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Experiments in Fluids

Erschienen in:

01.12.2004 | Original

Near-wall hindered Brownian diffusion of nanoparticles examined by three-dimensional ratiometric total internal reflection fluorescence microscopy (3-D R-TIRFM)

verfasst von: K. D. Kihm, A. Banerjee, C. K. Choi, T. Takagi

Erschienen in: Experiments in Fluids | Ausgabe 6/2004

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Abstract

A three-dimensional nanoparticle tracking technique using ratiometric total internal reflection fluorescence microscopy (R-TIRFM) is presented to experimentally examine the classic theory on the near-wall hindered Brownian diffusive motion. An evanescent wave field from the total internal reflection of a 488-nm bandwidth argon-ion laser is used to provide a thin illumination field on the order of a few hundred nanometers from the wall. Fluorescence-coated polystyrene spheres of 200±20 nm diameter (specific gravity=1.05) are used as tracers and a novel ratiometric analysis of their images allows the determination of fully three-dimensional particle locations and velocities. The experimental results show good agreement with the lateral hindrance theory, but show discrepancies from the normal hindrance theory. It is conjectured that the discrepancies can be attributed to the additional hindering effects, including electrostatic and electro-osmotic interactions between the negatively charged tracer particles and the glass surface.

Vorheriger Artikel Bubble-size distributions produced by wall injection of air into flowing freshwater, saltwater and surfactant solutions

Nächster Artikel Near-surface velocimetry using evanescent wave illumination

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Hosoda et al. (1998) have shown that the near-wall Brownian motion is found to be anisotropic with respect to the directions parallel and perpendicular to the interface using evanescent wave microscopy. Spectroscopic analysis was conducted, allowing a wide range of wave number, by varying the incident ray angle, and the resulting autocorrelation function of the image intensity showed evidence of the anisotropy. However, the scope of their work is far from being comprehensive in that no quantitative measurements of the near-wall hindered diffusion motion have been conducted and compared with the existing theories.

Refer to Fig. 10 in the Appendix for the calculation uncertainties in determining the penetration depth.

Model UP-1830 UNIQ with 1024×1024-pixel CCD elements and each pixel element is of dimension of 6.45×6.45 μm. The camera operates at 30 frames per second, with minimum illumination of 0.04 lux and a signal-to-noise ratio better than 58 dB. A certain level of image smearing because of the finite exposure time is inevitable, and this may result in the blurring of the particle image to a certain degree. However, the finite exposure time does not affect the ratiometric measurements where only the intensity ratios are analyzed and the intensity ratio is unaffected by the image blur. Note that the measured particle location is referred to its closest pole from the solid surface, i.e., the brightest point (refer to Sect. 2.3).

The dye particles are believed to be free from the “photo-bleaching” effect that can render the dye unable to fluoresce after being excessively exposed to high-intensity pumping light. As per the specifications of Molecular Probes (2004), the aqueous suspension of fluorescent beads do not fade noticeably when illuminated by an intense 250-watt xenon-arc lamp for 30 min. Since the current experiment uses approximately 40-mW illumination at 488-nm bandwidth from the 200-mW nominal laser for the total exposure time of up to 4 s, any errors associated with photo-bleaching should be negligibly minimal.

The high-NA objective-based TIRFM system adjusts the incident angle using a fiber optic laser guide attached to a precision positioning system traveling along the barrel axis (http://www.olympusmicro.com/primer/java/tirf/tirfalign/index.html).

The physical location of the brightest particle may not be exactly at zero at the solid surface; rather, it should be at the most probable separation distance. Since both the glass surface and the particles are negatively charged, there exists the most probable separation distance, which is equivalent to the minimum potential energy state ensuring the mechanical equilibrium. Thus, z=0 here indicates just a reference point for the relative locations of other less bright particles.

For d_p=200 nm, k=1.38054×10⁻²³ J/K, μ=0.001N s/m for water at T=293 K, the free Brownian diffusivity (Eq. 8) is given as D=2.1451 μm²/s and the averaged square displacement 〈Δz²〉=2DΔt=0.142 μm² for the time interval of 33 ms of the 30 fps imaging. The average displacement 〈|Δz|〉 can be approximated to \({\sqrt {{\left\langle {\Delta z^{2} } \right\rangle }} } = 377\;{\text{nm}}{\text{.}} \) The near-wall hindered displacement (Fig. 5) will reduce it to about a half, i.e., 〈Δz〉~±189 nm, which occupies approximately 70% of z_p.

When the ray angle increases to 65°, the uncertainty is noticeably reduced to ±6.85 nm, but its penetration depth will not be sufficient to accommodate the pertinent Brownian motion length scale.

Meiners and Quake (1999) attempted a direct measurement of hydrodynamic interaction between two spherical colloid particles, ranging from 3.1 µm to 9.8 µm, two order of magnitudes larger than the present nanoparticles, suspended by optical tweezers in an external potential. However, they measured the cross-correlations of only two-dimensional motions of particles without accounting for the near-wall hindrance.

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Titel: Near-wall hindered Brownian diffusion of nanoparticles examined by three-dimensional ratiometric total internal reflection fluorescence microscopy (3-D R-TIRFM)
verfasst von: K. D. Kihm
A. Banerjee
C. K. Choi
T. Takagi
Publikationsdatum: 01.12.2004
Verlag: Springer-Verlag
Erschienen in: Experiments in Fluids / Ausgabe 6/2004
Print ISSN: 0723-4864
Elektronische ISSN: 1432-1114
DOI: https://doi.org/10.1007/s00348-004-0865-4

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