Adsorption limiting

Adsorption isotherms in the micropore region may start off looking like one of the high BET c-value curves of Fig. XVII-10, but will then level off much like a Langmuir isotherm (Fig. XVII-3) as the pores fill and the surface area available for further adsorption greatly diminishes. The BET-type equation for adsorption limited to n layers (Eq. XVII-65) will sometimes fit this type of behavior. Currently, however, more use is made of the Dubinin-Raduschkevich or DR equation. Tliis is Eq. XVII-75, but now put in the form... 

Electrochemical reduction of iridium solutions in the presence azodye (acid chrome dark blue [ACDB]) on slowly dropping mercury electrode is accompanied by occurrence of additional peaks on background acetic-ammonium buffer solutions except for waves of reduction azodye. Potentials of these peaks are displaced to cathode region of the potential compared to the respective peaks of reduction of the azodye. The nature of reduction current in iridium solutions in the presence ACDB is diffusive with considerable adsorptive limitations. The method of voltamiuetric determination of iridium with ACDB has been developed (C 1-2 x 10 mol/L). 

The polymer radius has to be larger than 80% of the particle radius to avoid adsorption limitation under orthokinetic conditions. As a rule of thumb a particle diameter of about 1 pm marks the transition between perikinetic and orthokinetic coagulation (and flocculation). The effective size of a polymeric flocculant must clearly be very large to avoid adsorption limitation. However, if the polymer is sufficiently small, the Brownian diffusion rate may be fast enough to prevent adsorption limitation. For example, if the particle radius is 0.535 pm and the shear rate is 1800 s-, then tAp due to Brownian motion will be shorter than t 0 for r < 0.001, i.e., for a polymer with a... 

In a microbial system a 0-order reaction may proceed under conditions where the biomass or substrate concentrations are high compared with their changes. Such conditions are not typical for the wastewater phase in a sewer. However, a 0-order reaction may proceed when factors such as surface area available for adsorption limit the reaction rate. 

For undersaturated ([M] < Km) systems with relatively fast internalisation kinetics (kmt > k, ), the uptake of trace metals may be limited by their adsorption. Because the transfer of metal across the biological membrane is often quite slow, adsorption limitation would be predicted to occur for strong surface ligands (small values of k ) with a corresponding value of Km (cf. equations (35) and (36)) that imposes an upper limit on the ambient concentration of the metal that can be present in order to avoid saturation of the surface ligands. More importantly, as pointed out by Hudson and Morel [7], this condition also imposes a lower limit on the carrier concentration. Since the complexation rate is proportional to the metal concentration and the total number of carriers, for very low ambient metal concentrations, a large number of carriers are required if cellular requirements are to be satisfied. 

For adsorption limited by mass transfer kinetics, the educt should be significantly less retained than the most strongly adsorbed product. 

In the strong adsorption limit (X/b 1) the expression of the adsorbed layer thickness A, corresponding to the size of the largest loops or tails in the layer, reads in the mean field theory ... 

The weak adsorption limit (X/b 1) has been studied less extensively. The only... 

If the adsorption limits the overall rate, then we can assume that ks is relatively large and that... 

A host of attempts have been made to Improve BET theory, but most approaches have only limited applicability. They include better statistics of the stacking of molecules, account of lateral Interaction, or adsorption limited to a certain number of layers to mimic sorption in pores. Regarding this last attempt. Isotherms of types IV and V in fig. 1.13 can be predicted, but this is a mathematical rather than physical exercise since limitation is in reality not caused by a spontaneous cessation of adsorption after a given number of layers has been completed. Also in view of the additional complication of surface heterogeneity, the insight gained tends to be proportional to rather than to n, where n is the number of publications. 

An example of an adsorption-limited reaction is the synthesis of ammonia the reaction of carbon monoxide and nitric oxide is an example of a sm-face-limited reaction. The synthesis of ammonia from hydrogen and nitrogen,... 

For adsorption-limited reactions, is small and k and are large. Consequently, the ratios r /k and rjy/ko are very small (approximately zero), whereas the ratio is relatively large. The surfaee reaction rate expression is... 

For adsorption-limited reactions the surface specific reaction rate ks is large by comparison and we can set... 

If the cumene decompostion is adsorption limited, then the initial rate will be linear with the initial partial pressure of cumene as shown in Figure 10-12. 

Initiot portiol pressure of cumene, Poo Figure 10-12 Uninhibited adsorption-limited reaction. 

Cellulose nitrate (nitrocellulose) Good flow rate and total throughputs High non-specific adsorption Limited pH compatibility Not dry autoclavable... 

Polysulfone High flow rates and total throughputs Broad pH compatibility Moderate-to-high non-specific adsorption Limited solvent compatibility... 

Also a comparison of adsorption capacity with specific surface of carbons is not always correlated. It is connected with partial participation of surface in adsorption limited by geometric structure of pollutants. 

One way in split-peak measurements can be performed is by injecting a small amount of analyte onto an affinity column at various flow rates. A plot of the inverse negative log of the measured free fraction is then made versus the flow rate. The slope of this graph is related to the adsorption kinetics and mass-transfer rates within the column. If the system is known to have adsorption-limited retention or if the mass-transfer rates are known, then the association rate constant for ana-... 

Breakthrough curves from column experiments have been used to provide evidence for diffusion of As to adsorption sites as a rate-controlling mechanism. Darland and Inskeep (1997b) found that adsorption rate constants for As(V) determined under batch conditions were smaller than those necessary to model breakthrough curves for As(V) from columns packed with iron oxide coated sand the rate constants needed to model the breakthrough curves increased with pore water velocity. For example, at the slowest velocity of 1 cm/h, the batch condition rate constant was 4 times smaller than the rate constant needed to model As adsorption in the column experiment. For a velocity of 90 cm/h, the batch rate constant was 35 times smaller. These results are consistent with adsorption limited by diffusion of As(V) from the flowing phase to sites within mineral aggregates. Puls and Powell (1992) also measured more retardation and smaller rate constants for As(V) at slower flow velocities where there was sufficient time for diffusion to adsorption sites. 

The possibility that chemisorption sites are not saturated, or that cation exchange is involved, so that adsorption limits Zn solubility at a lower level than precipitation... 

SERS was discovered with pyridine. Other aromatic nitrogen- or oxygen-containing compounds, such as aromatic amines or phenols, also display strong enhancement due to SERS. The enhancement can also be seen with other electron-rich analytes such as carboxylic acids. Although SERS allows easy observation of Raman spectra from solutions with concentration in the micromolar (10 ) range, slow adsorption kinetics and competitive adsorption limit its application in analytical chemistry. 

The goal of the various investigations summarized in Table I was to find some electrode-electrolyte-temperature and pH combination that was favorable for the reduction of formate. None of the combinations tested, however, gave formate reduction at useful current densities. In general, formate reduction was more favorable at low temperatures than at high temperatures. This again suggests an adsorption-limited reaction. 

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