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Using Paramagnetic Particles as Repulsive Templates for the Preparation of Membranes of Controlled Porosity Pietro Tierno,† Klaus Thonke,‡ and Werner A. Goedel*,†,§,| Organic and Macromolecular Chemistry, OCIII, Abt. Halbleiterphysik, and Materials & Catalysis, ACII, University of Ulm, D-89081 Ulm, Germany, and Physical Chemistry, Chemnitz University of Technology, D-09111 Chemnitz, Germany Received February 28, 2005. In Final Form: June 1, 2005 Using mixtures of repulsive superparamagnetic polystyrene particles and a photopolymerizable organic liquid (trimethylolpropane trimethacrylate) that are applied to a water surface, it is possible to prepare porous membranes with controlled porosity. The particles were polarized by applying a magnetic field H perpendicular to the interface and spread out over the interface making use of the induced repulsive magnetic dipole interactions. As a consequence, the organic liquid in which the particles were embedded covered the water surface uniformly. Subsequent photo cross linking of the organic liquid and dissolution of the embedded particles gave rise to membranes whose porosities were controlled mainly by the chosen areas per particle. The spatial distribution of the pores and the deviation from a crystalline arrangement were characterized in terms of the 2D pair-correlation function and the mean nearest-neighbor interpore distance.
Introduction Porous membranes, besides others, can be used as filtration media,1,2 shadowing2 or etching masks for the generation of structured surfaces,3 or as optical filters and waveguides.4 In general, in all of the above-mentioned fields of science and technology, the control of the membrane thickness, pore size, pore uniformity, and distribution of pores within the membrane is decisive for the final properties. Especially advantageous are membranes of a thickness smaller than the pore size, best in combination with uniform pore diameter.2 In this context, we recently developed a method for the preparation of thin membranes with uniform pore size using a monolayer of colloidal particles as a template.5 The membranes were obtained by spreading mixtures of silica particles with a photopolymerizable organic liquid onto a water/air interface. The particles formed densely packed monolayers on the water surface, and these monolayers “assisted” the wetting of the water surface by the organic liquid. As a result, the particles were embedded in a thin organic layer and were protruding out of the upper and lower interfaces of this layer. The organic liquid was then solidified, and the particles were dissolved to finally yield a thin porous membrane composed of the solidified organic matrix. By choosing appropriate particle diameters, it was possible to tune the pore size in the range of 50 µm to 15 nm.6 This method has the potential * Corresponding author. E-mail: werner.goedel@ chemie.tu-chemnitz.de. Tel: +49(0)371-531 1713. † Organic and Macromolecular Chemistry, OCIII, University of Ulm. ‡ Abt. Halbleiterphysik, University of Ulm. § Materials & Catalysis, ACII, University of Ulm. | Chemnitz University of Technology. (1) Pusch, W.; Walch, A. Angew. Chem., Int. Ed. Engl. 1982, 21, 660. (2) Van Rijn, C. J. M. “Nano and Micro Engineered Membrane Technology” Elsevier: Amsterdam, 2004. (3) Ladenburger, A.; Haupt, M.; Sauer, R.; Thonke, K.; Xu, H.; Goedel, W. A. Physica E 2003, 17, 489-493. (4) (a) Ebbesen, T. W.; Lezec, H. J.; Ghaemi, H. F.; Thio, T.; Wolff, P. A. Nature 1998, 391, 667. (b) Masuda, H.; Fukuda, K. Science 1995, 268, 1466. (5) (a) Xu, H.; Goedel, W. A. Angew. Chem., Int. Ed. 2003, 42, 4694. (b) Xu, H.; Goedel, W. A. Langmuir 2002, 18, 2363. (c) Yan, F.; Goedel, W. A. Chem. Mater. 2004, 16, 1622.
to be cheaper, faster, and easier to upscale than previously established techniques such as photolithography7 or iontrack etching.8 However, in this process the membrane thickness is comparable to the pore size, thus membranes with pores smaller than 100 nm tend to be fragile. To increase the mechanical stability of the membranes,9 it is therefore desirable to decrease the packing density of the templating particles and thus to increase the width of the load-bearing parts between the holes. Unfortunately, until now the particles used in this procedure attracted each other because of capillary forces, and thus membranes were obtainable only if the number of templating particles was sufficient to yield a densely packed monolayer. If the number of particles used was below this limit, then clusters of particles inside lenses of the organic liquid were floating on the water surface.5,10 Thus, it was possible to tune the pore size of such membranes by choosing particles of different sizes, but it was not possible to tailor the number of pores per area independently. However, particles that repel each other (e.g., via electrostatic or magnetic interactions) can be evenly distributed over a 2D plane for a comparatively wide range of surface concentrations.11-13 Thus, using repulsive particles as a template, one should be able to prepare mixed layers composed of an organic liquid and embedded particles with the additional freedom to tune the interparticle distances while keeping the particle size constant. From these layers, it should be possible to derive porous membranes with pore distances and pore sizes that are tuneable independent of each other. In this article, we show that this can be achieved. (6) Xu, H.; Yan, F.; Tierno, P.; Marczewski, D.; Goedel, W. A. J. Phys.: Condens. Matter 2005, 17, S465. (7) Desai, T. A.; Hansford, D.; Ferrari, M. J. Membr. Sci. 1999, 159, 221. (8) (a) Price, P. B.; Walker, R. M. U.S. Patent 3,303,085, 1967. (b) Schiwietz, G.; Luderer, E.; Grande, P. L. Appl. Surf. Sci. 2001, 182, 286. (9) Even for thicker ones, if pressure filtration is considered. (10) Tierno, P.; Goedel, W. A. J. Chem. Phys. 2005, 122, 094712-1. (11) Pieranski, P. Phys. Rev. Lett. 1980, 45, 569. (12) (a) Aveyard, R.; Clint, J. H.; Nees, D.; Paunov, V. N. Langmuir 2000, 16, 1969. (b) Horozov, T. S.; Aveyard, R.; Clint, J. H.; Binks, B. P. Langmuir 2003, 19, 2822. (13) Zahn, K.; Mendez-Alcaraz, J. M.; Maret, G. Phys. Rev. Lett. 1997, 79, 175-178.
10.1021/la050528n CCC: $30.25 © 2005 American Chemical Society Published on Web 09/03/2005
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Experimental Section Superparamagnetic polystyrene particles with an average diameter of 1.97 ( 0.30 µm, a density of 1.25 g/cm3, and a ferrite content of 22% were purchased from Estapor Microspheres (Merck Chimie SAS, France). The particles have a saturation magnetization of 21.1 A m2/kg and a volumetric susceptibility of χV ) 0.052 ( 0.003. (These data are calculated from the magnetization curve reported in ref 10.) We measured the electrophoretic mobility of the particle (-2.32 ( 0.60 µ cm/Vs) and the ζ potential (-27.4 ( 6.5 mV) in a 10-3 NaCl aqueous solution at T ) 300 K using a Zetasizer Nano series (Malvern Instruments; the measured distributions for the ζ potential and the electrophoretic mobility are shown in the Supporting Information). As supplied, the particle dispersion contains a surfactant (sodium dodecyl sulfate, SDS) to prevent irreversible aggregation during storage. This surfactant was removed, and the particles were transferred to 2-propanol by several washing and redispersion cycles using a permanent magnet to collect the particles and a syringe to remove the supernatant (washing procedure: five times with an aqueous NaOH solution at pH 11, two times with a mixture of water and 2-propanol 1/1 by vol., and finally two times with pure 2-propanol). The photopolymerizable organic liquid used was a mixture of 97% by weight trimethylolpropane trimethacrylate (TMPTMA) and 3% by weight benzoin isobutyl ether as a UV photoinitiator (both from Aldrich). TMPTMA was made inhibitor-free by passing the liquid through a column filled with Al2O3. The solvents used as spreading agentssethanol and 2-propanolswere analytical grade (Aldrich), whereas toluene or xylene (Aldrich, tech. grade) was used to dissolve the particles. The final particle dispersion (5% by wt in 2-propanol) was mixed with a stock solution of the organic liquid in a spreading solvent (10% by wt organic liquid, 45% by wt ethanol, and 45% by wt 2-propanol). Before each experiment, this mixture was sonicated in an ultrasonic bath for 15-20 min and then shaken with a minishaker MS2 (IKA) for an additional 5 min. The experimental cell was a circular glass container of 1.50 ( 0.01 cm radius that was partially filled with deionized water (purified using a Milli-Q system, Millipore). The walls of the glass container were hydrophobized by treatment with hexamethyldisilazane. This cell was placed in the middle of a watercooled split-coil electromagnet (Bruker, Germany) with two manually adjustable iron pole pieces of 10 cm diameter and a 12 cm maximum gap between them. The axis of the coils was oriented perpendicular to the water surface in the glass container. The homogeneity and the strength of the magnetic field were measured at the sample position using a calibrated teslameter (Stute Magnet Technik). To improve the homogeneity further, we screwed two coaxial steel rings onto the pole pieces, and the final field deviation from the central position to the border of the glass container, Bwall - Bcenter, was less than 1 mT for the configuration used (pole distance 8.40 cm), whereas the central magnetic field can increase from 0 to 0.8 T for a distance of 8 cm between the poles. Close to the electromagnet pole pieces was mounted a UV medium-pressure mercury lamp (UMEX GmbH, Germany) with a wavelength peak of 250 nm, matching the absorption wavelength of the photoinitiator used. The UV light was reflected down towards the sample by a mirror made of an aluminum sheet that was mounted on top of the sample between the two pole pieces of the electromagnet. (See Figure 1 for a sketch; the tilt angle of the mirror was ∼25°.) In that configuration, the final light intensity at the sample position was I ) 26.9 ( 0.1 mW/cm2 (measured using a calibrated photometer, Polytec, Waldbronn, Germany). The part of the chamber comprising the glass container was sealed into a polyethylene bag filled with nitrogen. The temperature was controlled by the water-cooling system of the electromagnet and was kept constant at 300 ( 1 K during the experiment. After spreading the dispersion onto the water surface, the magnetic field was applied with a ramp of ∼0.1 mT/m up to the value of 0.29 T and then was kept constant for ∼45 min. The organic liquid was solidified by 5 min of illumination, and the resulting solid layer was cut and transferred horizontally to various substrates such as gilded electron microscopy grids (Plano Co., G204G), mica, or a plastic sheet.
Figure 1. Scheme of the experimental setup. To allow the UV light to reach the sample, a mirror made from an aluminum sheet was mounted on top of the sample at a tilt angle of ∼25°. The samples on these substrates were covered with an ∼20nm-thick layer of Au-Pd (vacuum sputtering) to prevent surface charging and imaged with a DSM 962 scanning electron microscope (Zeiss Germany). The size and positions of the particles, the mean nearestneighbor interparticle (or interpore) distance, and the pair correlation function of the pore positions were obtained from the analysis of the scanning electron microscope (SEM) images using a home-written code in Matlab. Calculation of the Amount of Particles and the Amount of Organic Liquid Needed. At a given area per particle A/N, the mass of particles mtot can be calculated as
mtot ) mpNtot )
4πR3FpAtot 3A/N
were Ntot is the number of particles, Atot is the container area, and mp ) (4/3)πR3Fp is the mass of an individual particle of radius R and density Fp. In the experiments, the amount of organic liquid Mol to be spread with the particles was chosen to form a layer of height h ) 600 nm thickness, taking into account the volume of the liquid displaced by the particles. (See Supplementary Information for details). Image Processing and Statistical Analysis. The electron microscopy images of the porous membranes were subject to image processing and statistical analysis. The images were acquired with an electron microscope using the lowest scanning rate, stored in a PC, and then filtered from noise and imperfections. A morphological operation was employed to obtain a uniform background and to adjust the image contrast automatically. Subsequently, a second filter operation was performed for an adjustment and enhancement of the contrast. Black and white versions of the images were obtained by an appropriate brightness gain and threshold adjustment. Then the particle/pore positions were determined from the center of mass of the black spots corresponding to projections of the particles (or pores) in the black and white image. To calculate the nearest-neighbor distance di between the particles/pores, that is, the distance from the center of one individual particle to the center of the nearest one, we performed a Delaunay triangulation15 on the known particle/pore positions. The mean nearest-neighbor interparticle distance 〈dp〉 was calculated following the relation:
〈dp〉 )
( )∑ 1
N
‚
di
i
To obtain a measure of the spatial order of the particles/pores in the membranes, we calculated the pair correlation function g(r) from the stored particle/pore positions. For a 2D pattern of (14) Araki T.; Oinuma S. I.; Iriyama K. Langmuir 1991, 7, 738. (15) Preparata, F. P.; Shamos, M. I. Computational Geometry; Springer: New York, 1985.
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Figure 2. Scheme of the preparation of the porous membranes. points having a lateral density F, the pair correlation function is given by
g(r) )
1
∑δ(r - r )〉
〈
2πrF
ij
i,j
where δ(r) is the δ function, rij ) ri - rj is the distance between particles i and j, and 〈 〉 is an average over all particle orientations. The shape of g(r) depends on the quality of the order in the pattern: patterns with good hexagonal order are expected to produce values of g(r) that decay with a power law of ∼1/r3, whereas patterns with poor translational order produce a g(r) that decays exponentially.16 To calculate g(r), we first chose one particle as the center point and then counted the particles present in annular rings around it, following the procedure described in ref 17, starting at a minimum distance of 0.1 µm. As described in ref 18, only particles at a sufficient distance from the image borders were chosen as the center to eliminate edge effects. The final values of g(r) for each porous layer were obtained from a set of 7 to 10 images taken from different regions of the same membrane.
Results The general procedure used to prepare polymeric membranes with controlled porosity is schematically depicted in Figure 2. First, the organic liquid was mixed with superparamagnetic polystyrene particles and was spread together with a volatile solvent onto a water surface. Then, immediately after the evaporation of the solvent, an external magnetic field was applied perpendicular to the interface. In the presence of the field, the magnetic particles repel each other because of induced dipolar interactions and drag the organic liquid with them to cover the water surface. The monolayer formed by the organic liquid with the embedded particles was then photo cross-linked via UV radiation. To dissolve the particles that were protruding out of the upper and lower interfaces of this solidified layer, a solvent for polystyrene (toluene) was injected directly into the water phase below the monolayer. After the dissolution process, the membranes were transferred to a solid substrate and imaged by electron microscopy. (16) Terao, T.; Nakayama T. Phys. Rev. E 1999, 60, 7157. (17) Quinn, R. A.; Cui, C.; Goree, J.; Pieper, J. B.; Thomas, H.; Morfill, G. E. Phys. Rev. E 1996, 53, R2049. (18) Hansen, P. H. F.; Ro¨dner, S.; Bergstro¨m, L. Langmuir 2001, 17, 4867.
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Figure 3 shows different parts of a membrane prepared by this method at an area per particle A/N of ∼77.4 µm2. Parts a, c, and d of Figure 3 show the solidified organic layer with embedded particles before the dissolution of the particles. Part a of Figure 3 shows an overview image that illustrates the lateral homogeneity of the membrane. (To facilitate transfer to the grid, the membrane had to be cut on the water surface; the fragment shown here covers most of the grid but is only a part of a membrane that covered the entire water surface.) We note that in the absence of the magnetic field no membranes are obtained; instead, the organic liquid forms lenses that include the particles. As can be seen from parts c and d of Figure 3, the particles are protruding out of the solidified organic layer on both interfaces. In both images, the particles are visible and are arranged in approximately the same pattern. For these two pictures, we calculated an average nearest-neighbor interparticle distance of 6.0 µm for part c of Figure 3 and 6.1 µm for part d of Figure 3. The porous membrane obtained after dissolution of the particles is shown in parts b, e, and f of Figure 3. (The corresponding overview image is indistinguishable from the one obtained before dissolution of the particles and is shown in the Supporting Information). The dissolution of the particles is obvious from the top-view and bottomview pictures in parts e and f of Figure 3 obtained at the same magnification as the images in parts c and d of Figure 3, as well as from the magnified image in part b of Figure 3. Also, in this case the pattern formed by the pores has the same appearance, whether observed from the top or the bottom interface. A close inspection reveals, however, that not all particles are converted into pores during the dissolution process. In accordance with this observation, we found that the mean interpore distances (6.5 µm for part e of Figure 3 and 6.4 µm part f of Figure 3) are slightly higher than the interparticle distances in parts c and d of Figure 3. To show that one can control the membrane porosity, we carried out a second series of experiments in which we varied the number of spread particles. The series of SEM images on the left side of Figure 4 shows four different porous membranes obtained by using four different values for the area per particle, namely, 7.1, 23.8, 77.4, and 123.7 µm2. From these images, we calculated the corresponding mean interpore distances: 2.44, 4.43, 7.42, and 10.07 µm. To the right of each of these images, we show the pair correlation functions g(r) (solid red line) calculated from the observed particle positions. Along the bottom of these graphs, we plot as a dotted black line the pair correlation function g(r)hex for an ideal 2D hexagonal pattern having a lattice constant equal to the mean neighbor interparticle distance 〈dp〉 of the corresponding picture. This g(r)hex was rescaled on the y axis so as not to interfere with the experimental g(r) (continuous red line), and because no broadening is involved, it shows up as a series of sharp lines. In addition to the membranes shown in Figures 3 and 4, we prepared membranes using a variety of areas per particle, imaged them with electron microscopy, and determined the mean interpore distance 〈d〉. In Figure 5, we plot the values of 〈d〉 of all of these membranes as a function of the experimentally used area per particle A/N. The straight line indicates the nearest-neighbor distances expected for an ideal hexagonal pattern. The maximum value for the mean interparticle distances 〈dp〉 was 27.4 µm, corresponding to the highest area per particle (484.3 µm2), whereas the minimum value corresponded to an almost close hexagonal packing (∼2 µm). At higher values
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Figure 3. SEM images of a porous membrane realized with an area per particle of 77.4 µm2 and the amount of organic liquid needed to obtain a 600 nm layer. (a) Overview of a piece cut out of the membrane; (b) cross section of the membrane after dissolution of the particles; (c) top view; (d) bottom view of the membrane before the dissolution of the particles; (e) top view; and (f) bottom view of the membrane after the dissolution process.
of the area per particle (>500 µm2), the particles were not numerous enough to induce the formation of a thin layer of the organic liquid on the water interface; as a consequence, the organic liquid retracted into lenses that incorporated the particles. This lens formation at a lower density of particles was observed independently from the strength of the applied magnetic field. Discussion and Conclusions The aim of this work was to use repulsive particles to prepare porous membranes with uniform pores and a freely tuneable interpore distance. As can be seen from Figures 3 and 4, this goal was achieved. As a side remark, we note that the polystyrene particles used here can easily be removed by an organic solvent; thus the more hazardous removal of silica particles with hydrofluoric acid used earlier5 can be avoided. The particles used were primarily chosen upon commercial availability and ease of handling. In principle, one might use particles of different diameters or repulsive forces other than the magnetic ones (e.g., electrostatic forces11,12). In the following text, we discuss the spatial distribution of the pores. From the statistical analysis of the processed
images, we obtain the nearest-neighbor interpore distance as well as the 2D pair correlation function (Figures 4 and 5). In all cases, the pair correlation function shows several peaks, with the major peak always being at an interpore distance very close to the mean nearest-neighbor pore distance. In images b-d of Figure 4, this major peak is preceded by one (or several) minor peaks corresponding to pairs or clusters of particles in close contact. As a general rule, the nearest-neighbor distance in any arrangement of particles should increase proportionally to the square root of the area per particle as long as the type of arrangement (e.g., hexagonal or random arrangement of points) is unchanged. This rule is in principle fulfilled, as can be seen from the double logarithmic plot of Figure 5 in which the experimental points roughly follow the expected straight line. We note, however, that for large areas per particle the observed interpore distances are higher than expected. This is in accordance with the observation mentioned before that not all particles are converted into pores in the dissolution process. Probably some of the particles were completely covered by the solidified organic layer instead of protruding out and so were not accessible to the solvent. The pair correlation
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Figure 4. SEM images (top view) of porous membranes with areas per particle of (a) 7.1, (b) 23.8, (c) 77.4, and (d) 123.7 µm2. The diagrams on the right side of the pictures show the corresponding pair correlation functions g(r) of the pore positions (continuous red line) and the corresponding g(r) for a perfect hexagonal pattern (dotted black line). The corresponding values of 〈d〉 are indicated by blue arrows.
function shows in all cases several peaks, the mayor peak always being at an interpore distance very close to the mean nearest-neighbor pore distance. There are several reports that repulsive particles in 2D systems assume a regular hexagonal arrangment.11-13 Comparing the shape of the pair correlation functions (parts a-d of Figure 4, solid red line) with the corresponding theoretical function
for a perfect hexagonal lattice (black line), we observe that the pores are not in a perfect hexagonal arrangement. Furthermore, the small peaks preceding the major peak indicate some degree of clustering; the regularity of the pattern decreases with increasing area per particle. The pair correlation functions obtained for areas per particle smaller than 30 µm2 (corresponding to a mean interpore
Paramagnetic Particles as Repulsive Templates
Figure 5. Double logarithmic plot of the mean interparticle distance as a function of the area per particle. The straight red line shows the behavior expected for a hexagonally ordered structure of maximum separations.
distance 〈d〉 of less than 4.4 µm) include some features characteristic of hexagonal order (e.g., the double-peak structure of the second harmonic16 and the significant number of higher harmonics visible). However, these features gradually decay from parts a-d of Figure 4. This loss in regularity has three main origins: (i) the observed incomplete dissolution of particles: (ii) The presence of small aggregates of particles containing two to seven magnetic beads, especially at large interparticle separations. These aggregates of particles were formed in the
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3D solution used for spreading. To obtain a non-watermiscible spreading solution, excess stabilizer (SDS) was removed, and the particles were transferred from water to a less-polar medium. This procedure was the best compromise but already induced a slow aggregation in the spreading solution. (iii) The magnetic repulsive forces’ decay is inversely proportional to the cubic power of the interparticle distances. Thus, at large separations they become weaker than the capillary attraction.10 In summary, using repulsive particles we succeeded in preparing membranes of uniform pore size with an independently controlled interpore distance, the latter being approximately proportional to the square root of the area per particle. This result may be advantageous in finding the best compromise between the porosity and mechanical strength of such membranes. We furthermore observed some degree of ordering of these pores. Thus, these membranes might serve not only as filtration media but also as masks, templates, and structuring tools for the generation of optical elements and waveguides. Acknowledgment. Support by M. Mo¨ller, B. Rieger, K. Landfester, and R. Sauer (University of Ulm) is greatly appreciated. We especially thank P. Walter for his help in using the SEM. This work was funded by the Deutsche Forschungsgemeinschaft (SFB 569, SPP1052). Supporting Information Available: Measured distributions for the ζ potential and the electrophoretic mobility. Calculation of the amount of organic liquid needed Mol. Overview SEM image of a piece cut out of a porous membrane after the dissolution of the particles. This material is available free of charge via the Internet at http://pubs.acs.org. LA050528N
