Surface concentration dependences

Our studies (19) indicated that proteins were readily adsorbed from aqueous solution onto hydrophobic polymer surfaces with Langmuir type adsorption and that the rate of adsorption toward a plateau surface concentration depends on the polymer nature. In the study of competitive adsorption from a protein mixture solution (20), fibrinogen and y-globulin adsorb onto FEP very rapidly compared with PEUU and SR. Therefore, the FEP surface in contact with blood has more acceptor sites for platelet adhesion than does the PEUU or SR surface. 

When the current density is so high that local concentration of the depositing metal changes, tertiary current distribution begins to affect the deposit thickness. The effect of concentration polarization depends on the ratio of surface concentration to bulk electrolyte concentration of the depositing metal. The surface concentration depends on the local mass-transfer... 

One of the more puzzling aspects of the work just completed has been the notable absence of a concentration dependence upon the spectral characteristics of the monolayer systems (5). It is suggested that the three-dimensional interface concept also handles the apparently anomo-lous behavior nicely. One notes that there can be a meaningful quantity known as concentration only if the volume of the system is well defined. Since the surface concentration depends only on number of molecules per unit area, one would expect that if the surfactant molecules were confined to a surface, there would have been a surface concentration dependence. However, if one is dealing with a three-dimensional interface, one must consider a 4 surface concentration function which depends upon thickness as well as upon area. If this thickness depends upon the number of molecules present in some unknown manner, then one has not defined concentration in any meaningful way. Thus if no surface concentration dependence of the spectral characteristics of these systems is noted, one must admit the possibility of delocalization. Specifically, at the surface pressures indicated, it is suggested that the air-water interface is a capacitive one for the molecules which were studied. 

The unstirred layer adsorption model can be generalized by the introduction of surface concentration dependent sorption rate constants k and This subject is currently being studied as well as the existence of a second, irreversible, surface reaction following reversible initial adsorption for fibrinogen and prothrombin on a 60% DOPS/40% DOPC mixture. 

From Eq.9 we see that the chemical modulation of the work function can originate from two effects action of the guest molecule on the energy state distribution in the bulk of the phase, i.e., by the absorption term fix, in Eq.9 or by modulation of the surface potential xl i e., by adsorption. These two terms have different dependence on the activity of the guest molecule. The chemical potential follows the logarithmic law while the surface concentration depends on the type of the applicable adsorption isotherm. This may, in fact, create some problems... 

An idealised model of the surface of a thin liquid film is one of a monolayer of evenly-distributed surfactant molecules. However, a more realistic model is one where the molecules are not evenly distributed therefore, the surface concentration depends on surface position. The result of this heterogeneous distribution is that gradients of surface concentration, and therefore surface tension, are present. One example of this was pointed out in Section 5.1 on the effect of Marangoni instabilities on film rupture. Regarding film drainage, a surface tension gradient exerts a surface stress that can either impede or... 

The surface concentration dependence of the lateral mobility of Fig. 7 was analyzed in terms of the free-volume theory of hard sphere liquids of Cohen and Turnbull [55, 56], as well as in view of the Enskog theory of dense gases [57] extended by Alder s molecular dynamics calculations to liquid densities [58]. The latter approach was particularly successful. It revealed that the lateral diffusion constant of the Fc amphiphiles does follow the expected linear dependence on the relative free area, Af/Ao, where Af = A — Ao, A = MMA, and Aq is the molecular area of a surfactant molecule. It also revealed that the slope of this dependence which is expected to inversely depend on the molecular mass of a diffusing particle, was more than 3 orders of magnitude smaller [54]. Clearly, this discrepancy is due to the effect of the viscous drag of the polar head groups in water, a factor not included in the Enskog theory. 

Individual surface concentrations depend on the time and the potential. Thus ... 

In this section, we will present results of microldnetics simulations based on elementary reaction energy schemes deduced from quantum chemical studies. We use an adapted scheme to enable analysis of the results in terms of the values of elementary rate constants selected. For the same reason, we ignore surface concentration dependence of adsorption energies, whereas this can be readily implemented in the simulations. We are interested in general trends and especially the temperature dependence of overall reaction rates. The simulations will also provide us with information on surface concentrations. In the simulations to be presented here, we exclude product readsorption effects. Microldnetics simulations are attractive since they do not require an assumption of rate-controlling steps or equilibration. Solutions for overall rates are found by solving the complete set of PDFs with proper initial conditions. While in kinetic Monte Carlo simulations these expressions are solved using stochastic techniques, which enable formation... 

It must be kept in mind that both pictures are modelistic and invoke extrather-modynamic concepts. Except mathematically, there is no such thing as a two-dimensional gas, and the solution whose osmotic pressure is calculated is not uniform in composition, and its average concentration depends on the depth assumed for the surface layer. 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

The course of a surface reaction can in principle be followed directly with the use of various surface spectroscopic techniques plus equipment allowing the rapid transfer of the surface from reaction to high-vacuum conditions see Campbell [232]. More often, however, the experimental observables are the changes with time of the concentrations of reactants and products in the gas phase. The rate law in terms of surface concentrations might be called the true rate law and the one analogous to that for a homogeneous system. What is observed, however, is an apparent rate law giving the dependence of the rate on the various gas pressures. The true and the apparent rate laws can be related if one assumes that adsorption equilibrium is rapid compared to the surface reaction. 

Cyclic voltammetry provides a simple method for investigating the reversibility of an electrode reaction (table Bl.28.1). The reversibility of a reaction closely depends upon the rate of electron transfer being sufficiently high to maintain the surface concentrations close to those demanded by the electrode potential through the Nemst equation. Therefore, when the scan rate is increased, a reversible reaction may be transfomied to an irreversible one if the rate of electron transfer is slow. For a reversible reaction at a planar electrode, the peak current density, fp, is given by... 

Therefore, in tire limiting case—tire surface concentration of tire reacting species is zero as all tire arriving ions immediately react—tire current density becomes voltage independent and depends only on diffusion, specifically, on tire widtli of tire Nerstian diffusion layer S, and of course tire diffusion coefficient and tire bulk concentration of anions (c). The limiting current density (/ ) is tlien given by... 

In a foam where the films ate iaterconnected the related time-dependent Marangoni effect is mote relevant. A similar restoring force to expansion results because of transient decreases ia surface concentration (iacteases ia surface tension) caused by the finite rate of surfactant adsorption at the surface. 

The chronoamperometric technique illustrates the principle that analytically useful current responses depend critically on the efficiency of analyte mass transport within the solution. The analyte mass transport in turn depends on the efficiency with which an appHed voltage can maintain the surface concentrations of oxidized and reduced species at values specified by the Nemst equation. It is generally the case in chronoamperometry that the bulk concentration of one of the species is zero whereas the surface concentration of the other species is forced to zero by the appHed potential, but this is not always so. 

The situation illustrated in Figure 4 allows both species to coexist. Either of the two sets of curves can be considered the oxidized species the other is the reduced species. The choice depends on whether oxidation or reduction is occurring at the surface. Assume the upper curve is the reduced species and the lower curve is its oxidized form. An appHed voltage has maintained fixed surface concentrations for some period of time including and The concentration profile of the oxidized species decreases at the electrode surface (0 distance) as it is being reduced. Electrolysis therefore results in an increase in the concentration of reduced species at the surface. The concentration profiles approach bulk values far from the surface of the electrode because electrolysis for short times at small electrodes cannot significantly affect the concentrations of species in large volumes of solution. 

A numerical solution of this equation for a constant surface concentration (infinite fluid volume) is given by Garg and Ruthven [Chem. Eng. ScL, 27, 417 (1972)]. The solution depends on the value of A. = n i — n )/ n — n ). Because of the effect of adsorbate concentration on the effective diffusivity, for large concentration steps adsorption is faster than desorption, while for small concentration steps, when D, can be taken to he essentially constant, adsorption and desorption curves are mirror images of each other as predicted by Eq. (16-96) see Ruthven, gen. refs., p. 175. 

Because of the close similarity in shape of the profiles shown in Fig. 16-27 (as well as likely variations in parameters e.g., concentration-dependent surface diffusion coefficient), a contrdling mechanism cannot be rehably determined from transition shape. If rehable correlations are not available and rate parameters cannot be measured in independent experiments, then particle diameters, velocities, and other factors should be varied ana the obsei ved impacl considered in relation to the definitions of the numbers of transfer units. 

FIG. 22-81 Permeant -concentration profile in a pervaporation membrane. 1— Upstream side (swollen). 2—Convex curvature due to concentration-dependent permeant diffiisivity. 3—Downstream concentration gradient. 4—Exit surface of membrane, depleted of permeant, thus unswollen. (Couttesy Elseoier )... 

Cu/ Zn0/Si02 catalyst reduced at 700 K [3.147]. These LEIS spectra were obtained at three different ion doses - 3 x 3.41 x 10 and 8.67 x 10 Ne" cm . Because of the use of isotopically enriched Cu and Zn, and of Ne" ions as projectiles, Cu and Zn can clearly be separated in the LEIS spectrum. Strong dose-dependence is apparent. Eig. 3.60b shows the dose-dependent surface concentrations of Cu and Zn. At low doses (<1.5 x lO " Ne cm ) the Zn concentration remains constant whereas the Cu concentration increases. At these low doses a hydroxyl layer on top of the catalyst is sputtered. The Zn signal stays constant despite removal of the adsorbate, indicating that at the virgin surface the Zn concentration was even higher. 

Quantification at surfaces is more difficult, because the Raman intensities depend not only on the surface concentration but also on the orientation of the Raman scat-terers and the, usually unknown, refractive index of the surface layer. If noticeable changes of orientation and refractive index can be excluded, the Raman intensities are roughly proportional to the surface concentration, and intensity ratios with a reference substance at the surface give quite accurate concentration data. 

Surface SHG [4.307] produces frequency-doubled radiation from a single pulsed laser beam. Intensity, polarization dependence, and rotational anisotropy of the SHG provide information about the surface concentration and orientation of adsorbed molecules and on the symmetry of surface structures. SHG has been successfully used for analysis of adsorption kinetics and ordering effects at surfaces and interfaces, reconstruction of solid surfaces and other surface phase transitions, and potential-induced phenomena at electrode surfaces. For example, orientation measurements were used to probe the intermolecular structure at air-methanol, air-water, and alkane-water interfaces and within mono- and multilayer molecular films. Time-resolved investigations have revealed the orientational dynamics at liquid-liquid, liquid-solid, liquid-air, and air-solid interfaces [4.307]. 

The relationship between adsorption capacity and surface area under conditions of optimum pore sizes is concentration dependent. It is very important that any evaluation of adsorption capacity be performed under actual concentration conditions. The dimensions and shape of particles affect both the pressure drop through the adsorbent bed and the rate of diffusion into the particles. Pressure drop is lowest when the adsorbent particles are spherical and uniform in size. External mass transfer increases inversely with d (where, d is particle diameter), and the internal adsorption rate varies inversely with d Pressure drop varies with the Reynolds number, and is roughly proportional to the gas velocity through the bed, and inversely proportional to the particle diameter. Assuming all other parameters being constant, adsorbent beds comprised of small particles tend to provide higher adsorption efficiencies, but at the sacrifice of higher pressure drop. This means that sharper and smaller mass-transfer zones will be achieved. 

We expect more insight from simulations in the future, particularly in situations where these multicomponent systems show effects of coupling between the different degrees of freedom, surface tensions depending on temperature and concentration, hydrodynamic flow induced by concentration gradients in addition to thermal buoyancy. 

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