几种吸附等温线动力学模型汇总$

Tempkin considered the effects of some indirect adsorbate/adsorbent interactions and suggested that because of these interactions the heat of adsorption of all the molecules in the layer would decrease linearly with coverage

Toth isotherm model
K RP Ce qe 1 aP Ce
qe is the amount of solute adsorbed per unit weight of adsorbent (mg g-1), Ce is the equilibrium concentration of solute in the bulk solution (mg L-1). KRP, aRP and β are Redlich-Peterson constants and the exponent, β, lies between 0 and 1.
Redlich and Peterson, 1959; Allen, 2004
7
Adsorption modelling
Adsorption isotherm or equilibrium experiment

Tempkin model

Slips or Langmuir-Freundlich isotherm model
Equilibrium concentration (mmol/L)
3
Adsorption modelling
Adsorption kinetics experiment
Mohan, 2011
Zero order kinetic model

Pseudo first order kinetic model
Ideal experiment design
Parameters may affect adsorption Solution: pH, Eh, temperature, ion strength,
competing or interaction with other ions, adsorbent dose, adsorbate concentration, contacting time.
1
Ideal experiment design
Adsorption kinetics experiment Experiments can be done under different
adsorbate concentrations, adsorbent dose, temperature, pH, etc.
Q0
(Langmuir, 1918; Freundlich, 1906; Appelo & Postma, 2005)
6
Adsorption modelling
Adsorption isotherm or equilibrium experiment

Redlich-Peterson model
Adsorption modelling
Adsorption isotherm or equilibrium experiment

Langmuir isotherms

Freundlich isotherms
1/ n qe K F Ce
Q 0bCe qe 1 bCe
G RT ln K

Pseudo second order kinetic model
Amount adsorbed (mmol/g)
Time (h, d)
Amount adsorbed (mmol/g)
Amount adsorbed (mmol/g)
Time (h, d)
dqt k0 dt
qt k0t
dqt k1 (qe qt ) dt
K LF Ce nLF qe 1 aLF Ce nLF
qe is the amount of solute adsorbed per unit weight of adsorbent (mg g-1), Ce is the equilibrium concentration of solute in the bulk solution (mg L-1). KLF, aLF, and nLF are the Slips constants.
(establish one and change another one)
Sample after equilibrium (established Βιβλιοθήκη Baiduarameter)
Amount absorbed (mmol/g)
Different temperature pH Ionic strength
qe is the amount of solute adsorbed per unit weight of adsorbent (mg g-1), Ce is the equilibrium concentration of solute in the bulk solution (mg L-1). KF is the constant indicative of the relative adsorption capacity of the adsorbent (mg g-1) and 1/n is the constant indicative of the intensity of the adsorption.
RT qe (ln ACe ) b
qe is the amount of solute adsorbed per unit weight of adsorbent (mg g-1), Ce is the equilibrium concentration of solute in the bulk solution (mg L-1). R, A, T and b are Tempkin constants.
Adsorbent: surface functional groups, surface area,
pHzpc, elemental composition, morphology, pore structure, particle size distribution, and other physical and chemical property.
qe is the amount of solute adsorbed per unit weight of adsorbent (mg g-1), Ce is the equilibrium concentration of solute in the bulk solution (mg L-1). Q0 is the monolayer adsorption capacity (mg g-1) and b is the constant related to the free energy of adsorption (b∝ e-∆G/RT) and represents the affinity of adsorbate and adsorbent. ∆G is the free energy, K is the Langmuir constant same as b. The sign of ∆G can be used to indicate the feasibility of adsorption process and the spontaneous nature of adsorption.
R-P model can be used to represent adsorption equilibria over a wide concentration range.
Toth model is derived from potential theory and is applicable to heterogeneous adsorption.
2
Ideal experiment design
Adsorption isotherm or equilibrium experiment Experiments can be done under different temperature, pH,
ionic strength.
Vary adsorbate concentration to adsorbent dose ratio
KT Ce qe (1 BCe )1/
qe is the amount of solute adsorbed per unit weight of adsorbent (mg g-1), Ce is the equilibrium concentration of solute in the bulk solution (mg L-1). KT, B, β are the Toth constants.
“Sorption extends infinitely as adsorbate concentrations increase.”
Amount absorbed (mmol/g)
Equilibrium concentration (mmol/L)
Amount absorbed (mmol/g) Equilibrium concentration (mmol/L)
Allen, 2004; Vijayaraghavan, 2006; Mohan, 2011
At low adsorbate concentrations it effectively reduces to the Freundlich isotherm. At high adsorbate concentrations, it predicts a monolayer sorption capacity characteristic of the Langmuir isotherm 8
5
Adsorption modelling
Adsorption isotherm or equilibrium experiment

Langmuir isotherms

Freundlich isotherms
The adsorption capacity (Q0) of adsorbent can be calculated.
Adsorbate: coordination number, ionic radius, electro
negativity, standard reduction potential, species in solution, and other physical and chemical property.
Sampling interval is increased from the
beginning to the end
Different adsorbate concentration Adsorbent dose Temperature pH
Amont adsorbed (mmol/g)
Time (h, d)
qt qe (1 e k1t )
dqt k2 (qe qt )2 dt t 1 t 2 qt k2 qe qe
Time (h, d)
t is the adsorption time; qt is the amount of adsorbate adsorbed at time " t "; qe is the amont adsorbed at equilibrium; k0 , k1 , k 2 are the adsorption rate constant . 4