Research Assistant , University of Chicago
Unprecedented Directionality in Random Walk has been Observed in High Aspect Ratio Nanowires
It is a random motion of a small particle suspended in a medium like water caused by collisions with molecules comprising the medium.
Silicon nanowires (SiNWs) suspended in water were examined using a microscope. Cylindrical NWs with higher aspect ratios than have previously been studied were examined.
These SiNWs displayed high anisotropy (or directionality) in their BM. Because the movement along the long axis experiences less drag due to its smaller cross sectional area, we expected the translational diffusivity along the NW’s long axis (D∥) be greater than that along the short axis (D⊥). In our experiment, the quotient values (D∥/D⊥) obtained from 30 different NWs ranged between 2 and 25, which exceeded those of previously reported smaller aspect ratio particles in non-crowded environments. Interestingly, no theoretical expressions gave D∥/D⊥ higher than 2: all the theories for diffusion of rods converged monotonically to a limit less than 2.
The new empirical results highlight the lack of robust theories for understanding diffusion of high aspect ratio particles. Regression analysis of my experimental result for translational BM of the NWs showed a clear deviation from the Stokes-Einstein relation, which relates diffusivity of a spherical particle to its radius. Experimental data will serve as an integral part to expand old theories and to shed light on the physics of high aspect ratio particle
Abstract: Brownian motion of slender particles near a boundary is ubiquitous in biological systems and in nanomaterial assembly, but the complex hydrodynamic interaction in those systems is still poorly understood. Here, we report experimental and computational studies of the Brownian motion of silicon nanowires tethered on a substrate. An optical interference method enabled direct observation of microscopic rotations of the slender bodies in three dimensions with high angular and temporal resolutions. This quantitative observation revealed anisotropic and angle-dependent hydrodynamic wall effects: rotational diffusivity in inclined and azimuth directions follows different power laws as a function of the length, ∼ L(-2.5) and ∼ L(-3), respectively, and is more hindered for smaller inclined angles. In parallel, we developed an implicit simulation technique that takes the complex wire-wall hydrodynamic interactions into account efficiently, the result of which agreed well with the experimentally observed angle-dependent diffusion. The demonstrated techniques provide a platform for studying the microrheology of soft condensed matters, such as colloidal and biological systems near interfaces, and exploring the optimal self-assembly conditions of nanostructures.
Pub.: 30 Oct '14, Pinned: 28 Jun '17
Abstract: We analyze the microscopic dynamics and transport properties of a gas of thin hard rods. Based on the collision rules for hard needles we derive a hydrodynamic equation that determines the coupled translational and rotational dynamics of a tagged thin rod in an ensemble of identical rods. Specifically, based on a pseudo-Liouville operator for binary collisions between rods, the Mori-Zwanzig projection formalism is used to derive a continued fraction representation for the correlation function of the tagged particle's density, specifying its position and orientation. Truncation of the continued fraction gives rise to a generalized Enskog equation, which can be compared to the phenomenological Perrin equation for anisotropic diffusion. Only for sufficiently large density do we observe anisotropic diffusion, as indicated by an anisotropic mean-square displacement, growing linearly with time. For lower densities, the Perrin equation is shown to be an insufficient hydrodynamic description for hard needles interacting via binary collisions. We compare our results to simulations and find excellent quantitative agreement for low densities and qualitative agreement for higher densities.
Pub.: 06 May '06, Pinned: 28 Jun '17
Abstract: Slender rods in concentrated suspensions constitute strongly interacting systems with rich dynamics: transport slows down drastically and the anisotropy of the motion becomes arbitrarily large. We develop a mesoscopic description of the dynamics down to the length scale of the interparticle distance. Our theory is based on the exact solution of the Smoluchowski-Perrin equation; it is in quantitative agreement with extensive Brownian dynamics simulations in the dense regime. In particular, we show that the tube confinement is characterised by a power law decay of the intermediate scattering function with exponent 1/2.
Pub.: 13 Jan '09, Pinned: 28 Jun '17
Abstract: Brownian motion has served as a pilot of studies in diffusion and other transport phenomena for over a century. The foundation of Brownian motion, laid by Einstein, has generally been accepted to be far from being complete since the late 1960s, because it fails to take important hydrodynamic effects into account. The hydrodynamic effects yield a time dependence of the diffusion coefficient, and this extends the ordinary hydrodynamics. However, the time profile of the diffusion coefficient across the kinetic and hydrodynamic regions is still absent, which prohibits a complete description of Brownian motion in the entire course of time. Here we close this gap. We manage to separate the diffusion process into two parts: a kinetic process governed by the kinetics based on molecular chaos approximation and a hydrodynamics process described by linear hydrodynamics. We find the analytical solution of vortex backflow of hydrodynamic modes triggered by a tagged particle. Coupling it to the kinetic process we obtain explicit expressions of the velocity autocorrelation function and the time profile of diffusion coefficient. This leads to an accurate account of both kinetic and hydrodynamic effects. Our theory is applicable for fluid and Brownian particles, even of irregular-shaped objects, in very general environments ranging from dilute gases to dense liquids. The analytical results are in excellent agreement with numerical experiments.
Pub.: 02 Jun '17, Pinned: 28 Jun '17
Abstract: The simple strategy of coating a closely packed colloid monolayer with a nanometer-thick metal film to connect colloidal spheres and then gently sonicating produces a series of colloid metastructures, including rods and planar sheets. These structures can be fluorescently labeled, which can serve as a probe to monitor their dynamics in complex environments. The metal coating modulates fluorescence emission as these structures rotate in suspension. By analyzing the time sequence of fluorescence images using single-particle tracking techniques, here we measure the rotational dynamics of a rodlike tetramer, quantifying rotation along the long axis.
Pub.: 09 Aug '06, Pinned: 28 Jun '17
Abstract: We synthesize colloidal particles with various anisotropic shapes and track their orientationally resolved Brownian trajectories using confocal microscopy. An analysis of appropriate short-time correlation functions provides direct access to the hydrodynamic friction tensor of the particles revealing nontrivial couplings between the translational and rotational degrees of freedom. The results are consistent with calculations of the hydrodynamic friction tensor in the low-Reynolds-number regime for the experimentally determined particle shapes.
Pub.: 18 Dec '13, Pinned: 28 Jun '17
Abstract: We present here an experimental, strictly one-dimensional rotational system, made by using single magnetic Janus particles in a static magnetic field. These particles were half-coated with a thin metallic film, and by turning on a properly oriented external static magnetic field, we monitor the rotational brownian motion of single particles, in solution, around the desired axis. Bright-field microscopy imaging provides information on the particle orientation as a function of time. Rotational diffusion coefficients are derived for one-dimensional rotational diffusion, both for a single rotating particle and for a cluster of four such particles. Over the studied time domain, up to 10 s, the variation of the angle of rotation is strictly brownian; its probability distribution function is gaussian, and the mean squared angular displacement is linear in time, as expected for free diffusion. Values for the rotational diffusion coefficients were also determined. Monte Carlo and hydrodynamic simulations agree well with the experimental results.
Pub.: 20 Apr '11, Pinned: 28 Jun '17
Abstract: Nanoparticle-based technologies, including platforms derived from plant viruses, hold great promise for targeting and delivering cancer therapeutics to solid tumors by overcoming dose-limiting toxicities associated with chemotherapies. A growing body of data indicates advantageous margination and penetration properties of high aspect-ratio nanoparticles, which enhance payload delivery, resulting in increased efficacy. Our lab has demonstrated that elongated rod-shaped and filamentous macromolecular nucleoprotein assemblies from plant viruses have higher tissue diffusion rates than spherical particles. In this study, we developed a mathematical model to quantify diffusion and uptake of tobacco mosaic virus (TMV) in a spheroid system approximating a capillary-free segment of a solid tumor. Model simulations predict TMV concentration distribution with time in a tumor spheroid for different sizes and cell densities. From simulations of TMV concentration distribution, we can quantify the effect of TMV aspect ratio (e.g., nanorod length-to-width) with and without cellular uptake by modulated surface chemistry. This theoretical analysis can be applied to other viral or nonviral delivery systems to complement the experimental development of the next generation of nanotherapeutics.
Pub.: 04 Apr '16, Pinned: 28 Jun '17
Abstract: The translational and rotational diffusion constants of tobacco mosaic virus (TMV) have been determined from homodyne and heterodyne measurements of the spectrum of laser light scattered from dilute aqueous solutions of TMV. Our results for the translational and rotational constants respectively, reduced to 20 degrees C, are: D(T) = 0.280 +/- 0.006 x 10(-7) cm(2)/sec, and D(R) = 320 +/- 18 sec(-1). We include a theoretical derivation of the spectrum of light scattered from rod-shaped molecules which reproduces results obtained previously by Pecora, but which is specialized at the outset to the problem of dilute solutions so that simple single-particle correlation functions may be utilized. An analysis of the photocurrent spectrum for both the homodyne and heterodyne detection schemes is given. Various data reduction schemes utilized in the analysis of our spectra are described in some detail, and our results are compared with values of the diffusion constants obtained from other experiments.
Pub.: 01 Apr '69, Pinned: 28 Jun '17
Abstract: We present here a method for sorting nanometer scale brownian rods by using a switching asymmetric periodic potential. A two stage sorting process is used to isolate particles with specific dimensions, with acceptable sorting times as well as realizable potential barrier lengths. The method was tested using computer simulations. The ability to sort the nanometer scale anisotropic particles, such as gold nanorods, portends important applications in large scale data recording, photothermal surgery, and bioimaging.
Pub.: 17 Feb '11, Pinned: 28 Jun '17
Abstract: We studied the Brownian motion of isolated ellipsoidal particles in water confined to two dimensions and elucidated the effects of coupling between rotational and translational motion. By using digital video microscopy, we quantified the crossover from short-time anisotropic to long-time isotropic diffusion and directly measured probability distributions functions for displacements. We confirmed and interpreted our measurements by using Langevin theory and numerical simulations. Our theory and observations provide insights into fundamental diffusive processes, which are potentially useful for understanding transport in membranes and for understanding the motions of anisotropic macromolecules.
Pub.: 28 Oct '06, Pinned: 28 Jun '17
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