Maximal pore size in UF membranes

Journal of Membrane Science 394–395 (2012) 89–97

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Maximal pore size in UF membranes Elizabeth Arkhangelsky a , Aviv Duek a , Vitaly Gitis a,b,∗ a b

Unit of Environmental Engineering, Ben-Gurion University of the Negev, PO Box 653, Beer-Sheva 84105, Israel van’t Hoff Institute for Molecular Sciences, University of Amsterdam, Science Park 904, 1098XH Amsterdam, The Netherlands

a r t i c l e

i n f o

Article history: Received 19 September 2011 Received in revised form 20 December 2011 Accepted 21 December 2011 Available online 30 December 2011 Keywords: Porous materials Monodispersed nanoparticles Aquasols Molecular separation Pathogens

a b s t r a c t The ultrafiltration membrane rejection capability is most often characterized by molecular weight cutoff (MWCO). The value is found by rejection of organic solutes and the evaluation of particle retention requires a conversion of either MWCO to pore size or particle diameter to molecular weight. The conversion affects the accuracy of reported values and results in a gap between reported and measured retentions. We suggest a novel, simple and effective pore size test based on synthesis and membrane transfer of rigid nanoparticles. Gold and silver 3–50 nm monodispersions had delivered a comprehensive pore size distribution including d100 , a pore diameter for which a membrane has a 100% retention capability. The maximal pore size in UF membrane structure can hardly be detected with other methods although it is much needed for precise separation analysis. The d100 values in tested UF membranes vary between 40 nm and 50 nm depending on the membrane material. The polymer membranes are more flexible than the ceramics and their d100 is usually much higher than MWCO. The d100 increases with high transmembrane pressure or after oxidative chemical cleaning. For some membranes the d100 values can be correlated with d90 but not with d50 . © 2011 Elsevier B.V. All rights reserved.

1. Introduction The ultrafiltration (UF) membranes currently become the leading separation method in various fields including biotechnology [1,2], medicine [3], chemical industry [4] and water treatment [5]. The key feature of UF membranes is the ability to control the permeate quality by effective retention of different species in the feed. The control is achieved by a careful selection of membrane characteristics such as the material and the pore size. The separation, in general, can be built on preferential adsorption or electrostatic attraction but the need to maintain a good flux makes the pore size exclusion the most important mechanism. The principle is simple – the solutes smaller than the pore size are passing through the pore while the solutes bigger than the pore size are rejected. A wise UF membrane separation requires the knowledge of the exact pore size. Unexpectedly and rather surprisingly the membrane pore diameter can hardly be determined directly. The actual skin layer of the asymmetric membranes is covered inside the polymer matrix and therefore is not observable by microscopic methods. Water permeability tests connect the flux with the mean pore

∗ Corresponding author at: Unit of Environmental Engineering, Ben-Gurion University of the Negev, PO Box 653, Beer-Sheva 84105, Israel. Tel.: +972 86479031. E-mail address: [email protected] (V. Gitis). 0376-7388/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2011.12.031

diameter d50 [6] only. Other methods, such as the gas flow bubble point [7] and mercury porosimetry [8], require very high pressure for small pores, such that the measurement itself destroys the pore structure [9]. Alternatively, permporometry is based on gas condensation inside the pores and suffers from low accuracy due to vapor pressure differences on both sizes of the membrane [10]. Poor reproducibility of the results along with difficulty of use and absence of a commercially available apparatus had been named as major drawbacks of liquid–liquid porosimetry [11–14]. Diffusional limitations and additional resistance of support layer limit implementation of recently developed binary gas diffusion [15]. Unisize of gold nanoparticles has limited their implementation in pore size distribution measurements [16,17]. The current state-ofthe-art method is based on penetration of homogeneous solutes such as polyethylene glycols (PEGs) [18] or dextrans [19,20] of different molecular weights. The method assumes that solutes can be rejected by the membrane pore but not adsorbed to the membrane surface, and the solutes with higher MW will be removed better. We have recently shown that both assumptions are problematic [21,22] and the inherent flexibility of the organic solutes is confusing. A penetration of molecules 300 times larger than the pore size was recently reported [23]. The PEG/dextran solutes are therefore applicable for a limited range of pore sizes up to molecular weight cut-off (MWCO) that displays 90% retention capability of organic molecule. A weak link between MWCO and actual pore diameter results in inaccurate prediction of particle retention [21]

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Table 1 Synthesis parameters, size and zeta potential of A–G gold nanoparticle samples. Sample

Sodium citrate (mM/mM of HAuCl4 )

mM of Tannic acid/mM of HAuCl4

Potassium carbonate (mM/mM of HAuCl4(aq) )

Size (nm)

A B C D E F G

1.3 1.3 1.3 0.7 0.3 0.3 0.2

0.256 0.031 0.002 – – – –

3.15 0.31 0.06 – – – –

3.1 4.8 9.2 18.3 27.5 37.4 45.0

± ± ± ± ± ± ±

0.5 0.5 0.8 0.9 2.0 1.8 2.2

Zeta potentiala (mV) −52.0 −61.0 −53.0 −47.0 −37.0 −36.3 −41.8

± ± ± ± ± ± ±

1.9 2.5 0.0 0.3 0.2 0.3 2.4

a The higher negativity of the smaller nanoparticles is due to addition of citric acid that has higher concentration at the outer core of the particles. The adsorption increases the negative charge and stability of the aquasols.

and increases a need for pilot UF studies [24]. Higher than predicted penetration is often reported and the gap is explained by the presence of abnormal pores [25,26]. Here we show that UF membranes are having maximal pores that can be detected and not just estimated. With a help of a new tool, monodispersions of gold and silver nanoparticles, we were able to provide a pore size distribution including the maximal d100 pore size detected by absolute 100% retention of test solutes. The d100 for tested polymer and ceramic UF membranes lies between 40 nm and 50 nm, and that value becomes larger if the membranes are operated at high transmembrane pressure (TMP) or after oxidative chemical cleaning. For some membranes the d100 can be correlated with d90 but not with d50 .

2. Materials and methods 2.1. Preparation and characterization of the nanoparticles Seven samples of monodispersed gold aquasols A–G were prepared by reduction of hydrogen tetrachloroaurate with sodium citrate and tannic acid [27,28]. For instance, 4.0 ml of a 1% solution of trisodium citrate and 5.0 ml of tannic acid were added to 40.0 ml of a 0.01% (w/v) solution of HAuCl4 . All chemicals were purchased from Sigma–Aldrich. The mixture was stirred for 5 min under gentle boiling, cooled to room temperature, and stored at 4 ◦ C. The six remaining suspensions (B–G) were similarly prepared, using the reagent concentrations listed in Table 1. The initial gold concentration was 52 mg/L. The 10 and 20 nm monodispersions of silver nanoparticles were prepared by reduction of silver nitrate with sodium citrate and tannic acid [28]. For instance, 4.0 ml of 1% trisodium citrate, 5.0 ml of tannic acid and 5 ml of 25 mM K2 CO3 in 6 ml of DIW were heated up to 60 ◦ C and added to a preheated solution of 1.0 ml of a 1% AgNO3 solution (v/w). The total mixture volume was completed to 100 ml with deionized water (DIW) and the mixture was boiled for 7 min under gentle stirring. The formation of silver nanoparticles was controlled by a gradual appearance of yellow-brown color. The suspension was cooled to room temperature and centrifuged for 30 min at 10,000 rpm. The centrifugation resulted in a separation of 10 nm particles to supernatant and 20 nm to the sediment. The 30.7 ± 3.1, 40.1 ± 3.9, and 64.7 ± 4.1 nm cubic silver nanoparticles were purchased from NRF [29]. The AuNP and AgNP suspensions were characterized by transmission electron microscopy (TEM) using a JEM-1230 instrument (JEOL) at 120 kV. The microscope was equipped with a TemCamF214 (TVIPS) camera. Size distribution and zeta potential were measured with a ZetaPlus (Brookhaven Instruments) zeta potential and particle size analyzer. The measurements were performed at a pH of 6, and at a flex angle of 90◦ . Each measurement was a composite of 10 runs of 10 s each.

2.2. Measuring nanoparticle concentration The concentration of Au3+ was determined after dissolving the suspension in 7.6 ml of aqua regia (3 M HCl:1 M HNO3 ). The solution was evaporated to exchange the aqua regia with 5 ml of DIW. Concentrations of gold in the feed and permeate solutions were established with atomic absorption spectrometer (Perkin Elmer AAnalyst200) at a wavelength of 242.8 nm with a slit of 2.7/1.35. The air flow was 12 L/min and acetylene flow was 1.9 L/min. The concentration of dissolved in aqua regia Ag+ was found with inductively coupled plasma mass spectroscopy (ICP/MS, Perkin Elmer ILAN6000). We also developed a faster and cheaper alternative detection based on fluorescence resonance energy transfer (FRET) between Rhodamine B (RB) dye and AuNPs. The noncovalent self-adsorption of RB on AuNPs results in fluorescence quenching because of the FRET of RB to AuNPs. No fluorescence was observed after 3 days of dialysis needed to remove extra dye. The addition of thiols and release of RB due to formation of stronger Au–S bonds results in renewed fluorescence proportional to the number of molecules released from the AuNPs surface. A pictorial scheme of FRET principle is provided on Fig. 1. The released fluorescence was measured at 540/625 nm excitation/emission wavelengths with FS-2 (Scinco) fluorescence spectrometer, and calibrated against known AuNPs concentrations assuming equal number of dye molecules per Au particle. The calibration plots of AuNPs for dissolved gold ions Au3+ and for RB fluorescence are shown on Fig. 2. Both plots calibrate absorbance/fluorescence and AuNPs concentration linearly with Pearson’s R2 coefficients higher than 0.999. 2.3. Bacteriophages The MS2 (ATCC 15597-B1), phi X174 (ATCC 13706-B1), T4 (ATCC 11303) and PRD-1 (ATCC BAA-769-B1) bacteriophages and their Escherichia coli host cells were purchased from Deutsche Sammlung von Microorganismen und Zellkulturen GmbH (DSMZ, Germany). The Vaccinia viruses (VV) were received from Department of Virology at Ben Gurion University of the Negev. Table 2 details the main characteristics of the microorganisms. A fresh stock was prepared for each experiment. E. coli cells were propagated by inoculation on Lauria–Bertani (LB) agar followed by incubation at 37 ◦ C for 16–18 h. The concentration of E. coli was determined by plating 100 ␮l of culture solution on LB agar and counting colony forming units (cfu) after overnight incubation at 37 ◦ C. Phages were propagated by inoculation of infected E. coli cells into LB medium followed by 24 h incubation at 37 ◦ C. During this time, the cells were at the exponential growth phase (suspension turbidity from 0.2 to 0.3 OD). The cell lysis was later performed with chloroform. The resulted suspension was centrifuged at 37,000 rpm for 40 min, the pellet was discarded, and the bacteriophage-containing supernatant was stored at 4 ◦ C. Bacteriophage concentration was determined by a pfu assay using the double-layer overlay method.

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Fig. 1. A pictorial FRET scheme where the attachment of RB to AuNPs results in fluorescence quenching, and only adsorption of l-cysteine release the sleeping RB and renew the fluorescence.

FRET

AA

2

R = 0,9999

Abs orbance, AU

0,3

Abs sorbance, AU

16000

0,2

0,1

R2 = 0,9989

12000

8000

4000

0

0 20

0

40

60

0

20

40

60

80

100

Au3+ concentration, ppm

Au concentration, ppm

Fig. 2. AuNPs calibration curves with Atomic absorption (left) and RB fluorescence (right).

The initial phage concentration varied between 1.3 × 107 and 5.0 × 107 pfu/ml. 2.4. Membranes and filtration Fresh polyethersulphone PES-10, PES-20 and PES-30, cellulose acetate CA-20, polyvinylidene fluoride PVDF-30, polycarbonate PC-30 and PC-100, and ceramic C-50 membranes (Sterlitech Corporation) were tested. In PES, CA, PVDF and C membranes, the numerical digits indicate the MWCO in kDa as provided by the supplier. In contrast, the numerical digits in the PC membranes indicate the pores size in nm. Prior to filtration, the membranes were soaked in NaOH solution (pH 9) and vibrated at 55 ◦ C for 2 h.

The cleaning resulted in similar feed and permeate total organic carbon (TOC) levels in filtration of deionized water DIW (RO quality). Filtration was performed in a 150 ml autoclaved stirred cell (magnetic stirring, 400 rpm) equipped with a back-pressure TMP controller [30]. The pore size was measured in ambient conditions, at a pH of 6 and 2 bars N2 TMP (99.99% purity), after 30 min compaction with DIW. The oxidative chemical cleaning of CA-20 was performed in closed Petri dishes with a fresh 0.15 g/l free NaOCl solution (Unilever) prepared daily. The cleaning time period varied between 1 min and 240 h, and after that the cleaned membrane was washed with DIW. The cleaning intensity was displayed as a Ct, a product of concentration of cleaning agent C and cleaning time t.

Table 2 Main virus characteristics. Virus

Family/group

Morphology

Nucleic acida

Size (nm)

Isoelectric point, pH

MS2 Phi X174 T4 PRD1 VV

Leviviridae Microviridae Myoviridae Tectiviridae Poxviridae

Symmetry icosahedral Icosahedral Tailed phage Symmetry icosahedral Icosahedral

Linear ss RNA Circular ss DNA Linear ds DNA Linear ds DNA Linear ds DNA

26–27 31–32 65 × 80, tail 120 × 20 65 360 × 250

3.9 6.6 3.2 4.2 4.8

a

ss, single-strained; ds, double-strained.

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2.5. Pore size tests The water permeability test determines the mean pore diameter d50 (nm) in symmetric membranes with Hagen-Poiseuille equation [6]



d50 = 2

8xM Ak

(1)

where  is the water viscosity (kg/m s−1 ), x is the membrane thickness (100 ± 50 nm), Ak is the membrane porosity determined by weighing the dry and wet samples, and M is the membrane permeability (L/m2 h−1 bar−1 ) calculated gravimetrically as: M=

m St P

(2)

where m is the permeate weight difference (kg) measured with Kern PLS 2100-2 (Germany), t is the frequency interval (h), P is the transmembrane pressure (TMP, bars), S is the active membrane surface area (0.0025 m2 ), and  is the permeate density (∼1000 kg/m3 ). The nanoparticle test determines the pore size with A–G gold or with 10, 20, 30, 40 and 65 nm silver suspensions. The tests were performed with constant 5.6 × 1010 particles/ml concentration achieved by diluting more concentrated suspensions of small nanoparticles. The tests were performed in a sequence of 15 min filtration of DIW, 5 min filtration of nanoparticle suspension, and additional 20 min of DIW filtration. Only 25 ml permeate were collected, to minimize a bias due to concentration polarization. The tests were performed with fresh suspensions to minimize possibilities for shape change and aggregation [31,32]. Retention was calculated with a ratio of total mass of nanoparticles in permeate and feed. The microorganism tests were used to detect the d100 only. The absolute 3.7 LRV and higher retentions were calculated from an average virus concentration of 3.1 × 107 pfu diluted in 150 ml filtration cell and the minimum countable 30 pfu/ml. Here LRV is a log removal value, a logarithm to base 10 of the ratio of microorganism concentrations in the feed to those in permeate. The pore diameter for the retentions lower than 3.7 logs was recalculated back from Ferry formulae [33] 2

R = 1 − 2(1 − size ) + (1 − size ) R = 1 for

size > 1

4

for

size ≤ 1

(3)



1−

Cp Cf



× 100 %

(5)

where Cp and Cf are the solute concentrations (g/L) in the permeate and in the feed respectively. For PEG, PEO and dextran, the conversion of MW into nm was performed with the correction formulae [34], d50 = 0.11(MW50 )0.46

Fig. 3 shows a design for a bubble point test. A 3.0 × 3.0 cm membrane piece was circle cut out with a sharp metal ring, placed on a metal-free filter (A-424, Upchurch Scientific) and held by two frits (A-346, Upchurch Scientific). The frit assembly, held by nuts (A-510, Upchurch Scientific), was tightly screwed into a PEEK fluoropolymer body so that the Teflon tube coming out of the N2 cylinder delivered the gas straight to the membrane surface. The loose end of the tube was immersed into a 50-ml beaker filled with DIW so a stream of nitrogen bubbles coming through the membrane could easily be visualized. The d100 maximal pore size was determined as [35] d100 (␮m) =

41.6 Pb (psi)

(7)

where Pb is a bubble point pressure. 3. Results and discussion 3.1. Detection of d100 with gold and silver nanoparticles

(4)

where R is the retention calculated as a function of size = dparticle /dpore and dparticle and dpore are the particle and pore diameters, respectively. The polymer tests were performed with 0.3 g/L solutions of PEGs, polyethylene oxides (PEOs) and dextrans (Sigma–Aldrich). The 0.6, 3.4, 6.0, 10.0, 20.0, 35.0 kDa PEG; 100, 200, 600 kDa PEO; 6, 40, 70, 100 kDa dextran polymers were used unmodified. The polymer concentration was measured with Apollo 9000 TOC analyzer (Tekmar Company). The rejection of test solutes was calculated using the formula: R=

Fig. 3. Bubble point test setup.

(6)

Here MW50 is the molecular weight of a large organic molecule that displays 50% rejection capability [21].

The TEM micrographs and size distributions of gold nanoparticles are depicted in Figs. 4 and 5, respectively. The highly stable, monodispersed, spherical gold nanoparticle suspensions with no visible aggregation are observable. Zeta potential measurements at pH of 6 (Table 1) demonstrated decreasing negative values from −61 mV for 3.1 nm colloids to −33 mV for 45 nm colloids (suspensions with absolute zeta potential values above 30 mV are considered stable, [36]). Fig. 6 shows the retention of gold nanoparticles by PVDF-30, C-50, PC-30, and PC-100 membranes. Note that connecting the tops of the retention bars results in sigmoidal curves, which are typical of natural processes [37]. Indeed, similar curve forms were reported also with PEG [18]. Conversion of 30 and 50 kDa in PVDF-30 and C-50 membranes to diameters (Eq. (6)) gives roughly 12.6 nm and 16.0 nm, however particles as large as 28 nm easily permeate through PVDF-30. This reflects the flexibility of the polyvinyl membrane that allows larger particles to pass. Conversely, the rigid pores of the ceramic membrane indeed retain 90% of particles of ca. 18 nm and fully retain the 37 and 45 nm particles. The pore size of PC-100 assumes that all the particles smaller than 100 nm will pass through. However, the average 10–15% retention of particles starting from 18.3 nm was measured. More than 99% retention of particles bigger than 9.2 nm by PC-30 was observed.

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Fig. 4. High resolution transmission electron micrographs of the gold nanoparticle suspensions A–F.

Fig. 5. Size distribution of gold nanoparticle suspensions determined with dynamic light scattering. The distribution function analysis is displayed as scattered intensity per particle sizes of 3.1, 4.8, 9.2, 18.3, 27.5 and 45 nm.

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Fig. 6. Percentage of gold nanoparticle rejection by C-50 (grey bars) and PVDF-30 (hatched bars) membranes (left), and by PC-30 (hatched bars) and PC-100 (grey bars) membranes (right). The tests were performed with constant 5.6 × 1010 particles/ml concentration. The error bars are the maximum and minimum values obtained during multiple tests.

The d100 at 27.5 nm reflected more on the test sensitivity highlighting the difference between 99.9 and 100% retention. Despite a relative success with the application is soon become apparent that gold nanoparticles are having a high affinity towards PES and CA, and therefore cannot be used for the entire membrane polymer range. The problem was considered related to the membrane hydrophobicity and therefore inherent. Fig. 7 depicts the retention of silver nanoparticles by PVDF-30, PES-30, PC-30 and PC-100 membranes. Here the retention of the smallest 10 nm nanoparticles is already more than 90% for all of the membranes excluding the PC-100. No rejection of 10 and 20 nm particles by PC-100 was obtained. There is no real explanation for reduced retention of 20 nm except for an insufficient separation of 10 and 20 nm particles after the synthesis. The procedure however was repeated many times, and always with the same result. Although the 20 nm were retained less than 10 nm particles, the retention of 30, 40 and 65 nm particles was close to 100% for all of the membranes except for PC-100. Even PC-100 showed a significant retention of 30 and 40 nm that accidently dropped down to 0% retention of 65 nm particles. Despite the good retention, the

application of silver nanoparticles was less informative, mainly due to their initial larger size and once again membrane hydrophobicity. Opposite to gold nanoparticle suspensions, here we were able to obtain a pore size distribution in PES membranes. Table 3 lists the d100 determined with gold and silver nanoparticle tests. The C-50 membrane has an absolute cut-off value of 37 nm, while the PVDF-30 membrane gives 100% retention at 45 nm. More than 99% retention of 18.3 nm gold nanoparticles by PC-30 was received, however the absolute retention of PC-30 is 27.5 nm for gold and 51.4 nm for silver. The absolute retention of PC-100 is above 45 nm. The absolute pore size of tested UF membranes lies between 40 nm and 50 nm, except for the PES-10 and PES-30, where the membrane d100 was below the smallest probe diameter. 3.2. Detection of d100 with bacteriophages and with bubble point tests Although not many, there are other methods to determine the absolute pore size. We were able to detect the d100 with viruses and bubble point tests. For the former, the d100 was set equal to the

Fig. 7. Percentage of silver nanoparticle rejection by PES-30 (grey bars) and PVDF-30 (hatched bars) membranes (left), and by PC-30 (hatched bars) and PC-100 (grey bars) membranes (right).

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Table 3 Absolute d100 membrane pore diameter (nm) obtained with gold and silver nanoparticle tests.

AuNPs AgNPs

PES-10

PES-30

PVDF-30

PC-30

C-50

PC-100

3.1 ± 1.4< 10.0 ± 0.6<

3.1 ± 1.4< 50.4 ± 1.1

47.8 ± 1.7 52.3 ± 1.1

27.5 ± 0.2 51.4 ± 5.1

37.4 ± 1.2 40.4 ± 0.9

>45.0 >65.0

hydrodynamic diameter of virus being rejected by 100%. The 3.7 LRV and higher retention was considered the absolute, and only E. Coli cells and large VV, T4, and PRD1 viruses were completely retained. The d100 for both PES-20 and PES-30 were 1000, 250, 80 and 65 nm in tests with E. Coli, VV, T4, and PRD1 respectively. The obtained value clearly reflected on the size of microorganism used in detection (Table 2). Retention of smaller MS2 and phi X174 bacteriophages was below 3.7 logs barrier. The similar method was earlier applied by Urase [26], and determined absolute (so called abnormal) pore diameters varied between 23 nm and 80 nm. Fig. 8 depicts the changes in absolute pore size in PES20 for the experiments performed with 1–5 bars transmembrane pressure. The absolute pore diameter was affected by the probe size and by the applied TMP. In a response to TMP raise from 1 to 5 bars, the d100 values increased from 80 nm to 82 nm and from 65 nm to 68 nm in T4 and PRD1 experiments respectively. The bubble point test and its derivatives such as diffusive air flow (DAF) and pressure decay test (PDT) are routinely applied for detection of membrane integrity [38]. The methods however are more applicable to assure the membrane impermeability to oocysts of Cryptosporidium parvum. A 100 bar TMP is needed to detect the 28 nm pores (Eq. (7)). The recommended TMP for the majority of UF membranes do not exceed 5 bars. We tried to detect d100 in all membranes but found the bubble point of PC-100 only. The 23.3 bars TMP was converted to 123 nm close to the supplier reported value. The bubble point of other intact membranes was above 50 bars, the self-limiting TMP value. However the maximal pore size drops quickly if the membrane is cleaned with an oxidant. Fig. 9 presents the influence of oxidative NaOCl cleaning of CA-20 membrane on d100 . Although the virgin membrane pore size was below 30 nm, already at 20 gh/L the d100 increased to 57 nm. The

continuous oxidation increased the value up to 430 nm observed after 180 gh/L NaOCl cleaning. At that TMP the bubble point test can be destructive so the real values can be lower. Significant error bars at low Ct values are a good evidence of less conclusive results. Both the trend and the measured values are less surprising as the cellulose acetate is not a chlorine-resistant polymer [38]. Using two independent methods we showed that chemical membrane cleaning and applied TMP can affect maximal pore size in virus membranes. 3.3. Comparison between d50 , d90 and d100 Measurements of the absolute pore size can accurately predict retention of viruses and small particles [24]. However, our method will not be implemented immediately and therefore we searched for correlations between d100 and other membrane pore sizes detectable by already existing tests. Conventionally the membrane is characterized by d50 and d90 pore values found by transmembrane water flux and PEG/PEOs and dextrans solute tests respectively. Table 4 indicates that PEG/PEOs tests predict the d50 value of 2–8 nm regardless of the MWCO value displayed by the supplier. The water permeability displayed larger 3–35 nm d50 values, suggesting a wider pore size distribution that is in closer agreement with the supplier data. The d90 diameter (Table 5) was mainly predicted by gold and silver nanoparticles, and only for 2 out of 6 membranes with PEG/PEO tests. The predicted d90 values in track-etch PC-30 and PC-100 membranes were confirmed by the supplier data and by microscopic observations [24], and therefore resulted in greater accuracy. The d90 in PC-30 and C-50 is 27 and 18 nm, significantly higher than MWCO-based conversion values of 9 and 11 nm, respectively. Fig. 10 presents the correlations between d50 , d90 and d100 . Insufficient correlation with d50 found by water permeability, PEG/PEO

500

Pore size d100, nm

400

300

200

100

0 20

40

60

80

180

Ct, g-h/L Fig. 8. The d100 determined with T4 and PRD1 bacteriophages in TMP range of 1–5 bars. The error bars are the maximum and minimum values obtained during multiple tests.

Fig. 9. The d100 in PE-20 as a function of NaOCl concentration C and contact time t. The tests were performed with CA-20 membrane.

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Table 4 Mean d50 membrane pore diameter (nm) obtained with gold and silver nanoparticles, PEG/PEO, dextrans and water permeability tests. PES-10

PES-30

– – 4.3 ± 0.6 2.1 ± 0.3 6.1 ± 0.6

– – 3.1 ± 0.6 6.0 ± 1.5 8.7 ± 1.5

AuNPs AgNPs Water permeability PEG/PEO Dextrans

PVDF-30 10.5 ± – 2.9 ± 6.9 ± 6.9 ±

0.4 0.4 1.5 1.5

PC-30

C-50

– – 18.1 ± 0.4 6.2 ± 0.2 6.7 ± 0.9

3.1 ± – 3.3 ± 6.5 ± 6.5 ±

PC-100 0.2 0.2 1.5 1.5

– 26.2 ± 0.8 35.1 ± 4.2 7.8 ± 0.7 –

Table 5 Geometric d90 membrane pore diameter (nm) obtained with gold and silver nanoparticles, PEG/PEO, dextrans and water permeability tests. PES-10

PES-30

3.1 ± 1.4< 10.0 ± 0.6< – – –

AuNPs AgNPs Water permeability PEG/PEO Dextrans

3.1 ± 1.4< 24.2 ± 0.8 – – –

and dextran tests was related to the complexity of membrane properties. The membrane cannot be simplified into a sieve, and therefore an initially low flux through PVDF and C membranes resulted in absence of significant correlation. Along with that the general trend of increased d100 for higher d50 with significantly different membranes was observed. More reliable prediction of the maximal pore size can be obtained with d90 measured with either nanoparticles or PEG/PEO. The former correlation in a form of d100 = 1.21 × d90 with R2 = 0.78 is not surprising, the latter in a form of d100 = 3.15 × d90 with R2 = 0.89 is encouraging. The detection of d90 in many membranes with the PEG/PEO tests is however, problematic [18], mainly due to pressure-induced linearilization of the molecules in water. At current the correlation is build on insufficient number of points and further investigation is needed.

4. Analysis The pore size is the most important and complex characteristic of UF membranes. The UF pore size can be measured by many indirect methods of which the microscopy, water flux, and PEG/dextran passive tests are the most popular. The tests link the pore size with visible cavities in the membrane upper layer, with water flux and with retention of linear polymers. Additional complications 50

PVDF-30

PC-30

C-50

PC-100

32.3 ± 1.2 31.8 ± 1.1 – – –

26.7 ± 0.8 27.2 ± 2.3 – 9.3 ± 2.4 –

18.3 ± 0.9 17.1 ± 0.7 – 11.4 ± 1.6 –

>45.0 >65.0 – – –

arise from wide diversity in pore sizes in a majority of polymer membranes. Thus, we need methods that can determine not only a mean pore size, but the entire pore size distribution. The passive solute tests [18] are the only method that is able to provide a pore size distribution based on rejection of test solutes. Two main problems of the linear polymer tests are the partial adsorption to the membrane surface [22], and TMP-induced stretch causing partial penetration through virtually any membrane [2,23,39]. Thus, there is no possibility to determine the absolute retention. In addition, the membrane pore size is related to MWCO, specified as a molecular mass of solute for which a membrane has a retention capability of greater than 90% [40]. Despite a variety of empirical relationships between the molecular weight and hydrodynamic radius of neutral polymer [34], PEG cannot be equalized to a rigid sphere of any diameter, since a spatial arrangement of this linear molecule is not steady under pressure [41]. Application of rigid inert nanoparticles provides the option to evaluate the size of the biggest pore in membrane matrix. The evaluation, based on 100% retention of particles of a certain diameter, provides the maximal instead of the abnormal pore size used before [25,26]. The new definition is way beyond the semantics as it states that the maximal is a part of normal that regularly exists in the membrane matrix. Thus a proper pore size characterization should now include the d100 for a better retention perspective of any solute having a hydrodynamic diameter. The found d100 values 50 PEG/PEO

PEG/PEO dextrans

A NP AuNPs

40

40

AgNP 30

water permeability 20

10

d100, n nm

d100, n nm

30

20

10

0

0 0

10

20

d50, nm

30

40

0

20

40

60

d90, nm

Fig. 10. Correlation between d50 and d100 (left) and d90 and d100 (right). The plots are based on Tables 3–5.

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differ from one membrane to another, and that is not surprising. More surprising is that d100 do not depend much on the membrane characteristics provided by the manufacturer. The d100 of polymer membranes is usually much higher than MWCO while the d100 of ceramic and polycarbonate membranes is much closer to the values provided by the manufacturer. Separation by PC and C membranes can be related to the pore size provided by the supplier, the extended flexibility of polymer membranes force to measure the d100 value. The provided correlation between d90 and d100 in polymer membranes is weak and can only be used for rough approximations. Besides, the MWCO test fails to provide the d90 value for many membranes and therefore MWCO-based prediction possibilities are narrow. 5. Conclusions Monodispersions of inert nanoparticles can conveniently determine the pore size distribution in a variety of UF membranes. The monodospersions are easily synthesized, non-pathogenic, and detectable by simple and rapid methods. The highly concentrated aquasols are stable for long periods of time. In addition, the nanoparticles offer a possibility to determine the absolute membrane pore size. The versatility of the tool will enhance the accurate determination of the relative and absolute retention of rigid nanoparticles. In addition to being a valuable research tool, this method may provide the means to confirm compliance of membrane systems with the stringent regulatory requirements of the drinking water industry. References [1] M.M. Rohani, A.L. Zydney, Role of electrostatic interactions during protein ultrafiltration, Adv. Colloid Interface Sci. 160 (2010) 40–48. [2] K. Ager, D.R. Latulippe, A.L. Zydney, Plasmid DNA transmission through charged ultrafiltration membranes, J. Membr. Sci. 344 (2009) 123–128. [3] K. Sakai, Determination of pore-size and pore-size distribution. 2. Dialysis membranes, J. Membr. Sci. 96 (1994) 91–130. [4] A. Higuchi, M. Tamai, Y.A. Ko, Y.I. Tagawa, Y.H. Wu, B.D. Freeman, J.T. Bing, Y. Chang, Q.D. Ling, Polymeric membranes for chiral separation of pharmaceuticals and chemicals, Polym. Rev. 50 (2010) 113–143. [5] E. Arkhangelsky, A. Lerch, W. Uhl, V. Gitis, Organic fouling and floc transport in capillaries, Sep. Purif. Technol. 80 (2011) 482–489. [6] C.S. Zhao, X.S. Zhou, Y.L. Yue, Determination of pore size and pore size distribution on the surface of hollow-fiber filtration membranes: a review of methods, Desalination 129 (2000) 107–123. [7] E. Jakobs, W.J. Koros, Ceramic membrane characterization via the bubble point technique, J. Membr. Sci. 124 (1997) 149–159. [8] A. Hernandez, J.I. Calvo, P. Pradanos, F. Tejerina, Pore size distributions of tracketched membranes; comparison of surface and bulk porosities, Colloids Surf. A 138 (1998) 391–401. [9] A.J. Burggraaf, L. Cot, Membrane Science and Technology, Elsevier, 1996. [10] M. Mulder, Basic Principles of Membrane Technology, Kluwer Academic Publishers, 2000. [11] M.W. Phillips, A.J. DiLeo, A validatible porosimetric technique for verifying the integrity of virus-retentive membranes, Biologicals 24 (1996) 243–253. [12] R.I. Peinador, J.I. Calvo, K. ToVinh, V. Thom, P. Pradanos, A. Hernandez, Liquid–liquid displacement porosimetry for the characterization of virus retentive membranes, J. Membr. Sci. 372 (2011) 366–372. [13] J.I. Calvo, R.I. Peinador, P. Pradanos, L. Palacio, A. Bottino, G. Capannelli, A. Hernandez, Liquid–liquid displacement porometry to estimate the molecular weight cut-off of ultrafiltration membranes, Desalination 268 (2011) 174–181.

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