Method for modeling and detecting content and distribution of phosphate ions in material

Abstract

The application relates to a model construction method and a detection method for the content and distribution of phosphate ions in a material. The model construction method for the content and distribution of phosphate ions in the material comprises the following steps: taking a test sample of the material; placing the test sample in pure water and performing extraction treatment under different temperature conditions; detecting the concentration of phosphate ions in the obtained extraction liquid; calculating the diffusion coefficient value of the outward diffusion of the phosphate ions according to the detected concentration of the phosphate ions and Fick's first law and Fick's second law; constructing a model for the content and distribution of the phosphate ions in the material according to the detected concentration of the phosphate ions and Fick's first law and Fick's second law, and verifying the model by using the diffusion coefficient value. The model constructed by the above model construction method has high detection accuracy and is suitable for evaluating the flame-retardant effect of phosphate flame retardants.

Description

Technical Field

[0001] This application relates to the field of analytical chemistry, and in particular to a model construction method and a detection method for the content and distribution of phosphate ions in a material. Background Technology

[0002] Phosphate-based flame retardants possess advantages such as low smoke, non-toxicity, low halogen content, and halogen-free properties, aligning with the development trend of flame retardants. Their flame-retardant mechanism involves thermal decomposition into phosphoric acid, metaphosphoric acid, and water, which adhere to the material surface, thereby achieving flame retardancy. Therefore, testing the phosphate content and distribution in materials containing phosphate-based flame retardants is crucial for evaluating their flame-retardant effect.

[0003] Traditional methods for detecting phosphate content involve measuring the amount of phosphate ions in a sample. These methods typically employ spectroscopic or chromatographic techniques. However, these methods are based on the chemical properties of phosphate ions and involve complex testing procedures. They are also highly dependent on the testing media and equipment, resulting in high costs and limited adoption by testing institutions. Summary of the Invention

[0004] Based on this, this application provides a model construction method and a detection method for the content and distribution of phosphate ions in materials. This detection method is simple in procedure, has little dependence on test media and equipment, and has low detection cost.

[0005] The first aspect of this application provides a method for constructing a model of the content and distribution of phosphate ions in a material, comprising the following steps:

[0006] Take test samples of the material;

[0007] The test sample was placed in an extraction solvent and extracted under different temperature conditions.

[0008] The concentration of phosphate ions in the extract obtained under different temperature conditions was detected.

[0009] Based on the detected phosphate ion concentration, and combined with Fick's first law and second law, the diffusion coefficient of phosphate ions diffuses outward under different temperature conditions.

[0010] Based on the detected concentration of phosphate ions, a model of the content and distribution of phosphate ions in the material is constructed using Fick's first law and Fick's second law. The model is then validated using the diffusion coefficient value and / or the concentration of phosphate ions in the extract obtained under at least one temperature condition.

[0011] In one embodiment, the diffusion coefficient value is calculated using the following formula (1):

[0012]

[0013] This indicates the concentration of phosphate ions in the extract obtained after extraction treatment for time t, in ppm.

[0014] C ∞ The concentration of phosphate ions in the extraction solvent before extraction is expressed in ppm.

[0015] C0 represents the concentration of phosphate ions in the test sample before extraction, in ppm;

[0016] D x This represents the diffusion coefficient value of phosphate ions under different temperature conditions, expressed in cm. 2 / s;

[0017] t represents the extraction and processing time, in seconds;

[0018] λ n k n And n is defined as in the nth-order Bessel function.

[0019] In one embodiment, the model is shown in equations (2a) to (2d). The distribution curve of phosphate ions in the material is obtained by solving equations (2a) to (2d). The distribution curve of phosphate ions in the material obtained by solving equations (2a) to (2d) is integrated to obtain the content of phosphate ions in the material.

[0020]

[0021]

[0022]

[0023] Where i = 1, 2, 3...m-3, m-2, m represents an integer greater than 2;

[0024]

[0025] In the formula Where Δx represents the spatial step size, and b = nΔx, Δt represents the time step size, b represents half the thickness of the test sample, D = D0exp(-Q / RT), where D0 represents a constant, Q represents the diffusion activation energy, R represents the molar gas constant, and T represents the thermodynamic temperature corresponding to the temperature.

[0026] Where Shape represents the shape coefficient and R represents the radius of curvature of the diffusion surface;

[0027] C i n The concentration of phosphate ions at the i-th node in the test sample is given when the extraction and processing time is t = nΔt.

[0028] In one embodiment, the test sample satisfies one or more of the following conditions (1) to (3):

[0029] (1) The thickness of the test sample is 2mm to 3mm;

[0030] (2) The concentration of phosphate ions in the test sample before extraction and treatment is 300 ppm to 700 ppm;

[0031] (3) The test sample is a square with a side length of 25mm to 35mm.

[0032] In one embodiment, the different temperature conditions are set to 58℃~62℃, 68℃~72℃, and 78℃~82℃, respectively.

[0033] In one embodiment, the extraction processing time is 20h to 30h.

[0034] In one embodiment, the extraction process is carried out under closed conditions, and the amount of extraction solvent used is 4 mL to 8 mL.

[0035] In one embodiment, the concentration of phosphate ions in the extract is detected by ion chromatography.

[0036] In one embodiment, the eluent used in the ion chromatography method includes Na2CO3 at a concentration of 4 mM to 5 mM and NaHCO3 at a concentration of 1 mM to 2 mM.

[0037] In one embodiment, the conditions for the ion chromatography further include one or more of the following conditions (1) to (5):

[0038] (1) The flow rate of the rinsing solution is 1 to 1.5 mL / min;

[0039] (2) The column temperature is 30℃~40℃;

[0040] (3) The detector temperature is 30℃~40℃;

[0041] (4) The current of the suppressor is 38mA to 43mA;

[0042] (5) The stationary phase of the chromatographic column is a microporous cross-linked resin.

[0043] A second aspect of this application provides a method for detecting the content and distribution of phosphate ions in a material, comprising the following steps:

[0044] Take a test sample of the material to be tested;

[0045] The test sample is placed in an extraction solvent for extraction.

[0046] The concentration of phosphate ions in the extract obtained from the extraction process was detected;

[0047] The concentration of phosphate ions obtained from the detection is substituted into the model constructed by the model construction method described in the first aspect to calculate the content and distribution curve of phosphate ions in the test sample.

[0048] In one embodiment, the test sample satisfies one or more of the following conditions (1) to (3):

[0049] (1) The thickness of the test sample is 2mm to 3mm;

[0050] (2) The concentration of phosphate ions in the test sample before extraction and treatment is 300 ppm to 700 ppm;

[0051] (3) The test sample is a square with a side length of 25mm to 35mm.

[0052] In one embodiment, the extraction temperature is set to 78°C to 82°C.

[0053] In one embodiment, the extraction processing time is 20h to 30h.

[0054] In one embodiment, the extraction process is carried out under closed conditions, and the amount of extraction solvent used is 4 mL to 8 mL.

[0055] In one embodiment, the concentration of phosphate ions in the extract is detected by ion chromatography.

[0056] In one embodiment, the eluent used in the ion chromatography method includes Na2CO3 at a concentration of 4 mM to 5 mM and NaHCO3 at a concentration of 1 mM to 2 mM.

[0057] In one embodiment, the conditions for the ion chromatography further include one or more of the following conditions (1) to (5):

[0058] (1) The flow rate of the rinsing solution is 1 to 1.5 mL / min;

[0059] (2) The column temperature is 30℃~40℃;

[0060] (3) The detector temperature is 30℃~40℃;

[0061] (4) The current of the suppressor is 38mA to 43mA;

[0062] (5) The stationary phase of the chromatographic column is a microporous cross-linked resin.

[0063] In one embodiment, the material to be tested is a polymer material containing phosphate flame retardants;

[0064] Optionally, the polymer material includes one or more of virgin material, recycled material, reclaimed material, and off-grade material.

[0065] The above model construction method calculates the diffusion coefficient of phosphate ions under different temperature conditions by testing the concentration of phosphate ions obtained under different temperature conditions in combination with Fick's first and second laws. Based on the known diffusion coefficient values, a model of the content and distribution kinetics of phosphate ions in the material is constructed and the model is verified. The model constructed in this way has high detection accuracy and is suitable for evaluating the flame retardant effect of phosphate flame retardants.

[0066] The above-mentioned testing method uses the above-mentioned model to detect the material under test. Unlike traditional testing methods that require experimental determination of phosphate ions in the material, this method can directly use the model to calculate the content and distribution of phosphate ions. The steps are simple, less dependent on the test medium and test equipment, have low detection cost, and high detection effect. It is easy to promote and apply, and is of great significance for the production and evaluation of materials such as phosphate flame retardants. Attached Figure Description

[0067] Figure 1 This is one of the schematic diagrams of phosphate ion diffusion in a sample according to one embodiment of this application;

[0068] Figure 2 This is a second schematic diagram of phosphate ion diffusion in a sample according to one embodiment of this application;

[0069] Figure 3 This is a distribution map of phosphate ions in a sample obtained by fitting in one embodiment of this application;

[0070] Figure 4 This is a distribution map of phosphate ions in the sample obtained by fitting in another embodiment of this application. Detailed Implementation

[0071] The following detailed description, in conjunction with specific embodiments, illustrates the model construction method and detection method for the content and distribution of phosphate ions in the materials of this application. This application can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the disclosure of this application.

[0072] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

[0073] In this article, "one or more" refers to any one, two or more of the listed items.

[0074] In this application, terms such as "first aspect" and "second aspect" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or quantity, nor should they be construed as implicitly indicating the importance or quantity of the indicated technical features. Moreover, terms such as "first" and "second" serve only as a non-exhaustive enumeration and should be understood not to constitute a closed limitation on quantity.

[0075] In this application, the technical features described in an open-ended manner include both closed technical solutions consisting of the listed features and open technical solutions that include the listed features.

[0076] In this application, numerical ranges are referred to as continuous unless otherwise specified, and include the minimum and maximum values ​​of the range, as well as every value between the minimum and maximum values. Furthermore, when the range refers to integers, it includes every integer between the minimum and maximum values ​​of the range. Additionally, when multiple ranges are provided to describe a feature or characteristic, the ranges may be merged. In other words, unless otherwise specified, all ranges disclosed herein should be understood to include any and all subranges to which they are incorporated.

[0077] Unless otherwise specified, the percentage content mentioned in this application refers to mass percentage for solid-liquid mixtures and solid-phase-solid mixtures, and volume percentage for liquid-phase-liquid mixtures.

[0078] Unless otherwise specified, all percentage concentrations mentioned in this application refer to the final concentration. The final concentration refers to the proportion of the added component in the system after the addition of that component.

[0079] Unless otherwise specified, the temperature parameters in this application may be either constant temperature processing or processing within a certain temperature range. The constant temperature processing allows for temperature fluctuations within the precision range controlled by the instrument.

[0080] In this application, room temperature generally refers to 4℃~30℃, and more preferably 20±5℃.

[0081] In this application, "pure water" refers to water that meets the requirements of Grade II or Grade III as specified in GB / T 6682-2008.

[0082] This application provides an example of a method for constructing a model of the content and distribution of phosphate ions in a material, comprising the following steps:

[0083] Take test samples of the material;

[0084] The test sample was placed in an extraction solvent and extracted under different temperature conditions.

[0085] The concentration of phosphate ions in the extract obtained under different temperature conditions was detected.

[0086] Based on the detected phosphate ion concentration, and combined with Fick's first law and second law, the diffusion coefficient of phosphate ions diffuses outward under different temperature conditions.

[0087] Based on the detected concentration of phosphate ions, a model of the content and distribution of phosphate ions in the material is constructed using Fick's first law and Fick's second law. The model is then validated using the diffusion coefficient value and / or the concentration of phosphate ions in the extract obtained under at least one temperature condition.

[0088] Understandably, the phosphate ion content and distribution described in this application refer to the content of phosphate ions at different nodes within the material along a direction perpendicular to the phosphate ion diffusion surface (usually the thickness direction), and the corresponding distribution obtained after combining the phosphate ion content at different nodes. A continuous distribution curve is plotted for each node, and the phosphate ion content in the material is obtained by integrating the distribution curve. Meanwhile, the flame-retardant mechanism of phosphate-based flame retardants involves thermal decomposition into phosphoric acid, metaphosphoric acid, and water, which adhere to the material surface, thereby achieving flame retardancy. Knowing the phosphate ion content and distribution in the material can, to some extent, explain the decomposition of phosphate-based flame retardants into phosphoric acid, metaphosphoric acid, and water when the material is heated, thus predicting the flame-retardant performance of the material.

[0089] Understandably, the extraction solvent can be any solvent that does not affect the determination of phosphate ion concentration, and no special limitations are imposed. Examples include pure water, or a solvent containing a low concentration (≤5wt%) of a component that is the same as or similar to the component precipitated from the sample. "Same" refers to phosphate, and "similar" could be a positively charged ion such as K+. + Salt, etc.

[0090] In one example, the diffusion coefficient value is calculated using the following formula (1):

[0091]

[0092] This indicates the concentration of phosphate ions in the extract obtained after extraction treatment for time t, in ppm.

[0093] C ∞ The concentration of phosphate ions in the extraction solvent before extraction is expressed in ppm.

[0094] C0 represents the concentration of phosphate ions in the test sample before extraction, in ppm;

[0095] D x This represents the diffusion coefficient value of phosphate ions under different temperature conditions, expressed in cm. 2 / s;

[0096] t represents the extraction and processing time, in seconds;

[0097] λ n k n The definition of n and n is as in the nth order Bessel function, which is a common definition in this field and can be found in existing literature in this field, including but not limited to: [1] Gu Chaohao, Li Daqian, Chen Shuxing, et al. Mathematical Physics Equations [M]. Beijing: Higher Education Press, 2005: 193-196; [2] Duan Zhiwen, Han Shuxia. Mathematical Physics Equations and Special Functions [M]. Beijing: Higher Education Press, 2008: 119-135; [3] Zhang Huiqing, Wu Xiaoyin, Yang Xiaojun. Mathematical Physics Equations and Special Functions [M]. Xi'an: Northwestern Polytechnical University Press, 2005: 147-149.

[0098] In one example, the model is shown in equations (2a) to (2d). The distribution curve of phosphate ions in the material is obtained by solving equations (2a) to (2d). The content of phosphate ions in the material is obtained by integrating the distribution curve of phosphate ions obtained by solving equations (2a) to (2d).

[0099]

[0100]

[0101]

[0102] Where i = 1, 2, 3...m-3, m-2, m represents an integer greater than 2;

[0103]

[0104] In the formula Where Δx represents the spatial step size, and b = nΔx, Δt represents the time step size, b represents half the thickness of the test sample, D = D0exp(-Q / RT), where D0 represents a constant, Q represents the diffusion activation energy, R represents the molar gas constant, and T represents the thermodynamic temperature corresponding to the temperature.

[0105] Where Shape represents the shape coefficient and R represents the radius of curvature of the diffusion surface;

[0106] C i n This indicates the phosphate ion concentration at the i-th node of the test sample when the extraction processing time is t = nΔt. Additionally, it can be understood that C0... n Definition and C i n Similar; C1 n+1 Definition and C i n Similarly, node n+1 represents the next moment after the extraction process ends; C n m-1 Definition and C i n similar.

[0107] In one example, the thickness of the test sample is 2 mm to 3 mm. Specifically, the thickness of the test sample includes, but is not limited to: 2 mm, 2.1 mm, 2.2 mm, 2.3 mm, 2.4 mm, 2.5 mm, 2.6 mm, 2.7 mm, 2.8 mm, 2.9 mm, 3 mm, or any two of the aforementioned values.

[0108] In one example, the concentration of phosphate ions in the test sample before extraction treatment is 300 ppm to 700 ppm. Specifically, the concentration of phosphate ions in the test sample before extraction treatment includes, but is not limited to: 300 ppm, 350 ppm, 400 ppm, 450 ppm, 470 ppm, 480 ppm, 490 ppm, 500 ppm, 510 ppm, 520 ppm, 530 ppm, 550 ppm, 600 ppm, 650 ppm, 700 ppm, or a range between any two of the aforementioned values.

[0109] In one example, the test sample is a square with a side length of 25mm to 35mm. Specifically, the side length of the test sample includes, but is not limited to, 25mm, 28mm, 30mm, 32mm, 35mm, or any two of the aforementioned values.

[0110] In one example, the different temperature conditions are set to 58℃~62℃, 68℃~72℃, and 78℃~82℃, respectively. Further, the different temperature conditions are set to 60℃, 70℃, and 80℃, respectively.

[0111] In one example, the extraction processing time is 20h to 30h. Specifically, the extraction processing time includes, but is not limited to: 20h, 22h, 23h, 24h, 25h, 26h, 28h, 30h, or any two of the aforementioned values.

[0112] In one example, the extraction process is performed under closed conditions. Without limitation, the extraction process can be performed in a completely sealable clean glass vessel. Specifically, the glass vessel can be a wide-mouthed ground glass bottle with a mouth size greater than 40 mm.

[0113] In one example, the volume of the extraction solvent used is 4 mL to 8 mL. Specifically, the volume of the extraction solvent includes, but is not limited to, 4 mL, 5 mL, 6 mL, 7 mL, 8 mL, or any range between two of the aforementioned values.

[0114] In one example, the concentration of phosphate ions in the extract was detected by ion chromatography.

[0115] In one example, the stationary phase of the chromatographic column used in the ion chromatography is a microporous cross-linked resin.

[0116] In one example, the eluent used in the ion chromatography method includes Na₂CO₃ at a concentration of 4 mM to 5 mM and NaHCO₃ at a concentration of 1 mM to 2 mM.

[0117] In one example, the flow rate of the eluent is 1 to 1.5 mL / min. Specifically, the flow rate of the eluent includes, but is not limited to: 1 mL / min, 1.1 mL / min, 1.2 mL / min, 1.3 mL / min, 1.4 mL / min, 1.5 mL / min, or a range between any two of the aforementioned values.

[0118] In one example, the ion chromatography method uses a column temperature of 30°C to 40°C. Specifically, the column temperature includes, but is not limited to, 30°C, 33°C, 35°C, 37°C, 40°C, or any two of the aforementioned values.

[0119] In one example, the ion chromatography uses a detector with a temperature of 30°C to 40°C. Specifically, the detector temperature includes, but is not limited to, 30°C, 33°C, 35°C, 37°C, 40°C, or any two of the aforementioned values.

[0120] In one example, the ion chromatography uses a suppressor current of 38mA to 43mA. Specifically, the suppressor current includes, but is not limited to: 38mA, 39mA, 40mA, 41mA, 42mA, 43mA, or any two of the aforementioned values.

[0121] In one example, the injection volume used in the ion chromatography is 20 μL to 30 μL. Specifically, the injection volume includes, but is not limited to, 20 μL, 23 μL, 25 μL, 27 μL, 30 μL, or any two of the aforementioned values.

[0122] In one example, the material is a polymer containing a phosphate-based flame retardant. Without limitation, the phosphate-based flame retardant can be of common types in the art, such as zinc phosphate, aluminum phosphate, ammonium phosphate, etc. The polymer material can be of common types in the art, such as general-purpose plastics and engineering plastics, for example, polypropylene, polyvinyl chloride, polystyrene, ABS, polybutylene terephthalate, or modified forms thereof. Furthermore, without limitation, the type of polymer material can include one or more of virgin materials, recycled materials, reclaimed materials, and off-grade materials.

[0123] Another example of this application provides a method for detecting the content and distribution of phosphate ions in a material, comprising the following steps:

[0124] Take a test sample of the material to be tested;

[0125] The test sample is placed in an extraction solvent for extraction.

[0126] The concentration of phosphate ions in the extract obtained from the extraction process was detected;

[0127] The concentration of phosphate ions obtained from the detection is substituted into the model constructed by the model construction method described above to calculate the content and distribution curve of phosphate ions in the test sample.

[0128] In one example, the extraction processing temperature was set to 78℃~82℃.

[0129] Understandably, the characteristics of the test sample of the material to be tested here are the same as those of the test sample in the aforementioned model construction method, and the characteristics of extraction, processing and detection are the same as those of extraction, processing and detection in the aforementioned model construction method, and will not be repeated here.

[0130] In one example, the test material is a polymer material containing a phosphate-based flame retardant. Without limitation, the phosphate-based flame retardant can be a common type in the art, such as zinc phosphate, aluminum phosphate, ammonium phosphate, etc. The polymer material can be a common type in the art, such as general-purpose plastics and engineering plastics, for example, polypropylene, polyvinyl chloride, polystyrene, ABS, polybutylene terephthalate, or modified materials thereof. Furthermore, without limitation, the type of polymer material can include one or more of virgin materials, recycled materials, reclaimed materials, and off-grade materials. Understandably, the test material needs to be the same as or similar to the test sample in the aforementioned model construction method to achieve the same or similar ion migration rate and improve the accuracy of the model.

[0131] The following are specific examples. Unless otherwise stated, the reagents used in the examples are all commercially available products or can be obtained by conventional methods.

[0132] Example 1

[0133] This embodiment describes the construction of a kinetic model for the content and distribution of phosphate ions in phosphate-based flame-retardant general-purpose plastics.

[0134] The sample was NHPP-FR NC501(SX), a modified polypropylene material containing ammonium phosphate, purchased from Kingfa Science & Technology Co., Ltd.

[0135] The construction method is as follows:

[0136] 1. Prepare a sample from the material. It is square with a side length of 30 mm, a thickness of 2.4 mm, and an internal phosphate ion content of 400 ppm.

[0137] 2. Place the sample in a clean, wide-mouth ground glass reagent bottle (mouth size greater than 40mm) that can be completely sealed. Transfer 5mL of pure water into the glass container and incubate it in a water bath at different temperatures (60℃, 70℃, 80℃) for 24 hours to extract phosphate ions from the sample.

[0138] 3. Take a portion of the extract solution and analyze it using an ion chromatograph to calculate the concentration of phosphate ions in the extract. The ion chromatograph test conditions are as follows:

[0139] The eluent flow rate was 1.2 mL / min; the column temperature was 35℃; and the column was an RFIC. TM AS22 4×250mm Analytical, detector temperature 35℃; suppressor current 41mA; eluent concentration 4.5mM Na2CO3+1.5mM NaHCO3, solvent water; injection volume 25μL.

[0140] IV. Establishment of a Phosphate Ion Diffusion Kinetic Model

[0141] A schematic diagram of phosphate ion diffusion in the sample is shown below. Figure 1 As shown, it is a square with a side length of 2a = 30 mm and a thickness of 2b = 2.4 mm. The concentration of phosphate ions inside the sample is set as C(x,t,T). There are two diffusion surfaces for the sample ions, namely diffusion surface I and diffusion surface II. Due to the complexity of phosphate ion diffusion in the sample, this application makes the following assumptions about the phosphate ion diffusion model of the sample:

[0142] (1) The bidirectional diffusion of pure water outside the sample and phosphate ions inside the sample is treated as two unidirectional diffusions, thus simplifying the complex three-component system into two independent two-component systems for study.

[0143] (2) Only the diffusion of phosphate ions along the direction from the center of the sample to the surface is considered, while the longitudinal diffusion of the sample inside the sample is not considered.

[0144] (3) During the entire diffusion process, phosphate ions inside the sample diffuse from the inside out layer by layer, and the size of the sample does not change as the diffusion proceeds.

[0145] (4) The pure water outside the sample is defined as an infinitely large area, and the diffusion will not affect the phosphate concentration outside the sample.

[0146] (5) The sample is assumed to be a model plate, that is, the diffusion of phosphate ions on the I diffusion surface is not considered, and only the diffusion of phosphate ions on the II diffusion surface is considered to establish a phosphate ion diffusion kinetic model.

[0147] Based on the above explanation, we can obtain the following from Fick's First Law:

[0148]

[0149] The diffusion mass transfer of a sample in pure water is a dynamic and unsteady process; therefore, Fick's second law can be used to derive the following equation:

[0150]

[0151] In the formula, D: diffusion coefficient;

[0152] C: Phosphate ion concentration inside the sample, 400 ppm;

[0153] x: diffusion distance;

[0154] Shape: Shape coefficient;

[0155] R: Radius of curvature of the diffusion surface;

[0156] The values ​​for Shape and R are detailed in Table 1.

[0157] Table 1. Shape Coefficient Values

[0158]

[0159] V. Derivation of the Phosphate Ion Diffusion Kinetic Model

[0160] like Figure 2 As shown, according to assumption (5), considering only the type II diffusion surface, the maximum diffusion distance of phosphate ions is b, which is half the thickness of the sample.

[0161] Based on the above description of the phosphate ion diffusion process in the sample, the diffusion process is solved using the finite difference method according to assumption (3), with a spatial step size of [missing information]. Δ x, i.e., b = n Δ x, time step is Δ If t, then formula (4) is:

[0162]

[0163] for Figure 2 The rectangular portion can be used as a flat plate diffusion model, with Shape = 0 and R being meaningless, resulting in:

[0164]

[0165] In the formula, C i n : indicates time t=n Δ t, the concentration of the i-th node;

[0166] n=1,2,3,4..., i=1,2,3,4,...m-3,m-2(m>2);

[0167] Sorting (6) yields:

[0168]

[0169] In the formula,

[0170] When i = 0, we get:

[0171]

[0172] The boundary conditions for diffusion are expressed using the finite difference method as follows:

[0173]

[0174] In the formula, D xThe diffusion coefficient of phosphate ions diffused outward under a given diffusion temperature, calculated according to equation (1). Equation (1) is shown below:

[0175]

[0176] This indicates the concentration of phosphate ions in the extract obtained after extraction treatment for time t, in ppm.

[0177] C ∞ The concentration of phosphate ions in the extraction solvent before extraction is expressed in ppm.

[0178] C0 represents the concentration of phosphate ions in the test sample before extraction, in ppm;

[0179] D x This represents the diffusion coefficient value of phosphate ions under different temperature conditions, expressed in cm. 2 / s;

[0180] t represents the extraction and processing time, in seconds;

[0181] λ n k n And n is defined as in the nth-order Bessel function.

[0182] The diffusion coefficients of phosphate ions under different temperature conditions are shown in Table 2 below:

[0183] Table 2. Diffusion coefficient values ​​at different water bath temperatures.

[0184]

[0185] D = D0exp(-Q / RT) (10)

[0186] In the formula, D0: constant;

[0187] Q: Diffusion activation energy;

[0188] R: Molar gas constant;

[0189] T: Thermodynamic temperature (i.e., the Kelvin temperature corresponding to the temperature in step two).

[0190] Without limitation, the parameters D0, Q, R, etc. are common definitions in this field and can be found in existing literature in this field, including but not limited to: Kalabin AL, Pakshver EA, Kukushkin N A. Modeling the filament formation in the wet spinning of synthetic fiber from polymer solutions[J]. Theoretical Foundations of Chemical Engineering, 1996, 30(3): 295-301.

[0191] Substitute into equations (8) and (9) and eliminate have to:

[0192]

[0193] From the boundary conditions, we get:

[0194]

[0195] Substituting i = m - 1 into equation (6) and substituting equation (12) into the equation, we get:

[0196]

[0197] The initial conditions (12), formulas (11), (8), and (13) are rearranged to obtain the following:

[0198]

[0199]

[0200]

[0201] i = 1, 2, 3...m-3, m-2

[0202]

[0203] The above m formulas can calculate the phosphate ion concentration at different locations in the sample. In this embodiment, Matlab is used for calculation, and Origin is used to fit the distribution map of phosphate ions in the sample. The phosphate ion distribution map at 80℃ is shown below. Figure 3 As shown, Figure 3 The horizontal axis represents the diffusion distance, and the vertical axis represents the concentration of phosphate ions. Figure 2 Understand, this diagram represents Figure 2 A phosphate ion distribution map showing the phosphate ion distribution from the horizontal centerline towards the phosphate diffusion direction up to the sample surface. Figure 3The curve is integrated, and the total amount of phosphate ions is subtracted from the integral to obtain a value. The phosphate ion content under experimental conditions of 60℃ and 70℃ is calculated using the same method to obtain a set of data. The covariance of the obtained data and the experimental test data are calculated respectively. If the covariance is positive, the two sets of data are positively correlated, and the model is valid.

[0204] Example 2

[0205] This embodiment describes a method for detecting the content and distribution of phosphate ions in phosphate-based flame-retardant engineering plastics. The steps are as follows:

[0206] The sample was PBT-FRG30 NC0815, a modified polybutylene terephthalate material containing ammonium phosphate, purchased from Kingfa Science & Technology Co., Ltd.

[0207] The specific implementation steps are as follows:

[0208] 1. Prepare a sample from the material. It is square with a side length of 25 mm, a thickness of 3 mm, and an internal phosphate ion content of 500 ppm.

[0209] 2. Place the sample in a clean, wide-mouth ground glass reagent bottle (mouth size greater than 30mm) that can be completely sealed. Transfer 8mL of pure water into the glass container and keep it in an 80℃ water bath for 26 hours to extract phosphate ions from the sample.

[0210] 3. Take a portion of the extract solution and analyze it using an ion chromatograph to calculate the concentration of phosphate ions in the extract. The ion chromatograph test conditions are as follows:

[0211] The eluent flow rate was 1.5 mL / min; the column temperature was 30 °C; and the column was an RFIC. TM AS22 4×250mm Analytical, detector temperature 30℃; suppressor current 40mA; eluent concentration 4.5mM Na2CO3+1.5mM NaHCO3, solvent water; injection volume 20μL.

[0212] IV. Substitute the experimental conditions described in section II into models 2(a), 2(b), 2(c), and 2(d) constructed in Example 1. In this example, the concentration of phosphate ions in the extraction solvent before the extraction treatment is C. ∞ The concentration of phosphate ions in the test sample, C0, is 500 ppm. The diffusion coefficient D, representing the outward diffusion of phosphate ions under the above temperature conditions, is... x The value of D is calculated by combining the test value obtained under the ion chromatography test conditions described in step three with formula (1) in Example 1. xThe value is 5.06 × 10 -8 cm 2 / s, the calculation tool described in this embodiment is Matlab, and the fitting software is Origin.

[0213] V. The distribution map of phosphate ions in the sample under the experimental conditions described in this embodiment was obtained by fitting, as shown below. Figure 4 As shown, Figure 4 The horizontal axis represents the diffusion distance, and the vertical axis represents the concentration of phosphate ions.

[0214] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0215] The embodiments described above are merely illustrative of several implementation methods of this application, intended to facilitate a detailed understanding of the technical solutions of this application, but should not be construed as limiting the scope of protection of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the scope of protection of this application. It should be understood that technical solutions obtained by those skilled in the art based on the technical solutions provided in this application through logical analysis, reasoning, or limited experimentation are all within the scope of protection of the appended claims. Therefore, the scope of protection of this patent application should be determined by the content of the appended claims, and the specification and drawings can be used to interpret the content of the claims.

Claims

1. A method for constructing a model of the content and distribution of phosphate ions in a material, characterized in that, Includes the following steps: Take test samples of the material; The test sample was placed in an extraction solvent and extracted under different temperature conditions. The concentration of phosphate ions in the extract obtained under different temperature conditions was detected. Based on the detected concentration of phosphate ions and combined with Fick's first law and second law, the diffusion coefficient value Dx of phosphate ions diffuses outward under different temperature conditions. Based on the detected concentration of phosphate ions, a model of the content and distribution of phosphate ions in the material is constructed using Fick's first law and Fick's second law. The model is then validated using the diffusion coefficient value and / or the concentration of phosphate ions in the extract obtained under at least one temperature condition. The diffusion coefficient value Dx is calculated using the following formula (1): ； (1) This indicates the concentration of phosphate ions in the extract obtained after extraction treatment for time t, in ppm. The concentration of phosphate ions in the extraction solvent before extraction is expressed in ppm. The concentration of phosphate ions in the test sample before extraction is expressed in ppm. This represents the diffusion coefficient value of phosphate ions under different temperature conditions, expressed in cm. 2 / s; t represents the extraction and processing time, in seconds; , And n is defined as in the nth-order Bessel function; The model is shown in equations (2a) to (2d). The distribution curve of phosphate ions in the material is obtained by solving equations (2a) to (2d). The content of phosphate ions in the material is obtained by integrating the distribution curve of phosphate ions obtained by solving equations (2a) to (2d). (2a) (2b) (2c) Where i = 1, 2, 3...m-3, m-2, m represents an integer greater than 2; (2d) In the formula ,in, x represents the spatial step size, and b = n x, t represents the time step, and b represents half the thickness of the test sample. Where D0 represents a constant, Q represents the diffusion activation energy, R represents the molar gas constant, and T represents the thermodynamic temperature corresponding to the stated temperature; Where Shape represents the shape coefficient and R represents the radius of curvature of the diffusion surface; C i n The extraction and processing time is t=n At time t, the phosphate ion concentration at the i-th node in the test sample.

2. The method for constructing a model of the content and distribution of phosphate ions in the material according to claim 1, characterized in that, The test sample satisfies one or more of the following conditions (1) to (3): (1) The thickness of the test sample is 2mm~3mm; (2) The concentration of phosphate ions in the test sample before extraction and treatment is 300ppm~700ppm; (3) The test sample is a square with a side length of 25mm~35mm.

3. The method for constructing a model of the content and distribution of phosphate ions in the material according to claim 1, characterized in that, The model construction method satisfies one or more of the following conditions (1) to (3): (1) The different temperature conditions are set to 58℃~62℃, 68℃~72℃ and 78℃~82℃ respectively; (2) The extraction and processing time is 20h~30h; (3) The extraction process is carried out under closed conditions, and the amount of extraction solvent used is 4 mL to 8 mL.

4. The method for constructing a model of the content and distribution of phosphate ions in the material according to any one of claims 1 to 3, characterized in that, The concentration of phosphate ions in the extract was detected by ion chromatography.

5. The method for constructing a model of the content and distribution of phosphate ions in the material according to claim 4, characterized in that, The eluent used in the ion chromatography method includes Na₂CO₃ at a concentration of 4 mM to 5 mM and NaHCO₃ at a concentration of 1 mM to 2 mM.

6. The method for constructing a model of the content and distribution of phosphate ions in a material according to claim 5, characterized in that, The conditions for the ion chromatography also include one or more of the following conditions (i) to (v): (i) The flow rate of the eluent is 1 mL / min to 1.5 mL / min; (ii) The column temperature is 30℃~40℃; (iii) The detector temperature is 30℃~40℃; (iv) The current of the suppressor is 38mA~43mA; (v) The stationary phase of the chromatographic column is a microporous cross-linked resin.

7. A method for detecting the content and distribution of phosphate ions in a material, characterized in that, Includes the following steps: Take a test sample of the material to be tested; The test sample is placed in an extraction solvent for extraction. The concentration of phosphate ions in the extract obtained from the extraction process was detected; The concentration of phosphate ions obtained from the detection is substituted into the model constructed by the model construction method described in any one of claims 1 to 6 to calculate the content and distribution curve of phosphate ions in the test sample.

8. The method for detecting the content and distribution of phosphate ions in the material according to claim 7, characterized in that, The test sample satisfies one or more of the following conditions (1) to (3): (1) The thickness of the test sample is 2mm~3mm; (2) The concentration of phosphate ions in the test sample before extraction and treatment is 300ppm~700ppm; (3) The test sample is a square with a side length of 25mm~35mm.

9. The method for detecting the content and distribution of phosphate ions in the material according to claim 7, characterized in that, The detection method satisfies one or more of the following conditions (1) to (3): (1) The extraction temperature was set to 78℃~82℃; (2) The extraction and processing time is 20h~30h; (3) The extraction process is carried out under closed conditions, and the amount of extraction solvent used is 4 mL to 8 mL.

10. The method for detecting the content and distribution of phosphate ions in the material according to claim 7, characterized in that, The concentration of phosphate ions in the extract was detected by ion chromatography.

11. The method for detecting the content and distribution of phosphate ions in the material according to claim 10, characterized in that, The eluent used in the ion chromatography method includes Na₂CO₃ at a concentration of 4 mM to 5 mM and NaHCO₃ at a concentration of 1 mM to 2 mM. 3。 12. The method for detecting the content and distribution of phosphate ions in the material according to claim 11, characterized in that, The conditions for the ion chromatography method also include one or more of the following conditions (1) to (5): (1) The flow rate of the rinsing solution is 1 mL / min to 1.5 mL / min; (2) The column temperature is 30℃~40℃; (3) The detector temperature is 30℃~40℃; (4) The current of the suppressor is 38mA~43mA; (5) The stationary phase of the chromatographic column is a microporous cross-linked resin.

13. The method for detecting the content and distribution of phosphate ions in the material according to any one of claims 7 to 12, characterized in that, The material to be tested is a polymer material containing phosphate flame retardants.

14. The method for detecting the content and distribution of phosphate ions in the material according to claim 13, characterized in that, The polymer material includes one or more of virgin material, recycled material, reclaimed material, and secondary material.

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