Fractional surface coverage

Figure 3. The effect of degree of polymerization on surface coverage (fractional site occupancy) at various polymer concentrations. The solid lines represent the present model and the symbols correspond to the theory of Scheutjens and Fleer. The parameter values are the same as in Figure 2.

We can now eliminate the surface coverage fractions from the chemical and mechanical rates ... 

In the special but not uncommon situation where the intermediates of a reaction are adsorbed onto the surface of the electrode substratef the activities of the intermediates in the surface region, as they are used in the present derivation, would have to be replaced with surface coverage fractions (0jS) since in this case the available electrode substrate area limits the extent of the reaction. If the electrode were to become completely covered by one or more of the intermediates (as with the application of a larger driving force q ), the potential dependence of the rate (i.e the Tafel slope, b) would no longer include the contribution that would otherwise arise for the non-rds coverage-limited reaction steps. 

No experimental evidence is available for the evaluation of. the critical surface coverage fraction a. Askwith, Cameron and Crouch [32] advanced arguments to show that substantial deviations from a mean value of 0.5 for a had only a small influence on the magnitude of the intercept AS° - R In [a/(1-fl)]. But if Eqn 10-7 is thrown into the form... 

It is necessary to introduce the sum of all surface coverage fractions, including the fraction of uncovered surface in (14-20) and (14-21), because the s are not normalized. In other words, t>ut... 

Since the vacant-site fraction v and the surface coverage fraction a must sum to unity, the consequence of stipulating that the net rate of adsorption must vanish is... 

Since surface coverage fractions for all species, including the intermediate, are finearly proportional to the vacant-site fraction, it is straightforward to calculate V by stipulating that all fractions must sum to unity. Hence,... 

When surface coverage fractions are written in terms of partial pressures via the Langmuir isotherm, one arrives at the following rate law ... 

It should be obvious at this stage of model development that an analytical solution exists for the vacant-site fi action because all surface coverage fractions exhibit linear dependence on v. Since... 

Obviously, all surface coverage fractions are linearly related to v, which is facilitated by the premise that the stable intermediate occupies a single site. The vacant-site fraction exhibits the following analytical solution ... 

The kinetic rate constant for this irreversible reaction is forward- Do not use Langmuir isotherms to describe surface coverage fractions by A2, B, and C. 

If the Freundlich isotherm is employed to calculate surface coverage fractions, then ... 

Answer If Langmuir-type adsorption is applicable, then the surface coverage fractions are represented by... 

For Langmuir-type adsorption, the surface coverage fraction for each species is linearly proportional to the vacant-site fraction, and the Hougen-Watson kinetic rate law scales as ( v) - Hence, y = 3 reveals that the rate-limiting step requires three active sites on the catalytic surface. 

Note that, at low surface coverage fractions (0 1), a proportionality law not unlike Henry s law is obtained ... 

Using as = 77 K and T2 = 90 K and the corresponding pressure ratios available in the problem, we can calculate the heat of adsorption (in kJ moU ) at the three values of surface coverage fraction VA m. -11-79, -12.66, -9.104. These values (essentially two values for the heat of adsorption, around 11 and 9 kJ moU ) seem to indicate a multilayer physical adsorption. 

Physically, this shows the surface coverage fraction is simply the ratio of the adsorption reaction to the total sum of parallel reactions. Then the current density i becomes... 

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