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European Journal of Applied Sciences – Vol. 12, No. 2
Publication Date: April 25, 2024
DOI:10.14738/aivp.122.16738
Bbumba, S., Karume, I., Nsamba, H. K., Kigozi, M., & Kato, M. (2024). An Insight into Isotherm Models in Physical Characterization
of Adsorption Studies. European Journal of Applied Sciences, Vol - 12(2). 115-134.
Services for Science and Education – United Kingdom
An Insight into Isotherm Models in Physical Characterization of
Adsorption Studies
Simon Bbumba
Department of Chemistry, College of Natural Sciences, Makerere University, P.O.
Box 7062, Kampala, Uganda and Department of Science, Faculty of Science and
Computing, Ndejje University, P.O. Box 7088, Kampala, Uganda
Ibrahim Karume
Department of Chemistry, College of Natural Sciences,
Makerere University, P.O. Box 7062, Kampala, Uganda
Hussein K. Nsamba
Department of Chemistry, College of Natural Sciences,
Makerere University, P.O. Box 7062, Kampala, Uganda
Moses Kigozi
Department of Chemistry, Busitema University,
P. O. BOX 236, Tororo, Uganda
Maxmillian Kato
Department of Science, Faculty of Science and Computing,
Ndejje University, P.O. Box 7088, Kampala, Uganda
ABSTRACT
Here in, we review the adsorption isotherm models and the related statistical and
error functions that give a mechanistic insight relating adsorption capacities with
the adsorbate concentration and nature of the adsorbent surface. One, two and
three-parameter isotherms are discussed in addition to isotherms that anticipate
mono and multilayer adsorption surfaces. The isotherms such as Langmuir,
Freundlich, Toth, Dubinin–Radushkevich, Sips, Temkin, Brunauer–Emmett–Teller,
and Redlich–Peterson (R-P), and their combined forms have been addressed. Non- linear regression gives an accurate interpretation of the adsorption process with
low error values compared to linear regression. The correlation coefficient as a tool
to choose the best isotherm model is assessed with the Chi test which gives
information about the fit with the best quality as well as the ANOVA that describes
the significance of variance of the different error functions. Further, the different
physiochemical parameters that affect the adsorption process are discussed.
Keywords: adsorption, isotherm models, error functions, adsorbent efficiency, statistical
analysis.
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INTRODUCTION
Adsorption by temporary physical interaction or entrapment of adsorbates is the most
common, however, cases of chemical interaction especially in carefully designed adsorbent
systems also exist. Physisorption and chemisorption show the interaction of the adsorbate on
the adsorbent surface which depends on the binding strength [1-4]. For decades, adsorption
has found several applications in the removal of pollutants from water because it is cheap,
highly efficient, simple in design, and environmentally benign [5]. Van der Waals forces and
weak electrostatic attractions are responsible for chemisorption while covalent bond
formation where electrons are shared or transferred between the adsorbate (pollutant) and
adsorbent causes chemisorption [6]. Monolayer adsorption of the substrate by the adsorbent
active surface groups describes chemisorption while multilayer interaction of the substrate on
the adsorbent shows physisorption (Figure 1). The study of adsorption mechanisms is mainly
by characterization of the adsorbent, simulation studies using density functional theory (DFT)
or molecular dynamics and equilibrium data modeling [7, 8].
Adsorbent
Adsorbates
Interface
Active sites
Monolayer
adsorption
Multilayer
adsorption
Figure 1: The interaction of the adsorbent and adsorbate.
The models used to describe adsorption include Langmuir, Freundlich, Sips, Toth, Redlich- Peterson, etc. Modeling using equilibrium data is the widely applied method to determine
whether the mechanisms is monolayer or multilayer through the adsorbate-adsorbent
interaction. In addition, information regarding the maximum capacity of the adsorbent and
intensity which give a better description of the strength of binding between the adsorbent- adsorbate molecules.
Isotherms used to define adsorption illustrate the interaction between the surface function
groups of the adsorbent and the adsorbate’s equilibrium concentration in solution. They are
expressed as equations at equilibrium occurring at constant temperature in which the
adsorbent surface and adsorbate molecules have interacted at a given time. To better
understand the surface functional groups, affinity and mechanism of the adsorbent the
isotherm models utilize several parameters [9] as shown in Figure 2. The classification of
adsorption isotherm models is done based on the International Union of Pure and Applied
Chemistry (IUPAC), and has six division types which arise from the shape of the adsorbent- adsorbate plotted data [10, 11]. The microporous surface mechanism is characteristic of type I,
type II describes adsorption on a microporous surface, type III describes weak adsorbate-
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Bbumba, S., Karume, I., Nsamba, H. K., Kigozi, M., & Kato, M. (2024). An Insight into Isotherm Models in Physical Characterization of Adsorption
Studies. European Journal of Applied Sciences, Vol - 12(2). 115-134.
URL: http://dx.doi.org/10.14738/aivp.122.16738
adsorbent interactions while type IV and V describe mono and multi-layer coverage. In
addition, Type VI describes adsorption processes that occur in steps.
Figure 2: Classification of Adsorption-desorption isotherms [11].
CLASSIFICATION OF ADSORPTION ISOTHERMS BASED ON STUDY PARAMETER
One-parameter isotherm models are the simplest for example they describe proportionality
between adsorbate on the surface and the adsorptive gas due to a given partial pressure as a
result of a positive correlation. For example, Henry’s isotherm model of adsorption describes a
better fit for adsorbate molecules which are further apart and at concentrations which are low
[12]. The linear expression of the equilibrium adsorbate concentration in the two phases i.e.,
adsorbed and liquid is shown in Equation 1.
qe= KHE Ce
(1)
Where qe is the adsorption capacity at equilibrium (mg/g), KHE is Henry’s adsorption constant
and Ce is the equilibrium concentration of the adsorbate (mg/L).
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With adsorption isotherms, two-parameter isotherms include; the Langmuir with an
assumption that the adsorbate makes continuous bombardment on the surface of the
adsorbent is governed by the kinetic principle [13, 14]. It has been applied in understanding
monolayer adsorption on the adsorbate surface but also to determine the adsorbent’s capacity
to adsorb [14, 15]. Assumptions made from this model are that the mechanism is due to
monolayer coverage and occurs at identical and equivalent sites [16] and the rate of desorption
and adsorption should be equal. Further, it specifies the homogeneity of adsorption in which
constant enthalpies and molecules possess an activation energy. In addition, the adsorbent
should interact with the adsorbate equally and no movement of the molecules on the surface
[15, 17]. The linear and non-linear model expressions are shown in Equations 2 and 3.
ce
qe
=
1
k1qmax
+
1
qmax
ce
(2)
qe =
qmbCe
1+bCe
(3)
Where Kl is the Langmuir constant (l/mg) and qmax is the maximum adsorbent capacity (mg/g).
The dimensionless constant called equilibrium parameter RL developed by Weber and
Chakravorti [18] is another expression of the model which is shown in Equation 4.
RL =
1
1+KL CO
(4)
Where the value of RL gives an insight into its description where desorption occurs when (RL >
1), (RL = 1) linearity of the adsorption process, desorption is equal to adsorption (RL = 0), and
adsorption is highly favorable (0 < RL < 1), and Co is the initial concentration.
Karume et al [19] investigated the adsorption of ciprofloxacin from synthetic water using
modified xerogel and the Langmuir gave 34.435 mg/g as the adsorbent maximum capacity, and
R2 of 0.9832. Ahsan et al [20] determined the adsorptive removal of Tetracycline using
Sulphonated spent coffee waste (SCW-SO3H) in which they used the Langmuir to determine the
adsorbent’s maximum capacity to be 473.93 mg/g and R2 of 0.988. The Langmuir has the
advantage of simplicity in design and the quantification of the maximum adsorption however
its disadvantage is it does not take into consideration multilayer adsorption.
Nevertheless, the isotherm developed by Toth [21] is an improvement to the Langmuir as it
best describes heterogeneous systems on which adsorption occurs, which is a determinant for
both high and low concentrations [16]. It illustrates that the active sites have a mean value with
lower energy of adsorption due to the correlation of an asymmetrical energy Gaussian
distribution [22]. Kumar et al [23] determined the adsorption of congo red using Cashew nuts
and the Toth gave an R2 of 0.999 which better describes the data. The group of Hamza et al [24]
investigated the adsorptive removal of Cristal violet using Tunisian Smectite Clay and the Toth
gave an R2 of 0.99.
Another important two-parameter isotherm was first reported by Freundlich [25] and it
illustrates non-ideal and reversible processes of adsorption. Since the affinities and heat of
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shows differences in chemical and physical metal ion adsorption [42]. The mean free energy, E
per molecule of adsorbate is calculated using Equation 7 [43].
In (qe
) = In(qs
) − kadε
2
(7)
The parameter ε describes a Polanyi potential and calculated using Equation 8.
ε = RTIn [1 +
1
Ce
] (8)
where T and R represent the absolute temperature and molar gas constant.
Sun et al [44] investigated the removal of nitroimidazole using Biomass carbon foam pellets
(BCFPs) and the Dubinin–Radushkevich showed an R2 of 0.9954. Mudhoo et al [45] determined
the removal of reactive read using Coco nucifera L. Shell Powder and the Dubinin–
Radushkevich isotherm showed an R2 value of 0.999. Worth to mention is the Temkin isotherm
which is among the earliest models that defines acidic media in which adsorption of hydrogen
on platinum electrodes occurs. It’s known to take into account adsorbent-adsorbate binding
using an explicit factor. It does not take into account high and low concentration values but
rather assumes a linear decrease of heat of the adsorbed molecules, unlike other models that
employ logarithmic decrease [46]. Further, the model dictates binding occurs when the energy
is uniformly distributed. It best describes those tightly packed structures which are not
identical and are in gas phase which it fails to predict complex liquid phases [47]. Shikuku et al
[48] determined the adsorptive removal of Sulfachloropyridazine using iron modified clay and
the Temkin gave an R2 value of 0.998. In addition, Sarma et al [49] investigated the adsorption
of Procion red using Temkin isotherm, and an R2 value of 0.99 was obtained.
Table 1: Other isotherm models that explain the adsorption process.
Isotherm Non -Linear Linear Application Reference
Hill
qe =
qsH
Ce
nH
KD + Ce
nH
log (
qe
qsH − qe
)
= nHlog(Ce
) − log(KD)
Explains mobile
adsorption and lateral
interactions
[50]
Flory- Huggins
θ
Co
= KFH(1 − θ)
nFH log (
θ
Co
) = log(KFH)
+ nFHlog(1
− θ)
Describes adsorbate- adsorbent surface
coverage surface
characteristics.
[51]
Koble- Corrigan
qe =
ACe
n
1 + BCe
n
1
qe
=
1
ACe
n +
B
A
Describes a more
comprehensive
expression of adsorb
[52]
Khan
qe =
qsbKCe
(1 + bKCe
)
aK
- Shows adsorption
from pure solutions.
[53]
Radke- Prausnitz
qe
=
aRPrRCe
β
R
aRP + rR Ce
β
R − 1
- Provides an insight
into adsorption
systems with low
adsorbate
concentrations
[16]
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Bbumba, S., Karume, I., Nsamba, H. K., Kigozi, M., & Kato, M. (2024). An Insight into Isotherm Models in Physical Characterization of Adsorption
Studies. European Journal of Applied Sciences, Vol - 12(2). 115-134.
URL: http://dx.doi.org/10.14738/aivp.122.16738
CLASSIFICATION OF ADSORPTION ISOTHERMS BASED ON ADSORBATE LAYERS
One of the most important multilayer isotherms is the Brunauer–Emmett–Teller [54, 55]
isotherm which is an equation, applied in the gas–solid equilibrium systems. The adsorption on
multilayer due to relative pressure ranges of 0.05-0.30 which corresponded to monolayer
coverage of the adsorbate that occurred at 0.50 and 1.50 led to the derivation of Brunauer–
Emmett–Teller [55]. It’s an extinction model relating liquid-solid interfaces as is shown in
Equation 9.
qe =
qsCBETCe
(Cs−Ce
) [1+(CBET−1)(
Ce
Cs
⁄ )]
(9)
where qs, qe, CBET, and Cs are the equilibrium adsorption capacity (mg/g), theoretical isotherm
saturation capacity (mg/g), BET adsorption isotherm (L/mg), and adsorbate monolayer
saturation concentration (mg/L) respectively. As CBET and Cs (Ce/Cs) are much greater than 1,
the equation is simplified as shown in Equation 10.
qe =
qs
1−(
Ce
Cs
⁄ )
(10)
Ringot et al [56] showed that Brunauer–Emmett–Teller [54] describes the adsorption of
Ochratoxin A (OA) using Yeast cell wall fraction (LEC) where the data fitted well with an R2
value of 0.997. Further Al-Qodah & Shawabkah [57] investigated Triadimenol on activated
carbon and the Brunauer–Emmett–Teller showed a better fit with an R2 value of 0.948 and
adsorption capacity of 110.0 mg/g. Brunauer–Emmett–Teller isotherm model has the
advantage of giving information about the adsorption on multilayer surfaces but also describes
the adsorbent capacity. However, in most cases the model may fail to account for adsorbents
with relatively high surface areas and small micropores.
The Frenkel–Halsey–Hill (FHH) isotherm is a multilayer adsorption which is defined as shown
in Equation 11.
qe = (
1
nH
) InKH − (
1
nH
) InCe
(11)
where a plot of In qe against In Ce gives the slope KH and the intercept nH. Palanisamy et al [58]
determined Cu (II) ions adsorption using modified leaves of Acacia nilotica, and the Frenkel–
Halsey–Hill showed an R2 of 0.9955 thus showing that adsorption was multilayer and occurring
on heterogeneous surfaces. MacMillan–Teller (MET) isotherm, is a modified BET with surface
tension effects as shown in Equation 12.
qe = qs (
K
In (
Cs
Ce
⁄
)
1
3
⁄
(12)
where k is an isotherm constant and when Cs/Ce is approaches unity, the logarithmic term can
be approximated as shown in Equation 13.
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qe = qs (
KCe
Cs − Ce
)
1
3
⁄
(13)
The relationship between the MacMillan–Teller and FHH isotherms at pressures higher than
0.8 and approximation of 0.35 of the Brunauer–Emmett–Teller is a description of the empirical
model
KEY STATISTICAL PARAMETERS IN ADSORPTION PROCESSES
Key mathematical rigorous error and statistical functions such as sum square error, summation
of absolute errors, hybrid fractional error function, average relative error, Spearman’s
correlation coefficient, coefficient of determination, , standard deviation of relative errors,
nonlinear chi-square test, coefficient of non-determination and sum of normalized errors are
employed to overcome the inherent bias resulting from the transformation, estimation of
parameter errors, and distortion of plotted fits. Common statistical parameters have been used
to understand many data sets for pollutant analysis as shown in Table 2.
Table 2: Mathematical error functions applied in analysis.
Entry Error Function Expression Reference
1 Sum squares errors
(ERRSQ/SSE) ∑(qe
, calc − qe
, meas)i
2
n
i=1
[59]
2 Hybrid fractional error function
(HYBRID)
100
n − p
∑[
qe
, meas − qe
, calc
qe
, meas ]
n
i=1
[60]
3 Average relative error (ARE) 100
n
∑|
qe
, meas − qe
, calc
qe
, meas |
i
n
i=1
[61]
4 Sum of absolute error (EABS) ∑|qe,meas − qe,calc|
n
i=1
[62]
5 Coefficient of determination
(R2
)
r
2
=
(qe,meas − q̅̅e̅̅,calc ̅̅̅̅)
2
∑(qe,meas − qe,calc) + (qe,meas − qe,cala)
2
[63]
6 Spearman’s correlation
coefficient (rs)
1-
∑ (qe,meas− qe,calc)
i
n 2
i=1
n(n−1)
2
7 Standard deviation of relative
errors √
∑ [(qe,meas − qe,calc)
i
− ARE]
i
2
n
i=1
n − 1
8 Sum of normalized errors [64] - [65]
9 Nonlinear chi-square test (χ
2
)
∑
(qe,calc − qe,meas)
2
qe,meas
n
i=1
[63]
10 Coefficient of non- determination (K2)
- [59]
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Bbumba, S., Karume, I., Nsamba, H. K., Kigozi, M., & Kato, M. (2024). An Insight into Isotherm Models in Physical Characterization of Adsorption
Studies. European Journal of Applied Sciences, Vol - 12(2). 115-134.
URL: http://dx.doi.org/10.14738/aivp.122.16738
The sum square error (ERRSQ) (Table 2, entry 1) has found great application as an error
function of liquid phases occurring at high concentrations in which a better fit increases with
the magnitude of errors. Hybrid fractional improves the drawbacks faced by the ERRSQ at low
concentrations [61]. Similarly, the sum of absolute errors (EABS) (Table 2, entry 4) provides a
better fit thus reducing bias in high-concentration data [15].
Another important error analysis approach is the Average relative error (ARE) (Table 2, entry
3) model which reduces the concentration error distribution due to under and over-estimation
of the experimental data. The result of varying error that brings about isotherm parameters
with different data sets, is solved by the sum of normalized errors [64] (Table 2, entry 8) which
has an approach of summing up the errors and giving a better fit for the isotherm data.
On the other hand, statistical tools such as the Coefficient of determination (R2) (Table 2, entry
5) represent the variation percentage of the dependent variable and explain the best fit for the
isotherm experimental data with values within ranges of 0-1. Spearman’s correlation
coefficient (rs) (Table 2, entry 6) determines the correlation in the global errors and standard
deviation of relative errors (Table 2, entry 7) for relative errors due to dispersion.
Second, the Nonlinear chi-square test (χ
2
) (Table 2, entry 9), gives a predictive insight into the
similarities in the experimental data through the differences between the calculated and
experimental sets [66]. Lastly, the Coefficient of non-determination (K2) (Table 2, entry 10),
minimizes the error but also predicts the isotherm and experimental data relationship [67].
Error Function and Statistical Analysis of Isotherm Data
Ho, 2004 [68] studied the selection of the best sorption isotherm using linear regression
correlation coefficient, coefficient of determination and non-linear chi-square test as shown in
Table 3 [68].
Table 3: Error analysis of isotherms using correlation coefficient, coefficient of
determination and chi-square test.
Isotherm R
2
rs χ
2
Langmuir 1 0.992 0.996 0.477
Langmuir 2 0.916 0.957 0.398
Freundlich 0.980 0.990 0.0878
Redlich-Peterson 0.997 0.999 0.0878
The importance of the non-linear chi-square test is that it compares isotherms on the same
ordinate and abscissa and determines the best fit with the best quality. The chi test with larger
values shows that there is poor fitting and with lower values this indicates that the fitting
function is equal to the real function. He used the absorption of phenol on peat and observed
that the Freundlich and Redlich-Peterson models with lower Chi test values compared to the
Langmuir were the most suitable models for adsorption to occur.
The ANOVA (Analysis of variance) test ( two factors without replication) is carried out to
evaluate the significance of the variance of the various error functions. Subramanyam and Das
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[33] studied the linearized and non-linearized isotherm models for the ANOVA. They explained
the significance of the Langmuir, Freundlich and Redlich-Peterson as shown in Table 4.
Table 4: Analysis of variance [33].
Variation df Sum of squares Mean sum of square F-statistics P-value
Linear Non- linear
Linear Non- linear
Linear Non- linear
Linear Non- linear
Among
Isotherms
2 600394.12 134.21 300197.06 67.11 1.74 3.73 0.23 0.06
Between error
functions
5 1627971.12 204.89 325594.22 40.98 1.88 2.28 0.18 0.13
Residual errors 10 1727359.62 179.72 172735.96 17.97 - - - -
From Table 4, it is observed that the p-values of the non-linear are higher than those of the
linear which indicates a higher significance of the non-linear model however at 0.05 the
variance is lower than the F-distributions. This explains that the variation in most error
functions is insignificant for the non-linear isotherm models.
APPLICATION OF ISOTHERMS IN THE REMOVAL OF POLLUTANTS
Adsorption isotherms have been used to determine the relationship between adsorbate and
adsorbent which are in equilibrium. They show the adsorption capacity of the adsorbent and
also give the intensity of the adsorption process but also give an insight into whether the
molecules are adsorbed on monolayer or multilayer surfaces.
Due to industrialization, farming, poor waste disposal, volcanic eruptions, and low waste
treatment methods, a variety of pollutants have found their way into the water systems. These
have paused health risks to both human and aquatic life systems such as liver, kidney, and brain
damage but also changes in the hormones. Activated carbon has been applied in the removal of
pollutants due to its large surface area, porosity, and presence of various surface functional
groups such as hydroxyl, carbonyl, and amine. However, activated carbon as an adsorbent
causes toxicity as such agricultural wastes have been extensively employed with some slight
modifications to improve the adsorption capacity. Scheme 1 shows the various adsorbents used
in the removal of dyes, pharmaceuticals, and organic pollutants from the ecosystems and the
best-fit adsorption isotherm models.
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Figure 2: Shows the dyes and the different adsorbents that are used in their removal. Where
ASP-CAB is Aspergillus carbonarius, MOF-125(Ti) is Metal-organic framework NHs-MIL- 125(Ti), (ISY@PEI) is Modified skin of Iron stick yam, ACID THIO is Acidithiobacillus
thiooxidans and HDPy+ modified clay.
Ahsan et al [20] studied the adsorptive removal of Tetracycline using Sulphonated spent coffee
waste (SCW-SO3H) in which he used the Langmuir adsorption isotherm to determine the
adsorption capacity to be 473.93 mg/g. Abazari et al [74] investigated the adsorption of
amoxicillin using a Metal-organic framework (MOF; [Zn6(IDC04(OH)2(Hprz)2]n) and through
the Langmuir isotherm an adsorption capacity of 486.4 mg/g was determined. Żółtowska- Aksamitowska et al [75] investigated the removal of Ibuprofen using Modified chitin where the
Langmuir adsorption isotherm gave a better fit with an adsorption capacity of 400.39 mg/g.
Zhuang et al [76] investigated the use of Graphene in the removal of Sulfamethazine (SMT)
where the Langmuir isotherm showed an adsorption capacity of 104.93 mg/g as shown in
Figure 3.
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Bbumba, S., Karume, I., Nsamba, H. K., Kigozi, M., & Kato, M. (2024). An Insight into Isotherm Models in Physical Characterization of Adsorption
Studies. European Journal of Applied Sciences, Vol - 12(2). 115-134.
URL: http://dx.doi.org/10.14738/aivp.122.16738
Figure 3: Shows some pharmaceuticals and the different adsorbents that are used in their
removal. Where (SCW-SO3H) is Sulphonated spent coffee waste and MOF is Metal-organic
framework.
Figure 4: Shows organics and the different adsorbents that are used in their removal.
Liu et al [77] determined the adsorptive removal of Bisphenol A (BPA) using Fe3O4@β-CD-CDI
and the adsorption capacity was 52.68 when the langmuir adsorption isotherm was used.
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Zango et al [78] determined the removal of Chrysene using MIL-88(Fe), and the adsorption
capacity was found to be 42.378 mg/g while using the Langmuir adsorption isotherm. Thang et
al [79] used chicken manure biochar to remove Phenol and 2,4-dinitrophenol (DNP) where the
Langmuir isotherm gave a better fit and the adsorption capacities were 106.2 and148.1 mg/g
respectively. Costa et al [80] investigated the removal of Benzo[a]pyrene using Si-MCM-41
mesoporous molecular sieve, and the Langmuir adsorption isotherm had a better fit with an
adsorption capacity of 164.69 mg/g as shown in Figure 4.
EFFECTS OF PHYSIOCHEMICAL PARAMETERS ON ADSORPTION
The effects of contact time, initial concentration, pH, adsorbent dosage and temperature
influence the adsorption of pollutants from water.
Kalavathy et al [81] studied the influence of the physiochemical parameters on the adsorption
of Cu2+ using activated sawdust. Figure 6 shows the variation of contact time, initial
concentration, pH, adsorbent dosage and temperature on the removal of Cu2+ ions.
Figure 6: Effects of physiochemical on the adsorption capacity [81].
Adsorption studies are carried out while varying one variable while the rest are kept constant.
Contact time (a) is observed to increase until 270 min and any further it does not change and
the maximum adsorption capacity also attains a maximum at that time. It gives us information
regarding the rate of absorption of the adsorbate but also the time taken for equilibrium to
occur. The adsorbent dosage (b) also influences the adsorption capacity as with smaller doses
(0.45g) it increases since there is complete interaction between the adsorbate and the
adsorbate. At high dosage (0.75g) it decreases the surface area due to aggregation of particles
but also reduction in active sites for the adsorption of pollutants. The percentage removal of
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Bbumba, S., Karume, I., Nsamba, H. K., Kigozi, M., & Kato, M. (2024). An Insight into Isotherm Models in Physical Characterization of Adsorption
Studies. European Journal of Applied Sciences, Vol - 12(2). 115-134.
URL: http://dx.doi.org/10.14738/aivp.122.16738
the pollutant (Cu2+) increases with pH (7) (c) which is the optimum and any further
precipitation occurs due to the formation of copper hydroxide. The nature of the pollutant and
adsorbent surface are greatly affected by the pH of the medium in which they are placed since
the charge can either be negative in alkaline or positive in acidic media. Temperature
dependency (d) on the adsorption capacity is observed to decrease since the exothermic
adsorbents decrease the interaction tendency of the adsorbate-adsorbent surface. This is
because as the temperature increases the surface function groups decrease thus the adsorbates
only interact with a few active sites.
CONCLUSIONS
The linear isotherm relationship is commonly employed as it best describes the adsorption of
pharmaceuticals, dyes, and other organic pollutants. The linear relationship is simple in design
however it does not give accurate information regarding the error functions. Recently the non- linear regression which minimizes the distribution error between the experimental and
predicted data has been utilized. Based on the adsorbate initial concentration, pH, contact time
and concentration the maximum adsorption capacity is obtained from both linear and non- linear plots. The isotherm models which include Sips, Temkin, and R-P models are also applied
in some adsorption processes. The order of application of the isotherms is as follows: Langmuir
> Freundlich > Temkin, Sips, linear, R-P > Others based on published work. The statistical
parameters R2, χ
2
,SSE, RMSE, and HYBRID are commonly used in evaluating fitting parameters.
The R2 gives better information as a statistical parameter. The non-linear Chi test has been used
to give a predictive insight into the fit with the best quality. Further, the ANOVA has also been
adopted to understand the significance of the variance of the different error functions. Pollutant
adsorption onto the adsorbent surface is mainly due to surface function groups, pore size, large
surface area, and ability to add other groups like the amino, carboxyl, and ester. This review
determined that non-linear isotherms give better information on the behaviour of the
adsorbent and adsorbent at equilibrium and this can be used to give an insight into the removal
of the pollutants from different media.
Author’s Contributions
S.B, I.K, M.K, K.M and H.K.N participated in writing the main manuscript. S.B and I.K discussed
the previous findings.
Funding
The authors did not receive funding for writing this review.
Acknowledgment
The authors acknowledge facilitation by Makerere University to access literature used in
writing this review.
Ethics Approval and Consent to Participate
Not applicable.
Consent for Publication
Not applicable.
Page 16 of 20
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European Journal of Applied Sciences (EJAS) Vol. 12, Issue 2, April-2024
Availability of Data and Materials
Not applicable.
Competing Interests
The authors declare no competing interests.
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