Magnetic solid-phase extraction-Fe3O4@ZIF-67-F activated persulfate nanoenzyme colorimetric sensor detection method

Abstract

The present invention discloses a magnetic solid phase extraction-Fe3O4@ZIF-67-F activated persulfate nanozyme colorimetric sensor detection method, which relates to the field of perfluorooctanoic acid (PFOA) detection technology, and includes the following steps: S1, preparation of a Fe3O4@ZIF-67-F catalyst; S2, magnetic solid phase extraction; S3, colorimetric detection process; S4, analysis and calculation. The method of the present invention utilizes magnetic solid phase extraction combined with a nanozyme-like colorimetric sensor to detect PFOA in water. The Fe3O4@ZIF-67-F prepared by the optimized preparation method, especially Fe3O4@ZIF-67-F (NaF7.5), has good stability and high detection accuracy, and has the advantages of the natural catalytic active sites of cobalt, which greatly reduces the detection limit and quantification limit of PFOA in water. It is also expected to play an important role in other pollutant and small molecule biomarker detection, pollutant degradation and removal, and biological diagnosis and treatment.

Description

Technical Field

[0001] The present invention relates to the technical field of perfluorooctanoic acid (PFOA) detection, and specifically to a magnetic solid phase extraction-Fe3O4@ZIF-67-F activated persulfate nanoenzyme colorimetric sensor detection method. Background Art

[0002] Perfluorooctanoic acid (PFOA) is a very important perfluoroalkyl PFASs, an organofluorine compound that has been widely produced and used in consumer products and various industrial processes since the 1940s. Many common household items, including carpet protectors, non-stick cookware, firefighting foams, medical devices, and electronic products contain PFOA. PFOA consists of a seven-carbon carbon fluorine chain as the tail and a carboxyl group as the head. Because the CF bond is one of the strongest chemical bonds, PFOA has very high thermal and chemical stability and is very difficult to degrade. In addition, even though its tail is hydrophobic, the hydrophilic carboxyl group makes it water-soluble. Therefore, PFOA that enters surface water with industrial wastewater, domestic sewage, etc. will cause great pollution to the environment and pose a serious threat to the biodiversity of aquatic organisms.

[0003] Among the many PFASs, PFOA is one of the most studied emerging persistent organic pollutants. Due to its widespread use and unique properties, PFOA has been found in many environmental media and the human body. According to studies on exposure to PFOA, PFOA can accumulate in human blood and have negative effects on human health (such as immunotoxicity and / or carcinogenicity). Therefore, the U.S. Environmental Protection Agency (EPA) announced a lifetime health advisory level of 70 parts per trillion (70 ng·L) for the combination of PFOA and PFOS in drinking water. -1 In 2016, Hu et al. reported a spatial analysis of exposure to several PFASs in drinking water in the United States. In some areas, particularly those near industrial sites where PFASs are used, concentrations of PFOA and PFOS in drinking water were significantly higher than the recommended health-based guidelines. Consequently, efforts have been made to develop a variety of testing methods to analyze PFOA concentrations in surface and drinking water to ensure public health.

[0004] The current gold standard detection method for PFOA is based on chromatography coupled with mass spectrometry (e.g., GC-MS, LC-MS, and HPLC-MS / MS). While chromatography combined with mass spectrometry provides the most accurate and sensitive measurement of PFOA, developing real-time and on-site monitoring systems for PFOA is also an important issue. Consequently, various fluorescent sensors, electrochemical sensors, and colorimetric sensors have emerged for PFOA detection. Colorimetric sensors are widely popular due to their good visibility, ease of use, and suitability for field testing and application. Megumi Takayose (Analytical Letters, 2012, 45, 2856-2864) synthesized thiol-terminated polystyrene-modified gold nanoparticles (AuPS) and applied them to the colorimetric detection of perfluorooctanoic acid (PFOA). The color change of the AuPS solution from red to bluish-purple after the addition of PFOA is easily confirmed by the naked eye. Transmission electron microscopy (TEM) shows that the addition of PFOA causes the polystyrene layer to separate from the gold nanoparticle surface, leading to interparticle aggregation and, in turn, a color change in the solution. Cai Yaqi et al. (Anal. Chem. 2014, 86, 4170-4177) developed a new sensing strategy that uses gold nanoparticles (Au@PEG-FNPs) modified with a mixture of polyethylene glycol (PEG-thiol) and perfluoroalkyl-terminated alkylthiols (F-thiol) as probes to detect perfluorinated compounds (PFCs) in water samples. The high density and long carbon chain of PEG-thiol allow the Au-NPs probe to be well dispersed in solution and stable even in highly concentrated salt solutions; F-thiol provides specific fluorine-fluorine interactions with PFCs, resulting in the adsorption of PFCs on the Au@PEG-FNPs. The adsorbed PFCs cause the Au@PEG-FNPs probe to become insoluble and directly precipitate from the reaction solution due to the superhydrophobicity of the perfluorocarbon monolayer, resulting in color and absorbance responses to the PFCs.

[0005] However, these colorimetric sensors often have problems such as complex probe synthesis process, low detection sensitivity and narrow application range. Summary of the Invention

[0006] In response to the above-mentioned problems, the present invention provides a magnetic solid phase extraction-Fe3O4@ZIF-67-F activated persulfate nanoenzyme colorimetric sensor detection method.

[0007] The technical solution of the present invention is:

[0008] The magnetic solid phase extraction-Fe3O4@ZIF-67-F activated persulfate nanoenzyme colorimetric sensor detection method includes the following steps:

[0009] S1. Preparation of Fe3O4@ZIF-67-F catalyst: 0.05 g of Fe3O4 powder and 2 g of PVP were mixed and dissolved in 30 mL of anhydrous methanol, and ultrasonically treated at room temperature for 30 min to obtain solution A. 1.2 g and 4 mmol of Co(NO3)2·6H2O were dissolved in 30 mL of anhydrous methanol and ultrasonically treated at room temperature for 5 min to obtain solution B. 1.232 g and 15 mmol of 2-methylimidazole and 3.75-30 mmol of F source were added to solution A. The temperature was raised to 40°C and solution B was added dropwise to solution A while ultrasonically treated. After the addition was completed, ultrasonic treatment was continued for 10 min to obtain a suspension. The suspension was transferred to a polytetrafluoroethylene-lined stainless steel autoclave and heated at 120°C for 4 h. The remaining solid product was collected by a magnet and washed 3-5 times with methanol solution, and then dried in an oven at 70°C to obtain Fe3O4@ZIF-67-F catalyst.

[0010] S2, magnetic solid phase extraction: add 100 mL of the sample solution of PFOA to be determined into a glass container, add 10 mg of the Fe3O4@ZIF-67-F catalyst prepared in step S1 to the sample solution to obtain a mixed solution, then place the mixed solution in a water bath shaker and shake at a frequency of 300±10 times / min for 30 minutes at room temperature, apply a magnet to the outside of the glass container to separate the solid phase and the liquid phase in the mixed solution, completely discard the liquid phase, and transfer the solid phase to a centrifuge tube, and then add TMB solution, PMS solution and acetate buffer to the centrifuge tube in sequence, wherein the TMB solution is 50 μL, 1-10 mmol, the PMS solution is 50 μL, 1 mmol, the acetate buffer is 0.1 mol, the pH is 3-4, and the total volume of the solution in the centrifuge tube after the addition of the acetate buffer is 1 mL, to obtain a detection system;

[0011] S3. Colorimetric detection process: The detection system obtained in step S2 is compared with the standard colorimetric system, and the recovery rate is used to evaluate the enrichment efficiency of the detection system for PFOA. The recovery rate refers to the ratio of the absorbance change value of the detection system after enrichment of PFOA to the absorbance change value of the system after directly adding the sample solution of PFOA to be determined to the standard colorimetric system.

[0012] Furthermore, the preparation method of Fe3O4 powder in step S1 is:

[0013] Take 1.95g, 12mmol of FeCl3·6H2O and 0.6g, 2.04mmol of Na3Cit·2H2O and dissolve them together in 60mL of ethylene glycol solution, add 3.6g, 0.04mmol of CH3COONa while stirring, and continue stirring for 30min at a stirring speed of 100-200rpm. Then place it in a polytetrafluoroethylene-lined stainless steel autoclave, heat the stainless steel autoclave to 200±5℃ and keep it warm for 10h, cool it to room temperature, and wash the obtained black product with EtOH solution and deionized water 3-5 times, and then dry it in a 70℃ oven to obtain Fe3O4 powder.

[0014] Note: The Fe3O4 powder prepared by this method is relatively pure, avoiding the presence of impurities that affect the subsequent reaction process.

[0015] Furthermore, the room temperature is 25-28° C., and the size of the polytetrafluoroethylene-lined stainless steel autoclave is 100 mL.

[0016] Note: The room temperature is controlled to ensure the smooth progress of the experiment. The size and specifications of the polytetrafluoroethylene-lined stainless steel autoclave are selected to meet the requirements of use.

[0017] Furthermore, in step S1, the frequency of the ultrasonic treatment is 40 Hz, the power is 800-1200 W, the dropping speed is 0.5-1 mL / s, and the mass fraction of the methanol solution is 60%.

[0018] Note: Dissolution can be accelerated by ultrasonic treatment.

[0019] Furthermore, in step S1, the F source is one of HF, NaF, KF, NH4F or NH4HF2, and the preferred method for the F source is:

[0020] Take 0.1 mol acetate buffer as the matrix, add the above-mentioned F sources into the matrix to prepare a mass concentration of 1 mg·mL -1 50 μL of the suspension was dispersed in 850 μL of 0.1 mol acetate buffer, 50 μL of PMS solution and 50 μL of TMB solution were added thereto, and the mixture was reacted at room temperature for 10 minutes to complete the full conversion of TMB to ox-TMB to obtain a mixture, and the absorbance of the mixture was recorded at 652 nm. A F source with strong absorbance was preferred.

[0021] Note: By further providing a method for optimizing the F source, a more accurate F source can be optimized.

[0022] Furthermore, in step S2, the TMB solution is prepared using TMB as the solute and dimethyl sulfoxide as the solvent, and the PMS solution is prepared using PMS as the solute and acetate buffer as the solvent.

[0023] Description: By optimizing the raw materials for the preparation of TMB and PMS, they can be made to meet the purpose of the method of the present invention.

[0024] Furthermore, the size of the centrifuge tube in step S2 is 5 mL.

[0025] Note: Using centrifuge tubes of appropriate size reduces losses during the preparation process.

[0026] Furthermore, the standard color development system in step S3 is to directly add a PFOA solution with a concentration of 2, 5, 10 or 20 ppb into 1 mL of the detection system.

[0027] Note: Direct comparison can be made by establishing a standard color development system.

[0028] Furthermore, the method further includes step S4, analyzing and calculating:

[0029] Calculation of detection limit LOD: LOD = 3SB / k;

[0030] Calculation of limit of quantification (LOQ): LOQ = 10SB / k;

[0031] Where SB is the standard deviation of the color development detection process of step S3 repeated three times, and k is the slope of the regression equation.

[0032] Note: The detection limit and quantification limit can be obtained through analysis and calculation, and can also reflect the detection effect of the colorimetric sensor of the present invention to a certain extent.

[0033] The beneficial effects of the present invention are:

[0034] (1) The magnetic solid phase extraction-Fe3O4@ZIF-67-F activated persulfate nanozyme colorimetric sensor detection method of the present invention utilizes magnetic solid phase extraction combined with nanozyme colorimetric sensors to detect PFOA in water. The Fe3O4@ZIF-67-F prepared by the optimized preparation method, especially Fe3O4@ZIF-67-F (NaF7.5), has good stability and high detection accuracy. It has the advantage of the natural catalytic active site of cobalt, which greatly reduces the detection limit and quantification limit of PFOA in water. It is also expected to play an important role in the detection of other pollutants and small molecule biomarkers, pollutant degradation and removal, and biological diagnosis and treatment.

[0035] (2) The magnetic solid phase extraction-Fe3O4@ZIF-67-F activated persulfate nanoenzyme colorimetric sensor detection method of the present invention has low cost and good color development effect, such as Figure 1 As shown, the detection principle is based on the activation of persulfate PMS catalyzed by the catalyst Fe3O4@ZIF-67-F to produce sulfate radicals and hydroxyl radicals, which then oxidize the colorless chromogenic substrate 3,3',5,5'-tetramethylbenzidine TMB to a blue oxidized state ox-TMB. When PFOA exists in the detection system, Fe3O4@ZIF-67-F will first adsorb PFOA in the system and enrich PFOA through the magnetic solid-phase extraction process. At this time, a certain amount of PFOA is adsorbed on the surface of the material, so that the active sites of the material are masked to a certain extent, and the activity of catalyzing PMS activation decreases, thereby reducing the production of blue ox-TMB. The number of active sites masked by PFOA at different concentrations is different, and the activity of the material changes, resulting in different amounts of blue ox-TMB produced, thereby realizing quantitative detection of PFOA. The detection limit can be reduced by another 100 times on the original basis through the magnetic solid-phase extraction method. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a schematic diagram of the principle of detecting PFOA using magnetic solid phase extraction combined with a nanozyme-like colorimetric sensor according to the present invention;

[0037] Figure 2 FESEM images (A) and (B) of Fe3O4@ZIF-67-F(NaF7.5) in Experimental Example 1 of the present invention; hysteresis curves (C): (a) Fe3O4, (b) Fe3O4@ZIF-67-F(NaF7.5); XRD patterns of the four materials (D); N2 adsorption-desorption isotherms of the three materials (E); XRD patterns of Fe3O4@ZIF-67-F(NaF7.5) after immersion for 24 hours under different conditions (F);

[0038] Figure 3 The full spectra of Fe3O4@ZIF-67-F(NaF7.5) and Fe3O4@ZIF-67-F in Experimental Example 2 of the present invention (A); (B)-(D) are the high-resolution spectra of Fe3O4@ZIF-67-F(NaF7.5): Co2p (B); N1s (C); C1s (D);

[0039] Figure 4UV-visible absorption spectra of different systems of different materials in Experimental Example 3 of the present invention in pH 4.0 acetate buffer (0.1M) (A); UV-visible absorption spectra of different systems of different materials with or without PFOA (3 ppm) in pH 4.0 acetate buffer (0.1M) (B); absorbance of the color development system of Fe3O4@ZIF-67-F (NaF) synthesized with different NaF addition amounts (C); absorbance change value of the color development system of Fe3O4@ZIF-67-F (NaF) synthesized with different NaF addition amounts after adding PFOA (1 ppm) (D);

[0040] Figure 5 Optimization diagram of extraction time (A) in Experimental Example 4 of the present invention; optimization diagram of extraction temperature (B); optimization diagram of pH (C); optimization diagram of ionic strength (D);

[0041] Figure 6 The experimental conditions that have a great influence on the construction of the nanozyme-like colorimetric sensor in Experimental Example 5 of the present invention are optimized: (A) the influence of TMB concentration; (B) the influence of the pH value of the system; (C) the influence of reaction time; (D) the influence of reaction temperature;

[0042] Figure 7 The following are ultraviolet absorption spectra of different reaction systems with different concentrations (0-100 ppb) of PFOA added in Experimental Example 6 of the present invention (A); a scatter plot of PFOA detection in the range of 1-100 ppb by the nanozyme-like sensor using Fe3O4@ZIF-67-F (NaF7.5) as a catalyst (B); illustration: photographs of different reaction systems with different concentrations of PFOA added (0-100 ppb); a linear calibration plot of PFOA detection in the range of 1-60 ppb by the nanozyme-like sensor using Fe3O4@ZIF-67-F (NaF7.5) as a catalyst (C);

[0043] Figure 8 This is the full XPS spectrum of Fe3O4@ZIF-67-F (NaF7.5) before and after adsorption of PFOA in Experimental Example 7 of the present invention (A); and the EPR spectra of different systems with PFOA added first and last (B). DETAILED DESCRIPTION

[0044] Example 1

[0045] The magnetic solid phase extraction-Fe3O4@ZIF-67-F activated persulfate nanoenzyme colorimetric sensor detection method includes the following steps:

[0046] Preparation of S1. Fe3O4@ZIF-67-F catalyst: 0.05 g of Fe3O4 powder and 2 g of PVP were mixed and dissolved in 30 mL of anhydrous methanol, and ultrasonicated at room temperature for 30 min to obtain solution A. 1.2 g and 4 mmol of Co(NO3)2·6H2O were dissolved in 30 mL of anhydrous methanol and ultrasonicated at room temperature for 5 min to obtain solution B. 1.232 g and 15 mmol of 2-methylimidazole and 7.5 mmol of F source were added to solution A, and the mixture was heated to 40 ℃ and while ultrasonically treating, solution B was added dropwise to solution A at a frequency of 40 Hz, a power of 1000 W, and a dropping speed of 0.8 mL / s. After the dropwise addition was completed, ultrasonic treatment was continued for 10 min to obtain a suspension, which was transferred to a polytetrafluoroethylene-lined stainless steel autoclave and heated at 120 ℃ for 4 h. The remaining solid product was collected by a magnet and washed four times with a methanol solution having a mass fraction of 60% by weight, and then dried in an oven at 70 ℃ to obtain the Fe3O4@ZIF-67-F catalyst;

[0047] The preparation method of Fe3O4 powder is:

[0048] 1.95 g (12 mmol) of FeCl3·6H2O and 0.6 g (2.04 mmol) of Na3Cit·2H2O were dissolved in 60 mL of ethylene glycol solution. 3.6 g (0.04 mmol) of CH3COONa was added while stirring. Stirring was continued for 30 min at a stirring speed of 150 rpm. The mixture was then placed in a polytetrafluoroethylene-lined stainless steel autoclave. The autoclave was heated to 200°C and kept warm for 10 h. The mixture was then cooled to room temperature. The resulting black product was washed four times with EtOH solution and deionized water, and then dried in an oven at 70°C to obtain Fe3O4 powder.

[0049] The method for optimizing F source is:

[0050] Take 0.1 mol acetate buffer as the matrix, add the above-mentioned F sources into the matrix to prepare a mass concentration of 1 mg·mL -1 50 μL of the suspension was dispersed in 850 μL of 0.1 mol acetate buffer, 50 μL of PMS solution and 50 μL of TMB solution were added thereto, and the mixture was reacted at room temperature for 10 minutes to complete the full conversion of TMB to ox-TMB to obtain a mixture, and the absorbance of the mixture was recorded at 652 nm. A F source with strong absorbance was preferred, and the F source was NaF;

[0051] S2, magnetic solid phase extraction: add 100 mL of the sample solution of PFOA to be determined into a glass container, add 10 mg of the Fe3O4@ZIF-67-F catalyst prepared in step S1 to the sample solution to obtain a mixed solution, then place the mixed solution in a water bath shaker and shake at a frequency of 300 times / min for 30 minutes at room temperature, apply a magnet to the outside of the glass container to separate the solid phase and the liquid phase in the mixed solution, completely discard the liquid phase, and transfer the solid phase to a centrifuge tube with a size of 5 mL. Then, TMB solution, PMS solution and acetate buffer are added to the centrifuge tube in sequence, wherein the TMB solution is 50 μL, 1-10 mmol, the PMS solution is 50 μL, 1 mmol, the acetate buffer is 0.1 mol, the pH is 3-4, and the total volume of the solution in the centrifuge tube after the addition of the acetate buffer is 1 mL, to obtain a detection system;

[0052] The room temperature is 26° C. The size of the polytetrafluoroethylene-lined stainless steel autoclave is 100 mL. The TMB solution is prepared using TMB as the solute and dimethyl sulfoxide as the solvent. The PMS solution is prepared using PMS as the solute and acetate buffer as the solvent.

[0053] S3. Colorimetric detection process: The detection system obtained in step S2 was compared with the standard colorimetric system, and the recovery rate was used to evaluate the enrichment efficiency of the detection system for PFOA. The recovery rate refers to the ratio of the absorbance change value of the detection system after enrichment of PFOA to the absorbance change value of the system after directly adding the sample solution of PFOA to be measured to the standard colorimetric system. The standard colorimetric system is to directly add a PFOA solution with a concentration of 10 ppb to 1 mL of the detection system.

[0054] S4. Analysis and calculation:

[0055] Calculation of detection limit LOD: LOD = 3SB / k;

[0056] Calculation of limit of quantification (LOQ): LOQ = 10SB / k;

[0057] Where SB is the standard deviation of the color development detection process of step S3 repeated three times, and k is the slope of the regression equation.

[0058] Example 2

[0059] The difference between this embodiment and embodiment 1 is that the specific parameters in the method are selected differently:

[0060] S1, Fe3O4@ZIF-67-F catalyst preparation: ultrasonic treatment power is 800W, drop rate is 0.5mL / s, the remaining solid product is collected by magnet and washed three times with methanol solution, the F source is 3.75mmol HF;

[0061] In the preparation method of Fe3O4 powder: the stirring speed is 100 rpm, the stainless steel autoclave is heated to 195℃ and kept warm for 10 hours, and the obtained black product is washed three times with EtOH solution and deionized water.

[0062] S2. Magnetic solid phase extraction: The mixture was shaken in a water bath shaker at 290 shakes / min for 30 min at room temperature in a 0.1 M acetate buffer solution with a pH of 3 and a room temperature of 25°C.

[0063] S3. During the color development detection process: the standard color development system is to directly add a PFOA solution with a concentration of 2 ppb into 1 mL of the detection system.

[0064] Example 3

[0065] The difference between this embodiment and embodiment 1 is that the specific parameters in the method are selected differently:

[0066] S1. Preparation of Fe3O4@ZIF-67-F catalyst: The ultrasonic treatment power was 1200 W, the droplet speed was 1 mL / s, the remaining solid product was collected by a magnet and washed 5 times with methanol solution, and the F source was 30 mmol of KF;

[0067] In the preparation method of Fe3O4 powder, the stirring speed is 200 rpm, the stainless steel autoclave is heated to 205°C and kept at this temperature for 10 hours, and the obtained black product is washed five times with EtOH solution and deionized water;

[0068] S2. Magnetic solid phase extraction: The mixture was shaken in a water bath shaker at 310 shakes / min for 30 min at room temperature. The acetate buffer was 0.1 M, pH 3.5, and the room temperature was 28°C.

[0069] S3. During the color development detection process: the standard color development system is to directly add a 20 ppb PFOA solution into 1 mL of the detection system.

[0070] Example 4

[0071] The difference between this embodiment and embodiment 1 is that the specific parameters in the method are selected differently:

[0072] The F source is 7.5 mmol of NH4F. S3. During the color development detection process: the standard color development system is to directly add a 5 ppb PFOA solution into 1 mL of the detection system.

[0073] Example 5

[0074] The difference between this embodiment and embodiment 1 is that the specific parameters in the method are selected differently:

[0075] The F source was 7.5 mmol of NH4HF2.

[0076] Experimental Example 1

[0077] The structure and surface morphology of Fe3O4@ZIF-67-F(NaF7.5) in Example 1 were characterized by SEM and HRTEM. The chemical formula and numbers in the brackets represent the fluorine source of the impurity F and the number of millimoles of fluorine source added during the material synthesis process, respectively. Figure 2 As shown in (A), the SEM image shows that the Fe3O4@ZIF-67-F(NaF7.5) nanoparticles have good dispersion and present a uniform rhombic dodecahedron morphology with a side length of about 600-800nm; Figure 2 As shown in (B), the TEM image shows that the obtained Fe3O4@ZIF-67-F(NaF7.5) has a typical core-shell structure, in which the diameter of Fe3O4 is about 100-200nm. The TEM results show that the unique magnetic Fe3O4@ZIF-67-F(NaF7.5) nanocomposite material was successfully prepared; Figure 2 As shown in (C), the vibrating sample magnetometer (VSM) is used to test the magnetic properties of the materials Fe3O4 and Fe3O4@ZIF-67-F(NaF7.5). The saturation magnetizations of Fe3O4 and Fe3O4@ZIF-67-F(NaF7.5) are 81.3 and 64.8 emu·g, respectively. -1 , indicating that the material has ferromagnetism. The reduced magnetic field intensity of Fe3O4@ZIF-67-F(NaF7.5) is due to the presence of the ZIF-67 coating layer. The prepared nanocomposite has strong magnetism and can be easily separated by an external magnetic field, facilitating collection and recovery.

[0078] like Figure 2As shown in (D), the crystal phase and chemical structure of the four materials were determined by XRD. The characteristic peaks of ZIF-67 are located at 7.3°, 10.3°, 12.7°, 14.7°, 16.4°, 18.0°, 24.6° and 26.7°, and these diffraction peaks are marked as (011), (002), (112), (022), (013), (222), (233) and (134) planes, respectively. The characteristic peaks of Fe3O4 can be referred to the XRD card of pure magnetite (JCPDS19- 0629), the characteristic peaks of Fe3O4 nanoparticles are located at 29.7°, 35.0°, 42.5°, 52.8°, 56.6° and 62.4°, which we designate as (220), (311), (400), (422), (511) and (440) planes, respectively; the XRD patterns of Fe3O4@ZIF-67 and ZIF-67 have the same characteristics, indicating that the sample is composed of ZIF phase, and also has the characteristic peaks of Fe3O4, indicating that Fe3O4 is successfully encapsulated therein. The introduction of Fe3O4 nanoparticles does not affect the crystallinity of ZIF-67, only the peak intensity of the sample is slightly reduced compared with the original ZIF-67; in Fe3O4@ZIF-67-F(NaF7.5), the doping of F does not change the crystal structure of Fe3O4@ZIF-67.

[0079] like Figure 2 As shown in (E), the specific surface areas of the three materials were analyzed by Brunuer-Emmett-Teller (BET) measurement. The specific surface area of pure Fe3O4 nanoparticles is only 8.58 m 2 ·g -1 The specific surface area of Fe3O4@ZIF-67-F(NaF7.5) is 778.30m 2 ·g -1 , lower than pure ZIF-67 (1087.65m 2 ·g -1 ), mainly due to the presence of Fe3O4 cores. The three isotherms shown in the figure conform to the characteristics of type I isotherms, indicating that the material has a typical microporous structure. Compared with the non-porous Fe3O4 precursor, this is a significant improvement. Generally speaking, the higher surface area and microporous structure can provide more active sites for pollutant enrichment and strongly promote the catalytic process.

[0080] like Figure 2As shown in (F), the high stability of Fe3O4@ZIF-67-F(NaF7.5) plays a crucial role in the construction of nanozyme-like colorimetric sensors in aqueous solutions at different pH values and in organic solvents. Therefore, the chemical stability of Fe3O4@ZIF-67-F(NaF7.5) was tested. The XRD patterns did not change significantly after immersion in different pH conditions and organic solvents for 24 hours, indicating that Fe3O4@ZIF-67-F(NaF7.5) is stable in organic solvents and aqueous solutions at pH values of 2, 7, and 12, clearly demonstrating its applicability for sensor construction.

[0081] Experimental Example 2

[0082] The elemental composition and valence state of Fe3O4@ZIF-67-F(NaF7.5) in Experimental Example 1 were characterized by XPS. Figure 3 As shown in (A), in the XPS total spectrum of Fe3O4@ZIF-67-F(NaF7.5), the characteristic peaks of C1s, O1s, N1s and Co2p are shown, indicating the presence of these four elements. In the XPS total spectrum of Fe3O4@ZIF-67-F(NaF7.5), in addition to the characteristic peaks of the above four elements, a peak of F1s is also found at 685.70eV, indicating the successful doping of F on Fe3O4@ZIF-67-F and the possible formation of Co-F bonds. The characteristic peak of Fe2p is not found in either material, indicating the successful encapsulation of Fe3O4 by ZIF-67. In the high-resolution spectrum of Co2p ( Figure 3 (B)) at 781.05eV (Co 3+ 2p 3 / 2 )、784.85eV(Co 2+ 2p 3 / 2 )、797.28eV(Co 3+ 2p 1 / 2 ) and 802.28eV(Co 2+ 2p 1 / 2 ) has four characteristic peaks, indicating that Co 3+ and Co 2+ Coexistence, Co 3+ With Co 2+ The ratio is 2.02. Figure 3 As shown in (C), the high-resolution spectrum of N1s can be fitted to two peaks at 404.52eV and 398.74eV, corresponding to the NO bond and the methylimidazole linker, respectively. The typical high-resolution XPS spectrum of C1s can be fitted to three peaks at 284.63eV, 285.15eV, and 286.12eV ( Figure 3(D)), corresponding to C-C, C-N-C, and C-O bonds, respectively. The presence of the C-N-C peak (285.1 eV) in the C1s high-resolution XPS spectrum indicates that nitrogen is indeed doped into the carbon molecular framework. All these findings demonstrate that Fe3O4@ZIF-67-F(NaF7.5) was successfully prepared using the method of this invention.

[0083] Experimental Example 3

[0084] We combine the magnetic solid-phase extraction (MSPE) process with a nanozyme-like colorimetric sensor to detect low-concentration PFOA in water. This sensor acts both as an MSPE extractant and as a catalyst for PMS activation. Therefore, we require the material to have both excellent catalytic activity and strong adsorption capacity for PFOA. We evaluate the performance of different materials based on these two aspects.

[0085] First, we investigated the catalytic activity of different materials. The catalytic activity of different materials was evaluated by the change in absorbance at 652 nm caused by the blueing of TMB activated by PMS. The experimental results are as follows: Figure 4 (A) As shown. In the system where PMS, TMB and materials are added at the same time, the absorbance at 652nm changes significantly, indicating the catalytic activity of this series of materials for PMS activation. Compared with Fe3O4@ZIF-67, when there is only Fe3O4 or ZIF-67, the absorbance at 652nm is significantly weakened, indicating a strong synergistic catalytic effect between Fe3O4 and ZIF-67. However, F doping will have a certain effect on the activity of Fe3O4@ZIF-67. When using F-doped Fe3O4@ZIF-67-F as a catalyst, the absorbance at 652nm is generally lower than that of the original Fe3O4@ZIF-67. This may be because F doping will affect the growth of ZIF-67 on Fe3O4. There is not enough ZIF-67 wrapped on the surface of Fe3O4, which reduces the activity of the material. We have also done some research on the effect of different F source doping with an addition amount of 7.5mmol on the activity of the material ( Figure 4(A) When HF, NH4F, and NH4HF2 were used as the F source for doping, the catalytic activity of the three materials obtained was not significantly different from that of pure Fe3O4. Combined with the fact that the colors of the materials were the same as those of pure Fe3O4, it can be concluded that ZIF-67 was almost completely uncoated on the Fe3O4 surface. This is likely due to the acidic nature of the solution made by HF, NH4F, and NH4HF2, which interfered with the growth of ZIF-67 on the Fe3O4 surface. When NaF and KF were used as the F source for doping, although the activity was somewhat lower than that of undoped Fe3O4@ZIF-67, the decrease was not significant (the absorbance changes were 0.1031 and 0.1631, respectively), fully meeting the requirements for our sensor construction. Furthermore, Fe3O4@ZIF-67 (NaF7.5) with NaF as the F source was slightly more active than Fe3O4@ZIF-67 (KF7.5) doped with KF. At the same time, we also tested the sensitivity of Fe3O4@ZIF-67(NaF7.5) and Fe3O4@ZIF-67(KF7.5) for PFOA detection. Figure 4 (B) When 3 ppm of PFOA was added to the system, PFOA adsorption on the material surface inhibited its activity. For Fe3O4@ZIF-67(NaF7.5), the absorbance of the system decreased by 0.2075, while for Fe3O4@ZIF-67(KF7.5), the absorbance decreased by 0.1887, indicating that Fe3O4@ZIF-67(NaF7.5) has a certain advantage in sensitivity to PFOA. Taking both aspects into consideration, we ultimately chose NaF as the F source.

[0086] After determining the F source, we also optimized the amount of NaF added during the doping process from the perspectives of catalytic activity and sensitivity. The results are as follows: Figure 4(C) and 4(D). As the amount of NaF added varied from 0 mmol to 30 mmol, the absorbance of the system changed from 1.1527 to 0.7572. This is likely due to the fact that the F doping interfered with the growth of ZIF-67 on the Fe3O4 surface, resulting in a decrease in catalytic activity. We also compared the effect of different NaF addition amounts on PFOA sensitivity by adding a low concentration of PFOA (1 ppm) to the system. When the NaF addition amount varied from 0 mmol to 7.5 mmol, the absorbance change increased from 0.0037 to 0.0845. However, as the addition amount continued to increase, the absorbance change decreased. This may be because when the NaF addition amount was too low, the material did not have enough F to form FF interactions to adsorb PFOA. However, when the NaF addition amount was too high, ZIF-67 could not fully form, resulting in a decrease in catalytic activity and a decrease in PFOA adsorption capacity. Based on the comparison of the above two aspects, we decided to choose Fe3O4@ZIF-67-F(NaF7.5) to construct a nanozyme-like colorimetric sensor.

[0087] Experimental Example 4

[0088] In order to obtain the best extraction effect, we optimized several factors that have a significant impact on the extraction effect and used the recovery rate to evaluate the optimization results. During the MSPE experiment, we used 10 mg of Fe3O4@ZIF-67-F (NaF7.5) as the extraction agent.

[0089] First, we optimized the extraction time. Figure 5 (A), when the extraction time increased from 10 min to 30 min, the recovery rate increased from 66.0% to 91.5%. A longer extraction time can promote the interaction between PFOA and the material. As the extraction time is further extended, the recovery rate stabilizes at around 90%, so we chose 30 min as the extraction time.

[0090] Next, we optimized the extraction temperature ( Figure 5 (B) When the extraction temperature increases from 10°C to 40°C, the molecular movement accelerates with the increase in temperature, which can promote the adsorption process. The recovery rate increases from 55.98% to 90.21%. However, as the extraction temperature further increases to 60°C, the recovery rate remains stable. Therefore, we choose 40°C as the appropriate extraction temperature.

[0091] Then, we optimized the pH value of the extraction system (2-12). When the system pH was 4, the extraction recovery rate reached the best level (92.16%) ( Figure 5(C)). This indicates that PFOA can be effectively adsorbed onto Fe3O4@ZIF-67-F(NaF7.5) under acidic conditions. The possible reason is that the pH value of the sample solution affects the form of PFOA in the water sample. PFOA has a pKa of 2.8, which is strongly acidic. Under acidic conditions, PFOA mainly exists in the form of non-ionic acid, while under neutral or alkaline conditions, PFOA is mainly dissolved in water in an ionized form, resulting in a decrease in the adsorption efficiency of PFOA by the adsorbent. Therefore, in subsequent experiments, the pH value of the sample was adjusted to 4 as in Example 1.

[0092] Finally, we optimized the ionic strength by increasing the NaCl concentration from 0% to 20% (w / v) to test the effect of ionic strength on the recovery of PFOA. Figure 5 As shown in (D), the PFOA recovery rate decreased with increasing NaCl dosage. This may be because the adsorption sites on the Fe3O4@ZIF-67-F(NaF7.5) surface may be occupied by NaCl, leaving no more spare sites to accommodate the target pollutant. In addition, the high solution viscosity and low diffusion rate caused by the increase in NaCl concentration may also reduce the PFOA recovery rate. Therefore, NaCl was not used in subsequent experiments.

[0093] The MSPE conditions we finally used were an extraction time of 30 min, an extraction temperature of 40°C, a sample pH of 4.0, and no NaCl was added.

[0094] Experimental Example 5

[0095] In addition to optimizing the MSPE conditions, we also needed to optimize the colorimetric conditions of the nanozyme-like sensor. We optimized the TMB concentration, pH value, reaction temperature, and time in the system. During the experiment, we selected 10 mg of Fe3O4@ZIF-67-F (NaF7.5) as the catalyst.

[0096] The concentration of TMB in the system needs to be optimized because only by adding an appropriate amount of TMB can a better color effect be obtained. Different concentrations of TMB (100-1000μM) in the system are used to test the effect of TMB concentration. Figure 6 As shown in (A), when the TMB concentration changes from 100 μM to 500 μM, the absorbance increases from 0.4683 to 0.9729. However, as the TMB concentration continues to increase, the absorbance remains constant at around 0.97. Therefore, 500 μM was set as the TMB concentration in the system for the following experiments.

[0097] pH value is also an important parameter for constructing colorimetric sensors. pH not only determines the presence of PFOA, but also affects the color development of TMB. Acetate buffer, phosphate buffer, and ammonia-ammonium chloride buffer with pH values ranging from 3.0 to 10.0 were used to test the effect of pH on the reaction system. Figure 6 As shown in (B), when the pH changes from 3.0 to 5.0, the absorbance increases from 0.8970 to 1.0373, but when the pH increases from 5.0 to 8.0, the color effect becomes very poor as the absorbance decreases from 1.0373 to 0.2812. And under the pH conditions of 9.0-10.0, the reaction system has almost no color change. The results show that the nanozyme-like sensor has a good color development effect in the pH range of 3.0-6.0, which may be because the color development reagent TMB achieves better color development under acidic and neutral conditions. In order to obtain the best color effect, a pH 5.0 acetate buffer was used to construct the colorimetric sensor in the following experiments.

[0098] The reaction time and temperature were optimized through a series of experiments ( Figure 6 (C) and Figure 6 (D)). The reaction system reaches a maximum absorbance of 0.9976 in just 10 minutes and maintains a constant absorbance for 120 minutes. Furthermore, the reaction system achieves excellent color development within a temperature range of 20-70°C, with an absorbance of approximately 1.08. For the following experiments, 10 minutes and room temperature were selected as the optimal testing time and temperature for the sensor.

[0099] Therefore, the sensor construction conditions we adopted in the following experiments are summarized as follows: 500 μM as the concentration of TMB in the system, 5.0 as the system pH, 10 min as the reaction time, and the reaction was carried out at room temperature.

[0100] Experimental Example 6

[0101] Utilizing the catalytic activity of Fe3O4@ZIF-67-F (NaF7.5) on PMS activation, the reaction system was used to construct a nanozyme-like colorimetric sensor to detect PFOA. Figure 7 As shown in the illustrations in (A) and (B), with the increase of PFOA concentration, the color of the reaction system solution gradually becomes lighter, and the absorbance of the solution at 652 nm gradually decreases.

[0102] Based on the fading phenomenon, a colorimetric detection method for PFOA was established. Figure 7As shown in (B), PFOA concentrations from 0 to 100 ppb were tested. As the PFOA concentration increased from 1 ppb to 60 ppb, the absorption intensity of the reaction system at 652 nm decreased accordingly, and the value of (A0-Ax) showed an obvious two-stage linear relationship with the PFOA concentration (A0 represents the initial absorbance without PFOA, and Ax represents the absorbance of PFOA after adding Cx). The LR of PFOA detection is as follows Figure 7 As shown in (C), when the concentration of PFOA is between 1 ppb and 30 ppb, the regression equation is A0-Ax=0.006Cx+0.020, and the correlation coefficient is 0.992; when the concentration of PFOA is between 30 ppb and 60 ppb, the regression equation is A0-Ax=0.020Cx+0372, and the correlation coefficient is 0.997.

[0103] According to the formula in step S4, LOD = 3 (SB / k), the LOD was calculated to be 0.252 ppb, and LOQ = 10 (SB / k), the LOQ was calculated to be 0.838 ppb. Furthermore, as shown in Table 1, this newly constructed PFOA colorimetric sensor achieved a lower LOD and a wider LR than other methods previously reported in the literature. Therefore, our constructed nanozyme-like sensor with high sensitivity and excellent detection capability has broad application prospects.

[0104] Table 1 Comparison of methods for analyzing PFOA a Selenium and nitrogen co-doped carbon quantum dots;

[0105] b Polyethylene glycol-terminated (PEG-thiol) and perfluoroalkyl-terminated (F-thiol) alkanethiols modified gold nanoparticles (Au@PEG-F NPs);

[0106] c Aggregation-induced emission probe molecules;

[0107] d Dye fluorescent surfactant (FSs)-Ag nanoparticles graphene oxide.

[0108] Experimental Example 7

[0109] We explored the mechanism of MSPE combined with nanozyme-like colorimetric sensor for detecting PFOA. First, we used XPS to characterize the changes in the surface elements of Fe3O4@ZIF-67-F (NaF7.5) before and after adsorption for 30 minutes, such as Figure 8As shown in (A), the F1s peak of the adsorbed material increased significantly, indicating that after 30 minutes of adsorption, most of the PFOA has been completely adsorbed on the surface of Fe3O4@ZIF-67-F(NaF7.5), causing an increase in the F content on the surface of Fe3O4@ZIF-67-F(NaF7.5), which is consistent with the results of our previous adsorption experiments. In addition, we further explored the detection principle of PFOA by adjusting the order of adding materials, PFOA and other substances in the system and then conducting EPR tests. Figure 8 As shown in Figure (B), when 50 ppb PFOA is added first to the reaction system and reacts with the material before PMS is added, the resulting EPR signal is very weak, indicating that PFOA adsorbs on the material surface, inhibiting the material's ability to activate PMS, resulting in a weaker EPR signal. However, when PFOA is added last, the resulting EPR signal is unaffected. These XPS and EPR results, along with the previous adsorption experiments, demonstrate that the principle of PFOA detection is that PFOA adsorbs on the Fe3O4@ZIF-67-F(NaF7.5) surface, masking its active sites and thereby suppressing color change and enabling quantification.

[0110] The excellent enrichment efficiency and high selectivity of Fe3O4@ZIF-67-F(NaF7.5) for PFOA are believed to be related to the structural characteristics of Fe3O4@ZIF-67-F(NaF7.5), which can be analyzed from the following perspectives: (1) Fe3O4@ZIF-67-F(NaF7.5) has a 778.30 m 2 ·g -1 The high BET surface area of Fe3O4@ZIF-67-F(NaF7.5) can fully expose the functional groups to the analyte and facilitate the subsequent adsorption; (2) Fe3O4@ZIF-67-F(NaF7.5) has a hydrophobic surface, which is conducive to the adsorption of hydrophobic PFOA; (3) F on the surface of Fe3O4@ZIF-67-F(NaF7.5) attracts PFOA through FF interaction, which is considered to be one of the most important factors in the selective adsorption of PFOA. We hypothesize that all these factors may play a synergistic role in the superior enrichment efficiency and selectivity of Fe3O4@ZIF-67-F(NaF7.5) for PFOA. Note that although it is impossible to quantitatively evaluate the contribution of each interaction, we can assume that the FF interaction is crucial for the high selectivity, while hydrophobic-hydrophobic interaction and electrostatic attraction are important factors affecting the adsorption capacity.

[0111] Experimental Example 8

[0112] A novel nanozyme-like colorimetric sensor based on Fe₃O₄@ZIF-67-F (NaFₐ₇) as a catalyst was applied to the detection and analysis of PFOA in real water samples, including tap water, Taihu Lake water, Yangshan Lake water, and Jiuxiang River water. The analytical results for the four water samples are shown in Table 2. PFOA was detected in the untreated wastewater from the kitchenware factory at a concentration of 14.825 ppb, while no PFOA was detected in the other four water samples. The spiked recoveries for the four samples (2, 5, 10, and 20 ppb) ranged from 94.8% to 119.3%, with relative standard deviations (RSDs) ranging from 0.11% to 7.49%, indicating that natural water has little effect on PFOA detection. This may be because only a small amount of actual sample solution is required for PFOA detection, and components such as humic acid in the water samples are insufficient to affect PFOA detection. Therefore, this novel nanozyme-like colorimetric sensor based on Fe₃O₄@ZIF-67-F (NaFₐ₇) is suitable for the rapid analysis of PFOA in real water samples.

[0113] Table 2 Analysis results of PFOA determination in five actual water samples

[0114]

[0115]

Claims

1. Magnetic solid phase extraction-Fe3O4@ZIF-67-F activated persulfate nanoenzyme colorimetric sensor detection method, characterized in that: The following steps are involved: S1. Preparation of Fe3O4@ZIF-67-F catalyst: 0.05 g of Fe3O4 powder and 2 g of PVP were mixed and dissolved in 30 mL of anhydrous methanol and sonicated at room temperature for 30 min to obtain solution A. 1.2 g and 4 mmol of Co(NO3)2·6H2O were dissolved in 30 mL of anhydrous methanol and sonicated at room temperature for 5 min to obtain solution B. 1.232 g and 15 mmol of 2-methylimidazole and 3.75~30 mmol of F source were added to solution A. The temperature was raised to 40°C and solution B was added dropwise to solution A while sonicating. After the addition was completed, sonication was continued for 10 min to obtain a suspension. The suspension was transferred to a polytetrafluoroethylene-lined stainless steel autoclave and heated at 120°C for 4 h. The remaining solid product was collected by a magnet and washed 3~5 times with methanol solution. Then, it was dried in an oven at 70°C to obtain the Fe3O4@ZIF-67-F catalyst. S2, magnetic solid phase extraction: add 100 mL of the sample solution of PFOA to be determined into a glass container, add 10 mg of the Fe3O4@ZIF-67-F catalyst prepared in step S1 to the sample solution to obtain a mixed solution, then place the mixed solution in a water bath shaker and shake at a frequency of 300±10 times / min for 30 min at room temperature, apply a magnet to the outside of the glass container to separate the solid phase and the liquid phase in the mixed solution, completely discard the liquid phase, and transfer the solid phase to a centrifuge tube, and then add TMB solution, PMS solution and acetate buffer to the centrifuge tube in sequence, wherein the TMB solution is 50 μL, 1~10 mmol, the PMS solution is 50 μL, 1 mmol, the acetate buffer is 0.1 mol, the pH is 3~4, and the total volume of the solution in the centrifuge tube after the addition of the acetate buffer is 1 mL, to obtain a detection system; S3. Colorimetric detection process: The detection system obtained in step S2 is compared with the standard colorimetric system, and the recovery rate is used to evaluate the enrichment efficiency of the detection system for PFOA. The recovery rate refers to the ratio of the absorbance change value of the detection system after enrichment of PFOA to the absorbance change value of the system after directly adding the sample solution of PFOA to be determined to the standard colorimetric system.

2. The magnetic solid phase extraction-Fe3O4@ZIF-67-F activated persulfate nanoenzyme colorimetric sensor detection method according to claim 1 is characterized in that: The preparation method of Fe3O4 powder in step S1 is: Take 1.95g, 12mmol of FeCl3·6H2O and 0.6g, 2.04mmol of Na3Cit·2H2O and dissolve them together in 60mL of ethylene glycol solution. While stirring, add 3.6g, 0.04mmol of CH3COONa and continue stirring for 30min at a stirring speed of 100-200rpm. Then place it in a polytetrafluoroethylene-lined stainless steel autoclave, heat the stainless steel autoclave to 200±5℃ and keep it warm for 10h, cool it to room temperature, and wash the obtained black product with EtOH solution and deionized water 3-5 times, and then dry it in a 70℃ oven to obtain Fe3O4 powder.

3. The magnetic solid phase extraction-Fe3O4@ZIF-67-F activated persulfate nanozyme colorimetric sensor detection method according to claim 2 is characterized in that: The room temperature is 25-28° C., and the size of the polytetrafluoroethylene-lined stainless steel autoclave is 100 mL.

4. The magnetic solid phase extraction-Fe3O4@ZIF-67-F activated persulfate nanoenzyme colorimetric sensor detection method according to claim 1, characterized in that: The frequency of the ultrasonic treatment in step S1 is 40 Hz, the power is 800-1200 W, the dropping speed is 0.5-1 mL / s, and the mass fraction of the methanol solution is 60%.

5. The magnetic solid phase extraction-Fe3O4@ZIF-67-F activated persulfate nanoenzyme colorimetric sensor detection method according to claim 1, characterized in that: In step S1, the F source is one of HF, NaF, KF, NH4F or NH4HF2.

6. The magnetic solid phase extraction-Fe3O4@ZIF-67-F activated persulfate nanoenzyme colorimetric sensor detection method according to claim 5, characterized in that: The method for selecting F source is: Take 0.1 mol acetate buffer as the matrix, add the above-mentioned F sources into the matrix to prepare a mass concentration of 1 mg·mL -1 Take 50 μL of the suspension and disperse it in 850 μL of 0.1 mol acetate buffer. Add 50 μL of PMS solution and 50 μL of TMB solution thereto. React at room temperature for 10 minutes to complete the full conversion of TMB to ox-TMB to obtain a mixture. Record the absorbance of the mixture at 652 nm, and select a F source with strong absorbance.

7. The magnetic solid phase extraction-Fe3O4@ZIF-67-F activated persulfate nanoenzyme colorimetric sensor detection method according to claim 5, characterized in that: In step S2, the TMB solution is prepared using TMB as the solute and dimethyl sulfoxide as the solvent, and the PMS solution is prepared using PMS as the solute and acetate buffer as the solvent.

8. The magnetic solid phase extraction-Fe3O4@ZIF-67-F activated persulfate nanoenzyme colorimetric sensor detection method according to claim 1, characterized in that: The size of the centrifuge tube in step S2 is 5 mL.

9. The magnetic solid phase extraction-Fe3O4@ZIF-67-F activated persulfate nanoenzyme colorimetric sensor detection method according to claim 1, characterized in that: The standard color development system in step S3 is to directly add a PFOA solution with a concentration of 2, 5, 10 or 20 ppb into 1 mL of the detection system.

10. The magnetic solid phase extraction-Fe3O4@ZIF-67-F activated persulfate nanoenzyme colorimetric sensor detection method according to claim 1, characterized in that: The step S4 is also included, analyzing and calculating: Detection limit LOD calculation: LOD=3SB / k; Calculation of limit of quantification (LOQ): LOQ = 10SB / k; Where SB is the standard deviation of the color development detection process of step S3 repeated three times, and k is the slope of the regression equation.

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