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Brownian rod scheme in microenvironment sensing
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/content/aip/journal/adva/2/1/10.1063/1.3699034
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Image of FIG. 1.

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FIG. 1.

Schematic description of the proposed microenvironment sensing scheme in which a rod is drawn to a cylindrical pillar using an attractive force (a). The motion is assumed to be exclusively in the x-y plane which in a practical implementation is based on the rod monitored by a camera placed in the z-axis (b). The distance R that the rod is able to venture from the cylinder axis has implications pertaining to the sensing accuracy. Depending on the attractive force applied, the rod is able to tether exclusively to the cylindrical pillar, be free, or to transition between both states (enhanced online). [URL: http://dx.doi.org/10.1063/1.3699034.1]10.1063/1.3699034.1

Image of FIG. 2.

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FIG. 2.

Plot of D θ against f, the proportion of samples not tethered. The dashed line joins the tethered and free diffusion coefficients at f = 0 and f = 1 respectively and each data point was calculated from 18,000 samples.

Image of FIG. 3.

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FIG. 3.

Plots of D θ against N, the number of sample points when the rod is in state I (a) and state II (b). Data points are the mean, error bars represent one sample standard deviation and both were determined from 100 realisations at each value of N.

Image of FIG. 4.

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FIG. 4.

Plots of μf (mean proportion of samples spent free) (a) and sf (sample standard deviation of samples spent free) (b) against the normalised charge product calculated from 18,000 samples. Increasing the magnitude of the charges such that the force is attractive reduces the proportion of time spent in state I. All simulations were begun with the rod touching the edge of the pillar.

Image of FIG. 5.

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FIG. 5.

Plots of the rod centroid position for equal and opposite charges on the rod and pillar of (a) 0, (b) 100 and (c) 300 electron charges (chosen to correspond with values of approximately 1, 0.5 and 0 respectively) over 18,000 samples. The plots in (d)-(f) correspond to the plots in (a)-(c) and represent the radial distance of the rod centroid from the centre of the pillar (r) against the angle the centroid of the rod makes with the positive x-axis (ψ). The circles in (a)-(c) and vertical dashed lines in (d)-(f) correspond to the points where the rod and pillar are in contact. Furthermore, the data points in (c) and (f) have been enlarged for clarity.

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/content/aip/journal/adva/2/1/10.1063/1.3699034
2012-03-22
2014-04-24

Abstract

Fluctuations of freely translating spherical particles via Brownian motion should provide inexhaustible information about the micro-environment, but is beset by the problem of particles drifting away from the venue of measurement as well as colliding with other particles. We propose a scheme here to circumvent this in which a Brownian rod that lies in proximity to a cylindrical pillar is drawn in by a tuneable attractive force from the pillar. The force is assumed to act through the centre of each body and the motion exclusive to the x-y plane. Simulation studies show two distinct states, one in which the rod is moving freely (state I) and the other in which the rod contacts the cylinder surface (state II). Information about the micro-environment could be obtained by tracking the rotational diffusion coefficient D θ populating in either of these two states. However, the magnitude of the normalized charge product in excess of 6.3x104 was found necessary for a rod of 6.81 × 0.93 μm2 (length × diameter) and 10μm diameter cylindrical pillar to minimize deviation errors. It was also found that the extent of spatial sensing coverage could be controlled by varying the charge level. The conditions needed to ascertain the rotational sampling for angle determination through the Hough transform were also discussed.

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Scitation: Brownian rod scheme in microenvironment sensing
http://aip.metastore.ingenta.com/content/aip/journal/adva/2/1/10.1063/1.3699034
10.1063/1.3699034
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