Molecule diffusion

Mobility of this second kind is illustrated in Fig. XVIII-14, which shows NO molecules diffusing around on terraces with intervals of being trapped at steps. Surface diffusion can be seen in field emission microscopy (FEM) and can be measured by observing the growth rate of patches or fluctuations in emission from a small area [136,138] (see Section V111-2C), field ion microscopy [138], Auger and work function measurements, and laser-induced desorption... 

Fig. XVIII-14. Schematic illustration of the movement of NO molecules on a Pt(lll) surface. Molecules diffuse around on terraces, get trapped at steps, escape, and repeat the process many times before eventually desorbing. [Reprinted with permission from M. Cardillo, Langmuir, 1, 4 (1985) (Ref. 140). Copyright 1985, American Chemical Society.]...

Here f denotes the fraction of molecules diffusely scattered at the surface and I is the mean free path. If distance is measured on a scale whose unit is comparable with the dimensions of the flow channel and is some suitable characteristic fluid velocity, such as the center-line velocity, then dv/dx v and f <<1. Provided a significant proportion of incident molecules are scattered diffusely at the wall, so that f is not too small, it then follows from (4.8) that G l, and hence from (4.7) that V v° at the wall. Consequently a good approximation to the correct boundary condition is obtained by setting v = 0 at the wall. ... 

Small solvent molecules diffusing from the main ion beam... 

Many neutral molecules diffusing and following approximateiy initial. direction. ... 

The flow of droplets is directed through a small orifice (Skimmer 1 Figure 12.1) and across a small region that is kept under vacuum by rotary pumps. In this region, approximately 90% of solvent and injected helium is removed from the incipient particle beam. Because the rate of diffusion of a substance is inversely proportional to its molecular mass, the lighter helium and solvent molecules diffuse away from the beam and are pumped away. The heavier solute molecules diffuse more slowly and pass through the first skimmer before they have time to leave the beam the solute is accompanied by residual solvent and helium. 

Liquid crystals represent a state of matter with physical properties normally associated with both soHds and Hquids. Liquid crystals are fluid in that the molecules are free to diffuse about, endowing the substance with the flow properties of a fluid. As the molecules diffuse, however, a small degree of long-range orientational and sometimes positional order is maintained, causing the substance to be anisotropic as is typical of soflds. Therefore, Hquid crystals are anisotropic fluids and thus a fourth phase of matter. There are many Hquid crystal phases, each exhibiting different forms of orientational and positional order, but in most cases these phases are thermodynamically stable for temperature ranges between the soHd and isotropic Hquid phases. Liquid crystallinity is also referred to as mesomorphism. 

Table 10 contains some selected permeabiUty data including diffusion and solubiUty coefficients for flavors in polymers used in food packaging. Generally, vinyUdene chloride copolymers and glassy polymers such as polyamides and EVOH are good barriers to flavor and aroma permeation whereas the polyolefins are poor barriers. Comparison to Table 5 shows that the large molecule diffusion coefficients are 1000 or more times lower than the small molecule coefficients. The solubiUty coefficients are as much as one million times higher. Equation 7 shows how to estimate the time to reach steady-state permeation t if the diffusion coefficient and thickness of a film are known. 

Diffusion. Diffusional dmg delivery systems utilize the physicochemical energy resulting from concentration differentials. Dmg molecules diffuse through a polymer matrix or through a polymer membrane film from a region of high concentration to one of low concentration. 

Here / is the number of ink molecules diffusing down the concentration gradient per second per unit area it is called the flux of molecules (Fig. 18.3). The quantity c is the concentration of ink molecules in the water, defined as the number of ink molecules per unit volume of the ink-water solution and D is the diffusion coefficient for ink in water - it has units of m s . ... 

In order to predict the speed of the process we must find out how quickly individual atoms or molecules diffuse under the influence of this driving force. 

W -IO"- Intermediate and large Aitken nuclei Dectron microscope Suspended — Vapor molecules — Diffusion... 

Consider spherical molecules A and B having radii and Tb and diffusion coefficients Da and Db- First, suppose that B is fixed and that the rate of reaction is limited by the rate at which A molecules diffuse to the B molecule. We calculate the flux 7(A- B) of A molecules to one B molecule. Let a and b be the concentrations (in molecules/cm ) of A and B in the bulk, and let r be the radius of a sphere centered at the B molecule. The surface area of this sphere is Aitr, so by Pick s first law we obtain... 

This value, often approximated as 1010 L mol"1 s 1, is referred to as the diffusion-controlled rate constant. It is rather insensitive to the chemical species that participate in the reaction. A larger molecule diffuses more slowly than a smaller one, but that effect is roughly compensated by a higher probability of encounter given its larger radius. 

In the previous discussion it has been assumed that the vapour is a pure material, such as steam or organic vapour. If it contains a proportion of non-condensable gas and is cooled below its dew point, a layer of condensate is formed on the surface with a mixture of non-condensable gas and vapour above it. The heat flow from the vapour to the surface then takes place in two ways. Firstly, sensible heat is passed to the surface because of the temperature difference. Secondly, since the concentration of vapour in the main stream is greater than that in the gas film at the condensate surface, vapour molecules diffuse to the surface and condense there, giving up their latent heat. The actual rate of condensation is then determined by the combination of these two effects, and its calculation requires a knowledge of mass transfer by diffusion, as discussed in Chapter 10. 

The molecule diffuses across the tube and samples many streamlines, some with high velocity and some with low velocity, during its stay in the reactor. It will travel with an average velocity near u and will emerge from the long reactor with a residence time close to F. The axial dispersion model is a reasonable approximation for overall dispersion in a long, laminar flow reactor. The appropriate value for D is known from theory ... 

This gives the concentration profile inside the pore, a l). The total rate of reaction within a pore can be found using the principle of equal rates. The reaction rate within a pore must equal the rate at which reactant molecules enter the pore. Molecules enter by diffusion. The flux of reactants molecules diffusing into a pore of diameter dp re equals the reaction rate. Thus,... 

When a solvent diffuses across a neat polymer, it must travel the thickness of the sample (do). When the same solvent diffuses through a nanocomposite film with nanoclays, its path length is increased by the distance it must travel around each clay layer it strikes. According to Lan et al. [99] the path length of a gas molecule diffusing through an exfoliated nanocomposite is... 

In Og (Figure 8.1.5b), xmlike in the Ig case, the fuel jet momentum dispersed and the centerline velocity decayed rapidly owing to the lack of buoyancy. As a result, the fuel molecules diffused in every direction and formed a quasi-spherical flame. The slow diffusion processes (1) limited the transport rates of the fuel and oxygen into the flame zone and (2) decreased... 

The lighter NH3 molecules diffuse more rapidly than the heavier HCl molecules, so the white band of salt forms closer to the HCl end of the tube, as can be seen in Figure 5-15. 

Actually, it is recognized that two different mechanisms may be involved in the above process. One is related to the reaction of a first deposited metal layer with chalcogen molecules diffusing through the double layer at the interface. The other is related to the precipitation of metal ions on the electrode during the reduction of sulfur. In the first case, after a monolayer of the compound has been plated, the deposition proceeds further according to the second mechanism. However, several factors affect the mechanism of the process, hence the corresponding composition and quality of the produced films. These factors are associated mainly to the com-plexation effect of the metal ions by the solvent, probable adsorption of electrolyte anions on the electrode surface, and solvent electrolysis. 

Imaging of single molecule diffusion. Proc. Nad. Acad. Sci. USA, 93, 2926-2929. 

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