A method for detecting ion transmembrane transport thermodynamic parameters based on a quartz crystal microbalance

Abstract

The application discloses a kind of ion transmembrane transport thermodynamic parameter detection methods based on quartz crystal microbalance.The method compares the frequency response difference of bare gold-silicon sheet sensor and the film sensor with the polyamide selective layer in deionized water and salt solution, calculates the distribution coefficient of ion in membrane, based on the thermodynamic analysis framework of transition state theory, the temperature dependence of distribution coefficient is analyzed, and the corresponding enthalpy change (ΔH) and entropy change (ΔS) are obtained.The method can effectively quantitatively analyze the Donnan effect and non-donnan effect in ion transmembrane transport process, including charge repulsion / attraction and dehydration and specific interaction and other non-charge factors.The method is simple in operation process, good in repeatability, suitable for single salt or mixed salt system and various polymer separation membranes, and can provide theoretical basis for membrane material selective regulation, performance optimization and mechanism research.

Description

Technical Field

[0001] This invention relates to the technical field of membrane technology and membrane mass transfer characterization, and in particular to a method for detecting thermodynamic parameters of ion transmembrane transport based on a quartz crystal microbalance. Background Technology

[0002] The ion selectivity of dense charged membranes such as nanofiltration and reverse osmosis originates from multiple coupling factors. Besides the Donnan repulsion / attraction caused by the membrane's fixed charge, non-charge factors such as ion dehydration, specific adsorption, solution-membrane interface interactions, and pore confinement effects can also significantly influence ion partitioning and transport. Existing characterization methods have limitations: membrane filtration experiments mainly obtain macroscopic flux and rejection rates, making it difficult to analyze intramembrane ion partitioning and distinguish between charged and non-charged effects; electrochemical or energy barrier inversion methods rely on multiple assumptions, limiting the comparability and traceability of results; conventional QCM methods are mostly used for quantitative analysis of surface adsorption or overall mass changes, making it difficult to effectively decouple the Donnan and non-Donnan effects in ion transmembrane partitioning, and also difficult to directly obtain corresponding thermodynamic parameters. Therefore, there is an urgent need for a method that can simultaneously characterize ion partitioning, Donnan potential, and their thermodynamic parameters under controllable solution and multi-temperature conditions using the same experimental platform, providing theoretical support for the study of membrane structure-energy barrier-selectivity relationships and membrane material optimization. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention provides a method for detecting thermodynamic parameters of ion transmembrane transport based on a quartz crystal microbalance. This method is applicable to dense charged separation membranes, including nanofiltration membranes, reverse osmosis membranes, and other polymer separation membranes. It can be used to quantitatively characterize the ion distribution behavior, Dornan potential, and its temperature dependence in single-salt or mixed-salt systems, and further obtain thermodynamic parameters related to ion transmembrane transport, including enthalpy change and entropy change. This provides a theoretical basis for the analysis of selective separation mechanisms, evaluation of membrane surface or pore modification effects, and optimization of separation performance. The method of this invention features a simple testing procedure, sensitive signal, strong repeatability, and wide applicability. It can simultaneously obtain Dornan potential and non-Dornnan distribution parameters on the same experimental platform, and further obtain relevant thermodynamic parameters, providing a quantitative basis for the analysis of membrane separation mechanisms and selective control.

[0004] The first objective of this invention is to provide a method for detecting thermodynamic parameters of ion transmembrane transport based on a quartz crystal microbalance, comprising the following steps: S1: Obtain the selective layer of the separation membrane and attach the selective layer to the surface of the gold-silicon wafer quartz crystal sensor to construct a coated quartz crystal sensor; install the bare gold-silicon wafer quartz crystal sensor and the coated quartz crystal sensor into the flow module of the quartz crystal microbalance, respectively, and sequentially introduce deionized water and the salt solution to be tested until the signal stabilizes, and record the corresponding resonance frequencies f1, f2, f3, f4 respectively: △f n = (f4-f3)-(f2-f1), The apparent distribution mass change Δm of salt within the separation membrane was calculated using the Sauerbrey relation. ; Where n is the frequency and C is the crystal mass sensitivity constant; Further subtracting the mass contribution from the solution within the free volume of the selected layer yields the true adsorbed mass m within the membrane. p : m p =△m-δf v C s,v MW salt ; Where δ is the thickness of the selection layer, f v To select the free volume fraction of the layer, C s,b To separate the salt concentration outside the membrane, MW salt Let be the molar mass of the salt; S2: Combine the mass contribution of ions and their hydrated water with the intramembrane ion distribution relationship and the electroneutrality constraint condition to solve for the surface density σ of co-ions and counterions. co σ ct and the intramembrane ion concentration σ co,m σ ct,m : m p =σ co (MW co +n co MW W )+σ ct (MW ct +n ct MW W ), , , z ct C ct,m +z co C co,m +X=0, Among them, MW W n is the molar mass of water. ct n coThese represent the hydration numbers of the counterion and coion, respectively, z. ct z co Let X be the valence state of the counterion and coion, X be the fixed charge density of the film, and Δφ be the valence state of the counterion and coion. D This is a dimensionless Dornan potential; S3: Under high-salt and low-pH conditions, the Dornan effect is negligible. Let ΔφD≈0, and obtain the non-Dornan partition coefficients Φct and Φ from the following formula. CO : , , S4: Under the actual concentration conditions of the sample to be tested, the Φ obtained in step S3 is... ct Φ CO Substitute the mass-distribution relationship: , The potential Δφ of the south side is solved by numerical iteration. D And based on the obtained △φ D Calculate the ion partition coefficient K including the contribution of the south. ct K co : , , S5: K under different temperature conditions i or Φ i The enthalpy change ΔH was obtained by performing a van't Hoff linear fit. i With entropy change ΔS i : or , Where R is the gas constant and T is the thermodynamic temperature.

[0005] In some embodiments of the present invention, in step S1, the separation membrane is a nanofiltration membrane or a reverse osmosis membrane, specifically including any one of a polyamide composite membrane, an ion exchange membrane, or a self-made separation membrane.

[0006] In some embodiments of the present invention, in step S1, the separation membrane sequentially includes a support layer, an intermediate porous layer, and a selection layer.

[0007] In some embodiments of the present invention, in step S1, the cation in the salt solution to be tested is Li. + Na + K + 、Rb + Cs + NH4 + Ca2+ Mg 2+ Ba 2+ Cu 2+ Zn 2+ Ag + Co 2+ Mn 2+ Fe 2+ Cr 3+ Al 3+ One or more of the following; the anion in the salt solution to be tested is F. - Cl - ,Br - I - SO4 2- SO3 2- NO3 - NO2 - PO4 3- CO3 2- and ClO4 - One or more of them.

[0008] In some embodiments of the present invention, in step S2, the testing temperature of the quartz crystal microbalance is 5°C to 60°C.

[0009] In some embodiments of the present invention, in step S2, the liquid inlet flow rate of the quartz crystal microbalance flow module is 20~200 μL / min.

[0010] In some embodiments of the present invention, in step S4, the salt concentration under high-salt and low-pH conditions is 0.8~2.0 mol / L, and the pH value is 4~5, so that Δφ D This can be ignored in calibration calculations.

[0011] In some embodiments of the present invention, in step S4, △φ D Numerical iterative methods are used to solve the problem, including the bisection method, Newton's method, or the secant method.

[0012] In some embodiments of the present invention, the hydration number n ct n CO Measured by external independent experiments or given by literature data.

[0013] In some embodiments of the present invention, the correlation coefficient of the van't Hoff linear fit is not less than 0.90.

[0014] In some embodiments of the present invention, the detection method is used to quantitatively characterize the ion distribution, Dornan potential and thermodynamic parameters of polyamide nanofiltration / reverse osmosis membranes, and to guide the regulation and optimization of the selective separation performance of membrane materials.

[0015] The technical solution of the present invention has the following advantages over the prior art: This invention combines QCM mass response with a modified Dornan partitioning model, utilizing a differential strategy of "bare gold-silicon wafer sensor / coated sensor" to eliminate non-specific effects such as solution density and viscosity. Based on this, by combining an ion-carrying hydrated water mass model and electroneutrality constraints, the partitioning behavior of counterions and like ions within the membrane can be determined separately, thereby achieving quantitative decoupling of the Dornan effect (charge interaction) and non-Dornan effects (such as dehydration, specific interactions, and other non-charge interactions).

[0016] The method described in this invention compares the frequency response differences between bare gold-silicon wafer sensors and coated sensors with polyamide selective layers in deionized water and salt solutions, calculates the ion partition coefficient within the membrane, and analyzes the temperature dependence of the partition coefficient based on the thermodynamic analysis framework of transition state theory to obtain the corresponding enthalpy change (ΔH) and entropy change (ΔS). This method can effectively and quantitatively analyze the Donnan effect and non-Donnan effects in the ion transmembrane transport process, including non-charge factors such as charge repulsion / attraction, dehydration, and specific interactions. The method is simple to operate, has good repeatability, and is applicable to single-salt or mixed-salt systems and various polymer separation membranes, providing a theoretical basis for the selective control, performance optimization, and mechanism research of membrane materials.

[0017] The detection method of this invention has strong decoupling capability, and can simultaneously obtain Δφ within the same QCM data framework. D With Φ ct Φ co This enables the quantitative separation of the Dornan effect from the non-Dornan effect.

[0018] The thermodynamics of this invention are traceable, and ΔH and ΔS can be directly obtained through multi-temperature van't Hoff fitting, which can explain the source of selectivity from the perspective of energy and entropy.

[0019] This invention has a wide range of applications and is reproducible. It can be used for different membrane materials, different ion valence states, and single / mixed salt systems. The step-by-step process facilitates standardized reproduction and horizontal comparison. Attached Figure Description

[0020] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein... Figure 1 This is a schematic diagram of the overall process of the method of the present invention; Figure 2 This is a schematic diagram of the QCM device in an embodiment of the present invention. Figure 3 In this embodiment of the invention, the 800 mmol / L NaCl solution was subjected to different temperatures at lnΦ i A schematic diagram of linear fitting with 1 / T; Figure 4 The 100 mmol / L NaCl solution in this embodiment of the invention was tested at different temperatures (lnK). i A schematic diagram of linear fitting with 1 / T. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0022] A schematic diagram of the QCM device used in the embodiments of the present invention is shown below. Figure 2 As shown, it includes: 1. Sample source: Used to store the sample solution to be tested. Under the suction of the pump, the liquid is introduced into the entire flow detection system from here as the source. 2. Detection Cell: The core reaction and detection area of ​​the system, which contains QCM chips. When liquid flows in from the inlet and passes over the surface of these chips, the adsorption, binding or desorption of molecules in the solution on the chip surface will cause changes in the oscillation frequency and dissipation rate of the quartz crystal, thereby achieving extremely sensitive detection of mass and structural changes. 3. Water pump: Provides power for the directional flow of liquid in the system; 4. Waste Liquid Collection: Used to collect waste liquid that has flowed through the QCM workshop and completed testing, to prevent contamination of the laboratory environment or backflow into the system; 5. Data Acquisition Workstation: The data acquisition, processing, and control terminal for the entire system. It connects to the QCM studio via a data cable (the black line in the diagram), receives electrical signals transmitted from the sensors in real time, and converts them into intuitive frequency variation graphs and data tables for researchers to perform visualization analysis. Example 1:

[0023] This embodiment provides a method for determining the non-Daunan partition coefficient Φ of sodium ions (counter ions, ct) and chloride ions (co ions, co ions) in a polyamide separation membrane under high salt concentration and low pH conditions using a quartz crystal microbalance (QCM). ct Φ co and under multiple temperature conditions, Φ i Perform van't Hoff linear fitting to obtain the enthalpy change ΔH i With entropy change ΔS i The method specifically includes the following steps: (1) The clean and dry QCM gold silicon wafer was loaded into the flow module of the quartz crystal microbalance. The QCM temperature was set to 15℃, 20℃, 25℃ and 30℃ respectively, and the peristaltic pump flow rate was set to 30 μL / min. Deionized water was first introduced, and the vibration frequency f1 was recorded after equilibration for 12 h. Then, 800 mmol / L NaCl solution was introduced, and the vibration frequency f2 was recorded after equilibration for 11 h.

[0024] (2) Take a commercial NF90 polyamide separation membrane, soak it in 25% (v / v) ethanol for 30 min, and then wash it three times with ultrapure water. Peel the washed membrane off the nonwoven substrate and place it in N,N-dimethylformamide (DMF) to dissolve the support layer until the support layer is completely dissolved. Take out the membrane with only the polyamide active layer remaining (membrane side up) and attach it to the surface of the gold silicon wafer, and dry it in a fume hood for 12 h.

[0025] (3) The obtained coated gold silicon wafer was placed into the QCM flow module, and after equilibration with deionized water for 15 h, the vibration frequency f3 was recorded; then, 800 mmol / L NaCl solution was introduced, and after equilibration for 10 h, the vibration frequency f4 was recorded.

[0026] (4) Subtract the frequency difference (f2-f1) of the blank sensor from the frequency difference (f4-f3) of the coated sensor to obtain the net frequency response Δf of the polyamide film to salt. Calculate the change in mass per unit area Δm (ng / cm³) using the Sauerbrey relation. 2 ): , Where n is the overtone order (in this embodiment, n=5); C is the crystal constant (5 MHz QCM corresponds to C=17.7ng / (Hz·cm)). 2 )); △f is the frequency change (Hz).

[0027] The calculation yielded: At 15℃, the mass change of sodium chloride on the polyamide film is Δm = 435.42 ng / cm³. 2 ; At 20℃, the mass change of sodium chloride on the polyamide film is Δm = 403.00 ng / cm³. 2 ; At 25℃, the mass change of sodium chloride on the polyamide film is Δm = 403.00 ng / cm³. 2 ; At 30℃, the mass change of sodium chloride on the polyamide film is Δm = 330.00 ng / cm³. 2 .

[0028] After deducting the solution contribution within the free volume of the selective layer, the true adsorbed mass m inside the membrane is obtained.p : m p =△m-δf v C s,v MW salt , Where δ is the thickness of the polyamide film (in this embodiment, δ = 120 nm = 1.2 × 10⁻⁶). -7 m); C s,v This refers to the salt concentration in the membrane pores (which is consistent with the bulk concentration, i.e., C). s,v =C s,b =800mmol / L); f v The porosity of the polyamide film is 0.3, based on literature review; MW salt That is the molecular weight of sodium chloride (58.44 g / mol).

[0029] The calculation yielded: At 15℃, the actual adsorbed mass m of sodium chloride in the membrane p =267.113ng / cm 2 ; At 20℃, the actual adsorbed mass m of sodium chloride in the membrane p =234.693ng / cm 2 ; At 25℃, the actual adsorbed mass m of sodium chloride in the membrane p =204.693ng / cm 2 ; At 30℃, the actual adsorbed mass m of sodium chloride in the membrane p =161.693ng / cm 2 ; (5) Combine the mass contribution of ions and their hydrated water with the ion distribution relationship within the membrane and the electroneutrality constraint condition to solve for the surface density σ of co-ions and counterions. co σ ct and intramembrane ion concentration C co,m C ct,m : m p =σ co (MW co +n co MW W )+σ ct (MW ct +n ct MW W ), , , , Where, σco σ ct Co-ion / counterion surface density (mol / m) 2 ); C co,m C ct,m The concentration of co-ion / counter-ion ions within the membrane (mol / m 3 ); Φ co Φ ct The non-Daonan partition coefficient for co-ion / counter-ion; Δφ D X is the dimensionless Dornan potential; X is the fixed charge density of the film (in this embodiment, X = -60 mol / m). 3 ), MW co MW ct The relative atomic mass of the co-ion / counterion (MW in this example) co =MW Cl =35.45 g / mol, MW ct= MW Na =22.99 g / mol); MW W n is the molar mass of water (18 g / mol). co n ct These are the co-ion / counter-ion hydration numbers (in this embodiment, n is taken as n). co =7,n ct =5.6); z co z ct The valence states of antiion and coion (z) co =-1, z ct =+1). The calculation results are shown in Table 1: (6) High salt content (800 mol / m 3 Furthermore, the Donnan effect is negligible under low pH conditions (pH=4.5), Δφ D ≈0, the non-Dao Nan allocation coefficient Φ is obtained from the following formula. ct Φ co : , , The calculation results under the conditions of this embodiment are shown in Table 2: (7) Φ was subjected to temperature changes at 15℃, 20℃, 25℃, and 30℃. i Perform van't Hoff linear fitting: , Where R is the gas constant and T is the thermodynamic temperature.

[0030] This example was fitted under conditions of high salt concentration and low pH (i.e., 800 mmol / L, pH=4.5): For co-ion (Cl) - ,See Figure 3 Left): InΦ co =4114.5·1 / T-16.474, R 2 =0.9604; △H co = -34.210 kJ / mol, ΔS co =-136.972J / (mol·K); For counterions (Na) + ,See Figure 3 right): InΦ ct =2058.1·1 / T-8.8325, R 2 =0.9785; △H ct =-9.301kJ / mol, ΔS ct =-33.865 J / (mol·K); Example 2:

[0031] This embodiment provides a method for utilizing the non-Daonan partition coefficient Φ obtained in Example 1 under general conditions (e.g., low salt concentration). co Φ ct The potential Δφ of the south side is solved by combining the mass-distribution relationship. D Furthermore, the ion partition coefficient K, which includes the contribution of Dornan, was obtained. ct K co and for K i Perform van't Hoff fitting to obtain ΔH i , △S i The method specifically includes the following steps: Repeat step (1) of Example 1, but set the NaCl concentration to C. s,b =100mol / m 3 (i.e., 100 mmol / L). Similarly, the following method was used: m p =△m-δf v C s,v MW NaCl , Where C s,v =C s,b .

[0032] Calculate Δm and m in this embodiment p The data is shown in Table 3: Under normal conditions, Φ is obtained from high-concentration salt solutions under low pH conditions. co Φ ct Substitute the mass-distribution equation: , The solution to Δφ is obtained by Newton's iteration method. D : 15℃: △φ D =-1.582; 20℃: △φ D =-1.473; 25℃: △φ D =-1.574; 30℃: △φ D =-1.500.

[0033] Based on the obtained △φ D Further calculations were performed on the ion partition coefficient K, which includes the contribution from Dornan. ct K co : , , The calculation yielded: K under multiple temperature conditions i Perform van't Hoff linear fitting: , The fitting calculation yielded the following: For co-ion (Cl) - ,See Figure 4 Left): InK co =3854.5·1 / T-17.126, R 2 =0.9355; △H co = -32.048 kJ / mol, ΔS co =-142.393 J / (mol·K); For counterions (Na) + ,See Figure 4 right): InK ct =2318.1·1 / T-8.1802, R 2 =0.9001; △H ct =-19.274kJ / mol, ΔS ct =-68.014J / (mol·K).

[0034] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for detecting thermodynamic parameters of ion transmembrane transport based on a quartz crystal microbalance, characterized in that, Includes the following steps: S1: Obtain the selector layer of the separation membrane and attach the selector layer to the surface of the gold-silicon wafer quartz crystal sensor to construct a coated quartz crystal sensor; install the bare gold-silicon wafer quartz crystal sensor and the coated quartz crystal sensor into the flow module of the quartz crystal microbalance, respectively, and sequentially introduce deionized water and the salt solution to be tested until the signal stabilizes, and record the corresponding resonance frequencies. f 1, f 2, f 3, f 4: △ f n = （ f 4- f 3）-（ f 2- f 1）， The apparent partition mass change of salt within the separation membrane was calculated using the Sauerbrey relation. △m : ； in, n The number of overtones. C Δ is the crystal mass sensitivity constant; f This is the change in frequency, measured in Hz. Further subtracting the mass contribution from the solution within the free volume of the selected layer yields the true adsorption mass within the membrane. m p : m p = △m - δf v C s,v MW salt ； in, δ To select the layer thickness, f v The void volume fraction of the separation membrane. C s,v This represents the salt concentration in the membrane pores. MW salt The molar mass of the salt; S2: the mass contribution of ions and their hydration water is coupled with the ion distribution in the membrane and the electroneutrality constraint to solve the surface densities of co-ion and counter-ion co , σ ct , and the ion concentration in the membrane σ co,m , σ ct,m : m p =s co ( MW co + n co MW W )+s ct ( M Wct +n ct MW W ), ， ， z ct C ct,m + z co C co,m + X =0， in, MW W For the molar mass of water, n ct , n co These are the hydration numbers of the counterion and coion, respectively. z ct , z co The valence states of the counterion and coion are... X To fix the charge density of the membrane, △φ D This is a dimensionless Dauran potential. MW co , MW ct These are the relative atomic masses of the co-ion and counterion, respectively. C co,m , C ct,m The concentrations of co-ion / counter-ion ions within the membrane are expressed in mol / m³. 3 C s,b To separate the salt concentration outside the membrane; S3: Under high-salt and low-pH conditions, the Donnan effect is negligible, making △φ D ≈0, the non-Dao Nan distribution coefficient is obtained from the following formula. Φ ct , Φ CO : ， ， S4: Under the actual concentration conditions of the sample to be tested, the result obtained in step S3... Φ ct , Φ co Substitute the mass-distribution relationship: ， The potential Δ of the south side is solved by numerical iteration. φ D And based on the obtained △ φ D Calculate the ion partition coefficient including the contribution of the south. K ct , K co : ， ， S5: Under different temperature conditions K i or Φ i Enthalpy change was obtained by performing a van't Hoff linear fit. △H i With entropy change △S i : or , in R The gas constant is T It is the thermodynamic temperature.

2. The method for detecting thermodynamic parameters of ion transmembrane transport based on a quartz crystal microbalance according to claim 1, characterized in that, In step S1, the separation membrane is a nanofiltration membrane or a reverse osmosis membrane.

3. The method for detecting thermodynamic parameters of ion transmembrane transport based on a quartz crystal microbalance according to claim 1, characterized in that, In step S1, the separation membrane sequentially comprises a support layer, an intermediate porous layer, and a selective layer.

4. The method for detecting thermodynamic parameters of ion transmembrane transport based on a quartz crystal microbalance according to claim 1, characterized in that, In step S1, the cation in the salt solution to be tested is Li. + Na + K + 、Rb + Cs + NH4 + Ca 2+ Mg 2+ Ba 2+ Cu 2+ Zn 2+ Ag + Co 2+ Mn 2+ Fe 2+ Cr 3+ Al 3+ One or more of the following; the anion in the salt solution to be tested is F. - Cl - ,Br - I - SO4 2- SO3 2- NO3 - NO2 - PO4 3- CO3 2- and ClO4 - One or more of them.

5. The method for detecting thermodynamic parameters of ion transmembrane transport based on a quartz crystal microbalance according to claim 1, characterized in that, In step S2, the testing temperature of the quartz crystal microbalance is 5℃~60℃.

6. The method for detecting thermodynamic parameters of ion transmembrane transport based on a quartz crystal microbalance according to claim 1, characterized in that, In step S2, the liquid inlet flow rate of the quartz crystal microbalance flow module is 20~200 μL / min.

7. The method for detecting thermodynamic parameters of ion transmembrane transport based on a quartz crystal microbalance according to claim 1, characterized in that, In step S4, the salt concentration is 0.8–2.0 mol / L and the pH value is 4–5 under high-salt and low-pH conditions. △ φ D This can be ignored in calibration calculations.

8. The method for detecting thermodynamic parameters of ion transmembrane transport based on a quartz crystal microbalance according to claim 1, characterized in that, In step S4, △φ D Numerical iterative methods are used to solve the problem, including the bisection method, Newton's method, or the secant method.

9. The method for detecting thermodynamic parameters of ion transmembrane transport based on a quartz crystal microbalance according to claim 1, characterized in that, The correlation coefficient of the van't Hoff linear fit is no less than 0.

90.

10. The method for detecting thermodynamic parameters of ion transmembrane transport based on a quartz crystal microbalance according to claim 1, characterized in that, The detection method is used to quantitatively characterize the ion distribution, Dornan potential and thermodynamic parameters of polyamide nanofiltration / reverse osmosis membranes, and to guide the regulation and optimization of the selective separation performance of membrane materials.

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