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We investigated the adsorption to granular activated carbon of two pharmaceuticals (carbamazepine and sildenafil citrate) and a personal-care product (methylparaben) in aqueous solution, characterized the carbon, and evaluated its influence on the kinetics and adsorption equilibrium of the compounds under study. We adjusted data for the analysis of equilibrium to Langmuir and Freundlich models of adsorption isotherms and described adsorption rate using pseudo first- and second-order models; that same analysis was made on the basis of the behavior of the initial rate. In addition, we analyzed the potentiality of a nonlinear adjustment for studying kinetics and equilibrium of adsorption, an approach requiring neither knowledge of equilibrium conditions nor a-priori hypothetical suppositions regarding the order of reaction. The results indicated that the nonlinear model was capable of describing adsorption kinetic behavior, in order to determine concentrations adsorbed at equilibrium, adsorption rates of the system, maximum adsorption capacity, and global rate constant. Granular carbon exhibited an adsorption capacity for carbamazepine and methylparaben of ca. 323 mg/g and for sildenafil citrate of ca. 142 mg/g, though with slow adsorption kinetics characterized by average adsorption times of at least 168 h.

Because of the current habits of consumerism in our society, a succession of contaminants have gone on accumulating in the environment whose presence has managed to escape attention until only a few years ago. These contaminants, referred to as emergent, are compounds of different origins and chemical natures; among which can be cited pesticides, hormones, drugs resulting from abuse, pharmaceuticals, and commercial products for personal hygiene or care [

Among those procedures, the technology of adsorption onto activated carbon― owing to its large specific surface, its micropore structure and high adsorption capacity― offers a great potential for its use within the system of treatment for removal of traces of emergent contaminants [

Within the information on the adsorption capacity, an understanding of the concentration of adsorbate at equilibrium (q_{e}), the maximum adsorption capacity (q_{m}), the apparent rate constants (k_{1} or k_{2}), the global rate constant (K), and the coverage fraction are essential in order to have a complete panorama of the adsorption kinetics and equilibrium. In the present investigation, we studied those processes through a nonlinear-regression analysis of the experimental information that obviated the hypothesis of pseudo first- and second-order kinetics, allowing us to resolve certain limitations of the classical models where hypotheses are proposed to consider the type of kinetics describing the system. Thus, the most fundamental parameters of the equations describing the adsorption arise without postulating any previous supposition, as will be discussed in detail below.

In the work reported here, we studied the kinetics and equilibrium of adsorption onto commercial granular activated carbon of three emergent contaminants: methylparaben (Mp), carbamazepine (Cbz), and sildenafil citrate (Sil); those selected as being representative of such pollutants in wastes within the environment [

The commercial granular-activated-carbon mesh-29 used had a surface area of 956 m^{2}/g, a pore size of 20 Å, a mean diameter of 1 mm, and a pore volume of 0.46 cm^{3}/g, as evaluated from Brunauer-Emmett-Teller (BET) measurements. The adsorbates used were two pharmaceuticals, Cbz and Sil, and a personal-care product, Mp, of pharmacopeia quality (Parafarm Drugstore, Saporiti, Argentina).

To determine the working mass of carbon to be used, batch experiments were maintained at a constant concentration of 5 mg/L for each separated sample in a fixed volume of 50 mL and varying quantities of activated carbon: 5, 25, 50, 100 and 200 mg,

Properties^{a } | Carbamazepine | Sildenafil citrate | Methylparaben |
---|---|---|---|

Molecular structure | |||

Cs | C_{15}H_{12}N_{2}O | C_{28}H_{38}N_{6}O_{11}S | C_{8}H_{8}O_{3} |

CAS | 298?46?4 | 171599?3?0 | 99?76-3 |

Mw (g/mol) | 236.09 | 666.70 | 152.05 |

Ws (mg/L) a 25˚C | 18 | 3500 | 2500 |

pKa | <2.3; >13.9 | 4; 5.5; 8.8 | 8.4 |

Log P | 2.45 | 2.70 | 1.96 |

H (atm-Cu m/mol) | 1.08 × 10^{−7} | 7.2 × 10^{−21} | 2.23 × 10^{−9} |

Calculations with the program Hiperchem | |||

Log P | 1.95 | 0.78 | 1.49 |

Surface area (Å^{2}) | 300.13 | 694.53 | 313.16 |

Molec. volume (Å^{3}) | 686.20 | 1303.37 | 488.48 |

a. Abbreviations used: Cs, chemical structure; CAS, Chemical Abstracts Service registry number; Mw, molar weight; Ws, water solubility; pKa, negative logarithm of the ionization constant of an acid; log P, partition coefficient; H, Henry`s constant.

then defining a working mass of 5 mg. Based on these results, to study kinetics and adsorption equilibrium, eight samples were prepared with 5 mg of adsorbent added to 50 mL of distilled water with sodium acid (0.01% as a antimicrobial agent) [

The quantities of the PPCPs adsorbed onto activated carbon were calculated as:

where q_{t} is the quantity (in mg/g) of PPCP adsorbed at time t, C_{0} the initial concentration (in mg/L), C_{t} the concentration (mg/L) remaining in solution at time t, V (L) the volume of the solution, and W (g) the weight of carbon used.

We used the models of Langmuir in Equation (2) and of Freundlich in Equation (3) for adjustment of the data of the adsorption isotherms by means of the following expressions:

where C_{e} is the concentration of adsorbate (in mg/L), at equilibrium, q_{e} the amount adsorbed per unit mass of adsorbent at equilibrium (in mg/g), q_{m} the maximal adsorption in the active-carbon monolayer, and K_{L} the adsorption constant at equilibrium (in L/mg) for the Langmuir model, it being related to the energy of adsorption. K_{F} is the equilibrium constant for the model of Freundlich and is related to the affinity between the adsorbent and the adsorbate; and if 1/n is 1, the adsorption is favorable.

We investigated the adsorption kinetics utilizing the pseudo-first-order model in Equation (4) and the pseudo second-order one in Equation (5). Those two linear equations for rate are the following:

where q_{t} and q_{e} are the mass (in mg) of adsorbate adsorbed per gram of adsorbent at time t and at equilibrium, respectively; k_{1} the apparent-rate constant for the pseudo- first-order equation; and k_{2} the rate constant for the pseudo second-order equation.

Two factors are important in the adsorption of the selected compounds. In fact, the adsorption of these PPCPs is a slow process. Therefore, for the practical point of view, a minimal quantity of activated carbon is required to allow the kinetic evaluation within a reasonable time window, and to assure the reproducibility of the experimental results. Thereby, a mass of 5 mg of activated carbon was selected for this study.

The pH before and after of the adsorption processes ranged between 6.4 - 6.6 for Cbz, 6.2 - 6.4 for Sil, 6.4 - 6.5 for Mp and 6.4 - 6.6 for the control solution with no PPCPs, showing no significant variations between tests and control. No noticeable adsorption on glass walls was registered according our tests with PPCPs solutions with no carbon. Additionally, no statistical differences were observed in treatments with and without methanol assessed by means of a t-test comparison.

The study of adsorption isotherms were analyzed with the Langmuir equation that accurately adjusted according to the data obtained (cf. _{e} obtained in the adsorption curves for the three compounds (cf.

The equilibrium concentration q_{e} is also required to analyze the adsorption kinetics; however, this was not possible for most of our results, as shown in _{e}, nevertheless, the

Langmuir | Freundlich | |||||
---|---|---|---|---|---|---|

K_{L} (L/mg) | q_{m} (mg/g) | R^{2} | K_{F} (mg/g) | 1/n | R^{2} | |

Mp | 0.3 ± 0.1 | 194 ± 17 | 0.90 ± 0.05 | 66 ± 12 | 0.32 ± 0.08 | 0.8 ± 0.2 |

Cbz | 0.5 ± 0.3 | 174 ± 54 | 0.93 ± 0.05 | 70 ± 3 | 0.28 ± 0.06 | 0.8 ± 0.1 |

Sil | 0.1 ± 0.1 | 114 ± 70 | 0.70 ± 0.40 | 19 ± 12 | 0.40 ± 0.30 | 0.7 ± 0.6 |

error of this evaluation becomes greater in the solutions of lower concentration, which complicates evaluating whether the kinetics follow any of the expressions described in Equation (4) and Equation (5).

At concentrations of 40 mg/L, methylparaben is the only compound which reached equilibrium as shown in the _{1}) of 0.026 ± 0.010 /h, 0.026 ± 0.020/h and 0.028 ± 0.020/h, and the equilibrium adsorptions were 160 ± 25 mg/g, 167 ± 23 mg/g and 164 ± 32 mg/g for initial concentrations of 30 mg/L, 35 mg/L and 40 mg/L, respectively.

Different approaches have been taken into account by several authors to study the adsorption kinetics of a contaminant dissolved in an aqueous system. The process has been explained by means of pseudo first and second order kinetics [_{e}.

The adsorption kinetics was studied considering a reversible process. If θ is the surface coverage fraction at the time t, and C is the concentration of the adsorbate in the solution, the rate of adsorption is given by the difference between the adsorption rate and desorption rate as follows

If C_{0} is the initial concentration (in mg/L), k_{a} and k_{d} the adsorption and desorption rate constants, then the remainder concentration C can be written as C = C_{0} − bq where bq is the adsorbed concentration and β has units of mg/L (see annex: evaluation of β).

After introducing C = C_{0} − bq in the Equation (6) and regrouping, the following expression can be obtained

Redefining as

Developing the integration [

Equation (9) can be analyzed by nonlinear regression and for convenience we will define the magnitudes A = q_{e}, B = λ, and C = e^{τ}.

The values for the parameter C obtained for each datum studied in the present work were much greater than 1. Therefore, in Equation (9) if

In Equation (10), λ represents the rate constant k_{1}, according to Equation (4).

Furthermore, since A = q_{e} (_{e} = q_{e}/q_{m} and by rearranging of terms, now the Equation (7) results in the following (see annex: evaluation of q_{m})

A linear dependence is observed between 1/q_{e} and 1/C_{0}, from which the maximum adsorption capacity (q_{m}) and the global equilibrium constant (K) values are obtained through the intercept and slope, respectively. The results are presented in

C_{0} | Mp | Cbz | Sil | |||
---|---|---|---|---|---|---|

A | B | A | B | A | B | |

5 | 45 ± 11 | 0.011 ± 0.004 | 47 ± 8 | 0.005 ± 0.001 | 33 ± 18 | 0.003 ± 0.008 |

10 | 87 ± 9 | 0.012 ± 0.003 | 91 ± 11 | 0.006 ± 0.002 | 53 ± 29 | 0.004 ± 0.002 |

15 | 114 ± 40 | 0.012 ± 0.010 | 120 ± 16 | 0.006 ± 0.002 | 66 ± 7 | 0.005 ± 0.001 |

20 | 141 ± 23 | 0.017 ± 0.002 | 155 ± 14 | 0.007 ± 0.002 | 84 ± 28 | 0.004 ± 0.002 |

25 | 151 ± 7 | 0.026 ± 0.006 | 168 ± 36 | 0.006 ± 0.001 | 90 ± 17 | 0.005 ± 0.002 |

30 | 158 ± 18 | 0.029 ± 0.013 | 165 ± 53 | 0.008 ± 0.001 | 83 ± 39 | 0.005 ± 0.002 |

35 | 166 ± 44 | 0.032 ± 0.019 | 175 ± 27 | 0.009 ± 0.004 | 106 ± 29 | 0.006 ± 0.003 |

40 | 160 ± 28 | 0.032 ± 0.025 | 163 ± 12 | 0.010 ± 0.003 | 95 ± 80 | 0.006 ± 0.002 |

C_{0} = initial concentration (mg/L); A = q_{e} in (mg/g) and B = λ = k_{1} in (1/h).

Sample | K (L/mg) | q_{m} (mg/g) | R^{2} | Slope = k_{a} | Intercept = k_{d} | R^{2} |
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Mp | 0.04 ± 0.02 | 322 ± 138 | 0.98 ± 0.02 | 7.2 × 10^{−4} | 5.1 × 10^{−3} | 0.9195 |

Cbz | 0.04 ± 0.03 | 325 ± 170 | 0.98 ± 0.01 | 1.2 × 10^{−4} | 4.6 × 10^{−3} | 0.8353 |

Sil | 0.07 ± 0.08 | 142 ± 68 | 0.86 ± 0.30 | 2.3 × 10^{−4} | 4.5 × 10^{−3} | 0.9003 |

Furthermore, the analysis of the parameter B as a function of C_{0} exhibits a linear behavior (_{d} and the slope the constant of adsorption k_{a}, as listed in

With the calculated value of q_{m}, the parameter β can be evaluated and defined as (see annex: Evaluation of β)

where m_{c} is the mass (g) of sorbent, q_{m} is the maximum capacity of sorbent, and V is the volume of solution (L).

This parameter permits discrimination between a kinetic of pseudo first order and one of pseudo second order. Then, if_{t}/q_{m}, the system will be described by a pseudo first order equation; but if βθ ≈ C_{0}, then a kinetics of pseudo second order is expected.

Another alternative for analyzing the behavior of the system is based on an analysis of the initial rate [_{t} versus t (

C_{0} (mg/L) | Mp | Cbz | Sil |
---|---|---|---|

5 | 3.9 ± 0.4 | 3.9 ± 1.0 | 2.0 ± 0.0 |

10 | 7.6 ± 0.2 | 7.9 ± 2.0 | 4.0 ± 2.0 |

15 | 9.1 ± 1.9 | 10.0 ± 1.0 | 5.0 ± 2.0 |

20 | 13.6 ± 2.0 | 14.0 ± 1.0 | 6.0 ± 1.0 |

25 | 15.2 ± 0.7 | 14.0 ± 3.0 | 7.0 ± 0.0 |

30 | 16.1 ± 2.3 | 15.0 ± 5.0 | 6.0 ± 3.0 |

35 | 16.8 ± 2.4 | 16.0 ± 4.0 | 9.0 ± 3.0 |

40 | 16.5 ± 3.3 | 16.0 ± 2.0 | 9.0 ± 8.0 |

*βθ (mg/L).

represents the slope of a straight line passing through the origin. Therefore, this behavior strongly suggest a pseudo first order kinetic, consistent with the analysis developed previously (Annex, Section: Analysis of the parameter λ) and

If in Equation (9), q_{t} is derived respect to time, the Equation (13) is obtained and then the rate of adsorption at a given time can be determined as shown in the annex (Expression of the rate of adsorption in terms of the model) and

where

The limit as t → 0 gives the expression for the initial rate (Equation (14)), as shown in

Sample | Experimental data | Theoretical data | ||||
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k (1/h) | Intercept | R^{2} | k (1/h) | Intercept | R^{2} | |

Mp | 0.109 | 0.307 | 0.858 | 0.127 | −0.067 | 0.916 |

Cbz | 0.033 | 0.177 | 0.961 | 0.040 | 0.124 | 0.966 |

Sil | 0.016 | 0.044 | 0.926 | 0.014 | 0.071 | 0.908 |

As it can be seen in

In the example of Mp, concentrations of 30 mg/L, 35 mg/L and 40 mg/L, did not show significant differences between data obtained from the different models―i.e., pseudo-first-order, nonlinear, initial rate by means of experimental data and the theoretical treatment. These considerations allow working on the basis of these models by combining the Equations (9) and (14) to evaluate the order of the kinetics. This non lineal model can be useful because, in certain studies [

Maximum adsorption capacity for Cbz and Mp according the non-lineal regression analysis is approximately 300 mg/g. Similar results were reported for the adsorption of Cbz onto the granular activated carbon obtained from peach seeds [

In the present work we performed studies on the kinetics and equilibrium of adsorption onto granular activated carbon for the purpose of demonstrating the viability of that technique for the elimination of three representative emergent contaminants―Mp, Cbz, and Sil―from aqueous solutions. The granular activated carbon used exhibited a high adsorption capacity for the three compounds at about 300 mg/g for Mp and Cbz and 150 mg/g for Sil (this molecule doubles the surface area respect the two others), but with a slow adsorption kinetics that required mean adsorption times of more than 168 h for the compounds to eventually reach equilibrium in the following order of completion: Mp < Cbz < Sil (

The adjustment of the nonlinear model proposed in Equation (9) allows the evaluation of the parameters of the adsorption kinetics, specifically q_{e} and q_{m}, employing experimental results in those system where the adsorption does not attain the saturation equilibrium. On the basis of this model, we determined that the parameter βθ was much lower than C_{0}, and hence the adsorption follows a pseudo first order kinetics. Suppositions on the kinetic order of adsorption or an analysis by trial and error test were not required.

From the knowledge of the adjustment of the data provided by Equation (9), an equation for the initial rate of adsorption can be deduced and compared with the experimental results under the previous analysis that showed that βθ = C_{0} as seen in

The results presented in this study have enabled us to obtain valuable information on the interaction of emergent contaminants with a commercial activated carbon. The use of granular carbon in water treatment plants for PPCPs removal should contemplate the slow adsorption rate at the moment of designing a reactor employing this material. To enhance the efficiency of removal further technology design of adsorption devices or combined technological approaches should be taken into account.

Dr. Donald F. Haggerty, a retired academic career investigator and native English speaker edited the final version of the manuscript. Funds were from PICT 2014 0919 Project from the Agencia Nacional de Promoción Científica y Tecnológica and Project X733 from the Universidad Nacional de La Plata.

Delgado, N.Y., Capparelli, A.L., Marino, D.J., Navarro, A.F., Peñuela, G.A. and Ronco, A.E. (2016) Adsorption of Pharmaceuticals and Personal Care Products on Granular Activated Carbon. Journal of Surface Engineered Materials and Advanced Technology, 6, 183-200. http://dx.doi.org/10.4236/jsemat.2016.64017

Considering the adsorption kinetics as a reversible process for a regent Z on a solid S

The adsorption rate can be expresses as seen in Equations (6) and (7). The magnitude b is required in order to analyze the adsorption kinetics.

As defined in the text, C is the concentration of the adsorbate in the solution at time t; which can be written as given by

βθ is the adsorbed concentration of the substrate, where the parameter β expresses the moles adsorbed per volume unit (mol/L). At the adsorption equilibrium b can be expressed in terms of θ_{e} (i.e. coverage fraction at equilibrium) and C_{e} (i.e. concentration of the adsorbate at equilibrium). Then, C_{e} = C_{0} − βθ_{e} and β = (C_{0} − C_{e})/θ_{e}.

Therefore β can be evaluated in terms of experimental data as

where m_{c} is the mass (g) of sorbent, q_{m} is the maximum capacity of sorbent, M_{w} is the molar weight of solute (g/mol) and V is the volume of solution (L).

We have seen that

As seen in the literature [

Renaming the terms in the previous equation as

Applying the antilogarithm and reorganizing the last equation, the following expression can be obtained for θ

Taking ε as a common factor in the numerator, q is given now by Equation (A6)

At the equilibrium (t → ∞), θ_{e}→ −ε/2a and knowing that e^{τ} = γ/ε; the following equation is obtained

The factors from the previous equation can be written in terms of the parameters evaluated experimentally. If θ = q_{t}/q_{m} and θ_{e} = q_{e}/q_{m}, so θ/θ_{e} = q_{t}/q_{e} and by rearranging, the Equation (A8) is obtained

Where q_{t}, q_{e} and q_{m} are the coverage at the time t, at the equilibrium and at the surface saturation, respectively. The parameters q_{t}, q_{e} and q_{m} are expressed in milligrams of sorbate adsorbed per gram of activated carbon.

By replacing:_{t} can be written in a simplified expression which can be analyzed by regression analysis in order to obtain the relevant parameters (see Equation (9) in the text).

Then, plotting q_{t} vs t the regression parameters A, C, and B can be calculated. Results for A and B are listed in

As far as C 1 in our system, the following expression can be deduced

Reorganizing,

Therefore, this expression is compatible with a first order kinetics if we identify l with pseudo first order rate constant k_{1} (See Equation 4 in the text).

Similarly, q_{e} values are obtained from the non-lineal regression analysis (Equation (9) in the text). As far as the C_{0} βθ at lower q, the term βθ can be ignored in the Equation (7). Then, this equation can be written as

_{m}

At equilibrium, dθ/dt = 0, and q_{t} becomes q_{m}. The adsorption equilibrium constant K is now = k_{a}/k_{d}. From Equation (7) we obtain q_{e}. Therefore, under the previous assumptions, Equation (A13) is obtained

Knowing that θ_{e} = q_{e}/q_{m} we obtain

From the plot of 1/C_{0} vs 1/q_{e}, the values q_{m} and K are calculated.

The theoretical expression for q_{t} obtained previously, _{t}/dt is the rate of adsorption as a function of time. This rate can be written as follow:

Applying the distributive property

This equation takes a very simple form introducing the parameters

Then, the adsorption rate as a function of time is given by Equation (A17)

The initial rate expressionν_{0} is obtained by analyzing the last equation in the limit of

t → 0

As far as C 1, the initial rate of adsorption can be written as follow

This theoretical rate can be tested against the experimental values obtained from the slope of a straight line passing through the origin on the adsorption curve at t = 0 (see