Article pubs.acs.org/IECR
Tracking Nanoparticle Diffusion in Porous Filtration Media Michael J. Skaug† and Daniel K. Schwartz* Department of Chemical and Biological Engineering, University of Colorado, Boulder, Colorado 80309, United States S Supporting Information *
ABSTRACT: Porous materials are used extensively in industrial filtration and mass separation processes, but it is often difficult to predict their mass transport behavior because porous materials are an inherently heterogeneous medium and multiple microscopic mechanisms can lead to macroscopic changes in transport. To provide a microscopic view of hindered porous transport, we present the results of single-particle tracking experiments in which we followed the diffusive motion of individual nanoparticles in commercial filtration media. We compared two materials, glass fiber and nitrocellulose, with similar nominal characteristics, but we found that the diffusion behavior of the embedded particles differed significantly. While diffusion in the glass fiber material was nearly unhindered, the dynamics were heterogeneous and significantly slowed in the nitrocellulose. We rationalized the observations based on differences in geometric hindrance, particle binding, and hydrodynamic interactions. Our results highlight the ability of single-particle tracking to differentiate between distinct dynamic mechanisms, and they suggest that nominal material characteristics may be a poor predictor of transport properties.
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INTRODUCTION Porous materials are frequently used in industrial processes like filtration,1 water treatment,2 heterogeneous catalysis,3 and mass separations.4 In all of these applications, hindered mass transport through the pore network is either essential to the process or a necessary, but undesirable, limitation. Therefore, to optimize mass transport through porous catalysts or provide higher resolution mass separations, researchers tune material and pore characteristics. Unfortunately, there are no universal models capable of predicting mass transport based on a description of the porous material. Part of the problem is the complexity of the pore network in real porous materials, and the other is that many microscopic dynamic mechanisms (e.g., steric, hydrodynamic, binding, etc.) give rise to the observed macroscopic transport. Similar complexity governs microscopic transport in biological systems.5 Experimental approaches are needed that expose the underlying microscopic transport processes in realistic porous materials. Nuclear magnetic resonance is a noninvasive method for studying transport in many porous materials,6,7 but it provides only an ensemble view of a highly heterogeneous process. Optical methods are also available to study transport processes, such as particle image velocimetry,8 fluorescence correlation spectroscopy,9,10 and single-particle tracking,11 but the refractive index difference between the voids and solid matrix scatters light and makes it difficult to optically access the interior of a three-dimensional porous material. One solution is to study two-dimensional microfabricated models.12−15 To optically probe three-dimensional porous networks, researchers have used materials with subwavelength pore sizes like nanoporous glasses16 or subwavelength solid matrix elements like polymer gels.17,18 However, many industrially relevant materials4,19,20 possess moderate porosity and pore sizes as large as, or larger than, typical optical wavelengths used experimentally. An alternative solution, which eliminates scattering regardless of the pore sizes, is to fill the pore space with a liquid of the same refractive index as the solid matrix.21 © XXXX American Chemical Society
This index-matching technique has been employed in colloidal suspensions22,23 and porous silica materials24 but, in general, could be applied to any porous material. In this work, we present the results of single-particle tracking experiments in which we observed the pore scale diffusive motion of individual nanoparticles in commercial porous filtration media. We investigated two materials with similar nominal characteristics (i.e., pore size and porosity) that exhibited distinctly different pore morphologies characteristic of different fabrication methods. The first was a glass fiber filter composed of a dense mat of randomly oriented glass fibers, and the second was a phase-separated polymer membrane made of nitrocellulose. The porous diffusion is also expected to depend on nanoparticle size,25 but in this work, we isolated and focused on the influence of qualitatively different porous structures. We permeated the porous materials with a unique index-matching liquid, which allowed us to track the diffusive motion of fluorescent tracer particles and directly image the threedimensional void network using confocal fluorescence microscopy. Although the two materials had similar nominal characteristics, we found significant differences in the diffusive motion of embedded particles. In the glass fiber material, there was only a minor reduction in particle mobility compared to the unconfined liquid, whereas in the nitrocellulose membrane, there was a significant slowing and heterogeneity between particle trajectories. Our results indicate that simple measures of pore structure, such as porosity and mean pore size, may not be sufficient to predict the diffusive motion of particles in the pore network. Special Issue: Scott Fogler Festschrift Received: October 1, 2014 Revised: December 4, 2014 Accepted: December 29, 2014
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DOI: 10.1021/ie503895b Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research
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MATERIALS AND METHODS Materials. Glass fiber (APFF04700) and nitrocellulose (DAWP04700) filter materials were obtained from Millipore. Nominal characteristics of the materials provided by the manufacturer are presented in Table 1. All other materials were purchased from Sigma-Aldrich unless otherwise indicated.
dimensions using a Nikon A1R laser scanning confocal microscope. The acquired volumes were 256 × 256 × 256 voxels with a voxel size of 0.10 or 0.12 μm. Isosurface renderings were prepared using Imaris software. To characterize the pore space structure, we used a chord length analysis.27 An intensity threshold was used to identify the void space in each two-dimensional confocal slice and measure the void fraction (i.e., porosity ϕ). Then, from random positions within the void space, chords were generated and expanded in four equiangular directions until they intersected the void boundary. The distribution of resulting chord lengths were fit with a k-Gamma function, f(S ) = (kk S k−1/ S ̅ kΓ(k))exp(−kS / S ̅ ), whose two parameters, S ̅ and k, characterize the mean void size and the relative variation around the mean.
Table 1. Nominal Material Characteristics Provided by the Manufacturer material
pore size (μm)
porosity
glass fiber nitrocellulose
0.7 0.65
0.9 0.81
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Single-Particle Tracking. We imaged the diffusion of 40 nm polystyrene spheres (dark red, F-8789, Life Technologies) suspended in a liquid that permeated the void space of the porous filters. The particles were dispersed in an 80:20 (by volume) mixture of thiodiethanol (TDE) and Triton X-100. This liquid mixture (refractive index n ∼ 1.51) closely matched the refractive indices of the two materials: glass fiber (n ∼ 1.52) and nitrocellulose (n ∼ 1.50). The fluorescent particle concentration was sufficiently low (volume fraction ϕ = 10−6) to avoid particle−particle interactions and allow identification of individual particles in the single-particle tracking experiments. Before an experiment, a 1 cm2 piece of material was cut from the supplied membranes and placed on a microscope coverslip. Approximately 50 μL of fluorescent particle suspension was then pipetted onto the top surface of the porous film, allowed to infiltrate the pores and saturate the film (∼10 min), and then equilibrated for 1 h. After the void space was saturated with the fluorescent particle suspension, the porous samples were imaged using a modified epifluorescence microscope (TE2000, Nikon). Fluorescence excitation was provided by a 640 nm diode-pumped solid-state laser (Crystal Laser). Excitation light was delivered and the fluorescence emission collected by a 60×, NA = 1.2, water-immersion objective (Nikon). The emitted light was passed through a 1.5× relay lens and imaged on an electron-multiplying CCD camera (Andor iXon3), resulting in 145 nm/pixel at the image plane. We imaged particle diffusion within the filter material, approximately 30 μm from the filter surface, at a frame rate of 20 Hz for a total of ∼1 h. The imaged particle density was approximately 0.1 particles/ μm2 (i.e., approximately 13 μm between neighboring particles). To identify and track the motion of individual particles in the image sequences, we used custom software that implemented the radial symmetry algorithm.26 Subpixel particle positions were linked frame-to-frame into two-dimensional trajectories using a nearest neighbor distance threshold of 2 pixels, or 0.29 μm. Based on control experiments, in which particles were immobilized in the absence of surfactant, we estimated that the precision with which we could identify the particle positions was approximately 25 nm. Pore Structure Characterization. We used laser scanning confocal microscopy to image the three-dimensional pore network of the filter materials. First, the index-matching liquid mixture described above (80:20 TDE/Triton X-100) was dyed with 0.1 g/L of fluorescein sodium salt or a rhodamine derivative (Atto Rho6G, Atto-Tec). A 1 cm2 piece of porous material was placed on a coverslip and permeated with the fluorescently dyed liquid, which was then imaged in three
RESULTS Characterizing the Pore Structure. The manufacturer of the filter materials provided some nominal pore characteristics, such as pore size and porosity, but porous transport is also influenced by details such as pore size distribution and pore connectivity. To provide a more complete picture of the pore network, we used confocal fluorescence microscopy. The primary obstacle to using an optical technique to image a porous material is the refractive index difference between the solid matrix material and the void space. The refractive index mismatch causes light to scatter from the many solid-void boundaries. To eliminate this refractive index difference and allow optical access deep within the three-dimensional porous material, one can fill the voids with a liquid of the same refractive index as the solid matrix, and thus index-match the material.21 We needed a liquid with a refractive index close to that of the glass fiber and nitrocellulose (1.50 < n < 1.52) that would not disturb the solid matrix materials or the polymer nanoparticles. There are few liquids that match these requirements, but we found the polar, high refractive index liquid (n = 1.52), thiodiethanol, to exhibit the necessary characteristics. A mixture of TDE and Triton X-100, a nonionic surfactant, was found to optimally match the refractive index of both the glass fiber and nitrocellulose materials and also prevent strong binding of the tracer particles to the pore walls. Although characterizing the colloidal interactions in this nonaqueous system was beyond the scope of this work, we hypothesize that steric repulsion (due to adsorbed surfactant) was responsible for preventing excessive binding of the nanoparticles to the pore walls. To image the pore network, we fluorescently dyed the indexmatching liquid, which permeated the voids of the material. Isosurface renderings of the confocal volumes clearly showed the different pore topologies of the two materials (Figure 1a,b). The glass fiber material was a mesh of randomly oriented fibers of different diameters. The nitrocellulose membrane consisted of more compact solid elements characteristic of the phase separation process likely used in its fabrication. The measured porosities of the two materials, ϕglass = 0.93 ± 0.05 and ϕnotro = 0.85 ± 0.09, were consistent with the nominal values of 0.9 and 0.81 (Table 1). However, the measured pore sizes were significantly different than the nominal values, 0.65 and 0.7 μm. The chord length analysis of the confocal images revealed much larger mean void sizes, Sglass = 10.7 μm and Snitro = 3.3 μm ̅ ̅ (Figure 1e). (The measured void sizes were moderately sensitive to the intensity threshold used to identify pores; a ±10% change in threshold resulted in a ∓8% change in mean B
DOI: 10.1021/ie503895b Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research
trajectories (indicated by the brackets), the mean square displacement as a function of lag time (Δt) ⟨ r 2(Δt )⟩ = ⟨ (r(t + Δt ) − r(t ))2 ⟩
(1)
was only slightly reduced in the glass fiber material compared to the unconfined liquid but significantly reduced in the nitrocellulose (Figure 2). We fit the mean square displacement
Figure 2. Mean square displacement as a function of lag time (eq 1) for nanoparticles within the porous materials and in unconfined liquid. Solid lines connecting symbols are guides for the eye. Also displayed is the expected linear scaling for Fickian diffusion. Error bars indicate the standard deviation between data from three independent samples or five subsets of data for the unconfined liquid.
curves to the model ⟨ r 2 ⟩ = 4DΔtα,5,25 which provides a value for the effective diffusion coefficient D and the anomalous diffusion parameter α, which quantifies deviations from normal Fickian diffusion (Table 2). In the glass fiber material, diffusion
Figure 1. Porous structures of the two materials and trajectories of single particles within the void space. Three-dimensional reconstructions of the solid matrix based on confocal images of the (a) glass fiber and (b) nitrocellulose materials. Shown at approximately the same spatial scale are single nanoparticle trajectories in the (c) glass fiber and (d) nitrocellulose materials. (e) Distributions of chord lengths, which characterize the void sizes in the two porous materials with the mean void size annotated. Symbols are experimental data and solid lines are a fit to the k-Gamma function.
Table 2. Diffusion Parameters Determined by Fitting the Mean Square Displacement Curves (Figure 2) with the Model ⟨ r 2 ⟩ = 4DΔtαa
void size.) The likely reason for this discrepancy is that the pore size provided by the manufacturer is meant to characterize the filtration behavior of the material and not necessarily the typical void size. Although this would explain the larger measured void sizes, it is interesting that two materials with similar filtration properties would possess very different structures and characteristic length scales. In materials like zeolites, which are composed of voids interconnected by narrow passages, it is clear that the average void size would not characterize the sieving properties of the material. Similarly, in the disordered materials we studied, the similar filtration properties might be the result of details related to correlations in the pore sizes and the network topology. Nanoparticle Diffusion. We tracked the diffusive motion of individual 40 nm tracer particles within the void space and found significant differences between the two materials, despite the fact that they shared similar nominal properties. Except for a few particles that became transiently immobilized (
