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Indonesian Journal of Science & Technology 6 .
205-234 Indonesian Journal of Science & Technology Journal homepage: http://ejournal.
edu/index.
php/ijost/ How to Calculate Adsorption Isotherms of Particles Using Two-Parameter Monolayer Adsorption Models and Equations Risti Ragadhita.
Asep Bayu Dani Nandiyanto* Departemen Kimia.
Universitas Pendidikan Indonesia Correspondence: E-mail: nandiyanto@upi.
ABSTRACT
Adsorption isotherm is the most important calculation to predict and analyze the various possible mechanisms that occur in adsorption process.
However, until now, most studies only presented the adsorption isotherm theory, and there are no studies that explain the adsorption isotherm thoroughly and in detail from theory to calculation.
Therefore, this study contains guidelines for selecting the type of adsorption isotherm to describe the entire adsorption data set, which is featured by the ten most common adsorption isotherms.
The steps of how to analyze the two-parameter monolayer adsorption are presented.
This study is expected to provide clear and useful information for researchers who are working and studying on the adsorption process.
A 2021 Tim Pengembang Jurnal UPI
ARTICLE INFO
Article History:
Submitted/Received 15 Nov 2020
First revised 30 Des 2020
Accepted 24 Feb 2021
First available online 28 Feb 2021
Publication date 01 Apr 2021
____________________
Keyword:
Adsorption Isotherms.
Carbon.
Curcumin.
Education.
Silica.
Tungsten.
Ragadhita.
How to Calculate Isotherm Adsorption of Particles Using Two-Parameter.
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INTRODUCTION
Adsorption is a surface phenomenon that involves adhesion of atoms, ions or molecules from a gas, liquid, or dissolved solid on a surface of substance.
The atoms, ions or molecules that attached on the solid surface is the adsorbate, and the place where the adsorbate accumulates is called the This process creates a film of the adsorbate on the surface of the adsorbent.
Definition of adsorption is different from The absorption involves a fluid .
s the absorbat.
is dissolved by or permeates a liquid or solid .
he absorben.
, and the process involves the whole volume of the material.
Illustration from the definition of adsorbate and adsorbent is presented in Figure 1.
Adsorption divided into two types based on molecular interactions: physical and chemical adsorptions (Al-Ghouti & DaAoana.
Kong & Adidharma, 2.
Adsorption process is widely applied and well-practiced in water treatment, purification, and separation processes.
This process is also one of the most effective and promising techniques, supported by facile, technically feasible, and economical processes (Rahmani & Sasani, 2016.
Hegazi, 2.
One of the important factors in the adsorption is adsorption isotherm.
The relationship in the adsorption isotherm explains the phenomena and interactions Generally, the adsorption performance can be predicted by modeling the adsorption isotherm data because the adsorption isotherm model can provide information about the adsorbent capacity, the adsorption mechanism, and the evaluation of the (Nandiyanto et al.
, 2020a.
Anshar & Raya.
In previous studies, we have performed isotherm analysis on various adsorbent systems (Nandiyanto et al.
, 2020a.
Nandiyanto et al.
, 2020b.
Nandiyanto et al.
Nandiyanto et al.
, 2020.
In this study, we used the most widely applied isotherm models to evaluate adsorption performance, such as Langmuir.
Freundlich.
Temkin.
Dubinin-Radushkevich.
FlorryHuggins.
Fowler-Guggenheim.
Hill-Deboer.
Jovanovic.
Harkin-Jura, and Halsey, while other researches only described the theory and the calculation method was not discussed deeply.
This study was also completed with the calculation strategies for getting the parameters in the adsorption Figure 1.
Illustration of monolayer .
and multilayer .
adsorption process (Rina Maryanti et al.
, 2.
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ADSORPTION ISOTHERM THEORY
Langmuir Isotherm 0 < RL < 1.
Favorable adsorption process .
ormal adsorptio.
Langmuir isotherm defines that the maximum adsorbent capacity occurs due to the presence of a single layer .
of adsorbate on the adsorbent surface.
There are four assumptions in this type of isotherm, namely (Langmuir, 1.
The molecules are adsorbed by a fixed site .
he reaction site at the adsorbent Each site can "hold" one adsorbate All sites have the same energy.
There is no interaction between the adsorbed molecules and the surrounding Adsorption process form monolayer.
Illustration of monolayer formation during adsorption is shown in Figure 1 .
Langmuir isotherm model is represented by equation .
ycEyce =ycE ycoycaycu yaya yayce ycE where Qe is the amount of adsorbed adsorbate molecule per gram of adsorbent .
Qmax is the capacity of the adsorbent monolayer .
Ce is the adsorbate equilibrium concentration .
g/L), and KL is the Langmuir adsorption constant.
The important factor in the Langmuir isotherm is the dimensionless constant or separation factor (RL) (Langmuir, 1.
which is expressed by equation .
ycIya = 1 ya ya ya yce This separation factor has the following .
RL > 1, unfavorable adsorption process .
llows the adsorption process to occur, most desorption processes occu.
RL = 1, linear adsorption process .
epending on the amount adsorbed and the concentration adsorbe.
RL = 0.
Irreversible adsorption process .
trong adsorptio.
Freundlich Isotherm Freundlich isotherm describes a physical type of adsorption in which the adsorption occurs in several layers and the bonds are not strong .
Multilayer formation is illustrated in Figure 1 .
Freundlich isotherm also assumes that the sites of adsorption are heterogeneous (Dada et al.
The empirical relationship for expressing Freundlich isotherm is given in equation .
ycoycuycEyce = ycoycuyayce ycu ycoycuyayce .
where Kf is Freundlich constant.
Ce is the equilibrium conditions .
g/L).
Qe is the amount of adsorbate absorbed per unit of adsorbent .
, and ycu is the value indicating the degree of linearity between the adsorbate solution and the adsorption process (Dada et al.
, 2.
The value of n is described as follows:
ycu = 1, linear adsorption.
ycu < 1, adsorption process with chemical .
ycu > 1, adsorption process with physical .
Favorable adsorption process is declared when 0 < 1/n < 1, and a cooperative adsorption process occurs when 1/n > 1.
Temkin Isotherm Temkin postulates, namely that the adsorption heat decreases linearly with increasing surface adsorbent coverage, the adsorption process assumes a uniform binding energy distribution on the adsorbent surface, and the adsorption interaction involves the interaction between adsorbate-adsorbent (Romero-Gonzales et al.
, 2.
Temkin isotherm is given in equation .
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ycEyce = yaAycN ycoycuya ycN yaAycN ycoycuyayce .
where BT is the adsorption heat constant .
f the BT < 8 kJ/mol, the adsorption process occurs physicall.
AT is the binding equilibrium constant, and T is the absolute Dubinin-Radushkevich Isotherm Dubinin-Radushkevich isotherm expresses the adsorption process on the adsorbent which has a pore structure or adsorbent which has a heterogeneous surface and expresses the adsorption free energy.
adsorption process is based on micropore volume filling (Romero-Gonzales et al.
Dubinin-Radushkevich isotherm is written in equation .
ycoycuycEyce = ycoycuycEyc Oe .
uyuA 2 ) .
where is the Dubinin-Radushkevich isotherm constant.
QS refers to the saturation capacity of theoretical isotherms, and a is the Polanyi potential (J/mo.
is calculated using equation .
yuA = ycIycNycoycu .
ya ] yce To calculate the free energy of adsorption per adsorbate molecule, it is calculated using equation .
ya= Oo2yu where Ce is the equilibrium concentration of solute and E is the adsorbate energy per molecule as the energy needed to remove molecules from the surface.
The equation .
E < 8 kJ/mol, physical adsorption.
8 < E < 168 kJ/mol, chemical adsorption.
Jovanovic Isotherm Jovanoic isotherm is based on the assumptions found in the Langmuir model, without allows some mechanical contact between the adsorbate and the adsorbent (Ayawei et al.
, 2.
The linear correlation of the Jovanovic model is shown in equation .
ycoycuycEyce = ycoycuycEycoycaycu Oe yaya yayce .
where Qe is the amount of adsorbate in the adsorbent at equilibrium .
Qmax is the maximum uptake of adsorbate, and KJ is the Jovanovic constant.
Halsey Isotherm Halsey isotherm evaluates a multililayer adsorption system (Dada et al.
, 2.
The Halsey model follows equation .
ya ya ycEyce = ycu ycoycuyaya Oe .
cu ) ycoycuyayce .
where KH dan n are the Halsey model Harkin-Jura Isotherm Harkin-Jura isotherm describes that the adsorption occurring on the adsorbent surface is a multilayer adsorption because the adsorbent has a heterogeneous pore distribution (Ayawei et al.
, 2.
This model is expressed by equation .
= yayaya Oe .
ycoycuyciyayce yaya where yuyaya value is related to specific surface area of adsorbent and yayaya are the Harkin Jura isotherm constants.
The modification of the Harkin-Jura equation .
is used to determine the surface area of the adsorbent.
The modified Harkin-Jura equation is written in equation .
Oeyc.
cI 2 ) yuyaya = 4.
606ycIycNycA Where q is the constant independent of the nature of the adsorbent.
S is the specific yco2 surface area ( yci ).
R is the universal gas ya constant .
314 ycoycuyco ).
T is the absolute AEya temperature, and N is the Avogadro number.
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ycI2 = Oe yuyaya y4.
606ycIycNycA yc For surface area calculations.
Table 1 shows several of q value.
Table 1.
List of qvalue various material.
Recalculated from reference (Shanavas et al.
Nandiyanto et al.
, 2020.
T (K) yeaya yee( ) yeO 053 y 1021 1,760 y 1021 727 y 1021 677 y 1021 662 y 1021 664 y 1021 011 y 1024 631 y 1023 552 y 1023 553 y 1023 633 y 1023 Silica 436 y 1022 Tungsten Trioxide (WO.
141 y 1024 Material Carbon Titanium Dioxide Flory-Huggins Isotherm Flory-Huggins isotherm takes into account the degree of surface coverage of the adsorbate on the adsorbent.
This isotherm also assumes that the adsorption process occurs spontaneously (Saadi et al.
, 2.
Flory-Huggins isotherm is expressed by equation .
yuE ycoycuyci ya = ycoycuyciyayaya ycu log.
Oe yuE) yce ya where yuE = .
Oe yayce ) is the degree of ycu surface coverage.
KFH is the FloryAeHuggins model equilibrium constant and nFH is the number of adsorbates occupying adsorption Furthermore, the Gibbs free energy of spontaneity .
GA) is calculated from the equilibrium constant (KFH).
The value of iGA corresponds to the KFH value as shown in equation .
iGA = OeycIycN ln yayaya The negative sign on the value iGA confirms that the adsorption process is spontaneous, which is a function of temperature (T).
Fowler-Guggenheim Isotherm Fowler-Guggenheim isotherm suggests that there is a lateral interaction at a set of localized sites with weak interactions (Van der Waals interaction effec.
between adsorbed species at neighboring sites (Hamdaoui and Naffrechoux, 2.
The empirical relationship of Fowler-Guggenheim model is expressed by equation .
OeyuE) ycoycu ( yce yuE yuE 2ycOyuE ) Oe 1OeyuE = Oeycoycuyayaya ycIycN .
where KFG is the constant.
W .
J/mo.
for the adsorbed adsorbate at the active site representing the interaction between the adsorbate and the adsorbent.
Ce is the equilibrium constant.
W is the empirical interaction energy between two adsorbed molecules at the adjacent neighboring site .
J/mo.
, and A is the fractional coverage of the surface.
The empirical interaction energy (W) has the following value:
If W > 0 kJ/mol, attractive interaction between adsorbed molecule.
If W < 0 kJ/mol, repulsive interaction between adsorbed molecule.
If W = 0 kJ/mol, no interaction between adsorbed molecule.
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Hill-Deboer Isotherm Hill-Deboer isotherm describes mobile adsorption and bilateral interactions between adsorbed molecules (Hamdaoui and Naffrechoux, 2.
Hill-Deboer isotherm approach is written in equation .
OeyuE) ycoycu [ yce yuE ]Oe yuE 1OeyuE ya yuE = Oeycoycuya1 Oe ycIycN where K1 is the Hill-Deboer constant (L/m.
and K2 is the energetic constant of the interactions between adsorbed molecules .
J/mo.
K2 > 0 kJ/mol, attraction between adsorbed molecules.
K2 < 0 kJ/mol, repulsion between adsorbed molecules.
K2 = 0 kJ/mol, no interaction between adsorbed molecules.
The quantity adsorbed by the unit mass of the adsorbent at equilibrium (Q.
is calculated using equation .
ya Oeya ycEyce = 0yco yce y ycO where C0 is the initial concentration .
gAEL).
Ce is the concentration at equilibrium .
gAEL), m is the mass of the adsorbent .
, and V is the volume of the adsorbate solution (L).
MATERIAL AND METHOD
There were several materials used as adsorbents which were the result of conversion from agricultural waste such as carbon converted from peanut shells (CPS), carbon obtained from rice husks (CRH), silica from rice husks (SRH).
Inorganic materials such as tungsten (WO.
was also used as adsorbents in this study.
Detailed information on how the process of converting agricultural waste into carbon and silica and fabrication process of WO3 was presented in our previous studies (Ragadhita et al.
, 2019.
Faindini et al.
, 2020.
Nandiyanto et al.
, 2020a.
Nandiyanto et al.
, 2017.
Nandiyanto et al.
, 2020.
The adsorbate solution used as an experimental model was curcumin solution.
Information on curcumin production was carried out in the same manner as provided in our previous study (Ragadhita et al.
, 2019.
Nandiyanto et al.
In general, the adsorption process was carried out in the following steps: specific mass amount of each CPS.
CRH.
SRH, and WO3 adsorbents were put into 200 mL of concentrations of 20, 40, 60, 80 ppm at constant pH and temperature.
The solution mixture was mixed in a borosilicate batch .
lass reacto.
with a capacity of 400 mL and has dimensions of 10 and 8 cm, respectively, for height and diameter.
Then, the solution mixture was stirred at 1000 rpm for 1 h.
Next, the solution mixture was filtered.
The filtrate was measured and analyzed with a UV-VIS spectrophotometer (Model 7205.
JENWAY.
Cole-Parmer.
US.
analyzed at wavelengths between 200 and 600 n.
After the adsorption process was completed, the next step was to evaluate the adsorption process.
Several adsorption isotherm models were used for the analysis of the adsorption process including Langmuir.
Freundlich.
Temkin.
DubininRadushkevich.
Florry-Huggins.
FowlerGuggenheim.
Hill-Deboer.
Jovanovic.
Halsey, and Harkin-Jura isotherms.
RESULTS AND DISCUSSION
Linearization and Curve Plotting to Obtain Two-Parameter Adsorption Isotherms from Several Models The adsorption process includes a series of adsorption experiments to calculate the adsorption parameters used to express the adsorption equilibrium model.
Several adsorption isotherm models were used to evaluate the adsorption process in this study are Langmuir.
Freundlich.
Temkin.
Dubinin Raduschkevich.
Flory-Huggins.
FowlerDOI: https://doi.
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Hill-Deboer.
Jovanovic.
HarkinJura, and Halsey isotherms.
The calculation of the adsorption isotherm is carried out through data fitting to obtain a linear equation .
= mx .
Then, we also need to consider the value of R2.
The greater R2 relates to similarity data to the model The fitting of this data is adjusted to the linear expression of the mathematical model of each adsorption isotherm.
From the results of the data fitting, several parameters in the adsorption process were obtained.
The phenomena occurring during the adsorption were predicted.
Information regarding curve data fitting, calculations, and parameters of the adsorption isotherm model that must be analyzed is presented in Table 2.
Experimental Adsorption Process Results The Data from the adsorption process of curcumin solution using CPS.
CRH.
SRH, and WO3 adsorbents are presented in Table 3.
Table 3 shows the adsorption data of curcumin solution for data fitting using twoparameter isotherm adsorptions: Langmuir.
Freundlich.
Temkin.
Dubinin-Radushkevich.
Jovanovic.
Halsey.
Harkin-Jura.
FloryHuggins.
Fowler-Guggenheim, and HillDeboer isotherm.
Plotting Analysis Isotherms Adsorption Isotherm for Adsorption Two-Parameter 1 Langmuir Langmuir model adsorption parameters were obtained using equation .
as presented as ycE = ycE ycoycaycu yaya yayce yce ycE ycoycaycu To get the Langmuir model parameters, we need to convert Ce and Qe values into the form of and ycE , which are used for fitting data .
ee ya yce yce Table .
The curves of fitting data result from equation .
are presented in Figures 2 .
The result of fitting data was used to determine the adsorption parameters.
The result of data fitting in the form of a gradient obtained is the ycE yya value and the intercept is the ycE ycoycaycu ycoycaycu ya Table 4 show parameters of the Langmuir model using CPS.
CRH.
SRH, and WO3 adsorbents.
Qmax and KL in Table 4 are the maximum monolayer adsorption capacity and Langmuir adsorption constant, respectively.
Based on Qmax value, adsorption process using CRH adsorbent is very good due to it has the highest maximum monolayer adsorption capacity (Qma.
value than others.
Langmuir adsorption constant (KL) shows the degree adsorbate-adsorbent interaction.
Higher KL value indicating strong adsorbate-adsorbent interaction while smaller KL value indicating weak interaction between adsorbate molecule and adsorbent surface.
The KL value for all adsorption systems show a relatively small value means weak interaction between the absorbent and adsorbate molecules due to the active site only adsorb one molecule.
Plotting analysis shows that CPS.
SRH, and WO3 have relatively high correlation value (R2 > 0.
than CRH, informing that CPS.
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Table 2.
Information regarding curve data fitting, calculation, and isotherm parameters Isotherm Type Langmuir Linier Equation ycEyce ycEycoycaycuya yayce ycEycoycaycu Plotting 1AE ycyc 1AE yayce ycEyce ya Parameter A = ycnycuycyceycycayceycyyc ycE ycoycaycu A ycEycoycaycu = A yaya = ln ycEyce = ln ycoyce ln yayce ycu Freundlich ycoycuyayce ycyc ycoycuycEyce A ycuya = ycyce = yaAycN ln ya ycN yaAycN ln yayce ycoycuyayce ycyc ycEyce ycycoycuycyyce A yaA = ycycoycuycyyce ycnycuycyceycycayceycyyc A ycoycuya ycN = A yaAycN = ln ycyce = ln ycyc DubininRadushkevich Flory Huggins FowlerGuggenheim Oe .
ua2 ) ycEycoycaycu yycycoycuycyyce A ycoycuyaya = ycnycuycyceycycayceycyyc A yaya = yce ycycoycuycyyce A = ycycoycuycyyce ycuya Temkin ycnycuycyceycycayceycyyc yaAycN ycIycN yaA u2 ycyc ycoycuycEyce A yu = yayaycI = ycycoycuycyyce A ya= yuE log ( ) ya0 ycyc ycoycuyci.
Oe yuE) A ycuyaya = ycycoycuycyyce A ycoycuyci ycoyaya = ycnycuycyceycycayceycyyc A yayaya = 10ycnycuycyceycycayceycyyc A iGo = RTln.
coyaya ) ya A yuE = 1 Oe ( yc.
Oo2yyayaycI ycoycuyci yuE yayce = ycoycuyciyayaya yculog.
Oe yuE) yayce .
Oe yuE) yuE 2ycOyuE ycoycu ( = Oeycoycuyayaya )Oe yuE 1OeyuE ycIycN ya0 yuE A ycO = ycycoycuycyyce ycyc A Oeycoycuyayaya = yayce .
Oe yuE) ycnycuycyceycycayceycyyc ycoycu [ yuE A yayaya = yce Oeycnycuycyceycycayceycyyc 2ycOyuE A yu .
= A ycO= ycIycN ycIycNyu 2yuE ya A yuE = 1 Oe ( yc.
Hill-Deboer Jovanovic Harkin-Jura Halsey yayce .
Oe yuE) yuE ya2 yuE ycoycu [ ]Oe = Oeycoycuya1 Oe yuE 1OeyuE ycIycN ycoycuycyce = ycoycuycycoycaycu Oe yaya yayce ycyce2 yaA ya ya = Oe ( ) ycoycuyciyayce ycoycuycEyce = ycoycuyaya Oe ycoycuyayce ycuya ycuya ya0 yuE ycyc yayce .
Oe yuE) ycoycu [ yuE yuE Oe 1OeyuE yayce ycyc ycoycuycEyce ycoycuyciyayce ycyc ycyce2 ycoycuyayce ycyc ycoycuycEyce A Oeycoycuyco1 = ycnycuycyceycycayceycyyc yco yuE A yu .
= 2 A yco2 = ycIycN ycIycNyu yuE ya A yuE = 1 Oe ( yc.
ya0 A yaya = ycycoycuycyyce A ycoycuycEycoycaycu = ycnycuycyceycycayceycyyc A ycEycoycaycu = yce ycnycuycyceycycayceycyyc A yaya = A A A yaAya yaya ycuya ycIycoycuycyyce = ycnycuycyceycycayceycyyc = ycycoycuycyyce ycycoycuycyyce = ycuya A ycoycuyaya = ycnycuycyceycycayceycyyc A yaya = yce ycnycuycyceycycayceycyyc DOI: https://doi.
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Curcumin solution adsorption data using CPS.
CRH.
SRH, and WO3 adsorbents Adsorbent
CPS
CRH
SRH
WO3
Ci .
Ce .
g/L) yuA yu Table 4.
Langmuir isotherm parameters using ycE = ycE
Adsorbent
CPS
CRH
SRH
WO3
ya ycyeI ya ycyeI ycoycaycu yaya yayce ycE ycoycaycu yeayeO yc ycyc Note ) ycyc ( yeO yeayeO 992- 0.
7374 A 0 < ycIya < 1, favorable A R2 > 0.
70, monolayer 954- 0.
2664 A 0 < ycIya < 1, favorable A R2 < 0.
70, there are not indicating monolayer 948- 0.
958 A 0 < ycIya < 1, favorable A R2 > 0.
70, monolayer ycyeayeCyeo ( 213- 0.
9876 A 0 < ycIya < 1, favorable A R2 > 0.
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Figure 2.
Langmuir isotherm model for adsorption system using .
CPS, .
CRH, .
SRH, and .
WO3 adsorbents Freundlich The Freundlich model adsorption parameters were obtained using equation .
ln ycEyce = ln ycoyce ln yayce.
To get the Freundlich ycu model parameters, we need to convert yayce and ycEyce values into the form of lnCe and lnQe, which are used for fitting data .
ee Table .
The curves of data fitting result are presented in Figures 3 .
The result of fitting data also used to determine adsorption The result of data fitting in the form of a gradient obtained is value, and the intercept is lnKF value.
Table 5 shows parameter results of Freundlich model using CPS.
CRH.
SRH, and WO3 adsorbents.
Freundlich isotherm is good represent of SRH and WO3 adsorption systems than CPS and CRH adsorption system, this is confirmed by the R2 value of higher than 0.
Thus.
SRH and WO3 adsorption system were assumed that adsorption process occurs in heterogeneous surface in multilayer form with weak adsorbate and adsorbent DOI: https://doi.
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Freundlich isotherm parameters using ln ycEyce = ln ycoyce ycu ln yayce ya yea
Adsorbent
CPS
CRH
SRH
WO3
Note ycu > 1, cooperative adsorption A ycu < 1, chemical interaction between adsorbate molecules A R2 < 0.
70, monolayer adsorption 4286 A 1 > 1, cooperative adsorption ycu A ycu < 1, chemical interaction between adsorbate molecules A R2 < 0.
70, monolayer adsorption 9687 A 1 > 1, cooperative adsorption ycu A ycu < 1, chemical interaction between adsorbate molecules A R2 > 0.
70, multilayer adsorption 9714 A ycu > 1, cooperative adsorption A ycu < 1, chemical interaction between adsorbate molecules A R2 > 0.
70, multilayer adsorption Figure 3.
Freundlich isotherm model for adsorption system using .
CPS, .
CRH, .
SRH, and .
WO3 adsorbents DOI: https://doi.
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Temkin Temkin model parameters were obtained using equation .
as presented as ycyce = yaAycN ln ya ycN yaAycN ln yayce .
To get the Temkin model parameters, we need to convert Ce and Qe values into the forms of ln Ce and Qe, which are used for data fitting .
ee Table .
The curves of data fitting result are presented in Figures 4 .
The result of fitting data also used to determine adsorption parameter.
The result of data fitting in the form of a gradient obtained is the yaA value to calculate yaAycN value and the intercept is the yaAycN ycoycuya ycN Table 6 shows parameter results of Temkin model using CPS.
CRH.
SRH, and WO3 AT value in Table 6 is the Temkin equilibrium constant corresponding to the maximum binding energy where the high AT shows attractive interaction between adsorbateadsorbent system.
The AT value for all adsorption systems shows a relatively small value means less affinity between the absorbent and adsorbate molecules since there are physical interaction dominate that confirmed by BT parameter.
Physical interaction only involves more interaction weak, for example in the form of adsorbate polarization with adsorbent.
Base on correlation coefficient value (R2 > 0.
SRH and WO3 are suitable with Temkin isotherm, while CPS and CRH adsorption system are not suitable.
Temkin isotherm informs that adsorption is characterized by uniform distribution adsorbate to adsorbent surface.
Dubinin-Radushkevich Dubinin-Radushkevich model adsorption parameters were obtained using equation .
as follow as ln ycyce = ln ycyc Oe .
ua2 ).
To get Dubinin-Radushkevich parameters, we need to convert Qe into the form of lnQe value and looking for the yuA value which are used for data fitting .
ee Table .
The curves of data fitting result are presented in Figures 5 .
The result of data fitting also used to determine adsorption The result of data fitting in the form of a gradient obtained is the yu value to calculate ya value.
Table 7 shows parameter results of Dubinin-Radushkevich using CPS.
CRH.
SRH, and WO3 adsorbents.
Parameter yu in Table 7 is Dubinin-Radushkevich isotherm constant related saturation capacity.
High yu value shows high adsorption capacity.
Based on yu parameter.
WO3 has higher yu value while CRH has smaller yu value than others.
yu value influenced by pore volume.
The larger pore volume impact on highest maximum binding energy value.
Plotting data of DubininRadushkevich show that SRH and WO3 adsorption system have the best correlation coefficient since correlation coefficient value is high (R2 > 0.
Thus.
SRH and WO3 adsorption system are considered by Dubinin-Radushkevich have adsorbent size proportional to the micropore Jovanovic Jovanovic model adsorption parameters were obtained using equation .
as presented as ycoycuycyce = ycoycuycycoycaycu Oe yaya yayce .
To get the Jovanovic model parameters, we need yayce data and we need to convert ycEyce into the form of ycoycuycEyce which are used for data fitting .
ee Table .
The curves of fitting data are presented in Figures 6 .
The result of fitting data also used to determine adsorption parameter.
The result of data fitting in the form of a gradient obtained is the yayc value and intercept is the ycoycu ycEycoycaycu Table 8 shows parameters of Jovanovic using CPS.
CRH.
SRH, and WO 3 KJ and Qmax in Table 8 are the Jovanovic constant and the maximum uptake of adsorbate molecule.
Qmax related with how much adsorbates are absorbed by a particular adsorbent where the higher Qmax value shows better adsorbent capacity.
CRH
and SRH adsorbents showed identically small adsorption capacity (Qma.
value as well as CPS and WO3.
Based on DubininRadushkevich isotherm.
WO3 and CPS adsorbent shows high adsorpstion capacity.
This condition is possible due to surface active site is efficient in adsorbing the adsorbate molecule although it has small DOI: https://doi.
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The Jovanovic isotherm reflects well the entire adsorption system .
CPS.
CRH.
SRH, and WO.
which is shown from the relatively high correlation coefficient value of each adsorption system (R2 > 0.
Compatibility with Jovanovic's model indicates that there is existence of monolayer adsorption.
Table 6.
Temkin isotherm parameters using ycyce = yaAycN ln ya ycN yaAycN ln yayce Adsorbent
CPS
ycyc ( ) yeO
yeayeayes 4851 A ycyc ( A CRH
SRH
WO3
Note yaAycN < 8 ycoya/ycoycuyco, physical interaction between adsorbate R2 < 0.
70, no uniform adsorbent surface yaAycN < 8 ycoya/ycoycuyco, physical interaction between adsorbate R2 < 0.
70, no uniform adsorbent surface yaAycN < 8 ycoya/ycoycuyco, physical interaction between adsorbate R2 > 0.
70, uniform adsorbent surface yaAycN < 8 ycoya/ycoycuyco, physical interaction between adsorbate R2 > 0.
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Figure 4.
Temkin isotherm model for adsorption system using .
CPS, .
CRH, .
SRH, and .
WO3 adsorbents Halsey Halsey model adsorption parameters were obtained using equation .
as presented as ycoycuycEyce = ycu ycoycuyaya Oe ycu ycoycuyayce .
To get ya the Halsey model parameters, we need to convert yayce and ycEyce data into the form of ycoycuyayce and ycoycuycEyce , which are used for data fitting .
ee Table .
The curves of data fitting result are presented in Figures 7 .
The result of data fitting also used to determine the adsorption parameter.
The result of data fitting in the form of a gradient obtained is the ycu value and intercept is the ycu ycoycuyaya value.
Table 9 shows parameter results of Halsey using CPS.
CRH.
SRH, and WO3 adsorbents.
and n in Table 9 are the Halsey isotherm Halsey isotherm reflect good adsorption system for SRH and WO3 since (R2 > 0.
is relatively high.
While.
CPS and CRH adsorption system are not suitable with Halsey isotherm.
Compatibility with Halsey model due to high R2 indicates that there is existence of multilayer adsorption.
From Halsey's parameter, we can identify that the higher the adsorption capacity (Q.
correlates with the increase in the value of n.
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Dubinin-Radushkevich isotherm parameters ln ycyce = ln ycyc Oe .
ua2 ) Adsorbent yesyeaycyeI
CPS
CRH
SRH
WO3
yeUyc Note yeayeayesya yc( yu( ya ) yeayeayes yeUyc 4996 A ya < 8 ycoya/ycoycuyco, physical interaction between adsorbate molecules A R2 < 0.
70, no micropore size is exist in adsorbent surface 455 A ya < 8 ycoya/ycoycuyco, physical interaction between adsorbate molecules A R2 < 0.
70, no micropore size is exist in adsorbent surface 9829 A ya < 8 ycoya/ycoycuyco, physical interaction between adsorbate molecules A R2 > 0.
70, micropore size is exist in adsorbent surface A ya < 8 ycoya/ycoycuyco, physical interaction between adsorbate molecules A R2 > 0.
70, micropore size is exist in adsorbent surface Figure 5.
Dubinin-Radushkevich isotherm model for adsorption system using .
CPS, .
CRH, .
SRH, and .
WO3 adsorbents DOI: https://doi.
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Table 8.
Jovanovic isotherm parameter using ycoycuycyce = ycoycuycycoycaycu Oe yaya yayce Adsorbent
CPS
CRH
SRH
WO3
ycyeI yesyeaycyeI ycyc ( yeayeO yc ) yeeyeayeCyeo ( yeO ) yeayeO Note R2 > 0.
70, the existence of monolayer on the surface of R2 > 0.
70, the existence of monolayer on the surface of R2 > 0.
70, the existence of monolayer on the surface of R2 > 0.
70, the existence of monolayer on the surface of Figure 6.
Jovanovic isotherm model for adsorption system using .
CPS, .
CRH, .
SRH, and .
WO3 adsorbents DOI: https://doi.
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Halsey isotherm parameters using ycoycuycEyce = ycu ycoycuyaya Oe ycu ycoycuyayce ya Adsorbent
CPS
CRH
SRH
WO3
yesyeaycyeI yesyeaycyeI ya yea yea ycyc Note R2 < 0.
70, the existence of monolayer on the surface of adsorbent R2 < 0.
70, the existence of monolayer on the surface of adsorbent R2 > 0.
70, the existence of multilayer on the surface of adsorbent R2 > 0.
70, the existence of multilayer on the surface of adsorbent Figure 7.
Halsey isotherm model for adsorption system using .
CPS, .
CRH, .
SRH, and .
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Harkin-Jura Harkin-Jura model adsorption parameters were obtained using equation .
as yaA presented as yc2 = ya Oe .
To get the yce Harkin-Jura model parameters, we need to convert Ce and Qe data into the form of logCe and yc A which are used for data fitting .
ee yce Table .
The curves of data fitting result are presented in Figures 8 .
The result of data fitting also used to determine adsorption parameter.
The result of data fitting in the form of a gradient obtained is yaA the ya value and intercept is the yaya value.
ya ya Table 10 shows parameter results of HarkinJura using CPS.
CRH.
SRH, and WO3 B and A in Table 10 are HarkinJura constants.
Based on R2 adsorption using CPS.
SRH.
WO3 adsorbent is suitable since R2 > 0.
From the Harkin-Jura parameter, we can identify that the higher values of parameters of AHJ and HJ, the worse the adsorption capacity (Q.
The Harkin-Jura model also explains the theoretical surface area by using equation .
as presented as ycI2 = Oe yuy4.
606ycIycNycA For example, if we use yc the assumption of q value of carbon, silica, and WO3 as in Table 1, and the temperature used is room temperature .
K), then the surface area value is presented in Table 11.
yaA Table 10.
Harkin-Jura isotherm parameters using yc2 = ya Oe .
ycoycuyciyayce yce
Adsorbent yesyeayeOycyeI
CPS
CRH
SRH
WO3
yuycyc ycycyc Note R2 > 0.
70, the existence of multilayer on the surface of R2 < 0.
70, the monolayer on the surface of adsorbent R2 > 0.
70, the existence of multilayer on the surface of R2 > 0.
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Harkin-Jura isotherm model for adsorption system using .
CPS, .
CRH, .
SRH, and .
WO3 adsorbent Table 11.
Calculation of the surface area with the Harkin-Jura model using equations ycI 2 = Oe yuy4.
606ycIycNycA yu ye.
CPS
3060 y 102
CRH
3060 y 1024
SRH
3060 y 1024
WO3
3060 y 1024 yce yculog.
Oe yuE).
To get the Flory-Huggins model parameters, we need to convert yuE data into yuE ya0 yeaya yeO Adsorbent Flory-Huggins Flory-Huggins parameters were obtained using equation yuE .
as presented as ycoycuyci ya = ycoycuyciyayaya the form of ycoycuyci yc and log.
Oe yuE) and which are used for data fitting .
ee Table .
The curves of data fitting result are presented in Figures 9 .
The result of data fitting also used to determine adsorption parameter.
The result of data fitting in the form of a gradient obtained is the nFH value and intercept is the logKFH value.
Table 12 shows parameter results of Flory-Huggins using CPS.
CRH.
SRH, and WO3 adsorbents.
KFH in Table DOI: https://doi.
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12 are the number of adsorbates occupying adsorption sites and the Flory-Huggins Adsorbent SRH and WO3 have good KFH value than CPS and CRH.
This condition showed SRH and WO3 have better adsorbentadsorbate interaction.
Moreover.
SRH and WO3 form multilayer adsorption which makes the adsorbate more attached to the adsorbent due to chemical bonds.
FowlerHuggins is poor suitable with all adsorption system .
CPS.
CRH.
SRH, and WO.
because R2 < 0.
yuE Table 12.
Flory-Huggins isotherm parameters using ycoycuyci ya = ycoycuyciyayaya yculog.
Oe yuE) yce Adsorbent a Oe y.
CPS
CRH
SRH
WO3
OIyco
Note
KFH
(L/m.
A OIyao > 0, spontaneously adsorption A ycuyaya < 1, represent more than one active adsorbent zone occupied by the A R2 < 0.
70, the existence of monolayer on the surface of adsorbent A OIyao > 0, spontaneously adsorption A ycuyaya < 1, more than one active adsorbent zone occupied by the adsorbate A R2 < 0.
70, the existence of monolayer on the surface of adsorbent A OIyao > 0, spontaneously adsorption A ycuyaya < 1, more than one active adsorbent zone occupied by the adsorbate A R2 < 0.
70, the existence of monolayer on the surface of adsorbent A OIyao > 0, spontaneously adsorption A ycuyaya < 1, more than one active adsorbent zone occupied by the adsorbate A R2 < 0.
70, the existence of monolayer on the surface of adsorbent yesyeayeO yeaycyc DOI: https://doi.
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Flory-Huggins isotherm model for adsorption system using .
CPS, .
CRH, .
SRH, and .
WO3 adsorbents Fowler-Guggenheim Fowler-Guggenheim model adsorption parameters were obtained using equation .
OeyuE) yuE 2ycOyuE ycoycu ( )Oe = Oeycoycuyayaya To get the yuE 1OeyuE ycIycN Fowler-Guggenheim model parameters, we ya .
OeyuE) need to plot yuE vs ycoycu yce yuE data .
ee Table .
The curves of data fitting result are presented in Figures 10 .
The result of data fitting also used to determine adsorption The result of data fitting in the 2ycOyuE form of a gradient obtained is the ycIycN value and intercept is the ycoycuyayaya value.
Table 13 shows parameter results of Fowler- Guggenheim using CPS.
CRH.
SRH, and WO3 KFG in Table 13 is FowlerGuggenheim constant represent adsorbentadsorbate interaction.
Higher KFG value indicates a good interaction between adsorbent-adsorbate.
All adsorbent system shows identically small KFG value means weak interaction adsorbent-adsorbate since there are surface active site is less efficient in adsorbing the adsorbate molecules due to domination of physical interaction.
FowlerGuggenheim is poor suitable with all adsorption system .
CPS.
CRH.
SRH, and WO.
because R2 < 0.
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OeyuE) Table 13.
Fowler Guggenheim isotherm parameters using ycoycu ( yce yuE ycyeI .
a Oe y.
KFG (L/m.
4 y 10Oe4 J/mo.
CRH
1 y 10Oe3
SRH
3 y 10Oe3
WO3
4 y 10Oe3
Adsorbent
CPS
yesyea )Oe yuE 1OeyuE = Oeycoycuyayaya 2ycOyuE ycIycN Note 2599 A ycO < 0 ycoya/ycoycuyco, interaction between adsorbed A R2 < 0.
70, the existence of monolayer on the surface of 4814 A ycO < 0 ycoya/ycoycuyco, interaction between adsorbed A R2 < 0.
70, the existence of monolayer on the surface of 1738 A ycO < 0 ycoya/ycoycuyco, interaction between adsorbed A R2 < 0.
70, the existence of monolayer on the surface of 28 A ycO < 0 ycoya/ycoycuyco, interaction between adsorbed A R2 < 0.
70, the existence of monolayer on the surface of Figure 10.
Fowler-Guggenheim isotherm model for adsorption system using .
CPS, .
CRH, .
SRH, and .
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as yayce .
OeyuE) yuE ya2 yuE ycoycu [ ] Oe 1OeyuE = Oeycoycuya1 Oe ycIycN .
To get the HillyuE Deboer model parameters, we need to plot ya .
OeyuE) A vs ycoycu yce yuE yuE Oe 1OeyuE data.
The curves of data fitting result are presented in Figures 11 .
The result of fitting data also used to determine adsorption parameter.
The result of data fitting in the form of a gradient ya yuE obtained is the ycIycN value and intercept is the lnK1 value.
Table 14 shows parameter results of a Hill-Deboer using CPS.
CRH.
SRH, and WO3 adsorbents.
K1 in Table 14 is the HillDeboer constant interaction between adsorbent and adsorbate.
Higher K1 value indicates a good interaction between adsorbent-adsorbate.
However, adsorbents system indicate a small value of K1 means poor interaction between adsorbent-adsorbate since active site is not effective in carrying out adsorption process.
Hill-Deboer is poor suitable with all adsorption system .
CPS.
CRH.
SRH, and WO.
because R2 < 0.
Approximately Isotherm Model The experimental data of the adsorption process in Table 2 were analyzed through regression analysis to match the linear correlation of the adsorption isotherm mathematical models.
Fitting data based on the plotted way in Table 1 for each adsorption model is used to determine the adsorption parameters that correspond to each adsorption model.
The parameters obtained after the data fitting process are summarized in Tables 3-12.
Figures 2-11 present the plotting of the experimental Figures 2 .
show the fitting data based on the Langmuir adsorption isotherm.
The Langmuir isotherm for the study of the adsorption of curcumin solution with the and CRH show poor adsorption characteristics because it gives a low correlation coefficient value (R2 <.
is too far closer to the 0.
Meanwhile, adsorption of CPS.
SRH, and WO3 adsorbents matches the Langmuir model with a coefficient correlation (R2> 0.
This means that the adsorption system using CRH does not allow monolayer formation.
However, the reverse phenomenon is for the adsorption system using cps.
SRH, and WO 3 The analysis of the separation factor (RL) shows RL value in the range between 0 and 1 for all cases which indicates that the adsorption process has favorable adsorption characteristics.
Figures 3 .
show the Freundlich isotherm curve.
Freundlich isotherm curve shows very small correlation coefficient value for adsorption system using CPS and CRH adsorbent compared to adsorption system with SRH and WO3 adsorbent.
This model suggests that the adsorption system with SRH and WO3 fits into the Freundlich model, which allows the formation of a multilayer structure.
Figures 4 .
are the linear curve of the Temkin adsorption.
The adsorption system with CPS and CRH adsorbents does not match with the Temkin model isotherm because the R2 value is less than 0.
While, the adsorption system with SRH and WO3 adsorbents are compatible with Temkin isotherm model.
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OeyuE) Table 14.
Hill-Deboer isotherm parameters using ycoycu [ yce yuE
Adsorbent
CPS
yesyea ycyeI .
a Oe y.
yu Oe yu yaOeyu yuE ya yuE ] Oe 1OeyuE = Oeycoycuya1 Oe ycIycN (L/m.
042 y 10Oe4 .
J/mo.
Note A ya2 < 0 ycoya/ycoycuyco, interaction between A R2 < 0.
70, the monolayer on the yu
CRH
y 10Oe3 A ya2 < 0 ycoya/ycoycuyco, interaction between A R2 < 0.
70, the monolayer on the SRH y 10Oe3 A ya2 < 0 ycoya/ycoycuyco, interaction between A R2 < 0.
70, the monolayer on the WO3 y 10Oe3 A ya2 < 0 ycoya/ycoycuyco, interaction between A R2 < 0.
70, the monolayer on the DOI: https://doi.
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Hill-Deboer isotherm model for adsorption system using .
CPS, .
CRH, .
SRH, and .
WO3 adsorbents Figures 5 .
are an analysis fitting based on the Dubinin-Radushkevich model.
Based on the correlation coefficient value, the adsorption system with SRH and WO3 adsorbents are compatible with the DubininRadushkevich adsorption system with CPS and CRH adsorbents does not.
Therefore, the adsorption system with CPS and CRH adsorbents was not well reflected by the Dubinin-Radushkevich isotherm model.
The Dubinin-Radushkevich isotherm reflects a good fit for the SRH and WO3 adsorbent.
Figures 6 .
are the isotherm curve of the Jovanovic model.
Based on the analysis of the coefficient correlation value, the Jovanovic isotherm model is the most suitable and most reflective of all cases of adsorption systems because the value of R2 > Figures 7 .
are an analysis fitting based on the Halsey model.
The adsorption system that is most suitable for this model is the adsorption system with SRH and WO3 Meanwhile, the Halsey model is not suitable in representing the adsorption system with CPS and CRH.
Figures 8 .
show the fitting analysis using the Harkin-Jura adsorption isotherm.
The adsorption system with CPS and CRH adsorbent are the least suitable because the R2 value is <0.
The incompatibility with the Harkin-Jura isotherm represents that the adsorption process does not follow a multilayer adsorption model.
On the other hand, the Harkin-Jura isotherm is compatible with the adsorption system with SRH, and WO3 adsorbents because the R2 value is close 9 which allows the formation of multilayers on the adsorbent surface.
Figures 9 .
, 10 .
, and 11 .
are the results of fitting data based on the Flory Huggins.
Fowler Guggenheim, and HillDeboer models.
These three models show poor correlation coefficient values for all DOI: https://doi.
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adsorption cases .
CPS.
CRH.
SRH, and WO.
, meaning that they reflect an adsorption system that is not suitable for all Discussion Based on the R2 value for each adsorption model, the adsorption system in CPS is compatible with Langmuir.
Harkin-Jura, and Jovanovic isotherm models.
CRH adsorbents is only compatible with the Jovanovic model.
Langmuir and Jovanovic model have same assumption that adsorption process occurs by forming a monolayer structure without the presence of adsorbate-adsorbent lateral interactions for CPS and CRH adsorbents (Ayawei et al.
, 2.
Besides assuming the adsorption is monolayer, the adsorption system with the CPS adsorbent is also assumed to have adsorption by forming a This is confirmed because it fits the Harkin-Jura model.
For adsorption systems with SRH and WO3 adsorbents, both of them are incompatible with the Harkin Jura.
Flory Huggins.
Fowler Guggenheim, and Hill-Deboer models.
Meanwhile, the other six models are The adsorption system with the SRH adsorbent followed suit with the order of the Temkin > Dubinin-Radushkevich > Freundlich > Halsey > Langmuir > Jovanovic models.
Meanwhile, the order of compatibility of the adsorption system with the WO3 adsorbent is summarized as follows Dubinin Radushkevich > Langmuir > Freundlich > Halsey > Jovanovic > Temkin models.
The adsorption system with SRH and WO3 adsorbents has a good correlation with the Langmuir model informing the monolayer adsorption process, in which the adsorbate molecules are distributed on all adsorbent surfaces (Langmuir, 1.
This monolayer adsorption process is also confirmed by the Jovanovic adsorption without the presence of lateral interactions (Ayawei et al.
, 2.
In the Langmuir model, adsorption is advantageous or not explained by the RL value, where the resulting RL value is between 0 and 1, which indicates the adsorption process is favorable.
Meanwhile.
Freundlich.
Temkin.
DubininRadushkevich, and Halsey isotherms support multilayer adsorption processes.
The degree of linearization between adsorbate and adsobent is indicated by the values of n < 1 and 1/n > 1 in the Freundlich model, the values show that adsorption follows cooperative adsorption with chemical Cooperative adsorption informs the occurrence of chemical and physical interactions at one time (Liu, 2.
The chemical interaction in the adsorption system is in accordance with the parameter value BT > 8 J/mol in the Temkin model.
The Dubinin-Radushkevich model also confirmed the physical interaction because the parameter value E < 8 kJ/mol.
Prediction Model for CPS Adsorbent The adsorption system uses CPS adsorbent following the Langmuir and Jovanovic model which assumes monolayer The CPS adsorption system is also compatible with the Harkin-Jura model which assumes multilayer adsorption.
Adsorption system using CPS shows weak physical interaction .
dsorbent-adsorbate interactio.
and chemical interaction .
dsorbate-adsorbate Prediction model for CPS adsorbent is illustrated in Figure 12.
Figure 12.
Prediction model for system adsorption using CPS adsorbent DOI: https://doi.
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hysical interactio.
since the KL has small values based on Langmuir.
Prediction model for CPS adsorbent is illustrated in Figure 13.
Figure 14.
Prediction model for system adsorption using SRH and WO3 adsorbents CONCLUSION Figure 13.
Prediction model for system adsorption using CRH adsorbent Prediction Model for SRH and WO3 Adsorbents The adsorption system uses SRH and WO3 adsorbents following monolayer and multilayer adsorption with weak chemical interaction .
dsobate-adsorbate interactio.
and physical interaction .
dsorbateadsorbent interactio.
since the KL and AT have small values based on Langmuir and Temkin parameter respectively.
The multilayer adsorption process results from the presence of a heterogeneous structure in the adsorbent which is assumed by the Temkin.
Dubinin-Radushkevich.
Harkin-Jura, and Halsey isotherm where filling pores occur (Dada et al.
, 2.
Prediction model for CPS adsorbent is illustrated in Figure 14.
This study demonstrates a simple way of understanding the calculation of the results of the adsorption data analysis by matching and reviewing the adsorption data in several demonstrating its application for the adsorption system of various adsorbents.
The criteria for selecting a suitable and optimal adsorption isotherm model for the adsorption process have also been discussed in this study.
Based on our study, the adsorption system with carbon obtained from peanut shells and carbon obtained from rice husks followed the Jovanovic isotherm.
Adsorption system with silica adsorbent extracted from rice husk and WO3 following Langmuir.
Freundlich.
Temkin.
DubininRadushkevich.
Halsey.
Jovanovic isotherms.
AUTHORSAo NOTE The authors declare that there is no conflict of interest regarding the publication of this article.
Authors confirmed that the paper was free of plagiarism.
REFERENCES