Particles diffusion, dynamic

We focus on the effects of crowding on small molecule reactive dynamics and consider again the irreversible catalytic reaction A + C B + C asin the previous subsection, except now a volume fraction < )0 of the total volume is occupied by obstacles (see Fig. 20). The A and B particles diffuse in this crowded environment before encountering the catalytic sphere where reaction takes place. Crowding influences both the diffusion and reaction dynamics, leading to nontrivial volume fraction dependence of the rate coefficient fy (4>) for a single catalytic sphere. This dependence is shown in Fig. 21a. The rate constant has the form discussed earlier,... 

Particles of a size of less than 2 turn are of particular interest in Process Engineering because of their large specific surface and colloidal properties, as discussed in Section 5.2. The diffusive velocities of such particles are significant in comparison with their settling velocities. Provided that the particles scatter light, dynamic light scattering techniques, such as photon correlation spectroscopy (PCS), may be used to provide information about particle diffusion. 

It is our objective in this chapter to outline the basic concepts that are behind sedimentation and diffusion. As we see in this chapter, gravitational and centrifugal sedimentation are frequently used for particle-size analysis as well as for obtaining measures of solvation and shapes of particles. Diffusion plays a much more prevalent role in numerous aspects of colloid science and is also used in particle-size analysis, as we see in Chapter 5 when we discuss dynamic light scattering. The equilibrium between centrifugation and diffusion is particularly important in analytical and preparative ultracentrifuges. 

In Section VI, we consider a classical particle diffusing in an out-of-equilibrium environment. In this case, all the dynamical variables attached to the particle, even its velocity, are aging variables. We analyze how the drift and diffusion properties of the particle can be interpreted in terms of an effective temperature of the medium. From an experimental point of view, independent measurements of the mean-square displacement and of the mobility of a particle immersed in an aging medium such as a colloidal glass give access to an out-of-equilibrium generalized Stokes-Einstein relation, from which the effective temperature of the medium can eventually be deduced. 

An interesting technique for the measurement of intraparticle diffusivity as well as longitudinal diffusion in the particle bed has been described by Deisler and Wilhelm (21). It deviates from all other techniques mentioned in that it is based on a dynamic flow study, analyzing the effect of the particles on the propagation of a sinusoidal variation of composition of a binary gas mixture passed through the catalyst bed. The authors have demonstrated the versatility of their general technique for determination of diffusion properties, as well as adsorption equilibria between the solids and the gas composition employed. If this general technique were modified to measure specifically the particle diffusivity, a very convenient and accurate method may result. 

Pt or Pt/Au particles have also been hosted in the hydrophobic holes of nonionic surfactants, e.g., polyethylene monolaurate [46a,62]. The structure and diffusive dynamics of a colloidal palladium aggregate sol have been studied under dilute and semidilute conditions by high-resolution small angle X-ray scattering and X-ray photon correlation spectroscopy. When the sizes of the aggregates determined in the static structure and as derived from the diffusive dynamics at low concentration are consistent with each other. 

If one is interested in properties that vary on very long distance and time scales it is possible that a drastic simplification of the molecular dynamics will still provide a faithful representation of these properties. Hydrodynamic flows are a good example. As long as the dynamics preserves the basic conservation laws of mass, momentum and energy, on sufficiently long scales the system will be described by the Navier-Stokes equations. This observation is the basis for the construction of a variety of particle-based methods for simulating hydrodynamic flows and reaction-diffusion dynamics. (There are other phase space methods that are widely used to simulate hydrodynamic flows which are not particle-based, e.g. the lattice Boltzmann method [125], which fall outside the scope of this account of MD simulation.)... 

The reaction space pertinent to our system is depicted in Figure 4. The proton is assumed to dissociate in the aqueous layer and diffuse in a three-dimensional space until its diffusion sphere contacts both membranes. At that point the diffusion loses its three-dimensional property and assumes a cylindrical configuration that, with respect to the volume increment between two shells, is identical to a two-dimensional diffusion. The shift from a three-to a two-dimensional space has a marked effect on the diffusion dynamics In the three-dimensional space the density of a particle in a concentric shell varies as r-3, whereas in the two-dimensional space the density varies as r-2. Consequently the concentration gradient in three-dimensional space is larger and drives a better diffusion away from the center. 

Colver and Howell (1980) used the electrostatic EPS (Electric Particulate Suspension) to measure diffusion of spherical copper spheres (74-88 and 125-147 pm) along a copper parallel plate duct having a 1 cm separation distance. The particles were dynamically suspended in the duct by inductive charging... 

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