Measurements of the minimum elevation of nano-particles by 3D nanoscale tracking using ratiometric evanescent wave imaging

The near-wall region is considered to be within one micron of the solid surface, in which both lateral and normal Brownian motions are substantially hindered due to the proximity of the no-slip wall (Brenner 1961; Goldman et al. 1967).

Prieve et al. (1987) and Prieve and Frej (1990) experimentally examined the potential energy profile of micro-sized non-fluorescent particles, ranging from 3.5 to 7.5 μm in radius, and measured their most probable separation distance as well. For the case of 5-μm radius particles a 67% decrease in the most probable distance was observed when the saline concentration was increased from 0.1 to 1 mM (Bike and Prieve 1990).

  θ _c is the critical angle, and n _t and n _i are the index of refraction for the rarer (target or external) and denser (incident or internal) mediums, respectively.

The Debye length thus can be estimated to 30.4, 9.6, and 3.0 nm for the saline concentration of 0.1, 1.0, and 10 mM, respectively (T = 298 K, R = 8.314 J/(mol K), ε = 6.95e−10 F/m, q = 1, F = 96480 C/mol, and C = 0.1, 1, or 10 mM/L).

The sample solution was allowed to equilibrate to ambient conditions of the thermally controlled laboratory. The temperature rise of the test well solution due to the incident laser beam was measured using a thermocouple probe to be less than 1 K from the reference temperature at 297.6 K. Since MSD is directly proportional to the absolute temperature scale, the effect of such a small temperature rise on Brownian motion is considered negligible. Besides, the present experiment focuses on the averaged z-locations of nanoparticles and the effect of Brownian should be minimal unlike the case of general PTV considerations. Accounting for both permittivity changes caused by the change in temperature as well as the temperature change itself in Eq. 7, the changes in the Debye length are estimated to be 0.01 nm for 0.1 mM, 0.003 nm for 1.0 mM, and 0.001 nm for 10 mM, for the case of the water temperature change of approximately 1 K. Thus the changes in the Debye length are negligible with regard to the small temperature fluctuations caused by the laser illumination.

Bike and Prieve (1990) used Derjaguin’s approximation along with linear superposition to estimate the potential energy profile of a sphere. Rather than calculating the Stern potential of individual spheres, which is a function of the charge density and needed to create the profile, a range of values (25 ∼ ∞ mV) were considered in order to bound the problem. Good agreement was found when compared to experimental data.

To determine the minimum numerical aperture (NA) of the special objective lens the following equation is used, NA = n ₁ sin θ ₁ = n ₂ sin θ ₂, where 1 and 2 denote glass (n ₁ = 1.515) and water (n ₂ = 1.33), respectively. When θ ₂ is 90°, the minimum NA is calculated to be 1.33 and hence an objective lens having an NA higher than 1.4 will be needed to allow for TIR imaging. More details may be referred to Kihm et al. (2004).

The EM-CCD (Hamamatsu Model C9100-02) boasts both functions of a cool-CCD and an intensified-CCD, and it runs at 30 frames per second (fps) at full spatial resolution of 1 K × 1 K pixels with 14-bit digitization. Its frame speed can be increased up to 520.8 fps by using the binning and sub-array features. The fps for current experiment was set to 47.7. The pixel size is 8 μm × 8 μm and the effective area is 8 mm × 8 mm with 1 K × 1 K pixels. For the case of a total magnification of 90, the pixel dimension is equivalent to the corresponding test field size of 88.9 nm × 88.9 nm. During the current 21-ms exposure time per frame, nanoparticles move a maximum distance of an order of 100-nm at the penetration depth of 272 nm near the outer edge of the measurement range where the maximum MSD is expected. This definitely should be accounted for in case of use of the present technique as velocimetry. The present results, however, should have been minimally biased by the image blurring since the determination of the minimum elevation does not critically depend on whether the particle image is clear or blurred.

The images were taken for dried samples and the particles were coagulated as the liquid shrunk during the dryout process. The particle coagulation was observed negligibly small in suspension because of their extremely low concentrations ranged from 0.00016 to 0.014% for the main experiments.

These maximum roughness values are equivalent to 29 and 1% of the penetration depth calculated to be 272 nm for an incident angle of 62. This implies that an uncleaned surface can result in serious bias on the elevation measurements, up to 30% of the penetration depth or approximately 100 nm.

Photobleaching is a property of fluorescent materials in which the intensity of the emitted light decreases both with time and with excitation intensity. For low power light sources, such as mercury arc lamps, significant reduction of intensity may be seen on the order of seconds to minutes. However for high power laser sources bleaching may be seen on the order of microseconds (Song et al. 1995).

The illuminated area can be estimated using \( d = {\text{NA}} \times 180/M, \) where d is the diameter of the illuminated area, NA is the numerical aperture of the illuminating fiber (0.08 given by Olympus), and M is the magnification (60) of the TIRF objective lens.