Method for estimating the molecular weight cut-off of a porous membrane using a three-step method of localization-search-determination

Abstract

The application provides a method for estimating the molecular weight cut-off of a porous membrane by using a positioning-search-determining three-step method, belongs to the field of membrane seawater desalination, and comprises three steps of positioning, searching and determining; a fitting formula for initially predicting the MWCO range of a to-be-detected membrane is obtained through theoretical modeling and experimental results of known commercial membranes, the initial positioning of the to-be-detected membrane is realized, and the approximate position of the to-be-detected membrane is determined; two standard substances with molecular weights close to the predicted value are selected to perform a cut-off rate experiment, and the MWCO range is further narrowed; and the MWCO value of the to-be-detected membrane is determined based on linear fitting of experimental data. The application significantly shortens the evaluation period of the MWCO of the porous membrane, reduces the types and amounts of chemical reagents required by the experiment, and reduces the test cost, so that the quantitative regulation of the intermediate layer of the high-performance desalination membrane can be realized, and the efficient research and development of the high-performance desalination membrane and the construction of the desalination membrane knowledge base driven by data are facilitated.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of membrane sea water desalination, and particularly relates to a method for estimating the molecular weight cut-off of a porous membrane by a positioning-searching-determining three-step method. BACKGROUND

[0002] As a new type of membrane construction pattern widely used in seawater desalination and wastewater treatment in recent years, the thin layer composite membrane based on the intermediate layer can optimize the structure and morphology of the desalination membrane through the construction of the intermediate layer, thereby improving the separation performance of the membrane. The polyamide separation layer of the thin layer composite membrane is the key to the performance of the desalination membrane. However, the composite membrane is not a simple combination of the polyamide separation layer and the support layer, and the formation of the polyamide separation layer greatly depends on the support layer. Studies have shown the influence of the support layer pore size on the formation of the polyamide layer and the water molecule transmission, and numerous experimental studies have also confirmed the importance of the support layer pore size. The current commonly used pore size quantification methods of the porous membrane include direct method and indirect method. The direct method is a method for directly obtaining the surface morphology, pore size and other information of the porous membrane by using large measuring instruments, mainly including scanning electron microscope (SEM) method, transmission electron microscope (TEM) method and atomic force microscope (AFM) method. The indirect method is a method for indirectly obtaining the equivalent pore size of the membrane by means of the physical phenomena related to the pore size of the porous membrane, through experimental determination of the corresponding experimental parameters, and according to the corresponding formula, mainly including bubble point method, molecular weight cut-off (MWCO) method and the like. However, the above methods have some disadvantages in evaluating the pore size of the porous membrane, such as complicated operation steps, high testing cost and high equipment investment cost. SUMMARY

[0003] The present application provides a method for estimating the molecular weight cut-off of a porous membrane by a positioning-searching-determining three-step method, which solves the above-mentioned problems, and the specific steps include: positioning step, searching step and determining step.

[0004] The positioning step is used to predict the numerical range of the molecular weight cut-off of the to-be-tested pore size ultrafiltration membrane.

[0005] The searching step is used to select two standard substances with molecular weight close to the numerical range, and determine the rejection rates of the two standard substances.

[0006] The determining step calculates the linear correlation between the rejection rates and the molecular weight cut-off of the two standard substances, and determines the accurate value of the molecular weight cut-off of the to-be-tested pore size ultrafiltration membrane.

[0007] In the preferred embodiment, in the positioning step, experiments are performed by using different pore size commercial ultrafiltration membranes, and the convection permeation coefficient L d , the rejection rate R tThe fitting formula between the molecular weight cut-off and the approximate correlation of the convective permeability coefficient L d , the pure water permeability coefficient A and the rejection rate R t Based on the fitting formula, the predicted value of the molecular weight cut-off of the porous membrane to be tested is calculated.

[0008] In the preferred embodiment, in the positioning step, the rejection rate of the porous membrane to polystyrene sulfonate sodium is determined, and the convective permeability coefficient L d and the rejection rate R t Approximate correlation:

[0009] 1 / R t = [A (1-Δπ / Δp) + 2L d ] / [A (1-Δπ / Δp) + L d ] (2);

[0010] Let α represent A (1-Δπ / Δp), and equation (2) is transformed into:

[0011] R t = (α + L d ) / (α + 2L d ) (3);

[0012] Taking the logarithm of both sides of the equation, equation (3) is transformed into:

[0013]

[0014] According to Taylor series expansion, equation (4) is transformed into:

[0015]

[0016] lnR t is expressed as a polynomial approximation with L d / A as the variable:

[0017]

[0018] Where Δp is the transmembrane pressure difference, ΔΠ is the osmotic pressure difference, B s is the solute permeability coefficient.

[0019] In the preferred embodiment, the specific steps for determining the approximate correlation of the molecular weight cut-off MWCO and the rejection rate R t are as follows:

[0020] The relationship between the solute diameter D s and the solute rejection rate is established by the Gaussian error function:

[0021]

[0022] where the variable x is expressed by the following equation:

[0023]

[0024] D is established by Einstein equation s Correlation with molecular weight MW:

[0025] lnD s = ln β + 1 / 3 ln MW (9);

[0026] where β is a parameter related to intrinsic viscosity of solute, and equation (9) is simplified as:

[0027] InD s = ln γ + δ ln MW (10);

[0028] where γ and δ are correlation parameters;

[0029] Substituting equation (10) into equation (8) gives:

[0030]

[0031] MWCO corresponds to R t = 90%, MW PSS corresponds to R t , the following equation is obtained:

[0032]

[0033] Subtracting equation (13) from equation (12) gives:

[0034]

[0035] R t The polynomial related to MWCO is:

[0036]

[0037] where a i and b are correlation parameters;

[0038] The approximate correlation between the convection permeation coefficient L d , the rejection R t and MWCO is obtained by combining equations (6) and (15).

[0039] In the preferred embodiment, the rejection R t of the standard substance is calculated by the following equation:

[0040]

[0041] where C pC represents the concentration of the permeate f C represents the concentration of the feed solution.

[0042] In preferred embodiments, the convective permeation coefficient L d is calculated by the following equation:

[0043] J s = C p ΔV / A m Δt (17);

[0044] J s / C f = L d ΔP+B s (C f -C p ) / C f (18);

[0045] where J s is the solute diffusion flux, ΔV is the permeation volume, A m is the membrane effective filtration area, Δt is the permeation time, B s is the solute permeation coefficient, and ΔP is the operating pressure.

[0046] In preferred embodiments, the pure water permeation coefficient A is obtained by the following equation:

[0047] J w = ΔV / A m Δt (19)

[0048] J w = (A+L d )ΔP (20);

[0049] where J w is the water flux.

[0050] In preferred embodiments, a i and b in equation (15) vary with (lnMW) Rt＝50％ / lnMW PSS and (lnMW) Rt＝84.13％ / lnMW PSS .

[0051] Beneficial technical effects: The present application explores a simple, effective and economical method to estimate the molecular weight cut-off of a porous membrane, which is of great significance to the improvement of the quantification accuracy of the pore size of the porous membrane and the reduction of the cost. The three-step method of positioning-searching-determining couples the MWCO prediction method based on R t or L d / A with the traditional MWCO measurement method, and combines the advantages of the pure prediction method and the pure measurement method, thereby improving the reliability and reducing the test cost. Attached Figure Description

[0052] Figure 1 A simplified flowchart for determining MWCO using the three-step method;

[0053] Figure 2 (a) shows commercial membranes with different pore sizes. d The values ​​of A and B, (b) are the predicted R values ​​by the polynomial fitting formula. t A table summarizing the value deviation and fitting parameters of the polynomial fitting formula;

[0054] Figure 3 A diagram illustrating a hybrid strategy of location-search-determine;

[0055] Figure 4 A comparison chart of measured and predicted Rt values ​​for PCM / 300, PCM / 1000, and PCM / 2000;

[0056] Figure 5 To determine L d / A and R t A schematic diagram comparing the predicted MWCO of PCM with the measured MWCO values. Detailed Implementation

[0057] The embodiments of the present invention will now be described in conjunction with specific examples.

[0058] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described in detail below. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0059] A method for estimating the molecular weight cutoff of porous membranes using a three-step method of location-search-determination, the specific steps of which include location, search, and determination;

[0060] The aforementioned positioning: A theoretical model is established using mathematical formulas to describe the convection permeability coefficient (L). d ), retention rate (R) t The fitting relationship between ) and MWCO. Experiments were conducted using commercial ultrafiltration membranes with different pore sizes, and an approximate fitting formula among the three was determined through polynomial fitting. Based on this formula, the L of the ultrafiltration membrane with the measured pore size was substituted into the equation. d A and R t The value is used to predict the range of molecular weight cutoff of the ultrafiltration membrane with the desired pore size, thus achieving its initial "positioning".

[0061] The search: according to the predicted value range of the molecular weight cut-off of the to-be-tested pore size ultrafiltration membrane in the "positioning", two standard substances (selected from the standard substance library) with molecular weight close to the value range are selected. The retention rate experiment is carried out on the to-be-tested membrane, and the retention rates of the two standard substances are respectively measured. Through the experimental data, the value range of the molecular weight cut-off of the to-be-tested pore size ultrafiltration membrane is further narrowed down, and further "search" is realized.

[0062] The determination: according to the retention rate data obtained in the "search", the MWCO value of the to-be-tested membrane is determined through the linear correlation between the retention rates of the two standard substances and the MWCO in the "search" step, and the final "determination" of the accurate value of the MWCO is realized.

[0063] A method for estimating the molecular weight cut-off of a porous membrane by a positioning-search-determination three-step method, comprising the following steps:

[0064] S1, positioning: establishing an approximate correlation between the convective permeability coefficient (L d ) and the retention rate (R t ), which can be obtained by measuring the retention rate of the porous membrane to sodium polystyrene sulfonate (PSS, MW=70kDa):

[0065] (1-R t ) / R t =(L d Δp+B s ) / [A(Δp-ΔΠ)+L d Δp] (1);

[0066] In the formula, Δp is the transmembrane pressure difference (bar), ΔΠ is the osmotic pressure difference (bar), B s is the solute permeability coefficient (LMH), and A is the pure water permeability coefficient (LMH / bar).

[0067] Simplified as

[0068] 1 / R t =[A(1-Δπ / Δp)+2L d ] / [A(1-Δπ / Δp)+L d ] (2);

[0069] Use the parameter α to represent the group A(1-ΔΠ / Δp), and the formula (2) can be converted to

[0070] R t =(α+L d ) / (α+2L d ) (3);

[0071] Taking the logarithm of both sides of the equation, the formula (3) can be converted to

[0072]

[0073] According to Taylor series expansion, equation (4) can be transformed into

[0074]

[0075] By selecting appropriate operating pressure and feed liquid concentration, a can be approximated by A. Based on this, lnR t can be approximated by a polynomial with L d / A as variable:

[0076]

[0077] In addition, the approximate correlation between MWCO and R t can be determined by the following equation:

[0078] The solute diameter (D s ) and solute rejection rate can be established by the Gaussian error function:

[0079]

[0080] In the equation, the variable x can be expressed by the following equation:

[0081]

[0082] In addition, the correlation between D s and MW (molecular weight) can be established by the Einstein equation:

[0083] InD s = lnβ + 1 / 3 lnMW (9);

[0084] where β is a parameter related to the intrinsic viscosity of the solute, and the intrinsic viscosity is related to MW, so lnβ can be expressed as a function of lnWM. Based on this, equation (9) can be simplified as:

[0085] lnD s = lnγ + δ lnMW (10);

[0086] where the correlation parameters γ and δ can be approximately regarded as constants. Substituting equation (10) into equation (8) gives:

[0087]

[0088] The MWCO corresponding to R t = 90% and the MW PSS corresponding to R t , the following equation can be obtained:

[0089]

[0090] Subtracting equation (13) from equation (12) gives:

[0091]

[0092]

[0093] Based on equation (14), R t The polynomial related to MWCO can be described as:

[0094]

[0095] Solving equations (6) and (15) gives the approximate correlation between the coefficient of convective flow (L d ), the rejection (R t ) and the MWCO.

[0096] The correlation parameters a i and b in equation (15) vary with (lnMW) Rt＝50％ / lnMW PSS and (lnMW) Rt＝84.13％ / lnMW PSS / lnMW Rt＝50％ / lnMW PSS and (lnMW) Rt＝84.13％ / lnMW PSS are defined as the relative molecular weight, denoted by β1 and β2 respectively, which vary with the difference of the pore size of the porous membrane, but the variation trend is not large.

[0097] Experiments are conducted using commercial ultrafiltration membranes with different pore sizes to determine their R t , MWCO and L d values (here R t and L d values are for a selected specific standard substance, such as PSS), and the fitting parameters are determined according to the fitting formula constructed above. Then, by measuring the L d , A and R t values of the membrane to be tested, the MWCO range is preliminarily predicted according to the obtained fitting formula, and the preliminary "positioning" is achieved.

[0098] In the preferred embodiment, the MWCO of commercial ultrafiltration membranes is measured using the conventional MWCO method, and the rejection (R t ) of the commercial membrane for standard substances with different molecular weights is calculated by the following formula:

[0099]

[0100] In this equation, C p represents the concentration of the permeate (g / L), and Cf The concentration of the feed solution is expressed in g / L. The retention graph is plotted against the standard substances, and the molecular weight corresponding to 90% retention on the curve represents the molecular weight retained by the sample membrane. The mathematical relationship between MWCO and R t t is established by a polynomial fit between Rand lnMWCO.

[0101] In a preferred embodiment, the flow permeability coefficient (L d ) can be calculated by the following equation:

[0102] J s = C p ΔV / A m Δt (17)

[0103] J s / C f = L d ΔP+B s (C f -C p ) / C f (18)

[0104] where J s is the solute diffusion flux (gMH), ΔV is the permeation volume (L), A m is the effective filtration area of the membrane (m 2 ), Δt is the permeation time (h), B s is the solute permeation coefficient (LMH), and ΔP is the operating pressure (bar).

[0105] In a preferred embodiment, the pure water permeability coefficient A is obtained by the following equation:

[0106] J w = ΔV / A m Δt (19)

[0107] J w = (A+L d )ΔP (20)

[0108] J w is the water flux, and based on the obtained L d , A can be obtained by substituting equation (20).

[0109] S2, search: according to the predicted value range of the retention molecular weight of the pore size ultrafiltration membrane in the "positioning", two standard substances (selected from the standard substance library) with molecular weight close to the value range are selected. The retention rate experiment of the pore size ultrafiltration membrane to be tested is carried out, and the retention rates of the two standard substances are measured respectively. Through the experimental data, the value range of the retention molecular weight of the pore size ultrafiltration membrane to be tested is further narrowed down, and further "search" is realized.

[0110] S3, determining: according to the rejection data obtained in the "search", the MWCO value of the membrane to be measured is determined by the linear correlation between the rejection of the two standard substances and the MWCO in the S2 step, and the "determination" of the final MWCO accurate value is realized.

[0111] The application will be further described below through specific examples.

[0112] Example 1:

[0113] Five kinds of commercial ultrafiltration membranes with nominal MWCO of 20 / 30 / 50 / 80 / 100 kDa were selected, named CUF-1 / 2 / 3 / 4 / 5. The L d and A values (as shown in Figure 2 (a)) were measured, and the lnR t and L d / A were polynomial fitted (as shown in Table 1). After 4-order polynomial fitting, R 2 = 1, and the deviation of the fitted polynomial was less than 0.2% (as shown in Figure 2 (b)). Based on this, a mathematical expression formula for describing the R t and L d / A of the porous membrane was obtained.

[0114] Table 1 Fitting parameter list of lnR t and L d / A polynomial fitting

[0115]

[0116]

[0117] Then, the MWCO value of the commercial membrane was measured by the conventional rejection molecular weight determination method (as shown in Figure 3 (a)), and the R t and lnMWCO were polynomial fitted (odd order), as shown in Table 2. After 5-order polynomial fitting, R 2 = 1, and the deviation of the MWCO predicted by the R t fitted polynomial was less than the deviation predicted by the L d / A fitted polynomial, but the deviation of both was less than ±5% (as shown in Figure 3 (b)). In addition, the relative molecular weights β1 and β2 changed with the pore size of the commercial membrane as shown in Table 3. The relative molecular weight changed little, which ensured that the approximate correlation between the MWCO of the porous membrane with different pore sizes and Rt could be fitted by the polynomial formula.

[0118] Table 2 Fitting parameter list of R t and lnMWCO polynomial fitting

[0119]

[0120] Table 3. Relative molecular weights β1 and β2 of commercial membranes with different pore sizes.

[0121]

[0122] Example 2:

[0123] Porous composite membranes (PCMs) fabricated by forming UF-level layers on microfiltration (MF) substrates using ZIF-8 nanoparticles of different sizes are shown in the figure below, comparing the measured and predicted Rt values ​​for PCM / 300, PCM / 1000, and PCM / 2000. Figure 4 As shown. When R t When located in the CUF (commercial membrane) region (0.80-0.97), the predicted MWCO values ​​for PCM / 300, PCM / 1000, and PCM / 2000 are close to the measured MWCO values. Furthermore, when R... t The deviation between the predicted and measured MWCO becomes larger in regions farther away from the CUF membrane. This result indicates that the R predicted using the existing fitting equation is inadequate. t and the measured L d Obtaining an approximate MWCO using / A can easily introduce considerable errors. Subsequently, by measuring L... d / A and R t Predict the MWCO of PCM separately and compare it with the measured MWCO value, such as Figure 5 As shown in the figure. The predicted values ​​obtained through the latter method have a smaller deviation from the measured values, but the deviation increases when the difference between the test membrane and the calibration membrane is large. Furthermore, the relative molecular weights β1 and β2 of porous composite membranes with different pore sizes are shown in Table 4.

[0124] Table 4. Relative molecular weights β1 and β2 of porous composite membranes with different pore sizes.

[0125]

[0126]

[0127] The B value represents the volume (ml) of ZIF-8 nanoparticle suspension used.

[0128] Example 3:

[0129] Based on Examples 1 and 2, it is evident that predictive methods alone are insufficient to accurately determine the MWCO of porous membranes. Therefore, a three-step method—location-search-determination—is proposed to determine the MWCO of porous membranes (e.g., Figure 1 (As shown). First, the MWCO value (MWCO1) of the PCM is predicted according to the fitting formula. Then, the convective permeability coefficient (L) of the PCM is measured.d ), L d The mathematical relationship between MWCO and MWPSS is shown in Equation 1. The MWPSS is used to quickly locate an approximate MWCO value, which provides a rough range for the subsequent search steps. Based on the value of MWPSS, two standard substances with molecular weights on both sides of MWPSS are selected. The retention rates of the two standard substances on PCM are measured, and the measured retention rate is ensured to be equal to 90% in order to more accurately locate the true MWCO and further narrow the range of MWCO. Based on the measured retention rates and the retention molecular weights of the two standard substances in the search steps, the MWCO value corresponding to the 90% retention rate (MWCO2) is calculated by linear interpolation to determine an accurate MWCO value as the final result of the evaluation of the pore size of PCM. Two adjacent standard substances are selected, and the corresponding retention rates are calculated, as shown in Table 5. The MWCO2 of PCM / 3000-0.25 is calculated as 368.73, with an error % of -3.95%. In addition, the error value of MWCO2 is not greater than 10% except for PCM / 1000-0.75, indicating that the method proposed in the present application can provide a relatively accurate MWCO value for the porous composite membrane.

[0130] Table 5. The retention molecular weights of PCM determined by the method proposed in the present application and the determination error

[0131]

[0132]

[0133] Explanation of Positioning: If R t,2 <90% indicates that the true value of MWCO is on the right side of MWPSS, and vice versa.

[0134] Err% is the ratio of the difference between MWCO2 and the true value of MWCO to the true value, and the true value of MWCO is obtained by measuring the retention rates of the seven standard substances.

[0135] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art cannot easily think of changes or substitutions within the technical scope disclosed in the present application, which should be covered within the protection scope of the present application; in the case of no conflict, the embodiments of the present application and the features in the embodiments can be combined with each other. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for estimating the molecular weight cut-off of a porous membrane using a locate-search-determine three-step procedure, characterized in that, Comprising: a positioning step, a searching step, a determining step; The positioning step is used to predict the numerical range of the molecular weight cut-off of the to-be-tested pore size ultrafiltration membrane; experiments are performed using different pore size commercial ultrafiltration membranes, and a fitting formula between the convective permeation coefficient L d , the rejection rate R t and the molecular weight cut-off is obtained through polynomial fitting, so as to obtain the convective permeation coefficient L d , the pure water permeation coefficient A and the rejection rate R t of the to-be-tested pore size ultrafiltration membrane based on the fitting formula, and calculate the predicted value of the molecular weight cut-off of the to-be-tested pore size ultrafiltration membrane; the searching step is used for selecting two standard substances with molecular weight close to the numerical range, and determining the retention rate of the two standard substances; the determining step is used for calculating the linear correlation between the retention rate and the retention molecular weight of the two standard substances, and determining the accurate value of the retention molecular weight of the to-be-measured pore size ultrafiltration membrane.

2. The method for estimating the molecular weight cut-off of a porous membrane using a locate-search-determine three-step method according to claim 1, characterized in that, In the positioning step, the retention rate of the porous membrane for sodium polystyrene sulfonate is measured, and the convective permeability coefficient L is established d The retention rate R t Approximate correlation: （2）； with representing A , formula (2) is converted to: （3）； Logarithmic operation is performed on both sides of the equation, and equation (3) is converted into: （4）； According to Taylor series expansion, equation (4) is converted into: （5）； lnR t with L d The polynomial approximation in terms of A is given by: (6）； wherein, is the transmembrane pressure difference, is the osmotic pressure difference, B s is the solute permeability coefficient.

3. The method for estimating the molecular weight cut-off of a porous membrane using a locate-search-determine three-step method according to claim 2, characterized in that, Determining the approximate correlation of the molecular weight cut-off MWCO and the retention rate R t The specific steps are as follows: The solute diameter D is established by the Gaussian error function s The relationship with the solute rejection rate: (7)； In the formula, the variable x is expressed by the following formula: (8)； D is established by Einstein's formula s Correlation with molecular weight MW: (9)； wherein is a parameter related to the intrinsic viscosity of the solute, and equation (9) simplifies to: (10)； wherein and is a correlation parameter; Substitute equation (10) into equation (8) to obtain: (11)； MWCO corresponds to R t = 90%, MW PSS corresponds to R t The following equation is obtained: (12)； (13)； Subtract equation (13) from equation (12) to obtain: (14)； R t The polynomial associated with the MWCO is: （15）； wherein a i and b are correlation parameters; From (6) and (15) we get the convective permeability coefficient L d , the rejection R t and the approximate correlation between R and MWCO.

4. The method for estimating the molecular weight cut-off of a porous membrane using a locate-search-determine three-step method according to claim 3, characterized in that, Retention R of the standard substance t Calculated by the following equation: （16）； where C p represents the concentration of the permeate, C f represents the concentration of the feed solution.

5. The method for estimating the molecular weight cut-off of a porous membrane using a locate-search-determine three-step method according to claim 4, characterized in that, The coefficient of convective permeability L d is calculated by the formula: （17）； （18）； where J is the solute flux, s is the solute diffusion flux, is the permeate volume, A m is the membrane effective filtration area, is the permeate time, B s is the solute permeability, is the operating pressure.

6. The method for estimating the molecular weight cut-off of a porous membrane using a locate-search-determine three-step method according to claim 5, wherein, The pure water permeability coefficient A is obtained by the following formula: (19)； (20)； where J w is the water flux.

7. The method for estimating the molecular weight cut-off of a porous membrane using a locate-search-determine three-step method according to claim 3, wherein, a in formula (15) i and b vary with (lnMW) Rt=50% / lnMW PSS and (lnMW) Rt=84.13% / lnMW PSS and (lnMW)

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