Comments concerning papers about cationic dyes sorption, published by Saeed et al. (2023), Tan et al. (2023) and Yıldız et al. (2023)

ABSTRACT Recently, the three independent papers cited in the title were published in this journal, dealing with the sorption of cationic dyes on specially prepared solid sorbents. Although kinetics, isotherm and thermodynamics are three important components for the correct description of any sorption process, the authors of these original papers introduced several fundamental errors in these parts. Therefore, we present detailed analyses of these errors in the hope that this “Comment” paper will also be useful to other researchers (especially early career researchers) to avoid replicating such errors elsewhere in the future. Research Highlights Recently, three independent papers were published in this journal by Tan et al. (2023), Saeed et al. (2023), and Yıldız et al. (2023), all dealing with the sorption of cationic dyes on specially prepared solid sorbents. Although kinetics, isotherm and thermodynamics are important components for the correct description of any sorption process, several fundamental errors and inconsistencies have been identified. Therefore, we present detailed analyses of these errors in the hope that this paper will also be useful to other researchers (especially early career researchers) to avoid replicating such errors elsewhere in the future. Furthermore, the present authors emphasize that this paper is not intended to discredit the subject of the considered experimental studies, and they hope that these comments will be read in the spirit in which they are intended, i.e. as constructive criticism to produce better final scientific papers.


Introduction
To fight against the pollution of surface waters from the textile industry, various techniques have been developed to remove dye residues, and sorption methods [1] on solid supports are welcome because of their ease of implementation and low cost. [2]any laboratory studies have been published, dealing with the preparation and characterization of new and original solids [3] and their application to the removal of organic dyes.
Among such studies, we focus here on three articles recently published in Separation Science & Technology, all dealing with commonly used cationic dyes.Yıldız et al. [4] worked on Malachite Green (MG) and its sorption on poplar sawdust activated carbon; Tan et al. [5] studied the sorption of Methylene Blue (MB) on a biochar prepared from a K-rich biomass; finally, Saeed et al. [6] prepared a chitosan composite of Znbased metal-organic framework (MOF) on which they compared the sorption of Methyl Orange (MO) and Methylene Blue (MB), separately studied.
These three articles are not related to each other, but they were posted simultaneously online.Therefore, we decided to comment on them together, as they contain several similar errors in the treatment of data related to the modeling of sorption phenomena, which we would like to point out and propose the necessary corrections.
Here, we'll focus on modeling kinetics and isotherms and calculating thermodynamic sorption parameters.Although other points related to the experiments and discussion in these reviewed articles may raise questions, they will not be addressed here.
Unfortunately, the respective authors do not seem to be well aware of the good practices for conducting sorption studies, nor for modeling them while questionable methods have been applied here.Therefore, we should first strongly recommend the review and tutorial papers by Tran et al. [7] and by Hubbe, [8] where everyone can find most of what we can reproach in the content of the studied papers.
Although the reported errors have already been the subject of several commentaries, we feel important to avoid their reproduction and dissemination in the scientific literature, where they risk distorting the knowledge of early career researchers.
However, we must emphasize that these critical comments do not call into question the original scientific work performed and published by Yıldız et al. [4} , Tan et al. [5] or Saeed et al. [6]

Sorption experiments
All these sorption studies were performed as batch experiments under controlled temperature T and pH.After an appropriate mixing time, the solid sorbent was separated from the sorbate aqueous solution either by paper filtration [6] or by an unspecified method. [4,5]At various stages of the experiments, the dye concentration in solution was determined by UV-visible spectroscopy at the wavelength of the absorption maximum for the studied dye.
From the experimental data, the amount q t of dye sorbed on the solid at any time t can be calculated according to the straightforward relationship (1) based on the law of conservation of matter: where C 0 and C t are the concentrations of the solute at the beginning and at time t, respectively; V (L) is the volume of the solution and w (g) is the mass of the solid sorbent.All the concerned authors have here privileged the specific case of equilibrium, thus with C e and q e in place of C t and q t .The units used vary depending on the article: q e in mg/ g [4,6] or in mmol/g [5] ; C 0 and C e in mg/L [6] or in mmol/L, [5] while even in mg/g [4] (a typo?).It should be noted that for a fair comparison of MO and MB sorption, [6] it would have been appropriate to use mmol of dye rather than mg.
Another point should be made: whether modeling kinetics or sorption isotherms, the authors almost always refer to specific examples and not to general references (preferably reviews), which are nevertheless numerous and easily accessible.This undoubtedly might explain why these three articles contain so many fundamental errors, which will be discussed in the following sections.

Kinetic modeling
Of course, in a logical way kinetic experiments should be performed before isothermal studies, in order to be able to select an appropriate optimum contact time and assessing the equilibrium sorption conditions; however, on the one hand Tan et al. [5] did not carry out any sorption kinetic studies, and on the other hand Saeed et al. [6] presented their kinetic results after those of isotherms.
Both Yıldız et al. [4] and Saeed et al. [6] tested three of the most popular models to describe their experimental sorption kinetics data: the pseudo-first order (PFO) model a.k.a. the Lagergren equation, [9] the pseudosecond order (PSO) model [10][11][12][13] and the intraparticle diffusion model. [14,15]However, they used the linearized version of PFO and PSO (Equation 2 and (Equation 3), resp.):whereas it is now well documented [16][17][18][19] that only the respective non-linear Equation 4 and (Equation 5) can lead to significant results for the rate constant parameters k 1 and k 2 from the q t = f(t) data.This shortcoming arises because transformations of non-linear equations into linear forms implicitly alter their error structure and may also violate standard least-squares error variance and normality assumptions.In this setting, the nonlinear method provides a mathematically rigorous method for determining model parameter values; fortunately, we all now have easy access to computer programs with non-linear least-squares (NLLS) fits that can be used in place of linear regression analyses.Another important drawback of using the linearized form of the PFO model is that q e must be known a priori.This constraint could clearly render unfair the results of fitting comparison.Therefore, Fig. S1 in Saeed et al. [6] (where the experimental points are even missing) and Fig. S2 and S3 in Yıldız et al. [4] should be deleted, and the contents of the original Table S1 in Saeed et al. [6] and Table S2 in Yıldız et al. [4] should be changed to new NLLS values. 1 Obviously, the value of the estimated error should be enclosed in order to assess the reliability of the results.Another popular sorption kinetic model is the socalled "intraparticle diffusion model," here applied by Yıldız et al. [4] and by Saeed et al. [6] in the form of where k and Ȼ are constants.Equation 6 is commonly known as the Weber -Morris plot.The constant Ȼ is often interpreted as a measure of the thickness of the boundary layer; however, asserting that Ȼ, with units of q t (mass of sorbate/mass of sorbent), signifies the thickness of the boundary layer which should be expressed in units of length, is inherently illogical.
Another deficiency in Equation 6is that it predicts a non-zero q t when t = 0, i.e., q t = Ȼ at t = 0, although it is commonly assumed that the sorbent is pristine at the onset of the sorption process, meaning that at time zero, the sorbent is free of any sorbate (q t = 0 at t = 0).
A more appropriate expression is given by Equation 7, which is exactly the same as the equation called by Saeed et al. [6] as Fick's law.This Equation 7dictates that a plot of q t versus t 1/2 should go through the origin. [14,15]quation 7 approximates Equation 8which is valid under conditions of (i) constant or nearly constant external solution concentration (equivalent to infinite bath) and (ii) intraparticle diffusion is the sole rate-limiting step.In Equation 8, F is the fractional approach to equilibrium (F = q t /q ∞ where q ∞ is the amount adsorbed after infinite time), D s is the solid diffusion coefficient, and r p is the adsorbent radius.The parameter k in Equation 7 is equal to In addition to the aforementioned conditions, Equation 7 should be used for short times only.Evidently, the use of Equation 7in data fitting must meet very restrictive conditions, which have been neglected in previous studies that employed Equation 7to fit batch kinetic data. [20]n summary, both the improper Equation 6 and the proper Equation 7 have been blindly applied to batch kinetic data, resulting in the publication of meaningless or misleading modeling results.In addition to the intraparticle diffusion model, Saeed et al. [6] used the socalled Reichenberg (misspelled as Richenberg) kinetic model. [21]Because this model, as given in the work of Saeed et al. [6] is also an approximate form of Equation 8, it is valid under certain restrictive conditions as well.

Isotherm modeling
A considerable number of equations, both empirical and theoretical, are available to model the results of batch sorption experiments; however, it should be borne in mind that these models are often subject to specific assumptions about the nature or mechanisms of the interactions between the solute and the surface or the pores of the solid sorbent.It is thus important to conveniently select an adequate model for a given sorption system. [8]iven the shape of the isothermal curves q e = f(C e ), referred to as Type I concave isotherms with the sorbed amount approaching a limiting value, it was logical for the different teams to use the most appropriate (and popular) equations for their modeling: the Langmuir equation, which is theoretically well established, [22] and the semi-empirical Freundlich equation. [23]owever, it is unfortunate that these three groups of researchers used them in their linearized form, i.e. respectively: whereas, once again, the respective original non-linear forms must be used to obtain meaningful parameter values. [7,19]Within these equations, q max is the maximum loading capacity of the corresponding solid sorbent for the given dye sorbate; K L is the Langmuir constant, K F the Freundlich constant, and 1/n a dimensionless parameter; their units are, of course, dependent of those chosen for C e and q e (see before).However, it should be noted that both Yildiz et al. [4] (right column on page 2102) and Saeed et al. [6] (in Table S1(A)) gave a wrong unit for K F , i.e.L g −1 whereas this should of course be [(mg g −1 )/(mg L −1 ) 1/n ].
Therefore, the parameters given for each discussed paper in Table S1(A) and Table S3 should be recalculated under the NLLS method: then, the authors could better discuss their results as the comparison of the three solid sorbents is concerned.Moreover, we suggest that Fig. S4 and Fig. S5 in Yıldız et al. [4] could be deleted; but unfortunately the corresponding direct isotherm curves q e = f(C e ) presented in Fig. S6, cannot allow to obtain any information about the formation of a plateau.
Both Tan et al. [5] and Saeed et al. [6] also tested the Dubinin-Radushkevich (DR) isotherm model equation, based on the potential theory and assuming a mechanism related to progressive micropore filling of the sorbent; they always used a linear equation like: However, as explained above, the DR model equation should better be expressed in non-linear form [24,25] as where β (mol 2 kJ −2 ) is a constant related to the sorption energy, and ε (kJ mol −1 ) is the Polanyi sorption potential; since these parameters are expressed in SI units (or multiples), the same is recommended for sorption capacity (mol kg −1 ) and concentration (mol dm −3 ), although the most important point is to have consistent units for these two values.Moreover, this sorption potential is expressed by Saeed et al. [6] as a function of equilibrium concentration C e of sorbate through a too common dimensionally inconsistent form like instead of the correct form where C s is the solubility of the sorbate. [24,25]onsequently, and despite the many caveats previously published, the DR modeling results obtained by Tan et al. [5] and by Saeed et al. [6] are of no real significance.
Finally, Saeed et al. [6] also chose to apply the Temkin isotherm model (spelled as Tempkin), in the form: where they defined B T (J mol −1 ) as a heat sorption constant and A T (L g −1 ) (if C e is given in mg L −1 , then A T should have units of L mg −1 ) as an equilibrium constant, respectively.Nevertheless, this equation presents inconsistent writing, with its two sides having different unit dimensions, and this was formerly discussed by Chu, [26] who explained that B T should be expressed as with b T (J mol −1 ) is really the heat of sorption, whence the Saeed et al. [6] parameter B T in fact has a g L −1 unit.Further, Chu [26] gave the correct Temkin equation as: For SI unit consistency, it is recommended to express concentrations in mol dm −3 and sorption capacities in mol kg −1 , although the most important point is to have consistent units for these two values.Then, all relative discussion from this isotherm model by Saeed et al. [6] has no scientific meanings.

Thermodynamic parameters
Thermodynamics is considered an essential part in the discussion of the mechanisms of sorption experiments; this is why the correct basic knowledge must be emphasized and thermodynamic calculations must be applied with due care.
Within the three papers discussed, it should be noted that Tan et al. [5] did not provide any data on thermodynamic parameters.As far as the works of Yıldız et al. [4] and Saeed et al. [6] are concerned, they (partially) used the classical thermodynamic relationships. [27]n the present case of sorption equilibria, the standard Gibbs free energy change ΔG° (kJ mol −1 ) is given [28] as: where K 0 Eq is the (dimensionless) standard equilibrium constant (a.k.a. the "thermodynamic equilibrium constant").
Starting from this Equation 20, it is possible to calculate other thermodynamic equilibrium parameters using the famous van't Hoff equation.The linear form of the van't Hoff equation (as applied by either Yıldız et al. [4] and Saeed et al. [6] ) may be (in a pinch) acceptable when the number of experimental points is small, as is the case in the original papers (data at only 3 temperatures, for each); however, it is important to remember that this linearization artificially maximizes the calculated confidence in the estimated parameters, although the non-linear adjustment [29,30] is obviously more representative of the true results. [19] correct choice of this important parameter, the standard sorption equilibrium constant K 0 Eq , has been recently discussed in detail for a great number of sorption isotherm equations, [28,31] because too often a wrong choice was made, as this is the case here.
Yıldız et al. [4] used as the equilibrium constant in Equation 21 the value from the following definition: that is in fact a distribution coefficient.The main mistake made by the authors is to consider K C as an equilibrium constant. [31]Indeed, it should be noted that an equilibrium constant is by definition invariant with the concentration; however, in the case of Yıldız et al. [4] work, K C does not satisfy this condition, as can be inferred by the nonlinearity of the q e vs. C e isotherm plots (Fig. S6).In addition, the authors have missed the fact that K C has a unit, i.e. making it unsuitable for calculating the standard free energy of sorption.
Moreover, when calculating an equilibrium constant, the only unit for the amount of substance and the solute concentration should be mol (not g or mg or any other) and mol L −1 , respectively, before taking the corresponding logarithm.Although this should be a well-known topic, [7,28,29,[31][32][33] it is too often forgotten (see also the discussion below on Equation 25).Therefore, it is impossible for Yildiz et al. [4] to introduce their distribution coefficient K C to calculate the thermodynamic parameters, whose published data in the original paper should be considered as insignificant.
As for Saeed et al. [6] they used the Langmuir constant K L with units of L mg −1 as their equilibrium constant, but this is another wrong choice. [28]Indeed, as previously reported, [34,35] in order to calculate the dimensionless "thermodynamic" Langmuir constant K L ° for the sorption process, the original authors should have made use of the equation: where M dye is the molar mass of the sorbed dye (M MB = 319.85g/mol for MB; M MO = 327.34g mol −1 for MO), and the factor 1,000 allows converting g to mg; C° (1 mol L −1 by definition) is the standard concentration of solute.
Assuming the K L values reported by Saeed et al. [6] (in Table S1(A)) are correct, the thermodynamic parameters have been re-calculated based on Equation 20, Equation 21 and Equation 25.Our results are presented in Table 1.The change in the units of K L from L mg −1 to L mol −1 produces a parallel shift upwards of the van't Hoff straight line.As a result, the newly calculated ΔH° remains the same wherein ΔS° increases.Interestingly, the sign of ΔG° becomes negative, not positive as calculated by Saeed et al. [6] It is worth recalling that the change in the sign of ΔG° from positive to negative does not reflect a change in the preferential direction of the sorption process.The sentence by Saeed et al. [6] " . . . the positive ΔG values . . .are the affirmation sign of the non-spontaneity of the adsorption process" is wrong because the authors erroneously evaluated the spontaneity of the process from the sign of ΔG° rather than of ΔG (see Equation 19 and Equation 20 in Saeed et al. [6] : the authors write ΔG, ΔH, and ΔS but actually those thermodynamic quantities are ΔG°, ΔH°, and ΔS°, respectively).As reported in any textbook of physical chemistry (e.g., Atkins and de Paula [27] ), a reaction is spontaneous in the direction of decreasing Gibbs energy, i.e. when ΔG < 0 and not when ΔG° < 0. It is clear from Equation 20 of the present paper that the sign of ΔG° merely depends on the value of K (when K < 1, then ΔG° > 0; when K > 1, then ΔG° < 0).It follows that the sign and the magnitude of ΔG° can be related to the favorability of the process rather than to its spontaneity. [36]And how can the spontaneity of a sorption process be practically assessed?This can be simply inferred by measuring the change in the solute concentration during time: if the concentration decreases (as it occurs in most of sorption experiments since the sorbent is usually "clean" at the initial stage), sorption is spontaneous; if the concentration increases, then desorption is spontaneous.
It should be noted that a similar work was published previously by Saeed et al. [37] concerning the sorption of MB and MO on a MOF-chitosan composite, this time with Fe instead of Zn.Since the same causes lead to the same effects, we could make the same criticism as above, which was done by Zhou et al. [38] regarding the misuse of the Langmuir constant (but on slightly different bases than ours) and with corrections to the thermodynamic parameters.
Finally, in any case, the comments in the original papers on the sign, magnitude and significance of the thermodynamic parameters should be moderated with reference to Salvestrini et al.. [32] Please also note that ΔG° cannot be called "Gibb's free energy" as it is printed in the right column of page 2095 in Tan et al. [5] : in fact, it is the "Gibbs free energy."

Conclusion
Several errors, problems, and inconsistencies have been identified in the three papers recently published in this journal by Yıldız et al., [4] Tan et al. [5] and Saeed et al. [6] It is recommended that the cited authors thoroughly correct their respective published papers to remove known errors.We hope that these comments will help other colleagues to analyze experimental results in terms of sorption kinetics, isotherm and thermodynamics.
It is, of course, important to emphasize that this "Comment" paper is not intended to discredit the subject of the considered experimental studies.Furthermore, the present authors hope that these comments will be read in the spirit in which they are intended, i.e., as constructive criticism to produce better final scientific papers.

Disclosure statement
No potential conflict of interest was reported by the author(s).

1
At the request of the Editor of Separation Science & Technology, we have compiled in a Supplementary Information file the Figures and Tables of the original articles discussed in our manuscript.

Table 1 .
Recalculated thermodynamic parameters for the removal of methylene blue (MB) and Methyl Orange (MO) onto CS/MOF-74 solid sorbent, from Langmuir isotherm equilibrium constant.
a From TableS1(C) in the Supplementary Information file.