Thin alumina nanoporous membranes for similar size biomolecule separation

Thin alumina nanoporous membranes for similar size biomolecule separation

Journal of Membrane Science 343 (2009) 1–6 Contents lists available at ScienceDirect Journal of Membrane Science journal homepage: www.elsevier.com/...

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Journal of Membrane Science 343 (2009) 1–6

Contents lists available at ScienceDirect

Journal of Membrane Science journal homepage: www.elsevier.com/locate/memsci

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Thin alumina nanoporous membranes for similar size biomolecule separation Hatice Ulku Osmanbeyoglu a , Tae Bong Hur b , Hong Koo Kim b,∗ a b

Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA 15213, USA Department of Electrical and Computer Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA

a r t i c l e

i n f o

Article history: Received 18 May 2009 Received in revised form 12 July 2009 Accepted 14 July 2009 Available online 22 July 2009 Keywords: Bioseparation Inorganic membranes Anodic aluminum oxide Protein diffusion

a b s t r a c t Anodic aluminum oxide (AAO) membranes are chemically and thermally stable and inert, and can be produced with wide variety of pore size distribution. We report thin alumina nanoporous membranes (0.7–1 ␮m thickness) with narrow pore size distribution (20–30 nm diameter) obtained by anodizing aluminum films that were deposited on silicon substrates for a biomolecule separation platform. We demonstrate the electrostatic sieving effect for separation of proteins with similar molecular weights with the thin nanoporous anodic aluminum oxide membranes. Without separate modification of the membrane surface, we have achieved high throughput (>10−8 M cm−2 s−1 ) and high selectivity (>42) for separation of bovine serum albumin (BSA) and bovine hemoglobin (BHb) at pH = 4.7, the isoelectric point of BSA. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Incorporating the capabilities of biological membranes in nanoscale devices is extremely important for devising new biomedical platforms for drug delivery, immunoisolation, separation and purification of biomolecules, etc. For example, transmembrane ion channels possess remarkable features such as high transport throughput and selectivity: 10,000 times more permeable to potassium than to sodium although both atoms have one positive net charge [1,2]. However, such performance has not been achieved by any artificial filtering systems. Advances in this field are possible by developing convenient and inexpensive methods to fabricate robust regular nanopore array structures with more elaborate geometrical constraints. Moreover, detailed knowledge of the transport behavior of the molecules on the nanoscopic scale is crucial for the understanding and optimization of prospective device structures. For efficient biomolecule separation for biomedical applications, materials with controlled pore diameter, length and surface chemistry are required. Some of the key properties that nanoporous membranes are required to possess for biomolecule separation applications include a pore size of a few tens of nanometers or less; a narrow pore size distribution in order to achieve high biomolecule selectivity; high porosity as well as small thickness in order to enable high analyte flux; mechanical stability; and chemical stability. Commercially available nanoporous membranes generally exhibit broad size distributions and relatively large thickness val-

∗ Corresponding author. Tel.: +1 412 624 9673; fax: +1 412 624 8003. E-mail address: [email protected] (H.K. Kim). 0376-7388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2009.07.027

ues. As a result, the materials usually possess poor size-cutoff properties and low transport rates. Moreover, separation of similar size materials with current commercially available nanoporous membranes is not feasible. Micro/nanofabricated membranes with various pore size, length, morphology and density have been synthesized from diverse material including using inorganic, organic, or composite materials [3–10]. Unlike organic polymer membranes, inorganic solid-state membranes exhibit no plastic deformation and immediately return to their flat state when the pressure is removed. Moreover, they open several avenues for future development including scalable production of membranes, straightforward integration into microfluidic devices, and surface functionalization using well-established chemistries that can modify surface charges. Many techniques have been devised to control the pore size and surface charge of the membranes in an effort to manipulate transport properties of membranes [6,11–17]. A gold-plating technique has been used to precisely tune the pore diameter as well as the surface chemistry of the pores. Au-thiol chemistry can be utilized to allow the incorporation of appropriate chemistries for separation and sensing, such as by adsorption of charged thiols or functional thiols. The poly(ethylene glycol) (PEG)-thiol film is used to prevent membrane clogging and fouling in the case of non-specific adsorption to the membrane surfaces. In pores modified by self-assembled monolayers (SAMs), the transport of species inside the pore can be manipulated by the functional headgroups of the SAM. Ku and Stroeve demonstrated that surface functionalization of pore walls of Au-coated poly(carbonate) track-etched (PCTE) membranes (6 ␮m thickness) with SAM-bearing carboxylic groups resulted in separation of bovine serum albumin (BSA) and bovine hemoglobin (BHb)

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with separation factor of 67 at pH = 4.7, which corresponds to the isoelectric point of BSA [12]. Both proteins are known to have similar sizes but different isoelectric points. Among inorganic membranes, anodic porous alumina, a self-organized nanostructured material with tunable nanosized channels in the range of 20–200 nm, pore densities of 1–1000 ␮m−2 and around 100 ␮m thickness has been extensively studied, especially with bulk aluminum foils [10,18–22]. Membranes of this type may also be obtained commercially with a variety of pore sizes. A porous surface film with an approximately close-packedhexagonal array of cells (each cell containing a cylindrical pore) develops when aluminum is anodized in certain acid electrolytes such as phosphoric acid. However, this porous film has also a configuration consisting of a non-porous barrier layer adjacent to the aluminum anode. If these films are to be used as membranes, it is necessary to detach the film from aluminum and remove non-porous barrier layer. This is achieved by progressively reducing the voltage while the metal is still immersed in the anodizing electrolyte [10]. The pore diameter and the pore density depend on the applied voltage during anodization process and can be varied. The resulting membrane has an asymmetric structure. Larger pores transverse through the bulk of its thickness interconnected with an array of smaller pores which formed at the surface originally attached to the aluminum. Although this channel geometry may be appropriate for size-based filtration, it does not allow utilizing the electrostatic sieving effect for separation of proteins with similar molecular weights. This is because the possible channel region for electrostatic interaction between proteins and pore walls is limited short compared to the membrane thickness. Alumina pores grown with aluminum films that are deposited on foreign substrates such as silicon or silica would potentially offer much broader application than those on bulk aluminum foils [23,24]. Obtaining thin-film alumina pores with their pore bottom walls fully opened, however, is known to be a challenging task in terms of thin-film processing. In this work, we report a viable method to fabricate thin (0.7–1 ␮m) anodic alumina nanoporous membranes on a silicon platform. The open-through nanopore membranes supported on a window-etched silicon substrate show narrow pore size distribution (20–30 nm) across the window area and uniform diameter throughout the membrane thickness. We note that the membrane thickness obtained in this work is almost two orders of magnitude smaller than commercial alumina membranes in terms of the overall thickness (1 ␮m versus 100 ␮m) whereas the thickness of the minimum pore size layer itself is an order of magnitude larger (1 ␮m versus 0.1 ␮m), as will be discussed below. In comparison with conventional alumina membranes, our alumina nanoporous membranes possess the following beneficial aspects for biomolecule separation applications: narrower pore size distribution (for improved cutoff rate); relatively small thickness (for higher analyte flux); regular channel geometry with uniform pore diameter throughout the membrane thickness (for efficient electrostatic interactions for separation). Moreover, the thin-film process on a Si substrate offers an efficient approach to integrating nanostructured materials and devices on a single chip for biomedical applications [3]. In this work, we explore the electrostatic sieving effect for separation of proteins with similar molecular weights with our thin nanoporous alumina membrane. We achieved high selectivity (>42) for separation of BSA and BHb at pH = 4.7, which corresponds to the isoelectric point of BSA [12]. No separate modification of the membrane surface was employed in this experiment. The separation performance of our membranes is compared with that of commercially available Whatman (Anopore) anodic nanoporous alumina membranes, which show relatively non-uniform pore sizes and irregular geometry.

2. Experimental 2.1. Materials and reagents Bovine serum albumin (66 kDa) and bovine hemoglobin (65 kDa) are from Sigma Co. (catalog nos. A-7906 and H-2500, respectively), and no further purification was carried out. BSA is a globular prolate ellipsoid, 14 nm × 3.8 nm × 3.8 nm, BHb is more spherelike, 6.4 nm × 5.5 nm × 5 nm [12]. The isoelectric points (pI) of BSA and BHb are 4.7 and 7.0, respectively. The buffer powder for phosphate buffered saline (PBS) was obtained from Sigma Co. (catalog no. P3563). Buffer solutions can be adjusted to desired pH value (4.7) by adding a small amount of HCl or NaOH. The ionic strength of the solutions is 0.01 M. Transport experiments were performed at solution pH of 4.7. Anodic aluminum oxide membranes (Anopore) were obtained from Whatman (Maidstone, Kent, UK: catalog no. 6809-7003). 2.2. Membrane fabrication We fabricated nanoporous alumina membranes using the procedure outlined in Fig. 1. We first grew an 850-nm-thick layer of SiO2 on both sides of a (1 0 0) silicon wafer. On the back side of the wafer, the SiO2 was patterned using standard photolithography techniques in order to form an etch mask for the membrane formation process. The back oxide layer (850 nm) was then removed by selectively etching with buffered hydrofluoric acid (BHF). The patterned backside was then exposed to a highly selective silicon etchant, KOH, which removes Si preferentially in the (1 0 0) plane. The window area was etched down to around 50-␮m thickness of Si. Then, aluminum films with thickness of 1 ␮m were then deposited on the front side, using a thermal evaporation method with 5N-purity aluminum source. In order to enhance adhesion between the aluminum film and the planar SiO2 surface, a 5-nm-thick Ti layer was sputter deposited at a chamber pressure of 5 mTorr in Ar with a deposition rate of 4.1 nm min−1 . Anodic oxidation was then carried out on the deposited aluminum films in dilute electrolyte (H3 PO4 + H2 O in 5:800 volume ratio) at room temperature using a Pt wire as a counter electrode. The anodization was conducted under a constant voltage mode (20 V) for approximately 2 h 30 min. When aluminum becomes oxidized, the volume expands by approximately a factor of 1.7 due

Fig. 1. A schematic of the fabrication procedure for thin anodic aluminum oxide (AAO) membranes.

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Fig. 2. Microscope images of thin nanoporous alumina membranes fabricated on a Si platform: (A) optical microscope image of a cell membrane (plan view from the KOH-etched, bottom side of Si substrate), (B) SEM image (plan view from the bottom side), and (C) SEM image (cross-section view).

Fig. 3. SEM images (cross-section view) of commercial membranes (Whatman): (A) larger pore side, and (B) fine pore side.

to the density difference between aluminum and alumina. After anodization, the samples were treated with short-time (1–2 min) wet etching (HCI + HNO3 + H2 O in 1:1:1 volume ratio) in order to remove remaining aluminum layer. Plasma etching was performed to remove residual Si and SiO2 layers. Etch rates of Si and SiO2 layers were ∼3.6 ␮m/min and ∼140 nm/min, respectively. Once the bottom of the alumina layer was revealed, another plasma etching was performed to open the pore bottom alumina layer. Etch rate of this alumina is approximately 67 nm/min. After the completed fabrication, the pore sizes were measured with a SEM at high magnification. The resulting membrane is around less than 1 ␮m

thick with relatively narrow pore size distributions (20–30 nm pore diameter). The pore diameter depends on the applied voltage during anodization process and can be varied. The pore density is estimated to be ∼200 ␮m−2 . The free-standing membrane area was 0.073 mm2 . Fig. 2 shows optical or electron microscope images of the fabricated membranes. Membrane surfaces were also characterized optically via a reflected light microscope for macroscopic defects in membrane fabrication. We have used this process to fabricate square membranes as large as 0.25 mm2 and as thin as 500 nm but in this work we focus on structurally more robust 1-␮m-thick, 0.073 mm2 membranes. On the other hand, commercially available Whatman membranes have a thickness of 60 ␮m with asymmetric nanopores and average nominal fine pore size of 26 nm and average nominal larger pore size of 204 nm [10,11]. The commercial membranes have a broader pore size distribution (15–65 nm) on the fine pore side compared to our thin nanoporous alumina membranes. Fig. 3 presents SEM images of the cross-section of large pore size side (Fig. 3(A)) and cross-section of fine pore size side of the commercial alumina membrane (Fig. 3(B)). Small pores are polygonal in shape and large pores are circular. The large pores span most of the 60 ␮m thickness of the commercial alumina membranes while the fine pored layer is approximately 100 nm thick. 2.3. Experimental procedure

Fig. 4. Experimental setup for biomolecule separation with nanoporous anodic aluminum oxide membranes.

Fig. 4 shows the schematics of the diffusion chamber system. The diffusion chamber, fabricated out of stereolithography (SLA) material, consists of two compartments with approximate volumes of 3 mL each, sealed with O-rings, and screwed together. The reservoir chamber is filled with solution of interest and the sink chamber is filled with solvent only. Phosphate buffer saline is used as the solvent. The effective permeation area of the commercial alumina membrane and our membrane was 50 mm2 and 7.3 × 10−2 mm2 , respectively. In the case of the commercial membrane, the larger pore surface of the membrane was placed toward

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reservoir side. All protein solutions prepared from the stock solution were stored at 4 ◦ C and used within 3 days of preparation. All experiments were carried out at room temperature. 2 mL protein solution was introduced into the reservoir compartment and the reservoir concentrations for BSA and BHb were 25 ␮M for mixed protein experiments. As the sink solution, 2 mL of 0.01 M PBS was placed inside the sink cell. The protein concentrations in the sink chamber are measured with a UV–vis spectrometer (BTC111E, B&WTek), referring to the absorption band at 278 nm for BSA and at 408 nm for BHb. For mixed protein experiments, the BHb concentration can be determined directly from the absorbance at 408 nm. BHb solutions exhibit maxima at two different wavelengths around 278 and 408 nm: while the BSA absorbance shows a maximum around 278 nm and is negligible around 408 nm. Thus, the BSA concentration at 278 nm can then be determined by subtracting the contribution associated with the BHb, which was evaluated directly from the BHb concentration. A deuterium/tungsten light source (BDS-100, B&WTEK) was used as a light source. Every 30 min measurement was taken. Vigorous stirring was made in both compartments by using two magnetic stirrers and a stirring plate (Nuova II, Thermolyne). 3. Results and discussion 3.1. Mixed protein separation Proteins possess an isoelectric point (pI) at a characteristic pH at which they exhibit no charge. For values of pH < pI, the protein is positively charged and for values of pH > pI the protein bears a negative net charge. At pH = 4.7, BSA and BHb exist mainly as a neutral or cation molecule, respectively, in accordance to their isoelectric points. Unmodified anodic aluminum oxide membranes were found to be positively charged at pH = 4.7 [13]. Moreover, low ionic strengths exhibit large double layer thickness on both the surfaces of the protein and the charged surfaces of nanoporous membranes. When ionic strength is 0.01 M, this double layer thickness is estimated be around 3.3 nm for pore walls. The double layer thickness [25] is given by LD =

 εRT 1/2 2F 2 q2 c

(1)

where c is the concentration, q is the charge number, R is the gas constant, T is the absolute temperature, and F is the Faraday constant. Under these conditions, we explore the electrostatic sieving effect for separation of proteins with similar molecular weights and different charges with our thin anodic aluminum oxide membrane. For comparison, a commercial alumina membrane was also tested: experiments for a mixture of BSA and BHb via thin anodic aluminum oxide membrane indicate that the flux of BSA is much higher than BHb at pH = 4.7 and I = 0.01 M as shown in Fig. 5. For mixed protein experiments at these conditions, the BSA flux is 5.32 × 10−8 M cm−2 s−1 while the BHb flux is 1.25 × 10−9 M cm−2 s−1 . The flux difference leads to a selectivity of about 42 with unmodified membranes. We note that the throughput obtained in this work is more than three orders of magnitude higher than those of polymeric membranes, e.g., 5 × 10−8 M cm−2 s−1 versus 1 × 10−11 M cm−2 s−1 [12]. This dramatic enhancement of throughput is ascribed to the very different pore density (200 ␮m−2 versus 6 ␮m−2 ) and membrane thickness (∼0.6 ␮m versus 6 ␮m). In the case of bulk alumina nanoporous membranes whose pore bottom layer is etched away, the protein transport experiments show a throughput of ∼10−11 M cm−2 s−1 (for membrane thickness of 40 ␮m, pore diameter of 20 nm and pore density of 200 ␮m−2 : see, for example, Ref. [26]). Separation of similar-sized proteins with commercially available membranes

Fig. 5. Sink concentrations versus time for a mixture of BSA and BHb at pH = 4.7, I = 0.01 M transported through a thin alumina nanoporous membrane.

(Whatman) is found to be difficult. The experiments for a mixture of BSA and BHb via the commercial alumina membranes indicate that the flux of BSA is similar to BHb at pH = 4.7 and I = 0.01 M as shown in Fig. 6. For mixed protein experiments at these conditions, the BSA flux is 2.68 × 10−10 M cm−2 s−1 while the BHb flux is 2.65 × 10−10 M cm−2 s−1 . The flux difference leads to a selectivity of about 1. The improved selectivity of the thin anodic aluminum membrane results from the relatively large flux of the neutrally charged BSA and the low flux of the positively charged BHb when nanochannel diameters become close to protein size. This is ascribed to the strong electrostatic interaction and adsorption inside the charged pore of the membrane at low ionic strength. When the pH of a solution is equal to the pI of the protein it contains, the neutral molecules do not interact electrostatically with the surface of the membrane pores, which leads to a maximum flux across it. So protein can diffuse through the pore easily. At pH values above and below the pI, charge interactions between the proteins, their counterions, and the pore surface lead to a decrease in transmembrane flux. Moreover, electrical double layer thickness also reduces the diffusion of the charged BHb through charged nanopore. Therefore, when pore size and protein size are close to each other, the transport of protein is highest at isoelectric point. In the case of Whatman membranes, however, the close direct interactions of proteins with the charged

Fig. 6. Sink concentrations versus time for a mixture of BSA and BHb at pH = 4.7, I = 0.01 M transported through a Whatman membrane.

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surface occurred over a much shorter distance (around 100 nm). The commercial membranes have asymmetric nanoporous structure (Fig. 3): the major part of the membrane thickness (60 ␮m thickness) is with 206-nm-wide channels while the minor part (<150 nm thickness) is with nanochannels. Therefore, charge-based selection/separation is difficult to occur during a mixed protein transport experiment via the commercial alumina membrane even if one side of the membrane has similar pore size distribution as our thin anodic aluminum oxide membrane. This shows the importance of pore size/geometry in order to make use of the electrostatic sieving effect for separation of proteins with similar molecular weights. Fig. 7 illustrates that the electrostatic interactions between proteins and pore walls are important factors in protein transport across porous membranes and that these interactions are complex. Although we achieved selectivity about 42 with unmodified thin inorganic alumina membrane with making use of its pore size/geometry, selectivity may be further improved by introducing self-assembled monolayers of molecules on pore surfaces. Previously, Ku and Stroeve reported selectivity of about 67 between BSA and BHb by further controlling electrostatic interactions between proteins and pore surfaces with SAM groups [12]. Applying external voltage to the functionalized pore walls may also further improve the selectivity. Voltage-induced pore surface charges can reduce the flux of charged protein via enhanced electrostatic interaction between the charged pore walls and proteins, as was demonstrated by Chun et al. [27]. Our work with thin nanoporous alumina membranes encourages the use in several near-term applications. We demonstrated that our membranes can be used to separate similarly sized molecules with different charges. First, the separation of BSA and BHb suggests that it can be used for membrane-based protein fractionation. BSA and BHb are too close in size (1.01 times MW difference) to be efficiently separated using conventional membrane processes. Second, because they are relatively thin in the overall channel length compared to the commercially available membranes, our membrane is expected to be highly efficient in transport and therefore in separation. Indeed, our diffusion measurements recorded that a transport rate is one order of magnitude higher than that of commercial alumina membranes. Finally, the silicon-based platform opens avenues for future developments such as straightforward integration into microfluidic devices.

Fig. 7. A schematic comparison of charge-based separation via a Whatman membrane (A) and a thin alumina nanoporous membrane (B).

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4. Conclusions This study demonstrates that anodization of aluminum films is a viable method to grow thin alumina nanoporous membrane with narrow pore size distribution. The proposed membrane technology may address and alleviate several of the problems associated with current commercially available separation membranes. Although several membranes, such as those by Whatman are available for size-based filtration, these membranes do not have all the desired ‘ideal’ membrane properties to separate similar size biomolecules. Results indicated that charge-based separation of similar-sized biomolecules can be achieved with our thin nanoporous alumina membrane. We achieved high throughput (>10−8 M cm−2 s−1 ) and high selectivity (>42) for separation of BSA and BHb at pH = 4.7, which corresponds to the isoelectric point of BSA. Moreover, the process developed in this work offers also an efficient approach to integrating nanostructured materials and devices on a single chip for biomedical applications. Acknowledgments This work was supported by the NSF Grant No. NIRT ECS0403865 and the CRDF of the University of Pittsburgh. References [1] J.N. Israelachvili, Intermolecular and Surface Forces, 2nd ed., Academic, London, 1992. [2] D.A. Doyle, J.M. Cabral, R.A. Pfuetzner, A. Kuo, J.M. Gulbis, S.L. Cohen, B.T. Chait, R. MacKinnon, The structure of the potassium channel: molecular basis of K+ conduction and sensitivity, Science 280 (1998) 69–77. [3] C.C. Striemer, T.R. Gaborski, J.L. McGrath, P.M. Fauchet, Charge- and size-based separation of macromolecules using ultrathin silicon membranes, Nature 445 (2007) 749–753. [4] H.D. Tong, H.V. Janson, V.J. Gadgil, C.G. Bostan, E. Berenschot, M. Elwenspoek, Silicon nitride nanosieve membrane, Nano Lett. 4 (2004) 283–287. [5] S.E. Létant, T.W. Van Buuren, L.J. Terminello, Nanochannel arrays on silicon platforms by electrochemistry, Nano Lett. 4 (2004) 1705–1707. [6] S.B. Lee, C.R. Martin, Electromodulated molecular transport in gold-nanotubule membranes, J. Am. Chem. Soc. 124 (2002) 11850–11851. [7] P.Y. Apel, Track etching technique in membrane technology, Radiat. Meas. 34 (2001) 559–566. [8] T.A. Desai, D. Hansford, M. Ferrari, Characterization of micromachined silicon membranes for immunoisolation and bioseparation applications, J. Membr. Sci. 159 (1999) 221–231. [9] W.H. Chu, R. Chin, T. Huen, M. Ferrari, Silicon membrane nanofilters from sacrificial oxide removal, J. Microelectromech. Syst. 8 (1999) 34–42. [10] R.C. Furneaux, W.R. Rigby, A.P. Davidson, The formation of controlled-porosity membranes from anodically oxidized aluminum, Nature 337 (1989) 147– 149. [11] S.W. Lee, H. Shang, R.T. Haasch, V. Petrova, G.U. Lee, Transport and functional behavior of poly(ethylene glycol)-modified nanoporous alumina membranes, Nanotechnology 16 (2005) 1335–1340. [12] J.R. Ku, P. Stroeve, Protein diffusion in charged nanotubes: “On–Off” behavior of molecular transport, Langmuir 20 (2004) 2030–2032. [13] B.H. Winkler, R.E. Baltus, Modification of the surface characteristics of anodic alumina membranes using sol–gel precursor chemistry, J. Membr. Sci. 226 (2003) 75–84. [14] K.-Y. Chun, P. Stroeve, Protein transport in nanoporous membranes modified with self-assembled monolayers of functionalized thiols, Langmuir 18 (2002) 4653–4658. [15] Z. Hou, N.L. Abbott, P. Stroeve, Self-assembled monolayers on electroless gold impart pH-responsive transport of ions in porous membranes, Langmuir 16 (2000) 2401–2404. [16] K.B. Jirage, J.C. Hulteen, C.R. Martin, Nanotubule-based molecular-filtration membranes, Science 278 (1997) 655–658. [17] S. Saksena, A.L. Zydney, Effect of solution pH and ionic strength on the separation of albumin from immunoglobulins (IgG) by selective filtration, Biotechnol. Bioeng. 43 (1994) 960–968. [18] H. Masuda, K. Fukuda, Ordered metal nanohole arrays made by a two-step replication of honeycomb structures of anodic alumina, Science 268 (1995) 1466–1468. [19] J.P. O’ Sullivan, G.C. Wood, The morphology and the mechanism of formation of porous anodic films on aluminum, Proc. R. Soc. Lond. Series A 317 (1970) 511. [20] D. Routkevitch, A.A. Tager, J. Haruyama, D. Almawlawi, M. Moskovits, J.M. Xu, Nonlithographic nano-wire arrays: fabrication, physics, and device applications, IEEE Trans. Electron Devices 43 (1996) 1646.

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