The study assessed the applicability of
Nitrophenols are classified as moderately to highly toxic even at low concentrations when present in wastewaters. Thus, they are a source of serious social and hygienic problems as important occupational and environmental pollutants [
The monosubstituted
The literature reports a number of studies on the efficiency of various adsorbents for phenols and substituted phenols removal from wastewaters [
The walls of
Over the past few decades, linear regression has been developed as a major option in designing adsorption systems [
In this context, the scope of the present study was to investigate the applicability of
The equilibrium experiments were accomplished using model solutions of
SPECORD UVVIS, Carl Zeiss Jena, spectrophotometer was used for concentration determinations at maximum absorption wavelength
The design and efficient operation of adsorption processes require equilibrium adsorption data for use in kinetic, dynamic, and mass transfer models [
The biosorption behavior of
Mathematical equations of the applied single component isotherm models.
Isotherm model  Nonlinear form  Linear expression  Plot  

Langmuir [ 
(1) 

(2) 


Freundlich [ 
(3) 

(4) 


Redlich and Peterson [ 
(5) 

(6) 


Multilayer [ 
(7) 

Secondorder polynomial form 


(8) 


Fritz and Schluender [ 
(9) 

—  — 
In the present study, linear and nonlinear regression analysis was performed to determine the values of the isotherm model parameters. Six different error functions (
Error functions used to discriminate between models.
Error function  Definition  References  

Coefficient of determination ( 
(10) 

[ 
Sum of the squares of errors (ERRSQ)  (11) 

[ 
Hybrid fractional error function (HYBRID)  (12) 

[ 
Marquardt’s percent standard deviation (MPSD)  (13) 

[ 
Average relative error (ARE)  (14) 

[ 
Sum of the absolute errors (EABS)  (15) 

[ 
Corrected Akaike information criterion (AIC_{C})  (16) 

[ 
(17) 
where 

Akaike weight for the 
(18) 


(19) 
where 
In order to assess the fate of nitrophenols in wastewater and to control their mobility and reactivity during remediation processes, the sorption behaviour and mechanism of these toxic contaminants must be understood and revealed. The knowledge of sorbate/sorbent adsorption behaviour at equilibrium is essential for environmental engineering and science as the derived isotherms reveal the specific relation between the pollutant concentration and its uptake degree by the solid phase at constant temperature.
In this section, among the five studied isotherms models, the bestfitting one was determined by the use of seven wellknown error functions to calculate the error deviation between experimental and predicted equilibrium adsorption data, after both linear and nonlinear analysis. In all of the error methods it was assumed that both the liquid phase concentration and the solid phase concentration contribute equally to weighting the error criterion for the model solution procedure. The experimental investigations were conducted at biomass concentration
The values of the model parameters and the isotherm error deviation data for the Langmuir, Freundlich, and RedlichPeterson equations determined by linear regression analysis and for the multilayer model obtained through the secondorder polynomial form of (7) (see Table
Isotherm error deviation data related to the biosorption of
Model  Langmuir  Freundlich  Redlich and Peterson  Multilayer ( 

Parameters 












 
Error functions  

0.9833  0.9956 

0.9967 
ERRSQ  0.7090 

0.5987  0.1827 
HYBRID  12.639 

19.1130  4.4978 
MPSD  35.5410 

58.3339  31.9740 
ARE  14.3110 

10.3833  7.1261 
EABS  0.7156 

0.5192  0.3563 
Alternative isotherm parameters were also determined by nonlinear regression using five error functions (ERRSQ, HYBRID, MPSD, ARE, and EABS) and the corrected Akaike information criterion (
Values of Langmuir, Freundlich, Redlich and Peterson, Multilayer, and Fritz and Schlunder model parameters for the system
ERRSQ  HYBRID  MPSD  ARE  EABS  AIC_{C} 
 

Langmuir model  

3.9939  6.1036  6.1037  6.1038  7.1577  

0.8428  1.4228  1.4228  1.4228  1.6142  
Error  0.6678  8.8101  29.6806  2.5861  1.6665  2.49 

 
Freundlichmodel  

2.1825  2.1945  2.1946  2.1946  2.2393  

0.3110  0.3073  0.3073  0.3073  0.3002  
Error 





− 
1.00 
 
Redlich and Peterson model  

1307.7861  1170.0995  1018.8770  1018.6101  1000.0155  

588.4872  531.9036  463.0101  462.8754  572.1642  

0.6974  0.6937  0.6938  0.6938  0.5793  
Error  0.0255  0.4483  6.7061  0.1799  1.2184  8.19 

 
Multilayer model  

2.8903  3.2225  3.2224  3.2224  2.7971  

0.0317  0.0336  0.0336  0.0336  0.0265  

3.1784  3.0834  3.0834  3.0834  3.4010  
Error  0.1218  2.0060  14.1635  0.8024  0.5022  16.01 

 
Fritz and Schlunder model  

4.4335  4.5110  5.9346  3.5962  2.7281  

0.3109  0.3073  0.3073  0.3075  0.2956  

1.0314  1.0555  1.7042  0.6388  0.2182  




0.0004  −0.0263  
Error  0.0226  0.8783  9.3716  0.1757  0.2213  −10.97  5.67 
The experimental data points of
Experimental equilibrium data and Langmuir isotherms of
Experimental equilibrium data and Freundlich isotherms of
The comparative analysis between the values of the error functions, obtained through the linear approach, outlined the threeparameter RedlichPeterson model as the one with the highest
Statistically, it is expected that the higher the number of parameters in a model equation, the closer the theoretical estimates should be to the empirical data. Moreover the error functions HYBRID and MPSD could be accepted as the most indicative, adequate and essentially meaningful when determining the best fit isotherm model, as the number of the isotherm parameters is accounted only by them [
To prove the latter observations, the modes of the experimental and model isotherms obtained on the basis of the linear and nonlinear approach were also compared (Figure
Among the five applied equations, the Freundlich (Figure
As stated earlier (Section Introduction), chitin and chitosan are the main components of
The proposed mechanism of
Experimental equilibrium data and multilayer isotherms of
Experimental equilibrium data and FritzSchlunder (fourparameter model) isotherms of
Hence, it is supposed that the adsorption of
The relatively high value of the regression coefficient
The comparison between the values of the six error estimating functions and the modes of experimental versus model isotherms outlined the Freundlich (Figure
The AIC developed by Akaike is a methodology for model selection in a situation where more than one model has been fitted to experimental data and screening of the candidate models is crucial to the objectives of the research work. Akaike’s general approach not only allows the best model to be identified, but also allows the ranking of the rest of the models under consideration [
The data in Table
Comparative analyses between the presented experimental results and the literature cited biosorption capacity of various
Biosorption capacities of
Biosorbent  Sorbate 

System parameters  References  





Cr, As  2.0  50.0  1.0  [ 

Zn  11.0  50.0  1.0  [ 

Cu  17.0  50.0  1.0  [ 

Cu  12.4  50.0  1.0  [ 

Rhodamine B  7.6  100.0  4.0  [ 

Lindane  0.375  1.0  1.7  [ 

Malathion  0.445  1.5  2.0  [ 

Reactive Black 5  157.82  250.0  1  [ 


4.5  25.0  3  Present study 
Considering the values of the individual system parameters (initial sorbate concentration, biosorbent concentration, etc.), it could be concluded that the maximum biosorption capacity of
The singlecomponent biosorption of
FritzSchlunder constant, dm^{3} g^{−1}
Langmuir isotherm constant, dm^{3} g^{−1}
RedlichPeterson isotherm constant, dm^{3} g^{−1}
Akaike information criterion
Corrected Akaike information criterion
The average relative error
FritzSchlunder constant, dm^{3} g^{−1}
RedlichPeterson isotherm constant
Equilibrium adsorbate concentration in the liquid phase, mg dm^{−3}
Initial adsorbate concentration in the liquid phase, mg dm^{−3}
Particle diameter, mm
The sum of the absolute errors
The sum of the squares of errors
FritzSchlunder model
The hybrid fractional error function
Langmuir isotherm constant, dm^{3} g^{−1}
Freundlich isotherm constant, dm^{3} g^{−1}
RedlichPeterson isotherm constant, dm^{3} g^{−1}
equilibrium constant for the first layer adsorption in the multilayer isotherm model
Equilibrium constant for multilayer adsorption in the multilayer isotherm model
The linear transform model
Adsorbent concentration, g dm^{−3}
Marquardt’s percent standard deviation
number of isotherm parameters
the heterogeneity factor in the Freundlich model
Number of experimental data points
Maximum monolayer adsorption capacity in the multilayer isotherm model, mg g^{−1}
The equilibrium sorbate concentration in the solid phase, mg g^{−1}
Experimental
Model calculated
The sorption capacity at equilibrium and at time
Correlation coefficient
The sum of the squares for the residual
Temperature, K
Time, min
Solution volume, dm^{3}
Adsorbent mass, g.
FritzSchlunder exponent
FritzSchlunder exponent
Maximum absorbance wavelength, nm
Akaike weight for the
The difference between the