Theoretical isotherm calculation method, method and device for characterizing pore size distribution

Abstract

The application provides a theoretical isotherm calculation method, a pore size distribution characterization method and device, which comprises the following steps: obtaining calculation parameters in a density functional theory model, and calculating the local density of a fluid in a model pore according to the calculation parameters; calculating the first excess adsorption corresponding to a first preset pore size point set and a first preset pressure point set according to an excess adsorption calculation formula and the local density, calculating the change rate of the first excess adsorption with the first preset pressure point set, and calculating the second excess adsorption corresponding to a second preset pressure point set between two pressure values corresponding to the change rate exceeding a threshold value; and fitting the first excess adsorption and the second excess adsorption to obtain theoretical isotherm data. The scheme realizes further refined calculation of the first excess adsorption, does not waste calculation resources, does not lose key information of the calculated isotherm data, and improves the accuracy and reliability of the theoretical isotherm data.

Description

Technical Field

[0001] This invention relates to the field of porous materials technology, and in particular to a method for calculating theoretical isotherms, a method for characterizing pore size distribution, and an apparatus. Background Technology

[0002] Porous nanomaterials such as zeolites, activated carbon, silica gel, and MOFs have been widely used in various fields, including environment, energy, optics, and electronics, due to their unique size effect, quantum effect, surface effect, and mechanical properties. Pore size distribution, as one of the important parameters of porous nanomaterials, is of great guiding significance for the design of new porous nanomaterials.

[0003] Currently, most commonly used methods for obtaining pore size distribution in China are based on macroscopic thermodynamic analysis. For example, the specific surface area of ​​a material is calculated using multi-point BET linear regression, and then the pore size distribution of mesoporous materials is obtained using the Barrett-Joner-Halenda (BJH) method and the Dolimore Heal (DH) method. The pore size distribution of microporous materials is obtained using the Dubinin-Astakhov (BJH) method, the Horvath-Kawazoe (HK) method, and the Saito-Foley method. However, these methods cannot describe the structure of the fluid within the confined pores, and their characterization of the pore size distribution of microporous materials is insufficient. Furthermore, the BJH method is only applicable to the characterization of pore size distribution in mesoporous materials, and the BET adsorption isotherm equation can only be used for porous materials with type II and IV adsorption isotherms.

[0004] Compared to traditional methods for characterizing pore size distribution based on macroscopic thermodynamic analysis, molecular-level models based on statistical thermodynamics offer higher accuracy and predictability. Density functional theory (DFT) calculation models, while maintaining high computational accuracy, can significantly shorten computation time and have been recognized by the International Organization for Standardization (ISO) as one of the standard methods for characterizing the pore size distribution of porous nanomaterials (Pure Appl. Chem. 2015, 87(9-10):1051-1069).

[0005] However, there is currently no mature method for calculating pore size distribution based on density functional theory in China. Therefore, it is necessary to develop a pore size distribution characterization method based on density functional theory to obtain more accurate micro-mesopore distribution characterization results and provide reliable experimental testing methods for the research, preparation and characterization of nano-functional carbon materials. Summary of the Invention

[0006] Therefore, it is necessary to provide a theoretical isotherm calculation method, a method and apparatus for characterizing aperture distribution to address the above-mentioned technical problems.

[0007] A method for calculating theoretical isotherms, comprising:

[0008] Obtain the calculation parameters in the weighted density functional theory model of Lennard-Jones fluid, including fluid-fluid energy parameters, fluid-fluid size parameters, fluid hard sphere diameter, fluid-solid energy parameters, and fluid-solid size parameters. Based on the calculation parameters, calculate the local density distribution of the fluid in the model orifice based on the weighted density functional theory model of Lennard-Jones fluid.

[0009] Based on the formula for calculating excess adsorption and the local density distribution, the surface excess adsorption point set corresponding to the first preset pore size point set and the first preset pressure point set is calculated to obtain the first excess adsorption.

[0010] Calculate the rate of change of the first excess adsorption amount with the change of the first preset pressure point set, and determine the two pressure values ​​corresponding to when the rate of change exceeds the threshold as the first preset pressure value and the second preset pressure value.

[0011] Calculate the surface excess adsorption point set corresponding to the second preset pressure point set located between the first preset pressure value and the second preset pressure value to obtain the second excess adsorption amount;

[0012] The first and second excess adsorption amounts were fitted to obtain theoretical isotherm data.

[0013] In one embodiment, the step of calculating the surface excess adsorption amount corresponding to the first preset pore size point set and the first preset pressure point set to obtain the first excess adsorption amount includes:

[0014] Calculate the surface excess adsorption point set corresponding to the first pore size subset and the first preset pressure point set to obtain the first sub-excess adsorption amount.

[0015] Calculate the surface excess adsorption point set corresponding to the second pore size subset and the first preset pressure point set to obtain the second sub-excess adsorption amount.

[0016] The first excess adsorption amount is obtained based on the first sub-excess adsorption amount and the second sub-excess adsorption amount.

[0017] The first preset aperture point set includes a first aperture subset and a second aperture subset. Each aperture value in the first aperture subset is less than a first standard aperture value. Each aperture value in the second aperture subset is greater than or equal to the first standard aperture value and less than or equal to the second standard aperture value. The first standard aperture value is less than the second standard aperture value. The number of apertures in the first aperture subset is greater than the number of apertures in the second aperture subset.

[0018] In one embodiment, the step of fitting the first excess adsorption amount and the second excess adsorption amount to obtain theoretical isotherm data includes:

[0019] Based on the data of the first excess adsorption amount and the second excess adsorption amount, the surface excess adsorption amount point set corresponding to the third preset pressure point set is calculated by interpolation to obtain the third excess adsorption amount.

[0020] Based on the third excess adsorption amount, the surface excess adsorption amount point set corresponding to the second preset pore size point set is calculated by interpolation to obtain the theoretical isotherm data.

[0021] The pressure value range of the third preset pressure point set includes the pressure value range of the first preset pressure point set and the pressure value range of the second preset pressure point set. The absolute value of the difference between any two adjacent pressure points in the third preset pressure point set is less than or equal to the absolute value of the difference between any two adjacent pressure points in the second preset pressure point set. The aperture value range of the second preset aperture point set includes the aperture value range of the first preset aperture point set. The absolute value of the difference between any two adjacent aperture points in the second preset aperture point set is less than or equal to the absolute value of the difference between any two adjacent aperture points in the first preset aperture point set.

[0022] In one embodiment, the theoretical isotherm data includes theoretical adsorption isotherm data and theoretical desorption isotherm data, and the method further includes:

[0023] Based on the principle of equal giant thermodynamic potential, the equilibrium isotherm is calculated according to the theoretical adsorption isotherm and the theoretical desorption isotherm.

[0024] Replace the theoretical desorption isotherm with the equilibrium isotherm.

[0025] In one embodiment, determining the equilibrium isotherm based on the principle of equal giant thermodynamic potential, according to the theoretical adsorption isotherm and the theoretical desorption isotherm, includes:

[0026] The adsorption giant potential line is obtained based on the theoretical adsorption isotherm, and the desorption giant potential line is obtained based on the theoretical desorption isotherm.

[0027] The adsorption equilibrium point is obtained by calculating the intersection of the adsorption giant potential line and the desorption giant potential line.

[0028] The theoretical adsorption isotherm data before the adsorption equilibrium point and the theoretical desorption isotherm data after the adsorption equilibrium point are used as the equilibrium isotherm data.

[0029] In one embodiment, the calculation model for the excess adsorption capacity is characterized by employing a slit-shaped pore model and / or a cylindrical pore model, and the theoretical isotherm data includes at least one of the following:

[0030] The slit-adsorption theoretical isotherm data obtained by calculating using the slit-hole model;

[0031] and

[0032] Isotherm data obtained by slit-equilibrium theory calculation using the slit aperture model;

[0033] and

[0034] Isotherm data obtained from the cylindrical hole model based on the cylindrical adsorption theory;

[0035] and

[0036] The cylindrical-equilibrium isotherm data were calculated using the cylindrical hole model.

[0037] A method for characterizing aperture distribution, comprising:

[0038] Receive experimental isotherm data of the target material;

[0039] The target theoretical isotherm data corresponding to the target material is determined. The target theoretical isotherm data is at least one of the theoretical isotherm data preset in the system. The theoretical isotherm data is calculated by applying any one of the above-mentioned theoretical isotherm calculation methods. The experimental isotherm data is measured using the same experimental materials, experimental gases, and temperatures as the theoretical isotherm data.

[0040] Based on the experimental isotherm data and the target theoretical isotherm data, the adsorption integral equation is solved to obtain the pore size distribution data of the target material.

[0041] In one embodiment, the step of solving the adsorption integral equation based on the experimental adsorption isotherm data and the target theoretical isotherm data to obtain the pore size distribution of the target material includes:

[0042] The adsorption integral equation is regularized to obtain the optimal regularization parameter;

[0043] Based on the regularization parameter, the adsorption integral equation is solved to obtain the pore size distribution of the target material.

[0044] In one embodiment, when the target material has both slit pores and cylindrical pores, the adsorption integral equation is calculated as follows:

[0045]

[0046] Where, N exp (P) represents experimental adsorption isotherm data, N theor,slit (P,H) represents the theoretical isotherm data calculated using the slit-hole model, N theor,cylind (P,H) represents the theoretical isotherm data calculated using the cylindrical hole model, H represents the half-hole width of the target material, f(H) represents the pore size distribution, and ω represents the proportion of slit holes in the target material.

[0047] In one embodiment, the method further includes:

[0048] Based on the pore size distribution data and the adsorption integral equation, the fitted isotherm data are calculated.

[0049] The difference between the fitted isotherm data and the experimental isotherm data is calculated to obtain the degree of fit.

[0050] A theoretical isotherm calculation device, comprising:

[0051] The first calculation module is used to obtain the calculation parameters in the weighted density functional theory model of Lennard-Jones fluid. The calculation parameters include fluid-fluid energy parameters, fluid-fluid size parameters, fluid hard sphere diameter, fluid-solid energy parameters, and fluid-solid size parameters. Based on the calculation parameters, the local density distribution of the fluid in the model orifice is calculated based on the weighted density functional theory model of Lennard-Jones fluid.

[0052] The second calculation module is used to calculate the surface excess adsorption point set corresponding to the first preset pore size point set and the first preset pressure point set according to the excess adsorption calculation formula and the local density distribution, so as to obtain the first excess adsorption amount.

[0053] The third calculation module is used to calculate the rate of change of the first excess adsorption amount with the change of the first preset pressure point set, and to determine the two pressure values ​​corresponding to the rate of change exceeding the threshold as the first preset pressure value and the second preset pressure value.

[0054] The fourth calculation module is used to calculate the surface excess adsorption point set corresponding to the second preset pressure point set located between the first preset pressure value and the second preset pressure value, and to obtain the second excess adsorption amount.

[0055] The fitting module is used to fit the first excess adsorption amount and the second excess adsorption amount to obtain theoretical isotherm data.

[0056] An apparatus for characterizing aperture distribution, characterized in that it comprises:

[0057] The receiving module is used to receive experimental isotherm data of the target material;

[0058] The selection module is used to determine the target theoretical isotherm data corresponding to the target material. The target theoretical isotherm data is at least one of the theoretical isotherm data preset in the system. The theoretical isotherm data is calculated by applying any one of the above-mentioned theoretical isotherm calculation methods. The experimental isotherm data is measured using the same experimental materials, experimental gases, and temperatures as the theoretical isotherm data.

[0059] The processing module is used to solve the adsorption integral equation based on the experimental isotherm data and the target theoretical isotherm data to obtain the pore size distribution data of the target material.

[0060] A computer device includes a memory and a processor, the memory storing a computer program, characterized in that the processor executes the computer program to implement the steps of the theoretical isotherm calculation method described in any of the above embodiments.

[0061] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the theoretical isotherm calculation method described in any of the above embodiments.

[0062] The aforementioned theoretical isotherm calculation method, pore size distribution characterization method, and apparatus first calculate the surface excess adsorption point set corresponding to the first preset pore size point set and the first preset pressure point set to obtain the first excess adsorption amount. Then, they calculate the changing trend of the first excess adsorption amount with pressure, automatically identify the target pressure segment where the changing trend exceeds a threshold, and calculate the second excess adsorption amount corresponding to the second preset pressure point set within the target pressure segment. This achieves further refined calculation of the first excess adsorption amount, without wasting computational resources or losing key information from the calculated isotherm data, thus improving the accuracy and reliability of the theoretical isotherm data. Attached Figure Description

[0063] Figure 1 This is a flowchart illustrating the theoretical isotherm calculation method in one embodiment;

[0064] Figure 2-1 This is a graph comparing the nitrogen saturated vapor pressure P-temperature T relationship curve in one embodiment with NIST standard data and experimental data.

[0065] Figure 2-2 This is a comparison diagram of the adsorption isotherm on the surface of a non-porous carbon material in one embodiment and the experimental adsorption isotherm.

[0066] Figure 3This refers to the theoretical isotherm corresponding to a preset aperture in one embodiment;

[0067] Figure 4 This is a schematic diagram of theoretical isotherms corresponding to different aperture sizes in one embodiment;

[0068] Figure 5 This is a schematic diagram of the equilibrium isotherm in one embodiment;

[0069] Figure 6 One embodiment is a method for characterizing aperture distribution;

[0070] Figure 7 This is a schematic diagram of the pore size distribution data of the target material in one embodiment;

[0071] Figure 8 For one embodiment, the fitted isotherm N cal (P) and experimental isotherm N exp A diagram illustrating the differences in (P);

[0072] Figure 9 This is a structural block diagram of a theoretical isotherm calculation device in one embodiment;

[0073] Figure 10 This is a structural block diagram representing an aperture distribution device in one embodiment;

[0074] Figure 11 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0075] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0076] Example 1

[0077] In this embodiment, as Figure 1 As shown, a method for calculating theoretical isotherms is provided, including:

[0078] Step 110: Obtain the calculation parameters in the weighted density functional theory model of Lennard-Jones fluid. The calculation parameters include fluid-fluid energy parameters, fluid-fluid size parameters, fluid hard sphere diameter, fluid-solid energy parameters, and fluid-solid size parameters. Based on the calculation parameters, calculate the local density distribution of the fluid in the model orifice based on the weighted density functional theory model of Lennard-Jones fluid.

[0079] In this embodiment, for porous activated carbon materials, the weighted density functional theory (WDFT) model of Lennard-Jones fluid is used to simulate the behavior of nitrogen molecules in the carbon pores of the model. Correspondingly, the above-mentioned calculation parameters are nitrogen-nitrogen energy parameters, nitrogen-nitrogen size parameters, nitrogen hard sphere diameter, nitrogen-carbon energy parameters, and nitrogen-carbon size parameters. The values ​​of these calculation parameters can be measured by experimental means or obtained by consulting existing literature data.

[0080] Specifically, the calculation formula for the weighted density functional theory model of Lennard-Jones fluid is as follows:

[0081] Ω[ρ(r)]=F id [ρ(r)]+F rep [ρ(r)]+F att [ρ(r)]+F cor [ρ(r)]+∫ρ(r)[V ext (r)-μ]dr

[0082] Among them, F id For the ideal term of the inherent Helmholtz free energy, F rep For hardball, F att For the gravitational term, F cor The relevant terms are: ρ(r) represents the local density distribution of the fluid inside the pore; and V represents the external field applied to the pore wall. ext The fluid chemical potential is μ.

[0083] Minimizing the giant thermodynamic potential at a given temperature and chemical potential, based on the above calculation parameters, the local density distribution ρ(r) of the confined fluid can be obtained by solving the Euler-Lagrange equation, i.e.:

[0084]

[0085] Wherein, the bulk phase fluid density is ρ b The density of the bulk phase fluid corresponding to nitrogen; the excess chemical potential of the fluid is μ. ex The excess chemical potential corresponding to nitrogen, ρ b and μ ex The value can be obtained through experimental measurement or literature review.

[0086] like Figure 2-1 The figure shown is a comparison of the nitrogen saturated vapor pressure P-temperature T relationship curve calculated using the weighted density functional theory of Lennard-Jones fluid in this embodiment, and NIST standard data and experimental data.

[0087] like Figure 2-2The figure shown is a comparison between the adsorption isotherm of the non-porous carbon material surface calculated by applying the weighted density functional theory of Lennard-Jones fluid to the "nitrogen / slit carbon pore" adsorption model in this embodiment and the experimental adsorption isotherm.

[0088] The corresponding model parameters were obtained by fitting experimental data on the gas-liquid equilibrium of the bulk nitrogen phase, surface tension, and adsorption isotherms on the non-porous carbon surface. Figure 2-1 and Figure 2-2 As can be seen, using the fitted model parameters, this theory can reproduce well the gas-liquid phase equilibrium of the bulk nitrogen, the experimental data of surface tension, and the experimental data of adsorption isotherms on the non-porous carbon surface. Therefore, it can be used to approximate the adsorption behavior of nitrogen in the pores of activated carbon.

[0089] Step 120: Calculate the surface excess adsorption point set corresponding to the first preset pore size point set and the first preset pressure point set according to the excess adsorption formula and the local density distribution, and obtain the first excess adsorption amount.

[0090] Surface excess adsorption capacity refers to the difference between the number of adsorbent molecules per unit area or unit volume on the surface of the adsorbent material and the adsorbent concentration when the pure gas phase is in equilibrium. It describes the adsorption situation of the adsorbent on a given surface. An isotherm is a measurement of the change in adsorption capacity with pressure while maintaining a constant temperature. The measured adsorption capacity can be the absolute adsorption capacity or the excess adsorption capacity. That is, the surface excess adsorption capacity is a data point on the isotherm.

[0091] In this embodiment, when calculating the excess adsorption amount using the weighted density functional theory model of Lennard-Jones fluid, it is necessary to preset different pore sizes and different pressure points. The set of excess adsorption amounts calculated under different pore sizes and different pressure points is the isotherm data.

[0092] Pore ​​size refers to the size of the channels or pores used for gas adsorption. When simulating excess adsorption, different pore sizes need to be considered because the size of the pore affects the interaction between nitrogen and porous activated carbon materials during adsorption. Therefore, presetting different pore sizes can better simulate the adsorption behavior of nitrogen in different pore sizes. By calculating the excess adsorption capacity based on the excess adsorption formula and local density distribution under a first preset pore size point set and a first preset pressure point set, comprehensive information on the adsorption behavior under different conditions can be obtained, thus helping to more accurately simulate theoretical isotherm data.

[0093] Specifically, when calculating the excess surface adsorption capacity, the excess surface adsorption capacity corresponding to the first pore size point in the first preset pore size point set at various pressure points in the first preset pressure point set can be calculated first, resulting in a series of first isotherm data with the pressure point as the x-axis and the excess surface adsorption capacity as the y-axis. Similarly, the excess surface adsorption capacity corresponding to the second pore size point in the first preset pore size point set at various pressure points in the first preset pressure point set can be calculated, resulting in second isotherm data. This process continues until the Nth isotherm data corresponding to the Nth pore size point (the last pore size point in the first preset pore size point set) is obtained. The set of the first to Nth isotherm data is the aforementioned first excess adsorption capacity data.

[0094] Step 130: Calculate the rate of change of the first excess adsorption amount with the change of the first preset pressure point set, and determine the two pressure values ​​corresponding to when the rate of change exceeds the threshold, namely the first preset pressure value and the second preset pressure value.

[0095] In order to more accurately capture the details of isotherm changes when calculating theoretical isotherm data, for target areas with large isotherm change rates detected during the calculation process, the pressure points of the target area are further refined and calculated based on the first preset pressure point set.

[0096] For example, the first preset pressure point set includes a first pressure point, a second pressure point, a third pressure point, and a fourth pressure point, with the values ​​of the first pressure point gradually increasing to the fourth pressure point. According to the calculation method in step 120, under the same preset pore size, the adsorption amount corresponding to the first pressure point is the first adsorption amount a1, the adsorption amount corresponding to the second pressure point is the second adsorption amount a2, the adsorption amount corresponding to the third pressure point is the third adsorption amount a3, and the adsorption amount corresponding to the fourth pressure point is the fourth adsorption amount a4. The preset threshold is K0. Then:

[0097] The rate of change from the first adsorption amount to the second adsorption amount is K1 = (a2 - a1) / a1;

[0098] The rate of change from the second adsorption amount to the third adsorption amount is K2 = (a3 - a2) / a2;

[0099] The rate of change of the adsorption amount from the third to the fourth adsorption amount is K3 = (a4 - a3) / a3;

[0100] When K3 is greater than K0, it indicates that the rate of change of the isotherm data corresponding to the pressure range from the third pressure point to the fourth pressure point is relatively large. Accordingly, the third pressure point is determined as the first preset pressure value and the fourth pressure point is determined as the second preset pressure value.

[0101] like Figure 3As shown, this is a theoretical isotherm corresponding to a preset pore size. Among the first excess adsorption amount, there are multiple target pressure segments where the rate of change exceeds the threshold, as well as the corresponding first preset pressure value and second preset pressure value.

[0102] Step 140: Calculate the surface excess adsorption point set corresponding to the second preset pressure point set located between the first preset pressure value and the second preset pressure value to obtain the second excess adsorption amount.

[0103] In this embodiment, after determining the third pressure point as the first preset pressure value and the fourth pressure point as the second preset pressure value through step 130, the surface excess adsorption amount point set corresponding to the preset second preset pressure point set between the third pressure point and the fourth pressure point is calculated to obtain the second excess adsorption amount.

[0104] Specifically, for example, if the value of the third pressure point is 10 Pa and the value of the fourth pressure point is 20 Pa, then the second preset pressure point set A can be {12 Pa, 14 Pa, 16 Pa, 18 Pa}. The excess adsorption amount on the surface corresponding to each pressure point in the second preset pressure point set is calculated to obtain the second excess adsorption amount.

[0105] In one embodiment, there are multiple target pressure segments with a rate of change exceeding a threshold. The surface excess adsorption amount point set corresponding to the second preset pressure point set of each of the multiple target pressure segments is calculated to obtain the second excess adsorption amount.

[0106] In this embodiment, K1 and K3 are both greater than K0. The excess adsorption amount Q1 corresponding to the second preset pressure point set B between the first pressure point and the second pressure point is calculated, and the excess adsorption amount Q2 corresponding to the second preset pressure point set A between the third pressure point and the fourth pressure point is calculated. The second excess adsorption amount is obtained based on the set of the excess adsorption amounts Q1 and Q2.

[0107] like Figure 3 As shown, this is a theoretical isotherm corresponding to a preset pore size, where there are multiple target pressure segments in the first excess adsorption amount where the rate of change exceeds the threshold, and the corresponding second preset pressure point set.

[0108] Step 150: Fit the first excess adsorption amount and the second excess adsorption amount to obtain theoretical isotherm data.

[0109] In actual calculations, considering computational costs and efficiency, it is difficult to achieve full coverage of preset aperture points and preset pressure points. However, to ensure the accuracy of theoretical isotherm data, more pressure points are arranged in areas where isotherm data changes drastically, thereby reflecting the key information of the isotherm data in a more targeted manner.

[0110] This embodiment first calculates the surface excess adsorption point set corresponding to the first preset pore size point set and the first preset pressure point set to obtain the first excess adsorption amount. Then, it calculates the change trend of the first excess adsorption amount with pressure, automatically identifies the target pressure segment where the change trend exceeds the threshold, and calculates the second excess adsorption amount corresponding to the second preset pressure point set within the target pressure segment. This achieves a further refined calculation of the first excess adsorption amount, without wasting computing resources or losing key information from the calculated isotherm data, thus improving the accuracy and reliability of the theoretical isotherm data.

[0111] In one embodiment, the step of calculating the surface excess adsorption amount corresponding to the first preset pore size point set and the first preset pressure point set to obtain the first excess adsorption amount includes:

[0112] Calculate the surface excess adsorption point set corresponding to the first pore size subset and the first preset pressure point set to obtain the first sub-excess adsorption amount.

[0113] Calculate the surface excess adsorption point set corresponding to the second pore size subset and the first preset pressure point set to obtain the second sub-excess adsorption amount.

[0114] The first excess adsorption amount is obtained based on the first sub-excess adsorption amount and the second sub-excess adsorption amount.

[0115] The first preset aperture point set includes a first aperture subset and a second aperture subset. Each aperture value in the first aperture subset is less than a first standard aperture value. Each aperture value in the second aperture subset is greater than or equal to the first standard aperture value and less than or equal to the second standard aperture value. The first standard aperture value is less than the second standard aperture value. The number of apertures in the first aperture subset is greater than the number of apertures in the second aperture subset.

[0116] It is understandable that the pore sizes in porous materials vary. Generally, smaller pores correspond to greater variations in excess adsorption capacity. This is because smaller pores typically have a larger specific surface area and stronger adsorption capacity, allowing them to interact more effectively with gas or solute molecules. Therefore, during adsorption, smaller pores have higher absolute adsorption energies, making it easier for gas or solute molecules to be adsorbed. Furthermore, they can adsorb more substances per unit volume, and the excess adsorption capacity of smaller pores is more sensitive to changes in pore size, pressure, or concentration.

[0117] Following the aforementioned natural laws, when setting the first preset aperture point set, more aperture points with smaller aperture values ​​can be set than aperture points with larger aperture values, in order to further ensure that the final theoretical isotherm data can contain as much characteristic information of the theoretical isotherm as possible.

[0118] Specifically, in this embodiment, the first standard pore size value and the second standard pore size value are set according to the size standards of micropores and mesopores. The first standard pore size value is 2nm and the second standard pore size value is 50nm. The trend of isotherms varies greatly near micropores (less than 2nm), while the trend of isotherms varies more regularly in the larger mesopore region (2nm~5nm). The logarithmic uniform sampling method is used to set the pore size values ​​of the first and second pore size subsets to ensure that the sampling point density gradually decreases from micropores to mesopores. That is, the number of pore sizes in the first pore size subset is greater than the number of pore sizes in the second pore size subset, thereby enabling the theoretical isotherm database to contain as much feature information of theoretical isotherms as possible, while improving the calculation efficiency.

[0119] In one embodiment, the step of fitting the first excess adsorption amount and the second excess adsorption amount to obtain theoretical isotherm data includes:

[0120] Based on the data of the first excess adsorption amount and the second excess adsorption amount, the surface excess adsorption amount point set corresponding to the third preset pressure point set is calculated by interpolation to obtain the third excess adsorption amount.

[0121] Based on the third excess adsorption amount, the surface excess adsorption point set corresponding to the second preset pore size point set is calculated by interpolation, and the theoretical isotherm data is obtained.

[0122] The pressure value range of the third preset pressure point set includes the pressure value range of the first preset pressure point set and the pressure value range of the second preset pressure point set. The absolute value of the difference between any two adjacent pressure points in the third preset pressure point set is less than or equal to the absolute value of the difference between any two adjacent pressure points in the second preset pressure point set. The aperture value range of the second preset aperture point set includes the aperture value range of the first preset aperture point set. The absolute value of the difference between any two adjacent aperture points in the second preset aperture point set is less than or equal to the absolute value of the difference between any two adjacent aperture points in the first preset aperture point set.

[0123] As described in step 140 above, the second excess adsorption amount is calculated based on the second preset pressure point set corresponding to the target pressure segment where the rate of change exceeds the threshold. Therefore, the second preset pressure point set is different for different pore sizes, meaning that different pore sizes require different pressure points to be calculated. In order to better utilize theoretical isotherm data for research in different scenarios, the pressure points for different pore sizes can be standardized.

[0124] The third preset pressure point set is the pressure point set after standardization, and similarly, the second preset aperture point set is also the aperture point set after standardization. To avoid losing crucial information from each isotherm data, the pressure value range of the third preset pressure point set includes the pressure value range of the first and second preset pressure point sets, and the value density of the third preset pressure point set is greater than that of the second preset pressure point set. Similarly, the aperture value range of the second preset aperture point set includes the aperture value range of the first preset aperture point set, and the value density of the second preset aperture point set is greater than that of the first preset aperture point set.

[0125] For example, the first preset pressure point set has a value range of 1-100, and the value interval between two adjacent pressure points is 10; the second preset pressure point set has a value range of 50-60, and the value interval between two adjacent pressure points is 2; the third preset pressure point set has a value range of 1-100, and the value interval between two adjacent pressure points is 1.

[0126] Based on the examples of pressure points above, when calculating the excess adsorption capacity on the surface, different pore sizes are all calculated using the pressure points in the third preset pressure point set, but the calculation process is divided into three stages:

[0127] In the first stage, the first excess adsorption amount is roughly calculated based on the pressure points of the first preset pressure point concentration, and the general trend of the theoretical isotherm is determined.

[0128] In the second stage, based on the changing trend of the first excess adsorption amount, the target pressure range with larger changes is determined, and the second excess adsorption amount under the second preset pressure point set corresponding to the target pressure range is calculated, thus completing the capture of the key features of the theoretical isotherm.

[0129] In the third stage, the excess adsorption amount of other pressure points is supplemented according to the unified pressure point set to further enrich the theoretical isotherm data and obtain the fitted excess adsorption amount.

[0130] In the third stage of calculation, it is not necessary to calculate the surface excess adsorption amount in the same way as calculating the first and second excess adsorption amounts. Instead, the surface excess adsorption amount is directly fitted by interpolation based on the first and second excess adsorption amounts, which greatly reduces the computational load of the system. Compared with directly calculating each pressure point in the third preset pressure point set according to the excess adsorption amount calculation formula, the scheme in this embodiment is significantly more efficient, and at the same time, it does not lose the key feature information of the isothermal data.

[0131] After fitting the adsorption amounts of each surface corresponding to the third preset pressure point set to obtain the third excess adsorption amount, the data of the third excess adsorption amount is then interpolated into the second preset pore size point set for calculation to obtain the final theoretical isotherm data. The second preset pore size point set contains a larger number of pore sizes, and when using the theoretical isotherm data to calculate the pore size distribution of the target porous material, the obtained pore size distribution result is smoother and contains more information.

[0132] like Figure 4 As shown, these are the theoretical isotherms of each aperture in the second preset aperture point set at each pressure point in the third preset pressure point set.

[0133] In one embodiment, the theoretical isotherm data includes theoretical adsorption isotherm data and theoretical desorption isotherm data, and the method further includes:

[0134] Based on the principle of equal giant thermodynamic potential, the equilibrium isotherm is calculated according to the theoretical adsorption isotherm and the theoretical desorption isotherm.

[0135] Replace the theoretical desorption isotherm with the equilibrium isotherm.

[0136] An adsorption isotherm is a curve representing the relationship between the concentrations of solute molecules in two phases at a given temperature when the adsorption process reaches equilibrium at the interface. A desorption isotherm describes the relationship between the amount of adsorbate adsorbed and the pressure during the desorption process from the adsorbent surface under different pressures. Typically, a desorption isotherm is obtained by observing the desorption process of the adsorbate after the adsorption operation has already taken place, by gradually decreasing the system pressure.

[0137] When calculating adsorption isotherms, the excess adsorption capacity is typically calculated sequentially from low to high pressure points. This is because during adsorption, the adsorption capacity gradually increases with increasing pressure until adsorption equilibrium is reached. Therefore, calculating the set of excess adsorption points by gradually increasing pressure yields the theoretical adsorption isotherm data. Conversely, when calculating desorption isotherms, calculating the excess adsorption points sequentially from high to low pressure points yields the theoretical desorption isotherm data.

[0138] In this embodiment, theoretical isotherms are calculated based on the thermodynamically stable state of the fluid. However, experimentally measured isotherm data are affected by kinetic and other practical factors, such as time. Therefore, the theoretical adsorption and desorption isotherms calculated through simulation cannot perfectly match the experimental adsorption and desorption isotherms. According to existing research, theoretically calculated adsorption isotherms are close to experimental adsorption isotherms, but the equilibrium isotherms derived from theoretically calculated adsorption and desorption isotherms according to the principle of equal potential are closer to the experimental desorption isotherms. In other words, the accuracy of theoretically calculated desorption isotherms is not high enough, and it is necessary to further derive equilibrium isotherms after calculating the theoretical adsorption and desorption isotherms.

[0139] In one embodiment, determining the equilibrium isotherm based on the principle of equal giant thermodynamic potential, according to the theoretical adsorption isotherm and the theoretical desorption isotherm, includes:

[0140] The adsorption giant potential line is obtained based on the theoretical adsorption isotherm, and the desorption giant potential line is obtained based on the theoretical desorption isotherm.

[0141] The adsorption equilibrium point is obtained by calculating the intersection of the adsorption giant potential line and the desorption giant potential line.

[0142] The theoretical adsorption isotherm data before the adsorption equilibrium point and the theoretical desorption isotherm data after the adsorption equilibrium point are used as the equilibrium isotherm data.

[0143] The adsorption giant potential curve describes the interaction between the adsorbate and the adsorbent in an adsorption system under different conditions. The desorption giant potential curve describes the change in Gibbs free energy as the adsorbate desorbs from the adsorbent surface and returns to the gas or liquid phase in an adsorption system. Using theoretical adsorption isotherm data, the change in Gibbs free energy during adsorption can be calculated, thus obtaining the adsorption giant potential value and plotting the adsorption giant potential curve. Similarly, the change in Gibbs free energy during adsorption and desorption can be calculated using theoretical adsorption isotherm data to obtain the desorption giant potential curve.

[0144] In this embodiment, the adsorption equilibrium point is determined as follows:

[0145] Within the adsorption hysteresis region, segmented spline interpolation is performed on the adsorption giant potential line and the desorption giant potential line. The intersection point is obtained according to their expressions, and this intersection point is the adsorption equilibrium point. The relative pressure corresponding to this intersection point is the relative pressure of the equilibrium point. Similarly, within the adsorption hysteresis region, segmented spline interpolation is performed on the adsorption and desorption isotherms. Substituting the relative pressure value of the equilibrium point, the excess adsorption capacity on the surface corresponding to the equilibrium point can be calculated.

[0146] Since the theoretical adsorption isotherm data and the theoretical desorption isotherm data are discrete points, after performing piecewise spline interpolation, the theoretical adsorption isotherm curve and the theoretical desorption isotherm curve can be fitted. Calculating the intersection point of the theoretical adsorption isotherm curve and the theoretical desorption isotherm curve is more convenient than manually determining the intersection point among the discrete points.

[0147] In chemical engineering and materials science, the adsorption hysteresis region typically refers to the nonlinear characteristics exhibited by an adsorbent during the adsorption process. When molecules in a gas or liquid interact with and are adsorbed onto a solid surface, the adsorption and desorption processes of the adsorbent may not be completely reversible, leading to the adsorption hysteresis effect. The adsorption hysteresis region manifests as the asymmetry of the adsorption isotherm, meaning that under the same conditions, the amount of adsorbed substance varies with pressure, resulting in different curves.

[0148] like Figure 5 As shown, in this embodiment, the theoretical adsorption isotherm is Γ-ad, the adsorption giant potential line is GP-ad, the desorption isotherm is Γ-de, and its corresponding giant thermodynamic potential GP-de. The equilibrium isotherm data before the adsorption equilibrium point are the same as the theoretical adsorption isotherm data, and after the adsorption equilibrium point are the same as the theoretical desorption isotherm data.

[0149] In one embodiment, the calculation model for the excess adsorption capacity employs a slit-shaped pore model and / or a cylindrical pore model, and the theoretical isotherm data includes at least one of the following:

[0150] The slit-adsorption theoretical isotherm data obtained by calculating using the slit-hole model;

[0151] and

[0152] Isotherm data obtained by slit-equilibrium theory calculation using the slit aperture model;

[0153] and

[0154] Isotherm data obtained from the cylindrical hole model based on the cylindrical adsorption theory;

[0155] and

[0156] The cylindrical-equilibrium isotherm data were calculated using the cylindrical hole model.

[0157] Slit-shaped pore models and cylindrical pore models are two common idealized models for describing the pore structure of adsorbents. The choice between slit-shaped pore models and cylindrical pore models depends on the actual situation of the adsorption system and the research requirements. Slit-shaped pore models are more suitable for describing non-uniform pore structures, while cylindrical pore models are more suitable for describing uniform pore structures.

[0158] In one embodiment, theoretical adsorption isotherm data and theoretical desorption isotherm data are calculated using a slit-shaped pore model, and equilibrium isotherm data are calculated. The theoretical adsorption isotherm data is used as the slit-adsorption theoretical isotherm data, and the equilibrium isotherm data is used as the slit-equilibrium theoretical isotherm data.

[0159] In one embodiment, theoretical adsorption isotherm data and theoretical desorption isotherm data are calculated using a cylindrical pore model, and equilibrium isotherm data are calculated. The theoretical adsorption isotherm data is used as the cylindrical-adsorption theoretical isotherm data, and the equilibrium isotherm data is used as the cylindrical-equilibrium theoretical isotherm data.

[0160] In one embodiment, both the slit-shaped pore model and the cylindrical pore model are used to calculate the corresponding theoretical adsorption isotherm data and theoretical desorption isotherm data, and the corresponding equilibrium isotherm data are calculated. Finally, the theoretical isotherm data of slit-adsorption, slit-equilibrium, cylindrical-adsorption, and cylindrical-equilibrium are obtained.

[0161] The more types of theoretical isotherm data obtained from calculations, the more comprehensive and reliable the results will be when using theoretical isotherm data to determine the pore size distribution of the target porous material.

[0162] Example 2

[0163] In this embodiment, as Figure 6 As shown, a method for characterizing aperture distribution is provided, comprising:

[0164] Step 610: Receive experimental isotherm data of the target material;

[0165] Step 620: Determine the target theoretical isotherm data corresponding to the target material. The target theoretical isotherm data is at least one of the theoretical isotherm data preset in the system. The theoretical isotherm data is calculated using the method described in any one of the above embodiments. The experimental isotherm data is measured using the same experimental materials, experimental gases, and temperatures as the theoretical isotherm data.

[0166] In this embodiment, experimental isotherm data of the target material can be obtained using an adsorption apparatus. This experimental isotherm data includes experimental adsorption isotherm data and / or experimental desorption isotherm data. The experimental isotherm data is measured using the same experimental materials, gases, and temperatures as the theoretical isotherm data. Specifically, the theoretical isotherm data of the target material is measured using nitrogen at 77 K during calculation; correspondingly, the experimental isotherm data of the target material is also measured using nitrogen at 77 K, thereby ensuring the accuracy of the final characterized pore size distribution.

[0167] The method for calculating the theoretical isotherm data in this embodiment is similar to that in Embodiment 1 above, and will not be repeated here. The received experimental isotherm data is one of the inputs used to calculate the pore size distribution data. The pore size distribution data is calculated by solving the adsorption integral equation, which is as follows:

[0168]

[0169] Where, N exp (P) represents experimental isotherm data, N theor (P,H) represents the target theoretical isotherm data. By solving the adsorption integral equation, the pore size distribution data f(H) of the target material can be obtained.

[0170] Specifically, the theoretical isotherm data for the target material includes four types: slit-adsorption theoretical isotherm data, slit-equilibrium theoretical isotherm data, cylindrical-adsorption theoretical isotherm data, and cylindrical-equilibrium theoretical isotherm data. When selecting the target theoretical isotherm data, users can manually choose a database that best matches the target material based on experience. For example, if it is known in advance what type of pore the target material is likely to have (more slit-like or more cylindrical), then the theoretical isotherm data corresponding to slit-like or cylindrical pores can be directly selected for characterization.

[0171] For example, if experimental adsorption isotherm data of the target material are obtained using an adsorption analyzer, and the target material has circular pores, after inputting this experimental adsorption isotherm data into the system, then the cylindrical adsorption theoretical isotherm data can be selected as the target theoretical isotherm data. Alternatively, cylindrical adsorption theoretical isotherm data and cylindrical equilibrium theoretical isotherm data can be selected sequentially for calculation to obtain the corresponding pore size distribution data. Combining and comparing the two sets of pore size distribution data provides a more comprehensive and accurate pore size distribution information.

[0172] In one embodiment, an automatic fitting function is provided. After receiving the experimental adsorption isotherm data of the target material, the system automatically selects theoretical isotherm data that better matches the experimental adsorption isotherm data by testing the Discrete Picard Condition (DPC). That is, each type of data in the theoretical isotherm data is fitted once as the target theoretical isotherm data to obtain the corresponding fitting results, and the database with the best fitting results is fed back to the user as the final target theoretical isotherm data.

[0173] Step 630: Based on the experimental isotherm data and the target theoretical isotherm data, solve the adsorption integral equation to obtain the pore size distribution data of the target material.

[0174] In one embodiment, before solving the adsorption integral equation, the system uses a piecewise spline interpolation method to truncate the pressure segment of the experimental isotherm data to the same pressure point as the theoretical isotherm data.

[0175] For example, the pressure range of the experimental isotherm data is 0-1.5 Pa, while the pressure range of the theoretical isotherm data is 0-1 Pa. By interpolating, the experimental isotherm data is truncated to 0-1 Pa and interpolated to a predetermined pressure node. Under the same comparative pressure point, the experimental and theoretical data can be better correlated, thus allowing for a more accurate comparison of the relationship between the experimental and theoretical isotherm data.

[0176] The method for characterizing pore size distribution in this embodiment provides a theoretical basis for the pore structure of the target material through theoretical isotherm data, while experimental isotherm data provides the actual adsorption characteristics of the target material. By comprehensively utilizing these two types of data to solve the adsorption integral equation, a more comprehensive understanding of the pore size distribution of the material can be obtained. On the other hand, the operation process is also convenient and worry-free for users. They only need to input the measured theoretical isotherm data of the target material into the system, select the preset theoretical isotherm data of the target material in the system, and the system can automatically calculate the pore size distribution data, which greatly improves the efficiency of studying the pore size distribution of the target material.

[0177] In one embodiment, the step of solving the adsorption integral equation based on the experimental adsorption isotherm data and the target theoretical isotherm data to obtain the pore size distribution of the target material includes:

[0178] The adsorption integral equation is regularized to obtain the optimal regularization parameter;

[0179] Based on the regularization parameter, the adsorption integral equation is solved to obtain the pore size distribution of the target material.

[0180] In this embodiment, when solving the adsorption integral equation, the system processes the adsorption integral equation using numerical integration and regularization methods (Tikhonov regularization and truncated singular value decomposition), and automatically calculates the optimal regularization parameter under the premise of solvability. The adsorption integral equation is then solved using the least squares method to obtain the pore size distribution data f(H).

[0181] Regularization can help improve the stability and robustness of a model, reducing overfitting caused by data noise or errors. By selecting the optimal regularization parameter, the model's fitting ability and generalization ability can be effectively balanced, making the solved pore size distribution results more reliable and stable, and providing more valuable data for subsequent materials research and applications.

[0182] In one embodiment, when the target material has both slit pores and cylindrical pores, the adsorption integral equation is calculated as follows:

[0183]

[0184] Where, N exp (P) represents experimental adsorption isotherm data, N theor,slit (P,H) represents the theoretical isotherm data calculated using the slit-hole model, N theor,cylind (P,H) represents the theoretical isotherm data calculated using the cylindrical hole model, H is the half-hole width of the target material, f(H) is the pore size distribution, and ω is the proportion of slit holes in the target material.

[0185] The theoretical formula used in step 620 above is:

[0186]

[0187] Since real-world materials typically possess both slit-like and cylindrical pores, this embodiment employs a cylindrical / slit-like composite pore model to calculate the adsorption integral equation. It provides an option to simultaneously select theoretical isotherm data corresponding to both the slit-like and cylindrical pore models, allowing for calculations using theoretical isotherm data from both models to obtain more accurate pore size distribution data. The value of ω can be obtained from the process described in the above embodiment of "regularizing the adsorption integral equation and obtaining the optimal regularization parameter."

[0188] In one embodiment, the method further includes:

[0189] Based on the pore size distribution data and the adsorption integral equation, the fitted isotherm data are calculated.

[0190] The difference between the fitted isotherm data and the experimental isotherm data is calculated to obtain the degree of fit.

[0191] In this embodiment, the system substitutes the calculated pore size distribution data f(H) into the adsorption integral equation to calculate the fitted isotherm N. cal (P), and then from the fitted isotherm N cal (P) and experimental isotherm N exp The difference in (P) yields the goodness of fit, which helps determine the applicability and limitations of the theoretical isotherm calculation model. A high goodness of fit and small differences indicate that the theoretical isotherm data for the target material are suitable for describing its adsorption characteristics; conversely, a low goodness of fit or large differences may necessitate correction or improvement.

[0192] In one embodiment, the fitting result is output, which includes pore size distribution data, fitted isotherms, fit degree, and total pore volume.

[0193] like Figure 7 The figure shows the pore size distribution data of the target material.

[0194] like Figure 8 As shown, the fitted isotherm N of the target material is... cal (P) and experimental isotherm N exp The difference (P) is shown in the figure. The difference (average error rate) is only 1.49%, and the goodness of fit is 98.51%, which indicates that the aperture distribution data is highly reliable.

[0195] Through the above steps, the pore size distribution and pore volume data of the material can be obtained, which can help different users meet their testing needs. For example, during material preparation, it can better determine the impact of different preparation methods on the pore structure and provide better pore structure design or material preparation optimization. In fields such as catalysis and adsorption, the pore structure data can be used to better understand the impact of different pore structure types on their catalytic or adsorption performance, thereby selecting appropriate pore structure materials to improve the performance of catalysts or adsorbents. Therefore, the method in this embodiment has broad and effective guiding significance for material preparation optimization and material performance improvement.

[0196] It should be understood that, although Figure 1 and Figure 6 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 and Figure 6 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0197] Example 3

[0198] In this embodiment, as Figure 9 As shown, a theoretical isotherm calculation device is provided, comprising:

[0199] The first calculation module 910 is used to obtain the calculation parameters in the weighted density functional theory model of Lennard-Jones fluid. The calculation parameters include fluid-fluid energy parameters, fluid-fluid size parameters, fluid hard sphere diameter, fluid-solid energy parameters, and fluid-solid size parameters. Based on the calculation parameters, the local density distribution of the fluid in the model hole is calculated based on the weighted density functional theory model of Lennard-Jones fluid.

[0200] The second calculation module 920 is used to calculate the surface excess adsorption point set corresponding to the first preset pore size point set and the first preset pressure point set according to the excess adsorption calculation formula and the local density distribution, so as to obtain the first excess adsorption amount.

[0201] The third calculation module 930 is used to calculate the rate of change of the first excess adsorption amount with the change of the first preset pressure point set, and to determine the two pressure values ​​corresponding to the rate of change exceeding the threshold as the first preset pressure value and the second preset pressure value.

[0202] The fourth calculation module 940 is used to calculate the surface excess adsorption point set corresponding to the second preset pressure point set located between the first preset pressure value and the second preset pressure value, and to obtain the second excess adsorption amount.

[0203] The fitting module 950 is used to fit the first excess adsorption amount and the second excess adsorption amount to obtain theoretical isotherm data.

[0204] Specific limitations regarding the theoretical isotherm calculation device can be found in the limitations of the theoretical isotherm calculation method described above, and will not be repeated here. Each unit in the aforementioned theoretical isotherm calculation device can be implemented entirely or partially through software, hardware, or a combination thereof. These units can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each unit.

[0205] Example 4

[0206] In this embodiment, as Figure 10 As shown, an apparatus for characterizing aperture distribution is provided, comprising:

[0207] Receiver module 1010 is used to receive experimental isotherm data of the target material;

[0208] Selection module 1020 is used to determine the target theoretical isotherm data corresponding to the target material. The target theoretical isotherm data is at least one of the theoretical isotherm data preset in the system. The theoretical isotherm data is calculated by applying the method described in any one of the above embodiments. The experimental isotherm data is measured using the same experimental materials, experimental gases, and temperatures as the theoretical isotherm data.

[0209] The processing module 1030 is used to solve the adsorption integral equation based on the experimental isotherm data and the target theoretical isotherm data to obtain the pore size distribution data of the target material.

[0210] Specific limitations regarding the apparatus for characterizing aperture distribution can be found in the limitations on the methods for characterizing aperture distribution described above, and will not be repeated here. Each unit in the aforementioned apparatus for characterizing aperture distribution can be implemented entirely or partially through software, hardware, or a combination thereof. These units can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each unit.

[0211] Example 5

[0212] In this embodiment, a computer device is provided. Its internal structure diagram can be shown as follows: Figure 11 As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computational and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and computer programs, and also contains a database for storing theoretical isotherm data of the target material. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The network interface is used to communicate with other computer devices that have deployed application software. When the processor executes the computer program, it implements a method for calculating theoretical isotherms. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0213] Those skilled in the art will understand that Figure 11The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0214] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to perform the following steps:

[0215] Obtain the calculation parameters in the weighted density functional theory model of Lennard-Jones fluid, including fluid-fluid energy parameters, fluid-fluid size parameters, fluid hard sphere diameter, fluid-solid energy parameters, and fluid-solid size parameters. Based on the calculation parameters, calculate the local density distribution of the fluid in the model orifice based on the weighted density functional theory model of Lennard-Jones fluid.

[0216] Based on the formula for calculating excess adsorption and the local density distribution, the surface excess adsorption point set corresponding to the first preset pore size point set and the first preset pressure point set is calculated to obtain the first excess adsorption.

[0217] Calculate the rate of change of the first excess adsorption amount with the change of the first preset pressure point set, and determine the two pressure values ​​corresponding to when the rate of change exceeds the threshold as the first preset pressure value and the second preset pressure value.

[0218] Calculate the surface excess adsorption point set corresponding to the second preset pressure point set located between the first preset pressure value and the second preset pressure value to obtain the second excess adsorption amount;

[0219] The first and second excess adsorption amounts were fitted to obtain theoretical isotherm data.

[0220] In one embodiment, when the processor executes a computer program, it also performs the following steps:

[0221] Calculate the surface excess adsorption point set corresponding to the first pore size subset and the first preset pressure point set to obtain the first sub-excess adsorption amount.

[0222] Calculate the surface excess adsorption point set corresponding to the second pore size subset and the first preset pressure point set to obtain the second sub-excess adsorption amount.

[0223] The first excess adsorption amount is obtained based on the first sub-excess adsorption amount and the second sub-excess adsorption amount.

[0224] The first preset aperture point set includes a first aperture subset and a second aperture subset. Each aperture value in the first aperture subset is less than a first standard aperture value. Each aperture value in the second aperture subset is greater than or equal to the first standard aperture value and less than or equal to the second standard aperture value. The first standard aperture value is less than the second standard aperture value. The number of apertures in the first aperture subset is greater than the number of apertures in the second aperture subset.

[0225] In one embodiment, when the processor executes a computer program, it also performs the following steps:

[0226] Based on the data of the first excess adsorption amount and the second excess adsorption amount, the surface excess adsorption amount point set corresponding to the third preset pressure point set is calculated by interpolation to obtain the third excess adsorption amount.

[0227] Based on the third excess adsorption amount, the surface excess adsorption point set corresponding to the second preset pore size point set is calculated by interpolation, and the theoretical isotherm data is obtained.

[0228] The pressure value range of the third preset pressure point set includes the pressure value range of the first preset pressure point set and the pressure value range of the second preset pressure point set. The absolute value of the difference between any two adjacent pressure points in the third preset pressure point set is less than or equal to the absolute value of the difference between any two adjacent pressure points in the second preset pressure point set. The aperture value range of the second preset aperture point set includes the aperture value range of the first preset aperture point set. The absolute value of the difference between any two adjacent aperture points in the second preset aperture point set is less than or equal to the absolute value of the difference between any two adjacent aperture points in the first preset aperture point set.

[0229] In one embodiment, the theoretical isotherm data includes theoretical adsorption isotherm data and theoretical desorption isotherm data. When the processor executes the computer program, it also performs the following steps:

[0230] Based on the principle of equal giant thermodynamic potential, the equilibrium isotherm is calculated according to the theoretical adsorption isotherm and the theoretical desorption isotherm.

[0231] Replace the theoretical desorption isotherm with the equilibrium isotherm.

[0232] In one embodiment, when the processor executes a computer program, it also performs the following steps:

[0233] The adsorption giant potential line is obtained based on the theoretical adsorption isotherm, and the desorption giant potential line is obtained based on the theoretical desorption isotherm.

[0234] The adsorption equilibrium point is obtained by calculating the intersection of the adsorption giant potential line and the desorption giant potential line.

[0235] The theoretical adsorption isotherm data before the adsorption equilibrium point and the theoretical desorption isotherm data after the adsorption equilibrium point are used as the equilibrium isotherm data.

[0236] Example 6

[0237] In this embodiment, a computer-readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, it performs the following steps.

[0238] Obtain the calculation parameters in the weighted density functional theory model of Lennard-Jones fluid, including fluid-fluid energy parameters, fluid-fluid size parameters, fluid hard sphere diameter, fluid-solid energy parameters, and fluid-solid size parameters. Based on the calculation parameters, calculate the local density distribution of the fluid in the model orifice based on the weighted density functional theory model of Lennard-Jones fluid.

[0239] Based on the formula for calculating excess adsorption and the local density distribution, the surface excess adsorption point set corresponding to the first preset pore size point set and the first preset pressure point set is calculated to obtain the first excess adsorption.

[0240] Calculate the rate of change of the first excess adsorption amount with the change of the first preset pressure point set, and determine the two pressure values ​​corresponding to when the rate of change exceeds the threshold as the first preset pressure value and the second preset pressure value.

[0241] Calculate the surface excess adsorption point set corresponding to the second preset pressure point set located between the first preset pressure value and the second preset pressure value to obtain the second excess adsorption amount;

[0242] The first and second excess adsorption amounts were fitted to obtain theoretical isotherm data.

[0243] In one embodiment, when the computer program is executed by the processor, it also performs the following steps:

[0244] Calculate the surface excess adsorption point set corresponding to the first pore size subset and the first preset pressure point set to obtain the first sub-excess adsorption amount.

[0245] Calculate the surface excess adsorption point set corresponding to the second pore size subset and the first preset pressure point set to obtain the second sub-excess adsorption amount.

[0246] The first excess adsorption amount is obtained based on the first sub-excess adsorption amount and the second sub-excess adsorption amount.

[0247] The first preset aperture point set includes a first aperture subset and a second aperture subset. Each aperture value in the first aperture subset is less than a first standard aperture value. Each aperture value in the second aperture subset is greater than or equal to the first standard aperture value and less than or equal to the second standard aperture value. The first standard aperture value is less than the second standard aperture value. The number of apertures in the first aperture subset is greater than the number of apertures in the second aperture subset.

[0248] In one embodiment, when the computer program is executed by the processor, it also performs the following steps:

[0249] Based on the data of the first excess adsorption amount and the second excess adsorption amount, the surface excess adsorption amount point set corresponding to the third preset pressure point set is calculated by interpolation to obtain the third excess adsorption amount.

[0250] Based on the third excess adsorption amount, the surface excess adsorption point set corresponding to the second preset pore size point set is calculated by interpolation, and the theoretical isotherm data is obtained.

[0251] The pressure value range of the third preset pressure point set includes the pressure value range of the first preset pressure point set and the pressure value range of the second preset pressure point set. The absolute value of the difference between any two adjacent pressure points in the third preset pressure point set is less than or equal to the absolute value of the difference between any two adjacent pressure points in the second preset pressure point set. The aperture value range of the second preset aperture point set includes the aperture value range of the first preset aperture point set. The absolute value of the difference between any two adjacent aperture points in the second preset aperture point set is less than or equal to the absolute value of the difference between any two adjacent aperture points in the first preset aperture point set.

[0252] In one embodiment, the theoretical isotherm data includes theoretical adsorption isotherm data and theoretical desorption isotherm data. When the computer program is executed by the processor, it further implements the following steps:

[0253] Based on the principle of equal giant thermodynamic potential, the equilibrium isotherm is calculated according to the theoretical adsorption isotherm and the theoretical desorption isotherm.

[0254] Replace the theoretical desorption isotherm with the equilibrium isotherm.

[0255] In one embodiment, when the computer program is executed by the processor, it also performs the following steps:

[0256] The adsorption giant potential line is obtained based on the theoretical adsorption isotherm, and the desorption giant potential line is obtained based on the theoretical desorption isotherm.

[0257] The adsorption equilibrium point is obtained by calculating the intersection of the adsorption giant potential line and the desorption giant potential line.

[0258] The theoretical adsorption isotherm data before the adsorption equilibrium point and the theoretical desorption isotherm data after the adsorption equilibrium point are used as the equilibrium isotherm data.

[0259] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0260] 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.

[0261] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. 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 protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for calculating theoretical isotherms, characterized in that, include: Obtain the calculation parameters in the weighted density functional theory model of Lennard-Jones fluid, including fluid-fluid energy parameters, fluid-fluid size parameters, fluid hard sphere diameter, fluid-solid energy parameters, and fluid-solid size parameters. Based on the calculation parameters, calculate the local density distribution of the fluid in the model orifice based on the weighted density functional theory model of Lennard-Jones fluid. Based on the formula for calculating excess adsorption and the local density distribution, the surface excess adsorption point set corresponding to the first preset pore size point set and the first preset pressure point set is calculated to obtain the first excess adsorption. Calculate the rate of change of the first excess adsorption amount with the change of the first preset pressure point set, and determine the two pressure values ​​corresponding to when the rate of change exceeds the threshold as the first preset pressure value and the second preset pressure value. Calculate the surface excess adsorption point set corresponding to the second preset pressure point set located between the first preset pressure value and the second preset pressure value to obtain the second excess adsorption amount; The first and second excess adsorption amounts are fitted to obtain theoretical isotherm data; The step of calculating the surface excess adsorption amount corresponding to the first preset pore size point set and the first preset pressure point set to obtain the first excess adsorption amount includes: Calculate the surface excess adsorption point set corresponding to the first pore size subset and the first preset pressure point set to obtain the first sub-excess adsorption amount. Calculate the surface excess adsorption point set corresponding to the second pore size subset and the first preset pressure point set to obtain the second sub-excess adsorption amount. The first excess adsorption amount is obtained based on the first sub-excess adsorption amount and the second sub-excess adsorption amount. The first preset aperture point set includes a first aperture subset and a second aperture subset. Each aperture value in the first aperture subset is less than a first standard aperture value. Each aperture value in the second aperture subset is greater than or equal to the first standard aperture value and less than or equal to the second standard aperture value. The first standard aperture value is less than the second standard aperture value. The number of apertures in the first aperture subset is greater than the number of apertures in the second aperture subset.

2. The method according to claim 1, characterized in that, The step of fitting the first excess adsorption amount and the second excess adsorption amount to obtain the theoretical isotherm data includes: Based on the data of the first excess adsorption amount and the second excess adsorption amount, the surface excess adsorption amount point set corresponding to the third preset pressure point set is calculated by interpolation to obtain the third excess adsorption amount. Based on the third excess adsorption amount, the surface excess adsorption point set corresponding to the second preset pore size point set is calculated by interpolation, and the theoretical isotherm data is obtained. The pressure value range of the third preset pressure point set includes the pressure value range of the first preset pressure point set and the pressure value range of the second preset pressure point set. The absolute value of the difference between any two adjacent pressure points in the third preset pressure point set is less than or equal to the absolute value of the difference between any two adjacent pressure points in the second preset pressure point set. The aperture value range of the second preset aperture point set includes the aperture value range of the first preset aperture point set. The absolute value of the difference between any two adjacent aperture points in the second preset aperture point set is less than or equal to the absolute value of the difference between any two adjacent aperture points in the first preset aperture point set.

3. The method according to claim 1, characterized in that, The theoretical isotherm data includes theoretical adsorption isotherm data and theoretical desorption isotherm data, and the method further includes: Based on the principle of equal giant thermodynamic potential, the equilibrium isotherm is calculated according to the theoretical adsorption isotherm and the theoretical desorption isotherm. Replace the theoretical desorption isotherm with the equilibrium isotherm.

4. The method according to claim 3, characterized in that, The determination of the equilibrium isotherm based on the principle of equal giant thermodynamic potential, according to the theoretical adsorption isotherm and the theoretical desorption isotherm, includes: The adsorption giant potential line is obtained based on the theoretical adsorption isotherm, and the desorption giant potential line is obtained based on the theoretical desorption isotherm. The adsorption equilibrium point is obtained by calculating the intersection of the adsorption giant potential line and the desorption giant potential line. The theoretical adsorption isotherm data before the adsorption equilibrium point and the theoretical desorption isotherm data after the adsorption equilibrium point are used as the equilibrium isotherm data.

5. The method according to claim 3 or 4, characterized in that, The calculation model for the excess adsorption capacity uses a slit-shaped pore model and / or a cylindrical pore model, and the theoretical isotherm data includes at least one of the following: Isotherm data obtained from the slit-adsorption theory calculated using the slit-shaped aperture model; and Isotherm data obtained by slit-equilibrium theory calculation using the slit-shaped aperture model; and Isotherm data obtained from the cylindrical hole model based on the cylindrical adsorption theory; and The cylindrical-equilibrium isotherm data were calculated using the cylindrical hole model.

6. A method for characterizing pore size distribution, characterized in that, include: Receive experimental isotherm data of the target material; The target theoretical isotherm data corresponding to the target material is determined. The target theoretical isotherm data is at least one of the theoretical isotherm data preset in the system. The theoretical isotherm data is calculated by applying the method of any one of claims 1-5. The experimental isotherm data is measured using the same experimental materials, experimental gases, and temperatures as the theoretical isotherm data. Based on the experimental isotherm data and the target theoretical isotherm data, the adsorption integral equation is solved to obtain the pore size distribution data of the target material.

7. The method according to claim 6, characterized in that, The step of solving the adsorption integral equation based on the experimental adsorption isotherm data and the target theoretical isotherm data to obtain the pore size distribution of the target material includes: The adsorption integral equation is regularized to obtain the optimal regularization parameter; Based on the regularization parameter, the adsorption integral equation is solved to obtain the pore size distribution of the target material.

8. The method according to claim 6, characterized in that, When the target material has both slit-like pores and cylindrical pores, the adsorption integral equation is calculated as follows: ， in, For the experimental adsorption isotherm data, These are theoretical isotherm data calculated using the slit-hole model. These are theoretical isotherm data obtained through calculation using a cylindrical aperture model. The half-width of the target material. For aperture distribution, The proportion of the slit-like pores in the target material.

9. The method according to claim 7 or 8, characterized in that, The method further includes: Based on the pore size distribution data and the adsorption integral equation, the fitted isotherm data are calculated. The difference between the fitted isotherm data and the experimental isotherm data is calculated to obtain the degree of fit.

10. A theoretical isotherm calculation device, characterized in that, include: The first calculation module is used to obtain the calculation parameters in the weighted density functional theory model of Lennard-Jones fluid. The calculation parameters include fluid-fluid energy parameters, fluid-fluid size parameters, fluid hard sphere diameter, fluid-solid energy parameters, and fluid-solid size parameters. Based on the calculation parameters, the local density distribution of the fluid in the model orifice is calculated based on the weighted density functional theory model of Lennard-Jones fluid. The second calculation module is used to calculate the surface excess adsorption point set corresponding to the first preset pore size point set and the first preset pressure point set according to the excess adsorption calculation formula and the local density distribution, so as to obtain the first excess adsorption amount. The third calculation module is used to calculate the rate of change of the first excess adsorption amount with the change of the first preset pressure point set, and to determine the two pressure values ​​corresponding to the rate of change exceeding the threshold as the first preset pressure value and the second preset pressure value. The fourth calculation module is used to calculate the surface excess adsorption point set corresponding to the second preset pressure point set located between the first preset pressure value and the second preset pressure value, and to obtain the second excess adsorption amount. The fitting module is used to fit the first excess adsorption amount and the second excess adsorption amount to obtain theoretical isotherm data. The second calculation module is specifically used for: Calculate the surface excess adsorption point set corresponding to the first pore size subset and the first preset pressure point set to obtain the first sub-excess adsorption amount. Calculate the surface excess adsorption point set corresponding to the second pore size subset and the first preset pressure point set to obtain the second sub-excess adsorption amount. The first excess adsorption amount is obtained based on the first sub-excess adsorption amount and the second sub-excess adsorption amount. The first preset aperture point set includes a first aperture subset and a second aperture subset. Each aperture value in the first aperture subset is less than a first standard aperture value. Each aperture value in the second aperture subset is greater than or equal to the first standard aperture value and less than or equal to the second standard aperture value. The first standard aperture value is less than the second standard aperture value. The number of apertures in the first aperture subset is greater than the number of apertures in the second aperture subset.

11. A device for characterizing aperture distribution, characterized in that, include: The receiving module is used to receive experimental isotherm data of the target material; The selection module is used to determine the target theoretical isotherm data corresponding to the target material. The target theoretical isotherm data is at least one of the theoretical isotherm data preset in the system. The theoretical isotherm data is calculated by applying the method of any one of claims 1-5. The experimental isotherm data is measured using the same experimental materials, experimental gases, and temperatures as the theoretical isotherm data. The processing module is used to solve the adsorption integral equation based on the experimental isotherm data and the target theoretical isotherm data to obtain the pore size distribution data of the target material.

12. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 5.

13. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 5.

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