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Sorting of Brownian rods by the use of an asymmetric potential
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Image of FIG. 1.
FIG. 1.

(a) Directions of diffusion coefficients superimposed on a typical rod under consideration, with the static laboratory frame in the top left. (b) PDFs for small and large spheres at a given time t. The greatest difference in probability between the small and big spheres occurs at the intersection of the PDFs (marked as b). (c) Diagrammatic representation of the position and alignment of rods near the end of the on period from both top and side views.

Image of FIG. 2.
FIG. 2.

Plot of D yy (upper curves) and D xx (lower curves) vs time for two different rods with dimensions 595.2 × 168 × 168 nm 3 (black, dashed) and 864 × 72 × 72 nm 3 (red, solid). Horizontal lines represent and vertical lines represent τθ.

Image of FIG. 3.
FIG. 3.

Contour plots of diffusion coefficient in the laboratory x direction over a range of rod sizes taken at time (a) 30 and (b) 400 μs. The percentage difference in length (L) and diameter (D) are taken from a 960 × 120 × 120 nm 3 base rod. The circles on the plot indicate the rod sizes used in simulations, with the blue colored circles indicating the rods that were taken to the second stage of sorting. The red and black circles are rod sizes on adjacent contours at 30 μs, and are overlaid in (b) to emphasize the change in diffusion coefficient over time. The largest diffusion coefficients correspond to the smallest particle sizes in the lower left corner of the plot (red contours) and decrease toward the top right (blue contours). The colors of dots used correspond to the curves in Fig. 5.

Image of FIG. 4.
FIG. 4.

Separation time (blue squares) and number of cycles for separation (green squares) vs off time for three different rod sizes taken to stage 2 of sorting. Rod sizes used were 595.2 × 168 × 168, 710.4 × 120 × 120, and 864 × 72 × 72 nm 3 . Separation time has been defined as number of cycles for separation multiplied by the off time, and is shown as it is a more meaningful performance characteristic than number of cycles required to separate rod populations.

Image of FIG. 5.
FIG. 5.

[(a) and (c)] Plots of 10th and 90th percentiles of expected rod populations vs cycles, and [(b) and (d)] expected number of particles in each potential well at 20 000 cycles using an initial population of 10 000 particles. These were determined for [(a) and (b)] first stage sorting using 30 μs off time with nine different rod dimensions (as shown in Table I) along three contours (overlaid dots in Fig. 3), and [(c) and (d)] second stage sorting using 400 ms off time with the blue population from the first stage (curve colors correspond to circles in Fig. 3).


Generic image for table
Table I.

Actual rod dimensions used in simulations, along with percentage differences compared to a 960 × 120 × 120 nm 3 base rod and diffusion coefficients in the laboratory x direction at both early and late off times. Entries are arranged in the same way as in Fig. 3, with the left column corresponding to the red circles, center column to blue circles, and right column to black circles.

Generic image for table
Table II.

Scale factors used to adjust the theoretical diffusion coefficients in the three degrees of freedom considered.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Sorting of Brownian rods by the use of an asymmetric potential