Biosorption of Organic Dyes: Research Opportunities and Challenges - Green Chemistry for Dyes Removal from Wastewater - page 316

homogeneous or in heterogeneous systems due to its versatility. The
Redlich-Peterson isotherm is given by Equation 8.3 [122]:

kC
1aC

q

RP e

(8.3)

e

RP e

where k RP and a RP are the Redlich-Peterson constants (L g -1 ) and (L mg -1 ) β ,
respectively, and β is the heterogeneity coefficient, which varies between 0
and 1. The Redlich-Peterson model was adequate to represent the bio-
sorption of FD&C Red 40 onto chitosan [59] and food dyes onto chitosan
films [69].
Another model usually employed to represent the biosorption pro-
cesses is the Dubinin-Radushkevich model [123], as demonstrated in
Equation 8.4:

qq ( B)

2

(8.4)

e S

where q s is the D-R constant (mg g -1 ) and ε can be related as Equation 8.5:

1
C

(8.5)

RTln(1 )

e

where R is the universal gas constant (8.314 J mol −1 K −1 ) and T the tem-
perature (K). The B constant is relative to the biosorption free energy E (kJ
mol -1 ), as demonstrated in Equation 8.6 [123]:

1
2B

(8.6)

E

The Dubinin-Radushkevich model was adequate to describe the bio-
sorption of Basic Blue 9 onto nut shells and Eichhornia [128].
The Sips isotherm is a combination of the Langmuir and Freundlich
isotherms, and is given by Equation 8.7 [124]:

m

q(kC)
1+(k C )

(8.7)

q

mS S e

e

m

Se

where q mS is the maximum biosorption capacity from the Sips model
(mg g -1 ), k S is the Sips Constant (L mg -1 )and m the fractionary exponent
related with the biosorption mechanism [124]. The Sips model was ade-
quate to describe the biosorption of food dyes onto Spirulina platensis [19],
Reactive Black 5 onto aqai stalks [32] and Remazol Black B onto Brazilian
pine-fruit shells [129].