Functionalized Magnetic Nanoparticles for Heavy Metal Removal from Aqueous Solutions: Kinetics and Equilibrium Modeling - Advanced Materials for Agriculture, Food and Environmental Safety - page 318

Isotherm Functional form Linear form Plot Advantages Disadvantages References

Langmuir Has Henry law and i nite

saturation limit so
valid over a wide
range of concentration

Based on monolayer
assumption

[100]

qKC C 1 1

C VS C
q

mLe e

e

q = C

qKqq

= +

. e

e e

1 + KC

e

Le e L m m

Freundlich

Simple expression and
has parameter for sur-
face heterogeneity

Does not have Henry
law and no satu-
ration limit, not
structured, not
applicable over
wide range of
concentration

[101] 1/ n

1 ln qVS C .ln

qKC =

ln q = ln K + ln C

e e

e F

e

e F e

n

Te m k i n Simple expression Same as Freundlich.

It does not have
correct Henry law
limit and i nite
saturation limit,
not applicable
over wide range
of concentration

[102]

qVS C

RT RT RT .ln e e

q = ln ( K C ) q = ln K + ln C

e T e e T e

b b b

Redlich-
Peterson
(R-P)

Approaches Freundlich
at high concentration

No special
advantages

[103]

KC

KC KC

RP e

q =

RP e RP e

ln −= 1 ln + ln C ln − 1 VS .ln C

e

1 + C

RP e e

q q RP e

e e