The mean $R$ of F-T diesel particulates is 14.5 nm. Compared with FM0 particulates, the mean $R$ of FM5 particulates, FM10, and FM15 particulates is reduced by 10.3%, 27.3% and 41.7%, respectively. This is because the diameter of the mixed fuel primary particle is smaller than the F-T primary particle, and it is easier for particles to stack closely under the action of mechanical characteristics such as the van der Waals force and adhesion force, which makes the pore width decrease. The mean $S_{BET}$ of FT diesel particulates is 62.2 m²·g⁻¹. The mean S values of FM5, FM10, and FM15 particulates increased by 10.6%, 26.7%, and 50.5%, respectively, relative to those of FM0 particulates. The mean $S_{BET}$ values of FM5, FM10, and FM15 particulates increased by 10.6%, 26.7%, and 50.5%, respectively, relative to those of FM0 particulates. As illustrated in Figure 4, the primary particles composing diesel engine exhaust are nearly spherical in shape. For spherical solids, the external specific surface area increases with the decrease in radius. After blending methanol, the $S_{BET}$ of the particulates increased, which is consistent with the change in the primary particle diameter. This finding indicates that diesel engine particulate emissions blended with methanol exhibit a higher adsorption capacity compared to those from pure F-T diesel.

Figure 7 shows the fitting line of the FHH equation for isothermal adsorption data of particulates. The fitting results are listed in

Table 4. The fitting results of the fractal dimension by the FHH equation.

Fuel	Fitted Equation	Regression Coefficient (R2)	${\mathit{D}}_{\mathit{f}}$
FM0	$y=-0.467x+3.080$	0.995	2.533
FM5	$y=-0.433x+3.233$	0.996	2.567
FM10	$y=-0.424x+3.417$	0.997	2.576
FM15	$y=-0.403x+3.561$	0.997	2.597

. All four fitting equations have correlation coefficients (R²) exceeding 0.99, confirming the strong reliability and accuracy of the model fit. It can be illustrated that the fractal dimension ($D_f$) of exhaust particulates mixed with methanol is higher, which indicates that the surface of oxygenated fuel particulates is rougher. There may be two reasons for this phenomenon. One is that the combustion of oxygenated fuel will produce more SOF adsorbed in the particulate; however, the pretreatment before the test makes the SOF adsorbed volatilize, resulting in increasing the vacancies in the particulates and the surface roughness of the particulates. The other is that the blending of methanol makes the mean $R$ smaller, brings the agglomeration degree of particles closer, and causes the pore structure to be more intensive. The $D_f$ values of FM5, FM10, and FM15 particulates increased by 1.3%, 1.7%, and 2.5%, respectively, in comparison to those of FM0 particulates.

3.2. Nanostructure Characteristics of Primary Particles

For each particle sample, 1500 primary particles belonging to different aggregates were randomly selected from multiple TEM images to determine the particle size distribution, thereby generating sufficient, reliable statistical data. The Digital Micrograph software was used to measure the particle size of the selected primary particles. After statistical analysis of the measurement data, the histogram of the particle size distribution of the particles was plotted. Figure 8 displays the distribution of the primary particle diameter ($d_p$). As can be seen, the diameter of the primary particle ranges from 10 nm to 60 nm, and is mainly concentrated between 20 nm and 40 nm. With the increase in the methanol mixture ratio, the primary particle distribution curve gradually moves to the small size direction, and the value of mean $d_p$ decreased. Compared with FM0 primary particles, the mean $d_p$ of FM5, FM10, and FM15 primary particles decreased by 2.8%, 7.5% and 13.3%, respectively. Verma et al. [18] reported that the oxygen content of fuel plays a key role in the size of primary particles, and pointed out that the higher the oxygen content of fuel, the smaller the mean value of $d_p$. In addition, Li et al. [39] researched that the increase in primary particle $d_p$ mainly depends on surface growth in the early stage of combustion, while the $d_p$ gradually decreases due to the oxidation process in the later stage of combustion. The blending of oxygenated fuel reduces the amount of polycyclic aromatic hydrocarbons in the cylinder and slows down the surface growth process of particles. Moreover, methanol combustion will release more oxygen-containing groups, accelerating the oxidation of primary particles.

The HRTEM images of methanol/F-T diesel particulates are shown in Figure 9. It can be seen that the primary particle presents a “shell-core” structure with one or more cores inside. To further analyze the effect of methanol blending on the nanostructure of diesel engine exhaust particulates, at least 200 different primary particles were randomly selected from each particulate sample to ensure that the data had sufficient statistical representativeness. All images were collected at different positions on the TEM grid to minimize the influence of local inhomogeneities in each sample. When measuring the fringe separation distance ($d$), fringe length ($L_a$), and fringe tortuosity ($T_f$) of the primary particles using Digital Micrograph software, complete microcrystal fringes were selected as much as possible, and broken, overlapping, and blurred microcrystal fringes were excluded.

Figure 10a displays the distribution of the fringe separation distance ($d$) of the primary particles. The $d$ of the primary particles is mainly distributed in 0.31 nm~0.36 nm, representing 52% to 79% of the total fringe count, as clearly demonstrated by the figure. As the amount of methanol increases, the normal distribution curve obtained by fitting gradually shifts to the right, indicating that the primary particles contained more widely spaced fringes. Figure 10b shows the fringe length ($L_a$) distribution of the primary particles. As can be seen, the lengths of fringes are mostly concentrated within 2 nm, accounting for 74%~82% of the total number of fringes. The blending of methanol reduces the percentage of large-sized fringes and increases the percentage of fringes with a length of less than 1 nm. Figure 10c is the fringe tortuosity ($T_f$) distribution of the primary particles. It can be found that with the increase in the methanol mixture ratio, the tortuosity of the fringe shows an increasing trend, which means that the blending of methanol causes the particles to have a more disordered nanostructure. The proportion of fringes with a tortuosity exceeding 1.2 in FM0 primary particles reaches 26%, and when FM15 is used, this proportion reaches 67%, which is more than twice that of FM0. Figure 10d plots the mean value trend of nanostructure parameters for primary particles. As could be observed, when the amount of methanol increases, both the distance between fringes and the degree of fringe irregularity become greater, while the rule of fringe length is opposite. In general, higher tortuosity inhibits the extension of graphene layers, increasing the spacing between adjacent fringes, leading to the disordering of the carbon skeleton [40]. Compared with FM0 primary particles, the mean separation distance of FM5, FM10, and FM15 primary particles widens by 4% by 3.3%, 4.9%, and 5.5%, the mean length of fringes reduces by 4.1%, 11.3%, and 20.9%, and the mean tortuosity of fringes increases by 3.6%, 9.7% and 15.3%, respectively. This indicates that when methanol is blended with coal-based fuel, the particles tend to exhibit a more disordered nanostructure, potentially due to the higher oxygen content in the fuel mixture. Oxygen-enriched fuels promote the generation of additional oxygen-containing radicals during combustion. Furthermore, such conditions suppress the formation of soot precursors, reduce the growth rate of graphene layers, and make the lattice fringes within primary particles more susceptible to oxidation.

3.3. Oxidation Reactivity of Particulates

The TG-DTG curves of methanol/F-T diesel particulates are presented in Figure 11. It is not difficult to find that, under the test conditions, the change rules of the particulate TG-DTG curves are basically similar. The low-boiling SOF adsorbed in particulates is oxidized in the first stage, and the soot, which constitutes the primary element of particulates, is oxidized in the second stage. It can be observed that, at the same temperature, the mass loss of FM0 particulates is the smallest among all particulate samples, indicating that the oxidation reactivity of pure F-T diesel particulates is weaker than that of oxygenated coal-based fuel. Further, from 200 °C to 400 °C, the mass loss of FM0 particulates is significantly lower than that of the other three blends particulates, which means that the blending of methanol leads to an increase in the SOF content in particulates. The higher the methanol mixture ratio, the higher the SOF mass fraction. The DTG curve indicates that, in comparison to the first stage, the peak weight loss rate during the second stage of decomposition is more pronounced. Based on the magnitude of the weight loss rate, the particulates follow the sequence FM15 > FM10 > FM5 > FM0.

Figure 12 shows the oxidation characteristic temperatures along with the apparent activation energy ($E_a$) of methanol/F-T diesel particulates. It is easy to see from Figure 12a that among the particulates produced by the four coal-based fuels, FM0 particulates have the highest characteristic temperature. And on the contrary, FM15 has the lowest characteristic temperature. Compared with FM0 particulates, the $T_i$, $T_{\max }$, and $T_b$ of FM15 particulates are reduced by 31.9, 6.4%, and 11.9%, respectively, which indicates that the blending of methanol makes the particulates more easily oxidized, and the same result is also reflected in Figure 12b. Figure 12b shows that the $E_a$ of the methanol/F-T diesel particulates is in the range of 128~163 kJ·mol⁻¹. Compared with FM0 particulates, the E_a of FM5, FM10, and FM15 particulates are reduced by 9.8%, 13.6%, and 21.1%, respectively. In the range of 0%~15% methanol mixture ratio, the oxidation reactivity of particulates is proportional to the methanol mixture ratio.

3.4. Correlations Between Nanostructure Characteristics and Oxidation Reactivity of Particulates

Figure 13 illustrates the correlation between nanostructure characteristic parameters and the apparent activation energy ($E_a$) of particulates. Obviously, there is a close correlation between them. Among the discussed eight nanostructure characteristic parameters, the linear relationship between the E_a of particulates and two characteristic parameters is the strongest, including the fringe tortuosity ($T_f$) and fractal dimension ($D_f$), and the value of R² obtained by linear fitting is 0.98 and 0.99, respectively. As can be seen from Figure 13a, when the $S_{BET}$ of particulates is larger, the E_a of particulates is lower. In addition, when $V_p$ and $D_f$ of particulates are larger and $R$ of particulates is smaller, the oxidation reactivity of particles is weaker, which reaffirms the research results of Du et al. [20]. In Figure 13b, it is observed that particulates with a wider separation distance, shorter length of fringe, and larger tortuosity of fringe have lower $E_a$ and stronger oxidation reactivity. This occurs because a wider $d$ of primary particles enhances the likelihood of oxygen accessing the carbon layer edges. Given that a longer $L_a$ indicates a larger carbon layer surface, and considering that carbon atoms on the basal plane exhibit significantly lower oxidation reactivity compared to those at the edges, an increased number of less reactive carbon atoms contributes to greater particulate stability. A higher $T_f$ value indicates a greater number of odd-membered rings within the carbon layer, which leads to an increased SP²/SP³ hybridization ratio and reduced electron resonance stability, making the particles more susceptible to oxidation. Additionally, Liati et al. [41] believed that the oxidation reactivity of particulates depends on their size; the smaller primary particle diameter ($d_p$) is more prone to cause an oxidation reaction due to the particulate’s high specific surface area ($S_{BET}$).

Partial least squares (PLS), combined with the variable importance in projection (PLS-VIP) criterion, has become a key method for identifying variables with the strongest associations. [42]. They can be used to evaluate the importance of the eight nanostructure parameters for oxidation reactivity of particulates, which are discussed in this study. PLS-VIP is capable of assessing the contribution of every predictor variable to the PLS model, and the threshold criterion “VIP > 1” is commonly adopted to identify significant variables. The importance of the jth predictor variable can be calculated by Equation (9) shown below:

$$VI{P}_j=\sqrt{p{\displaystyle \sum _{k=1}^h\left({\widehat{c}}_k^2{t^{\prime }}_k{t}_k\right){\left(w_{(kj)}\right)}^2}/{\displaystyle \sum _{k=1}^h{\widehat{c}}_k^2{t^{\prime }}_k{t}_k}}$$

(9)

where $p$ is the number of predictor variables, $t_k$ and $w_k$ is the kth column of $T$ and $W$, respectively, ${\hat{\mathrm{c}}}_k={t^{\prime }}_k{y}_{(k)}/{t^{\prime }}_k{t}_k$.

The $E_a$ of particulates is taken as the response variable of the PLS model and recorded as Y; the nanostructure characteristic parameters $V_p$, $R$, $S_{BET}$, $D_f$, $d_p$, $d$, $L_a$, and $T_f$ are taken as the latent variables of the model and recorded as $X$ ($x_1$, $x_2$, $x_3$, $x_4$, $x_5$, $x_6$, $x_7$, and $x_8$). The cumulative variance contribution rate (R²) and cross-validation (Q²) are the main parameters that verify the prediction ability of the PLS model. When the number of model groups reaches two, the cumulative variance contribution rate R²X (cum) of all principal components to latent variable X equals 0.997, the cumulative variance contribution rate R²Y (cum) of that to response variable Y equals 0.992, and the cross-validity Q² (cum) of latent variable equals 0.976, which indicates that the model has a high prediction ability. Figure 13 displays the tolerance ellipse plot of nanostructure characteristic parameters of particles (X-variables) drawn based on Hotelling’s T2, where R²X[1] is 0.969 and R²X[2] is 0.0281. The variables t[1] and t[2] represent transformed scores that capture the essential information from the X-variables, with t[1] accounting for the greatest proportion of variance in the X space, followed by t[2]. The scatter plot of t[1] against t[2] reveals potential outliers, clusters, similarities, and other underlying patterns within the dataset. It can be seen from Figure 14 that the scatters of t[1] vs. t[2] fall outside the ellipse, indicating that there is no specific point, and the model has a good fitting effect.

Figure 15 displays the coefficient of the linear regression equation between the apparent activation energy ($E_a$) and the nanostructure characteristic parameters of particulates. Consistent with the results in Figure 12, it can be seen from Figure 14 that the coefficient of the latent variables $x_2$, $x_5$, and $x_7$ is positive, while that of latent variables $x_1$, $x_3$, $x_4$, $x_6$ and $x_8$ is negative, which means that the E_a increases with the increase in the $R$ of particulates and $d_p$ and $L_a$ of the primary particles. Moreover, when $d$ and $T_f$ of primary particles and $V_p$, $S_{BET}$, and $D_f$ of particulates increase, the E_a of particles decreases. Hence, the regression equation between the $E_a$ (Y-variable) and the nanostructure characteristic parameters (X-variables) of particulates is as follows:

$$y=-0.114x_1+0.054x_2-0.054x_3-0.281x_4+0.043x_5-0.274x_6+0.0419x_7-0.151x_8$$

Figure 16 shows the VIP of X-variables in the PLS model of particle apparent activation energy (E_a). As can be observed, the VIP of variables $x_4$, $x_8$, $x_1$, and $x_6$ exceed 1, which are 1.03618, 1.01142, 1.00514, and 1.00223, indicating that the roughness ($D_f$) and total pore volume ($V_p$) of particulates, together with the tortuosity ($T_f$) and separation distance ($d$) of primary particles, are the chief factors affecting the oxidation reactivity of particles. In addition, the half-width of pores ($R$), primary particle size ($d_p$), the specific surface area of particulates ($S_{BET}$), and fringe length ($L_a$) are the secondary factors, and the influence decreases in the sequence of $R$ > $d_p$ > $S_{BET}$ > $L_a$.

4. Conclusions

In this study, the exhaust particulates of a diesel engine burning methanol/F-T diesel blends with different proportions were collected by bench test. The Brunauer–Emmett–Teller (BET) method, high-resolution transmission electron microscope (HRTEM), and thermogravimetric analysis (TGA) were used to discuss the characteristic parameters of nanostructure and oxidation reactivity. Partial least squares (PLS) and variable importance in the projection (PLS-VIP) theories were used to explore the relationship between nanostructure and oxidation reactivity. Based on this study, the following conclusions can be drawn.

(1)

There are many pore structures in particulate aggregates, with the mean half pore width ($R$) ranging from 8 to 76 nm, including two types of pores: mesopore and macropore. As the methanol mixture ratio increases, the pore structure of particulates becomes more abundant, and the roughness of particulates increases. Compared with FM0 particulates, the total pore volume ($V_p$) and specific surface area ($S_{BET}$) of FM15 particulates increased by 18.4% and 50.5%, and the respective $R$ and fractal dimension ($D_f$) decreased by 41.7% and 2.5%.

(2)

With the increase in the methanol mixture ratio, both the fringe separation distance ($d$) and fringe tortuosity ($T_f$) of primary particles increase, while the fringe length ($L_a$) and primary particle diameter ($d_p$) decrease. Compared with the FM0 primary particles, the mean value of $d_p$ and L_a of FM15 primary particles decreased by 13.3% and 20.9%, and the mean $T_f$ and L_a increased by 5.5% and 15.3%. It is indicated that the blend of methanol makes the carbon structure of primary particles more disordered.

(3)

When the methanol mixture ratio was within 0%~15%, more methanol blended, more of the soluble organic fraction (SOF) attached to the particulates, and there were lower oxidation characteristic temperatures and apparent activation energy ($E_a$). Compared with FM0 particulates, $T_i$, $T_{\max }$, $T_b$, and E_a of FM15 particulates decreased by 31.9%, 6.4%, 11.9% and 21.1%. The blend of methanol enhances the oxidation reactivity of particulates; that is, oxygenated coal-based fuel particulates are easier to oxidize.

(4)

There are two nanostructure parameters that have the strongest linear relationship with the E_a, which are the roughness of particles and the tortuosity of primary particles, with R² equal 0.99 and 0. 98. The E_a of particulates is positively correlated with $R$, $d_p$, and $L_a$, and negatively correlated with $V_p$, $S_{BET}$, $D_f$, $d$, and $T_f$. Among these parameters, $D_f$, $T_f$, $V_p$, and $d$ are the chief factors affecting the oxidation reactivity of particulates, whose VIP > 1, and the others are secondary.