Juntian Xiao, Qian Sun, Liying Liu, Zhongwei Ding,*

1 Beijing Key Laboratory of Membrane Science and Technology, College of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, China

2 Beijing Advanced Innovation Center for Soft Matter Science and Engineering, State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology Beijing 100029, China

Keywords:Alternating current impedance Spontaneous membrane wetting Hydrophobic membrane Dynamic monitoring

A B S T R A C T In the process of membrane absorption, spontaneous wetting of hydrophobic microporous membrane causes membrane modification and increases membrane phase mass transfer resistance, which have attracted wide interest. However, due to the limitations of previous testing methods, the study of the spontaneous membrane wetting process is limited.Herein,we present a method for monitoring spontaneous membrane wetting by measuring its alternating current (AC) impedance. The impedance tests of the PVDF flat membranes and hollow fiber membranes were conducted in a two-electrode system. The results of equivalent circuit fitting indicate that the impedance value of the unwetted membrane is about 1.02 × 1010 Ω, which is close to the theoretical value of 1.4 × 1010 Ω, and this method can quantify the electrochemical impedance value of membranes with different degrees of spontaneous wetting.In addition,a method of impedance test for real-time monitoring of spontaneous wetting was designed.During the experiment, the timeliness and continuity of this method are confirmed with exact judgment under different conditions. In future work, the impedance data will be used to build model to predict the percentage of membrane wetting degree.

1. Introduction

AC impedance spectroscopy is a kind of electrochemical test method with sensitive responsiveness and low cost,and it is available to describe the phase status and process information at multiple research views [1,2]. Based on a proper equivalent circuit model, a sinusoidal alternating current with specific frequency is applied to a system to generate a responding current. By measuring the magnitude and phase angle between input and output,the complex impedance information can be obtained in the system[3,4].It is found that the fitting result visibly reflects the pores and physical properties of the membrane materials [5-7]. Therefore,the AC impedance is promising with membrane structure characterization and membrane process monitoring [8,9]. Currently, AC impedance spectroscopy is widely applied in neotype membrane synthesis and membrane pollution monitoring [10-15].

In recent years, there has been an increasing amount of literature on membrane wetting.Research shows that when diethanolamine (DEA) is adopted as an absorbent with a hydrophobic microporous membrane in CO2absorption, and the contact angle is less than 90°, leading to the spontaneous penetration(wetting)of the membrane without the effect of transmembrane pressure difference [16]. The spontaneous wetting indicates a possible universal phenomenon during gas absorption in membrane contactors. The monitoring of spontaneous wetting is important for the perfection of its kinetic model and infiltrative laws. However, currently there are few researches emphasize the study of spontaneous wetting. Therefore, some referable studies are needed to perfect it.

The purpose of this paper is to monitor the spontaneous wetting of hydrophobic membranes with AC impedance spectroscopy.As a pioneered research, it is revolutionary to present the test for the first time to the best of our knowledge, and a challenging lowconductive impedance measurement of insulating microporous membrane is processed simultaneously. In this paper, a twoelectrode system is applicated to test the AC impedance spectra of PVDF flat membranes and hollow fiber membranes in 1 mol·L-1DEA solution with different wetting degrees.The equivalent circuit was fitted to determine the change of membrane electrochemical parameters after theoretical verification, thereby a set of impedance test method for continuous wetting monitoring is developed to directly reflect the change of the process.

2. Theoretical Background

2.1. Basic principles of AC impedance

The AC impedance technology is an electrochemical measurement method that applies a small amplitude AC voltage as a disturbance signal. The small amplitude disturbance signal makes the response feedback of the system under the test close to linear,which facilitates data analysis and improves accuracy.The formula for calculating AC impedance is:

whereZis the impedance,Utis the sinusoidal AC input voltage,andItis the output current, both of which are functions of time;Utcan also be expressed in a complex form:

whereUω is the AC voltage amplitude, ω is the AC angular frequency, andjis a complex unit.

The corresponding representation of the response current is:

In the formula,Iω is the amplitude of the sinusoidal response current, and φ is the phase angle between the voltage and the response current.

Put the Eqs. (2) and (3) into (1) to get the complex representation of AC impedance:

whereZω is the impedance test value at different frequencies.Establish an appropriate equivalent circuit and fit the wide frequency impedance test results to obtain the physical and structural characteristics of the membranes. The equivalent circuit composed of standard elements including resistanceRand capacitorC,according to the characteristics of the testing system, combine the above standard components in series or parallel, then the impedance test value in Eq. (4) can be effectively fitted.

The impedance of the ohmic resistorR,which is independent of the frequency, is:

The value of the element used to represent the resistance of the membranes are independent of the test frequency but related to the type of materials and the shape of the membranes.The theoretical calculation formula is:

Eqs. (6) and (7) are the resistance calculation formulas of flat membranes and hollow fiber membranes, where σ is the conductivity of the membrane material,andLandSare the thickness and cross-sectional area of the flat membranes,respectively.As for the hollow fiber membranes, the area through which the current passes changes with the membrane radius,the cross-sectional area is the integral of the membrane radius,r1,r2are the inner and outer diameters of the membranes, andAis the surface area of the hollow fiber membranes.

CapacitorCis an impedance equivalent component, and its expression is:

The impedance of a capacitor is related to the frequency. The complex unit indicates that the sinusoidal AC voltage is 90°behind the current.

The theoretical calculation of the hollow fiber membrane capacitance is similar to the resistance,both related to the current path:

wherein ε0is dielectric constant of vacuum, εirelative dielectric constant of the film material.

2.2. Impedance model of spontaneous wetting

The impedance model of a porous membrane is usually represented by an ideal capacitor in parallel with a resistor. Therefore,the theoretical calculation of the impedance of a hollow fiber membrane is:

When wetting happens, the air in the membrane pores is replaced by liquid,so the membrane can be considered as a parallel connection of three parts: wetted pores, unwetted pores, and the polymer body(Fig.1).The impedance value of each part can be calculated by Eq. (10) [17].

3. Experimental

3.1. Chemicals

Hydrophobic PVDF flat membranes (membrane porosity 0.8,average pore radius 0.11 μm, 0.225 μm, 0.325 μm, thickness 90 μm) were provided by Beijing Plastics Research Institute.Hydrophobic PVDF hollow fiber membrane(porosity 0.82,average pore radius 0.08 μm, membrane filament 0.8 mm, inner diameter 1.2 mm outer diameter) were provided by Tianjin University of Technology. Diethanolamine (DEA) was purchased from Tianjin Fuchen Chemical Reagent Factory. Potassium chloride (KCl) and sodium chloride (NaCl) was purchased from Beijing Chemical plant. All the chemical reagents were analytically pure and used without further purification.

3.2. The device built-up

Fig. 2(a) and (b) show the two-electrode devices for measuring the AC impedance of flat membranes and hollow fiber membranes respectively. A flat membrane with a diameter of 1.5 cm was placed at the connection of an H-type electrolytic cell, and two square platinum electrodes were used as the test electrodes(1 cm2); the AC impedance test of the hollow fiber membranes was used the platinum wire electrode with a length of 10 cm, a platinum ring electrode with an inner diameter of 1 cm and a length of 5 cm.The rest of the electrodes are composed of insulating materials that to prevent current from conducting through the electrolyte without passing through the membranes. Connecting the electrolytic cell mentioned before to an electrochemical workstation (Shanghai Chenhua CHI660E) for impedance testing,as shown in Fig. 2(c).

Fig. 1. Impedance model for the porous membrane. : Porosity; :Wetting degree.

Fig. 2. Experimental device diagram.

3.3. Impedance measurement and data fitting

For conducting the variable frequency impedance measurement, membranes were first immersed in 1 mol·L-1DEA solution in different length of time, and then placed in an electrolytic cell.The electrolyte is a 0.1 mol·L-1KCl solution in order to avoid secondary wetting during the measurement. The impedances were measured with a range of 0.1-106Hz, and solution temperature of (20 ± 2) °C. The fitting of the experimental data is based on the equivalent circuit model shown in Fig. 3. The model includes the resistance of the electrolyte which can be represented by an ohmic resistance and a capacitor in parallel (ReandCe); the resistance of the membranes (Rm,Cm); and the diffusion impedance between the solution and the electrode (W). The platinum electrode with smooth and clean surface was used in the measurement system, so the charge can reach the electrode surface without resistance. Therefore, the resistance at the interface between the solution and the electrode can be ignored.On the other hand,high electrolyte concentration without concentration distribution cause no resistance to the solution, so the resistance of the membranes become the main fitting object in this system [1,18-20]. In the spontaneous wetting continuity measurement, the choice of frequency should base on maintaining the angle of phase shift at 0°.

Fig. 3. Equivalent circuit model used to fitting the experimental impedance data.

4. Results and Discussion

4.1. Data fitting and analysis

Fig. 4 shows the impedance results of flat membranes and hollow fiber membranes with different wetting degrees. In this work,the impedance measurements were performed on membranes with initial state of spontaneous wetting (soak in DEA solution for about 5 mins) and equilibrium state (soak in DEA solution for about 24 h), at the same temperature with the electrolyte mentioned above. Table 1 shows the numerical results by fitting the impedance data according to the designed equivalent circuit model. When the membranes were placed in the electrolytic cell and the phase shift is 0°, the platform stage in the Bode diagram shows the frequency-independent resistance value of the membranes,and the impedance value equals the mode resistance value.When the wetting degree increases,the phase shift tends to 0°faster, and the plateau stage remains unchanged over a wide frequency range, which may illustrate that the current hysteresis phenomenon is diminished, so the membrane’s impedance value was the dominant factor. When the spontaneous wetting phenomenon appeared in the early stage, membrane resistance shows a sudden decrease. The reason is that when part of the air in the membrane pores begin to be replaced by the DEA solution,the pores become conductive, proving that spontaneous wetting has occurred. In the process of spontaneous wetting tending to equilibrium, the change in the membrane resistance is relatively small because the large membrane pores in the initial wetting have formed a current path composed of the wetting solution, and the subsequent process increases the cross-sectional area of the current path,but the dominant factor is still the depth of the pathway formed before.In terms of membranes capacitance fitting,the wetting equilibrium membranes capacitance value is higher than the unwetted membranes value, because when the wetting enters the membrane pores, the membrane capacitance obtained by Eq. (9) will increase accordingly. The spontaneous wetting of the membrane can be qualitatively analysed (see Tables 2 and 3).

Table 3 Analysis of unwetted membrane impedance model.

Fig. 4. Bode diagram of AC impedance measurement in each period of spontaneous membrane wetting.

Table 1 Fitting parameters.

Table 2 ElectrTable 2 Electric constant.

The impedance measurement was performed on an empty cell without membranes (0.1 mol·L-1KCl solution). The results are shown in Fig. 3(a).The impedance value of the system is less than 1%of the impedance value of membrane-containing system.So the membrane impedance is the main fitting object in the equivalent circuit and the other impedances in the system could be ignored.To verify whether the fitted results of the simplified circuit model can correctly reflect the real impedance of the membranes, after finding out the electrical constants of each substance (Fig. 2), the Eqs. (6)-(10) were carried out to calculate the impedance of the unwetted hollow fiber membranes theoretically. The results are shown in Fig.3.The comparison results are fitted within the range of the unwetted membranes,which confirm the correctness of the equivalent circuit model and the fitting results used in this paper.

Fig. 5. Continuous impedance measurement of spontaneous membrane wetting.

4.2. Continuity impedance measurement

According to the analysis in Section 4.1, when the spontaneous wetting happens, the change of the membrane resistance is larger than the membrane capacitance, so the membrane resistance can become the main parameter for analyzing the degree of spontaneous wetting.At the same time,the value of the membrane impedance at the phase angle of 0° obtained from the circuit fitting is the same as the actual membrane resistance value, and this platform stage is maintained in a wide test frequency. Therefore, it is ensured that each data point reflects the same properties during the continuous measurement process, the spontaneous wetting of the membranes can be monitored in real time.

Fig. 4 shows the results of continuous impedance measurements with a fixed test frequency. In this system, DEA solutions of different concentrations were used as both an electrolyte and a wetting solution. During the entire measurement, the phase angle of the impedance was close to 0°, which indicates that each data point in the whole process reflects the membrane resistance value. In the test of nearly 700 min, Fig. 4(a) shows that the flat membrane has a larger decrease in resistance value of about 14%in a 1 mol·L-1DEA solution, which means that the wetting rate in a 1 mol·L-1DEA solution is faster than in a 2 mol·L-1DEA solution.The reason is that the viscosity of the high-concentration wetting solution increases greatly, which prevents the liquid from penetrating into the membrane pores.The hollow fiber membrane measurements in Fig.4(b)also show a similar law,and the overall decline in membrane resistance is lower than that of the flat membrane. The reason is that the spontaneous wetting rate of the hydrophobic membrane with the same material is related to the membrane structure parameters such as the pore size,and the hollow fiber membranes used in this experiment has a smaller average pore size, which delays the degree of wetting. In general,during the monitoring process, the decrease in the membrane resistance gradually tends towards balance, and the final impedance value remained at a high level. This is because during wetting process, a small number of membrane pores are completely wetted, current can be transmitted by the wetting fluid; while most of the membrane pores are still occupied by air, this type of membrane pores contribute less to current transfer.For membrane wetting equilibrium state, most of the membrane pores are completely wetted which make the membrane resistance drop to a lower level.

Fig. 6. (a) Continuous impedance measurement of different membrane pore size in 1 mol·L-1 DEA; (b) Continuous impedance measurement of adding inorganic salt in 1 mol·L-1 DEA.

4.3. Application of continuous impedance measurement

The previous section illustrates the theoretical basis and feasibility analysis of the continuous impedance measurement, which proves that this method can be effectively applied to monitor the spontaneous wetting of hydrophobic membranes. This section illustrates the universality of this method.

Fig. 5(a) shows the continuous impedance measurement of flat membranes with different pore diameters in a 1 mol·L-1DEA solution. Larger pores have faster wetting rate, which reflects in the smaller impedance value at the starting point. The impedance of a flat film with a hole radius of 0.225 μm decreases by about 33%which also demonstrates that membranes with larger pore size is wetted faster. The impedance value of the flat membrane with the largest pore size is nearly constant. It may be explained that the excessively large pore diameter makes the spontaneous wetting of the flat membranes approach the equilibrium state faster,resulting in the impedance value change is no longer obvious.

A certain concentration of inorganic salts can suppress spontaneous wetting [24], and the continuous impedance measurement can also respond correctly to this situation.Fig.5(b)shows the continuous impedance test results at a frequency of 0.1 Hz with 0.1 mol·L-1(KCl/NaCl)in a 1 mol·L-1DEA solution.The impedance value applied was maintained at about 1010.3Ω,which is the same as the value of the unwetted membranes in Fig. 3(a). The impedance value provides evidence that the membranes used in this experiment was still unwetted with no spontaneous wetting occurs (see Fig. 6).

5. Conclusions

The obtained impedance test results show strong correlation with the membrane wetting rates with high sensitivity, proving the high responsiveness of the method to small changes during spontaneous wetting in the membrane without intervene.In addition, the equipment was designed for testing the AC impedance spectroscopy of flat membranes and hollow fiber membranes.The impedance data of the membranes is properly fitted,and their accuracy was verified through relevant theories based on the appropriate equivalent circuit.More importantly,a real-time monitoring method was developed for spontaneous wetting process based on AC impedance spectroscopy measurement.Its timeliness,continuity, and effectiveness were confirmed during the experiment of this paper,so it may become a useful tool for better understanding membrane wetting.

Acknowledgements

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

Fanatical support from the National Natural Science Foundation of China(21576011)and the kind supply of electrochemical workstation from Prof. Zhonghua Xiang are gratefully acknowledged.