Abstract

SEPARATION PROCESSES

Biosorption study of Ni²⁺ and Cr³⁺ by Sargassum filipendula: kinetics and equilibrium

A. A. Seolatto^I; T. D. Martins^II,IV; R. Bergamasco^III; C. R. G. Tavares^III; E. S. Cossich^III; E. A. da Silva^IV,*

^ISchool of Chemistry, Federal University of Goiás - UFG, P.O. Box, CEP: 74001-970, Goiânia - GO, Brazil

^IISchool of Chemical Engineering, University of Campinas, Av. Albert Einstein 500, CEP: 13083-852, Campinas - SP, Brazil

^IIIDepartment of Chemical Engineering, State University of Maringá - UEM, Av. Colombo 5790, CEP: 87020-900- Maringá - PR, Brazil

^IVSchool of Chemical Engineering, Western State University of Paraná - UNIOESTE, Phone: + (55) (45) 33797039; Fax: + (55) (45) 33797002, Rua da Faculdade 645, Jardim La Salle, CEP: 85903-000, Toledo - PR, Brazil. E-mail: edsondeq@hotmail.com

ABSTRACT

In this work, the biosorption of Cr³⁺ and Ni²⁺ by Sargassum filipendula pre-treated with CaCl₂ was studied. Kinetic and equilibrium experiments were carried out for mono- and multi-component solutions in a batch reactor at pH 3.0 and 30 ºC. The results from the kinetic experiments showed that Cr³⁺ adsorbs slower than Ni²⁺. This behavior was explained by means of a mechanistic analysis, which showed that Cr³⁺ uptake presented three adsorption stages, whereas Ni²⁺ adsorption presents only two. The mono-component equilibrium data, along with binary kinetic data obtained from mono-component experiments, showed that, although the kinetics for Cr³⁺ removal are slower, the biomass had a stronger affinity for this ion. Almost all Ni²⁺ is desorbed from the biomass as Cr³⁺ adsorbs. The binary equilibrium data also presented this behavior. The binary data was also modeled by using modified forms of the Langmuir, Jain and Snoeyink, and Langmuir-Freundlich isotherms. However, the prediction obtained presented low accuracy. An alternative modeling with artificial neural networks was presented and the results showed that this technique could be a promising tool to represent binary equilibrium data. The main contribution of this work was to obtain experimental data for Cr³⁺/Ni²⁺ adsorption, which is a system rarely found in the literature and that provides information that could be used in process modeling and simulation.

Keywords: Algal biomass; Mathematical modeling; Neural networks; Single solution; Binary solution.

INTRODUCTION

Many industrial segments are responsible for the increasing amount of metallic ions released into the environment. For example, Cr³⁺ is released in wastewaters by several industrial sectors, such as mining, iron sheet cleaning, chrome plating, leather tanning, finishing industries, and wood preservation. It is known to be toxic if absorbed in excess by the human body and may cause serious health concerns. Ni²⁺ can be found mainly in wastewater from electroplating, electronics, and metal cleaning industries. Human contact with Ni²⁺ causes severe damage to lungs and kidneys, gastrointestinal distress, pulmonary fibrosis, renal edema, and skin dermatitis.

There are several unit operations that could be used to remove heavy metals from wastewaters, such as: flocculation, precipitation, electrolysis, crystallization, adsorption, chemical precipitation etc. However, these methods often demand high initial and maintenance costs, have low inefficiency (especially at low concentrations), offer no regeneration, need large amount of chemicals, generate new types of contaminants etc. To overcome these problems and enhance the removal efficiency, research groups all over the world have focused their attention on biosorption processes. Indeed, these studies showed that biosorption could be a promising alternative for heavy metal removal (Farooq et al., 2010).

Biosorption is a method to remove target substances from solution by using living or non-living biomass, based on the interaction present between the two (Volesky and Holan, 1995). Due to its low cost in comparison with other technologies, high efficiency, and minimization of chemical or biological sludge, biosorption has received significant attention over the last years.

Experimental studies on biosorbent selection for heavy metal removal include bacteria, yeast, fungi, and algal and plant derived materials (Farooq et al., 2010; Vieira et al., 2012). Moreover, studies in which seaweed is used, especially the Sargassum species, confirm that this biomass can remove several metallic ions (chromium, cadmium, copper, nickel, zinc etc.) very efficiently (Rocha et al., 2006; Tsui et al., 2006; Al-Homaidan, 2008; Hajar, 2009; Sivaprakash et al., 2010).

The aim of this work was to perform kinetic and equilibrium studies of Cr³⁺ and Ni²⁺ biosorption from single and binary solutions, using Sargassum filipendula algal biomass as biosorbent.

MATERIALS AND METHODS

Biomass and Solutions Preparation

The biomass used in this work was the brown seaweed Sargassum filipendula, commonly found in the Brazilian coast. First, it was washed with deionized water and dried at 60 °C for 24 h. The biomass was then treated according to the methodology described by Matheickal et al. (1999) and Matheickal and Yu (1999). The dried biomass was then chopped and sieved to different fraction sizes. Dry particles with an average diameter of 2.20 mm were used in all sorption experiments.

Chromium and nickel solutions were prepared by dissolving chromium chloride hexahydrate (CrCl₃.6H₂O) and nickel chloride hexahydrate (NiCl₂.6H₂O) in deionized water.

Kinetic Studies

Kinetic experiments were carried out in 2 L Erlenmeyer flasks, containing 1 L of metal solution (Cr³⁺, Ni²⁺ or their mixture) and 1.5 g of dry biomass. Among all parameters that affect the process kinetics, only heavy metal initial concentration is considered here. All the other parameters were kept fixed. The tests for the mono-component system were carried out with the following initial concentrations: 2 meq Ni²⁺/L, 5 meq Ni²⁺/L, 3 meq Cr³⁺/L, 8 meq Cr³⁺/L. For binary systems, the following initial concentrations were used: 4 meq Ni²⁺/L and 8 meq Cr³⁺/L (experiment 1), 2 meq Ni²⁺/L and 6 meq Cr³⁺/L (experiment 2), and 5 meq Ni²⁺/L and 3 meq Cr³⁺/L (experiment 3). The flasks were kept at 30 ºC under 200 rpm agitation. The pH was kept fixed at 3.0. During the experiments pH tends to rise, thus it was adjusted with a 1 M HCl solution whenever needed.

Equilibrium Studies

Equilibrium experiments in mono-component and binary systems of Cr³⁺ and Ni²⁺ were carried out in a batch reactor. For all experiments, the initial solution concentration ranged from 1 to 18 meq/L. Erlenmeyer flasks containing 0.23 g of dry biomass and 50 mL of each metallic ion solution were kept under constant agitation at 200 rpm in a rotary shaker, at a fixed temperature of 30 °C and pH 3. A solution of 1 M HCl was used to adjust the pH whenever needed. To ensure that the systems reached equilibrium, all the experiments lasted 72 hours.

Data Analysis

In all kinetic and equilibrium tests, the adsorbed amount of the corresponding ion (Cr³⁺ or Ni²⁺) in the biosorbent (q_t) was calculated by the following equation:

where V is the volume of solution, C₀ is the initial concentration of ion in solution, C_t is the concentration of ion in solution at a time t, and M is the biosorbent's dry mass.

The ions concentrations in solution (Ni²⁺ and/or Cr³⁺) were determined by atomic absorption spectrometry (Varian SpectrAA-10 plus). Standard solutions were prepared at concentrations of 0.05, 0.1, 0.2, 0.4, and 0.5 meq/L (Merck-Tritisol). All equilibrium sorption experiments were carried out in duplicate and the data presented here correspond to the average value.

RESULTS AND DISCUSSION

Kinetic Studies

Mono-Component System

Kinetics experiments are an important aspect that needs to be addressed in all sorption studies. A proper analysis of adsorption kinetics can provide information about the process speed, the time required to reach equilibrium, as well as some insights into the adsorption mechanisms. The results obtained in kinetic experiments for Ni²⁺ and Cr³⁺ biosorption are shown in Figure 1(a) and 1(b). Concentrations in the fluid phase are shown on the main axis and the amount of heavy metal adsorbed in the inset.

The kinetic data presented in these graphs haves a familiar behavior. The removal rate was high at the beginning followed by a rate decrease when the process approaches equilibrium. The kinetic rate became zero at the equilibrium. Besides, it seems that the initial heavy metal concentration had no significant effect on the kinetic rate. Cr³⁺ biosorption was slower than Ni²⁺ (in just one hour, around 85 % of Ni²⁺ and 62 % of Cr³⁺ was removed from the solution), and the total time required for its removal to reach equilibrium was about 7.5 times (~30 h) that required for Ni²⁺ (~4 h).

Cr³⁺ an Ni²⁺ kinetics can be explained using speciation diagrams. Fahim et al. (2006) presented a speciation diagram of chromium in the pH range of 2-12. According to this graph, an aqueous solution of pH 3.0 has approximately 80% and 20% of Cr³⁺ and CrOH²⁺ ions, respectively. Srivastava et al. (2009) stated that, in a similar solution, Ni²⁺ ions are predominant. It is possible that the lower adsorption rate of chromium ions is due the presence of CrOH²⁺, which presents lower diffusivity than Cr³⁺ and Ni²⁺.

To quantify the kinetic aspects of biosorption, mathematical modeling has been used in several studies over the years. To obtain as much information as possible about the Ni²⁺ and Cr³⁺ biosorption kinetics, we modeled the experimental data obtained by using four theoretical models: pseudo-first-order (Lagergren, 1898), pseudo-second-order (Ho and McKay, 1998), three-stage (Choi et al., 2007), and the intra-particle diffusion model (Ruthven, 1984).

The pseudo-first-order model is expressed by the differential equation:

where: q_t and q_eq are the amount adsorbed at the time t and at equilibrium, respectively (meq.g^-1), k₁ is the pseudo-first-order kinetic rate parameter (s^-1), and t is the time (s). Integrating Eq. (2) between 0 and t, and 0 and q, it becomes:

The pseudo-second-order model is expressed as:

where: k₂ is the pseudo-second-order kinetic rate parameter (g. meq^-1.s^-1). Similarly, an explicit equation for q_t can be obtained by integrating Eq. (4) between 0 and t, and 0 and q:

In order to explain different adsorption mechanisms, Wilczak and Keinath (1993) proposed a new model based on three-stage kinetics. Figure 2 illustrates how this process occurs.

According to the authors, the first step is an instantaneous and irreversible adsorption on the adsorbent exterior surface (type-1 sites). Mathematically, it can be described by the equation:

where q_1,∞ is the maximum amount that can be adsorbed on type-1 sites. The second step is a slow intra-particle adsorption at type-2 sites described by the equation:

where α is the rate constant for mass transfer from the fluid phase to the interior sites (s^-1), q_2,∞ is the maximum amount adsorbed at type-2 sites (meq.g^-1), and β is a limiting factor for q_1,∞ that lies in the [0;1] range (dimensionless). β=0 is characteristic of an instantaneous adsorption only, whereas β=1 defines two-stage adsorption kinetics. A three-stage kinetic process takes place when β∈(0,1). In this case, the ion concentration in the fluid phase does not approach zero at the end of the experiment. Instead, the type-2 adsorption is suppressed by some mass transfer barrier (such as: small particle size, high fluid phase concentration) at a time t and the amount of adsorbed material at type-2 sites is a fraction β different from the values of one theoretically possible.

Integrating Eq. (7), along with the mass balance for the system, the analytical solution can be obtained (details can be found in Wilczak and Keinath (1993)):

where:

is the fraction of the ion adsorbed at type-1 sites, , is the fraction of the ion adsorbed at type-2 sites, and γ = (1− ξ1 −βξ₂ )α βξ₂.

The constant effective diffusion model was previously described by Ruthven (1984). It is based on the mass balance for the solid phase and the following hypotheses are considered: the particle has a spherical form, the equilibrium concentration in the fluid phase does not differ much from its initial concentration, and heat transfer between the particle and the surrounding fluid is rapid, so temperature gradients can be considered to be negligible. Mathematically, this model can be expressed by the differential equation:

with the following initial and boundary conditions:

An analytical solution for Eqs. (9)-(12) can be derived and is given by (Ruthven, 1984):

In Equations (9)-(13), r_p is the particle radius (cm), D_eff is the constant effective diffusion coefficient (cm².s^-1), n is the number of terms of the infinite series, q₀ is the amount adsorbed at the particle surface, in equilibrium with the fluid phase, and q is the average concentration through the particle (meq.g^-1):

The kinetic parameters of all models considered here were determined by using the Nelder and Mead (1965) method to minimize the objective function:

where N is the total number of samples collected in the experiments. The superscripts EXP and MOD correspond to experimental and calculated data, respectively. After the adjustments, the accuracy of the kinetic models was evaluated by comparing some statistical parameters such as: average absolute deviation – defined by Eq. (16)– and correlation coefficients. To estimate D_eff in the intra-particle diffusion model, 5000 terms of the infinite series were considered.

All estimated kinetic parameters and the statistical parameters calculated for the kinetic modeling are shown in Table 1. The curves obtained from the models are also present in Figure 1. The parameter values showed that the initial concentration indeed influenced the removal kinetics. In general, kinetic parameters for Ni²⁺ decreased as C₀ increased. The opposite behavior occurred for Cr³⁺ removal. Our results are in agreement with several recent studies which present the same pattern of Ni²⁺ and Cr³⁺ removal, even when using different types of adsorbents (Nehrenheim and Gustafsson, 2008; Calero et al., 2009; Karaoğlu et al., 2010; Anoop Krishnan et al., 2011; Fernandes and Gando-Ferreira, 2011; Suazo-Madrid et al., 2011; Alomá et al., 2012).

The statistical parameters obtained show that all models were in good agreement with the experimental data, the maximum calculated AADs were 5.50%. The pseudo-second-order and three stage models best fit the experimental data for Ni²⁺ and Cr³⁺ removal, respectively. These models presented the lowest AAD and the highest correlation coefficient among all models tested.

This result raises an important question: "What's the difference between Ni²⁺ and Cr³⁺ kinetic removal?" The answer to this question could be found by analyzing the mechanisms involved in the process. One way to perform this task is by using the pore-diffusion model proposed by Weber and Morris (1963). The authors suggested that sorption processes involve three main steps: (i) diffusion in the liquid film, (ii) pore diffusion and (iii) adsorption at the available sites. The one which occurs slowly is said to be the rate-limiting step and corresponds to the speed of the process. The last step (iii) is assumed to occur rapidly and therefore it is considered to be negligible.

To evaluate whether steps (i) or (ii) are the rate-controlling factor, one should plot and analyze q_t x t^0.5. If the plot behaves linearly, i.e.:

Then intra-particle diffusion is the rate-limiting step. In Eq. (17), k_D is the intra-particle diffusion coefficient (meq.g^-1.s^-0.5) and C (meq.g^-1) is a parameter that gives an idea about the boundary layer effect. A typical kinetic experiment usually leads to a plot with several linear segments, representing pore-diffusion in progressively smaller sizes. The equilibrium is represented by a horizontal line, where q_t is constant. The number of linear segments and which points belong to each segment can be chosen visually; however, this is not a reliable practice. Recently, Malash and El-Khaiary (2010) showed that the results obtained by applying Piecewise Linear Regression (PLR) are more accurate than the ones obtained by using the visual determination. In this work, the number of linear segments (and the boundaries between then) of the mono-component kinetic data were estimated by using the PLR technique. Details of the calculation procedures can be found in the original paper.

The linear segments obtained for the Ni²⁺ and Cr³⁺ kinetic data are shown in Figure 3. Table 2 shows the estimated parameters, the break times, and the correlation coefficients of each segment. The results show that the kinetic process was multi-linear for both metals. Besides, there is a clear difference between Cr³⁺ and Ni²⁺ removal: the number of adsorption stages. Three and two linear segments were calculated for Cr³⁺ and Ni²⁺, respectively. This is confirmed by the high correlation coefficients obtained.

The first curve segment is often related to the external surface adsorption. It is generally the fastest part of the process, where the adsorbate diffuses through the bulk solution to the particle surface. When the surface reaches saturation, intra-particle diffusion takes place and the second curve segment forms. This stage is related to the macro-pore diffusion, where the intra-particle diffusion is the rate-controlling step on the adsorbent. A third curve segment is the equilibrium stage, where the adsorbate diffuses through the micro-pores. In this stage, the process slows down and the maximum adsorption is attained (Alkan et al., 2008). The description above is in perfect agreement with the k_D values presented in Table 2, where k_D,1 > k_D,2 > k_D,3. The results from the intra-particle model also confirmed that the initial concentration affect the process kinetics: for a different C₀, the diffusion parameters, as well as the break time values were also different.

Several authors reported the multi-step behavior of Cr³⁺and Ni²⁺ adsorption using various different adsorbents (Oliveira et al., 2005; Nuhoglu and Malkoc, 2009; Chen et al., 2010; Ijagbemi et al., 2010; Karaoğlu et al., 2010; Aravindhan et al., 2012). In this work, Cr³⁺ biosorption occurs at the external surface and macro- and micro-pore regions, and Ni²⁺ biosorption occurs at the external surface and macro-pore region. This different multi-step behavior is the answer to the question addressed earlier.

Binary System

Industrial wastewaters often present more than one component. Thus, obtaining experimental data from multicomponent adsorption experiments is also important to evaluate the synergism that arises in such systems. In this work, kinetic experiments for Cr³⁺/Ni²⁺ mixture biosorption were performed to evaluate the effect of Ni²⁺ over Cr³⁺ biosorption and vice-versa. The results obtained in these experiments are shown in Figure 4.

From this figure one can see that the time required for the system to reach equilibrium was 50 h. Besides, in the first two hours the biosorption rate for Ni²⁺ was higher than that for Cr³⁺, which is comparable to the behavior observed in the mono-component kinetic runs. After this time, a significant amount of the adsorbed Ni²⁺ was replaced by Cr³⁺ ions and returned to the solution. The influence of Cr³⁺ ions on Ni²⁺ biosorption is clearly evident: the higher the Cr³⁺ initial concentration, the higher is the Ni²⁺ desorption from the biomass.

In these binary biosorption tests only 9.5%, 2.6%, and 1.2% of the Ni²⁺ ions were removed from the solution in experiments 1, 2, and 3 respectively. This probably occurred due to the competition for a determined adsorption site: Ni²⁺ has higher mobility and it adsorbs first, but since Cr³⁺ has a higher affinity to the adsorption sites, an ion exchange occurs and Ni²⁺ is desorbed.

Silva et al. (2003) studied the binary removal of Cr³⁺ and Cu²⁺ by Sargassum sp. in a batch reactor. The authors observed the same pattern presented here: that there was an initial biosorption of Cu²⁺; however during the process, Cr³⁺ ions adsorbed onto the biosorbent surface, occupying the available sites and some of the sites previously occupied by Cu²⁺ ions. According to the authors, this replacement occurred due to the higher affinity of Cr³⁺ for the active sites.

Equilibrium Experiments

Mono-Component System

The first step in the design of adsorption/ biosorption processes is the choice of the biosorbent material. The main criteria for the selection of the adsorbent/biosorbent are cost, removal capacity and selectivity. Thus, equilibrium studies are also an important aspect that demands proper attention in adsorption studies. Equilibrium data provide information about the biosorbent's performance, its maximum capacity of adsorption and selectivity, as well as some insights about the removal mechanism. In this work, experimental data for Ni²⁺ and Cr³⁺ adsorption equilibrium from single component solutions were obtained, and are shown in Figure 5.

From Figure 5, one can see that the Sargassum filipendula biomass adsorbs preferentially Cr³⁺ over Ni²⁺. Its saturation value was two times higher than for Ni²⁺. At lower concentrations, the equilibrium concentration of Cr³⁺ has higher than for Ni²⁺. This pattern also repeats in others types of adsorbents. Results obtained by Barros et al. (2007), Farajzadeh and Monji (2004), and Rafatullah et al. (2009) also indicated that Cr³⁺ is adsorbed preferentially over Ni²⁺ in sanitary sewage, wheat bran, and meranti sawdust, respectively.

In addition to kinetic studies, mathematical modeling can also provide quantitative information about the equilibrium data obtained. For this purpose, the equilibrium data for Ni²⁺ and Cr³⁺ biosorption were used to fit the model parameters in the Langmuir and Sips isotherms. The Langmuir isotherm is frequently used to describe the equilibrium in mono-component systems, and is expressed by the following equation:

where: C_eq (meq.L^-1) is the ion concentration in the fluid phase at equilibrium, and b (L.meq^-1) and q_max (meq.g^-1) are adjustable parameters. The parameter b in Eq.(18) corresponds to the initial slope of the curve and indicates the biosorbent affinity for the adsorbed substance: a higher initial slope corresponds to a higher affinity constant. The parameter q_max is the Langmuir monolayer saturation capacity (maximum amount of adsorbate per unit weight of adsorbent to form a complete monolayer) (Ruthven, 1984).

The Sips or Langmuir-Freundlich isotherm is represented by the following equation:

where q_max and b have the same meaning as those in the Langmuir isotherm and the parameter k is a measure of the adsorbent heterogeneity. When 0 < k < 1, the heterogeneity is considered to correspond to variations in the solid surface. When the adsorbed molecule has strong affinity for the adsorbent molecules (a positive cooperative effect), k will be greater than 1 (Tóth, 2001).

In this work, the isotherm parameters were determined using the Nelder and Mead (1965) method to minimize the objective function:

In Table 3 the isotherm parameters, r² and AAD are presented. The curves obtained using the isotherms are shown in Figure 5.

From Table 3, one can see that, for the same metal, the Langmuir and Sips parameters do not differ significantly, which indicates that the biosorbent presents low heterogeneity. Also, the Sips isotherm fitted the experimental data better than the Langmuir model. This fact can be confirmed by the AAD and correlation coefficient values.

Indeed, the values of the Langmuir (and Sips) isotherm parameters confirmed that Cr³⁺ was adsorbed preferentially over Ni²⁺. Both q_max and b presented higher values for Cr³⁺. Also, the value of k in the Sips isotherm indicates that the biosorbent has high affinity for Cr³⁺ (k > 1).

In Table 4 are presented values for maximum uptake capacity for Cr³⁺ and Ni²⁺ removal in different adsorbents. Comparing these numbers with the ones obtained in this work, one can see that this biomass presents a good performance. Moreover, this seaweed species is abundant on the Brazilian coast and can be obtained at low coast. Therefore, Sargassum filipendula algal biomass has a high potential to be used in industrial adsorption processes for Cr³⁺/ Ni²⁺ removal.

Binary System

Adsorption equilibrium studies are also required for multi-component solutions. In this work, equilibrium data for Ni²⁺/Cr³⁺ mixture adsorption were also obtained in order to complete this adsorption study. A comparison between Cr³⁺ and Ni²⁺ uptake in each experiment performed are presented in Figure 6.

The results obtained show that, for all binary adsorption experiments, the biosorbent selectivity remains Cr³⁺ > Ni²⁺. Besides, the amount of Cr³⁺ adsorbed at equilibrium was at least three times higher than for Ni²⁺ in all experiments. This affinity order was also verified for different types of adsorbents. The results obtained by Parab et al. (2006), Sekhar et al. (1998), and Oliveira et al. (2005), who investigated the adsorption of solutions containing Cr³⁺ and other metallic ions, showed that this ion is preferentially adsorbed over the other ones in solution.

Adsorption isotherms are also used to model binary equilibrium data and, over the last decades, several models were proposed. In this work, we modeled the experimental data using three isotherms: competitive Langmuir, competitive Langmuir-Freundlich and Jain and Snoeyink. The competitive form of the Langmuir isotherm is widely used to model multi-component equilibrium data. It is an extension obtained from the single component model. For binary systems, it can be described by the following equations (Ruthven, 1984):

where q_max,1, and b₁ are the parameters calculated for the Cr³⁺ mono-component Langmuir isotherm and q_max,2 and b₂ are the parameters calculated for the Ni²⁺ mono-component Langmuir isotherm. The Langmuir–Freundlich isotherm can be obtained by adding two new parameters (k₁, k₂) as concentration exponents in the Langmuir isotherm model (Ruthven, 1984):

The parameters of Eqs. (23) and (24) and are derived from the mono-component Langmuir-Freundlich isotherm. Jain and Snoeyink (1973) proposed an adsorption model for binary mixtures based on the hypothesis that part of adsorption occurs without competition. If q_max1 > q_max2, the mathematical expression can be written as:

All the parameters present in the Jain and Snoeyink isotherm are also derived from the mono-component Langmuir isotherm. Although this is a practice commonly used, the results obtained for mono-component systems generally do not predict the behavior of a binary system. This behavior is observed because the parameters do not take into account the interactions between the ions present (Repo et al., 2011). Aksu et al. (2002) proposed that an interaction parameter should be added to Eqs. (21)-(26) to characterize these effects. Thus, a modified form of the competitive Langmuir model can be written as:

The modified Langmuir-Freundlich isotherm can be written as:

Finally, the modified form of the Jain and Snoeyink isotherm can be written as:

In Eqs. (27)-(32) only the dimensionless interaction parameters, η₁ and η₂, should be estimated using the binary equilibrium data by solving simultaneously both equations. All the others are derived similarly to the conventional models. In this work, the interaction parameters were calculated using the Nelder and Mead (1965) method to minimize the objective function:

where i = 1 correspond to Cr³⁺ ions and i = 2, to Ni²⁺. The parameters q_max,1, q_max,2, b₁, and b₂ were taken from the mono-component results (Table 3). The interaction parameters obtained for each binary isotherm, AAD and r² calculated for each ion are shown in Table 5.

The values of η_i obtained deviate from unity in all cases. This indicates that the parameters obtained by using the mono-component isotherms would not lead to good predictions if used in multi-component models. The model that best fitted the experimental data was the modified Langmuir-Freundlich isotherm, for which the calculated AAD were 8.30% and 26.2% for Cr³⁺ and Ni²⁺, respectively.

An affinity parameter, B_i, can also be calculated for binary isotherms and is given by the product η_i x b_i. The values of B_i are also shown in Table 5, where one can see that, for all binary models: B_Cr³⁺ > B_Ni²⁺ This result confirms that Cr³⁺ has an inhibitory effect over Ni²⁺.

It has been reported that brown seaweeds present several functional groups, such as: carboxyl/hydroxyl groups in alginic acid, amine/amide groups in the peptidoglycans and proteins, and sulfonate and thiol groups in the sulfate polysaccharides and amino acids (Raize et al., 2004). All these groups are known to bind heavy metals.

Infrared spectra obtained by Fourier transform infrared spectrometry (FT-IR) can be used to determine which functional groups play a role in adsorption processes. In the literature it has been reported that Ni²⁺ ions can be bonded by: amine, amide, carboxyl, hydroxyl, and sulfonate groups (Kleinübing et al., 2010; Çelekli and Bozkurt, 2011; Ramana et al., 2012).

In other studies it has been found that Cr³⁺ ions can be bound by carboxyl, hydroxyl, aldehyde, amine, phosphate, thiol, and ether groups (Karaoğlu et al., 2010; Dos Santos Lima et al., 2011; Fathima et al., 2012). As mentioned above, several of these groups are present in Sargassum filipendula's surface and the inhibition of Ni²⁺ removal by Cr³⁺ ions is probably caused by the competition of both ions for the same functional group.

In Figures 8a-c are shown the relation between the experimental q_eq and the ones calculated by the isotherm models. Also, a comparison between the original and modified models is presented. If the results for conventional and modified isotherms were similar, the open and filled symbols should overlap. From these graphs, it is evident that there is a difference between the two modeling approaches. The results obtained from the original and modified competitive Langmuir isotherms show that they were practically equivalent. For the Jain and Snoeyink isotherm, the results obtained for the modified model were slightly better for Cr³⁺, and almost equivalent for Ni²⁺. However, for the Langmuir-Freundlich isotherm the results obtained for the modified one were significantly better when compared to the original model. This fact corroborates the importance of estimating the interaction parameters in multi-component adsorption processes.

Modeling adsorption equilibria of binary solutions is still a challenge. Several studies that suffer from bad predictions can be found on the literature. For example, Fagundes-Klen et al. (2007) used several adsorption isotherms to model the removal of Cd²⁺/Zn²⁺ mixtures by Sargassum filipendula and obtained poor predictions. Luna et al. (2010) modeled Cd²⁺/Zn²⁺ biosorption onto Sargassum filipendula and obtained errors between 16.5% and 37.4%. Also, Repo et al. (2011) obtained errors between 15% and 140% when modeling Co²⁺/Ni²⁺ adsorption onto EDTA- and DTPA-modified silica gel.

To improve the quality of data fitting, Jha and Madras (2005) proposed that another modeling tool could be used: Artificial Neural Networks (ANNs). ANNs are mathematical algorithms that have the capacity to relate independent to dependent variables of a process by learning from given examples, without requesting any knowledge about the mathematical formulation of the process.

An ANN is based on the structure of the biological neuronal system and consists basically of a set of artificial neurons that are interconnected and organized into layers. The information process in an ANN begins by relating the input (x_i) of each neuron to a synaptic weight (w_ij) that assesses the influence of this entry on the output of this neuron (activation coefficients). The sum of all the activation coefficients causes the neuron activation. The answer of the input stimulus is obtained by applying an activation function to the neuron activation, generally the sigmoid or the hyperbolic tangent function. This procedure extends to the output layer of the network, where the ANN answers are the dependent variables of the problem (Braga et al., 2000).

The determination of the network structure is not a simple task: there is no rule or theorem to find the optimal topology of a network for a given data set. Modeling with ANNs consists of varying the number of neurons of the input and hidden layers to find the suitable synaptic weights that minimize the deviation among observed and calculated data. This process consists of a step called network training and it is in this step that the network learning is evaluated. ANNs have been widely used in problems concerning food processing, process control, phase equilibrium, and biotechnological processes (Schmitz et al., 2006; Rivera et al., 2007; da Cruz et al., 2009). In the adsorption field, ANNs were successfully used to model several multi-component systems (Carsky and Do, 1999; Jha and Madras, 2005; Fagundes-Klen et al., 2007; Canevesi et al., 2012).

To illustrate that ANNs could be used to describe the equilibrium of binary adsorption processes, we used feedforward ANNs with two hidden layers to model the data from Cr³⁺/Ni²⁺ mixture biosorption. The input variables were the equilibrium concentrations of Cr³⁺ and Ni²⁺ in the fluid phase, while the uptake amount of Cr³⁺ and Ni²⁺ were used as output. A schematic diagram of the ANN structures tested is shown in Figure 7.

To obtain the ANN structure that better fit the experimental data, different numbers of neuron combinations were tested in the hidden layers (from 2 to 10). To estimate the value of the synaptic weights, the Simulated Annealing method (Albrecht and Wong, 2001) was used to minimize the objective function given by Eq. (33). The hyperbolic secant (hidden layers) and linear function (output layer) were used as activation functions. All the simulations were conducted with our own Fortran code.

Once the synaptic weights are determined, the next step is to validate the model. Usually, this is performed by presenting new data to the network and comparing the new outputs with the corresponding experimental ones. Since we have only 26 experimental data and the objective is to suggest a new tool that to be used to model binary equilibrium data, we choose to use all 26 data collected to train the ANN and perform a preliminary study. Further experiments will be performed in the future in order to do an extensive study related to neural network modeling in adsorption processes.

Among all network architectures considered, the best results were obtained using ANNs with two hidden layers and two neurons in the second hidden layer. In Table 6 are shown the objective function, the AAD and the r² obtained for these structures. From these values, one can see that the ANN modeling is superior when compared to the isotherm performance. The simplest ANN architecture (2-2-2-2) was able to describe the equilibrium data with success. The best result was achieved by the ANN with 2 neurons in the first hidden layer and 8 neurons in the second hidden layer. The AAD obtained were 2.15 % and 6.72 % for Cr³⁺ and Ni²⁺, respectively. In Figure 8d the relation between the experimental q_eq and the values calculated by the ANN 2-8-2-2 is shown and the better performance obtained from the ANN modeling can be confirmed.

The accuracy obtained using ANN modeling is mainly due to the versatility of the technique. The ANN algorithm is based on the functioning of the human brain. Their principal feature is that they can relate input and output variables without requiring a detailed mathematical knowledge of the process. Thus, an ANN can be used to model almost any known process. On the other hand, isotherm models are based on several hypotheses that often are not related to the reality of any experiment (e.g.: homogeneous adsorbent hypotheses of the Langmuir isotherm). Its formulation is complicated because biosorption processes are usually a combination of adsorption, ion exchange, complexation, quelation, etc. and its application is limited to specific cases. Regarding this work, it seems that ANN may be a promising tool due to the uncertainties in the mechanism of Cr³⁺/Ni²⁺ removal, that would be needed for multi-component isotherm formulation.

CONCLUSION

In this work mono- and multi-component biosorption of Cr³⁺ and Ni²⁺ ions by Sargassum filipendula pre-treated with CaCl₂ was investigated. Kinetic and equilibrium studies were performed for both systems. A simple comparison with other studies showed that the algae biomass has great potential for use in a process unit. Our results showed that Cr³⁺ adsorption kinetics were slower than for Ni²⁺ in both mono-component and binary experiments. A mechanistic analysis revealed that this difference could be attributed to the number of adsorption stages of each metallic ion: Cr³⁺ uptake presented three adsorption stages, whereas for Ni²⁺ there are only two. A strong competitive behavior was observed in binary studies: when both ions are present in solution, Ni²⁺ ions were gradually removed from the biomass. Besides, the higher the initial concentration of Cr³⁺, the higher the Ni²⁺ desorption. Equilibrium experiments confirmed that Cr³⁺ is preferentially adsorbed by the biosorbent in both mono- and multi-component experiments. Finally, results obtained by using adsorption isotherms showed that these models fail to describe the binary equilibrium. On the other hand, preliminary simulations with Artificial Neural Networks showed that they could be a viable alternative to model complex processes, such as the adsorption of heavy metals using natural materials as adsorbents.

Submitted: June 24, 2010

Revised: April 11, 2012

Accepted: May 2, 2013

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