Carbon black-high-entropy alloy composite particle and preparation method and application thereof
Through the carbon black-high entropy alloy composite particle catalyst, the problem of high cost and easy poisoning of precious metal-based catalysts in electrocatalytic oxidation of glycerol is solved, and efficient conversion and industrial application of glycerol is achieved, providing an efficient and safe catalytic solution.
Patent Information
- Application Number
- CN202411046334.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-01
- Publication Date
- 2024-12-17
AI Technical Summary
In the prior art, noble metal-based catalysts have high cost and easy poisoning problems in the electrocatalytic oxidation of glycerol, which limits their application and lacks efficient and simple catalysts to achieve high added value conversion of glycerol.
A carbon black-high entropy alloy composite particle was developed, including support carbon black particles and supported Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles, and prepared by reduction reaction to form a catalyst with excellent catalytic properties.
This catalyst has a small precious metal content, excellent catalytic performance and good stability. It can effectively convert glycerol into a variety of high-value-added products. It is suitable for large-scale industrial production and application, and reduces production costs.
Smart Images

Figure CN119144991A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of electrocatalytic oxidation, and in particular to a carbon black-high entropy alloy composite particle and a preparation method and application thereof. Background Art
[0002] Biodiesel refers to fatty acid methyl esters / ethyl esters formed by the esterification reaction of vegetable oils (such as rapeseed oil, soybean oil, peanut oil, corn oil, cottonseed oil, etc.), animal oils (such as fish oil, lard, tallow, sheep oil, etc.), waste oils or microbial oils with methanol or ethanol. Biodiesel is a typical "green energy" with good environmental performance, good engine starting performance, good fuel performance, wide raw material sources, and renewable, and has a very broad application prospect.
[0003] In recent years, with the rapid development of the global biodiesel industry, a large amount of byproduct glycerol has been produced, resulting in a significant overproduction of glycerol in the market and a lower and lower price of glycerol. There is an urgent need to convert glycerol into high value-added products to achieve the sustainable development of the biodiesel industry. At present, the main means of converting glycerol into value-added products include selective oxidation, hydrogenation reduction, acid-catalyzed dehydration, chlorination, pyrolysis, gasification and esterification. Glycerol can be selectively oxidized to produce various important derivatives (e.g., dihydroxyacetone, hydroxypyruvic acid, meta-oxalate, etc.) by green and sustainable electrochemical methods. These derivatives can be widely used in the cosmetics, food, medicine and other industries, and the market demand is very large. Precious metal-based catalysts have the advantages of good stability and high catalytic activity, and are widely used in the electrocatalytic oxidation of glycerol. However, due to the high price and easy poisoning of precious metals, their practical application is greatly limited.
[0004] Therefore, it is of great significance to develop a catalyst for electrocatalytic oxidation reaction with simple synthesis, excellent catalytic performance, excellent selectivity and good stability. Summary of the invention
[0005] The purpose of the present invention is to provide a carbon black-high entropy alloy composite particle and a preparation method and application thereof.
[0006] The technical solution adopted by the present invention is:
[0007] A carbon black-high entropy alloy composite particle comprises carrier carbon black particles and supported Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles.
[0008] Preferably, the particle size of the carbon black particles is 30 nm to 80 nm.
[0009] Preferably, the particle size of the Pd—Rh—Fe—Co—Ni high entropy alloy nanoparticles is 3 nm to 10 nm.
[0010] Preferably, the weight of the Pd—Rh—Fe—Co—Ni high entropy alloy nanoparticles in the carbon black-high entropy alloy composite particles accounts for 5% to 45% of the weight of the carbon black particles.
[0011] Preferably, the molar percentages of Pd, Rh, Fe, Co and Ni in the Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles are all 5% to 35%.
[0012] Further preferably, the molar percentages of Pd, Rh, Fe, Co and Ni in the Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles are all 10% to 30%.
[0013] A method for preparing the carbon black-high entropy alloy composite particles as described above comprises the following steps:
[0014] 1) dispersing Pd salt, Rh salt, Fe salt, Co salt, Ni salt and a reducing agent in a solvent for reduction reaction to obtain Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles;
[0015] 2) fully dispersing carbon black particles and Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles in a solvent, and then removing the solvent to obtain carbon black-high entropy alloy composite particles.
[0016] Preferably, the Pd salt in step 1) is at least one of palladium acetylacetonate, palladium acetate, and sodium chloropalladate.
[0017] Preferably, the Rh salt in step 1) is at least one of rhodium acetylacetonate, rhodium acetate, and sodium hexachlororhodate.
[0018] Preferably, the Fe salt in step 1) is at least one of ferric acetylacetonate, ferric acetate and ferric chloride.
[0019] Preferably, the Co salt in step 1) is at least one of cobalt acetylacetonate, cobalt acetate and cobalt chloride.
[0020] Preferably, the Ni salt in step 1) is at least one of nickel acetylacetonate, nickel acetate and nickel chloride.
[0021] Preferably, the reducing agent in step 1) is at least one of ascorbic acid and glucose.
[0022] Preferably, the dispersion method in step 1) is ultrasonic dispersion.
[0023] Preferably, the ultrasonic dispersion time is 1 h to 3 h.
[0024] Preferably, the solvent in step 1) is oleylamine.
[0025] Preferably, the reduction reaction in step 1) is carried out at a temperature of 200° C. to 240° C., and the reaction time is 10 min to 180 min.
[0026] Preferably, the dispersion method in step 2) is ultrasonic dispersion.
[0027] Preferably, the ultrasonic dispersion time is 1 h to 3 h.
[0028] Preferably, the solvent in step 2) is at least one of cyclohexane and ethanol.
[0029] Preferably, the method of removing the solvent in step 2) is vacuum drying.
[0030] Preferably, the vacuum drying is carried out at a temperature of 30° C. to 60° C., and the drying time is 12 h to 16 h.
[0031] A catalyst comprises the carbon black-high entropy alloy composite particles.
[0032] A method for electrocatalytic oxidation of glycerol, using the above-mentioned carbon black-high entropy alloy composite particles as the catalyst.
[0033] The beneficial effects of the present invention are as follows: the carbon black-high entropy alloy composite particles of the present invention have the advantages of less precious metal content, excellent catalytic performance, good stability, simple preparation process, etc., can be used as a catalyst for the electrocatalytic oxidation of glycerol to convert glycerol into a variety of high value-added products, and are suitable for large-scale industrial production and application.
[0034] Specifically:
[0035] 1) The present invention forms a single-phase solid solution crystal structure by doping transition metals Fe, Co and Ni into Pd and Rh, thereby greatly improving the electrocatalytic glycerol oxidation performance of the composite particles and reducing the amount of precious metals in the composite particles, and ultimately significantly reducing the production cost of the composite particles and the cost of glycerol electrocatalytic oxidation;
[0036] 2) The Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles in the carbon black-high entropy alloy composite particles of the present invention have a small particle size and a large specific surface area. The Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles are uniformly dispersed on the carrier carbon black particles, which effectively increases the number of exposed active sites, and ultimately enables the composite particles to exert excellent glycerol electrocatalytic oxidation performance;
[0037] 3) The carbon black-high entropy alloy composite particles of the present invention have good electrocatalytic performance and stability, and the mass activity of electrocatalytic glycerol oxidation is significantly better than that of commercial palladium-carbon catalysts, and can electrocatalytically oxidize glycerol into a variety of high value-added products;
[0038] 4) The preparation method of the carbon black-high entropy alloy composite particles of the present invention has the advantages of simple operation, mild conditions, safety and controllability, and is suitable for large-scale industrial production. BRIEF DESCRIPTION OF THE DRAWINGS
[0039] Figure 1 TEM image, HRTEM image, XRD image and element composition bar graph of the carbon black-high entropy alloy composite particles in Example 1.
[0040] Figure 2 The SEM image and EDS energy spectrum of the carbon black-high entropy alloy composite particles in Example 1.
[0041] Figure 3 TEM image and element composition bar chart of the carbon black-alloy composite particles in Comparative Example 1.
[0042] Figure 4 TEM image and element composition bar chart of the carbon black-alloy composite particles in Comparative Example 2.
[0043] Figure 5 TEM image and element composition bar chart of the carbon black-alloy composite particles in Comparative Example 3.
[0044] Figure 6 It is a performance test result graph of the carbon black-high entropy alloy composite particles in Example 1, the carbon black-alloy composite particles in Comparative Examples 1 to 3, and the commercial Pd / C catalyst in Comparative Example 4 for electrocatalytic oxidation of glycerol.
[0045] Figure 7 It diagram of the glassy carbon electrode modified with carbon black-high entropy alloy composite particles in Example 1 and the glassy carbon electrode modified with commercial Pd / C catalyst in Comparative Example 4.
[0046] Figure 8 This is a graph showing the product selectivity test results of glycerol oxidation catalyzed by the carbon black-high entropy alloy composite particles in Example 1. DETAILED DESCRIPTION
[0047] The present invention will be further explained and illustrated below in conjunction with specific embodiments.
[0048] Embodiment 1:
[0049] A carbon black-high entropy alloy composite particle, the preparation method of which is as follows:
[0050] 1) 0.025mmol of acetylacetonate palladium (Pd(acac)2), 0.025mmol of acetylacetonate rhodium (Rh(acac)3), 0.025mmol of acetylacetonate iron (Fe(acac)3), 0.025mmol of acetylacetonate cobalt (Co(acac)3), 0.025mmol of acetylacetonate nickel (Ni(acac)2) and 180mg of ascorbic acid (AA) were added to 5mL of oleylamine, ultrasonically dispersed for 2h, then heated to 220°C and reacted at constant temperature for 2h, naturally cooled to room temperature, and then added 20mL of anhydrous ethanol and centrifuged at a centrifuge speed of 10000rpm for 5min, and then the solid obtained by centrifugation was washed several times with a cyclohexane-acetone-anhydrous ethanol mixed solution (the volume ratio of cyclohexane, acetone and anhydrous ethanol was 2:2:1) to obtain Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles;
[0051] 2) 40 g of Cabot Vulcan XC-72 carbon black (particle size of 30 nm to 80 nm) was dispersed in 50 mL of cyclohexane, and then 10 g of Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles were added and ultrasonically dispersed for 1 hour, and then centrifuged at a centrifuge speed of 10,000 rpm for 5 minutes. The solid obtained by centrifugation was washed several times with a cyclohexane-acetone-anhydrous ethanol mixed solution (the volume ratio of cyclohexane, acetone, and anhydrous ethanol was 2:2:1), and then vacuum dried at 50°C overnight to obtain carbon black-high entropy alloy composite particles (denoted as PdRhFeCoNi / C).
[0052] Performance Testing:
[0053] 1) The transmission electron microscope (TEM) image, high resolution transmission electron microscope (HRTEM) image, X-ray diffraction (XRD) image and element composition bar graph of the carbon black-high entropy alloy composite particles in this embodiment are as follows: Figure 1 (a is a TEM image, b is a HRTEM image, c is an XRD image, and d is an element composition bar graph). Note: Inductively coupled plasma atomic emission spectroscopy (ICP-OES) was used to test the element content in the carbon black-high entropy alloy composite particles.
[0054] Depend on Figure 1 From a in the figure, we can see that the particle size of the Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles in the carbon black-high entropy alloy composite particles is 3nm~10nm, and the average particle size is about 5.8nm.
[0055] Depend on Figure 1From b and c in the figure, we can see that the lattice fringe spacing of the Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles in the carbon black-high entropy alloy composite particles is 0.22nm, corresponding to the (111) crystal plane of the Pd crystal. Combined with the XRD pattern, it can be confirmed that the Pd-Rh-Fe-Co-Ni high entropy alloy has a single-phase fcc solid solution structure.
[0056] Depend on Figure 1 From d in the figure, we can see that the molar ratio of Pd, Rh, Fe, Co and Ni in the carbon black-high entropy alloy composite particles is approximately 26:18:14:19:22, which is consistent with the range of 5% to 35% of the molar content of each component in the Pd-Rh-Fe-Co-Ni high entropy alloy.
[0057] 2) The scanning electron microscope (SEM) image and EDS spectrum image of the carbon black-high entropy alloy composite particles in this embodiment are as follows: Figure 2 shown.
[0058] Depend on Figure 2 It can be seen that the elements Pd, Rh, Fe, Co and Ni are uniformly distributed in the carbon black-high entropy alloy composite particles.
[0059] In summary, carbon black-high entropy alloy composite particles with the expected composition and microstructure were indeed prepared in this embodiment.
[0060] Embodiment 2:
[0061] A carbon black-high entropy alloy composite particle, except that the "ascorbic acid" in step 1) is replaced by "glucose" during preparation, the rest is exactly the same as Example 1.
[0062] After testing (the testing method is the same as that in Example 1), the composition structure and micromorphology of the carbon black-high entropy alloy composite particles in this example are very similar to those of the carbon black-high entropy alloy composite particles in Example 1.
[0063] Comparative Example 1:
[0064] A carbon black-alloy composite particle (denoted as Pd3RhFeCoNi / C) is exactly the same as Example 1 except that the amount of acetylacetonate palladium in step 1) is adjusted from "0.025mmol" to "0.075mmol" during preparation.
[0065] The TEM image and element composition bar graph of the carbon black-alloy composite particles in this comparative example are as follows: Figure 3 (a is TEM image, b is element composition bar graph).
[0066] Depend on Figure 3It can be seen that the molar contents of the elements Pd, Rh, Fe, Co and Ni in the Pd-Rh-Fe-Co-Ni alloy nanoparticles in the carbon black-alloy composite particles in this comparative example are 52%, 14%, 13%, 10% and 11%, respectively, which are significantly different from the carbon black-high entropy alloy composite particles in Example 1.
[0067] Comparative Example 2:
[0068] A carbon black-alloy composite particle (denoted as PdRh3FeCoNi / C) is exactly the same as Example 1 except that the amount of rhodium acetylacetonate in step 1) is adjusted from "0.025mmol" to "0.075mmol" during preparation.
[0069] The TEM image and element composition bar graph of the carbon black-alloy composite particles in this comparative example are as follows: Figure 4 (a is TEM image, b is element composition bar graph).
[0070] Depend on Figure 4 It can be seen that the molar contents of the elements Pd, Rh, Fe, Co and Ni in the Pd-Rh-Fe-Co-Ni alloy nanoparticles in the carbon black-alloy composite particles in this comparative example are 15%, 43%, 13%, 15% and 14%, respectively, which are significantly different from the carbon black-high entropy alloy composite particles in Example 1.
[0071] Comparative Example 3:
[0072] A carbon black-alloy composite particle (denoted as PdRh / C), which is exactly the same as Example 1 except that the metal salt raw material in step 1) is adjusted to "0.025mmol of acetylacetonate palladium (Pd(acac)2) and 0.025mmol of acetylacetonate rhodium (Rh(acac)3)" during preparation.
[0073] The TEM image and element composition bar graph of the carbon black-alloy composite particles in this comparative example are as follows: Figure 5 (a is TEM image, b is element composition bar graph).
[0074] Depend on Figure 5 It can be seen that the molar contents of the elements Pd and Rh in the Pd-Rh alloy nanoparticles in the carbon black-alloy composite particles in this comparative example are 53% and 47%, respectively, which are significantly different from the carbon black-high entropy alloy composite particles in Example 1.
[0075] Comparative Example 4:
[0076] Commercial Pd / C catalyst (denoted as Pd / C; Macklin Company, the content of carbon carrier is 90wt%, and the content of active component Pd is 10wt%).
[0077] Electrocatalytic performance test:
[0078] The testing process is as follows:
[0079] 1) Pretreatment of glassy carbon electrode: A glassy carbon electrode (cylindrical) with a diameter of 3 mm was polished into a mirror surface with Al2O3 powder with a particle size of 0.02 μm to 0.05 μm, and then ultrasonically cleaned with distilled water, anhydrous ethanol and distilled water for 2 min respectively, and then the electrode surface was cleaned with distilled water and dried at room temperature to obtain a pretreated glassy carbon electrode;
[0080] 2) Preparation of a working electrode: 2.5 mg of a catalyst (carbon black-high entropy alloy composite particles in Example 1, carbon black-alloy composite particles in Comparative Examples 1 to 3, and commercial Pd / C catalyst in Comparative Example 4), 500 μL of water, 500 μL of isopropanol, and 4 μL of a 5% Nafion solution were mixed and ultrasonically dispersed for 1 hour to prepare a catalytic ink, and then 5 μL of the catalytic ink was dripped onto the pretreated glassy carbon electrode, and dried overnight at room temperature under a vacuum environment to prepare a catalyst-modified glassy carbon electrode (as a working electrode); before performing an electrochemical test, the working electrode needs to be pre-activated to remove impurities that may exist on the electrode surface, that is, it is activated by rapidly scanning hundreds of cycles in a KOH solution (electrolyte) with a concentration of 0.1 mol / L at a scanning rate of 500 mV / s in the range of -1V to 1V;
[0081] 3) Electrochemical test: The working electrode, reference electrode (Hg / HgO electrode) and counter electrode (platinum sheet) were assembled into a three-electrode system, and a mixed solution of 0.1 mol / L KOH + 0.1 mol / L glycerol saturated with N2 was used as the electrolyte. The catalytic glycerol oxidation activity of the catalyst at room temperature was evaluated by cyclic voltammetry curves. The test results are shown in Figure 2. Figure 6 (a is the cyclic voltammetry curve, b is the mass activity bar graph).
[0082] Depend on Figure 6 It can be seen that:
[0083] a) The oxidation peak mass current density of the carbon black-high entropy alloy composite particles in Example 1 is 219.2 mA·mg -1 Pd , while the oxidation peak mass current density of the commercial Pd / C catalyst in Comparative Example 4 is 43.4 mA·mg -1 Pd The catalytic performance of the carbon black-high entropy alloy composite particles in Example 1 is about 5 times that of the commercial Pd / C catalyst in Comparative Example 4, indicating that the Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles in the carbon black-high entropy alloy composite particles of the present invention greatly improve the electrocatalytic oxidation of glycerol performance of the composite particles;
[0084] b) The oxidation peak mass current density of the carbon black-alloy composite particles in Comparative Examples 1 to 3 was 175.3 mA·mg -1 Pd 、142.6mA·mg -1 Pd and 86.2mA·mg -1 Pd The carbon black-high entropy alloy composite particles in Example 1 have better glycerol catalytic oxidation activity than the binary alloy catalyst with the same components (carbon black-alloy composite particles in Comparative Example 3), indicating that the incorporation of transition metals Fe, Co and Ni in the Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles improves the electrocatalytic oxidation of glycerol by the composite particles;
[0085] c) The carbon black-high entropy alloy composite particles in Example 1 have higher glycerol catalytic oxidation activity than the carbon black-alloy composite particles in Comparative Examples 1 to 2, indicating that the Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles have optimal glycerol oxidation electrocatalytic activity when the molar percentages of transition metals Pd, Rh, Fe, Co and Ni in the nanoparticles are close to equal.
[0086] The chronoamperometric (it) graph of the carbon black-high entropy alloy composite particle modified glassy carbon electrode in Example 1 and the commercial Pd / C catalyst modified glassy carbon electrode in Comparative Example 4 at a potential of 0.05 V in 0.5 mol / L KOH+0.5 mol / L glycerol electrolyte is shown in the figure below: Figure 7 shown.
[0087] Depend on Figure 7 It can be seen that the glassy carbon electrode modified with the carbon black-high entropy alloy composite particles in Example 1 has good stability, indicating that the carbon black-high entropy alloy composite particles in Example 1 have good catalytic stability.
[0088] The glassy carbon electrode modified with carbon black-high entropy alloy composite particles in Example 1 was subjected to it at a potential of 0.05 V in a 0.5 mol / L KOH+0.5 mol / L glycerol electrolyte for 2 h. The reaction solution was collected and analyzed by high performance liquid chromatography. The product selectivity test results of the catalytic glycerol oxidation were as follows: Figure 8 shown.
[0089] Depend on Figure 8It can be seen that the carbon black-high entropy alloy composite particles in Example 1 catalyze the oxidation of glycerol to produce seven high value-added products, namely dihydroxyacetone (DHA), lactic acid (LA), glyceraldehyde (GLAD), glyceric acid (GLA), oxalic acid (OA), tartaric acid (TA) and glycolic acid (GA), among which dihydroxyacetone (DHA) and lactic acid (LA) are the main products, indicating that the carbon black-high entropy alloy composite particles have good selectivity for the electrocatalytic oxidation of glycerol.
[0090] In addition, through the same test, it was found that the catalytic performance of the carbon black-high entropy alloy composite particles in Example 2 was very close to that of the carbon black-high entropy alloy composite particles in Example 1.
[0091] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.
Claims
1. A carbon black-high entropy alloy composite particle, characterized in that: The composition includes carrier carbon black particles and supported Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles.
2. The carbon black-high entropy alloy composite particles according to claim 1, characterized in that: The particle size of the carbon black particles is 30nm to 80nm; the particle size of the Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles is 3nm to 10nm.
3. The carbon black-high entropy alloy composite particles according to claim 1 or 2, characterized in that: The weight of the Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles in the carbon black-high entropy alloy composite particles accounts for 5% to 45% of the weight of the carbon black particles.
4. The carbon black-high entropy alloy composite particles according to claim 1 or 2, characterized in that: The molar percentages of Pd, Rh, Fe, Co and Ni in the Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles are all 5% to 35%.
5. A method for preparing carbon black-high entropy alloy composite particles according to any one of claims 1 to 4, characterized in that: The following steps are involved: 1) dispersing Pd salt, Rh salt, Fe salt, Co salt, Ni salt and a reducing agent in a solvent for reduction reaction to obtain Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles; 2) fully dispersing carbon black particles and Pd-Rh-Fe-Co-Ni high entropy alloy nanoparticles in a solvent, and then removing the solvent to obtain carbon black-high entropy alloy composite particles.
6. The preparation method according to claim 5, characterized in that: The Pd salt in step 1) is at least one of palladium acetylacetonate, palladium acetate, and sodium chloropalladate; the Rh salt in step 1) is at least one of rhodium acetylacetonate, rhodium acetate, and sodium hexachlororhodate; the Fe salt in step 1) is at least one of ferric acetylacetonate, ferric acetate, and ferric chloride; the Co salt in step 1) is at least one of cobalt acetylacetonate, cobalt acetate, and cobalt chloride; the Ni salt in step 1) is at least one of nickel acetylacetonate, nickel acetate, and nickel chloride; the reducing agent in step 1) is at least one of ascorbic acid and glucose.
7. The preparation method according to claim 5 or 6, characterized in that: Step 1) The reduction reaction is carried out at a temperature of 200°C to 240°C and a reaction time of 10min to 180min.
8. The preparation method according to claim 5, characterized in that: Step 2) the solvent is at least one of cyclohexane and ethanol.
9. A catalyst, characterized in that The carbon black-high entropy alloy composite particles include the carbon black-high entropy alloy composite particles described in any one of claims 1 to 4.
10. A method for electrocatalytic oxidation of glycerol, characterized in that: The catalyst used is the carbon black-high entropy alloy composite particles described in any one of claims 1 to 4.
