Direct electronetting of high-performance membranes based on self-assembled 2D nanoarchitectured networks

There is an increasing demand worldwide on advanced two-dimensional (2D) nanofibrous networks with applications ranging from environmental protection and electrical devices to bioengineering. Design of such nanoarchitectured materials has been considered a long-standing challenge. Herein, we report a direct electronetting technology for the fabrication of self-assembled 2D nanoarchitectured networks (nano-nets) from various materials. Tailoring of the precursor solution and of the microelectric field allows charged droplets, which are ejected from a Taylor cone, to levitate, deform and phase separate before they self-assemble a 2D nanofibre network architecture. The fabricated nano-nets show mechanical robustness and benefit from nanostructural properties such as enhanced surface wettability, high transparency, separation and improved air filtration properties. Calcination of the nano-nets results in the formation of carbon nano-nets with electric conductivity and titanium dioxide nano-nets with bioprotective properties.

Due to the tiny weight, the effect of gravity on the dynamic evolution of the studied liquid is negligible; therefore, their ejection modes are mainly driven by the competition between Coulombic repulsion Fe and hydrostatic pressure Fγ (refs 4-6). When > , two distinct ejection modes could occur: jet mode and droplet mode. For the jet mode, a cylindrical fluid (i.e., jet) is assumed to eject from the Taylor cone, which is a common phenomenon during the electrospinning process. The Fγ caused by the surface tension of the fluid can be calculated using the following formula: For simplicity, the charged fluid and external electric field were studied as a closed and independent system. Considering that the conductivity of the receiving substrate would greatly influence the electric field distribution, the correction factor (δ) developed from the relative permittivities of the substrates was introduced to evaluate the contribution of the electric potential, concentrating on enhancing the charge density of the liquids compared with conventional electrospinning. According to classical electromagnetism, the electric field intensity E at the extension cord of the axis of the cylindrical jet can be expressed as: Then, we can deduce the electric potential V and electric energy W at the end of the cylindrical jet: When the charge of the jet remains unchanged while its length increases from l to l + dl, the change in electric energy dW can be expressed as: Based on the work-energy theorem, we can also obtain the dW through calculating the work done by Coulomb repulsion: Then, the Coulomb repulsion Fe can be deduced on the basis of Supplementary Equations (6) and (7): In addition, the mass of the studied cylindrical fluid m is: Therefore, the jet threshold can be deduced on the basis of Supplementary Equations (1), (2), (8) and While for droplet mode, the Fγ of the droplet can be calculated by: Then, the electric field intensity E can be deduced according to Gauss's law: And the electric energy (W) at the surface of the charged droplet and its change (dW) when the radius is increased from R to R + dR can be obtained: Based on the work-energy theorem, the dW can also be calculated: Thus, Additionally, the mass of the charged droplet m is: Similarly, the droplet threshold can be deduced on the basis of Supplementary Equations (1), (10), (15) and (16):

Supplementary Discussion
The possible formation process for 2D self-assembled nano-nets.
Mother Nature's legacy not only makes Voronoi cells visible in nature, as in dragonfly wings, turtle carapaces and honeycombs, but shows ordered dynamic evolution phenomena as well. To decrease the entropy similarly to Rayleigh-Bé nard convection, many dissipative structures form, for instance, naturally growing snow crystals and levitating clusters of water droplets in clouds or on a heated water surface. Here, our obtained nano-nets may be regarded as another similar case. By revealing the deformation and self-assembly of the charged droplets during direct electronetting, we proposed a possible formation process for 2D nanofibrous networks. The schematic showing this process is illustrated in Supplementary Fig. 3. During direct electronetting, abundant charged droplets were ejected from Taylor cone and flew with a high speed toward the collector, which could be regarded as a levitating cluster within a stable and continuous process. The levitating droplets repelled with each other and powered by the electric field gradient, underwent rapid self-assembly of their spatial position based on dissipative effect to achieve an energy/material minimum state. Meanwhile, rapid stretching deformation occurred in the droplets flying toward the topographically structured collectors due to the electrostatic force stemming from the differential microelectric fields (Fig. 1d).
This deformation and deposition driven by microelectric fields were a common phenomenon for patterning of electrospun fibres, and have been widely used to tailor nanofibre structures for some special applications. Further stretching and solvent evaporation might result in the connection of adjacent deformed droplets to reduce the surface energy of the whole droplet cluster. Thus, nanofibre membranes with ideal or weighted 2D networks (i.e., nano-nets or beaded nanofibre nets) were obtained after evaporation of the solvent phase and solidification of the polymer phase.

The effect of solution systems on the formation of 2D self-assembled nano-nets.
In addition to the collectors, the solution system was also an important factor that greatly influenced the formation of the self-assembled architectures; therefore, we also established the numerical prediction diagram for various PVDF/LiCl solutions with different components and concentrations for direct electronetting, as illustrated in Supplementary Fig. 4.  Table 3 and Supplementary Note 1).
In addition to solution concentration, the effect of molecular weight on the formation of 2D selfassembled nano-nets was also investigated. Typical SEM images of the nano-nets formed from PVDF solutions with different molecular weights are illustrated in Supplementary Fig. 6a-d. Besides the molecular weight, these four membranes are fabricated using the same solution concentration, processing conditions and deposition duration. Obviously, almost all the membranes exhibited 2D network structures. With increasing the molecular weight, the deposition density of the nanofibrous networks decreased significantly, resulting in an obviously increased pore size of the membranes. As shown in Supplementary Fig. 6f, an increase in the molecular weight from 320,000 to 1,100,000 caused a sharp increase in the pore size of the resulted membranes from 120 to 310 nm. This result can be ascribed to the change of charge density of the liquid, which greatly affects the formation efficiency of the droplets during direct electronetting process. As illustrated in Supplementary Fig. 6e, the PVDF solutions with lower molecular weight are usually much easier to be charged and would carry more charges. For example, the charge density of liquid from PVDF solution with molecular weight of 320,000 is ~37 c kg -1 , while that of the solution with molecular weight of 1,100,000 is ~26 c kg -1 . And this increased charge density would enhance the formation of charged droplets and then lead to more deposition of the nanofibrous networks in the same electronetting duration. Meanwhile, from the SEM images we can see that, the number density of beads on the fibres obviously decreased with increasing the PVDF molecular weight. This phenomenon could be attributed to the better molecular entanglement of higher molecular weight, which can facilitate the formation of uniform jets during electrohydrodynamic process.
As observed in Supplementary Fig. 7a-

Large-area fabrication of 2D self-assembled nano-nets.
With respect to the large-area fabrication, even industrial process, two important issues should be carefully considered: raw materials and fabrication process. Here, raw materials are commercialized with low cost. Because of the simplicity of the one-step self-assembly process of our methodology and the facile availability of the designed precursor solutions and collectors, we think large-scale fabrication of 2D nano-nets was possible. Actually, using our lab equipment (DXES-V spinning machine, SOF Nanotechnology Co., Ltd., China), we could easily obtain an uniform nano-net membranes with an area of 55 × 70 cm 2 using 3 syringes and a collecting roller (length of 60 cm and diameter of 24 cm), as shown in Supplementary Fig. 9. And we have confidence in the fabrication of nano-net membranes with larger area using more syringes and larger collector.

Crystallinity of the PVDF nano-net membranes.
PVDF, as one of the semicrystalline thermoplastic polymers, has been found to have a strong piezo, pyro, and ferroelectric property, and its piezoelectric coefficient is almost 10 times larger than other polymers 7 . PVDF has five crystalline phases: non-polar α-phase and ɛ-phase, as well as polar β-phase, δ-phase, and γ-phase, in which the β-phase can lead to the highest permanent dipole and then improve piezoelectric property. The electrical poling and stretching processes usually can align the dipoles in the crystalline PVDF structures to facilitate the formation of β-phase. Here, we also investigated the influence of electronetting process on the PVDF crystallinity. The FTIR spectra of the PVDF powder and the nano-net membrane are shown in Supplementary Fig. 13a. Obviously, the bands at 840 and 1278 cm -1 which correspond to the β phase can be observed for the nano-net membrane.
We further calculated the relative content of α and β polymorphs using the following equation:

Surface roughness of the PVDF nano-nets.
The material hydrophobicity is usually due to hierarchical micro/nanostructures. In this work, we have performed AFM observation of the PVDF nano-nets, the result is shown in Supplementary Fig.   14a and b. The AFM measurement was performed using an NT-MDT Ntegra AFM equipped with polysilicon lever with a monocrystal silicon tip (tip curvature radius <10 nm). Cantilever type is length of 94 μm, width of 34 μm, thickness of 1.85 μm, force constant of 12 N m -1 , resonant frequency of 235 kHz. And the AFM mode used during the experiment is tapping mode. Here, the used PVDF nano-net samples for AFM testing were collected using SiO2 wafer, which is a kind of dielectric film without porous structure (similar as the substrate of paper used in this work). Due to lack of the microelectric field, we only got the broken nanofibres and microspheres on the SiO2 wafer; and the fibres typically can not tightly attach on the wafer. Therefore, during the AFM testing, the tapping of the tip easily caused the moving of the tiny nanofibre with diameter of ~40 nm, leading to an image which is not clear enough to check the roughness on the single nanofibre surface (Supplementary Fig. 14a). While, obvious roughness on a larger scanning area can be found on the SiO2 wafer, which is due to the deposition of the PVDF nanofibres ( Supplementary Fig. 14b). To further check the surface roughness on single nanofibre in the nano-nets, we have also performed the high-resolution FE-SEM imaging.
As illustrated in Supplementary Fig. 14c, dense and obvious bulges or wrinkles formed on the surface of PVDF nanofibres, which can be attributed to the fast phase separation and solidification of the charged liquid during direct electronetting 8,9 . These nanostructures on fibre surface were beneficial for enhancing the surface roughness and creating hierarchical structure, and then resulted in an enhancement effect for the hydrophobicity of PVDF nano-nets.

Quality factor of 2D nano-net air filters.
In general, the quality factor (QF) is an important trade-off indicator to evaluate the filtration capacity of air filters based on their removal efficiency and air resistance and can be defined by the formula: QF = −ln(1 − η)/Δp, in which the η is the removal efficiency and the Δp is the pressure drop [10][11][12][13] . From Supplementary Fig. 15, we can find that, upon increasing the base weight of the nano-net filters, their QF for the removal of PM with various sizes gradually decreased. This result could be due to the increased packing density of the nano-net filters with higher base weights. However, all QF values of the nano-net air filters maintained high levels for PM0.3, PM1 and PM2.5 removal when compared with commercial air filters or electrospun nanofibre membranes. For instance, the QF values were in the ranges of 0.22−0.4 Pa -1 for PM0.3 removal, 0.3−0.9 Pa -1 for PM1 removal, and 0.6−1.3 Pa -1 for PM2.5 removal. Commercial materials with macrosized diameters (for example, melt-blown fibres and glass fibres), although they can achieve a similar removal efficiency by virtue of the electret effect and the unlimited increase of basis weight (>100 g m -2 , even nearly 300 g m -2 ), still suffer from the low QF level owing to high air resistance and the potential safety hazard due to electret degradation.
Therefore, our novel nano-net filters stand out from all other existing HEPA filters by virtue of their superlight weight of ~80 mg m -2 and extremely high QF values as a HEPA or ULPA filters, fully supporting intriguing potential applications in the fields of high-performance respirators, filter canisters, engine intakes, appliances, medical equipment, and cleanrooms.

Removal of PM and bacterium using 2D nano-nets.
Supplementary Fig. 16a shows the PVDF nano-net membrane after filtrating NaCl PM. Almost all PM particles were captured and gradually accumulated on the membrane surface; even the smaller ones (PM0.3) were effectively trapped by the networks (the inset of Supplementary Fig. 16a). Obviously, the completely covered nanofibrous networks with small pore size successfully eliminated the leaking of almost all PM particles, while having a lighter weight and thinner thickness than most of existing cutting-edge nanofibre filters. Moreover, the SEM observation of bacterium removal pre and post killing process using TiO2 nano-net membrane is also conducted, the resulted images are illustrated in Supplementary Fig. 16b and c. Abundant S. aureus particles with diameters of ~0.8 μm were captured on the top surface of TiO2 nano-net membranes. And then the bacteria were effectively killed after contacting with anatase TiO2 (Supplementary Fig. 20), meanwhile, the killed-bacteria were continuously attached and filtered by the nano-nets with small pores, avoiding the re-pollution of the pathogens. More interestingly, all the membranes well maintain their structural integrity during the filtration process with high airflow or liquid stream, further confirming the robust mechanical property of the self-assembled nano-nets.

Comparison of electrical conductivity of electrospun PAN based carbon nanofibres and carbon nano-nets.
As illustrated in Supplementary Fig. 19, compared with most of existing electrospun PAN based carbon nanofibre membranes (1-150 S cm -1 ), the single carbon nanofibre showed the increased conductivity of 100-450 S cm -1 due to the lack of conductive path between isolated nanofibres [14][15][16][17][18] . In contrast, our resultant carbon nano-nets fabricated by carbonization of PAN nano-nets could achieve 39 electrical conductivities ranging from 180 to 750 S cm -1 , indicating the promising potential application in supercapacitors, batteries, sensors, electromagnetic interference shielding, electrostatic discharge protection.

Crystallinity of the TiO 2 nano-nets.
We have analyzed the crystalline phases of the TiO2 nano-net membrane using XRD, the result is illustrated in Supplementary Fig. 20. Obviously, all the diffraction peaks could be assigned to the anatase phase of TiO2, which typically has robust antibacterial capacity. Combined with the large surface area and ultrathin thickness, this anatase phase allowed the TiO2 nano-nets to rapidly kill the S. aureus with a high killing efficiency of 99.99% while having only 1/10 weight of most existing antibacterial nanofibres 19 .

Supplementary Methods
Simulation of electric field of the direct electronetting.
The finite element simulation of the electric field during direct electronetting was performed using Optical transmittance measurement of the nano-net air filters.
The optical transmittances of the free-standing PVDF nano-net air filters were measured using an Ideaoptics IS-30-6-R integrating sphere attached to the PG 2000+ fibre optic spectrometer. The wrinkle-free nano-net filter samples were first peeled off from the PAN fibre membranes and then placed tightly on a glass slide. Afterward, we placed them in front of the integrating sphere, and the same glass slide was used as the control. Therefore, both the specular transmittance and the diffuse transmittance were included for this measurement. The transmittance spectrum was then tested by the solar spectrum from 400 to 780 nm to obtain the average transmittance.

Filtration measurement of the nano-net air filters.
We used the LZC-K filter tester (Huada Filter Technology Co., Ltd.) to evaluate the filtration performance of the nano-net air filters. A 2 wt% NaCl aqueous solution was used to process the aerosol particles with diameters of 0.3−10 μm and a geometric standard deviation of <1.86 using the QRJ-1 NaCl atomizer. The membranes were clamped onto the filter holder with an area of 100 cm 2 . Then, 300,000−500,000 charge-neutralized solid NaCl aerosol particles, which can be generated by the atomizer, were delivered through the testing filter by the air pump. Note that these particles were neutralized using an electrostatic neutralization device and could pass through the filter steadily and uniformly. The removal efficiencies of the filters were measured by two laser particle counters, which can detect the number of PM particles in the upstream and downstream of the particle airflow. The detection limit of this filter tester can achieve 0.0001%, meaning that filtration efficiencies of 99.9999% can theoretically be tested. To ensure the accuracy of the results, here, we recorded only data with a precision of 0.001%. The pressure drops of air filters could also be collected using two electronic pressure transducers. All tests were conducted at room temperature, 25 ± 2 °C, and a relative humidity of 40−50%.
The long-term PM purification test concerning smoke PM2.5 and PM10 was performed in a 0.1 m 3 enclosed cabin using the nano-net filter with a >99% removal efficiency and a 20 Pa pressure drop for PM0.3 capture. Here, the model PM particles were generated by burning cigarettes and showed a broad diameter distribution from <0.3 μm to >10 μm, and most were in the range of <1 μm. Then, an artificial environment in which the air was severely polluted (PM2.5 concentration >500 μg m -3 and PM10 concentration >700 μg m -3 ) could be created, and the air could be fed through our nano-net filters with an area of ~25 cm 2 under a continuous airflow of 14 L min -1 using an axial fan. The real value of PM2.5 and PM10 concentrations can be tested using a detection instrument (SDL 301, Nova Fitness). We recorded the PM2.5 and PM10 concentrations once per minute until they decreased to 35 μg m -3 . The long-term recycling performance was evaluated by testing for 15 cycles.
Cycling separation measurement of the nano-net membranes.
To exam the reusability of our PAN nano-net membranes, a cycling separation for TiO2 suspension was performed using the dead-end filtration device. With this device, the prewetted PAN nano-net membrane was fixed, and the 100 ppm TiO2 nanoparticle (diameter 200-400 nm) suspension was kept pouring into the top tube to test the performance of the membranes (Supplementary Fig. 18).
We recorded the initial and final rejection efficiencies and permeation fluxes of each cycle (10 min) and then backwashed the membrane with clean water 2 times before the next cycling test. The whole cycling process lasted for 50 min.

Bioprotective activity evaluation of the nano-net membranes.
A clinical isolate of Staphylococcus aureus (S. aureus, SA 1004) obtained from Ruby Memorial Hospital (Morgantown, WV, US) was first cultured in tryptic soy broth (TSB) for 16 h at 37 °C and then diluted with fresh TSB and cultured in at 37 °C for an additional 3 h to achieve log-phase growth.
Next, 5 ml inoculum with a concentration of ~1.0 × 10 8 CFU ml -1 was fed through our TiO2 nano-net membranes or electrospun TiO2 nanofibre membranes, and the feed and filtrate inoculum were diluted in sterile Dulbecco's phosphate buffered saline (PBS, pH = 7.0), plated on 5% sheep blood agar plates, and incubated for 24 h at 37 °C. Then, the S. aureus removal efficiency could be calculated by dividing the difference between the number of colony forming units (CFUs) in the feed and that in the filtrate by the number of CFUs in the feed and then multiplying the result by 100. After air-drying for 2 min, the membrane filters used for filtering the S. aureus inoculum were treated in three ways: (i) immediately immersed in 3 ml PBS and sonicated for 2 min, (ii) placed under UV light of 312 nm (6 absence of light for 30 min, then immersed in 3 ml PBS and sonicated for 2 min. Then, 400 μl medium from each of these three solutions was taken out, plated on 5% sheep blood agar plates and incubated to inspect the S. aureus contact killing efficiency.