Competitive surface diffusion

An improvement in foam stability was observed as R was increased to >0.15 (Figure 17). This was accompanied by the onset of surface diffusion of a-la in the adsorbed protein layer. This is significantly different compared to our observations with /8-lg, where the onset and increase in surface diffusion was accompanied with a decrease in foam stability. Fluorescence and surface tension measurements confirmed that a-la was still present in the adsorbed layer of the film up to R = 2.5. Thus, the enhancement of foam stability to levels in excess of that observed with a-la alone supports the presence of a synergistic effect between the protein and surfactant in this mixed system (i.e., the combined effect of the two components exceeds the sum of their individual effects). It is important to note that Tween 20 alone does not form a stable foam at concentrations <40 jtM [22], It is possible that a-la, which is a small protein (Mr = 14,800), is capable of stabilizing thin films by a Marangoni type mechanism [2] once a-la/a-la interactions have been broken down by competitive adsorption of Tween 20. 

Once the thermodynamic parameters of stable structures and TSs are determined from quantum-chemical calculations, the next step is to find theoretically the rate constants of all elementary reactions or elementary physical processes (say, diffusion) relevant to a particular overall process (film growth, deposition, etc.). Processes that proceed at a surface active site are most important for modeling various epitaxial processes. Quantum-chemical calculations show that many gas-surface reactions proceed via a surface complex (precursor) between an incident gas-phase molecule and a surface active site. Such precursors mostly have a substantial adsorption energy and play an important role in the processes of dielectric film growth. They give rise to competition among subsequent processes of desorption, stabilization, surface diffusion, and chemical transformations of the surface complex. 

A major challenge in simulating such problems is that nucleation occurs at the nanometer scale whereas self-organization entails competition between numerous pattern blocks for reagents over microns to millimeters. These problems do not exhibit an obvious separation of length scales. From a different point of view, the stochasticity is built within the PDE as a source or sink term (if one were able to write such a PDE). Furthermore, surface diffusion is faster than the other microscopic processes by many orders of magnitude, but PE cannot be applied since the actual value of diffusion dictates the presence or absence of patterns. 

The major difference between the various GRM models is due to the mechanism of intraparticle diffusion that they propose, namely pore diffusion, siuface diffusion or a combination of both, independent or competitive diffusion. The pore diffusion model assumes that the solute diffuses into the pore of the adsorbent mainly or only in the free mobile phase that impregnates the pores of the particles. The surface diffusion model considers that the intraparticle resistance that slows the mass transfer into and out of the pores proceeds mainly through surface diffusion. In the GRM, diffusion within the mobile phase filling the pores is usually assumed to control intraparticle diffusion (pore diffusion model or PDM). This kind of model often fits the experimental data quite well, so it can be used for the calculation of the effective diffusivity. If this model fails to fit the data satisfactorily, other transport formulations such as the Homogeneous Surface Diffusion Model (HSDM) [27] or a model that allows for simultaneous pore and siuface diffusion may be more successful [28,29]. However, how accurately any transport model can reflect the actual physical events that take place within the porous... 

The competitive equilibrium isotherm model best fitting the FA experimental data for the R and S enantiomers of 1-phenyl-l-propanol on cellulose tiibenzoate was the Toth model. This model was used to calculate the elution profiles of samples of mixtures of the two enantiomers [29]. The General Rate model combined with the Generalized Maxwell-Stefan equation (GR-GMS) was used to model and describe surface diffusion (see Chapter 5). The mass transfer kinetics is slow and this model fits the experimental data well over a wide concentration range with one single set of numerical parameters to account for the band profiles in a wide range of concentrations, as shown in Figure 16.24. 

Figure 5.48 Theoretical spectral dependencies of the selectivity of photocatalysts toward a reductive pathway within a step-like absorption band at different surface potentials Us. Note the reversal in the behaviour of Sj-ed at Us = 0.3 V and 0.5 V , and the band-like behaviour when U = 0.2 V due to competition between diffusion and drift of charge carriers. Reprinted with permission from EmeUne et al.. (2003). Copyright (2003) American Chemical Society.

Competitive adsorption and mobility of adsorbates on the surface attribute to the coadsorption-induced reconstmction of adsorbate overlayers. If surface species is immobile because of a high activation energy for surface diffusion, coadsorption cannot take place. On the other hand, the adsorption energy of one adsorbate must be sufficient to compress the other adsorbate into a more compact layer. If coadsorbates have a very low heat of adsorption, the thermodynamic driving force for adsorbate overlayer reconstruction is absent. 

Interpretation of urinary excretion data following topical application Is presented for 9 compounds. It Is shown that the model has predictive potential based upon recognized cutaneous biology and penetrant physical chemistry, In particular the diffusive and partitioning properties of the substrate. Refinements and developments of the approach (e.g., to multiple exposure and competitive surface removal situations) are Indicated and discussed. 

The dynamic process of dealloying was discussed using Monte Carlo simulations [30, 36, 37]. The dissolution of the less-noble atoms from the topmost surface resulted in steps and kinks, where the coordinated numbers of noble atoms increased. This induced a surface diffusion of noble atoms. The competition between the dissolution rate of less-noble metals and the surface diffusion of noble metals is considered to be a key factor that controls the morphology of the dealloyed product. In bulk alloys, surface diffusion rate of the noble atoms is slow across the extended surface, which causes a Rayleigh surface instability [37] and leads to the formation of nanoporosity. 

Unlike the general case, the diffusion coefficient of Q inside the film does not appear in the above expressions. The reason is that there is no competition between diffusion of Q and enzymatic reaction since the entire enzyme is confined within a single monolayer. If, in the particular case, an estimate of I were to be derived from experimental values of the plateau current, one would have to know from independent sources, the three rate constants, ki, nd 3, the surface concentration of enzyme in each layer, Fg, the ratio of the distance between the electrode and the first enzyme layer to the distance between two successive layers, /o, in case it differs from 1, the diffusion coefficient of the cosubstrate in the solution, D, the partition coefficient of the cosubstrate and substrate depicting their passage from the solution to the film, /cq, and /rs, respectively, and, for P, the product /cp5p, that is, one parameter less than in the general case. 

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