Expansion of adsorption isotherms into equilibrium surface

Reactive & Functional Polymers 48 (2001) 37–51 www.elsevier.com / locate / react Expansion of adsorption isotherms into equilibrium surface Case 1: solvent impregnated resins (SIR) a, a b Joan Serarols *, Jordi Poch , Isabel Villaescusa a ` ` ` ´ Santalo´ , s /n, i Matematica Aplicada, Universitat de Girona, Escola Politecnica Superior, Av. Lluıs Departamento d’ Informatica 17071 Girona, Spain b ´ ` ´ Santalo´ , s /n, 17071 Girona, Spain , Universitat de Girona, Escola Politecnica Superior, Av. Lluıs Departamento d’ Enginyeria Quımica Received 1 July 2000; accepted 5 January 2001 Abstract In this work, the adsorption of Au(III) and Zn(II) by impregnated resins has been studied in batch and column experiments. In batch experiments successive contacts for each metal concentration were made until saturation was reached. Equilibrium points corresponding to each contact brought a different isotherm. By introducing a new variable it was observed that all the equilibrium points fitted a surface that we call the equilibrium surface. Once the equilibrium surface was determined it was found that the different isotherms, obtained in batch and column experiments, were fitted on the surface. Traditional isotherms and the equations of the equilibrium surfaces for zinc(II) and gold(III) adsorption with impregnated resins have been compared and discussed. The equilibrium surface equation proposed in this work has been proven to be a good tool for modelling adsorption by impregnated resins in batch and column experiments.  2001 Elsevier Science B.V. All rights reserved. Keywords: Gold(III) extraction; Zinc(II) extraction; Impregnated resins; Isotherms; Equilibrium surface 1. Introduction Adsorption has been widely used to eliminate metals from aqueous solutions. In an adsorption process, the adsorption isotherm, the relation between the amount of solute adsorbed (qe ) and the remaining concentration in the aqueous phase (Ce ) is basically important to describe how adsorbates interact with adsorbents and so *Corresponding author. Tel.: 134-972-418-413; fax: 134-972418-399. E-mail address: serarols@ima.udg.es (J. Serarols). it is critical in optimising and modelling the process. In order to obtain the adsorption isotherms, researchers perform batch or column experiments. Batch experiments can be carried out in two different ways: (a) a fixed amount of adsorbent material (carbon, resin, biomaterial, etc.) is put into contact with solutions containing different concentrations of adsorbate [1– 4]. (b) A fixed volume of a solution containing a known concentration of adsorbate is put into contact with different amounts of adsorbent material [5,6]. In both cases the vessel containing adsorbent and adsorbate is continuously 1381-5148 / 01 / $ – see front matter  2001 Elsevier Science B.V. All rights reserved. PII: S1381-5148( 01 )00045-1 38 J. Serarols et al. / Reactive & Functional Polymers 48 (2001) 37 – 51 agitated. After equilibrium is reached, the residual adsorbate concentration in the solution is determined by the most suitable technique. Normally, in this kind of experiment the adsorbent material is free of adsorbate and a unique contact is performed for each different adsorbate concentration or the amount of adsorbent material used, respectively. Nevertheless, Veeraraghavan [7] used a preloaded activated carbon for phenol adsorption and Zhou [8] studied a second adsorption of aromatic compounds on activated carbon and obtained a new adsorption isotherm that he called ‘complementary adsorption’. Column experiments can be performed in fixed or fluidised beds. Fixed bed experiments consist in packing a known amount of adsorbent material in a column. Solutions containing different adsorbate concentrations flow through the column. The system can be open, that is, fresh solution of a known adsorbate concentration is flowed through the column until final adsorbate concentration is equal to the initial concentration [9,10]. When the system is closed, the initial solution is recycled, that is, reintroduced into the column until its concentration becomes constant [7,11,12]. During the operation, samples are taken out and the adsorbate concentration is determined. Fluidised bed column experiments consist in putting a known amount of adsorbent material in a column and pass upward through the bed of particles a solution of known concentration at the fluidisation flow rate. This methodology was used by Nakhla et al. [13] to adsorb toxic compounds with activated carbon. From the results achieved with any of the described experiments a set of equilibrium points are obtained from which the corresponding isotherms can be determined. In the last few years, solvent impregnated resins (SIR) introduced by Warshawsky et al. [14,15], have been used in metal separation and recovery processes. Several authors used Amberlite XAD-2 resins impregnated with different extractants containing different types of functionalities for the selective extraction of metals from aqueous solutions [16,17]. SIR can be considered as a link between solvent extraction and ion-exchange technologies [18], thus, impregnated resins containing this kind of extractant have a similar behaviour to ion-exchange resins [19]. In this work, the adsorption isotherms of Au(III) and Zn(II) by Amberlite XAD-2 impregnated resins containing triisobutyl phosphine sulphide (TIBPS) and di(2-ethylhexyl) phosphoric acid (DEHPA), respectively, have been obtained in batch and column experiments. In batch experiments, the adsorption was carried out by successive contacts and in column experiments, by recycling the solution until equilibrium was reached. The different isotherms obtained from both types of experiments did not represent the global equilibrium of the system. Thus, these results led us to study the equilibrium of those systems by introducing a new concept that we call equilibrium surface. 2. Experimental 2.1. Reagents and solutions Amberlite XAD-2 purchased from Rohm and Haas was washed as described elsewhere [16]. After washing, the resin was sieved to obtain the particle size used in this work (840–630 mm). Triisobutyl phosphine sulphide (TIBPS) provided as Cyanex 471 by Cyanamide Co. was purified by recrystallisation from ethanol–water mixture. Ethanol (Merck A.R.) was used without further purification. Di(2-ethylhexyl) phosphinic acid provided by Laboratory Supplies Poole BH15 1TD was used without further purification. A solution of TIBPS of 1300 mg / dm 3 in 66% ethanol–water and a solution of 12.5 v / v of DEHPA in acetone were used as impregnation solution for gold(III) and zinc(II) adsorption, respectively. In both cases, the impregnation procedure was the same used in the abovementioned work. J. Serarols et al. / Reactive & Functional Polymers 48 (2001) 37 – 51 Stock solutions of Au(III) were prepared from solid HAuCl 4 ? 3H 2 O (Aldrich) in a 0.5 mol / dm 3 NaCl solution. The pH in all gold solutions was pH 2. NaCl and HCl (Merck A.R.) were used to adjust the ionic strength and the pH of gold solutions. Stock solutions of Zn(II) were prepared by dissolving ZnCl 2 (Merck A.R.) in MilliQ water. Gold and zinc solutions of 1000 mg / dm 3 from Carlo Erba were used as standard solutions for atomic absorption spectrophotometry determinations. 2.2. Experimental procedure 2.2.1. Batch experiments Amounts of 0.2 g of impregnated resin were put into contact with 20 cm 3 of metal solutions of different concentrations (19.9–212.9 mg / dm 3 for Au(III) and 10.2–162.5 mg / dm 3 for Zn(II)), and stirred for 2 h and 24 h for gold and zinc, respectively. After filtration, the resin was put again into contact with fresh gold or zinc solution and the filtrate was kept for the determination of gold or zinc concentration by atomic absorption spectrometry. For each initial gold concentration this operation was repeated eight times until the resin did not adsorb more gold. For zinc, 17 contacts were performed for each initial zinc concentration. The amount of gold and zinc adsorbed was determined by mass balance. All the experiments were performed at room temperature twice. 39 2.2.2. Column experiments The column consisted of a 10-cm glass tube with an internal diameter of 4 mm. The same experimental set-up was used in a previous work [11]. For each experiment 0.2 g of impregnated resin was introduced into the column. Two pieces of glasswool were used to keep the resin packed. A volume of 100 cm 3 of metal solution of different initial metal concentration (39.3–196.0 mg / dm 3 or 9.4–248.2 mg / dm 3 ) for gold and zinc, respectively, contained in a recipient continuously agitated was passed through the column at a flow rate of 2 cm 3 / min. The outflow metal solutions were recycled back to the column until the reservoir metal concentration became almost constant. Samples of 2.0 cm 3 of the reservoir solution were taken every 5 min and the metal concentration was analysed by atomic absorption spectrometry. The amount of metal adsorbed on the resin was determined by mass balance. All the experiments were carried out twice at room temperature. 3. Results and discussion 3.1. Batch experiments The results obtained for Au(III) and Zn(II) adsorption are presented in Tables 1 and 2. In these tables can be seen the initial metal concentration C0 , number of contact i, the final Table 1 Gold adsorption by impregnated resin TIBPS / XAD-2 C0 19.97 i Ce,i qe,i 43.15 Ce,i qe,i Ce,i 75.97 qe,i 101.87 Ce,i qe,i 134.79 Ce,i qe,i 161.01 Ce,i qe,i 193.07 Ce,i qe,i Ce,i qe,i 1 2 3 4 5 6 7 8 0.96 1.55 5.23 10.46 12.77 15.85 17.77 19.68 1.90 3.74 5.22 6.17 6.89 7.30 7.52 7.53 1.31 12.07 19.34 28.57 31.37 31.79 34.95 41.12 4.18 7.29 9.67 11.13 12.31 13.44 14.26 14.28 8.47 36.55 50.95 52.35 64.69 66.49 69.31 73.12 6.75 10.69 13.19 15.56 16.68 17.63 18.30 18.32 23.12 66.49 78.54 81.87 91.62 94.95 101.10 101.47 7.88 11.41 13.75 15.75 16.77 17.46 17.54 17.55 41.02 78.03 107.77 106.23 126.05 134.79 134.21 134.78 9.38 15.05 17.76 20.61 21.49 21.49 21.54 21.54 54.73 114.98 131.88 135.96 155.77 157.52 156.35 160.86 10.63 15.23 18.14 20.65 21.17 21.52 21.99 22.00 84.69 139.45 160.43 166.26 177.33 186.66 193.07 193.06 10.84 16.20 19.46 22.14 23.72 24.36 24.36 24.36 104.44 159.27 180.24 186.07 197.14 206.47 212.30 212.62 10.84 16.21 19.47 22.15 23.72 24.36 24.42 24.43 C0 in mg Au(III) / dm 3 , Ce,i in mg Au(III) / dm 3 , qe,i in mg Au(III) / g XAD-2; i, number of contact. 212.88 40 C0 (mg Zn(II)/dm 3 ) 10.25 i Ce,i mg Zn(II)/ dm 3 qe,i mg Zn(II)/g XAD-2 Ce,i mg Zn(II)/ dm 3 qe,i mg Zn(II)/g XAD-2 Ce,i mg Zn(II)/ dm 3 qe,i mg Zn(II)/g XAD-2 Ce,i mg Zn(II)/ dm 3 qe,i mg Zn(II)/g XAD-2 Ce,i mg Zn(II)/ dm 3 qe,i mg Zn(II)/g XAD-2 Ce,i mg Zn(II)/ dm 3 qe,i mg Zn(II)/g XAD-2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1.25 2.12 3.05 3.98 4.86 5.55 6.21 6.97 7.05 7.91 8.23 9.05 9.96 10.07 10.18 10.20 10.20 0.90 1.71 2.43 3.06 3.60 4.07 4.47 4.80 5.12 5.36 5.56 5.68 5.71 5.72 5.73 5.74 5.74 9.00 19.00 22.16 29.51 31.94 33.68 35.42 34.72 36.11 37.64 38.19 38.89 39.72 40.15 40.25 40.30 40.32 3.13 5.27 7.09 8.17 9.01 9.68 10.17 10.73 11.15 11.42 11.64 11.78 11.84 11.86 11.87 11.88 11.88 25.71 42.14 53.68 57.58 61.36 65.15 66.67 68.18 69.70 70.45 71.50 71.57 71.57 71.57 71.57 71.57 71.57 4.59 7.53 9.32 10.73 11.75 12.39 12.88 13.23 13.41 13.53 13.54 13.54 13.54 13.54 13.54 13.54 13.54 47.22 74.32 85.14 89.19 92.78 94.44 96.11 100.00 101.71 102.20 102.23 102.23 102.23 102.23 102.23 102.23 102.23 5.51 8.30 10.01 11.32 12.27 13.05 13.67 13.90 13.95 13.96 13.96 13.96 13.96 13.96 13.96 13.96 13.96 51.43 107.14 113.57 125.71 127.71 128.57 129.14 131.43 132.86 132.86 132.86 132.86 132.86 132.86 132.86 132.86 132.86 8.15 10.73 12.67 13.40 13.92 14.36 14.74 14.89 14.90 14.91 14.91 14.91 14.91 14.91 14.91 14.91 14.91 80.11 139.77 143.18 146.59 151.14 153.41 158.64 160.23 160.68 162.50 161.36 162.50 162.50 162.50 162.50 162.50 162.50 8.24 10.51 12.44 14.04 15.17 16.08 16.47 16.69 16.88 16.88 16.99 16.99 16.99 16.99 16.99 16.99 16.99 40.34 71.59 102.27 132.95 162.50 J. Serarols et al. / Reactive & Functional Polymers 48 (2001) 37 – 51 Table 2 Zinc adsorption by impregnated resin DEHPA / XAD-2 J. Serarols et al. / Reactive & Functional Polymers 48 (2001) 37 – 51 concentration at equilibrium for each contact Ce,i , and the total adsorbed metal amount at each contact taking into account the accumulated amount of metal adsorbed in the previous contact, qe,i . The qe,i were calculated with the following expression: FO G n sC0 2 Ce,id .V i 51 qe,i 5 ]]]]]] WXAD-2 (1) where, V is the volume of gold or zinc solution (dm 3 ) and WXAD-2 the amount of impregnated resin used (g). In these tables, it can be observed that the major percentage of adsorption takes place during the first four and 10 contacts for gold and zinc, respectively (see the increase of Ce,i ). This percentage decreases with the successive contacts until the solution concentration coincides with the initial concentration. This fact indicates that for all the studied concentrations the resin does not adsorb more metal. Concerning the total metal amount adsorbed it can be seen that for each contact at the beginning qe,i, increases with the initial concentration. Up to a determined value of C, qe,i becomes almost constant. This fact indicates that the resin cannot adsorb more metal. The 41 total amount of metal adsorbed in the resin was 24.43 mg Au(III) / g XAD-2 and 16.99 mg Zn(II) / g XAD-2. 3.2. Column experiments The results obtained in column experiments for Au(III) and Zn(II) adsorption are presented in Tables 3 and 4. In these tables, the time at which samples were taken out for their analysis can be seen in the first column. The total operation time was 60 and 80 min for gold and zinc, respectively. The metal initial concentration is indicated in the first row of these tables (t50). In these tables, C shows the metal solution concentration in the recycling recipient at different times and q the amount of adsorbed metal on the resin. When calculating the q, the sample volume used for metal analysis by atomic absorption has been taken into account (2 ml per sample). As it can be seen in Table 3, for each initial concentration used, the amount of gold adsorbed on the resin increases during the adsorption process up to a value of 24.30 mg Au(III) / g XAD-2 for the initial concentration of 196 mg 3 Au(III) / dm . This value fairly matches the obtained one in the batch experiments, 24.43 mg Au(III) / g XAD-2 (see Table 1). Table 3 Results in column adsorption of gold by impregnated resin TIBPS / XAD-2 Time (min) C mg Au(III)/ dm 3 q mg Au(III)/g XAD-2 C mg Au(III)/ dm 3 q mg Au(III)/g XAD-2 C mg Au(III)/ dm 3 q mg Au(III)/g XAD-2 C mg Au(III)/ dm 3 q mg Au(III)/g XAD-2 C mg Au(III)/ dm 3 q mg Au(III)/g XAD-2 0 5 10 15 20 25 30 35 40 45 50 55 60 39.32 36.32 35.71 33.92 32.01 28.74 26.64 24.43 22.72 22.21 21.50 21.22 21.21 0.00 1.51 1.82 2.70 3.61 5.12 6.02 7.06 7.75 7.92 8.22 8.31 8.32 78.62 69.42 65.34 64.65 63.10 59.81 56.90 52.84 51.75 48.82 46.97 46.62 46.55 0.00 3.22 5.71 7.02 7.73 9.36 10.74 12.69 13.12 14.41 15.36 15.48 15.50 118.01 113.93 108.14 98.34 98.32 92.18 85.35 83.68 80.91 79.50 77.81 76.54 76.44 0.00 2.92 5.43 8.87 9.81 12.79 15.94 16.72 18.04 18.67 19.48 20.08 20.10 157.03 143.02 138.20 133.44 131.54 123.92 122.42 121.04 116.76 112.47 113.46 112.42 112.50 0.00 5.65 8.28 10.85 12.73 16.42 17.12 17.77 19.84 21.82 21.49 21.88 21.90 196.03 187.35 182.48 174.83 165.23 159.65 157.69 155.55 153.40 149.33 147.95 147.32 147.30 0.00 6.15 8.52 11.63 15.31 18.06 18.07 20.08 21.01 23.08 23.78 24.29 24.30 42 Time C q (min) mg Zn(II)/ mg Zn(II)/g mg Zn(II)/ mg Zn(II)/g mg Zn(II)/l mg Zn(II)/g mg Zn(II)/ mg Zn(II)/g C q C q C q dm 3 XAD-2 dm 3 XAD-2 0 9.43 0.00 36.96 0.00 5 7.39 1.05 33.93 1.52 10 5.94 1.76 31.96 15 5.29 2.07 30.71 20 4.79 2.31 25 4.13 30 C q C C q mg Zn(II)/ mg Zn(II)/g mg Zn(II)/ mg Zn(II)/g q C mg Zn(II)/ mg Zn(II)/g q C mg Zn(II)/ mg Zn(II)/g q mg Zn(II)/ mg Zn(II)/g dm 3 XAD-2 dm 3 dm 3 dm 3 dm 3 XAD-2 XAD-2 dm 3 XAD-2 70.24 0.00 97.62 0.00 130.95 0.00 158.33 0.00 189.54 0.00 218.45 0.00 248.21 0.00 67.00 1.62 92.86 2.38 126.19 2.38 144.05 7.14 170.93 9.30 194.64 11.90 224.41 11.90 2.48 65.48 2.37 90.48 3.55 120.24 5.30 140.48 8.89 161.63 13.86 191.67 13.36 218.45 14.82 3.08 61.91 4.08 88.10 4.69 114.29 8.15 128.57 14.61 159.30 14.98 188.69 14.79 215.48 16.25 28.57 4.09 57.86 5.98 85.71 5.81 107.14 11.51 126.19 15.72 154.65 17.16 182.74 17.59 212.50 17.65 2.61 26.49 5.05 55.24 7.19 83.33 6.90 104.76 12.61 125.00 16.27 152.33 18.23 180.95 18.41 210.12 18.74 3.00 3.12 24.58 5.90 52.38 8.47 78.57 9.05 102.38 13.68 125.00 16.27 152.33 18.23 180.95 18.41 210.12 18.74 35 2.29 3.43 25.60 5.46 51.07 9.05 76.19 10.10 100.00 14.73 124.29 16.59 152.33 18.23 180.95 18.41 210.12 18.74 40 1.57 3.74 23.81 6.23 49.64 9.66 73.81 11.12 97.62 15.75 124.29 16.59 152.33 18.23 180.95 18.41 210.12 18.74 45 1.57 3.74 21.07 7.38 47.00 10.77 71.43 12.12 97.62 15.75 124.29 16.59 152.33 18.23 180.95 18.41 210.12 18.74 50 1.43 3.80 21.49 7.20 47.00 10.77 71.43 12.12 97.62 15.75 124.29 16.59 152.33 18.23 180.95 18.41 210.12 18.74 55 1.43 3.80 20.83 7.47 47.00 10.77 71.43 12.12 97.62 15.75 124.29 16.59 152.33 18.23 180.95 18.41 210.12 18.74 60 1.43 3.80 20.83 7.47 47.00 10.77 71.43 12.12 97.62 15.75 124.29 16.59 152.33 18.23 180.95 18.41 210.12 18.74 65 1.43 3.80 20.83 7.47 47.00 10.77 71.43 12.12 97.62 15.75 124.29 16.59 152.33 18.23 180.95 18.41 210.12 18.74 70 1.43 3.80 20.83 7.47 47.00 10.77 71.43 12.12 97.62 15.75 124.29 16.59 152.33 18.23 180.95 18.41 210.12 18.74 75 1.43 3.80 20.83 7.47 47.00 10.77 71.43 12.12 97.62 15.75 124.29 16.59 152.33 18.23 180.95 18.41 210.12 18.74 80 1.43 3.80 20.83 7.47 47.00 10.77 71.43 12.12 97.62 15.75 124.29 16.59 152.33 18.23 180.95 18.41 210.12 18.74 XAD-2 XAD-2 XAD-2 J. Serarols et al. / Reactive & Functional Polymers 48 (2001) 37 – 51 Table 4 Results in column adsorption of zinc by impregnated resin DEHPA / XAD-2 J. Serarols et al. / Reactive & Functional Polymers 48 (2001) 37 – 51 In Table 4 it can be seen that the amount of zinc that the resin adsorbs for each initial concentration is also increasing during the adsorption process up to 18.74 mg Zn(II) / g XAD2 corresponding to the initial concentration of 248.21 mg Zn(II) / dm 3 . This value is greater than that obtained in batch experiments, 16.99 mg Zn(II) / g XAD-2 (see Table 2). 3.3. Isotherms Previous studies demonstrated that the Langmuir isotherm fits the experimental data obtained for Au(III) and Zn(II) adsorption by XAD-2 impregnated resins with TIBPS and DEHPA, respectively [11,12]. The Langmuir isotherm is represented by the equation: bC aC qe 5 qmax ]]] 5 ]]]. 1 1 bC 1 1 bC (2) In batch experiments, as said before, most of the authors use one contact to determine the adsorption isotherm. Thus, the first step was to determine the isotherm that fitted the experimental data obtained in the first contact for both systems studied. The Langmuir coefficients 43 Table 5 Langmuir coefficients of first contact isotherm Metal a b R2 Au(III) Zn(II) 1.9670 0.8203 0.1720 0.1164 0.9954 0.9919 (a, b) as well as the correlation coefficient R 2 for gold and zinc are presented in Table 5. As can be seen, the experimental data fit quite well the Langmuir equation. These isotherms were plotted in Fig. 1. In the same figure, the equilibrium points obtained in the successive batch contacts were also plotted. It can be noticed that these isotherms fit the data corresponding to the first contact but do not fit the set of equilibrium data obtained by the successive contacts. The next step was the determination of the Langmuir isotherms corresponding to the experimental data obtained in the successive batch contacts and in column. As a result of this, for each contact a different isotherm was reached. As an example, in Fig. 2 the total experimental data and the Langmuir isotherm 1 (1st batch contact), Langmuir isotherm 2 (2nd contact) and column Langmuir isotherm have been Fig. 1. Gold and zinc Langmuir 1st contact isotherms with all batch equilibrium data. 44 J. Serarols et al. / Reactive & Functional Polymers 48 (2001) 37 – 51 Fig. 2. Gold and zinc 1st and 2nd contact and column Langmuir isotherms. plotted. It can be observed that each isotherm fits only the corresponding experimental data. From these results, it can be concluded that: • none of the isotherms fits the set of experimental data; • the amount of metal adsorbed on the resin (qe,i ) seems to be dependent on the number of contacts; qe,i increases with the number of contacts but the rate of this increase lowers in each contact. Observing these conclusions, we thought that another variable related to the number of contacts could have influenced the process. By introducing a new variable we may obtain a new equation capable of describing the equilibrium. This new variable could be the time of the experiment operation, the initial metal concentration or the previous metal preload on the resin at the beginning of each contact. Considering that the time used was necessary for the system to reach the equilibrium, it may be considered that once the equilibrium is reached the adsorption process is independent of the operation time. On the other hand, the initial concentration does not vary according to the number of contacts and it is taken into account for each series of data, so, the obtained data are related to this variable. Finally, the only possible variable is qp , that is, the metal preload on the resin at the beginning of each contact. This variable can be easily quantified and some other authors have considered it. Zhou studied a second adsorption of phenol on activated carbon [8] and Veeraraghavan studied the phenol adsorption on a 25% preloaded activated carbon [7]. Taking into account this third variable and plotting C, qp and qe , we obtain a surface instead of a curve. 4. Equilibrium surface In a metal adsorption process by impregnated resins, we call the equilibrium surface, the surface that contains all the possible equilibrium points, at a constant temperature, obtained in batch and column experiments with independence of the experimental procedure used. The equation describing this surface should be a function of C and qp : qe 5 F(C, qp ) (3) J. Serarols et al. / Reactive & Functional Polymers 48 (2001) 37 – 51 where qe (mg / g) is the amount of metal per weight of impregnated resin, C (mg / dm 3 ) is the metal concentration in the liquid phase and qp (mg / g) the preloaded amount of metal per weight of impregnated resin. In order to determine the equilibrium surface for a given system the following assumptions were made. • There is no desorption process, thus, if the preloaded amount of metal qp is greater than the maximum amount of metal that can be adsorbed for a given concentration then the amount of metal per weight of impregnated resin must be equal to the preload (qe 5 qp ). This maximum amount of metal adsorbed is a function of the concentration C, h(C). In particular, if the concentration is nil (C50), h(C)50 and the adsorbed amount coincides with the preload (qe 5 qp ). • When the resin is not preloaded, qp 5 0, at equilibrium, the amount of the adsorbed metal qe must coincide with the value obtained from the intersection of function (3) with the plane Cqe . This intersection curve coincides with the isotherm of first contact in batch. Taking into account these assumptions, the surface equation must be: qe 5 F(C, qp ) 5 H qp 1 f(C, qp ) if qp , h(C) qp if qp $ h(C) (4) And, if qp 5 h(C) then f(C, qp ) 5 0. In the studied systems, the isotherms of the first contacts fit a Langmuir curve, thus, the equation of the equilibrium surface (4) when qp 5 0 must be: aC qe 5 F(C, 0) 5 ]]]. 1 1 bC (5) Therefore, the intersection of the equilibrium surface with the plane Cqe is a Langmuir curve. And considering the experimental data obtained by successive contacts (all of them fit a 45 Langmuir curve type) an expression of Langmuir type is expected for h(C): k5C h(C) 5 ]]] 1 1 k6C (6) and the function f(C, qp ) will also be a Langmuir curve with correction factors A(qp )(C 2 C*) f(C, qp ) 5 ]]]]]] 1 1 B(qp )(C 2 C*) (7) where C* is the concentration value determined by the equation qp 5 h(C*). On the other hand, from one contact to another the amount of adsorbed metal on the resin diminishes until the resin does not adsorb more metal thus, at the end of the process Dq 5 0 that implies qe 5 qp . Then, the coefficients A(qp ) and B(qp ) of the expression (7) are considered as: A(qp ) 5 k 1 e 2k 3 q p B(qp ) 5 k 2 e 2k 4 q p (8) . (9) If qp , h(C), then by isolating C of expression (6) the C* value can be calculated: qp k5C qp 5 h(C) 5 ]]] ⇒ C* 5 ]]]. 1 1 k6C k 5 2 k 6 qp (10) By introducing the expressions (6)–(10) in Eq. (4) a possible expression of the equilibrium surface for the studied systems would be: qe 5 F(C, qp ) 5 S S D D qp k 1 e 2k 3 q p C 2 ]] k 5 2 k 6 qp k5C qp 1 ]]]]]] if qp , ]] qp 1 1 k6C 2k 4 q p 1 1 k2e C 2 ]] k 5 2 k 6 qp 5 (11) k5C qp if qp $ ]] 1 1 k6C where qe is the amount of metal adsorbed in the resin, mg Au(III) or Zn(II) / g XAD-2; qp is the amount of metal preload in the resin, mg Au(III) or Zn(II) / g XAD-2; C is the solution concentration at equilibrium, mg Au(III) or J. Serarols et al. / Reactive & Functional Polymers 48 (2001) 37 – 51 46 Zn(II) / dm 3 and k 1 , k 2 , k 3 , k 4 , k 5 and k 6 are parameters to be determined. The surface defined in this way verifies the above made assumptions. • When qp $ h(C) 5 k 5 C /(1 1 k 6 C) and C →0, high preload and low concentration, then, qe 5 F(C, qp ) 5 qp , and in particular, if the concentration C 5 0, qe 5 F(0, qp ) 5 qp . In this case, the amount of metal on the resin is equal to the preload (qp ), and the intersection of the equilibrium surface with the plane qp qe is the bisecting first quadrant. • If the preload of metal on the resin is nil (qp 5 0), the equilibrium surface equation is the Langmuir isotherm obtained in the first contact: k1C qe 5 F(C, 0) 5 ]]] 1 1 k2C (12) • For a given preload on the resin (qp 5 constant) and for high concentrations (C → `), the following equation is obtained: k 1 2(k 3 1k 4 )q p e sqed C →` 5 qp 1 ] k 2 5 qp 1 qmax (13) where qmax 5 k 1 /k 2 e 2(k 3 1k 4 )q p . The expression (13) indicates that the maximum amount of metal (gold or zinc) that the resin can adsorb depends on the parameters k 1 , k 2 , k 3 , k 4 and on the initial preload (qp ). In particular, if qp 5 0, the maximum adsorption capacity would be attained for the first contact: C →` k1 5 qmax, 0 . sqed q p 50 5 ] k (14) 2 In the expression (14) it can be observed that the maximum amount of metal adsorbed on the resin, without preload and for the first contact, is given by the quotient of the parameters k 1 and k 2 of the proposed equilibrium surface equation. Therefore, in this case, the coefficients k 1 and k 2 have the same meaning as the parameters a and b of the Langmuir isotherm equation. The six parameters k 1 , k 2 , k 3 , k 4 , k 5 and k 6 of the expression (11) must always be positive in order to avoid discontinuities in the surface. From the chemical point of view: k 1 /k 2 is the maximum amount of metal that the resin can adsorb in the first contact (14). k 2 is the adsorption affinity of the resin, similar to the corresponding parameter (b) of the Langmuir isotherm (12). k 3 , k 4 are correctors of the maximum increase of the adsorption and the affinity while the preload is increasing (13). k 5 , k 6 provide, for a given concentration, the maximum preload up to the one where there will not be any adsorption (6). 4.1. Determination of the coefficients for the two studied systems In order to determine the coefficients of the surface equation, only the equilibrium points obtained in batch experiments were considered (Tables 1 and 2). For each contact i, the used points are the values (C, qp , qe ) where C 5 Ce,i was considered as the equilibrium concentration, qp 5 qe,i21 as the amount of metal preload on the resin and qe 5 qe,i as the amount of metal adsorbed on the resin. In order to obtain the coefficient values, the sum square errors were minimised: Os q N SSE 5 j 51 e, j 2 F(Cj , qp, j )d 2 (15) where qe, j is the experimental data; F(Cj , qp, j ) are calculated values from the equilibrium surface Eq. (11) and N is the number of experiences. From the batch experiments data indicated in Tables 1 and 2, a non-lineal fit was done by means of the program SPSS 7.5 for Windows in order to obtain the values of the parameters k 1 , k 2 , k 3 , k 4 , k 5 and k 6 . These values are presented in Table 6 for each system. J. Serarols et al. / Reactive & Functional Polymers 48 (2001) 37 – 51 47 Table 6 Equilibrium surface parameters. Maximum amount of metal adsorbed (qmax,0 ) in the first contact without preload Metal k1 k2 k3 k4 k5 k6 qmax,0 mg (metal) / g XAD-2 R2 Au(III) Zn(II) 1.3108 0.4638 0.1110 0.0469 0.2172 0.3000 0.1774 0.2411 0.9325 1.1519 0.0328 0.0625 11.8090 9.8891 0.9819 0.9942 4.2. Validation and fitness of the equilibrium surface equation In Fig. 3 the surface and the experimental data (batch and column) are presented for gold and zinc, respectively. When plotting the equilibrium points corresponding to the batch experiments, (C, qp , qe ), we considered C 5 Ce,i , qp 5 qe,i21 (amount of adsorbed metal in previous contacts) and qe 5 qe,i . As said before, the results obtained in column experiments were not taken into account to determine the surface equation. Nevertheless, the column equilibrium points were included in Fig. 3. When doing this, it was considered that in a process with or without recycling for a time t there is a concentration C(t) in the liquid phase and a load q(t) in the resin that can be considered as the preload corresponding to the time t. When time increases C(t) tends to Ce and q(t) tends to qe . Hence, qp has been considered to be equal to qe . Thus, the equilibrium points obtained in the column were represented as (C, qe , qe ). When observing Fig. 3, all the experimental data seem to be placed on the corresponding surface. In order to confirm that these surfaces describe the equilibrium with accuracy, we plotted the qe,cal calculated vs. the experimental qe,exp . As can be seen in Fig. 4 the points (included the points obtained in column experiments) are distributed on the bisecting first quadrant. The fact that the equilibrium points of the column experiments fit properly the surface may validate it. The corresponding regression equations turned out to be qe,cal 5 0.9982 qe,exp 1 0.0016 (R 2 5 0.9916), and qe,cal 5 1.0095 qe,exp 2 0.0826 (R 2 5 0.9974) for gold and zinc, respectively. The comparison of the isotherms with the equilibrium surface can be done in two ways. Fig. 3. Equilibrium surface and experimental data (batch and column) for: (a) gold, (b) zinc. 48 J. Serarols et al. / Reactive & Functional Polymers 48 (2001) 37 – 51 Fig. 4. Calculated vs. experimental qe values: (a) gold, (b) zinc. 1. Taking into account the isotherms obtained in Section 3.3 and the introduction of the new variable (qp , preload) it is possible to get a curve in the space (C, qp , qe ) whose projection on the plane Cqe is the corresponding isotherm. For each batch contact i the points (Ci , qe,i 21 , qe,i ) were fitted to a space curve that has the form si (C) 5 (C, qp,i (C), qe,i (C)) where qp,i (C) 5 a 9i C /(1 1 b i9 C) and qe,i (C) 5 a i C /(1 1 b i C) (ith contact isotherm) (see Fig. 5). The projection of this si (C) on the plane Cqe corresponds to the isotherm of contact i. In this sense, si (C) is the plotting of the isotherm i on the equilibrium surface. In the case of the column the same procedure was followed. The points (C, qe , qe ) were fitted to a space curve sc (C) 5 (C, qp,c (C), qe,c (C)) where qp,c (C) 5 qe,c (C) 5 aC /(1 1 bC) (column isotherm). In Fig. 5, the surface and the space curves si (C) and sc (C) have been plotted. It can be observed that the set of curves is properly placed on the respective equilibrium surfaces (gold and zinc). It can also be observed that in both systems the isotherm corresponding to the first contact Fig. 5. Gold and zinc isotherms on the equilibrium surface: (a) gold, (b) zinc. J. Serarols et al. / Reactive & Functional Polymers 48 (2001) 37 – 51 practically coincides with the intersection of the surface and the plane Cqe . 2. It is also possible, from the equilibrium surface, to obtain the curve on the surface that corresponds to a given experimental process (i.e. the curve of the 3rd contact in batch) and project it on the plane Cqe for its comparison to the isotherm obtained with the experimental data. In order to obtain the curve corresponding to the contact in batch i the procedure is the following: for i51 qp,1 (C) 5 0 qe,1 (C) 5 F(C, 0) i52 qp,2 (C) 5 qe,1 (C) qe,2 (C) 5 F(C, qp,2 ) i53 qp,3 (C) 5 qe,2(C ) qe,3 (C) 5 F(C, qp,3 ) : i5n qp,n (C) 5 qe,n 21 (C) qe,n (C) 5 F(C, qp,n ) And the curve on the surface for a contact i is: si (C) 5 (C, qp,i (C), qe,i (C)) (16) where qp,i (C) 5 qe,i21 (C) and qe,i (C) 5 F(C, qp,i ), called the theoretical isotherm (see Fig. 6a.1 and b.1). When this curve si (C) is projected on the plane Cqe , the following curve is obtained: di (C) 5 (C, qe,i (C)) (17) that must be interpreted as the isotherm of contact i obtained from the equilibrium surface equation, called the calculated isotherm (see Fig. 6a.1 and b.1). In the case of column experiments, taking into account that qe,c 5 qp,c , the curve on the surface is sc (C) 5 (C, qp,c (C), qe,c (C)) (18) where qe,c (C) 5 qp,c (C) 5 h(C) is called the theoretical isotherm (see Fig. 6a.2 and b.2). 49 When the curve sc (C) is projected on the plane Cqe , the following curve is obtained: dc (C) 5 (C, h(C)) (19) that must be interpreted as the column isotherm obtained from the equilibrium surface equation, called the calculated isotherm (see Fig. 6a.2 and b.2). In Fig. 6 the isotherms (calculated and experimental) corresponding to the 3rd contact and the column are presented. In both cases experimental and theoretical isotherms almost coincide. Similar results were found for the rest of the contacts. 5. Conclusions From the results, it has been demonstrated that the traditional isotherms do not permit us to represent all the equilibrium points obtained in the adsorption of gold and zinc by the impregnated resins used in this work. In this study, the concept of equilibrium surface has been defined and developed. The equilibrium surface equation has been obtained for the two studied systems and the corresponding parameters determined. The two calculated equilibrium surfaces for gold and zinc have successfully fitted all the equilibrium points obtained for each system. Their fitness has been demonstrated by comparison of both theoretical and calculated isotherms. The equilibrium surface has been validated with the equilibrium points obtained in column experiments. Thus, the equilibrium surface equation proposed in this work has been proven to be a good tool for modelling adsorption by impregnated resins in batch and column experiments. As the general equation has been proposed from very general assumptions, it could be valid for other adsorption systems. The significance of this study is to provide a tool to be applied in the modelling of adsorption processes. 50 J. Serarols et al. / Reactive & Functional Polymers 48 (2001) 37 – 51 Fig. 6. Theoretical and calculated isotherms on equilibrium surface. (a.1) Gold 3rd contact isotherm, (a.2) gold column isotherm; (b.1) zinc 3rd contact isotherm, (b.2) zinc column isotherm. 6. Notation a, b C C0 Ce,i qe qe,i qp isotherm parameters gold or zinc concentration in the liquid phase (mg Au(III) or Zn(II) / dm 3 ) initial concentration in the liquid phase (mg Au(III) or Zn(II) / dm 3 ) equilibrium concentration for a contact i in liquid phase (mg Au(III) or Zn(II) / dm 3 ) gold or zinc concentration in the resin (mg Au(III) or Zn(II) / g) gold or zinc concentration in the resin for a contact i (mg Au(III) or Zn(II) / g) gold or zinc concentration pre- qe,cal qe,exp qmax ki N t V WXAD-2 loaded in the resin (mg Au(III) or Zn(II) / g) gold or zinc concentration calculated by the surface equilibrium equation (mg Au(III) or Zn(II) / g) gold or zinc experimental concentration (mg Au(III) or Zn(II) / g) gold or zinc maximum concentration in the resin (mg Au(III) or Zn(II) / g) equilibrium surface parameters, i5 1, 2, 3, 5, 6 number of experiences time (s) sample volume (dm 3 ) resin weight (g) J. Serarols et al. / Reactive & Functional Polymers 48 (2001) 37 – 51 Acknowledgements This work was supported by the University of Girona project (UdG-9100087). The assistance ´ of Ms. Montserrat Caceres with the laboratory work is gratefully acknowledged and Mr. Christian Serarols for English language revision. References [1] E.G. Furuya, H.T. Chang, Y. Miura, H. Yokomura, S. Tajima, S. Yamashita, K.E. Noll, Intraparticle mass transport mechanism in activated carbon adsorption of phenols, J. Environ. Eng. 122 (10) (1996) 909–916. [2] H. Tamura, M. Kudo, R. Furuichi, Polyfunctionality of carboxyl sites on IRC-50, a MR-type ion exchange resin, evaluated by modelling with the Frumkin isotherm, React. Funct. Polym. 38 (1998) 177–181. [3] E. Guibal, C. Milot, J.M. Tobin, Metal-anion sorption by chitosan beads: equilibrium and kinetic studies, Ind. Eng. Chem. Res. 37 (1998) 1454–1463. [4] R.-L. Tseng, F.-C. Wu, R.-S. 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