Surface Diffusion Constant

The surface diffusion constant has been calculated by several authors (37,61,35,62). Lennard-Jones s theory (37) was used by Ward (63) to interpret the slow sorption of hydrogen by copper. 

In this expression a denotes a constant or J), v denotes the average velocity of an adsorbed atom for the period r during which it is activated and r is the time between successive activations. The attempt to calculate t and r has been made for two cases  

The corresponding values of r are of course strongly dependent on temperature, since they contain the Boltzmann factor It can also be shown (6i) that 

These equations may as an example be applied to a simple tyi e of potential energy field. The field is supposed to consist of cylindrical potential energy holes separated from each other by walls of height occupying a fraction j of the whole surface, whose area is A. Then 

Finally, when Eq tends to zero, D = avH, where t is the interval between successive collisions in a two-dimensional gas. In this case simple theories give to a the value J. Applications of the theory to the diffusion of sodium on oxygen-tungsten surfaces (26) led to a mean free path in the activated state of cm. 

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Mechanisms of micellar reactions have been studied by a kinetic study of the state of the proton at the surface of dodecyl sulfate micelles [191]. Surface diffusion constants of Ni(II) on a sodium dodecyl sulfate micelle were studied by electron spin resonance (ESR). The lateral diffusion constant of Ni(II) was found to be three orders of magnitude less than that in ordinary aqueous solutions [192]. Migration and self-diffusion coefficients of divalent counterions in micellar solutions containing monovalent counterions were studied for solutions of Be2+ in lithium dodecyl sulfate and for solutions of Ca2+ in sodium dodecyl sulfate [193]. The structural disposition of the porphyrin complex and the conformation of the surfactant molecules inside the micellar cavity was studied by NMR on aqueous sodium dodecyl sulfate micelles [194]. 

In the recent simulation by Matties and Hentschke [36, 37], the adsorption and melting of benzene on graphite was studied via MD simulations. In addition to determining static properties such as the center of mass density distributions and tilt angles as a function of temperature by obtaining time averages, they were also able to obtain dynamic properties such as the surface diffusion constants in the monolayer and the orientational velocity autocorrelation function (OVAF). 

It has been shown that PEEM is a versatile instrument that can be used to determine the thermodynamic and kinetic properties of molecular systems. The preliminary results presented here are presently being analysed to yield statistically significant values for the molecular binding energy as well as for the molecular surface diffusion constant and other kinetic parameters of interest. 

Here, a laser beam totally internally reflects at a sohd/hquid interface, creating an evanescent field, which penetrates only a fraction of the wavelength into the liquid domain. When using planar phosphoHpid bilayer and fluorescently labeled proteins, this method allows the determination of adsorption/desorption rate constants and surface diffusion constants [171—173]. Figure 6.29 shows a representative TIRF-FPR curve for fluorescein-labeled prothrombin bound to planar membranes. In this experiment the experimental conditions are chosen such that the recovery curve is characterized by the prothrombin desorption rate. It should be mentioned that, similar to other applications of fluorescence microscopy, two and three photon absorption might be combined with FRAP in the near future. 

Using (2.11) and (2.12) one can determine the surface diffusion constant by measuring the effective biaxiality. For saturated A < Asat) 5CB surface depositions, jS satj 0.14 and T/sat 0.24 at Troom, yielding Ds 7 X 10" m s. This value is only about an order of magnitude smaller than the hulk 5CB value Pscb 6 x 10 m s , indicating possible collectiveness in the behavior of 2D LC molecular films. A gradual decrease of... 

While Table 1 shows both the bulk and surface diffusion constants, only the bulk data will be discussed here, with the surface data discussed below. 

The methods based upon the thermionic and photoelectric properties of surfaces form an interesting study in themselves. The sequel will show that the surface diffusion constant D is not independent of the surface concentration, and this fact constitutes the major objection to these analyses. Only by using the Pick law in the form... 

The migration of caesium on the surface of tungsten was first observed by Becker (45). It is interesting to compare values of the surface diffusion constant D obtained by different methods. By the method which depends on freeing the centre of the filament from caesium (p. 362), Langmuir and Taylor (35, 46) found values of D in cm. sec. at JV = 2 73 x 10 atoms/cm. and at temperatures of 654, 702, 746 and 812° K. which conformed to the equation... 

Table 86. Surface diffusion constants for caesmm in a memo-layer and in the surface layer of a thick deposity of caesium on tungsten...

Quantitative measurements on the surface diffusion constant are somewhat scanty, the most complete analysis being that of Brattain and Becker (24), who followed the diffusion of thorium evaporated on to tungsten from the covered to the uncovered side of the tungsten strip, by measuring the changes in thermionic emission with time. The theory of their method has been described earlier (p. 351). 

The spreading rate of a polymer droplet on a surface has been measured (363,364). The diffusion constant was at least an order of magnitude smaller than that of the bulk. The monomer—surface friction coefficient for polystyrene has been measured on a number of surfaces and excellent... 

Figure 16-27 compares the various constant pattern solutions for R = 0.5. The curves are of a similar shape. The solution for reaction kinetics is perfectly symmetrical. The cui ves for the axial dispersion fluid-phase concentration profile and the linear driving force approximation are identical except that the latter occurs one transfer unit further down the bed. The cui ve for external mass transfer is exactly that for the linear driving force approximation turned upside down [i.e., rotated 180° about cf= nf = 0.5, N — Ti) = 0]. The hnear driving force approximation provides a good approximation for both pore diffusion and surface diffusion. 

FIG. 16-27 Constant pattern solutions for R = 0.5. Ordinant is cfor nfexcept for axial dispersion for which individual curves are labeled a, axial dispersion h, external mass transfer c, pore diffusion (spherical particles) d, surface diffusion (spherical particles) e, linear driving force approximation f, reaction kinetics. [from LeVan in Rodrigues et al. (eds.), Adsorption Science and Technology, Kluwer Academic Publishers, Dor drecht, The Nether lands, 1989 r eprinted with permission.]... 

Chemicals have to pass through either the skin or mucous membranes lining the respiratory airways and gastrointestinal tract to enter the circulation and reach their site of action. This process is called absorption. Different mechanisms of entry into the body also greatly affect the absorption of a compound. Passive diffusion is the most important transfer mechanism. According to Pick s law, diffusion velocity v depends on the diffusion constant (D), the surface area of the membrane (A), concentration difference across the membrane (Ac), and thickness of the membrane (L)... 

Here, D is the diffusion constant for heat or material and the kinematic viscosity of the liquid. A consequence of the existence of such a diffusive surface barrier is that the diffusion length = D/F is to be replaced by in all formulas, as soon as growth rate V the more important become the hydrodynamic convection effects. 

Equations 4.31 and 4.32 also suggest another important fact regarding NEMCA on noble metal surfaces The rate limiting step for the backspillover of ions from the solid electrolyte over the entire gas exposed catalyst surface is not their surface diffusion, in which case the surfacediffusivity Ds would appear in Eq. 4.32, but rather their creation at the three-phase-boundaries (tpb). Since the surface diffusion length, L, in typical NEMCA catalyst-electrode film is of the order of 2 pm and the observed NEMCA time constants x are typically of the order of 1000 s, this suggests surface diffusivity values, Ds, of at least L2/t, i.e. of at least 4 10 11 cm2/s. Such values are reasonable, in view of the surface science literature for O on Pt(l 11).1314 For example this is exactly the value computed for the surface diffusivity of O on Pt(lll) and Pt(100) at 400°C from the experimental results of Lewis and Gomer14 which they described by the equation ... 

In this exercise we shall estimate the influence of transport limitations when testing an ammonia catalyst such as that described in Exercise 5.1 by estimating the effectiveness factor e. We are aware that the radius of the catalyst particles is essential so the fused and reduced catalyst is crushed into small particles. A fraction with a narrow distribution of = 0.2 mm is used for the experiment. We shall assume that the particles are ideally spherical. The effective diffusion constant is not easily accessible but we assume that it is approximately a factor of 100 lower than the free diffusion, which is in the proximity of 0.4 cm s . A test is then made with a stoichiometric mixture of N2/H2 at 4 bar under the assumption that the process is far from equilibrium and first order in nitrogen. The reaction is planned to run at 600 K, and from fundamental studies on a single crystal the TOP is roughly 0.05 per iron atom in the surface. From Exercise 5.1 we utilize that 1 g of reduced catalyst has a volume of 0.2 cm g , that the pore volume constitutes 0.1 cm g and that the total surface area, which we will assume is the pore area, is 29 m g , and that of this is the 18 m g- is the pure iron Fe(lOO) surface. Note that there is some dispute as to which are the active sites on iron (a dispute that we disregard here). 

Diffusion is proportional to the surface area of the blood-gas interface (A) the diffusion constant (D) and the partial pressure gradient of the gas (AP). Diffusion is inversely proportional to the thickness of the blood-gas interface (T). 

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