Adsorption-desorption process equilibrium

It is interesting to note that, although the intrinsic rate of desorption is slower than that of adsorption, both rates were found to be sufficiently fast under our experimental conditions so that the adsorption-desorption process on the Pt surface can be assumed to rapidly equilibrate at all times that is, even a ten-fold increase in both the adsorption and desorption rate constants (while keeping their ratio constant) did not significantly change the predicted step responses. With the assumption of chemisorption equilibrium, Equations (1) and (4) can be combined into the form (35)... 

Here, we do not discuss P transformation resulting from chemical equilibrium and adsorption-desorption processes the reader is directed to the comprehensive... 

Irrespective of the sources of phenolic compounds in soil, adsorption and desorption from soil colloids will determine their solution-phase concentration. Both processes are described by the same mathematical models, but they are not necessarily completely reversible. Complete reversibility refers to singular adsorption-desorption, an equilibrium in which the adsorbate is fully desorbed, with release as easy as retention. In non-singular adsorption-desorption equilibria, the release of the adsorbate may involve a different mechanism requiring a higher activation energy, resulting in different reaction kinetics and desorption coefficients. This phenomenon is commonly observed with pesticides (41, 42). An acute need exists for experimental data on the adsorption, desorption, and equilibria for phenolic compounds to properly assess their environmental chemistry in soil. 

The above stm study also discovered a facile transport of surface gold atoms in the presence of the liquid phase, suggesting that the two-step mechanism does not provide a complete picture of the surface reactions, and that adsorption/desorption processes may have an important role in the formation of the final equilibrium structure of the monolayer. Support for the importance of a desorption process comes from atomic absorption studies showing the existence of gold in the alkanethiol solution. The stm studies suggest that this gold comes from terraces, where single-atomic deep pits are formed (281-283). 

The constant K characterizes the equilibrium adsorption/desorption between a bare surface site and an adsorbate-covered one (i.e., reaction 11.39). In the higher-adsorption / desorption processes (e.g., reaction 11.41) the adsorption (left-hand side) and desorption (right-hand side) sites are already adsorbate covered such reactions are physically very similar no matter what the particular number of adsorbed layers i is involved. Therefore the approximation is made that... 

If, on the other hand, surface reaction determined the overall chemical rate, equation 3.68 (or 3.69 if an Eley-Rideal mechanism operates) would represent the rate. If it is assumed that a pseudo-equilibrium state is reached for each of the adsorption-desorption processes then, by a similar method to that already discussed for reactions where adsorption is rate determining, it can be shown that the rate of chemical reaction is (for a Langmuir-Hinshelwood mechanism) ... 

For adsorbed hydrocarbons, the adsorption—desorption process can be thought of as a reaction and the adsorption isotherm as a description of the reaction at equilibrium. For the Langmuir isotherm,... 

These applications are described comprehensively for several different mechanistic models of the adsorption-desorption process at equilibrium by S. Goldberg, op. cit.8 Kinetics applications are discussed by D. L. Sparks and D. L. Suarez, Rates of Soil Chemical Processes, Soil Science Society of America, Madison, WI, 1991. 

Here we consider the simple adsorption-desorption reaction equilibrium of a reversible mobile adsorption process without any chemical reactions ... 

The Langmuir model describes, for a uniform surface and a non-self-interacting adsorbate, the relationship between amount adsorbed and exposure concentration. The parameters of the model are the maximum amount adsorbed as a full monolayer and the equilibrium constant for the adsorption-desorption process which indirectly reflects the strength of the adsorbate-substrate interaction. For the present situation the analysis is modified in the following ways ... 

Summarizing this section it can be stated that the adsorption bonds in filled PDMS have a dynamic origin. With increasing temperature, the frequency of adsorption-desorption processes in the adsorption layer increases and the adsorption-desorption equilibrium shifts to the chain desorption. At room temperature, the lifetime for the dimethylsiloxane chain units in the adsorption state is very short chain units adhere to the filler surface only for tens of microseconds. 

This brings up the question of how this scheme has to be modified when equilibrium is not attained. The answer is that the identity of thermod3mamical and mechanical measurement persists, but that the value obtained for y differs from y (eq.) in fact, often y (non-eq.) > y (eq.). Suppose a given interface is created very rapidly and then starts to relax with a time scale r. At any time t equilibrium state, characterized by the pertaining y (non-eq.). Even then, this non-equilibrium surface tension can be measured, provided the time-scale of our measurement is short in comparison with t. When different methods of measurement, either thermodynamical or mechanical, do not yield the same y this may either mean that there have been errors in the measurement or that they apply to different moments (or time intervals) of the relaxation period. The downward tendency of y(f) reflects the general trend of F(V,T,n) and G(p,T, n) to become minimal at equilibrium (sec. 1.2.12). When only relaxation of the interface takes place, y must decrease. However, when the bulk phases also relax slowly or when the relaxation is determined by adsorption-desorption processes, y may also increase. For instance, this would be observed if... 

The development of normalized desorption isotherms is an attempt to quantify the degree to which the adsorption/desorption processes are reversible. Examination of Tables 4 and 5 reveals that a significant correlation can be achieved using this method. It is also interesting to note that, in general, the sorption to the Cohansey soil exhibits significantly less reversibility than to the PRM soil. This observation is intuitively acceptable since tbe equilibrium adsorption isotherms showed a more favorable tendency for net adsorption to the Cohansey soil than to the PRM soil. It can then be postulated that the driving force for these systems is predominantly controlled by solute/adsorber attraction than by hydrophobicity. 

The adsorption/desorption process was assumed to be relatively slow compared with the mass transfer and the assumption of local equilibrium is no longer valid. Consequently, the solid phase concentration must be related to the adsorption and the desorption rates, via a kinetic equation. The second-order kinetic is accoimted for by the following equation... 

When the adsorption/desorption kinetics are slow compared to the rate of diffusional mass transfer through the tip/substrate gap, the system responds sluggishly to depletion of the solution component of the adsorbate close to the interface and the current-time characteristics tend towards those predicted for an inert substrate. As the kinetics increase, the response to the perturbation in the interfacial equilibrium is more rapid and, at short to moderate times, the additional source of protons from the induced-desorption process increases the current compared to that for an inert surface. This occurs up to a limit where the interfacial kinetics are sufficiently fast that the adsorption/desorption process is essentially always at equilibrium on the time scale of SECM measurements. For the case shown in Figure 3 this is effectively reached when Ka = Kd= 1000. In the absence of surface diffusion, at times sufficiently long for the system to attain a true steady state, the UME currents for all kinetic cases approach the value for an inert substrate. In this situation, the adsorption/desorption process reaches a new equilibrium (governed by the local solution concentration of the target species adjacent to the substrate/solution interface) and the tip current depends only on the rate of (hindered) diffusion through solution. 

As we have already seen, the state of soluble as well as insoluble monolayers can deviate from a equilibrium state defined at constant temperature, pressure, bulk and surface concentrations. A deviation from the equilibrium state of the corresponding adsorption layer can be triggered by vertical and lateral concentration gradients due to adsorption/desorption processes or by hydrodynamic or aerodynamic shear stresses, as shown in Fig. 3.1. 

The kinetics of the adsorption/desorption process are complex and consist of an initial period where equilibrium is achieved essentially in a few seconds. 

In a specific case, when the rate of surfactant exchange between the external liquid and drop s surface is restrained by the adsorption-desorption process, the concentration of surfactant on the drop s surface is close to the equilibrium value. 

We note here that there are other theories of adsorption/desorption kinetics that offer expressions for the adsorption/desorption rate that are different from the ART expression but also lead to the Langmuir isotherm when d0/dt = 0. It is rather strange that adsorption systems with different kinetics of the adsorption/ desorption processes have the same form at equilibrium. 

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