Diffusion-related molecular processes characterizing

The development of micro-chromatography systems has been motivated by the fact that as the system size is reduced, its performance is improved. The improvements that include reduction in analysis time and increase in separation efficiencies are a direct consequence of miniaturization as described in Janasek et al. (see Further Reading) and summarized here. The benefits of miniaturization can be demonstrated considering proportionalities within the system. We assume that miniaturization is a three-dimensional downscaling process characterized by a typical length parameter d. The separation system is a diffusion-related system in which hydro-dynamic, heat and molecular diffusion behave exactly... 

As examined in the next chapter, transition-state theory is applicable when the rate-limiting step of a molecular process is controlled by a slow passage over a barrier. Not only reactions but also some diffusion processes are characterized by equilibration of a molecule on a surface site, in a cavity of a zeolite, and by movement of a molecule over a barrier (Figure 4.17). For diffusion, the relation between distance of motion and time is given by... 

Transport Coefficients The reactivity of zeolites is determined by the ability of molecules (reactants and products) to diffuse to and from an active site. Therefore, knowledge about the diffusion process is essential for understanding zeolite chemical activity. The diffusion process is characterized by a diffusion coefficient which can be calculated two ways. The first makes the use of the Einstein relationship that relates mean-square displacement of a molecular CoM position... 

T( characterizes the time of a single diffusion step. Since the same process of molecular diffusion governs the fluctuations of both scalar and dipolar coupling T, Xp and x are assumed to be related, in that all three correlation times have an equal temperature dependence. 

The binary molecular diffusion coefficient, ab> has units of length /time and characterizes the microscopic motion of species A in solvent B, for example. Hab is also the molecular transport property that appears in the linear law that relates diffusional fluxes and concentration gradients. In this respect, the same quantity, Bab. represents a molecular transport property for mass transfer and a diffusion coefficient. This is not the case for the other two transport processes. 

In this chapter we examine some issues in mass transfer. The reader has already been introduced to some of the key aspects. In Chapter 3 (Section 7), flocculation kinetics of colloidal particles is considered. It shows the importance of diffusivity in the rate process, and in Equation 3.72, the Stokes-Einstein equation, the effect of particle size on diffusivity is observed, leading to the need to study sizes, shapes, and charges on colloidal particles, which is taken up in Chapter 3 (Section 4). Similarly some of the key studies in mass transfe in surfactant systems— dynamic surface tension, smface elasticity, contacting and solubilization kinetics—are considered in Chapter 6 (Sections 6, 7, 10, and 12 with some related issues considered in Sections 11 and 13). These emphasize the roles played by different phases, which are characterized by molecular aggregation of different kinds. In anticipation of this, the microstructures are discussed in detail in Chapter 4 (Sections 2,4, and 7). Section 2 also includes some discussion on micellization-demicellization kinetics. 

Porous membranes are widely used in the filtration of liquid mixtures in pressure driven processes. Their rejection is mainly determined by the pore size and pore size distribution rather than by the membrane material properties. However, the direct contact of a porous membrane with a liquid phase can cause swelling of the polymer, which, in turn, causes complete squeezing of the nanopores, resulting in a dense membrane suitable for pervaporation [54]. Knudsen diffusion is the dominating mechanism in micropores (2-50 nm). It is characterized by a Hnear relation between the gas permeability and the inverse square root of the gas molecular weight. 

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