- Fundamentals of Adsorption Theory
When a solid surface comes in contact with a gas or a liquid, some chemical species in the gas or liquid will attach to the solid surface and be removed from the gas or liquid. The process by which substance is removed is called adsorption. Adsorption involves the interphase accumulation or concentration of substances at a surface or interface. The substance attached to the solid surface is called adsorbate and the substance to which it is attached is known as the adsorbent.
1.1 Adsorption Kinetics
Adsorption kinetics shows the evolution of the adsorption capacity through time and is necessary to identify the adsorption mechanisms in a given system. Adsorption kinetics are described by diffusion through thesorbent, such as film, pore and surface diffusions, and poresurfacesorption or any combination of those steps. Mathematical expressions or models are often formulated and utilized to understand and predict the kinetics of an adsorption process. Numerous empirical and mechanistic kinetic models exist in literature for liquid-solid adsorption system. Two used empirical models cited in our paper for liquid-solid adsorption system are described below.
The pseudo-first-order and pseudo-second-order kinetics model can be expressed as nonlinear forms by the following equation:
(1)
(2)
where qe (mg/g) and qt (mg/g) are the amounts of adsorbate adsorbed on the adsorbent at equilibrium and at any time t; k1 (1/min) and k2 (g/mg min) are the rate constant of the first-order adsorption and pseudo-first-order kinetics model; t (min) is time.
In pseudo-second order model, the rate-limiting step is the surface adsorption that involves chemisorption, where the adsorbate removal from a solution is due to physicochemical interactions through sharing or exchange of electrons between the two phases.The pseudo-second order kinetic model also assumes that chemisorptions of the adsorbate takes place on the adsorbent.
1.2 Equilibrium Adsorption Isotherms
In an adsorption process, there is a defined distribution of adsorbates between the fluid phase and the adsorbent surface at equilibrium. An adsorption isotherm is a functional expression relating the amount of solute adsorbed on an adsorbent at equilibrium, qe (mg/g), to the equilibrium solute concentration in the fluid phase, Ce (mg/L), at a fixed temperature. In other words, equilibrium adsorption can be described by mathematical isotherm equations or models whose parameters express the surface properties and affinity of an adsorbent at a fixed temperature.Adsorption isotherms are often used to compare the adsorption capacities of different adsorbents
for a particular adsorbate species.
1.2.1 Langmuir Model
The Langmuir isotherm equation is the first theoretically developed adsorptionisotherm. Many of the equations proposed later and which fit the experimental resultsover a wide range are either based on this equation, or these equations have beendeveloped using the Langmuir concept. Thus, the Langmuir equation still retains animportant position in physisorption as well as chemisorption theories. The equationhas also been derived using thermodynamic and statistical approaches.
The nonlinear form of Langmuir isotherm is:
(1)
where (mg/g)is the amount adsorbed per unit mass of adsorbent at equilibrium concentration; (mg/L)is the equilibrium concentration of the adsorbate; (mg/g)is the maximum adsorption capacity; b is the adsorption equilibrium constant, characteristic of the affinity between the adsorbent and adsorbate.
The key assumptions underlying the Langmuir isotherm model are listed below:
•The adsorbed entites (atoms or molecules or ions) are attached to thesurface at definite localized sites.
•Each site accommodates one and only one adsorbed entity.
•The energy state of each adsorbed entity is the same at all sites on thesurface independent of the presence or absence of other absorbed entitiesat neighboring sites. Thus, the Langmuir model (also called localizedmodel) assumes that the surface is perfectly smooth and homogenous andthat the lateral interactions between the adsorbed entities are negligible.
The Langmuir equation is said to have a fundamental thermodynamic basis as it effectively reduces to Henry’s Law at dilute adsorbate concentrations
1.2.2 Freundlich Model
The Freundlich model, an empirical isotherm model, the nonlinear form of Freundlich isotherm is:
(2)
where is a Freundlich constant representing the adsorption capacity (g/L); n refers to the adsorption capacity.
The model was derived by assuming that the adsorption sites have an exponentially decaying energy distribution. In other words, the model assumes that the adsorbent surface is energetically heterogeneous. This assumption suggests a multilayer adsorption process.There is no limitation for the formation of the monolayer with Freundlich isotherm and also the isotherm refers the reversible adsorption.