Nanoparticle Brownian motion

Direct observation of molecular diffusion is the most powerful approach to evaluate the bilayer fluidity and molecular diffusivity. Recent advances in optics and CCD devices enable us to detect and track the diffusive motion of a single molecule with an optical microscope. Usually, a fluorescent dye, gold nanoparticle, or fluorescent microsphere is used to label the target molecule in order to visualize it in the microscope [31-33]. By tracking the diffusive motion of the labeled-molecule in an artificial lipid bilayer, random Brownian motion was clearly observed (Figure 13.3) [31]. As already mentioned, the artificial lipid bilayer can be treated as a two-dimensional fluid. Thus, an analysis for a two-dimensional random walk can be applied. Each trajectory observed on the microscope is then numerically analyzed by a simple relationship between the displacement, r, and time interval, T,... 

The high photostability and acute fluorescence intensity are two major features of DDSNs compared to dye molecules in a bulk solution. The early DDSN studies have focused on these two properties [8, 13]. For example, Santra et al. studied the photostability of the Ru(bpy)32+ doped silica nanoparticles. In aqueous suspensions, the Ru(bpy)32+ doped silica nanoparticles exhibited a very good photostability. Irradiated by a 150 W Xenon lamp for an hour, there was no noticeable decrease in the fluorescence intensity of suspended Ru(bpy)32+ doped silica nanoparticles, while obvious photobleaching was observed for the pure Ru(bpy)32+ and R6G molecules. To eliminate the effect from Brownian motion, the authors doped both pure Ru(bpy)32+ and Ru(bpy)32+-doped silica nanoparticles into poly(methyl methacrylate). Under such conditions, both the pure Ru(bpy)32+ and Ru(bpy)32+ doped silica nanoparticles were bleached. However, the photobleaching of pure Ru(bpy)32+ was more severe than that of the Ru(bpy)32+ doped silica nanoparticles. 

Once nanoparticles have been formed, whether in an early state of growth or in a more or less final size, their fate depends on the forces between the individual particles and between particles and solid surfaces in the solution. While particles initially approach each other by transport in solution due to Brownian motion, convection, or sedimentation, when close enough, interparticle forces will determine their final state. If the dominant forces are repulsive, the particles will remain separate in colloidal form. If attractive, they will aggregate and eventually precipitate. In addition, they may adsorb onto a solid surface (the substrate or the walls of the vessel in which the reaction is carried out). For CD, both attractive particle-sur-... 

Generally, mean size and size distribution of nanoparticles are evaluated by quasi-elastic light scattering also named photocorrelation spectroscopy. This method is based on the evaluation of the translation diffusion coefficient, D, characterizing the Brownian motion of the nanoparticles. The nanoparticle hydro-dynamic diameter, is then deduced from this parameter from the Stokes Einstein law. 

A mathematical model of a nanoparticles growth during evaporation of a micron size droplet in a low pressure aerosol reactor is developed. The main factor is found to be evaporating cooling of droplets which affects formation of supersaturated solution in the droplet. The rate of cooling can reach 2T0 K/s. The final radius of nanoparticles was found to be independent on the precursor radius. Manifestation of Lifshitz-Slezov instability is illustrated by experimental data. Effects of Brownian motion of nanoparticles inside the droplet are discussed. 

Brownian motion of nanoparticles makes the assumption about average density of a soluble impurity in a droplet more reasonable due to some mixing effects. It also leads to formation of different structures of nanoparticles. The investigation of contribution of Brownian motion of nanoparticles to the structure formation in the evaporating droplet is in progress now. 

In a solution, nanoparticles interact with each other in a number of ways. Widely separated nanoparticles may be brought into contact by Brownian motion. As they approach each other, electrostatic, van der Waals forces, and hydrogen bonding, in addition to Brownian motion, can cause two nanoparticles to rotate with respect to each other, and collide. Evidently, under some conditions, the collisions that result in fusion are those that involve two nanoparticles in appropriate orientations to form a coherent (or semicoherent) interface. Particle rotation in the absence of a fluid has been modeled computationally (Zhu and Averback 1996), implying that oriented assembly-based crystal growth can also occur in dry systems. 

This statement is trae only when Brownian motion is neglected, which is an implicit assumption in the derivation of the equilibrium model. Since Brownian motion is important for sub-micron particles suspended in a fluid, the equilibrium model is not intended for describing, for example, nanoparticle transport. 

Jang and Choi [39] devised a theoretical model that includes four modes of energy transport the collision between basefluid molecules, the thermal diffusion of nanoparticles in the fluid, the collision between nanoparticles due to Brownian motion, and the thermal interactions of dynamic nanoparticles with base fluid molecules. 

Deposition of nanoparticles was investigated in the free molecular regime approximation for thermophoretic force and the Brownian motion. The analytical solution was obtained by the Galerkin method for the heat transfer between gas flow and substrates and convective diffusion. Relative roles of two channels of nanoparticle deposition are discussed. 

Mechanisms of transport and retention in saturated porous media include solid-water interface attachment and pore straining. The movement and interactions of particles in these mechanisms are illustrated in Figure 21.14 (25). Solid-water interface attachment is the dominant mechanism of filtration for nanomaterials in samrated media. In this process, nanoparticles or aggregates collide with solid media and adhere to the surface. Nanoparticle movement, such as Brownian motion or... 

DLS (dynamic light scattering)—in dynamic light scattering laser light is scattered by the nanoparticles. Due to the Brownian motion of the particles, a time-dependent fluctuation is imparted to the scattered light intensity. Analysis of the signal intensity yields information about the diffusional motion of the particles, which is in turn related to the hydrodynamic size via the Stoke-Einstein equation. 

In the presence of an external electric field, the nanoparticle mainly moves due to electrophoresis and electroosmosis (the electrokinetic effects). Here, it should mention that the Brownian motion is one of the main signatures of the nanoparticle motion. However, it was shown previously that the effect of the Brownian force on the nanoparticle is negligible compared with the electrokinetic effects (the electrophoretic and the electroosmotic forces) [5]. In the presence of the external electric field, the nanoparticles are mainly manipulated by the electrokinetic effects, and the Brownian force has negligible effect on the nanoparticle motion. 

Jang and Choi [26] numerically investigated the cooling performance of a microchannel heat sink with nanofluids. Two kinds of nanofluids were investigated in this study, i.e., d = 6 nm nanoparticles in a copper-water mixture and dp = 2 nm diamond-in-water nanofluid. A theoretical model was employed for the thermal conductivity of nanofluids that accounts for four modes of energy transport the thermal diffusion in the base fluid, the thermal diffusion of nanoparticles, the collision between the nanoparticles, and the nanoconvection due to Brownian motion. Specifically,... 

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