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The adsorption rate is dependent on the temperature, the diffusion rate of the solute (related to mean free path for pure gas), and the energy barrier between the molecule and the surface. The diffusion and key elements of the adsorption rate can be calculated using Fick's laws of diffusion and Einstein relation (kinetic theory).
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.
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]
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:
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
Another method that is used to determine the extent of adsorption at an air-water interface is the emulsion technique, which can be used to estimate the relative surface excess with respect to water. [3] Additionally, the Gibbs surface excess of a surface active component for an aqueous solution can be found using the radioactive tracer method.
For measurement of adsorption isotherms, a controlled gas pressure and temperature determine the coverage when adsorption and desorption rates are in balance. [ 2 ] [ 9 ] The coverage can then be measured with various surface sensitive methods like AES or XPS .
This relationship between water activity and moisture content at a given temperature is called the moisture sorption isotherm. These curves are determined experimentally and constitute the fingerprint of a food system. [2] BET theory (Brunauer-Emmett-Teller) provides a calculation to describe the physical adsorption of gas molecules on a solid ...