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The adsorption sites (heavy dots) are equivalent and can have unit occupancy. Also, the adsorbates are immobile on the surface. The Langmuir adsorption model explains adsorption by assuming an adsorbate behaves as an ideal gas at isothermal conditions. According to the model, adsorption and desorption are reversible processes.
Let us assume that the adsorption rate R ads,i-1 for molecules on a layer (i-1) (i.e. formation of a layer i) is proportional to both its fractional surface θ i-1 and to the pressure P, and that the desorption rate R des,i on a layer i is also proportional to its fractional surface θ i:
The adsorption of ensemble molecules on a surface or interface can be divided into two processes: adsorption and desorption. If the adsorption rate wins the desorption rate, the molecules will accumulate over time giving the adsorption curve over time. If the desorption rate is larger, the number of molecules on the surface will decrease over time.
where A is the reactant and S is an adsorption site on the surface and the respective rate constants for the adsorption, desorption and reaction are k 1, k −1 and k 2, then the global reaction rate is: = = where: r is the rate, mol·m −2 ·s −1
Source: [2] If a solid body is modeled by a constant field and the structure of the field is such that it has a penetrable core, then = ′ [ ()] ′ [ ()]. Here ′ is the position of the dividing surface, = is the external force field, simulating a solid, is the field value deep in the solid, = /, is the Boltzmann constant, and is the temperature.
The coefficient is a function of surface temperature, surface coverage (θ) and structural details as well as the kinetic energy of the impinging particles. The original formulation was for molecules adsorbing from the gas phase and the equation was later extended to adsorption from the liquid phase by comparison with molecular dynamics ...
The Hertz–Knudsen equation describes the non-dissociative adsorption of a gas molecule on a surface by expressing the variation of the number of molecules impacting on the surfaces per unit of time as a function of the pressure of the gas and other parameters which characterise both the gas phase molecule and the surface: [1] [2]
The Freundlich equation or Freundlich adsorption isotherm, an adsorption isotherm, is an empirical relationship between the quantity of a gas adsorbed into a solid surface and the gas pressure. The same relationship is also applicable for the concentration of a solute adsorbed onto the surface of a solid and the concentration of the solute in ...