Physicochemical properties of the studied pesticides, where pKa is the value based on partial charge distribution in a molecule, log D is the octanol-water coefficient at a given pH, log P is the partition coefficient of a compound between octanol and water, and Dmin and Dmax are measures between the most distant molecule atoms.
Abstract
The adsorbate structural properties such as the type, number, and position of substituents on benzene ring of organic compound, as well as a length and arrangement of hydrocarbon chain in a space, exert a significant influence on the adsorption process. The measurements of adsorption equilibria and kinetics of several pesticides belonging to the group of halogenated phenoxyacids differentiated in terms of structural and physicochemical properties were studied in order to characterize the adsorption mechanism and correlate it with the pollutant properties. Regarding a complexity of investigations (capacity and rate) comprising 21 structurally closely related active substances showing the carcinogenic activity on living organisms and relatively long half-life time in the environment, the proposed intensive studies on the removal of pollutants by adsorption process are very important in cognitive and practical terms.
Keywords
- pesticide adsorption
- activated carbon
- adsorption equilibrium
- adsorption kinetics
1. Introduction
The improvement of effectiveness of pollutant removal from water and sewage using activated carbons has been a subject of numerous studies. The influence of adsorbate, adsorbent, solution properties, and experiment conditions on adsorption process has been analyzed.
Noteworthy is the impact of adsorbate properties on adsorption process such as solubility, molecule dimension, ability to dissociation, and physicochemical properties. Hydrophobicity which can be expressed by solubility is the main driving force of adsorption process of organics from aqueous solutions on activated carbons. The lower solubility of a pollutant is the highest adsorption on hydrophobic carbon is observed. Additionally, analyzing adsorption of pollutants from aqueous solutions on microporous materials, it is necessary to take into account molecule dimension due to a possible sieve effect. Moreover, the influence of functional groups on adsorbate aromatic ring on the differentiation of adsorptive affinity of organic compounds to activated carbon should be also regarded.
The influence of adsorbate substituents on adsorption mechanism is similar to that of surface groups of adsorbent. Depending on their nature, they can attract or repel electrons and affect the dispersive interactions between adsorbate aromatic ring and graphene layers of activated carbon. The adsorbate functional groups that are electron donors activate the aromatic ring by moving electrons toward it, and thereby they enhance the interactions between adsorbate molecule and π electrons of adsorbent graphene planes. On the other hand, the deactivating groups as electron acceptors reduce the electron density of aromatic ring; thus, interactions of adsorbate-adsorbent surface are weakened [1, 2, 3, 4, 5, 6, 7].
The research on effect of adsorbate properties on adsorption process is an extension of the studies already published in the paper [8]. The pesticides belonging to a group of chloride phenoxyacid derivatives were used as adsorbates in view of their common usage in agriculture and hence a high probability of infiltration to surface and underground waters. Their presence in water affects its quality, worsens its properties, and in some cases makes it unsuitable to consume. These pesticides show a carcinogenic activity on living organisms and a relatively long half-life time in the environment; therefore, the intensive study on their removal by adsorption process is very important for practical applications. The experimental studies include measurements of the adsorption isotherms and concentration rate profiles as well as their interpretation on the basis of the generalized Langmuir (GL) equation for equilibrium data and diffusion models (intraparticle diffusion model (IDM) and pore diffusion model (PDM)) and multi-exponential (m-exp) equation for kinetic data. Based on the obtained results, the correlations between adsorbate structure, its properties, and adsorption uptake and rate were analyzed. The evaluation of the theoretical equilibrium and kinetic equations and models based on a fitting quality and consistency with adsorption mechanism was also made.
2. Experimental
2.1 Materials and methods
The selected adsorbates comprise 21 compounds which are structurally differentiated with regard to the number, position, and type of the functional groups and length and spatial arrangement of the hydrocarbon part in a molecule. Not all of these substances are used as pesticides because of their low biological activity. However, due to complexity of the research issues, it seems to be reasonable to include them as a subject of the investigation.
Table 1 presents the physicochemical properties of the adsorbates collected on the basis of literature data or calculations using computer programs generally available. All the substances are analytical reagent grade purity. The chemical names and abbreviations of them are as follows: 4-chlorophenoxyacetic acid (4-CPA); 2,4-dichlorophenoxyacetic acid (2,4-D); 2,4,5-trichlorophenoxyacetic acid (2,4,5-CPA); 2,4,6-trichlorophenoxyacetic acid (2,4,6-CPA); 4-chloro-3-methylphenoxyacetic acid (4-CMPA); 4-chloro-2-methylphenoxyacetic acid (MCPA); 2,4-dibromophenoxypropionic acid (2,4-BrPA); 2,4,6-tribromophenoxypropionic acid (2,4,6-BrPA); 2-(3-chlorophenoxy)propionic acid (3-CPP); 3-(4-chlorophenoxy)propionic acid (4-CP); 2-(4-chlorophenoxy)propionic acid (4-CPP); 2-(2,4-dichlorophenoxy)propionic acid (2,4-CPP); 2-(2,5-dichlorophenoxy)propionic acid (2,5-CPP); 2-(3,4-dichlorophenoxy)propionic acid (3,4-CPP); 2-(2,4,5-trichlorophenoxy)propionic acid (2,4,5-CPP); 2-(4-chloro-2-methylphenoxy)propionic acid (MCPP); 2-(4-chloro-3-methylphenoxy)propionic acid (4-CMPP); 2-(4-chlorophenoxy)-2-methylpropionic acid (CFA); 2-(4-chlorophenoxy)butanoic acid (4-CPB); 4-(4-chloro-2-methylphenoxy)butanoic acid (MCPB); and 2-(4-chloro-2-methylphenoxy)butanoic acid (4-CMPB).
Common name | pKa [9] | Solubility g/dm3 20–25°C | Kow/log D [9] | Kow/log P | Dmin /Å [9] | Dmax /Å [9] | |
---|---|---|---|---|---|---|---|
pH = 1.81 | pH = 10.38 | ||||||
4-CPA | 3.14 | 0.848 [10] | 1.88 | −1.63 | 1.85 [11] | 4.33 | 9.38 |
2,4-D | 2.80 | 0.682 [10] | 2.46 | −1.03 | 2.37 [11] | 4.88 | 9.49 |
2,4,5-CPA | 2.56 | 0.268 [10] | 3.04 | −0.42 | 2.89 [11] | 6.22 | 8.88 |
2,4,6-CPA | 2.57 | 0.247 [10] | 3.04 | −0.42 | 2.89 [11] | 5.42 | 8.84 |
4-CMPA | 3.36 | 0.650 [12] | 2.40 | −1.12 | 5.42 | 8.96 | |
MCPA | 3.36 | 0.825 [10] | 2.40 | −1.12 | 3.25 [13] | 5.47 | 9.52 |
2,4-BrPA | 1.96 | 0.059 [14] | 2.60 | −0.70 | 5.03 | 9 | |
2,4,6-BrPA | 1.50 | 0.015 [15] | 3.12 | 0.07 | 5.71 | 9 | |
3-CPP | 3.27 | 1.200 [16] | 2.45 | −1.06 | 5 | 7.79 | |
4-CP | 3.70 | 0.770 [12] | 2.13 | −1.39 | 4.33 | 9.87 | |
4-CPP | 3.27 | 1.475 [10] | 2.45 | −1.06 | 5.22 | 8.65 | |
2,4-CPP | 2.95 | 0.829 [10] | 3.04 | −0.46 | 5.59 | 9.03 | |
2,5-CPP | 2.95 | 0.181 [14] | 3.04 | −0.46 | 5.62 | 8.63 | |
3,4-CPP | 2.94 | 0.130 [12] | 3.04 | −0.46 | 5.5 | 8.76 | |
2,4,5-CPP | 2.70 | 0.140 [10] | 3.62 | 0.15 | 3.80 [13] | 5.62 | 9 |
MCPP | 3.47 | 0.895 [10] | 2.97 | −0.55 | 3.13 [13] | 5.86 | 8.64 |
4-CMPP | 3.46 | 0.690 [15] | 2.97 | −0.55 | 5.86 | 7 | |
CFA | 3.37 | 0.582 [17] | 2.89 | −0.63 | 2.84 [13] | 4.42 | 9.14 |
4-CPB | 3.42 | 0.315 [14] | 2.98 | −0.54 | 5.22 | 9.7 | |
MCPB | 3.59 | 0.048 [10] | 3.50 | −0.03 | 3.28 [18] | 6.36 | 9.65 |
4-CMPB | 3.59 | 0.17 [12] | 3.50 | −0.03 | 5.86 | 9.28 |
The microporous activated carbon F300 was used as adsorbent (
3. Results and discussion
3.1 Adsorption equilibria
3.1.1 Effect of type and number of adsorbate substituents
Substituents on benzene ring of aromatics have a great influence on adsorption process on activated carbon. It is not directly related to their interaction with an adsorbent but mainly with changes in molecular properties of adsorbed compound [19, 20, 21, 22, 23]. The crucial factors are the nature of the substituents, number, and their mutual position on benzene ring. In the study the adsorption process of compounds with substituents with electron-acceptor (▬Cl, ▬Br) and electron-donor properties (▬CH3) was analyzed. It is well known that substituents affect acid-base properties (pKa), water solubility, hydrophobicity (Kow), dipole moment, molecular weight, and spatial dimension in space of an organic compound. In turn, these properties affect a mechanism and a range of adsorption process. Nevertheless, solubility in water and hydrophobicity of substance most often play a superior role in adsorption process.
As pKa values of the studied pesticides are within the range of 1.50–3.70, thus, the buffers of pH = 1.81 or 10.38 were used to prepare the experimental solutions. Thus, the compounds in solutions were nearly undissociated and completely dissociated, respectively. In the case of the compounds of very low solubility, the studies at alkaline pH conditions were carried out. For the systems for which the adsorption process was carried out in acidic solutions, the isotherms both in the standard linear
In Figures 1 and 2 the comparison of the adsorption isotherms of chlorophenoxyacetic and chlorophenoxypropionic acid derivatives with a different type and number of substituents on aromatic ring on activated carbon F300 at pH = 1.81 is shown. In the case of phenoxyacetic pesticides, relatively small changes in capacities are observed which can be arranged as follows: 2,4-D ∼ 4-CPA > MCPA. The differences in the course of adsorption isotherms for the phenoxypropionic pesticides are greater. Taking into account their affinity to the carbon F300, it looks as follows: 2,4-CPP ∼ 4-CPP > MCPP > 4-CMPP.
The solubility values were collected from literature, and partition coefficients between octane and water (
The mechanism of adsorption process is mainly based on the dispersion or donor-acceptor interactions (pH = 1.81, thus both adsorbates and functional groups on active carbon surface are undissociated) and the local repelling electrostatic interactions between positively charged sites on adsorbent surface (as a result of attraction and localization of graphene plane electrons by oxygen functional groups) and a local positive charge in adsorbate molecule (as a result of electron-acceptor properties of chlorine on benzene ring). Generally, the more substituents in a molecule, the greater the local charge and stronger the local electrostatic interactions.
Another aspect concerns a spatial structure of compounds, as the ones with substituents in a para-position have better access to adsorbent micropores. In particular, this applies for halogenophenoxyacetic acids, where the hydrocarbon part is not branched, like in β-halogenophenoxypropionic acids. Therefore, the capacities for 4-CPA and 2,4-D, as well as for 4-CPP and 2,4-CPP, are similar, although comparing the solubility and log D values, one could assume a different situation. A simple explanation is a symmetrical structure of 4-CPA, which means that its molecular volume is smaller than for 2,4-D which enables a better access and greater packing density in the adsorptive space. In a group of phenoxypropionic acid derivatives, the 4-CPP and 2,4-CPP adsorptions are higher than for MCPP and 4-CMPP. The molecules of all these compounds have at least one
In Figure 3, the comparison of the adsorption isotherms of chloro- and bromophenoxyacetic derivatives from solutions at pH = 10.38 is presented. The adsorption decreases in the series: 2,4,6-BrPA > 2,4-BrPA > 2,4,6-CPA ∼ 2,4-D > 4-CPA > MCPA. At alkaline conditions the electrostatic interactions are predominant in adsorption mechanism due to dissociated forms of both the adsorbate and the adsorbent functional groups. The repulsive forces between the pesticide anions and negatively charged adsorbent groups appear. However, a halogen with the electron-withdrawing properties on benzene ring decreases the total electron charge of the aromatic ring and shows a local positive charge. The obtained effect results in the creation of local attractive interactions which decrease the electrostatic repulsion between adsorbate and adsorbent. If a degree of halogen substitution increases, the strength of interactions increases, and it leads to stronger adsorption on active carbon. This explanation is true if substituents in a molecule are of the same type, e.g., bromine or chlorine. Comparing the adsorption affinities in the systems with different substituents, it can be observed that the compounds containing bromine show a stronger affinity for the adsorbent surface compared to compounds with chlorine, regardless of a number of substituents in molecule. In the case of MCPA containing a methyl group with electron-donor properties, the weakest adsorption is observed. Increase of the electron density within aromatic ring raises the electrostatic repulsion with the negatively charged surface of the activated carbon. A similar effect is observed in the case of phenoxypropionic acid derivatives with a different halogen substituent in the para-position at acidic pH.
In Figure 4a a comparison of the adsorption isotherms for 2,4-D, 2,4,5-CPA, and 2,4,6-CPA, i.e., the compounds with a differentiated number and position of chlorine atoms on benzene ring, is presented. Similar adsorption is observed for 2,4-D and 2,4,6-CPA, whereas for 2,4,5-CPA the process is significantly greater. 2,4-D shows the weakest hydrophobic properties; its molecule contains two chlorine atoms. The other two compounds 2,4,5-CPA and 2,4,6-CPA are characterized by the similar log D values, but they contain three chlorine atoms. Therefore, the differences in adsorption affinity to adsorbent should be attributed to the steric effect. In the group of chlorophenoxypropionic acids differentiated in terms of a number of substituents in a molecule, the adsorbate affinity to the adsorbent active sites increases in the order 2,4,5-CPP > 2,4-CPP > 2,5-CPP > 4-CPP (Figure 4b). The octanol/water partition coefficient values (log D) for these compounds at pH = 10.38 are 0.15, −0.46, −0.46, and −1.06, respectively. 2,5-CPP is weakly removed at a given pH than its isomeric form 2,4-CPP although its hydrophobicity should promote the adsorption process. Probably an arrangement of the substituents in 2,5-CPP leads to difficulties in diffusion of the adsorbate molecules into small pores of adsorbent that consequently decreases adsorption.
The comparison of the 4-CMPA and 4-CPA (pH = 10.38) adsorption isotherms (Figure 5) shows that removal of the methyl group weakens the adsorption affinity. Similar behavior occurs for their phenoxypropionic and phenoxybutanoic homologs, for which the adsorption of 4-CMPP > 4-CPP and 4-CMPB > 4-CPB (Figures 6 and 7). The observed trend fully coincides with the hydrophobicity of pesticides. For the series of 4-CMPA and 4-CPA, log D is −1.12 and −1.63, respectively; for 4-CMPP and 4-CPP, log D is equal to −0.55 and −1.06, respectively, while for 4-CMPB and 4-CPB, this parameter is −0.03 and −0.54, respectively.
3.1.2 Effect of substituent position on aromatic ring
The adsorption affinity of organics depends on a number and type of substituents, as well as on their position on the benzene ring. This is related to the occurrence of the steric and inductive effects of adsorbate. The courses of adsorption isotherms measured at alkaline pH for 2,4,5-CPA and 2,4,6-CPA (Figure 8) and 2,4-CPP and 2,5-CPP (Figure 9a) indicate that the less symmetric distribution of electron charge density in benzene ring is, the stronger adsorption affinity is observed. Therefore, higher affinities for 2,4,5-CPA and 2,4-CPP than for 2,4,6-CPA and 2,5-CPP are found. Analyzing the solubility of these substances, one can say that this parameter is not a main factor controlling the adsorption process.
As results from Figure 9b at basic conditions for the isomers of dichlorophenoxypropionic acid, their affinity to the activated carbon increases as follows: 3,4-CPP > 2,4-CPP > 2,5-CPP. The strongly adsorbed compound is characterized by two adjacent chlorine atoms with electron-acceptor properties, causing the overlap of local positive charges in the benzene ring. The negatively charged oxygen groups on the carbon surface interact electrostatically with the positive local charge of the pesticide rings, intensifying the adsorption process. The interactions of other compounds with F300 are disturbed by the steric effect due to the position of substituent at the second carbon in the ring and in the case of 2.5-CPP additionally due to a symmetrical distribution of the σ+ charge. This explains the differentiation in adsorption of these compounds.
The comparison of the isotherms for 4-CMPP and MCPP at alkaline pH (Figure 10a) gives information that a shift of methyl group position on aromatic ring from ortho- to meta-position does not affect adsorption process. The same situation is observed for their homologs from the phenoxybutanoic group; the adsorption affinity of both compounds to activated carbon is similar (Figure 10b).
3.1.3 Effect of structure of hydrocarbon chain in adsorbate molecule
To analyze the impact of hydrocarbon chain structure on the adsorption process, the systems with chlorogenic phenoxyacetic derivatives and their homologs—phenoxypropionic and phenoxybutanoic derivatives—were studied. The graphs are grouped with regard to hydrocarbon chain structure, while the aromatic part of molecules is the same. In the case of adsorption processes carried out at pH = 10.38, the adsorption affinities of the studied compounds are as follows: 2,4,5-CPA > 2,4,5-CPP (Figure 11a), 2,4-D > 2,4-CPP (Figure 11b), MCPP ∼ MCPB (Figure 12a), 4-CMPA > 4-CMPP > 4-CMPB (Figure 12b), and 4-CPA ∼ 4-CP > 4-CPP ∼ 4-CPB > CFA (Figure 13). For the systems for which it was possible to measure the adsorption process at pH = 1.81, the adsorption affinities of pesticides are 2,4-D ∼ 2,4-CPP (Figure 14), MCPA > MCPP (Figure 15), and 4-CPA > 4-CPP > CFA (Figure 16).
Analyzing the coefficient
3.2 Analysis of experimental isotherms by means of the GL isotherm
All the studied experimental systems were analyzed by the generalized Langmuir isotherm equation (GL) [24, 25, 26] that for the specific values of heterogeneity parameters are reduced to four equations: Langmuir (L, m = n = 1), Langmuir-Freundlich (LF, 0 < m = n ≤ 1), generalized Freundlich (GF, 0 < m ≤ 1, n = 1), and Tóth isotherm (T, m = 1, 0 < n ≤ 1). These isotherms were obtained from the global integral equation assuming that the Langmuir isotherm is a local one. In the optimization procedure, a method of the minimal sum of square deviations of adsorption values was used assuming the limitation of adsorption capacity (am ≤ 20 mmol/g) and the equilibrium constant K (K ≤ 105 l/mmol). Table 2 presents the parameters of this equation, the correlation coefficients R2, and standard deviations SD(a).
System, pH (type of isotherm) | am | m | n | log K | R2 | SD(a) |
---|---|---|---|---|---|---|
4-CPA/F300, pH 1.81 (T) | 3.34 | 1 | 0.40 | 1.59 | 0.957 | 0.087 |
4-CPA/F300, pH 10.38 (GL) | 1.25 | 0.25 | 0.78 | −0.35 | 0.940 | 0.043 |
2,4-D/F300, pH 1.81 (T) | 3.69 | 1 | 0.35 | 1.81 | 0.968 | 0.079 |
2,4-D/F300, pH 10.38 (GF) | 1.19 | 0.35 | 1 | 0.14 | 0.960 | 0.035 |
2,4,5-CPA/F300, pH 10.38 (GF) | 1.29 | 0.25 | 1 | 0.01 | 0.907 | 0.054 |
2,4,6-CPA/F300, pH 10.38 (GF) | 1.07 | 0.38 | 1 | 0.46 | 0.923 | 0.036 |
4-CMPA/F300, pH 10.38 (GF) | 15.11 | 0.17 | 1 | −7.25 | 0.936 | 0.030 |
MCPA/F300, pH 1.81 (GF) | 3.09 | 0.34 | 1 | −0.45 | 0.937 | 0.110 |
MCPA/F300, pH 10.38 (GF) | 20 | 0.20 | 1 | −7.04 | 0.766 | 0.064 |
2,4-BrPA/F300, pH 10.38 (GF) | 1.83 | 0.33 | 1 | −0.49 | 0.957 | 0.046 |
2,4,6-BrPA/F300, pH 10.38 (GL) | 20 | 0.32 | 0.29 | −3.71 | 0.949 | 0.056 |
3-CPP/F300, pH 1.81 (L) | 1.92 | 1 | 1 | 0.93 | 0.948 | 0.082 |
4-CP/F300, pH 10.38 (GF) | 20 | 0.24 | 1 | −5.53 | 0.955 | 0.033 |
4-CPP/F300, pH 1.81 (L) | 2.02 | 1 | 1 | 0.96 | 0.977 | 0.058 |
4-CPP/F300, pH 10.38 (GF) | 20 | 0.18 | 1 | −7.73 | 0.939 | 0.031 |
2,4-CPP/F300, pH 1.81 (T) | 2.41 | 1 | 0.48 | 1.79 | 0.96 | 0.081 |
2,4-CPP/F300, pH 10.38 (GF) | 1.02 | 0.32 | 1 | 0.181 | 0.916 | 0.035 |
2,5-CPP/F300, pH 10.38 (T) | 1.32 | 1 | 0.29 | 2.94 | 0.896 | 0.032 |
3,4-CPP/F300, pH 10.38 (GF) | 1.03 | 0.22 | 1 | 0.05 | 0.937 | 0.026 |
2,4,5-CPP/F300, pH 10.38 (GL) | 1.07 | 0.56 | 0.75 | 0.83 | 0.942 | 0.041 |
MCPP/F300, pH 1.81 (T) | 2.83 | 1 | 0.40 | 1.67 | 0.951 | 0.083 |
MCPP/F300, pH 10.38 (GF) | 1.12 | 0.11 | 1 | −1 | 0.822 | 0.034 |
4-CMPP/F300, pH 1.81 (GF) | 2.60 | 0.34 | 1 | −0.41 | 0.961 | 0.070 |
4-CMPP/F300, pH 10.38 (GF) | 12.90 | 0.16 | 1 | −7.35 | 0.949 | 0.026 |
CFA/F300, pH 1.81 (GF) | 2.02 | 0.66 | 1 | 0.53 | 0.995 | 0.061 |
CFA/F300, pH 10.38 (GF) | 20 | 0.21 | 1 | −7.03 | 0.928 | 0.030 |
4-CPB/F300, pH 10.38 (GF) | 10.42 | 0.15 | 1 | −7.81 | 0.952 | 0.022 |
MCPB/F300, pH 10.38 (GL) | 4.65 | 0.45 | 0.08 | 5 | 0.934 | 0.025 |
4-CMPB/F300, pH 10.38 (T) | 1.02 | 1 | 0.59 | 1.54 | 0.923 | 0.027 |
The parameters for two systems correspond to the simple L isotherm equation which is characteristic for energetically homogeneous system. For the other systems, satisfying optimization using the T and GF equations or the general form of the GL isotherm was obtained. The GL equation corresponds to the quasi-Gaussian function of adsorption energy distribution; the heterogeneity parameters characterize the extension of this function toward the higher (
Analyzing the heterogeneity parameters which characterize the experimental systems, one can conclude that in most cases they achieve values much lower than one. It indicates a significant impact of the energetic heterogeneity. Attention should be paid to high values of the adsorption capacity for several experimental systems. In the case of experimental isotherms with a narrow range of relative adsorption
Analyzing the calculated curves, one can observe the different nature of the GF equation in relation to the other isotherms being special cases of the GL isotherm. For the LF equation (
The above observations are confirmed by the results of model calculations presented in Figure 18 as the dependences of relative slope
Referring to a general problem of accuracy of the determination of adsorption isotherm parameters, it should be emphasized that a key problem is to determine the adsorption capacity
It should be stated that a fully reliable optimization of the theoretical model can be obtained if the experimental data are distributed evenly in a range of both low and high concentration/adsorption regions. It is important that the range of relative adsorption is symmetrical in relation to
3.3 Adsorption kinetics
In order to investigate an effect of the adsorbate properties on adsorption rate, the measurements of adsorption kinetics for selected systems were conducted. As the activated carbon is characterized by high porosity, it seemed reasonable to include diffusion effects in a kinetic description. The Crank model (intraparticle diffusion model) in a standard form as well as in a simplified one is a fundamental model of intraparticle diffusion process. The full IDM model takes into account the changes of adsorbate concentration during adsorption process and a spherical shape of adsorbent particles with a radius
where
However, for the analyzed experimental kinetics, the full IDM equation describes the data very poorly (the curves and points are marked as “Crank” in Figure 19). The Crank model analysis for MCPP/F300 at pH = 2 was chosen and presented as representative for all experimental systems; the quality of optimization of all of them was very similar. If effective concentration of the adsorbate in a surface layer is different than in a volume phase, it can be assumed that
As one can see, the adsorption data can be described quite satisfactorily by using the simplified form of Crank model. It should be assumed that as a result of the rapid initial adsorption stage, the outer part of the granules becomes an adsorbate reservoir providing constant conditions for adsorbate penetration inside the granules. The standard deviation of concentration for the simplified Crank model decreased 3–5 times compared to the full IDM model. In turn, the obtained values of parameter D/r2 of the order 10−3–10−5 are acceptable, while those determined on the basis of the full model IDM were unsatisfactory. Nevertheless, nonlinearity of experimental data in the initial range in c ∼ t1/2 coordinates (linearity is the fundamental assumption of all variants of the Crank model) proves that this model is not suitable for the description of the adsorption process for the studied systems
In practice, a somewhat better choice was the McKay model (pore diffusion model) [31]. It additionally takes into account a resistance during adsorbate transfer through adsorbent surface layer and assumes that the adsorbate evenly penetrates the granules, and a clear boundary between an area in which adsorption equilibrium is established, and the one without adsorbate is formed:
Here,
As shown in Figure 20, the McKay model describes quite well the kinetics of experimental systems in the initial range, and it does not exhibit the same feature as the IDM model. The initial part of curve is a characteristic for typical adsorption systems. However, in the subsequent stage of experiment, one can see significant discrepancies between the model and data, because this model predicts that the system comes to equilibrium after a finite time (curve bend corresponds to reaching the equilibrium state). It is reflected in the increase of the standard deviations with time, inversely to the IDM model. It should be added that obtaining an acceptable optimization using the McKay model was associated with treating a parameter
Very good results in the analysis of the kinetic data were obtained for the multi-exponential equation (Figure 21). This equation describes kinetics as an independent parallel series of first-order processes or approximation of follow-up processes [8, 32, 33, 34]. Generally, the multi-exponential equation characterizes well enough the experimental systems with a heterogenous pore structure or a complex pore system with differentiated pore distribution. A mathematical form of the multi-exponential equation is as follows:
where
Both the experimental and optimized concentration profiles for the studied systems are presented in two coordinate systems: the relative concentration (
Analyzing the values of adsorption half-time and time needed to reach a nearby equilibrium state, one can state that the kinetics of studied pesticides on a given type of carbon material is relatively slow as a result of the micropore predominant contribution in the adsorbent structure. The kinetic curves for the selected adsorbates can be set from the fastest to the slowest ones in order: 2,4-CPP > MCPP > MCPA > 3-CPP > 2,4-D > 4-CPP. The differences are not very significant, but it is clearly noticeable that adsorption of compounds with hydrocarbon chain of propionic acid is faster compared to their homologs of acetic acid, i.e., 2,4-CPP > 2,4-D and MCPP > MCPA. This is undoubtedly a result of the increase of the hydrophobic interactions between the adsorbate and activated carbon surface (pHpzc ∼ 9.8). These interactions along with dispersive ones are the main mechanism of adsorption process in aqueous systems at fixed pH = 2. One can say that in the case of these pairs of compounds, differences in a length of the hydrocarbon chain (a molecule dimension as well) do not affect differentiation of the diffusion rate in the microporous structure of activated carbon. Completely reverse trend in the adsorption capacity for these compounds determined on the basis of equilibrium isotherms was observed. The shorter hydrocarbon chain of adsorbate, the greater adsorption capacity for a given compound due to possibility of greater packing in the adsorbent structure.
Additionally a comparison of the adsorption kinetics for the studied systems is presented as spectrum of m-exp optimized parameters in the coordinate system: the adsorbed amounts
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