Langmuir-Hinshelwood isotherms

Kinetic models referred to as adsorption models have been proposed, especially for olefin polymerisation with highly active supported Ziegler-Natta catalysts, e.g. MgCl2/ethyl benzoate/TiCU AIR3. These models include reversible processes of adsorption of the monomer (olefin coordination at the transition metal) and adsorption of the activator (complexation via briding bonds formation). There are a variety of kinetic models of this type, most of them considering the actual monomer and activator concentrations at the catalyst surface, m and a respectively, described by Langmuir-Hinshelwood isotherms. It is to be emphasised that M and a must not be the same as the respective bulk concentrations [M] and [A] in solution. Therefore, fractions of surface centres complexed by the monomer and the activator, but not bulk concentrations in solution, are assumed to represent the actual monomer and activator concentrations respectively. This means that the polymerisation rate equation based on the simple polymerisation model should take into account the... 

For SiC deposition from CH3SiCl3, the adsorption processes are competitive adsorption of H and SiCl3 on the C site, as well as Cl and CH3 on the Si site of the SiC crystal structure. This leads to the general equation of the Langmuir-Hinshelwood isotherm adsorption equation [3] ... 

Obviously all the assumptions involved in the development of the Langmuir-Hinshelwood isotherm are included in this derivation. Any other equilibrium isotherm relating the surface concentration to the gas phase concentration can be used depending on the physical... 

Absorption of monomer onto the catalyst surface, that is, complex formation, can be described by a Langmuir-Hinshelwood isotherm. The fraction of surface /mon occupied by monomer is consequently... 

These expressions define Langmuir-Hinshelwood isotherms. (Cyril Norman Hinshelwood was a British chemist who won a 1956 Nobel Prize for studying chemical reaction mechanisms.)... 

The dependence of the Instantaneous maximuin polymerization rate on the was studied using two models based on the Langmuir-Hinshelwood isotherm, one used by Keii et al (1) and the other by Tait et al (12). 

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 problem posed by Eq. (6.22), without the additional complication of the O dependence, is a classical problem in heterogeneous catalysis. The usual approach it to use Langmuir isotherms to describe reactant (and sometimes product) adsorption. This leads to the well known Langmuir-Hinshelwood-Hougen-Watson (LHHW) kinetics.3 The advantage of this approach is... 

Reaction rates for the start-of-cycle reforming system are described by pseudo-monomolecular rates of change of the 13 kinetic lumps. That is, the rates of change of the lumps are represented by first-order mass action kinetics with the same adsorption isotherm applicable to each reaction step. Following the same format as Eq. (4), steady-state material balances for the hydrocarbon lumps are derived for a plug-flow, fixed bed catalytic reformer. A nondissociation, Langmuir-Hinshelwood adsorption model is employed. Steady-state material balances written over a differential fractional catalyst volume dv are the following ... 

Fig. 12.1. The Langmuir-Hinshelwood adsorption isotherm, showing the fractional coverage of the catalyst surface as a function of the partial pressure of p in the gas phase.

The model that will be used for forced oscillation studies is one which was first proposed by Takoudis et al. (1981) as a simple example of an isothermal surface reaction without coverage dependent parameters in which limit cycles can occur. The bimolecular reaction between species A and B is presumed to occur as a Langmuir-Hinshelwood bimolecular process except that two adjacent vacant sites on the surface are required for the reaction to take place. 

In several photocatalytic reactions, a linear relation between the rate of photocatalytic reaction and amount of substrate(s) adsorbed on the surface of photocatalyst has been reported.3,1(M2) When the Langmuirian adsorption isotherm was expected, this behavior was sometimes called Langmuir-Hinshelwood (L-H) mechanism even if only a kind of adsorbed substrate was assumed. Strictly speaking, however, this is wrong, because L-H mechanism involves the surface reaction of two kinds of adsorbed species, which is not realized in photocatalytic... 

The oxidation of propylene oxide on porous polycrystalline Ag films supported on stabilized zirconia was studied in a CSTR at temperatures between 240 and 400°C and atmospheric total pressure. The technique of solid electrolyte potentiometry (SEP) was used to monitor the chemical potential of oxygen adsorbed on the catalyst surface. The steady state kinetic and potentiometric results are consistent with a Langmuir-Hinshelwood mechanism. However over a wide range of temperature and gaseous composition both the reaction rate and the surface oxygen activity were found to exhibit self-sustained isothermal oscillations. The limit cycles can be understood assuming that adsorbed propylene oxide undergoes both oxidation to CO2 and H2O as well as conversion to an adsorbed polymeric residue. A dynamic model based on the above assumption explains qualitatively the experimental observations. 

A simple Langmuir-Hinshelwood model explains quantitatively the steady-state behavior (4) but it fails to explain the oscillatory phenomena that were observed. The origin of the limit cycles is not clear. Rate oscillations have not been reported previously for silver catalyzed oxidations. Oxidation of ethylene, propylene and ethylene oxide on the same silver surface and under the same temperature, space velocity and air-fuel ratio conditions did not give rise to oscillations. It thus appears that the oscillations are related specifically to the nature of chemisorbed propylene oxide. This is also supported by the lack of any correlation between the limits of oscillatory behavior and the surface oxygen activity as opposed to the isothermal oscillations of the platinum catalyzed ethylene oxidation where the SEP measurements showed that periodic phenomena occur only between specific values of the surface oxygen activity (6,9). 

Figure 19. Effectiveness factor ij of an irreversible monomolecular reaction with Langmuir-Hinshelwood-type kinetics versus the Weisz modulus 4>. Influence of intraparticle diffusion on the effective reaction rate (isothermal reaction in a flat plate, X/>iiS as a parameter, adapted from Satterfield [91]).

---