Method for comparing influence of electrostatic interaction in nano-channels with different sizes on ion transmission rate

By measuring the ion transmission rate and channel south potential at different pHs in nanochannels of different sizes and normalized processing, the problem of comparing the impact of electrostatic action on ion transmission rate in nanochannels of different sizes is solved, and an effective evaluation of the impact of electrostatic action in nanochannels is achieved.

CN120142424APending Publication Date: 2025-06-13RES CENT FOR ECO ENVIRONMENTAL SCI THE CHINESE ACAD OF SCI
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Patent Information

Application Number
CN202510326201.9
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-03-19
Publication Date
2025-06-13

AI Technical Summary

Technical Problem

The prior art is difficult to compare the impact of electrostatic action on ion transmission rate in nanochannels of different sizes, and there is a lack of effective evaluation methods.

Method used

By preparing nanochannel nanofiltration membranes of different sizes, the ion transfer rate and ion transfer rate changes are measured at different pHs, and the ion transfer rate changes are normalized to evaluate the impact of electrostatic effects on ion transfer.

Benefits of technology

This method can be easy to operate and simple to calculate, and evaluate the impact of electrostatic action in nanochannels of different sizes on ion transmission rates, providing an evaluation of the ion transmission capacity of unit channels in nanochannels.

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Abstract

The invention provides a method for comparing the influence of electrostatic interaction in nano channels with different sizes on ion transmission rate, which comprises the following steps: measuring the ion transmission rate and nanofiltration membrane channel south potential under different pH values, calculating the change delta P and delta phi of the ion transmission rate and nanofiltration membrane channel south potential, and finally normalizing the ion transmission rate delta P to the channel south potential delta phi to obtain the ion transmission rate. The influence delta P / delta phi of the unit channel south potential on the ion transmission rate is calculated, the unit channel south potential adjusting ion transmission capacity in the nano channel can be obtained, and the influence of the electrostatic interaction in channels of different sizes on ion transmission is evaluated; the method has the advantages of being convenient to operate, simple in calculation and the like.
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Description

Technical Field

[0001] The present invention relates to the technical field of water treatment, specifically to nanofiltration membranes, and particularly to a method for comparing the influence of electrostatic interactions on ion transport rates in nanoscale channels of different sizes. Background Art

[0002] The potential distribution at the membrane interface plays an important role in ion transmembrane transport. Due to the fixed charges in the membrane matrix, the ions in the membrane phase are unevenly distributed, creating a potential difference across the membrane, which is called the Donnan potential. The Donnan potential can characterize the magnitude of the electrostatic interaction during ion transmembrane transport. The larger the Donnan potential, the greater the electrostatic force on the ions. Electrostatic interaction and steric sieving are the main mechanisms of nanofiltration membrane separation. By adjusting the size and charge distribution of the nanofiltration membrane, the selective separation ability of the nanofiltration membrane for ions can be effectively improved, and the application potential of the nanofiltration membrane in seawater desalination, lithium-magnesium separation, drinking water purification, and industrial wastewater treatment can be stimulated. Exploring the individual effects and coupling mechanisms of electrostatic interaction and steric sieving on ion transport helps to deeply understand the separation mechanism of nanofiltration membranes and assist in the development of functional membrane materials.

[0003] Currently, the individual effects of electrostatic interaction and steric sieving on ion transport have been widely studied, but few people have investigated the influence of electrostatic interaction on ion transport in nanoscale channels of different sizes. This is because it is very difficult to construct ion channels with different sizes but the same Donnan potential. Therefore, there is an urgent need to develop an evaluation method to compare the influence of electrostatic interaction on ion transport in nanoscale channels of different sizes. Summary of the Invention

[0004] In view of the problems existing in the prior art, the present invention provides a method for comparing the influence of electrostatic interaction on ion transport rates in nanoscale channels of different sizes. The method can normalize the ion transport rate with respect to the Donnan potential to evaluate the variation law of electrostatic interaction with the size of the nanoscale channel, and has the advantages of convenient operation and simple calculation.

[0005] To achieve this purpose, the present invention adopts the following technical solutions:

[0006] The purpose of the present invention is to provide a method for comparing the influence of electrostatic interaction on ion transport rates in nanoscale channels of different sizes, and the method includes the following steps:

[0007] (1) Prepare nanofiltration membranes with at least 3 different sizes of nanoscale channels, and measure the pore diameter M of the nanofiltration membranes i , i≥3, so as to construct nanoscale channels of different sizes;

[0008] (2) Place the nanofiltration membrane described in step (1) between the stock solution tank filled with the cation solution and the receiving tank filled with deionized water, adjust the pH of the cation solution, and measure the ion transport rate and the Donnan potential of the nanofiltration membrane at two different pH values respectively.

[0009] For the same size of nanochannels, take the difference between the ion transport rates P at two different pH values to obtain the change in ion transport rate ΔP, and take the difference between the Donnan potentials of the nanofiltration membrane at two different pH values to obtain the change in Donnan potential Normalize the change in ion transport rate ΔP with respect to the change in Donnan potential The obtained is used as the influence of the unit Donnan potential on the ion transport rate in the corresponding size of nanochannels.

[0010] Calculate the corresponding to at least three different sizes of nanochannels respectively, and compare the influence of electrostatic interaction on the ion transport rate in nanochannels of different sizes.

[0011] In the method of the present invention, by measuring the ion transport rate and the Donnan potential of the nanofiltration membrane at different pH values, the changes in the ion transport rate and the Donnan potential of the nanofiltration membrane, ΔP and are calculated. Finally, the ion transport rate ΔP is normalized with respect to the Donnan potential to calculate the influence of the unit Donnan potential on the ion transport rate The ability of the unit Donnan potential to regulate the ion transport in nanochannels can be obtained to evaluate the influence of electrostatic interaction on the ion transport in nanochannels of different sizes.

[0012] As a preferred technical solution of the present invention, the value range of the different sizes of nanochannels is For example or etc.

[0013] It should be noted that the nanofiltration membrane described in the present invention can be commercially purchased or prepared by oneself, and there is no limitation here.

[0014] As a preferred technical solution of the present invention, in step (1), according to the hindered transport model, through the neutral solute molecule retention experiment, the flux and retention rate of the membrane at different pressures are measured, and a specific pore size of a nanofiltration membrane is calculated.

[0015] As a preferred technical solution of the present invention, the calculation formula corresponding to the neutral solute molecule retention experiment is:

[0016]

[0017] In formula (1): R is the retention rate; c f and c pare the concentrations of the feed liquid and the permeate liquid; K i,a and K i,d are the convection factor and the diffusion factor, respectively, and φ S,i is the steric factor, and all three are related to the pore size of the nanofiltration membrane and the solute size; L e is the membrane thickness, and D i,∞ is the solute diffusion coefficient, and the two are the inherent parameters of the membrane; J v is the permeation flux; i is the ion species;

[0018] In Equation (1), the convection factor K i,a has the following expression:

[0019]

[0020] In Equation (1), the diffusion factor K i,d has the following expression:

[0021]

[0022] In Equations (2) and (3), λ is the ratio of the solute Stokes radius r i to the membrane pore radius r p and satisfies the following relationship:

[0023]

[0024] In Equation (1), the steric factor φ S,i has the following expression:

[0025]

[0026] In Equation (5): r i is the solute Stokes radius, and r p is the membrane pore radius.

[0027] It should be noted that, by combining Equations (1)-(5), it can be seen that the unknowns in Equation (1) are only the rejection, the flux, and the membrane pore size. Therefore, the pore size of the membrane can be calculated from the relevant measurement data of the rejection and the flux.

[0028] As a preferred technical solution of the present invention, in step (2), the nanofiltration membrane described in step (1) is respectively placed in the center of an H-type electrolytic cell. One side of the membrane is a stock solution tank filled with a cation solution, and the other side of the membrane is a receiving tank filled with deionized water. The pH of the cation solution is controlled, and the ion transport rate and the Donnan potential of the nanofiltration membrane are respectively measured at acidic pH and basic pH.

[0029] It should be noted that in order to reduce the systematic error, after adjusting the pH of the cation solution, let it stand for more than 1 h before conducting relevant measurements. Since the ion transport rate is very slow, first let it stand for more than 1 h for transport to reduce the systematic error.

[0030] As a preferred technical solution of the present invention, the solute ions in the cation solution include Li + , Na + , K + , Ca 2+ or Mg 2+ or a combination of any one or at least two of them.

[0031] As a preferred technical solution of the present invention, the acidic pH ranges from 2 to 5, such as 2, 2.5, 3, 3.5, 4, 4.5 or 5, etc.

[0032] As a preferred technical solution of the present invention, the alkaline pH ranges from 8 to 11, such as 8, 8.5, 9, 9.5, 10, 10.5 or 11, etc.

[0033] As a preferred technical solution of the present invention, in step (2), for the pH of a specific cation solution, the expression for measuring the ion transport rate P is:

[0034]

[0035] In formula (6): P is the ion transport rate; c 0 and c t are the ion concentrations at the start and end of the experiment, respectively; V is the volume of the cation solution or deionized water; A is the effective area of the membrane; t is the time used in the experiment;

[0036] It should be noted that the volumes of the cation solution and deionized water are the same to control the liquid levels on both sides of the nanofiltration membrane to be the same, minimize the pressure effect as much as possible, ensure that the driving force of the ions is free diffusion, and exclude the pressure difference caused by the liquid level difference on both sides.

[0037] In step (2), the expression for the change in ion transport rate ΔP is:

[0038] ΔP = |P 1 -P 2 | (7).

[0039] As a preferred technical solution of the present invention, in step (2), for the pH of a specific cation solution, the expression for measuring the Donnan potential of the nanofiltration membrane is:

[0040]

[0041] In formula (8): ci,m is the solute concentration in the membrane phase; c i,p is the solute concentration in the permeate; e is the elementary charge; is the Donnan potential of the nanofiltration membrane; k is the Boltzmann constant; z i is the ionic valence; i is the ion species; T is the absolute temperature;

[0042] In Equation (8), for the permeate and the membrane phase, considering the electroneutrality condition, the following expressions are respectively available:

[0043]

[0044] In Equation (9) and Equation (10): c i,m is the solute concentration in the membrane phase; c i,p is the solute concentration in the permeate; X is the volume charge density; i is the ion species; z i is the ionic valence;

[0045] It should be noted that i (from 1 to N) represents all the cation and anion species in the solution.

[0046] In Equation (10), assuming that the total charge is evenly distributed in the membrane pores, the volume charge density X is calculated through the following expression:

[0047]

[0048] In Equation (11): σ is the surface charge density; r p is the membrane pore radius; F is the Faraday constant;

[0049] In Equation (11), the calculation expression of the surface charge density σ is:

[0050]

[0051] In Equation (12): ε is the solvent dielectric constant; ε 0 is the vacuum permittivity; k is the Boltzmann constant; T is the absolute temperature; c i is the ion concentration; i is the ion species; N A is the Avogadro constant; ζ is the membrane surface Zeta potential; z i is the ionic valence; e is the elementary charge;

[0052] In step (2), the change in the Donnan potential has the following expression:

[0053]

[0054] Compared with the existing technical solution, the present invention has at least the following beneficial effects:

[0055] In the method of the present invention, by measuring the ion transport rate and the Donnan potential of the nanofiltration membrane at different pH values, the changes ΔP of the ion transport rate and the Donnan potential of the nanofiltration membrane are calculated, and Finally, the ion transport rate ΔP is normalized with respect to the Donnan potential to calculate the influence of the unit Donnan potential on the ion transport rate The ion transport ability regulated by the unit Donnan potential in the nanochannel can be obtained to evaluate the influence of the electrostatic interaction in nanopores of different sizes on the ion transport. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a graph showing the ion transport rate when ions pass through the nanofiltration membrane numbered M at acidic pH = 3 and alkaline pH = 9 in a specific embodiment of the present invention; 1 nanofiltration membrane ;

[0057] Figure 2 It is a graph showing the ion transport rate when ions pass through the nanofiltration membrane numbered M at acidic pH = 3 and alkaline pH = 9 in a specific embodiment of the present invention; 2 nanofiltration membrane ;

[0058] Figure 3 It is a graph showing the ion transport rate when ions pass through the nanofiltration membrane numbered M at acidic pH = 3 and alkaline pH = 9 in a specific embodiment of the present invention; 3 nanofiltration membrane ;

[0059] Figure 4 It is a graph showing the ion transport rate when ions pass through the nanofiltration membrane numbered M at acidic pH = 3 and alkaline pH = 9 in a specific embodiment of the present invention; 4 nanofiltration membrane ;

[0060] Figure 5 It is a graph showing the ion transport rate when ions pass through the nanofiltration membrane numbered M at acidic pH = 3 and alkaline pH = 9 in a specific embodiment of the present invention; 5 nanofiltration membrane ;

[0061] Figure 6 It is a bar graph showing the influence of the electrostatic interaction in five different-sized nanochannels on the ion transport rate when five cations, namely Li + , Na + , K + , Ca 2+ and Mg 2+ , are compared in a specific embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0062] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings and through specific embodiments.

[0063] The present invention provides a specific embodiment, providing a method for comparing the influence of electrostatic interaction on the ion transport rate in nanochannels of different sizes. The method includes the following steps:

[0064] (1) Prepare commercial nanofiltration membranes with 5 different sizes of nanochannels, and number them as M 1 , M 2 , M 3 , M 4 , M 5 in ascending order of pore size. According to the hindered transport model, through the neutral solute molecule rejection experiment, measure the flux and rejection rate of the membrane under different pressures, and calculate the pore size of a specific nanofiltration membrane, so as to construct nanochannels of different sizes;

[0065] Specifically, the calculation formula corresponding to the neutral solute molecule rejection experiment is:

[0066]

[0067] In formula (1): R is the rejection rate; c f and c p are the concentrations of the feed liquid and the permeate respectively; K i,a and K i,d are the convection factor and the diffusion factor respectively, and φ S,i is the steric factor, and the three are related to the pore size of the nanofiltration membrane and the solute size; L e is the membrane thickness, D i,∞ is the solute diffusion coefficient, and the two are the inherent parameters of the membrane; J v is the permeation flux; i is the ion species;

[0068] In formula (1), the expression of the convection factor K i,a is:

[0069]

[0070] In formula (1), the expression of the diffusion factor K i,d is:

[0071]

[0072] In formulas (2) and (3), λ is the ratio of the solute Stokes radius r i to the membrane pore radius r p , and satisfies the following relational expression:

[0073]

[0074] In formula (1), the steric factor φ S,i has the following expression:

[0075]

[0076] In formula (5): r i is the solute Stokes radius, and r p is the membrane pore radius.

[0077] Combining formulas (1)-(5), it can be seen that the unknowns in formula (1) are only the rejection, flux, and membrane pore size. Therefore, the pore size of the membrane can be calculated through the relevant measurement data of rejection and flux; through the neutral solute molecule rejection experiment, for the nanofiltration membrane numbered M 1 the pore size of the nanofiltration membrane is for the nanofiltration membrane numbered M 2 the pore size of the nanofiltration membrane is for the nanofiltration membrane numbered M 3 the pore size of the nanofiltration membrane is for the nanofiltration membrane numbered M 4 the pore size of the nanofiltration membrane is for the nanofiltration membrane numbered M 5 the pore size of the nanofiltration membrane is

[0078] (2) Place the nanofiltration membrane described in step (1) in the center of the H-shaped electrolytic cell. On one side of the membrane is the stock solution pool filled with the cation solution, and on the other side of the membrane is the receiving pool filled with deionized water. First, adjust the pH of the cation solution, and then let it stand for 1 h to reduce the systematic error. Measure the ion transport rate and the Donnan potential of the nanofiltration membrane at acidic pH = 3 and alkaline pH = 9 respectively; wherein, the solute ions in the cation solution are Li + , Na + , K + , Ca 2+ , and Mg 2+ these 5 kinds of cations;

[0079] For the same-sized nanochannel, take the difference between the ion transport rates P at two different pH values to obtain the change in ion transport rate ΔP; specifically, for a specific pH of the cation solution, the expression for measuring the ion transport rate P is:

[0080]

[0081] In formula (6): P is the ion transport rate; c 0 and c t are the ion concentrations at the start and end of the experiment respectively; V is the volume of the cation solution or deionized water; A is the effective area of the membrane; t is the time used in the experiment;

[0082] Among them, Table 1 shows the Δc = c corresponding to the cation concentration permeated by 5 nanofiltration membranes during the experiment at an acidic pH = 3 t -c 0 experimental results, and Table 2 shows the experimental results of Δc = c corresponding to 5 nanofiltration membranes at a basic pH = 9 t -c 0 ; the unit is mg / L for both

[0083] Table 1

[0084] Item Δc <![CDATA[Δc(Na + )]]> <![CDATA[Δc(Li + )]]> <![CDATA[Δc(Ca 2+ )]]> <![CDATA[Δc(Mg 2+ )]]> <![CDATA[M 1 > 1.7181 0.4115 0.0556 0.1502 0.0664 <![CDATA[M 2 > 7.5098 3.3902 0.6303 2.6427 1.4092 <![CDATA[M 3 > 6.6479 2.3301 0.3233 1.1383 0.5209 <![CDATA[M 4 > 32.6466 12.2203 2.2410 10.0651 5.1240 <![CDATA[M 5 > 49.5887 25.6825 4.9777 21.5365 10.2937

[0085] Table 2

[0086]

[0087]

[0088] In step (2), the expression for the change in ion transport rate ΔP is:

[0089] ΔP = |P 1 -P 2 | (7);

[0090] For the same-sized nanochannels, the difference between the Donnan potentials of the nanofiltration membranes at two different pH values is taken to obtain the change in Donnan potential Specifically, for the pH of a specific cation solution, the expression for measuring the Donnan potential of the nanofiltration membrane is:

[0091]

[0092] In Equation (8): c i,m is the solute concentration in the membrane phase; c i,p is the solute concentration in the permeate; e is the elementary charge; is the Donnan potential of the nanofiltration membrane; k is the Boltzmann constant z i is the ionic valence; i is the ion species; T is the absolute temperature;

[0093] In Equation (8), for the permeate and the membrane phase, considering the condition of electrical neutrality, the following expressions are respectively:

[0094]

[0095] In Equations (9) and (10): c i,m is the solute concentration in the membrane phase; c i,p is the solute concentration in the permeate; X is the volume charge density; i is the ion species; z i is the ionic valence;

[0096] In Equation (10), assuming that the total charge is evenly distributed in the membrane pores, the volume charge density X is calculated through the following expression:

[0097]

[0098] In Equation (11): σ is the surface charge density; r p is the membrane pore radius; F is the Faraday constant;

[0099] In Equation (11), the calculation expression of the surface charge density σ is:

[0100]

[0101] In Equation (12): ε is the solvent dielectric constant; ε 0 is the vacuum permittivity; k is the Boltzmann constant; T is the absolute temperature; c i is the ion concentration; i is the ion species; N A is the Avogadro constant; ζ is the membrane surface Zeta potential; z i is the ion valence; e is the elementary charge;

[0102] In step (2), the expression of the Donnan potential change is:

[0103]

[0104] Table 3 shows the calculation results of the Donnan potential change in 5 nanofiltration membranes in different cation solutions;

[0105] Table 3

[0106]

[0107] Normalize the ion transport rate change ΔP with respect to the Donnan potential change to obtain as the influence of the unit Donnan potential on the ion transport rate in the corresponding size nanochannels.

[0108] Figure 1 shows the ion transport rate curves when ions pass through the nanofiltration membrane numbered M 1 at acidic pH = 3 and alkaline pH = 9; Figure 2 shows the ion transport rate curves when ions pass through the nanofiltration membrane numbered M 2 at acidic pH = 3 and alkaline pH = 9; Figure 3 shows the ion transport rate curves when ions pass through the nanofiltration membrane numbered M 3 at acidic pH = 3 and alkaline pH = 9; Figure 4 shows the ion transport rate curves when ions pass through the nanofiltration membrane numbered M4 Ion transport rate curve of nanofiltration membrane; Figure 5 Shows the ion transport rate curve of nanofiltration membrane numbered M at acidic pH = 3 and alkaline pH = 9. 5 Ion transport rate curve of nanofiltration membrane. As Figures 1 - 5 can be seen, in each nanofiltration membrane, as the size of the cation increases, the ion transport rate decreases because larger ions are subject to stronger size sieving effects. As the pore size of the membrane increases, the ion transport rate increases because larger pores result in smaller size sieving effects. Also, in each nanofiltration membrane, an increase in pH causes an increase in the cation transport rate because for nanofiltration membranes, the higher the pH, the more charged the membrane surface, the stronger the electrostatic interaction, and the stronger the electrostatic attraction to cations, making cations more likely to migrate from the solution to the membrane phase, ultimately increasing the cation transport rate.

[0109] Figure 6 Shows Li + 、Na + 、K + 、Ca 2+ and Mg 2+ bar graphs comparing the effects of electrostatic interactions on ion transport rates in five different-sized nanochannels for these five cations respectively. As Figure 6 can be seen, as the pore size of the membrane decreases, the ability of the Donnan potential to regulate ion transport per unit first increases and then decreases. This is because the Donnan potential represents the magnitude of the electrostatic interaction, and the magnitude of the electrostatic force on an ion is related to the distance between the ion and the tube wall. The smaller the distance, the greater the force. Therefore, the regulatory ability of the Donnan potential increases as the size decreases initially. However, as the pore size further decreases to , the pore size is similar to or even smaller than the ion hydration size, and the ion needs to complete the dehydration process to enter the pore interior, which requires overcoming an additional energy barrier. That is, it becomes increasingly difficult for ions to enter the pore interior, and at this time, size sieving gradually dominates the membrane's selective separation mechanism, and the regulatory ability of the electrostatic interaction on ion transport rapidly decreases. When the pore size decreases to , most ions do not enter the pore interior, and the Donnan potential generated by the fixed charges on the pore wall has no effect on ion transport, meaning that the electrostatic interaction has little effect on ion transport.

[0110] The present invention uses the above embodiments to illustrate the detailed structural features of the present invention, but the present invention is not limited to the above detailed structural features, that is, it does not mean that the present invention must rely on the above detailed structural features to be implemented. Those skilled in the art should understand that any improvement to the present invention, equivalent replacement of the components selected by the present invention, addition of auxiliary components, and selection of specific methods, etc., all fall within the protection scope and disclosure scope of the present invention.

[0111] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various simple modifications can be made to the technical solutions of the present invention, and these simple modifications all fall within the protection scope of the present invention.

[0112] In addition, it should be noted that, in the various specific technical features described in the above specific embodiments, they can be combined in any appropriate manner without contradiction. To avoid unnecessary repetition, the present invention will not separately describe various possible combination manners.

[0113] Furthermore, any combination can be made between various different embodiments of the present invention, as long as it does not violate the idea of the present invention, and it should also be regarded as the content disclosed by the present invention.

Claims

1. A method for comparing the effect of electrostatic interaction on ion transport rate in nanochannels of different sizes, characterized in that: The method comprises the following steps: (1) Prepare at least three nanofiltration membranes with nanochannels of different sizes and measure the pore size M of the nanofiltration membranes respectively. i , i ≥ 3, thereby constructing nanochannels of different sizes; (2) placing the nanofiltration membrane described in step (1) between a stock solution tank containing a cationic solution and a receiving tank containing deionized water, adjusting the pH of the cationic solution, and measuring the ion transfer rate and nanofiltration membrane potential at two different pH values; For the same size nanochannel, the ion transport rate P at two different pH values ​​is subtracted to obtain the ion transport rate change ΔP. Subtract and get the change of Daonan potential The change of ion transport rate ΔP to the change of Donnan potential After normalization, the obtained as the effect of unit Donen potential on ion transport rate in nanochannels of corresponding size; Calculate the corresponding values ​​of at least three nanochannels of different sizes. Compare the effects of electrostatic interactions on ion transport rates in nanochannels of different sizes.

2. The method according to claim 1, characterized in that In step (1), the value range of the nanochannels of different sizes is 3. The method according to claim 1, characterized in that In step (1), according to the hindered transport model, the flux and retention rate of the membrane under different pressures are measured through a neutral solute molecule retention experiment, and the pore size of a specific nanofiltration membrane is calculated.

4. The method according to claim 3, characterized in that The calculation formula corresponding to the neutral solute molecule interception experiment is: In formula (1): R is the interception rate; c f and c p are the concentrations of the feed and permeate, respectively; K i,a and K i,d are the convection factor and the diffusion factor, φ S,i is the steric factor, and the three are related to the pore size of the nanofiltration membrane and the size of the solute; L e is the film thickness, D i,∞ is the solute diffusion coefficient, both of which are intrinsic parameters of the membrane; J v is the permeate flux; i is the ion species; In formula (1), the convection factor K i,a The expression is: In formula (1), the diffusion factor K i,d The expression is: In formula (2) and formula (3), λ is the Stokes radius of the solute r i and membrane pore radius r p The ratio satisfies the following relationship: In formula (1), the steric factor φ S,i The expression is: In formula (5): r i is the solute Stokes radius, r p is the membrane pore radius.

5. The method according to claim 1, characterized in that In step (2), the nanofiltration membrane described in step (1) is respectively arranged in the center of an H-type electrolytic cell, one side of the membrane is a stock solution pool filled with a cationic solution, and the other side of the membrane is a receiving pool filled with deionized water. The pH of the cationic solution is controlled, and the ion transfer rate and nanofiltration membrane potential at acidic pH and alkaline pH are respectively measured.

6. The method according to claim 5, characterized in that The solute ions in the cationic solution include Li + 、Na + , K + , Ca 2+ or Mg 2+ Any one or a combination of at least two of the following.

7. The method according to claim 5, characterized in that The acidic pH value is in the range of 2-5.

8. The method according to claim 5, characterized in that The alkaline pH is in the range of 8-11.

9. The method according to claim 5, characterized in that In step (2), for the pH of a specific cationic solution, the expression for determining the ion transfer rate P is: In formula (6): P is the ion transport rate; c0 and c t are the ion concentrations at the beginning and end of the experiment, respectively; V is the volume of the cationic solution or deionized water; A is the effective area of ​​the membrane; t is the time taken for the experiment; In step (2), the expression for the change in ion transport rate ΔP is: ΔP=|P1-P2| (7).

10. The method according to claim 5, characterized in that In step (2), for the pH of a specific cation solution, the nanofiltration membrane potential is determined. The expression is: In formula (8): c i,m is the solute concentration in the membrane phase; c i,p is the solute concentration in the permeate; e is the elementary charge; is the nanofiltration membrane potential; k is the Boltzmann constant; z i is the ion valence; i is the ion species; T is the absolute temperature; In formula (8), for the permeate and membrane phase, considering the electrical neutrality condition, the following expressions are respectively obtained: In formula (9) and formula (10): c i,m is the solute concentration in the membrane phase; c i,p is the solute concentration in the permeate; X is the volume charge density; i is the ion species; z i is the ion valence; In formula (10), assuming that the total charge is evenly distributed in the membrane pores, the volume charge density X is calculated by the following expression: In formula (11), σ is the surface charge density; r p is the membrane pore radius; F is the Faraday constant; In formula (11), the calculation expression of surface charge density σ is: In formula (12), ε is the dielectric constant of the solvent; ε0 is the dielectric constant of vacuum; k is the Boltzmann constant; T is the absolute temperature; c i is the ion concentration; i is the ion species; N A is Avogadro's constant; ζ is the Zeta potential of the membrane surface; z i is the ion valence; e is the elementary charge; In step (2), the potential of Daonan changes The expression is: