Letter pubs.acs.org/ac
Behavior of Nanoparticles in Extended Nanospace Measured by Evanescent Wave-Based Particle Velocimetry Yutaka Kazoe, Kazuma Mawatari, and Takehiko Kitamori* Department of Applied Chemistry, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan ABSTRACT: The transport and behavior of nanoparticles, viruses, and biomacromolecules in 10−1000 nm confined spaces (hereafter “extended nanospaces”) are important for novel analytical devices based on nanofluidics. This study investigated the concentration and diffusion of 64 nm nanoparticles in a fused-silica nanochannel of 410 nm depth, using evanescent wave-based particle velocimetry. We found that the injection of nanoparticles into the nanochannel by pressure-driven flow was significantly inhibited and that the nanoparticle diffusion was hindered anisotropically. A 0.2-pN repulsive force induced by the interaction between the nanoparticles and the channel wall is proposed as the dominant factor governing the behavior of nanoparticles in the nanochannel, on the basis of both experimental measurements and theoretical estimations. The results of this study will greatly further our understanding of mass transfer in extended nanospaces. icrofluidics using 10−100 μm spaces has developed rapidly to improve performance by integrating various chemical operations and is now nearing the application stage. Nanofluidics using confined spaces smaller than 1000 nm is expected to become a new engineering field. Using volumes in the attoliter−femtoliter range, which are much smaller than that of a single cell, and the uniqueness by dominant surface effects, novel functional devices can be fabricated for use in biology, medicine, and energy engineering. Our group has developed research tools for 10−1000 nm spaces (hereafter “extended nanospace”) and discovered that liquids confined to nanochannels are significantly affected by surface effects, attaining various unique properties, such as higher viscosity and higher proton mobility.1 Exploiting the extended nanospace, we developed methodologies for analytical applications. For example, an 86-fL immunochemical reaction space was constructed by patterning antibodies in a nanochannel to realize 100% capture of target protein molecules.2 In addition, using a nanochannel as a separation column, ultrahigh-efficiency chromatography with a number of plates on the order of a million per meter was achieved with a 180-aL sample volume.3 Thus, novel ultrahigh performance has been demonstrated by using the extended nanospace. However, the behavior of substrates such as nanoparticles, viruses, and biomacromolecules (DNA, proteins, etc.) suspended in liquids confined to extended nanospaces remains poorly understood, despite its importance in nanofluidic bioanalytical devices. Several groups have reported entropic trapping of DNA in nanochannels4 and the energy barrier of nanoparticle injection into a nanopore,5 but these studies have mainly dealt with electrophoresis. More generally, molecular and particle transport through confined nanospaces has been studied in the fields of separation and membrane science by numerical simulation and experiments using nanopores,
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© XXXX American Chemical Society
suggesting the inhibition of injection and the hindrance of diffusion.6,7 However, few studies could reveal and verify the transport inside confined nanospaces because the spaces involved are smaller than the wavelength of light. Most recently, we have developed spatially resolved measurement methods for extended nanospaces with a resolution on the order of 10 nm.8,9 Evanescent wave-based particle velocimetry was developed to investigate the profiles of pressure-driven flows in nanochannels.9 Since the position and displacement of nanoparticles in a nanochannel can be determined, this method is applicable to the study of nanoparticle behavior in extended nanospaces. Thus, the present study employed evanescent wave-based particle velocimetry to study the concentration and diffusion of nanoparticles in a nanochannel. We found that nanoparticle injection into the nanochannel is significantly inhibited, and the diffusion in the nanochannel is hindered anisotropically between the directions parallel and normal to the wall. Surface interaction was concluded to be the dominant effect on nanoparticle behavior.
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EXPERIMENTAL SECTION Materials and Chemicals. Carboxylate-modified fluorescent polystyrene particles 64 ± 6 nm in diameter were seeded into a 1 mmol/L Na2B4O7 solution at pH 9.1 at a volume fraction of 0.0002%, which corresponds to a concentration, cb, of 1.9 × 1016/m3. The zeta potential of the nanoparticles was found to be −39 ± 6 mV using a Malvern Instruments Zetasizer. As a reference of the fused-silica nanochannel, the Received: February 4, 2015 Accepted: March 25, 2015
A
DOI: 10.1021/acs.analchem.5b00485 Anal. Chem. XXXX, XXX, XXX−XXX
Letter
Analytical Chemistry
particles and zp is the penetration depth. Since the whole region in the z direction in the nanochannel was illuminated by the evanescent wave, the minimum and maximum fluorescent intensities of a nanoparticle with zero displacement were assumed to be those attached to the two walls of the nanochannel and used as reference to determine h. The position along the z direction was obtained via z = h + a, where a is the nanoparticle radius, with a 33 nm uncertainty due to the nanoparticle size distribution and the image noise. The penetration depth of the evanescent wave, zp, was 138 ± 4 nm.
zeta potential of 500 nm silica particles was measured to be −74 ± 3 mV. Microchip Fabrication and Flow Control. Nanochannels of 50 μm width, 410 nm depth, and 2 mm length were fabricated on a fused-silica plate by electron beam lithography and plasma etching.10 Then, microchannels of 500 μm width, 6 μm depth, and 60 mm length for sample injection were fabricated on another fused-silica plate. Holes were made for inlets and outlets, and the channels were sealed by thermal fusion bonding. The sample solution was driven and injected into the nanochannels by an air pressure of 100−300 kPa. Since the microchannels were designed so that the ratio of the pressure loss in the nanochannel to that in the microchannel would be more than 99.9%, the applied pressure can be taken as that applied to the nanochannel. Evanescent Wave-Based Particle Tracking in a Nanochannel. The motion of nanoparticles in the nanochannel was measured using an apparatus similar to one reported previously.9 Figure 1 illustrates an optical system coupled
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RESULTS AND DISCUSSION Concentration of Nanoparticles in Nanochannel. The nanoparticles in the nanochannel were counted in order to estimate the injected nanoparticle concentration. Figure 2
Figure 2. Concentration of nanoparticles in the nanochannel, c, normalized by the bulk concentration, cb, as a function of the pressure applied to the nanochannel.
shows the concentration of nanoparticles in the nanochannel, c, as a function of the applied pressure, compared to the bulk concentration, cb. The concentration of nanoparticles dropped significantly, to 20−40% of cb, depending on the applied pressure. From this result, we found the resistive factor of the nanoparticle injection, even when the nanoparticle size was 6 times smaller than the nanochannel depth. In order to examine the force acting on the nanoparticles, the nanoparticle distribution in the nanochannel was obtained (see Figure 3a). Within 100 nm of the channel wall, the PDF is almost zero. Then, the potential energy of the nanoparticles, ϕ, was obtained from the Boltzmann distribution
Figure 1. Schematic of an optical system for evanescent wave illumination in a nanochannel. (a) A microchip coupled with a prism for total internal illumination of a laser beam. (b) The evanescent wave illumination in the nanochannel bridging two microchannels.
ϕ − ϕr kT
with a microchip. Briefly, a laser beam with a wavelength of 532 nm was introduced into a prism, and the evanescent wave was generated by total internal reflection at the interface between the fused-silica wall and the liquid in the nanochannel. The fluorescence emitted from the nanoparticles was captured by an EMCCD camera through an objective lens. The time resolution of the image acquisition was 260 μs. Using the fluorescence images, the position of each nanoparticle in the x (streamwise) and y (spanwise) directions was estimated with a 37 nm uncertainty by a homemade algorithm based on binarization with a dynamic threshold, the point spread function, and multitime particle tracking. In the z (depthwise) direction, the particle edge-wall distance h was estimated by using the fluorescent intensity excited by the evanescent wave with an exponential decaying intensity, Ip ∝ exp(−h/zp), where Ip is the fluorescent intensity of nano-
⎧c⎫ = ln⎨ ⎬ ⎩ cr ⎭
(1)
where ϕr and cr are the potential energy and concentration at the reference position, respectively, z = 205 nm, k is the Boltzmann constant, and T is the temperature. As seen in Figure 3b, the potential energy is in the order of 10−20 J and much higher than the motion energy of flowing nanoparticle of 10−25 J (flow velocity of mm/s at applied pressure of 100−300 kPa). Hence the potential energy profiles seem to be independent of the applied pressure and can be approximated to the static fluid condition. ϕ decreases steeply away from the wall, and the distance at which the potential energy decreases to 1/e (approximately 37%) is 40−50 nm. Using the potential energy profile, the repulsive force acting on each nanoparticle was estimated to be Fs = 2.2 × 10−13 N by averaging the derivatives of the potential energy, ∂ϕ/∂h, over the region 0 < h < 60 nm (32 nm < z < 92 nm). This repulsive force causing the B
DOI: 10.1021/acs.analchem.5b00485 Anal. Chem. XXXX, XXX, XXX−XXX
Letter
Analytical Chemistry
the gas constant, zi is the ion valence, F is the Faraday constant, and ci is the ion concentration. Electrostatic interaction may be the dominant effect because nanoparticle injection was more inhibited in the case of water (c/cb < 10%) with a Debye length of over 100 nm, as estimated from our previous data.9 However, the decay distance of the potential energy shown in Figure 3b, i.e., 40−50 nm, is 6 times longer than the λD of 6.8 nm. This inconsistency between experiment and theory has also been reported by other groups using the evanescent wave-based method.11,12 For example, a depletion of 42 nm particles within 40 nm of the wall in a nanochannel was found for λD < 1 nm.12 Whether these represent new findings is still under debate. Previous study reported that the nanoparticle distribution obtained by the evanescent wave-based method is blurred by the camera exposure time and the system noise.13 This blurring effect can be one reason for the decay distance of the potential energy longer than the Debye length and should be considered in our experimental results. We are establishing a model for evanescent wave-based particle velocimetry to extract inherent errors by the measurement method. Diffusion of Nanoparticles in a Nanochannel. Figure 4 shows the displacements of nanoparticles in the x (streamwise), y (spanwise), and z (depthwise) directions at a time resolution, Δt, of 260 μs. As shown in Figure 4a, in the x direction, the nanoparticle displacements are roughly in agreement with the Hagen−Poiseuille flow, as in our previous report.9 In the y direction, the distribution and PDF of the nanoparticle displacement are symmetric, owing to the diffusion without a fluid flow component (see Figure 4b). In the z direction, the nanoparticle displacement is biased by the presence of the wall, but the PDF of all nanoparticle displacements in the nanochannel becomes symmetric (Figure 4c). Using the PDFs of nanoparticle displacements in the y and z directions, the diffusion coefficients of nanoparticles parallel and normal to the wall, respectively, were estimated by Gaussian fitting, as listed in Table 1. Note that the diffusion coefficient in the bulk was calculated by the Stokes−Einstein relation, Db = kT/ (6πμa), where μ is the bulk viscosity of 0.894 × 10−3 Pa s. We observed anisotropically hindered diffusion of nanoparticles in the nanochannel: the diffusion coefficient parallel to the wall,
Figure 3. (a) Probability density function (PDF) of nanoparticles as a function of the depthwise position, z. (b) Potential profile of nanoparticles estimated from the PDF. The dashed line indicates the boundary of the region where the nanoparticle can exist physically.
nanoparticle depletion near the wall is thought to prevent nanoparticle injection into the nanochannel. According to the conventional Derjaguin−Landau−Verwey− Overbeek (DLVO) theory, the repulsive force on the nanoparticles is mainly due to the electrostatic interaction with the electric double layer between the negatively charged fused-silica wall and the nanoparticles. The Debye length, λD, which determines the length scale of the electrostatic force, was estimated to be 6.8 nm at 1 mmol/L Na2B4O7, as obtained by λD = {εRT/(2zi2F2ci)}, where ε is the dielectric constant, R is
Figure 4. Displacement of nanoparticles as a function of the depthwise position, z, and probability density functions (PDFs) of the displacements in the (a) x direction (streamwise), (b) y direction (spanwise), and (c) z direction (depthwise). Solid line indicates theoretical profile of fluid displacement by the Hagen−Poiseuille flow. The dashed line indicates the boundary region where the nanoparticles can exist physically. C
DOI: 10.1021/acs.analchem.5b00485 Anal. Chem. XXXX, XXX, XXX−XXX
Letter
Analytical Chemistry Table 1. Diffusion Coefficients of Nanoparticles in a Nanochannel, Parallel and Normal to the Walla parallel to the wall, D∥/Db (−)
solution 1 mM Na2B4O7 water9 a
experimental results theoretical estimation, Dave experimental results theoretical estimation, Dave
0.77 ± 0.02 (D∥ = 5.9 ± 0.2 × 10−12 m2/s) 0.80 0.80 ± 0.04 (D∥ = 6.1 ± 0.3 × 10−12 m2/s) 0.79
normal to the wall, D⊥/Db (−) 0.21 ± 0.01 (D⊥ = 1.5 ± 0.1 × 10−12 m2/s) 0.61 0.28 ± 0.01 (D⊥ = 2.1 ± 0.1 × 10−12 m2/s) 0.59
The diffusion coefficients of the nanoparticle suspended in water in the nanochannel were estimated using the data of our previous study.9
Table 2. Forces Acting on Nanoparticle, Normal to the Wall diffusional force, FD force by gradient of D⊥, FΔD surface force, Fs drag force by fluid flow, Ff (micronanochannel interface: U < 10−4 m/s)
D∥, decreased to 77% of the bulk, while that normal to the wall, D⊥, decreased to 21%. In classical hydrodynamics, the hindrance of diffusion near the surface has been studied. Because of the hydrodynamic drag due to the wall, the hindrance factor for diffusion parallel to the wall is given by14 f =
include the effect of the intermittent particle adsorption by collision to the surface. On the other hand, in our study, we consider that the effect of the intermittent adsorption of nanoparticles to the channel wall could be excluded because of the diffusion distance of 10 nm by the time resolution of 100 μs. On the basis of our results, the electroviscous effect may not have significant influence on the diffusion parallel to the wall in the nanochannel. For the diffusion normal to the wall, the measured diffusion coefficients are 2−3 times lower than the theoretical values. Thus, we propose another hindrance factor for diffusion normal to the wall, in addition to the hydrodynamic wall effect. That additional hindrance factor is thought to be the repulsive force induced by the surface interaction, Fs, because it governs the distribution of diffusing nanoparticles. Nanoparticle Transport in Extended Nanospace. Our experimental results suggest that the repulsive force induced by the surface interaction is dominant in both the injection and transport of nanoparticles in a nanochannel. In order to verify these results, we estimated the forces acting on nanoparticles in a nanochannel theoretically. To compare with the surface interaction, only the normal component of the forces exerted toward the channel wall was considered. A previous hydrodynamics study suggested that the dominant factors in particle motion are diffusion, gradient of diffusion coefficient, force due to surface interaction, and fluid flow.21 The forces due to these factors are roughly given by the Stokes’ law:
D Db 9 ⎛⎜ a ⎞⎟ 1 ⎛⎜ a ⎞⎟ 45 ⎛⎜ a ⎞⎟ 1 ⎛⎜ a ⎞⎟ + − − 16 ⎝ z ⎠ 8⎝z⎠ 256 ⎝ z ⎠ 16 ⎝ z ⎠ 3
=1−
4
5
(2) 15,16
while that normal to the wall is given by f⊥ =
D⊥ 6h2 + 2ah = 2 Db 6h + 9ah + 2a 2
(3)
In a nanochannel, the hindrance factor is superposed to express the two-wall effect as follows f = f (z ) + f (H − z ) − 1
0.4 × 10−13 N 0.2 × 10−13 N 2.2 × 10−13 N
