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• As an important fossil energy source [1], the long-chain n-alkanes with carbon numbers between 9 and 22 in diesel are responsible for the poor cold flow properties (CFPs) of diesel fuel [2]. These long-chain n-alkanes in diesel tend to crystallize and accumulate [3], eventually forming larger wax crystals with three-dimensional (3D) network structures in cold regions [4]. These 3D structures can lead to the clogging of fuel pipelines of diesel engines, thus hindering their normal operation [5].

  To overcome this cold flow difficulty, methods such as antifreeze technology [6], blending with coal-to-liquids [7], crystallization modifiers [8], and additives can be considered [9]. Among them, additives are recognized as some of the most cost-effective methods. Cold flow improvers (CFIs) are additives that effectively improve the CFPs of diesel [10]. SP refers to the lowest temperature at which diesel loses its flow properties, and CFPP represents the lowest temperature at which diesel passes through the screen of a diesel engine filter within 60 s [11]. CFI addition can significantly improve the cold cartridge performance of diesel fuel, including lowering the cold filter plugging point (CFPP) and solid point (SP) [12]. Polymethyl acrylate (PMA) is receiving considerable research attention because of its excellent structural diversity and ability to significantly improve CFPs [13]. Many PMA-based CFIs have been successfully developed as commercial CFIs (CCFIs) and are widely used to enhance the CFPs of diesel, biodiesel, or crude oils [14]. However, they are always limited by the required large dosages [15]. To develop better CFIs with low dosages and high efficiency, polarity and carbon-matching principles are extensively used to design and prepare new high-efficiency CFIs by modifying various polar/nonpolar groups and their monomer ratios [16]. Several studies have been performed in this respect [17]. Xie et al. [18]. synthesized a series of benzyl methacrylate–methacrylate copolymers (MB-R₁MC, R₁ = C₁₂, C₁₄, C₁₆, C₁₈) and benzyl methacrylate–tetradecyl methacrylate (MB-C₁₄MC) in different molar ratios of the functional monomers. They explored the effects of chain length on the CFPs of diesel. Results show that the presence of tetradecyl groups in CFIs of PMA systems is the most effective in improving the CFPs of diesel. The reduction in 3000 ppm MB-C₁₄MC (1:10) on the SP and CFPP of diesel is 26 ℃ and 12 ℃, respectively. Chen et al. [2]. also synthesized a series of maleic anhydride–methyl benzyl acrylate co-polymer (MA-MB) and modified it with long-chain fatty amine and long-chain fatty alcohol (RNH₂ and ROH, R = C₁₄, C₁₆, C₁₈). They found that CFPP decreases by 8 ℃ when the amount of C₁₄MA-MB copolymer is 500 ppm. Therefore, the appropriate side-chain lengths can obviously enhance the depressive performance of CFIs. Generally, single polar and nonpolar monomers do not always produce beneficial effects, so third polar monomers are often introduced into the PMA polymeric system to solve such issues. A series of PMA of tetradecyl methacrylate-N-benzylmaleimide (C₁₄MC-BMI), tetradecyl methacrylate-4-acryloylmorpholine copolymers (C₁₄MC-ACM), and C₁₄MC-BMI-ACM has been synthesized by Yang et al. [19]. They comparatively studied the depressive effects of these binary and ternary polymers. Discussions have also been made about the synergy between the different nitrogen-containing parts contained in the trimers to improve the CFPs of diesel by adding a third polar group to these binary polymers as CFIs. Results show that adding the third polar part to the binary polymer can further enhance the performance of CFIs by adjusting the ratio between the parts.

  In our previous work, trans anethole (TA) has been successfully extracted from star anise, a naturally renewable substance [20]. A novel natural CFI of alkyl methacrylate-TA copolymers (C₁₄MC-TA) were prepared to improve the CFPs of diesel. C₁₄MC-TA reduced the CFPP of diesel by 14 ℃ at a higher dosage of 2000 ppm. Nevertheless, the performance of C₁₄MC-TA was limited by its higher addition amount due to the structural particularity of the extract. Therefore, many different monomers based on PMA systems were explored, and found that the depressive effect of PMA-type CFIs could be improved effectively by taking the acidic anhydride monomer as the polar part. Also, 1,2,3,6-tetrahydrophthalic anhydride (THPA) with large spatial position resistance was always used as a synthetic material for surfactants. This study attempts to introduce 1,2,3,6-tetrahydrophthalic anhydride (THPA) as the third monomer for preparing terpolymers of alkyl methacrylate-TA-1,2,3,6-tetrahydrophthalic anhydride copolymers (C₁₄MC-TA-THPA). Meanwhile, the depressive effects of C₁₄MC-TA-THPA were evaluated and compared with those of binary copolymers of C₁₄MC-TA and C₁₄MC-THPA. Finally, a ternary nonlinear surface diagram fitted by a mathematical model was used to better understand the contribution of monomer ratios and dosages of CFIs for their depressive effects.

  The composition and physicochemical properties of diesel fuel used in this work are given in Fig. S1 and Table S1 (Supporting information). The synthesis steps of the CFIs of C₁₄MC-TA-THPA, C₁₄MC-TA, and C₁₄MC-THPA are shown in Figs. S2 and S3 (Supporting information), and their chemical structure and molecular-weight distribution are given in Figs. S4 and S5, and Table S2 (Supporting information). Diesel fuel treated with these CFIs were formulated at 250, 500, 1000, 1250, and 1500 mg/L by weight.

  As shown in Fig. 1, Figs. S6 and S7 (Supporting information), the dosages and monomer ratios of CFIs greatly influenced the inhibition effect of diesel CFPP and SP. The depressive effect of C₁₄MC-TA and C₁₄MC-THPA were obviously lower than that of C₁₄MC-TA -THPA. For C₁₄MC-TA, the depressive effect generally increased with increased dosage. It obtained the optimum performance at a C₁₄MC: TA molar ratio of 1:1, and the CFPP and SP reduction (ΔCFPP and ΔSP) achieved the maximum of 12 ℃ and 18 ℃ at a dosage of 1500 mg/L. Conversely, the depressive effect of C₁₄MC-THPA leveled off after the initial increase with the dosage range of 250–750 mg/L and 750–1500 mg/L. The optimum depressive effect on ΔCFPP and ΔSP reached 11 and 15 ℃ at a molar ratio of 6:1 and a dosage of 750 mg/L. Significantly, although the depressive effect of C₁₄MC-THPA failed to achieve the optimum inhibition effect of C₁₄MC-TA, the optimum dosage of C₁₄MC-THPA was only half of C₁₄MC-TA, whereas the difference in ΔCFPP between them was just 1 ℃. Therefore, the introduction of THPA in C₁₄MC-TA-THPA obviously decreased the dosage of CFIs and increased the depressive effects at lower dosages. When the molar ratio of C₁₄MC:TA:THPA was 6:0.6:0.4 and the dosage was 1000 mg/L, C₁₄MC-TA-THPA achieved the optimum depressive effect. CFPP and SP also decreased by 13 ℃ and 19 ℃, respectively. In PMA-type CFIs, the presence of long-chain alkyl groups can effectively be eutectic with the wax crystals in diesel, thereby changing the growth of wax crystals [21]. Accordingly, the wax crystals in diesel fuel cannot form a 3D network structure at low temperatures. However, when the polymer contained an excess of long-chain alkyl groups, it led to an increase in cross-linking between the polymer and the paraffin wax after eutectic, resulting in a poorer inhibition of CFPP in diesel by CFIs [22]. Meanwhile, THPA and TA had larger spatial site resistance than C₁₄MC, and the synthesized polymers had certain spatial site resistance compared with long-chain alkyl groups. The synergistic effect of two different polar groups in the polymer at an appropriate molar ratio can effectively make the long-chain alkyl groups in the polymer eutectic with the wax crystals to produce a certain degree of repulsion. This phenomenon exerted a significant inhibitory effect on the CFPP of diesel.

  Figure 1

  

  Figure 1.  Effects of various dosages and monomer ratios of C₁₄MC:TA:THPA on ΔCFPP (a) and ΔSP (b) of diesel.

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  In general, finding maxima by fitting multiple sample data to 3D surfaces is a highly efficient and scientific approach [23]. As shown in Fig. 2, the Levenberg–Marquardt (LM) optimization algorithm was used, whereas the independent and dependent variables were fitted using the polynomial model. The fitting equation of 3D surface model is shown in Eq. 1, where Z is the height of a point from the surface, X and Y are coordinate points on the surface, Z₀, A_1–5 and B_1–5 are fitting parameters. By determining the fitting parameters, the optimal fitting surface is obtained, the residual difference between the fitting surface and the original data is minimized, finally the optimal solution is obtained. In this model, the molar ratio between the non-polar and polar part is 6:1, while the independent variable X denotes the molar ratio of THPA in the polar part (TA and THPA), the independent variable Y denotes the amount of CFIs added, and the dependent variable Z denotes the value of the change in diesel CFPP and SP. The CFPP and SP fitting parameters are shown in Tables S3 and S4 (Supporting information), respectively, where σ is the standard error and R² is the correlation. Notably, the fitted parameters R² were all close to 1, indicating that the effectiveness of the model for predicting the contribution of the addition and the monomer ratio to the effect of CFIs was extremely significant. Thus, it was ideal for predicting the inhibition of diesel fuel by CFIs with only a small sample. Response surface analysis results showed that C₁₄MC-TA-THPA reached the optimum depressive effect reduced at 6:0.66:0.34 molar ratio and 1000 mg/L dosage. The CFPP and SP of diesel fuel were reduced by 14 ℃ and 19 ℃, respectively. Significantly, there are two peaks of ΔCFPP with the increase of proportion of THPA in Fig. 2, the main cause of this phenomenon is that the relative quantity of between TA and THPA changed the polarity and solubility of C₁₄MC-TA-THPA, therby changing the CFPP by modifying the crystallization behaviors of paraffins and isoparaffins in diesel. With the proportion of THPA increased, the ΔCFPP was first rising and reached the first peak at the monomer ratio of 6:0.66:0.34 by the synergies produced from TA and THPA. Giving it a larger steric hindrance, the polarity of C₁₄MC-TA-THPA became large and the solubility in diesel got worse after the first peak. More larger crystals were formed and irregular distribution in diesel, ultimately the ΔCFPP began to fall. According to our previous work [20], C₁₄MC-TA only works in enhancing the CFPs of diesel at high dosages. Small proportion of TA in C₁₄MC-TA-THPA is difficult to produce a positive synergistic effect with THPA in improving the CFPs of diesel. When the ratio of THPA: TA exceeds a certain value, the ΔCFPP was determined by the THPA in C₁₄MC-TA-THPA. Therefore, the ΔCFPP presented a slight increase, and formed the second peak in Fig. 2.

  Figure 2

  

  Figure 2.  Response surface analysis of the CFIs dosages and mononer rations effect of on the CFPP (a) and SP (b) of diesel fuel.

  DownLoad: Full-Size Img PowerPoint

  Therefore, the C₁₄MC-TA-THPA (6:0.66:0.34) was also prepared based on the best predicting date from the 3D surface and compared with other reported CFIs and CCFIs (Fig. S8 in Supporting information). Result show that the prepared C₁₄MC-TA-THPA (6:0.66:0.34) exerted better depressive effects on the CFPs of diesel at lower dosages, and the optimum improvement effect on SP and CFPP were consistent with the results of response surface analysis. Therefore, considering cost and performance, C₁₄MC-TA-THPA with a molar ratio of 6:0.66:0.34 was considered to be the optimum low-dosage, high-efficiency CFI for diesel fuels.

  (1)

  To deeply understand the performance mechanism and the crystallization behavior is an essential precondition for the low dosage and high-efficiency CFIs for diesel fuel [24]. Polarizing optical microscopy (POM) can present the changes in quantity, size, shape, and crystal morphology before and after diesel treatment with CFIs [25]. Microscopy images of untreated diesel and diesel treated with various CFIs (1000 mg/L) at low temperatures are given in Fig. 3.

  Figure 3

  

  Figure 3.  Polarized optical micrographs at −15 ℃, −25 ℃, and −35 ℃ of untreated diesel (a₁, a₂, and a₃), diesel treated with 1000 mg/L C₁₄MC-TA (1:1) (b₁, b₂ and b₃), 1000 mg/L C₁₄MC-THPA (6:1) (c₁, c₂ and c₃) and 1000 mg/L C₁₄MC-TA-THPA (6:0.66:0.34) (d₁, d₂ and d₃). Scale bar: 100 µm.

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  As shown in Fig. 3 and Fig. S11 (Supporting information), in untreated diesel, the number and sizes of wax crystals increased significantly with decreased temperature from −15 ℃ to −35 ℃, and 3D network structures were formed by the cross-linking and stacking of these wax crystals at −35 ℃. By comparison, the presence of various CFIs and CCFIs in diesel significantly modified the quantity, size, shape, and morphology of wax crystal. The prepared CFIs of C₁₄MC-TA, C₁₄MC-THPA, and C₁₄MC-TA-THPA in diesel exerted better improvement effect on reducing the quantity and sizes of crystals than the CCFIs of Hote and Nabren. Remarkable differences in quantity and sizes can be observed between C₁₄MC-TA, C₁₄MC-THPA, and the ternary polymer C₁₄MC-TA-THPA treated diesel. The wax crystals in C₁₄MC-TA-THPA treated diesel were considerably smaller and less than that of C₁₄MC-TA or C₁₄MC-THPA. The reason for this phenomenon was the presence of polar parts of THPA in C₁₄MC-TA-THPA generated a certain amount of spatial resistance, which destroyed the mutual cross-linking and aggregation of wax crystals and prevented the wax crystals forming into 3D network structures. Thus, the smaller number and sizes of wax crystals appeared at low temperature, but the liquid phase and crystals from passing through the filter and pipeline of engine cannot prevented. Consequently, the CFPP and SP of diesel significantly improved after diesel treatment with 1000 mg/L C₁₄MC-TA-THPA (6:0.66:0.34) (Fig. 3d). As shown in Fig. S12 (Supporting information), the wax crystal sizes of the microscopic images in the same region during the cooling process were calculated by ImageJ (image-processing software). With the decrease of temperature, the average size of diesel treated with C₁₄MC-TA-THPA was the smallest at each temperature. It was worth noting that the average size of diesel treated EVA12 and EVA18 was smaller than that of diesel treated Hote at −15 ℃, and both gradually exceed Hote as the temperature decreases, which leads to the better depressive of CFPP and worse SP compared Hote as the temperature decreases.

  For another, the macroscopic viscosity changes at different temperatures and the quantitative energy change and amount of precipitated wax crystals during the phase transition of diesel were explored by rheology and differential scanning calorimeter (DSC) in Figs. S9 and S10, and Table S5 (Supporting information). All these results were consistent with the conclusions for CFPP, SP, and POM.

  The possible mechanism of the effect of C₁₄MC-TA-THPA on paraffin growth during diesel cooling is shown in Fig. 4. Without C₁₄MC-TA-THPA addition, diesel began to crystallize gradually at low temperatures. With further decreased temperature, paraffin waxes continued to deposit and grow on the initial nuclei, forming larger wax crystals, which cross-linked and adsorbed onto one another. Eventually, they formed a 3D network structure. The liquid phase of diesel was gradually wrapped by a large number of wax crystals with a 3D network structure, resulting in a gradual loss of diesel fuel fluidity at low temperatures. However, after adding C₁₄MC-TA-THPA to diesel, the paraffin in diesel preferred to co-crystallize with the long-chain alkyl groups in the polymer when the temperature started to decrease. Consequently, unstable small crystals were produced, which effectively retarded the growth of wax crystals. The polar part of the polymer can effectively weaken the mutual attraction between the wax crystals and prevent them from cross-linking and adsorbing, which greatly reduced the possibility of paraffin waxes in diesel forming a 3D network structure at low temperatures. Ultimately, many small-sized wax crystals formed. These small and uniform wax crystals replaced the large-sized 3D network structure wax crystals, enabling diesel to show excellent CFPs and effectively reducing its CFPP and SP.

  Figure 4

  

  Figure 4.  Possible mechanism of C₁₄MC-TA-THPA for improving the flowability of diesel fuel.

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  In summary, to obtain low dosage and high-efficiency CFIs for diesel, the terpolymers of alkyl methacrylate-TA-1,2,3,6-tetrahydrophthalic anhydride copolymers (C₁₄MC-TA-THPA) were synthesized and compared with the binary copolymers of C₁₄MC-TA and C₁₄MC-THPA. Results showed that THPA introduction significantly improved the depressive effects of C₁₄MC-TA. When the monomer ratio and dosage were 6:0.6:0.4 and 1000 mg/L, C₁₄MC-TA-THPA reduces the CFPP and SP of diesel by 13 ℃ and 19 ℃, respectively. For the first time, the relationship among monomer ratio, dose, and CFI inhibition effect was better understood using 3D nonlinear surface diagrams fitted with mathematical models. Surface analysis results showed that C₁₄MC-TA-THPA achieved the optimum depressive effects at monomer ratios of 6:0.66:0.34 and dosage of 1000 mg/L, and CFPP and SP decreased by 14 ℃ and 19 ℃, respectively. Therefore, the C₁₄MC-TA-THPA (6:0.66:0.34) was also prepared and the predicted results were consistent with the actual ones. Finally, through viscosity–temperature curve, DSC, and POM analysis, the action mechanism of C₁₄MC-TA-THPA in diesel was discussed in depth.

  Declaration of competing interest

  The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

  CRediT authorship contribution statement

  Bowen Xu: Data curation, Investigation, Methodology, Validation, Writing – original draft. Jiahao Chen: Investigation, Methodology. Lulu Cui: Investigation, Validation. Xinyue Li: Methodology, Validation, Visualization. Yuan Xue: Conceptualization, Data curation, Methodology, Resources, Supervision, Writing – review & editing. Sheng Han: Conceptualization, Funding acquisition, Project administration, Supervision.

  Acknowledgments

  This work was supported from the Natural Science Foundation Project of Shanghai (Nos. 23ZR1425300 and 22ZR1426100), Experimental Technical Team Construction Project of Shanghai Education Commission (No. 10110N230080), National Natural Science Foundation of China (No. 22075183), and Research and Innovation Project of Shanghai Municipal Education Commission (No. 2023ZKZD54).

  Supplementary materials

  Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.cclet.2024.110196.

  
  
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  Figure 1  Effects of various dosages and monomer ratios of C₁₄MC:TA:THPA on ΔCFPP (a) and ΔSP (b) of diesel.

  下载: 全尺寸图片 幻灯片
  

  Figure 2  Response surface analysis of the CFIs dosages and mononer rations effect of on the CFPP (a) and SP (b) of diesel fuel.

  下载: 全尺寸图片 幻灯片
  

  Figure 3  Polarized optical micrographs at −15 ℃, −25 ℃, and −35 ℃ of untreated diesel (a₁, a₂, and a₃), diesel treated with 1000 mg/L C₁₄MC-TA (1:1) (b₁, b₂ and b₃), 1000 mg/L C₁₄MC-THPA (6:1) (c₁, c₂ and c₃) and 1000 mg/L C₁₄MC-TA-THPA (6:0.66:0.34) (d₁, d₂ and d₃). Scale bar: 100 µm.

  下载: 全尺寸图片 幻灯片
  

  Figure 4  Possible mechanism of C₁₄MC-TA-THPA for improving the flowability of diesel fuel.

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