Effects of filter structure, flow velocity, particle concentration and fouling on the retention efficiency of ultrafiltration for sub-20 nm gold nanoparticles

Separation and Purification Technology 241 (2020) 116689

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Effects of filter structure, flow velocity, particle concentration and fouling on the retention efficiency of ultrafiltration for sub-20 nm gold nanoparticles

T

Handol Leea, Doris Segetsb, Sebastian Süßc,d, Wolfgang Peukertc,d, Sheng-Chieh Chene, , David Y.H. Puia ⁎

a

Particle Technology Laboratory, Mechanical Engineering, University of Minnesota, 111 Church St., S.E., Minneapolis 55455, USA Process Technology for Electrochemical Functional Materials, Institute for Combustion and Gas Dynamics-Reactive Fluids, and Center for Nanointegration Duisburg-Essen (CENIDE), University of Duisburg-Essen (UDE), Carl-Benz-Straße 199, 47057 Duisburg, Germany c Institute of Particle Technology (LFG), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Cauerstraße 4, 91058 Erlangen, Germany d Interdisciplinary Center for Functional Particle Systems (FPS), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Haberstraße 9a, 91058 Erlangen, Germany e Department of Mechanical and Nuclear Engineering, Virginia Commonwealth University, 401 West Main St., Richmond, VA 23284, USA b

ARTICLE INFO

ABSTRACT

Keywords: Ultrafiltration Fouling effects Concentration effects Diffusion deposition Surface interactions

Ultrafiltration techniques with membranes of pore sizes under 100 nm have been widely applied in drinking water, wastewater, semiconductor and pharmaceutical process water treatments for nanoparticle (NP) and pathogen removal. The most direct way to evaluate the membrane performance is to experimentally obtain the size fractional retention efficiency. However, the real-life performance of the membrane in terms of fouling (or loading) characteristics and the effects of the concentration of challenging particles and rate of flux (or filtration velocities) on the filtration efficiency during fouling have not been well understood. In this study, systematic filtration experiments for filtration efficiency at clean and loaded conditions were conducted for three different 50 nm rated membrane filters, including PTFE (Polytetrafluoroethylene), PCTE (Polycarbonate Track-Etched) and MCE (Mixed Cellulose Ester) membranes, against 5, 10 and 20 nm Au NPs at different feed concentrations and fluxes. The results showed that the effects of feed concentration and flux are significant. This study provides important insights of retention mechanisms and efficiency for different ultrafiltration membrane structures at varied filtration velocities and fouling characteristics giving clear directions of future NP ultrafiltration research.

1. Introduction

viruses, typically with small sizes clearly below 100 nm, is also important for providing safe water sources [19–22]. Here, Au and Ag NPs have been applied as well as model particles in the virus filtration tests [19,21]. Moreover, NP removal is an important routine procedure in the semiconductor manufacturing industry. Due to the reduced feature sizes down to sub-10 nm, an effective removal of sub-10 nm NPs in process water and chemicals has been in great demand for avoiding defects of photomasks and wafers. According to ITRS (International Technology Roadmap for Semiconductors), the criteria for the critical particle sizes for ultrapure water are set to 10 nm and 5 nm in 2017 and 2021, respectively. In terms of small NP removal for industrial purposes as well as for the virus mitigation in water plants, liquid filtration using membrane filters has been considered to be an efficient treatment, especially using ultrafiltration and nanofiltration techniques [19,21–27]. To determine the quality of membrane filters, the pore size of the

Due to the high surface to volume ratio, nanoparticles (NPs) are usually very reactive and catalytically active. This results in dramatically increased demands of engineered nanomaterials in many nanotechnology-based applications [1,2]. Especially techniques producing small NPs with particle sizes less than 20–30 nm have been intensively researched and developed [3–8]. With the wide usage of small NPs, however, increased risks and new hazards to the environments have to be entailed [9–12]. Release of engineered NPs during manufacturing and/or from commercially available consumer products into water environments including groundwater, surface water, synthetic freshwater and tertiary wastewater effluent was studied with an emphasis of the importance to mitigate NPs in the sources of drinking water [13–18]. In addition to engineered NPs, the control of pathogens, e.g., ⁎

Corresponding author. E-mail address: [email protected] (S.-C. Chen).

https://doi.org/10.1016/j.seppur.2020.116689 Received 21 August 2019; Accepted 8 February 2020 Available online 08 February 2020 1383-5866/ © 2020 Elsevier B.V. All rights reserved.

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filter is usually considered as an important parameter because particles larger than the pore size are expected to be retained [28]. Thereby the pore size distributions of most membranes applied on technical scale are usually reduced to one distinct nominal pore size. However, already in the 1990 s, it has been found that nominal pore sizes do not correlate well with the expected retention efficiency [28,29]. To determine the pore size distributions of membranes, researchers applied Au or Ag NPs to measure the retention efficiency of the membranes assuming size exclusion as the only prevailing retention mechanism [19,21]. However, analytical centrifugation in combination with Brownian dynamics simulations revealed that the transport of small NPs, especially below 20 nm is more and more governed by diffusion and the permeate quality may not be correlated well with the pore sizes determined by size exclusion [30]. Moreover, the retention of small NPs depends not only on the pore size but effects of surface interactions [19,31]. Thus, for the time being, the most efficient and accurate way of evaluating the quality of membrane filters for NPs is to perform filtration experiments to measure the particle retention efficiency directly. However, there is a lack of standard methodologies for measuring the size and (low) concentration of very small NPs, e.g., sub20 nm, in the filter upstream and downstream for obtaining the size fractional efficiency of membranes. One of the currently available detectors is the liquid-borne particle counter which is based on light scattering. However, due to the low light scattering intensity of small particles in the Mie/Rayleigh regime, the counter has limited detection sensitivity for all kinds of NPs below 100 nm [32]. This limitation holds for all instruments that are based on light scattering, e.g., turbidimeter or nephelometer. Recently, ultrafiltration membranes have been frequently evaluated with NPs smaller than 30 nm and the retention efficiency was analyzed by means of spectrophotometers such as UV/vis or fluorescence spectrophotometers. Thus, absorption and/or emission properties of the particles was used instead of scattering [27,33–35]. However, the detection capability of small number concentrations is still limited. Regarding studies on filtration performance for small NPs, Striemer et al. [36] developed a free-standing, ultrathin porous nanocrystalline silicon membrane with a thickness of only 15 nm. Then, Gaborski et al. [33] characterized properties of this membrane using Au NPs with sizes ranging from 5 to 30 nm, showing an excellent performance in sizeexclusion separations. Wu et al. [35] performed filtration tests of fluorescent CdTe quantum dots with sizes ranging from 1.5 to 4.5 nm. They examined several membranes with the minimum pore size down to 1.6 nm. Another filtration test also used sub-10 nm Cd-based quantum dots to evaluate sub-10 nm pore size membranes [34]. However, all abovementioned studies on ultrafiltration and nanofiltration focused on membrane filters with pore sizes comparable with the dimensions of the challenging NPs. Moreover, they used relatively high concentrations of NPs around 50 mg/l that were required for spectrophotometric analysis. Therefore, the underlying separation mechanisms are mostly standard sieving followed by cake formation. In contrast, to verify the effect of diffusion on the retention efficiency, Chen et al. [27] recently reported a study on ultrafiltration where sub-50 nm Au NPs and sub-10 nm ZnO and ZnS quantum dots were used to challenge membranes with relatively large pore sizes of 50–400 nm. The filtration tests were performed with varying feed concentrations ranging from 500 to 2000 mg/l and 25 to 200 mg/l for Au NPs and quantum dots, respectively. In the tests of challenging 50 nm rated PCTE (polycarbonate track-etched) membranes with 12.4 and 34.4 nm Au NPs, they found that increasing feed concentration resulted in enhanced retention due to multiple particles entering the same pore and blocking the pore at this concentration range. On the contrary, the filtration of 1.7 and 6.6 nm quantum dots through large pore size membranes showed that retention efficiency increased with decreasing feed concentration. Here we claimed that an even much higher efficiency could be achieved in the presence of lower feed

concentrations, however without being able to prove this hypothesis due to the aforementioned detection limits of absorption spectroscopy that was used for analysis. Thus, the main conclusion of the work of Chen et al. [27] was that NP filtration tests should be performed in the lower feed concentration range to better understand the complex interplay between diffusion, membrane structure, particle and pore size distribution and fouling and their combined effects on filtration performance. In this study, the filtration efficiency of three different membranes, including PTFE (Polytetrafluoroethylene), PCTE and MCE (Mixed Cellulose Ester) membranes with the same nominal pore size of 50 nm was examined by challenging them with sub-20 nm Au NPs at different feed concentrations and fluxes. By strictly choosing particle to pore diameter ratio (PPD) below 1, the membrane performance with regard to particle adsorption was systematically studied to unravel the effects of different parameters such as feed concentration, membrane structure and surfactant concentration. The lowest feed concentration for each particle size was around 0.1, 1.36 and 5.3 mg/l for 5, 10 and 20 nm Au NPs, respectively and thus several orders of magnitude lower than the usually analyzed filtration conditions. Particle concentrations were measured by the newly developed electrospray-scanning mobility particle sizer (ES-SMPS, model 3480 and 3936, TSI Inc., Shoreview, MN), which enabled for the first time to investigate filtration performance at these low concentration ranges for such small particles [31,37]. The aim of this study is to better understand the complex NP retention on the dependence of feed concentration and particle fouling (or loading) which is the inevitable fate of all liquid membranes [21,38,39]. 2. Materials and methods 2.1. Particle and filter system Throughout the whole study, challenging particles were commercially available 5, 10 and 20 nm Au NPs purchased from Ted Pella (Ted Pella Inc., Redding, CA, USA). The Au NPs were stabilized with tannic acid as surface ligand and were all negatively charged. Zeta potentials of the Au NP samples were measured using the Stabino Zeta Potential Analyzer (Particle Metrix GmbH, Meerbusch, Germany). The average values of zeta potentials for 5, 10 and 20 nm Au NPs were −63.1 ± 1.2, −63.5 ± 1.9 and −70.4 ± 2.0 mV, respectively, measured at pH ~7. These high values indicated very stable dispersions, although zeta potential is known to be not a universal measure for colloidal stability of such small NPs [40]. As test filters, 25 mm diameter Gore® PTFE (W. l. Gore & Associates, Inc., Newark, DE), Whatman® PCTE (GE Healthcare Biosciences, Pittsburgh, PA) and Millipore® MCE (EMD Millipore Inc., Darmstadt, Germany) membranes were applied. A general impression of the membrane structure of the clean filters was obtained by scanning electron microscopy (SEM, Hitachi S-4700, Japan) as shown in Fig. 1. For comparison of the detailed pore structure and pore size distribution, the same magnification of ×50,000 was used for all three filters prior fouling (or loading). Both, PTFE and MCE membranes consist of strongly interconnected networks with comparatively broad pore size distributions (Fig. 1a and c), while the PCTE membranes are filters with non-connected microscopic cylindrical holes (tubes) leading to a narrow pore size distribution (Fig. 1b). Table 1 summarizes the detailed information of the filter media tested in this study. The hydrophobic PTFE membranes were pre-wetted in 2-propanol (> 99.5%, Avantor Performance Materials, Center Valley, PA) over 30 min before conducting filtration tests. This was necessary to assure pre-wetting of the filter with a water-based solution to ensure that the aqueous Au NP suspension is not repelled. In contrast, the PCTE and MCE membranes are hydrophilic so they could be used as received without any pretreatment. As mentioned, all three different filter media have the same nominal pore size of 50 nm provided by the 2

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Fig. 2. Dead-end and constant flux filtration setup.

2.2. Filtration setup and filtration procedure Filtration experiments were conducted in a dead-end filtration mode as shown in Fig. 2. Prior to each experiment, 500 ml ultrapure water (18 MΩ cm resistivity ultrapure water, Milli-Q system, EMD Millipore Corp., Billerica, MA) was introduced to each filter installed in a 25 mm filter holder by a peristaltic pump (Cole Parmer Masterflex L/S, Vernon Hills, IL). This was required to clean any surface preserving agents and impurities until the number concentration of the downstream water was assured to be with acceptable low particle concentration, i.e., no particles measured by the ES-SMPS. More details of ES-SMPS will be shown later. Then, the Au NP suspension under investigation was introduced under the respective experimental conditions, i.e., defined flow rate and particle concentration. The peristaltic pump was used for the filtration experiments to provide a constant flow rate of Au NP suspension after carefully checking that the little pulsation inevitably originating from the peristaltic pump had no impact on the filtration results. This means all experiments were performed under constant flux mode and the pressure difference was measured over the duration of each experiment. Therefore, the face velocity toward the filter media was kept constant even though the pressure drops across the filters were different between the experiments. For orientation, at a water flux of 158 l/m2·h (lower flux, 0.00439 cm/s, or 1 ml/min through the filter), the average pressure drops across the clean PTFE, PCTE and MCE membrane filters were 0.083, 1.03 and 0.75 bar, respectively. The pressure drop at higher water flux of 1580 l/m2·h (0.0439 cm/s, or 10 ml/min through the filter) was found to be over 3 bar for the PCTE and MCE membrane filters whereby the highest pressure drop was measured for the PCTE membrane filter due to the considerably low porosity even though it had the lowest thickness. Along the same line, due to its relatively high porosity and low thickness, PTFE showed the lowest pressure drop amongst all three membranes. Table 2 summarizes the matrix of the applied experimental conditions. In order to understand the effect of particle feed concentration and filtration velocity on filtration performance, two different particle feed methods, in terms of varied (labelled as “A”) and constant (labelled as “B”) particle feed concentration, and two different flow rates (labelled as “1” for low flow speed, i.e., 1 ml/min, and “2” for high flow speed, i.e., 10 ml/min), were conducted. It should be already noted here that the Au suspension with a higher particle concentration also contained a larger amount of free surfactant molecules in solution

Fig. 1. SEM images of clean (a) PTFE, (b) PCTE and (c) MCE membrane filters.

manufacturers. According to the manufacturer and in line with the images from Fig. 1, the porosity of the PCTE membrane is much lower than those of the other two. For the thickness, to be mentioned, the major PTFE membrane is thin but it is usually supported with a thick layer of very coarse fibers. Therefore, the overall thickness of the PTFE membrane shown in Table 1 is as thick as MCE. Nevertheless, the coarse layer contributed negligibly to pressure drop and particle retention, so it is excluded in the following discussion of particle retention analysis. Table 1 Filter media and filtration flux information. Membrane

Material (wettability)

Mean pore size [nm]

Porosity [%]

Thickness [µm]

Water flux [l/m2·h] (flow rate)

PTFE PCTE MCE

Polytetrafluorethylene (hydrophobic) Polycarbonate (hydrophilic) Cellulose acetate & cellulose nitrate (hydrophilic)

50

60 1.2 72

120 6 100

158 (1 ml/min)

3

1580 (10 ml/min)

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Table 2 Filtration conditions and final cumulative number of Au NPs used to challenge the filters (i.e., cumulative particle number, CPN). A and B denote varied and constant Au feed concentration, respectively, and 1 and 2 denote low and high filtration flux, respectively. Flow rate [ml/min]

Au NP size [nm]

Liquid-borne particle concentration [#/ml](volume)

Case A1 Case A2

1 10

5 10 20

1 × 1011 (30 ml) 8 × 1010 (30 ml) 8 × 1010 (20 ml)

Case B1 Case B2

1 10

5 10 20

1 × 1011 (800 ml) 8 × 1010 (600 ml) 8 × 1010 (200 ml)

because of the lower dilution of the original Au NPs purchased from the manufacturer with ultrapure water. In cases A1 (varied feed concentration with low flow rate) and A2 (varied feed concentration with high flow rate), first a defined volume of NP suspension with the lowest concentration was introduced to the filter media, followed by the introduction of a second defined volume with medium concentration and a third defined volume with the highest concentration. In contrast, for cases B1 (constant feed concentration with low flow rate) and B2 (constant feed concentration with high flow rate), suspensions with a fixed concentration corresponding to the lowest particle concentrations of cases A1 and A2 were prepared and used to challenge each filter with the same total amount of particles having passed through the filter at the end of the experiment as in cases A1 and A2, respectively. Thus, for every particle size, the cumulative particle number (CPN), i.e., the total number of particles used to challenge the membrane along the whole cycle of each filtration test (i.e., until the end of each filtration experiment) was in a similar range, however, with varying fouling (or loading) history. As only exception, for 5 nm Au NPs, we aborted the experiment and conducted a lower final CPN for case B (i.e., 8.0 × 1013) than that of case A (i.e., 7.2 × 1014) due to the extremely long duration time of the experiments with over 120 h, which directly followed from the low flow rate of only 1 ml/min. During each filtration experiment, ~2 ml of suspension downstream the filter samples were collected in a separate centrifuge tube at defined time intervals and analyzed for the underlying particle number concentration. This allowed analysis of filtration efficiency over time with high resolution over the entire fouling tests. The collected downstream samples and three to five upstream samples were stored in a 5 °C refrigerator before the analysis to inhibit any microbial growth and agglomeration of Au NPs. It should again be noted that due to the large volume of suspension (200–800 ml) and low flow rates (down to 1 ml/ min), the duration of the filtration experiments was around three to ten hours for case B1. Therefore, checking the upstream concentration during the long experimental period was seen to be indispensable ensuring that no adhesion of the particles to vials and tubing or secondary processes like agglomeration did occur. We collected and analyzed the upstream samples every one or two hours until the filtration tests were totally completed. It was found that the concentration of upstream samples stayed nearly constant. The whole experimental process was repeated three times for all combinations using cases A1, A2 and B1 (i.e., three particle sizes, three filters and three cases, thus a total of 27 experiments and 54 repeats) and all combinations using case B2 (i.e., 10 nm Au NP through PCTE and MCE filters, thus two experiments and four repeats) to obtain statistically reliable results.

4 × 1012 (30 ml) 5 × 1011 (30 ml) 3 × 1011 (20 ml)

CPN [–] 2 × 1013 (30 ml) 3 × 1012 (15 ml) 8 × 1011 (10 ml)

7.2 × 1014 6.2 × 1013 1.6 × 1013 8.0 × 1013 4.8 × 1013 1.6 × 1013

Fig. 3. ES-SMPS setup for particle concentration measurement.

particles by pushing the liquid through a capillary tube and exerting an electric field at the capillary tip. The liquid jet formed at the capillary tip is broken down into charged droplets by the Coulombic force. Then, the droplets containing particles, with one particle in one droplet, flow along with sheath air and the liquid evaporates before particles exit ES. Unlike the conventional nebulizer (e.g., Collison atomizer), the size distribution of dispersed liquid droplets from ES is very narrow and can be controlled by the electrical property of solution and liquid feed rate through the capillary tube. In the operation, the sheath air flow rate was maintained at 2 l/min and the capillary tube with an inner diameter of 40.1 µm was used. We applied 2 psig (13.79 kPa) chamber pressure for 5 nm Au NPs and 3 psig (20.68 kPa) for 10 and 20 nm Au NPs. The liquid feed rates through the capillary tube at the 2 and 3 psig chamber pressures were measured to be 0.128 and 0.191 µl/min, respectively. The applied voltage with 2–2.5 kV in ES was found to form the cone-jet mode, which is considered to be a proper dispersion mode of the liquid jet at the capillary tip. The collected liquid samples should have the proper electrical conductivity to be dispersed by ES, which was set to be around 1,000 µS/cm by adding ammonium acetate according to Lee et al. [37]. The size distribution of dispersed NPs was measured by the SMPS consisting of an electrostatic classifier (EC, model 3082, TSI Inc., Shoreview, MN), a nano-differential mobility analyzer (Nano-DMA, model 3085, TSI Inc., Shoreview MN) and an ultrafine condensation particle counter (UCPC, model 3776, TSI Inc., Shoreview MN). Sheath air and aerosol flow rates through the Nano-DMA were set to 15 and 1.5 l/min, respectively. 2.4. Particle size distributions (PSDs) Fig. 4 shows the particle size distributions (PSDs) of Au NPs as they were measured by ES-SMPS. Residue particles around 4 nm were formed during the evaporation when producing droplets which contained no Au NPs. These were caused by impurities and stabilizing chemicals in the liquid phase. For accurate measurements of Au NP concentrations it had to be ensured that these undesirable residue particles did not interfere with the PSD of Au NPs. Due to the relatively small size of dispersed droplets from the ES, the size distribution of residue particles can be controlled in the smaller size range (xmax < 5 nm), as shown in Fig. 4, completely baseline separated with

2.3. Particle concentration measurement Fig. 3 depicts the schematic of the experimental system for particle concentration measurement using ES-SMPS. The ES-SMPS method for liquid filtration application has been developed and details can be found elsewhere [37]. In brief, the collected suspensions of Au NPs were dispersed by ES, which converts the liquid sample to aerosol 4

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particle detection for the ES-SMPS method and thus reduces the required liquid-borne particle concentrations. However, a higher chamber pressure also produces larger residue particles due to the larger droplets dispersed from ES [37,41]. These larger residue particles can interfere with the Au NPs to be classified. We tried to distinguish the 5 nm Au NPs from residue particles clearly by using a chamber pressure of 2 psig (13.78 kPa) as shown in Fig. 4a. However, because the PSDs of the 10 and 20 nm Au NPs are reasonably far away from that of the residue particles, an even larger chamber pressure of 3 psig (20.68 kPa) could be used for the 10 and 20 nm Au NP cases, respectively (Fig. 4b and c). The ES-SMPS measurement shows that all test Au NPs had narrow PSDs with low geometric standard deviations of around 1.1. Thus, the filters were challenged with nearly monodisperse particles. Compared to the manufacturer’s diameter specification for 5, 10 and 20 nm Au NPs, which are given as 4.6 ± 0.5, 12.0 ± 1.0 and 18.6 ± 2.3 nm, we observed somewhat larger measured mean diameters, which were 7.1 ± 0.1, 15.1 ± 0.4 and 20.7 ± 1.1 nm, respectively. This is expected due to the fact that when using the aerosolization method, droplets are not only containing the main particles but also water impurities like ions, stabilizing chemicals (here mainly tannic acid) or other residues [31,37]. These can condensate around the surface of the main particles during solvent evaporation. However, as for the present study only the downstream number concentration had to be detected, the slight deviation in terms of mean size (which is always the case for NP size analysis with different methods) does not affect the results discussed in the following. 2.5. Correlation between liquid-borne and airborne particle concentrations and retention efficiency To apply the ES-SMPS method for determining the filtration efficiency, a calibration curve was established, i.e., the prepared (or calculated) liquid-borne particle concentration according to the concentration provided from the manufacturer was plotted versus the measured aerosolized airborne particle concentration. Fig. 5 depicts the calibration curve showing a linear relationship that nearly perfectly follows the 1:1 line between the normalized liquid-borne and airborne Au NPs concentration. The x- and y-axis in Fig. 5 represent the normalized values with respect to the highest initial liquid-borne particle concentration and the accordingly measured airborne particle concentration, respectively. The highest concentrations prepared in the calibration for 5, 10 and 20 nm Au NPs were 5.1 × 1012, 1.1 × 1012 and 8.0 × 1011 particles/ml. Then a sequent and stepwise dilution with a fixed ratio of 1:2 by 18 MΩ cm resistivity ultrapure water was

Fig. 4. PSDs of residues and (a) 5 nm, (b) 10 nm and (c) 20 nm Au NPs. The distributions for 10 and 20 nm are highlighted by a red circle and enlarged in the respective inset. For the chosen measurement conditions, clear baseline separations between NPs and residue particles were achieved.

that of the Au NPs (xmin > 5 nm). Noteworthy, we confirmed a complete baseline separation between two sets of size distributions for all particle sizes under the desired operation conditions of ES, i.e., solution electrical conductivity of 1000 µS/cm and liquid feed rate with 0.128 and 0.191 µl/min. Furthermore, we obtained zero residue particles at the size larger than 5 nm when pure water was aerosolized by ES. That is, the total concentration of the undisturbed Au NPs can be easily obtained from the measurement data of SMPS by excluding the concentration from the residues. It should be mentioned that the use of higher chamber pressures can generate a higher airborne particle concentration. This is particularly advantageous for the present study as it improves the sensitivity of the

Fig. 5. Calibration curve of 5, 10 and 20 nm Au NPs for ES-SMPS. Error bars refer to the standard deviations on the average of values from three independent measurements. 5

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conducted to obtain the whole curve covering three orders of magnitude. As the linearity between the liquid-borne and airborne concentration was very high (R2 = 0.9989) and nearly passing the 1:1 line, the retention efficiency could be calculated as:

Efficiency = 1 =1

Downstream Conc.liquid

were involved for these small particles. In general, the efficiency was higher for all filters in case of low flux conditions (open symbol). This was because of the higher residence times of the particles inside the membrane, giving them more time to be transported to the filter surface by convection-diffusion. Fairly good filtration results, e.g., efficiencies above 0.7, could only be obtained with PCTE and MCE membranes, respectively, whereas the PTFE membrane resulted in low filtration efficiencies with only about 0.2, even at low flux conditions. For PCTE membrane filters (straight pores, narrow pore size distribution, low porosity and thin), the retention efficiency at high flux was around or slightly less than 0.1 while the retention efficiency at low flow rate exceeded 0.7 for all particle sizes. At this point it must be mentioned that the high efficiency was not only due to particles adsorbing inside the pores but mostly due to particles that deposited on top of the membrane surface (for details please refer to the SEM images shown in Fig. 8). Thus, the high retention efficiency at low flow rate is rather likely caused by the combination of electrostatic rejection of the NPs at the pore inlet and particle adhesion on top of the membrane surface, resulting in a large portion of particles remaining on the upstream side of the filter. Also, it is possible for particles to adsorb to the pore wall, however, because of the low particle to pore diameter ratio (PPD), retention by size exclusion (sieving) is unfavorable. In contrast, at higher flow rate, particles are forced to penetrate the membrane without successful adhesion to the membrane surface because of both, short residence time and high hydrodynamic drag. For MCE membrane filters (pore network, wide pore size distribution, high porosity and thick), the retention efficiency was generally high. A slight increase from around 0.6 at high flux to a value of 0.8 at low flux was observed. This is explained by the significant positive diffusional effect on the retention efficiency of Au NPs, which is further enhanced by the longer residence time of the NPs inside the filters at lower flow rate. By comparing the retention efficiencies of PCTE and MCE membranes at high flux (closed triangles vs. closed squares), a much higher retention efficiency in case of the MCE membrane was observed. Again, we explain this to be the consequence of the longer residence time of NPs inside the filter media, now due to the much larger thickness (> 16 fold) and much higher porosity (60 fold) of MCE membrane filters. In addition, more pronounced hydrodynamic drag induced by the much higher velocity due to the very low porosity of PCTE membranes generally favors the detachment of NPs inside the pores. This effect has been reported and discussed in detail in our previous work [42]. Finally, for PTFE membrane filters (fibrous pore network, wide pore size distribution, high porosity and thick), as mentioned earlier, the lower flux did only slightly improve the efficiency which was generally low. More details on this particular behavior will be discussed in Section 3.1.2.

borne

Upstream Conc.liquid borne Downstream Conc.airborne Upstream Conc.airborne

(1)

To be mentioned, the highest concentrations applied in cases A1 and A2 to challenge the filters were situated above the maximum concentration used for the calibration line. Therefore, the upstream and downstream samples obtained from the filtration tests of 5 and 10 nm Au NPs at high concentration were diluted to lie within the constraints of the calibration curve. However, as dilution can be performed with high accuracy and special emphasis was spent on proper dispersion of the particles by intense ultrasonication throughout all our experiments, together with the high reproducibility of all the collected filtration data in general, we think this procedure is sufficiently justified. 3. Results and discussion 3.1. Initial filtration efficiency Fig. 6 shows the initial retention efficiency for the three 50 nm rated membrane filters (i.e., PTFE – circles, PCTE – triangles and MCE – squares) against 5, 10 and 20 nm Au NPs for low and high flux conditions. The initial retention efficiency, representing the clean filter performance, was assumed to be the efficiency we obtained from challenging the membranes with the first 2 ml of Au suspensions with the lowest concentration (see Table 2). In the following section, we will quickly discuss the obtained results and give preliminary explanations for the observations. Noteworthy, already from these comparatively simple initial filtration efficiency experiments, the three determining factors on depth filtration of small NPs can be deduced: (i) transport efficiency to the membrane, (ii) hydrodynamic flow drag and (iii) surface interaction forces (particle-membrane interactions). 3.1.1. Transport including hydrodynamic drag At a first glance, the filtration efficiency shown in Fig. 6 is independent of particle size. However, from fouling (or loading) experiments, shown later, it was found that different deposition mechanisms

3.1.2. Interactions In terms of structure, PTFE membrane filters are, except for the thickness (as mentioned, the relevant part is thin), quite similar to the MCE membrane filters, i.e., presence of a pore network, wide pore size distribution and high porosity in general. However, in spite these structural similarities, much lower efficiencies were recorded. PTFE membranes showed relatively low retention efficiencies with less than or around 0.2 at both, low and high flux conditions. In principle, the hydrodynamic drag forces to which the particles are exposed after deposition are expected to be similar because of the comparable porosities of PTFE and MCE filters, which determine the flow velocities inside membranes. Thus, we conclude that another, materials-related influencing factor, namely the interaction energy between particle and filter surfaces that finally determines whether deposition occurs or not, critically affects the retention efficiency for PPD 1. For better understanding the effect of particle-membrane interaction energy on retention efficiency, the interaction energy was calculated. In the simplest case, namely the classical Derjaguin-Landau-

Fig. 6. Retention efficiency of clean PTFE, PCTE and MCE membrane filters at different filtration fluxes. 6

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Verwey-Overbeek (DLVO) theory, the interaction energy profile is expressed by the sum of two contributions, van der Waals and electrical double layer interactions, as a function of separation distance between a particle and a collector surface. Under the condition of like-charged interacting surfaces, i.e., unfavorable filtration conditions, the typical DLVO (or extended DLVO, xDLVO, with additional interactions like Born repulsion or steric effects) interaction energy profile is characterized by a primary minimum, a maximum energy barrier and on occasion a shallow secondary minimum. Particle deposition in the presence of electrical repulsion can occur in either of the two minima. Repulsion caused by steric or electrostatic interactions is balanced against van der Waals attraction. In case of aqueous systems, electrostatic repulsion is usually in focus to tailor interactions to the needs of a specific application. The effect of van der Waals attraction is often underestimated, although it has already been shown to be quite important for phenomena like unexpected high colloidal stability of small NPs [40,43] and sub-10 nm classification by size selective precipitation [44–46]. The magnitude of van der Waals interaction linearly depends on the Hamaker constant (A), while the electrostatic double layer interaction is independent of this parameter. For a first instance, the Hamaker constant between nonconducting and conducting media across an intervening liquid can be approximated from optical properties [47]:

A=

3 8 2

h v1v3 ·v2 n12 n32 n12 + n32 ( v1v3 + v2 n12

n32 )

their low retention efficiencies of 10–20% as shown in Fig. 6. A more detailed discussion is provided in SI 1. 3.2. Fouling and concentration effects on filtration efficiency Finally, for the analysis of fouling (or loading) effects, Figs. 7–9(a–c) show the retention efficiency of 5, 10 and 20 nm Au NPs through PTFE, PCTE and MCE as a function of CPN. All graphs are organized as follows: The open and closed symbols depict the retention efficiency obtained under low flux (cases A1 and B1) and high flux (cases A2 and B2) conditions, respectively. The data for the A-cases indicating three different feed concentrations (i.e., low, medium and high), as described in Table 2, are shown with different symbols. To be mentioned, reduced data points for the constant feed cases B1 and B2 are shown to avoid a too busy figure. Moreover, the SEM surface images of the three membrane filters at the end of the fouling experiments at low flux for both cases, varied and constant feed conditions (A1 vs. B1) are compared in panels d and e. While Figs. 7d, 8d and 9d represent the PTFE, PCTE and MCE membrane filters after fouling with 10 nm Au NPs with increasing feed concentrations (case A1), Figs. 7e, 8e and 9e show images of the same filters after fouling with 10 nm Au NPs using constant feed concentrations (case B1). In the following, the results for these three membranes will be analyzed and discussed. Although being aware that the discussed results are far from being complete, we are convinced that in combination with numerical works [49,50], the experimental strategy followed in here is the only solution to shed light on the complex issue of how to understand fouling (or loading) kinetics with regard to PPD, membrane structure, flux, residence time and particlesolvent-membrane interaction.

(2)

where n is the refractive index and ν is the absorption frequency. h is Planck's constant of 6.626 × 10−34 J·s. The subscripts 1, 2 and 3 denote the dielectric materials that are metal (i.e., Au NP, 1), membrane (i.e., PTFE/PCTE/MCE, 3), and liquid (i.e., water, 2), respectively. Table 3 shows the properties of materials used in this study and the derived Hamaker constants for each filtration system as estimated by Eq. (2). For the system Au-water-PTFE, the Hamaker constant is much lower (by a factor of 13–23, due to the lower refractive index of PTFE) than those of the other two systems (i.e., Au-water-PCTE and Au-waterMCE). Hence, due to the relatively weak van der Waals attraction in case of Au-water-PTFE, even though transport, which is defined by the fraction of particles approaching the filter surface, is significantly increased by reducing the flux, the retention efficiency is generally low. In contrast, due to the high Hamaker constant of the system Au-waterMCE, considerably high initial efficiencies for both, low and high flux conditions were monitored. This underlines the crucial role of the membrane material for the deposition of small particles governed by van der Waals attraction in addition to structural aspects as discussed in the previous section. In line with these hypotheses, Fig. S1 of the Supporting Information (SI 1) depicts the interaction energy profiles for Au NPs with sizes of 5, 10 and 20 nm in the three membranes (PTFE, PCTE and MCE). As expected, the energy barrier for 5 nm Au NPs in PTFE is reduced. However, the low level of adhesion from the shallow primary minimum in combination with hydrodynamic drag leads to

3.2.1. PTFE membrane Varied feed concentrations, A1 and A2. Fig. 7a to c reveal that at varied feed concentration conditions, around or less than 20% of Au NPs were retained in the PTFE membrane filters, regardless of particle size and filtration flux (both A1 and A2). We attribute this small fraction of retention to sieving (mechanical deposition) in some smaller pores or intercrossing fibers of the PTFE membranes. This is due to the fact that adsorption by diffusion to the membrane surfaces is expected to be generally weak because of the low van der Waals attraction between Au NPs and PTFE. Thus, diffusion deposition plays a negligible role for the retention efficiency of Au NPs in PTFE membrane filters. In line with these observations, there is not much difference amongst the results between low (open symbols) and high flux conditions (closed symbols), A1 vs. A2, with a slightly higher efficiency for the low flux in general due to the longer residence time. Constant feed concentration, B1. At CPN ~1013–1014 (i.e., end of the filtration experiments), an increasing retention efficiency with increasing CPN for all particle sizes was observed for case B1. This effect is getting more and more pronounced with increasing particle size. Comparison between varied and constant feed, A1 and B1. From the different results between the varied and constant feed concentrations in case of PTFE, it becomes clear that the different deposition behavior and pattern, i.e., the fouling (or loading) history, is of vital importance. The increasing efficiency at high CPN in case of constant feed concentration B1 is ascribed to be a consequence of the small amount of deposited particles (~10–20%) that cluster at the membrane surface acting as filtering obstacles. Clustering can be induced, for instance, by reduced colloidal stability at the herein applied high dilution that potentially leads to desorption of stabilizing ligands from the particle surface into the bulk [40,51]. This is supported by comparison of SEM images depicted in Fig. 7e where pronounced clustering of Au NPs due to particle-particle adhesion was observed (see arrows). Worth being mentioned here is that Lohaus et al. [38] performed simulations to understand microscopic mechanisms of membrane fouling on different pore geometries, and observed similar phenomena to the obstacle effect for all fouling simulations conducted. This

Table 3 Properties of materials used in this study and the calculated effective Hamaker constant for each filtration system [48]. Material

Membrane Particle Liquid

PTFE PCTE MCE Au Water

Refractive index, n

Absorption frequency, v [×1015 s−1]

Hamaker constant, A [×10−20 J]

1.36 1.58 1.50 0.25 1.33

2.9 3.2 3.0 6.2 3.0

Au-water-PTFE 0.24 Au-water-PCTE 5.6 Au-water-MCE 3.2

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Fig. 7. Evolution of the retention efficiency of (a) 5, (b) 10 and (c) 20 nm Au particles on PTFE membranes as a function of CPN for different fouling (or loading) patterns. Error bars represent the standard deviations on the average of values from three independent experiments. Figs. (d) and (e) represent the SEM images of PTFE membranes after being challenged with 10 nm Au particles at an increasing feed (case A1) and a constant feed concentration (case B1), respectively.

so-called “obstacle effect” leads to an enhanced deposition by sieving that is getting more pronounced with increasing particle diameter and CPN of the challenge particles. Furthermore, the gradually increased surface roughness by the deposited particles could also enhance particle deposition by reducing the maximum energy barrier [52,53] and result in more low-flow regions due to the increased thickness of the boundary layer [54]. All these effects favor adhesive torques overwhelming hydrodynamic torques after deposition [55–57]. At this point it has to be mentioned that adhesive and hydrodynamic torques acting on the deposited particles are of great importance during particle detachment [31]. Especially rolling of the deposited particles was found to be the most dominant detachment mechanism in the laminar flow condition. Adhesive torques are derived from surface interactions depending on chemical conditions, while hydrodynamic torques are induced by fluid drag and shear forces due to the hydrodynamic flow. In contrast, in case of A1 with varied feed concentrations, only few of such clusters were observed (Fig. 7d). This is explained by the fact that at higher particle concentrations also high concentrations of free surfactant in the liquid phase do exist. At low dilution, desorption of stabilizing ligands from the particle surface into the bulk liquid is rather unlikely, ensuring good electrosteric stabilization of the NPs. Thus, particle–particle adhesion, which is the main factor for NP clustering, is unfavored and no obstacle effect is recognized for case A1, at least not within the CPN and particle sizes analyzed in this study.

3.2.2. PCTE membrane Varied feed concentration, A1 and A2. From Fig. 8a to c, it immediately becomes clear that for both cases A1 (low flux) and A2 (high flux) at varied feed concentrations, the filtration efficiency of PCTE membrane filters strongly depends on the size of the challenge particles. For the 5 nm Au NPs and low flux conditions (Fig. 8a, case A1, open symbols), decreasing efficiencies from high values around 75% (open circles) to 25% (open squares) were found with increasing feed concentrations. Whereas the former is ascribed to the high van der Waals attraction between PCTE and Au NPs, the reduced efficiency for the latter may be explained by the so-called surfactant effect reported by Du et al. [58]. Similar to the obstacle effect described above, the high surfactant concentration in the liquid caused by the high particle concentration leads to steric stabilization that unfavorably lowers the attraction between particle surface and membrane [58]. For details, we refer to the works of Olcay et al. [59] and Hahn and O’Melia [60] where the complexity of all possible interactions of membrane filters with contaminant in the presence of surfactant has been addressed in detail. In brief, in the current study, feeding with high particle concentration is inevitably accompanied with high concentration of surfactant in solution (here: tannic acid) due to the low dilution ratio. Now, depending on its specific interaction with the membrane material, this surfactant can be adsorbed at the membrane surface. There it either screens the effective van der Waals interaction by the creation of an additional 8

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Fig. 8. Evolution of the retention efficiency of (a) 5, (b) 10 and (c) 20 nm Au particles on PCTE membranes as a function of CPN. Error bars represent the standard deviations on the average of values from three independent experiments. Figs. (d) and (e) represent the SEM images of PCTE membranes after being challenged with 10 nm Au particles at an increasing feed (case A1) and a constant feed concentration (case B1), respectively.

ligand shell or even creates an additional steric repulsion between the membrane surface and the incoming NPs. A simple experiment to analyze the adsorption of tannic acid onto the three filters was conducted and the methodology and findings are described around Fig. S2 of SI 2. In line with our observations, we could show that tannic acid strongly adsorbed on both, MCE and PCTE membranes, while the adsorption on PTFE was negligible. In contrast, for high flux conditions and 5 nm particles (case A2, closed symbols, Fig. 8a), in general very low retention efficiencies of less than 20% were obtained. This is due to the very short residence times of particles passing through the very thin PCTE membrane filters. Regarding the results for larger particle sizes of 10 and 20 nm shown in Fig. 8b and c, respectively, a constantly high deposition at low flux was observed. In contrast, high flux conditions and low CPN initially led to low deposition which was however followed by higher retention efficiencies that were even approaching the values of the low flux case A1, as soon as a kind of a threshold CPN ~1013 was exceeded. The constantly high deposition at low flux is explained by the larger particle sizes (10 and 20 nm) that are close to the pore diameter of 50 nm, in particular when keeping in mind that the PCTE filters consist of straight pores with narrow pore size distribution (Figs. 1b and 8d and e). With the increased particle size, the physical deposition mechanisms, e.g., interception on pore openings, become significant. Besides, adsorption

of larger particles to pore walls can cause pore constriction, clogging and decreased passage more readily, i.e., a pronounced obstacle effect [61]. In addition, van der Waals adhesion is getting more dominant for larger particle diameters. At high flux conditions, the low deposition in the beginning is ascribed to pronounced hydrodynamic drag and low residence time while the pronounced deposition at higher feed concentration is ascribed to a kind of an overload of the pores causing congestion. This is in line with findings of Ramachandran et al. [62] who found that the physical capture of colloidal particles occurred due to pore constriction or particle bridging (two or three particles entering a pore together) for PPD = 0.22, i.e., 1 µm rated PCTE membrane with 0.22 µm polystyrene latex particles. This is a highly plausible scenario for the deposition behavior observed here with PPD = 0.2 and 0.4 for 10 and 20 nm Au NPs challenging a 50 nm PCTE membrane. Constant feed concentration, B1 and B2. For constant feed conditions and low flux (B1), generally high efficiencies between 0.8 and 1 were observed independent of the size of the challenge particles. This is explained by the combination of high van der Waals attraction, long residence time and low hydrodynamic drag as well as low surfactant effect due to the high dilution ratio. In contrast, the high flux (B2) exemplarily investigated for 10 nm Au NPs, led to a low efficiency, < 20% in the beginning, due to short residence time and high 9

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Fig. 9. Evolution of the retention efficiency of (a) 5, (b) 10 and (c) 20 nm Au particles on MCE membranes as a function of CPN. Error bars represent the standard deviations on the average of values from three independent experiments. Figs. (d) and (e) represent the SEM images of MCE membranes after being challenged with 10 nm Au particles at an increasing feed (case A1) and a constant feed concentration (case B1), respectively.

hydrodynamic drag. However, as already observed for the case of increasing feed concentration and high flux, after exceeding the CPN of about 1012, the efficiency was largely increased. This is again attributed to the accumulation of a critical amount of particles around the membrane front surface, the pore openings and inside the pores, causing obstacles and particle bridging that result in retention efficiencies of nearly 100%. Comparison between varied and constant feed, A1 and B1. From Fig. 8b and c, it became clear that in contrast to the PTFE membrane, for the retention efficiency of 10 and 20 nm challenge particles in the straight-through pore geometry of the PCTE filters, the total CPN, filtration velocity and PPD (or particle size) are more decisive than the feeding mode, i.e., varied vs. constant concentration. This is further confirmed from the SEM images shown in Fig. 8d and e where for both cases A1 and B1, 10 nm Au NPs were collected in a similar amount on the filter surface. However, for the smallest 5 nm Au NPs the fouling pattern became important which might be due to the fact that the influence of surfactants is getting more and more significant, eventually causing particle-particle or particle-filter repulsion for small particles and small PPD.

results on retention efficiency gained from the MCE membrane filters. Comparing the cases of varied particle feed concentrations, at both, low and high flux (cases A1 and A2), two observations are made. First, during fouling with increasing feed concentration, low flux conditions generally resulted in a better deposition, again due to longer residence time and reduced hydrodynamic drag. Second, while in the beginning the efficiency is generally high with minimum values ~60%, due to the high Hamaker constant and thus remarkable van der Waals adhesion, a reduced filtration efficiency was observed along the higher feed concentration. This is again ascribed to the surfactant effect as MCE is the most adsorptive membrane for tannic acid among the three media (see SI 2). Constant feed concentration, B1 and B2. Also for feeding with constant feed concentration, the initial filtration efficiency is above 60% due to remarkable van der Waals attraction between particles and membrane material. In case of low flux (open circles) it is even ~80% due to the long residence time. The slight increase of the efficiency up to ~100% is ascribed to the obstacle effect as explained earlier. Interestingly, for the high flux exemplarily analyzed for medium sized 10 nm particles (case B2, closed circles, Fig. 9b) at a CPN around 6 × 1012, a switch of the deposition mode was observed causing a remarkable increase of the filtration efficiency from ~50 to ~100%. In the absence of pronounced surfactant effects because of the high

3.2.3. MCE membranes Varied feed concentration, A1 and A2. Fig. 9a to c summarize the 10

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dilution, this is explained by the obstacle effect. Comparison between varied and constant feed, A1 and B1. Thus, also in case of the MCE membrane, large differences were monitored depending on the filtration velocity but also depending on the fouling (or loading) history of the membrane. From SEM images for low flux and varied feed (Fig. 9d) as well as low flux and constant feed (Fig. 9e), it becomes clear that the fairly high Hamaker constant of the MCE membrane resulted in pronounced deposition of Au NPs on the membrane surface. However, the clearly reduced deposition in case of the increasing feed concentration A1, rather likely caused by the surfactant effect, led to a slightly larger amount of particles found in case of B1.

4. Conclusion Performances of three membrane filters, i.e., PTFE, PCTE and MCE, with the same nominal pore size of 50 nm against 5, 10 and 20 nm Au nanoparticles (NPs) were investigated by a series of systematic filtration experiments. Not only the initial, but also the evolution of retention efficiencies during fouling (or loading) was investigated to unravel different particle deposition mechanisms. Special emphasis was put on the influence of membrane material and structure, feed concentration and flux as well as particle size at particle to pore diameter ratios (PPDs) clearly below 1. The retention efficiency of the membrane filters was obtained from a pre-established calibration curve, which revealed a linear relationship between the concentrations of liquid-borne NPs provided by the manufacturer and the aerosolized NP number concentrations measured by electrospray-scanning mobility particle sizer (ES-SMPS). The minimum detection limit of ES-SMPS was determined to be around 0.005 mg/l for 5 nm Au NPs, which enabled to obtain the retention efficiency of filters with clean condition, i.e., the initial retention efficiency. We found that in dependence of feed concentration and fouling (or loading) pattern, each filter showed a significant difference in the final retention efficiency at similar CPN. This was ascribed to the complex interplay of physical effects and specific interactions between particle and filter surfaces. In particular with regard to the latter, it has to be mentioned that adsorption of surfactants like tannic acid can cause superimposed steric effects that can remarkably change the filtration mode. We believe that the systematic experiments conducted in this study, considering pore size, PPD and membrane structure as filter parameters, residence time, hydrodynamic drag and feeding mode as process parameters, that are superimposed by highly specific particle-membrane surface interactions, will shed light on the complex particle deposition in membrane processes of small PPDs.

3.2.4. Comparison of filtration performance among different membranes From our systematic filtration experiments, the most important conclusions from the cross comparison of filtration results can be summarized as follows: (1) From the comparison of retention efficiency of 5 nm Au NPs with the medium feed concentration at low flux (i.e., open triangles) in Figs. 7a, 8a and 9a, the highest retention efficiency around 40% was obtained for the PCTE membrane, followed by MCE (around 25%) and then PTFE (less than 10%). Thus, filtration performance scales with the effective Hamaker constant. This experimental finding agrees with the previous theoretical explanation about the retention efficiency for small PPD (i.e., PPD = 0.1), where diffusion deposition is more dominant than other physical deposition mechanisms, e.g., sieving or interception, and particle-membrane interactions are expected to play an important role. For PTFE and MCE membrane filters, it can be clearly observed that more particles were retained by the filter media when challenged by a constant feed concentration of Au NPs (case B1). (2) The clean filter efficiencies of PCTE and MCE at low flux were enhanced due to the diffusional effect of small NPs, but the efficiency of PTFE was very low at both low and high flux. This indicates that not only the residence time of the particles in the filter but also the interaction energy between particle and filter surfaces plays an important role for NP removal for PPD 1.0. (3) The different feed concentrations did not affect the retention efficiency of PCTE membranes when challenged with 10 and 20 nm Au NPs (i.e., 0.2 and 0.4 of PPD, respectively), which indicated that the dominant retention mechanisms originated from physical effects caused by particle size, e.g., pore constriction, clogging and interception. (4) For small PPD, the diffusional deposition is the most probable retention mechanism. Higher feed concentrations resulted in lower retention efficiency for PCTE and MCE membranes due to steric effects caused by the stabilizer, tannic acid, which adsorbs at the membrane surface (for details see SI 2) and thus prevents NP deposition due to larger contact distance caused by the ligand shell or even repulsive surface interactions [58]. Based on these findings, in future work we recommend to firstly adsorb the stabilizing ligand molecule on the fiber surface to achieve saturation prior to filtration tests conducted.

Acknowledgments The authors thank the support of members of the Center for Filtration Research: 3M Corporation, A.O. Smith Company, Applied Materials Inc., BASF Corporation, Boeing Company, Corning Inc., China Yancheng Environmental Protection Science and Technology City, Cummins Filtration Inc., Donaldson Company, Inc., Entegris, Inc., Ford Motor Company, W. L. Gore & Associates Inc., Guangxi Wat Yuan Filtration System Co., Ltd, MSP Corporation; Samsung Electronics Co., Ltd., Shigematsu Works Co. Ltd.; TSI Inc.; W. L. Gore & Associates, Inc., Xinxiang Shengda Filtration Technique Co. Ltd., and the affiliate member National Institute for Occupational Safety and Health (NIOSH). Parts of this work were carried out in the Minnesota Nano Center which receives partial support from NSF through the NNIN program. Parts of this work were carried out in the Characterization Facility, University of Minnesota, which receives partial support from NSF through the MRSEC program. D.S., S.S. and W.P. acknowledge the funding of the Deutsche Forschungsgemeinschaft (DFG) through the Cluster of Excellence “Engineering of Advanced Materials” (bridge funding). Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.seppur.2020.116689.

At this point it has to be mentioned that our findings are far from being complete and more data for different particle and membrane materials, CPN, PPD, particle and pore size distribution, surfactants and fouling (or loading) history are required. Moreover, the investigation of NP systems where particle feed concentration and surfactant concentration can be varied independently from each other will eventually shed further light on the occurrence of dynamic steric effects. However, we believe that our work is an excellent starting point for more systematic studies leading to comprehensive models and finally optimum membrane structures with respect to the application.

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