Activated Carbons as Effective Adsorbents of Non-Steroidal Anti-Inflammatory Drugs

Abstract

In this study, the adsorption of naproxen sodium, ibuprofen sodium, and diclofenac sodium on activated carbon is investigated. Comprehensive studies of adsorption equilibrium and kinetics were performed using UV-Vis spectrophotometry. Thermal analysis and zeta potential measurements were also performed for pure activated carbon and hybrid materials (activated carbon–drug) obtained after adsorption of naproxen sodium, ibuprofen sodium, and diclofenac sodium. The largest amount and rate of adsorption was demonstrated for naproxen sodium. A significant impact of temperature on the adsorption of the tested salts of non-steroidal anti-inflammatory drugs was also indicated. Faster kinetics and larger amounts of adsorption were recorded at higher temperatures. Thermodynamic parameters were also determined, based on which it was indicated that adsorption in the tested experimental systems is an endothermic, spontaneous, and thermodynamically privileged process of a physical nature. The generalized Langmuir isotherm was used to study the equilibrium data. The adsorption rate data were analyzed using numerous adsorption kinetics equations, including FOE, SOE, MOE, f-FOE-, f-SOE, f-MOE, and m-exp.

1. Introduction

The rapid growth of the pharmaceutical industry and the increase in sales of medicinal products have resulted in these types of substances appearing in industrial and municipal sewage, as well as in surface waters. Non-steroidal anti-inflammatory drugs (NSAIDs) are undoubtedly one of the most commonly used drugs today. They are mainly used symptomatically to combat fever and pain of various origins and severity. It should be added that many NSAIDs belong to the OTC group (over-the-counter drugs available without a prescription), which also adds to the widespread use of these pharmaceuticals. The most common source of this type of pollution is sewage from households, hospitals, clinics, or drug-producing factories. An interesting but, at the same time, quite problematic feature of these substances is their solubility in water, which may prove disastrous for living organisms during long-term exposure [1,2]. When released into the environment, nontoxic, non-steroidal anti-inflammatory drugs may adsorb on the surfaces of solid particles, such as soil or sediment, located at the bottom of tanks. This is both an advantage and a disadvantage. On the one hand, after adsorption, the bioavailability of problematic substances decreases, and on the other, sorption may lead to bioaccumulation and then to the slow but progressive release of the drug into the environment [3]. NSAIDs in water pose a serious threat to all trophic levels of food chains due to their ability to accumulate. As a result of the long-term action of these drugs, they have an adverse effect on so-called “non-target” organisms. The effects of chronic toxicity may include developmental, metabolic, and reproductive disorders [4,5,6,7].

Therefore, developing effective methods for removing these types of contaminants from water and sewage is not only of interest to scientists but is an absolute necessity. Currently, adsorption methods based on activated carbon as an adsorbent find applications in water and sewage treatment processes [8]. Carbon materials are characterized by high sorption capacity toward many pollutants, in particular, aromatic organic compounds, and demonstrate high chemical and thermal resistance. Moreover, they are characterized by non-toxicity, a highly developed porous structure, and low production costs, which encourage their use. Of course, the efficiency of removing pollutants from aqueous solutions is influenced by a number of factors that relate not only to the properties of the adsorbent but also to the characteristics of the adsorbate (e.g., solubility, particle diameter, pKa, and charge) as well as the adsorption conditions (e.g., pH, temperature, mixing speed, and the presence of accompanying substances) [8,9,10,11,12,13,14,15].

The aim of the presented manuscript is to investigate the adsorption of sodium salts in non-steroidal anti-inflammatory drugs, i.e., naproxen sodium, ibuprofen sodium, and diclofenac sodium, on activated carbon. As part of a comprehensive analysis, equilibrium and adsorption kinetics measurements were conducted using UV-vis spectrophotometry. The adsorption processes were carried out at different temperatures: 15, 25, and 35 °C and 25 and 35 °C for equilibrium and adsorption rates, respectively. The equilibrium data were analyzed using the generalized Langmuir isotherm, which describes adsorption on energetically heterogeneous solids. Adsorption rate data were analyzed using simple kinetic equations: first- (FOE) and second- (SOE) order, 1,2-mixed-order MOE, fractal-like MOE (f-MOE), fractal-like FOE (f-FOE), fractal-like SOE (f-SOE), and multi-exponential (m-exp). Thermal analysis and zeta potential measurements were also performed for pure activated carbon and hybrid materials (activated carbon–drug) obtained after adsorption of naproxen sodium, ibuprofen sodium, and diclofenac sodium. Obtaining high-quality adsorption amount and rate data (kinetic curves consisting of at least seventy experimental points) and their detailed analysis using multiple equations and models of adsorption equilibrium and kinetics, as well as additional studies of thermal stability and electrokinetic potential enabled detailed information on the mechanism of adsorption of non-steroidal anti-inflammatory drugs on activated carbon.

2. Materials and Methods

2.1. Chemicals

Sodium salts of therapeutic agents, such as ibuprofen sodium (IBP; Fluka, Mumbai, India), diclofenac sodium (D; Sigma, Beijing, China), and naproxen sodium (NPX, Sigma, Beijing, China), were used as adsorbates for testing. The basic physicochemical properties of these substances are presented in

Table 1. Selected physicochemical properties of tested non-steroidal anti-inflammatory drugs [16,17].

Adsorbate	Chemical Formula	Molar Mass [g/mol]	Solubility in H2O [mg/L at 25 °C]	Ionization Constant pKa	Melting Point [°C]	Boiling Point [°C]	Chemical Safety
Ibuprofen Sodium		228.26	100	4.91	75–77	319.6	Corrosive Irritant Health Hazard
Naproxen Sodium		252.24	76	4.15	250–251	403.9	Irritant Health Hazard
Diclofenac Sodium		318.13	50	4.15	288–290	412	Acute Toxic Irritant Health Hazard Environmental Hazard

.

GAC 1240W activated carbon (GAC), purchased from Norit (Utrecht, The Netherlands), was selected as the adsorbent for the experiment. The reason for this is that this adsorbent is widely used in water treatment plants [8,18,19]. Its textural properties were studied using low-temperature nitrogen adsorption/desorption isotherms. Based on the results of these tests, the basic structure parameters were estimated—specific surface area S_BET = 900 m²g⁻¹, external surface area S_EXT = 523 m²g⁻¹, total pore volume V_t = 0.52 cm³g⁻¹ including micropore volume V_mic = 0.20 cm³g⁻¹ using the t-plot method and the average hydraulic pore size d_h = 2.31 nm from the relationship d_h = 4V/S. Potentiometric titration was used to estimate the acid–base properties of GAC. Based on the obtained test results, the zero charge point pH_PZC was determined to be 10.8 [8].

2.2. Methods

2.2.1. Adsorption Equilibrium

Equilibrium adsorption measurements of ibuprofen, diclofenac, and naproxen sodium salts on activated carbon were carried out. The amount of adsorption was determined by using the following procedure. Initially, in order to remove physically adsorbed water, the GAC was dried at 110 °C for 16 h. Then, a series of the GAC weights were prepared, and the sediment was placed in an Erlenmayer flask and contacted with IBP, D, and NPX solutions. The prepared systems were mixed for 7 days in an incubator shaker (New Brunswick Scientific, Edison, NJ, USA) at a speed of 110 rpm at 15 °C, 25 °C, and 35 °C. Next, the solutions were decanted. Using a Cary 4000 UV-Vis spectrophotometer (Varian Inc., Belrose, Australia), absorption was analyzed in the wavelength range of 200–450 nm against redistilled water as a reference. The absorption maximum was observed at wavelengths of 222, 276, and 271 nm for IBP, D, and NPX, respectively. The amount of adsorption was calculated using the material balance:

$${\mathrm{a}}_{\mathrm{e}\mathrm{q}}=\frac{\left({\mathrm{c}}_0-{\mathrm{c}}_{\mathrm{e}\mathrm{q}}\right)·\mathrm{V}}{\mathrm{m}}$$

(1)

where a_eq—relative adsorption, c₀—initial concentration, c_eq—equilibrium concentration, V—solution volume, m—adsorbent mass [20,21].

The received equilibrium data were fitted by using the Marczewski–Jaroniec (M-J) isotherm, which is most often called the generalized Langmuir (GL) isotherm. This isotherm perfectly describes the adsorption processes from solutions onto energetically heterogeneous solids:

$$\mathsf{\theta }={\left[\frac{{\left(\overline{\mathrm{K}}·{\mathrm{c}}_{\mathrm{e}\mathrm{q}}\right)}^{\mathrm{n}}}{{1+\left(\overline{\mathrm{K}}·{\mathrm{c}}_{\mathrm{e}\mathrm{q}}\right)}^{\mathrm{n}}}\right]}^{\frac{\mathrm{m}}{\mathrm{n}}}$$

(2)

where θ—relative adsorption (surface coverage), θ = a/a_m, m, n—heterogeneity parameters (0 < m, n ≤ 1), K—the adsorption equilibrium constant related to the characteristic energy of the energy distribution function. The GL isotherm can be reduced to the equations of other isotherms: the generalized Freundlich isotherm (GF; n = 1), Langmuir–Freundlich (LF; m = n), Tóth (T; m = 1), and Langmuir (L; m = n = 1) [22,23].

2.2.2. Adsorption Kinetics

The adsorption rate tests were performed with a flow cell, which allows operation in a closed system (Cary 100 UV-Vis spectrophotometer, Varian Inc., Belrose, Australia). The initial concentration of pharmaceuticals was 0.298 mmol/L, and the mass of GAC was 0.05 g. The adsorption measurements were conducted in a thermostated double-walled vessel at 25 °C and 35 °C (Ecoline RE 207 thermostat (Lauda, Lauda-Königshofen, Germany)). The analyzed solution was stirred with a digitally controlled mechanical stirrer (IKA, Raszyn, Poland) at a speed of 110 rpm during the measurements. The applied adsorption rate testing methodology allowed for obtaining from 70 to 120 experimental points for one system.

Data on the adsorption rate of pharmaceuticals were analyzed using numerous equations and models of adsorption kinetics. The simplest of them is the first-order kinetic equation (FOE)/pseudo-first-order equation (PFOE), which has the form:

$$\mathrm{l}\mathrm{n}\left({\mathrm{c}}_{\mathrm{e}\mathrm{q}}-\mathrm{c}\right)=\mathrm{l}\mathrm{n}{(\mathrm{c}}_{\mathrm{e}\mathrm{q}}-{\mathrm{c}}_{\mathrm{o}})-{\mathrm{k}}_1$$

(3)

or

$$\mathrm{l}\mathrm{n}\left({\mathrm{a}}_{\mathrm{e}\mathrm{q}}-\mathrm{a}\right)=\mathrm{l}\mathrm{n}{\mathrm{a}}_{\mathrm{e}\mathrm{q}}-{\mathrm{k}}_1\mathrm{t}$$

(4)

where c—temporary concentration, a—actual adsorbed amount, the “o” and “eq” indices correspond to the initial and equilibrium values, and k₁—adsorption rate coefficient [24,25].

• The next uncomplicated relation is the second-order equation (SOE)/pseudo-second-order equation (PSOE). It is expressed in the following form:

  $$\mathrm{a}={\mathrm{a}}_{\mathrm{e}\mathrm{q}}\left[{\mathrm{k}}_2\mathrm{t}/\left(1+{\mathrm{k}}_2\mathrm{t}\right)\right]$$

  (5)

  or its linear forms:

  $$\mathrm{t}/\mathrm{a}=\left(1/{\mathrm{a}}_{\mathrm{e}\mathrm{q}}\right)\left(1/{\mathrm{k}}_2+\mathrm{t}\right)$$

  (6)

  and

  $$\mathrm{a}={\mathrm{a}}_{\mathrm{e}\mathrm{q}}-\left(1/{\mathrm{k}}_2\right)\left(\mathrm{a}/\mathrm{t}\right)$$

  (7)

  where k₂ = k_2aa_eq and k_2a are the rate coefficients for pseudo-second-order kinetics [25,26,27].
• Hereafter, the kinetic data were analyzed using a 1,2-mixed-order kinetic equation (MOE), which is a generalization of the first- and second-order kinetics. This dependence (mathematically) corresponds to a linear combination of first- and second-order units. The above-mentioned relationship might also be expressed as the relative progress of adsorption over time F.

  $$\mathrm{F}=\mathrm{a}/{\mathrm{a}}_{\mathrm{e}\mathrm{q}}=\frac{1-\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\mathrm{k}}_1\mathrm{t}\right)}{1-{\mathrm{f}}_2\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\mathrm{k}}_1\mathrm{t}\right)}$$

  (8)

  or

  $$\mathrm{l}\mathrm{n}\left(\frac{1-\mathrm{F}}{1-{\mathrm{f}}_2\mathrm{F}}\right)=-{\mathrm{k}}_1\mathrm{t}$$

  (9)

  where f₂ < 1—the normalized share of the second-order process in the kinetics. One should notice that in some cases, the MOE equation may be reduced to the first-order (f₂ = 0) and the second-order (f₂ = 1) kinetic equations [28,29].
• The kinetic data were also analyzed by applying a modified MOE equation that takes into account heterogeneity effects. The fractal-like MOE equation (f-MOE) can be presented as:

  $$\mathrm{F}=\frac{{1-\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\mathrm{k}}_1\mathrm{t}\right)}^{\mathrm{p}}}{{1-{\mathrm{f}}_2\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\mathrm{k}}_1\mathrm{t}\right)}^{\mathrm{p}}}$$

  (10)

  where p—fractal coefficient. Under particular conditions, the dependence can be reduced to the MOE (p = 0), f-FOE (f₂ = 0), and f-SOE (f₂ = 1) equations [30,31].
• The multi-exponential equation (m-exp) was also used for the specification of kinetic data. This relationship is often used to describe adsorption on heterogeneous solids and may indicate the occurrence of a series of first-order or subsequent processes. This can be written as:

  $$\mathrm{c}=\left({\mathrm{c}}_0-{\mathrm{c}}_{\mathrm{e}\mathrm{q}}\right){\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{f}}_{\mathrm{i}}\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\mathrm{k}}_{\mathrm{i}}\mathrm{t}\right)+{\mathrm{c}}_{\mathrm{e}\mathrm{q}}$$

  (11)

  or

  $$\mathrm{c}={\mathrm{c}}_0-{\mathrm{c}}_0{\mathrm{u}}_{\mathrm{e}\mathrm{q}}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{f}}_{\mathrm{i}}\left[1-\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\mathrm{k}}_{\mathrm{i}}\mathrm{t}\right)\right]$$

  (12)

  where “i”—the term of the m-exp equation. k_i—the rate coefficient. u_eq = 1 − c_eq/c₀—the relative loss of adsorbate from the solution [8,26].

2.2.3. Zeta Potential Measurements

The zeta potential was measured using a NanoZS Zetasizer (Malvern Instruments, Ltd., GB, Worcestershire, UK), which uses Laser Doppler Velocimetry to determine electrophoretic mobility. The electrophoretic mobility of the sample was recalculated into the zeta potential by means of the Smoluchowski equation. For the measurements, the universal dip cell, including an electrode assembly with palladium electrodes with 2 mm spacing, was used. The experiment was carried out in PCS1115 cuvettes. All the experiments were performed at 25 °C. To ensure maximum accuracy, each measurement was performed six times, and average values are presented in the manuscript.

2.2.4. Thermal Analysis

The thermal analysis was performed using a QMS 403D Aelos equipped with mass spectrometer STA449F1 Jupiter (Netzsch, Waldkraiburg, Germany) and TGA-IR Tensor 27 (Bruker). The samples of GAC and the hybrid materials after pharmaceutical adsorption were placed in an alumina crucible and heated at a speed of 10 °C/min in a wide temperature range of 30–950 °C. Measurements were carried out under an air atmosphere (flow rate of 25 mL/min).

3. Results

3.1. Adsorption Equilibrium

Figure 1 compares the adsorption isotherms of naproxen sodium, ibuprofen sodium, and diclofenac sodium on the GAC activated carbon at 15, 25, and 35 °C. Under the tested experimental conditions, the largest adsorption amount was noticed for NPX and the smallest for IBP. The reasons for this phenomenon are the different solubilities and molecular structures of the tested compounds. Substances that are, in general, less soluble in water are more hydrophobic, i.e., they have a better affinity for the lyophilic surface of the used adsorbent [8,21]. Among the tested adsorbates, ibuprofen sodium has the highest solubility in water, and diclofenac sodium has the lowest solubility in water. This means that IBP has the worst affinity for the lyophilic surface of GAC [6]. At the same time, D, despite its most hydrophobic character, has the largest particle size among the adsorbed substances selected for testing, which may hinder its adsorption to the microporous spaces of the adsorbent.

The equilibrium data were analyzed using the GL isotherm. All related parameters are presented in

Table 2. Parameters of the generalized Langmuir equation for the adsorption of ibuprofen sodium, diclofenac sodium, and naproxen sodium on GAC activated carbon.

System	Isotherm Type	am a	m b	n b	logK c	R2 d	SD(a) e
IBP/GAC_15 °C	T	0.50	1	0.77	2.57	0.939	0.042
IBP/GAC_25 °C	T	0.41	1	0.61	3.93	0.954	0.045
IBP/GAC_35 °C	T	0.31	1	0.17	8.45	0.909	0.085
D/GAC_15 °C	GF	0.59	0.36	1	0.36	0.955	0.048
D/GAC_25 °C	GL	0.48	0.54	0.61	0.64	0.985	0.033
D/GAC_35 °C	GF	0.39	0.37	1	0.16	0.902	0.088
NPX/GAC_15 °C	GF	0.64	0.39	1	−0.28	0.978	0.047
NPX/GAC_25 °C	GF	0.87	0.45	1	0.07	0.972	0.061
NPX/GAC_35 °C	GF	1.09	0.47	1	0.12	0.985	0.048

^a a_m—sorption capacity, ^b m, n—heterogeneity parameters, ^c logK—logarithm of the adsorption equilibrium constant, ^d R²—determination coefficient, ^e SD(a)—standard deviation.

. In systems with ibuprofen sodium, the heterogeneity parameter m is equal to 1, after which the GL isotherm is simplified to the T equation. For the D/GAC_25 °C system, the full GL isotherm equation was the best for its analysis. For the remaining systems, the heterogeneity parameter n is equal to 1, after which the GL isotherm reduces to the GF equation. Therefore, it can be concluded that medium heterogeneity effects were observed in the studied experimental systems. The adjustment values of the adsorption capacity are comparable with the experimental values. The quality of the fitting is very good, which is confirmed by the low value of standard deviations (SD(a) ranging from 0.033 to 0.088) and high determination coefficient values (R² ranging from 0.909 to 0.985).

Figure 2 compares the adsorption isotherms of ibuprofen sodium, diclofenac sodium, and naproxen sodium on GAC activated carbon at 15 °C, 25 °C, and 35 °C. Under the given experimental conditions, a clear impact of temperature on the amount of adsorption of these compounds was observed. It was shown that higher temperatures favor the sorption of IBP, D, and NPX, which indicates the endothermic nature of this process. It is also apparent that, in the case of sorption from solutions, the system is a three-component system, where an adsorbate, a solvent, and an adsorbent can be distinguished, which interact with each other. In the experimental systems tested, the adsorption mechanism is based mainly on dispersion interactions between π electrons from the aromatic rings of diclofenac sodium and π electrons from the graphene layers of GAC activated carbon. Additionally, hydrogen bonds can also be distinguished between solvent and adsorbate molecules, adsorbate/solvent molecules, and the surface groups. Interestingly, the strength of these forces changes with temperature. At higher temperatures, increased dehydration of both the molecules of sodium salts of drugs and the activated carbon grains occurs. This makes the adsorbate–water aggregates more flat, which allows them to penetrate the micropores of the adsorbent more easily. Moreover, there is also an increase in the dipole moment, which significantly intensifies the interactions between activated carbon and ibuprofen sodium, diclofenac sodium, or naproxen sodium [8,32,33].

Thermodynamic parameters were also determined, which are critical design variables for sorption and the characterization and optimization of this process. The Gibbs free energy ΔG°, enthalpy ΔH°, and entropy ΔS° were estimated from the relationship:

$$\ln \left(\mathrm{K}{\mathrm{c}}^{\mathrm{o}}\right)=\frac{∆{\mathrm{S}}^{\mathrm{o}}}{\mathrm{R}}-\frac{∆{\mathrm{H}}^{\mathrm{o}}}{\mathrm{R}\mathrm{T}}$$

(13)

where Kc°—equilibrium constant scaled with reference to standard conditions by using the standard concentration c° = 1 mol/L R—gas constant, T—temperature [8,34]. The obtained values of thermodynamic parameters are summarized in

Table 3. Thermodynamic parameters for the adsorption of ibuprofen sodium, diclofenac sodium, and naproxen sodium on GAC activated carbon.

System	ΔG° a [kJ/mol]	ΔH° b [kJ/mol]	ΔS° c [kJ/mol]
IBP/GAC_15 °C	−2.66
IBP/GAC_25 °C	−3.07	22.73	0.07
IBP/GAC_35 °C	−3.97
D/GAC_15 °C	−1.98
D/GAC_25 °C	−2.72	21.61	0.06
D/GAC_35 °C	−3.25
NPX/GAC_15 °C	−0.10
NPX/GAC_25 °C	−0.73	26.41	0.087
NPX/GAC_35 °C	−1.62

^a ΔG°—the Gibbs free energy, ^b ΔH°—enthalpy, ^c ΔS°—entropy.

.

It was observed that for all studied systems, the values of ΔG° were negative, which means that the adsorption processes were spontaneous and thermodynamically favored (Table 3). Moreover, it was noticed that ΔH° was positive, indicating that the sorption of ibuprofen sodium, diclofenac sodium, and naproxen sodium on GAC activated carbon is an endothermic process. Moreover, both the above-mentioned values indicate that physisorption occurred in the tested experimental systems (ΔH < 40 kJ/mol [35] and 0 < ΔG < 20 kJ/mol [36]). As one can see, the entropy value was also positive, which indicates that the number of degrees of freedom increased in the studied systems. This fact can also be referred to as the increase in disorder at the phase boundary in the sorption process.

3.2. Adsorption Kinetics

As part of a comprehensive analysis of the adsorption of ibuprofen sodium, diclofenac sodium, and naproxen sodium on GAC activated carbon, adsorption kinetics measurements were also performed.

Figure 3 shows a comparison of the kinetic curves of the experimental systems. It can be underlined that both at 25 °C and 35 °C, the highest adsorption rate (the fastest concentration loss and the fastest achievement of the equilibrium state) was recorded for naproxen sodium and the lowest for diclofenac sodium. The smaller dimensions of the NPX molecule compared to D and its greater hydrophobicity compared to IBP enabled highly effective and rapid adsorption of this drug on GAC activated carbon.

Figure S1 (Supplementary Material) shows a comparison of kinetic curves for the adsorption of naproxen sodium, ibuprofen sodium, and diclofenac sodium at different temperatures: 25 °C and 35 °C. A larger adsorption rate accompanying an increase in temperature was noticed. The observed phenomenon is a consequence of the larger kinetic energy of the elements present in the adsorption system and the increased dehydration of adsorbate molecules and adsorbent grains [8].

Figure S2 (Supplementary Material) presents the kinetic data in linear Bangham coordinates. This made it possible to initially determine the adsorption mechanism [37]. The graphs are practically linear, and their initial slopes, in the interval from 10 to 500 min, are 0.76–0.77, 0.76–0.84, and 0.78–0.80 for naproxen sodium, ibuprofen sodium, and diclofenac sodium, respectively. As is known, in the case of a pure intramolecular diffusion model (IDM), the slope is equal to 0.5. Therefore, it can be concluded that the adsorption of the tested pharmaceuticals on GAC can not be described using a diffusion model.

The obtained experimental data of the adsorption rate were estimated using numerous equations and models of adsorption kinetics. The relative deviations are listed in

Table 4. The relative standard deviations SD(c)/c_o (%) of m-exp, FOE, SOE, MOE, f-FOE, f-SOE, f-MOE equations for the adsorption of ibuprofen sodium, diclofenac sodium, and naproxen sodium on GAC activated carbon.

System	m-exp [%]	FOE [%]	SOE [%]	MOE [%]	f-FOE [%]	f-SOE [%]	f-MOE [%]
IBP/GAC 25 °C	0.526	2.568	3.191	1.145	0.683	2.584	0.664
IBP/GAC 35 °C	0.443	2.710	2.187	1.107	0.683	5.805	0.879
D/GAC 25 °C	0.335	2.771	3.276	1.499	0.620	2.615	0.520
D/GAC 35 °C	0.500	2.750	2.969	1.541	0.531	2.589	0.485
NPX/GAC 25 °C	0.695	3.242	2.407	1.360	0.829	2.336	0.778
NPX/GAC 35 °C	0.720	2.778	2.603	1.014	0.771	1.860	0.673

, which shows that the best quality of fitting is achieved for the multi-exponential equation and the fractal-like MOE equation, the parameters of which are presented in

Table 5. The optimized parameters of m-exp eq for the adsorption of ibuprofen sodium, diclofenac sodium, and naproxen sodium on GAC activated carbon.

System	f1 a, log k1 b	f2 a, log k2 b	f3 a, log k3 b	ueq c	t1/2 d [min]	SD(c)/co e  [%]	1 − R2 f
IBP/GAC 25 °C	0.071, −3.931	0.746, −3.206	0.183, −2.211	1	866.4	0.526	2.3 × 10−4
IBP/GAC 35 °C	0.051, −4.259	0.719, −3.010	0.230, −2.148	1	495.4	0.443	1.5 × 10−4
D/GAC 25 °C	0.568, −3.606	0.275, −3.249	0.157, −2.372	1	1562.4	0.335	9.4 × 10−5
D/GAC 35 °C	0.486, −3.445	0.368, −2.996	0.146, −2.112	1	902.9	0.500	2.2 × 10−4
NPX/GAC 25 °C	0.667, −3.006	0.333, −2.174	-	1	355.9	0.695	4.6 × 10−4
NPX/GAC 35 °C	0.647, −2.908	0.353, −2.150	-	1	286.7	0.720	4.9 × 10−4

^a f₁, f₂, f₃—the terms of m-exp equation, ^b log k₁, log k_2, log k₃—logarithm of the rate constant, ^c u_eq—the relative loss of adsorbate from the solution, ^d t_1/2—half-time, ^e SD(c)/c_o—relative standard deviation, ^f 1 − R²—indetermination coefficient.

(m-exp) and

Table 6. The optimized parameters of f-MOE eq for the adsorption of ibuprofen sodium, diclofenac sodium, and naproxen sodium on GAC activated carbon.

System	f2 a	p b	log k1 c	ueq d	t1/2 e  [min]	SD(c)/co f  [%]	1 − R2 g
IBP/GAC 25 °C	0.332	0.685	−3.03	1	830.7	0.664	3.7 × 10−4
IBP/GAC 35 °C	0.460	0.816	−3.12	1	471.8	0.879	6.0 × 10−4
D/GAC 25 °C	0.435	0.654	−3.19	1	1486.9	0.520	2.3 × 10−4
D/GAC 35 °C	0.388	0.666	−3.03	1	872.7	0.485	2.2 × 10−4
NPX/GAC 25 °C	0.336	0.785	−2.93	1	358.9	0.778	5.8 × 10−4
NPX/GAC 35 °C	0.440	0.839	−2.88	1	288.9	0.673	4.3 × 10−4

^a f₂—the normalized share of the second order process in the kinetics, ^b p—the fractal coefficient, ^c log k₁—logarithm of the rate constant, ^d u_eq—the relative loss of adsorbate from the solution, ^e t_1/2—half-time, ^f SD(c)/c_o—relative standard deviation, ^g 1 − R²—indetermination coefficient.

(f-MOE).

The adsorption of naproxen sodium, ibuprofen sodium, and diclofenac sodium on GAC activated carbon is a sophisticated process, the rate of which can be described by two (NPX) or three (IBP and D) terms of the multi-exponential equation (Table 5). Moreover, half-times t_1/2 were determined for all experimental systems tested. This parameter is the time it takes to achieve half the change in concentration. Thus, in this particular case, the loss of adsorbate from the solution is 100% (u_eq = 1), and the half-time will correspond to the time after which the pharmaceuticals concentration value was 0.5·c₀. The determined half-time values were 286.7–355.9, 495.4–866.4, and 902.9–1562.4 min for the adsorption of naproxen sodium, ibuprofen sodium, and diclofenac sodium, respectively. This confirms the largest adsorption rate for NPX and the smallest for D. What is more, it was noticed that the values of the t_1/2 parameter decreased with the increasing temperature, which certifies the greatest adsorption kinetics at 35 °C. The fitting quality is very good, which is attested by the low values of relative standard deviations 0.335% < SD(c)/co < 0.720% and low values of indetermination factors 9.4 × 10⁻⁵ < 1 − R² < 4.9 × 10⁻⁴.

Very good fitting quality was also obtained for the f-MOE equation. The estimated relative standard deviations ranged from 0.520% to 0.879%, and the coefficients of indetermination ranged from 2.2 × 10⁻⁴ to 6.0 × 10⁻⁴. The value of the f₂ parameter is estimated between 0.332 and 0.460 (Table 6), which indicates a greater contribution of first-order kinetics.

Marczewski et al. [18] proposed presenting the temperature dependencies of adsorption kinetics using half-time. Figure S3 (Supplementary Material) shows the logarithm of half-times on 1/T for naproxen sodium, ibuprofen sodium, and diclofenac sodium adsorption on GAC activated carbon at 25 and 35 °C. As can be seen, this relationship is practically linear and additionally confirms the fastest adsorption kinetics for naproxen sodium and the lowest for diclofenac sodium.

3.3. Zeta Potential Measurements

Figure 4 presents a comparison of the electrokinetic potential of pure GAC activated carbon as well as the hybrid materials containing the tested pharmaceuticals. As can be seen, the zeta potential of pure GAC activated carbon in the tested pH range is from +7.9 to –41.3 mV. The electrokinetic potential of activated carbon after adsorption varies under test conditions from +14.7 to −41.9 mV, from +11.5 to −41.9 mV, and from +8.3 to −37.8 mV for samples with NPX, IBP, and D, respectively. Additionally, it can be concluded that the zeta potential value is lower for samples after the adsorption of naproxen sodium, ibuprofen sodium, and diclofenac sodium. The observed decrease is the result of the presence of negatively charged sodium salts of the tested non-steroidal anti-inflammatory drugs originating from their dissociation. Moreover, the largest decrease in zeta potential was recorded for the sample with NPX, which confirms its highest efficiency of removal from solutions using activated carbon. The least visible effect was observed for the sample from D, which is probably caused by the presence of the -NH group in the diclofenac sodium molecule.

3.4. Thermal Analysis

The thermal stability of GAC, as well as the hybrid materials obtained after the adsorption of naproxen sodium, ibuprofen sodium, and diclofenac sodium, were analyzed. Figure 5 shows a comparison of the TG, DTG, and DSC curves for the tested samples, whereas

Table 7. The thermal decomposition data of pure GAC activated carbon and after ibuprofen sodium, diclofenac sodium, and naproxen sodium adsorption.

Sample		TG		DTG	DSC
	ΔT [°C]	Mass Loss [%]	Total Mass Loss [%]	Tmin [°C]	endo/exo
GAC	30–480	1.34	86.50	-	-
	480–930	85.16		653	exo
IBP/GAC	30–200	1.64	81.46	79.7	endo
	200–600	79.24		274.1 454.7	exo exo
				550.2	exo
	600–930	0.58		-	-
D/GAC	30–200	2.62	84.85	78.7	endo
	200–600	78.24		252.7 583.6	exo exo
	600–930	3.99		874.3	endo
NPX/GAC	30–200	3.49	81.79	81.6	endo
	200–600	77.44		266.6 516.6	exo exo
	600–930	0.86		-	-

presents data estimated on the basis of these curves (TG, DTG, and DSC).

It was noticed that the GAC activated carbon decomposition process occurs in two stages with a total weight loss of 86.50%. The first of them was in the 30–480 °C temperature range and with a weight loss of 1.34%. This can be attributed to the desorption of physically bound water and the removal of hydroxyl functional groups of the adsorbent [8]. The other step was registered in the 480–930 °C range with a weight loss of 85.16%. Here, an exothermic oxidation process of the sample was recorded at 653 °C [8].

In the case of activated carbon after pharmaceutical adsorption, the decomposition process takes place in three stages.

For GAC after the ibuprofen sodium adsorption system, the total weight loss in the studied temperature range was 81.46%. The first decomposition stage recorded in the 30–200 °C temperature range (weight loss of 1.64%) was endothermic, with a peak at 79.7 °C related to the desorption of physically adsorbed water and the initial degradation of IBP. In the next stage, at the 200–600 °C temperature range, with weight loss of 79.24%, the exothermic processes of further decomposition of ibuprofen sodium, dehydration and degradation of the GAC activated carbon took place. In this temperature range, the peak maximum was observed at the temperatures of 274.1, 454.7, and 550.2 °C, of which the most intensive was registered at the highest temperature given. The last stage occurred in the 600–930 °C temperature ranges, with weight losses of 0.58%, which can also be correlated with carbon combustion.

In GAC activated carbon after the diclofenac sodium adsorption system, the total weight loss in the examined temperature range was 84.85%. The first decomposition step registered in the 30–200 °C temperature range (weight loss of 2.62%) was endothermic, with the peak at 78.7 °C and corresponded to the desorption of physically adsorbed water and the initial degradation of the D. In the second step, at the 200–600 °C temperature range, with weight loss 78.24%, the exothermic processes of further decomposition of diclofenac sodium, dehydration and degradation of GAC occurred. In this temperature range, the peak maximum was recorded at 252.7 and 583.6 °C, which more intensive was registered at the highest temperature given. The third step, which appeared in the 600–930 °C temperature range, was endothermic (the peak maximum at 874.3 °C), with weight losses of 3.99%, which can also be correlated with the carbon combustion.

For activated carbon after naproxen sodium adsorption system, the total weight loss in the studied temperature range was 81.79%. The first decomposition step took place in the 30–200 °C temperature range (weight loss of 3.49%) and was endothermic, with a peak at 81.6 °C, which corresponded to the desorption of physically adsorbed water and the initial degradation of NPX. In the next stage, at the 200–600 °C temperature range, with weight loss of 77.44%, the exothermic processes of further decomposition of naproxen sodium, dehydration and degradation of GAC occurred. The peak maximum was observed at the temperatures of 266.6 and 516.6 °C, of which more intense was recorded at the highest temperature given. The last stage took place in the 600–930 °C temperature range, with weight losses of 0.86%, which can also be correlated with carbon combustion.

In summary, a larger total mass loss was observed for pure GAC activated carbon compared to samples after pharmaceutical adsorption. At the same time, it should be noted that intensive decomposition of pure carbon material occurred at 653 °C. For the postadsorption samples, it occurred at 454.7, 516.6, and 583.6 °C for the system with ibuprofen sodium, naproxen sodium, and diclofenac sodium, respectively. This means that pure GAC activated carbon is more resistant to high temperatures than after the sorption of pharmaceuticals.

4. Discussion

The adsorption of sodium salts of non-steroidal anti-inflammatory drugs, naproxen sodium, diclofenac sodium, and ibuprofen sodium, on GAC activated carbon is presented in the manuscript. As part of a comprehensive analysis of the process of removing pharmaceuticals from aqueous solutions, studies of the equilibrium and kinetics of adsorption at various temperatures were performed. The applied adsorption rate testing methodology made it possible to conduct research under strictly controlled conditions of temperature and mixing speed to obtain high-quality kinetic data. Each kinetic curve contained at least 70 experimental points. The use of numerous models and equations of adsorption kinetics and equilibrium to analyze data on the size and rate of sorption, as well as the estimation of thermodynamic parameters, allowed for a precise determination of the mechanism and nature of adsorption of NPX, IBP, and D on GAC activated carbon. Additionally, the study presents changes in the value of zeta potential and thermal stability of GAC due to the adsorption of selected pharmaceuticals. The literature on the subject contains many studies on similar subjects, but there is a clear lack of accurate and detailed equilibrium data and, in particular, adsorption kinetics.

Costa et al. [38] analyzed the adsorption of ibuprofen sodium and diclofenac sodium on activated carbons synthesized from murumuru waste. The adsorption isotherms were obtained at temperatures of 28, 35, and 45 °C. The kinetic curves were also obtained at ambient temperature, in a narrow time range, consisting of several experimental points. Baccar and colleagues [39] studied the adsorption of ibuprofen, ketoprofen, naproxen, and diclofenac on activated carbon obtained from olive waste. The equilibrium and adsorption kinetics studies were carried out at 25 °C. Moreover, sorption rate data were recorded for approximately 26 h and included several experimental points. Zhang et al. [40] studied the adsorption of ibuprofen on activated carbon (Radix Angelica Dahuricaresidue) over a wide temperature range at 20, 30, 40, 50, and 60 °C. Jedynak and colleagues [41] studied the adsorption of paracetamol, ibuprofen, and naproxen on ordered mesoporous carbons at 25 °C. Lach and Szymonik studied the adsorption of naproxen sodium [42] and diclofenac sodium [43] on commercially available activated carbons ROW 08 Supra, F-300, and WG-12. Isotherms at 20, 30, and 40 °C and kinetic curves (including several experimental points) at 20 °C were obtained. Yaneva [44] studied the equilibrium and kinetics of ibuprofen adsorption on green activated carbon at 25 °C. In the future, the adsorption process of other drugs from aqueous solutions should be optimized, for example, antibiotics, heart medications, and other non-steroidal anti-inflammatory drugs. Moreover, it is necessary to look for other adsorbents obtained from waste raw materials, which is in agreement with the principles of sustainable development and green chemistry.

5. Conclusions

Studies on the adsorption of sodium salts of non-steroidal anti-inflammatory drugs were carried out. The adsorption equilibrium studies were conducted at 15, 25, and 35 °C, while adsorption kinetics were studied at 25 and 35 °C.

The largest amount (adsorption value ranging from 0.61 to 0.98 mmol/g) and rate (half-time in a range from 286.7 to 355.9 min) of adsorption were demonstrated in the presence of naproxen sodium. Moreover, the lowest adsorption amount was observed in the system with ibuprofen sodium (adsorption value ranging from 0.26 to 0.45 mmol/g), and the slowest kinetics was recorded for diclofenac sodium (half-time in a range from 902.9 to 1562.4 min). This is the effect of different solubility and various molecular structures of the studied pharmaceuticals. Additionally, a strong influence of temperature on the adsorption of sodium salts of non-steroidal anti-inflammatory drugs was demonstrated. Higher adsorption amounts and rates were recorded at higher temperatures. This effect is the result of increased dehydration of both adsorbate molecules and adsorbent grains, which facilitates diffusion into the porous structure of the carbon material. The values of thermodynamic parameters confirmed the endothermic nature of naproxen sodium (ΔH°_15–35°C = 26.41 kJ/mol), ibuprofen sodium (ΔH°_15–35°C = 22.73 kJ/mol), and diclofenac sodium (ΔH°_15–35°C = 21.61 kJ/mol) adsorption on GAC activated carbon. Additionally, it has been shown that the adsorption of pharmaceuticals is physisorption (ΔH < 40 kJ/mol and 0 < ΔG°_{NPX_15°C} = −0.10 kJ/mol, ΔG°_{NPX_25°C} = −0.73 kJ/mol, ΔG°_{NPX_35°C} = −1.62 kJ/mol, ΔG°_{IBP_15°C} = −2.66 kJ/mol, ΔG°_{IBP_25°C} = −3.07 kJ/mol, ΔG°_{IBP_35°C} = −3.97 kJ/mol, ΔG°_{D_15°C} = −1.98 kJ/mol, ΔG°_{D_25°C} = −2.72 kJ/mol, ΔG°_{D_35°C} = −3.25 kJ/mol < 20 kJ/mol). The adsorption equilibrium data were analyzed using the generalized Langmuir equation. However, only for D/GAC_25 °C the full form of the GL equation correctly describes the behavior of this system. In other cases, simplifications of the GL isotherm were used: the Tóth isotherm (IBP/GAC_15 °C, IBP/GAC_25 °C, IBP/GAC_35 °C) and the generalized Freundlich isotherm (D/GAC_15 °C, D/GAC_35 °C, NPX/GAC_15 °C, NPX/GAC_25 °C, NPX/GAC_35 °C). In practice, this means that medium heterogeneity effects were observed in the experimental systems. The adsorption rate data were analyzed using numerous adsorption kinetics equations. The best fitting quality was obtained for the multi-exponential equation (0.335% < SD(c)/co < 0.720% and 9.4 × 10⁻⁵ < 1 − R² < 4.9 × 10⁻⁴) and good for the fractal-like MOE equation (0.520% < SD(c)/co < 0.879% and 2.2 × 10⁻⁴ < 1 − R² < 6.0 × 10⁻⁴). The analysis of the estimated parameters showed that the adsorption processes of naproxen sodium, ibuprofen sodium, and diclofenac sodium on GAC activated carbon proceeds approximately with first-order kinetics. Moreover, for activated carbon samples after adsorption of the tested pharmaceuticals, compared to pure carbon material, lower resistance to high temperatures and a decrease in zeta potential were observed.