Additional Material Section
Experimental procedures
Materials
Amberlite XAD-7 was supplied by Sigma-Aldrich (Saint-Louis, U.S.A.). This is a polyacrylic
acid ester type resin ([CH2–CH(COOR)]n). Amberlite XAD-7 can be considered as a
nonionic, moderately hydrophilic porous polymer (pore diameter: 80-85 Å). It is
commercialized as a macroporous polymer, although it must be considered as a mesoporous
material (pore diameter: 20-500 Å) according to IUPAC. The size range of resin particle was
250-850 µm (20/60 mesh). The specific surface area was 450 m2 g-1, the porosity was 0.55
and the pore volume was in the range 0.97-1.14 cm3 g-1 (skeletal density close to 1.24 g cm-3)
[1]. The resin was conditioned by the supplier with NaCl and Na2CO3 to retard bacterial
growth. It was necessary to clean it to remove salts and monomeric material present on the
resin. The resin was therefore put into contact with ketone for 24 h at 25 °C. After filtration
under vacuum to remove excess ketone, the resin was rinsed with de-mineralized water. Then,
it was washed with nitric acid (0.1 M) for 24 h. The resin was filtered under vacuum and then
rinsed with de-mineralized water to constant pH. Finally, the resin was put into contact with
ketone for 12 h before being filtered under vacuum and dried in a roto-vapor at 50 °C.
Cyphos®IL-101 was kindly supplied by Cytec (Canada). This is a phosphonium salt
(tetradecyl(trihexyl)phosphonium chloride, C.A.S. number: 258864-54-9, formula weight:
519.4 g mol-1). It is a slightly viscous room temperature ionic liquid. It is less dense than
water and colorless to pale yellow. It is immiscible with water although it is sparingly soluble
in water and can dissolve up to 8 % water. The chemical structure is [P R3R’]+ Cl-, where R =
hexyl and R’ = tetradecyl. Other reagents (salts, acids…) were analytical grade and supplied
by KEM (Mexico). Standard metal solutions were supplied by Perkin Elmer (U.S.A.).
1
Resin impregnation
In the present work the extractant was immobilized on the resin by a physical technique.
Different processes may be used for the physical impregnation of the resin including (i) the
wet method, (ii) the dry method, (iii) the impregnation in the presence of a modifying agent,
or (iv) the dynamic method [2]. Previous studies have shown that the dry method increases
the stability of the extractant on the resin. The dry impregnation of the resin was actually
performed by contact of 5 g of conditioned Amberlite XAD-7 with 25 mL of ketone for 24 h.
Varying amounts of Cyphos®IL-101 diluted in ketone (0.5 M) were added to resin slurry for
24 h, under agitation. The solvent was then slowly removed by evaporation in a roto-vapor.
The amount of extractant immobilized on the resin (qIL) was quantified by the following
procedure. A known amount of impregnated resin (250 mg) was mixed with methanol (5 mL)
for 24 h to dissolve the extractant and the solvent was separated from the resin by decantation.
This washing treatment was carried out twice. Finally, the resin was dried at 50 °C for 24 h
for complete evaporation of solvent. The mass difference (MCyphos IL-101) between impregnated
(MXAD-7/Cyphos IL-101) and washed resin (MXAD-7) was used to calculate the amount of extractant
immobilized on the EIR:
q IL 
M XAD-7/Cyphos IL-101 - M XAD-7
M XAD-7/Cyphos IL -101
(A1)
The experimental procedure allowed the preparation of EIRs containing 88 mg extractant g−1
EIR up to 579 mg extractant g-1 EIR.
Sorption and desorption studies
2
Fe(III) solutions were prepared in HCl solutions of different concentrations (0.01 – 8 M) with
metal concentrations ranging between 80 and 600 mg Pt L−1. The sorption experiments were
performed by mixing the resin with Fe(III) solutions for 24 h with a solid/liquid ratio (sorbent
dosage, SD) fixed to m/V = 4 g L−1 (m: mass of sorbent, V: volume of solution). The contact
was operated on a reciprocal shaker (Cole Parmer 51502) with an agitation speed of 150
movements per minute at constant temperature. After filtration the samples were analyzed by
UV-visible spectrophotometry at the wavelength of λ: nm. The amount of metal adsorbed (q,
mg Fe g−1) was calculated by the mass balance equation: q=V(C0−Ceq)/m, where C0 and Ceq
(mg Fe L−1) are the initial and equilibrium Fe(III) concentrations, respectively.
Several sorption kinetic experiments were performed by contact under agitation of a fixed
amount of SIR (loading in the range 88-402 mg extractant g−1) with a fixed volume (m/V: 4 g
L−1) of 3 M HCl solution containing varying Fe(III) concentrations (in the range 20-60 mg
Fe(III) L−1). Temperature was varied in the range 10–40 °C. The agitation speed was set at
150 movements per minute. Detailed experimental conditions are reported in the caption of
the figures. The Fe(III) concentration was measured on line using a pump for driving the
solution into a loop connected to a UV-visible spectrophotometer (Varian Cary 50 Probe,
Agilent Technologies, Santa Clara, CA, USA). The measurements were taken every 12 s. A
smoothing procedure was used for removing measurements artifacts (unmeaning peaks),
taking into account the noise introduced by the spectrophotometer loop (bubbles, etc.). All the
data for the first thirty minutes were used for testing the model of resistance to film diffusion
(see below), while for the other systems (resistance to film diffusion, chemical reaction rates
etc.) the exploitation of data was limited to discrete time values (fixed along the first 24 hours
of contact). For experiments performed in bi-component solutions, the respective
concentrations of Fe(III) and Zn(II) were varied in the range 10-160 mg metal L-1). The same
operating conditions (3 M HCl solutions; m/V: 4 g L-1) were used. The residual concentration
3
of both Fe(III) and Zn(II) metal ions was determined using a Perkin Elmer 3110 AAS (atomic
absorption spectrometer).
For the study of Fe(III) desorption, an amount of 100 mg of EIR (extractant loading: 193 mg
IL g−1) was mixed with 25 mL of Fe(II) solution (3 M HCl solution, initial metal
concentration: 20 mg Fe(III) L−1) for 24 h. The residual concentration measured by UVvisible spectrometry after filtration served to determine the amount of metal bound to the
resin. The metal-loaded resin was mixed for 24 h with 25 mL of a series of eluents: water, 0.1
M Na2SO4, 0.1 M HNO3, 0.1 M H2SO4. After filtration the metal concentration in the eluent
was determined by UV-visible spectrophotometry in order to obtain the amount of Fe(III)
desorbed from the resin. The amount of metal desorbed divided by the amount of metal bound
to the SIR served for calculating the desorption yield (or efficiency). For the evaluation of
sorption/desorption cycles, the same procedure was used for eight cycles.
Modeling of sorption isotherms and uptake kinetics
Sorption isotherms represent the distribution of the solute at equilibrium between the solid
phase (the sorbent) and the liquid phase (the solution). The plot of q versus Ceq can be
modeled using a number of equations. The equations of Freundlich and Langmuir are the
most commonly used. The Freundlich equation supposes an exponential trend while the
Langmuir is characterized by an asymptotic shape. Since the sorption capacity tended to an
asymptotic value (experimental maximum sorption capacity) the isotherm will be
preferentially described by the Langmuir equation rather than the Freundlich equation.
Langmuir equation:
𝑞=
𝑞𝑚 𝑏 𝐶𝑒𝑞
1+𝑏 𝐶𝑒𝑞
(A2)
with qm (mg metal g-1 or mmol metal g-1), b (L mg-1 or L mmol-1) are the constants of
the Langmuir equation: the sorption capacity at saturation of the monolayer and the affinity
4
coefficient, respectively. The parameters of the Langmuir equation were obtained using the
non-linear regression package of Mathematica®.
For bi-component solutions, the modeling of sorption isotherms was performed using the
Langmuir extended equation, using as model parameters (qm,Fe and qm,Zn, bFe and bZn) the
values obtained in the modeling of respective mono-component systems [3, 4].
Extended Langmuir equation:
𝑞𝐹𝑒 = 1+𝑏
𝑞𝑚,𝐹𝑒 𝑏𝐹𝑒 𝐶𝑒𝑞,𝐹𝑒
𝐹𝑒
𝐶𝑒𝑞,𝐹𝑒 +𝑏𝑍𝑛 𝐶𝑒𝑞,𝑍𝑛
𝑞𝑚,𝑍𝑛 𝑏𝑍𝑛 𝐶𝑒𝑞,𝑍𝑛
𝑞𝑍𝑛 = 1+𝑏
𝐹𝑒
𝐶𝑒𝑞,𝐹𝑒 +𝑏𝑍𝑛 𝐶𝑒𝑞,𝑍𝑛
(A3a)
(A3b)
The uptake kinetic can be controlled by a series of mechanisms including the proper chemical
reaction rate but also by diffusion mechanisms (including resistance to bulk diffusion, to film
diffusion and to intraparticle diffusion). The identification of the controlling step is important
for optimizing the process; this allows selecting best experimental conditions or optimizing
the design of the sorbent (for limiting, for example, resistance to intraparticle diffusion).
Actually, the modeling of uptake kinetics should take into account all these mechanisms (film
diffusion, intraparticle diffusion, reaction rate, equilibrium distribution …) at the expense of
using complex numerical analysis systems [5]. Juang and Ju discussed a series of simplified
modeling systems derived from the homogeneous diffusion model (HDM) and the shrinking
core model (SCM) [6]. The HDM involves counterdiffusion of exchangeable species in quasi
homogeneous media, with a contribution from film diffusion (HDM-FD) and/or particle
diffusion (HDM-PD). Solute molecules and exchangeable species (immobilized on the resin)
follow a similar diffusion mechanism (but in the opposite direction). In the case of the SCM, a
sharp virtual boundary exists between the reacted shell of the particle and the unreacted core,
and this boundary moves towards the center of the particle [7, 8]. This model was developed
with different systems depending on the controlling step: film diffusion (SCM-FD), particle
5
diffusion (SCM-PD) and chemical reaction rate (SCM-CR) [6]. A number of mathematical
equations have been developed to simulate these mechanisms, they are listed below:
Homogeneous Diffusion Model
Film Diffusion:
F1 (X)  - ln 1 - X  f(t)
(4)
Particle Diffusion:
F2 (X)  - ln 1 - X 2  f(t)

(5)
Film Diffusion:
t

G 1 (X)  X  g  C(t) dt 
0

(6)
Particle Diffusion:
G 2 (X)  3 - 31 - X 
Chemical Reaction Rate:
G 3 (X)  1 - 1 - X 

Shrinking Core Model
2/3
1/3
t

- 2X  g  C(t) dt 
0

t

 g  C(t) dt 
0

(7)
(8)
Where X is the fractional approach to equilibrium (i.e., q(t)/qeq), the amount adsorbed at time
t divided by the amount of metal adsorbed at equilibrium. Plotting Fi and Gi functions versus
time and the integral term (respectively) determined the most appropriate mechanism for
describing the controlling step. The curve giving a straight line (good correlation measured by
the correlation coefficient) is the predominant limiting step.
The kinetics have been modeled using four conventional models: (a) the pseudo-first order
rate equation (the so called Lagergren equation), (b) the pseudo-second order rate equation,
(c) the resistance to film diffusion, and (d) the simplified approach of intraparticle diffusion
(the so called Crank equation).
6
The reaction rate equations were initially designed for describing chemical reactions in
homogeneous systems. However, they are frequently used for the description of sorption
kinetics; though they underestimate the contribution of diffusion mechanisms.
Pseudo-first order equation (PFORE) [9]:
dq(t )
 k1 ( qeq  q(t ))
dt
(9a)
and after integration:
 q(t ) 
   k1t
ln 1 


q
eq 

(9b)
where qeq (mg g-1) is the sorption capacity at equilibrium (parameter of the model, determined
by data analysis to be compared to the experimental value as a validation criterion), k1 (min-1)
is the pseudo-first order rate constant.
Pseudo-second order rate equation (PSORE) [10]:
dq(t )
 k 2 ( qeq  q(t )) 2
dt
(10a)
and after integration:
q( t ) 
qeq2 k2t
1  qeq k2t
(10b)
where qeq (mg g-1) is the sorption capacity at equilibrium (parameter of the model, determined
by data analysis to be compared to the experimental value as a validation criterion), k2 (g mg-1
min-1) is the pseudo-second order rate constant.
7
The parameters of the models (Eqs. 7.b and 8.b) were determined using the non-linear
regression analysis of experimental data with the Mathematica® software.
Apart of these models that take into account only the reaction, diffusion mechanisms can be
also involved in the control of uptake kinetics: (a) resistance to external diffusion (through the
film surrounding the particles) and (b) the resistance to intraparticle diffusion. The resistance
to bulk diffusion is generally neglected since this limiting step can be easily overcome
providing sufficient agitation to the reactor. The resistance to film diffusion is generally the
predominant step in the initial phase of the sorption process while the resistance to
intraparticle diffusion plays a greater role in the later phase.
In the case of a system described by the Langmuir equation and in the initial step of the
process, the film diffusion kinetic rate can be approached using the equation [11]:
𝐶(𝑡)
Film diffusion resistance: ln ( 𝐶 −
0
1
𝑚
𝑉
1+ 𝑞𝑚 𝑏
) = ln (
𝑚
𝑞 𝑏
𝑉 𝑚
𝑚
1+ 𝑞𝑚 𝑏
𝑉
𝑚
𝑉
𝑚
𝑞 𝑏
𝑉 𝑚
1+ 𝑞𝑚 𝑏
)−(
) 𝑘𝑓 𝑆 𝑡
(11a)
where kf is the film diffusion coefficient (m min-1) and S is the specific outside surface
area (m-1) with:
𝑆=𝑑
6
𝑚
𝑉
(11b)
𝑝 𝜌𝑝(1−𝜀𝑝 )
where dp is the average diameter of the size class (m), ρp is the density of sorbent
particles (g mL-1) and εp is the porosity of the particle.
The slope of the plot ln φ(t) = ln (
𝐶(𝑡)
𝐶0
−
1
𝑚
𝑉
1+ 𝑞𝑚 𝑏
) = 𝑓(𝑡) in the initial linear part allows
determining the film diffusion kinetic rate kf x S (min-1).
8
The intraparticle diffusion coefficient (Deff, effective diffusivity, m2 min-1) has been
determined using the Crank’s equation [12], assuming the solid to be initially free of metal,
and external diffusion resistance not being the limiting step at long contact time:
 - D q2t 
6 (  1)exp  eff2 n 


r
q(t)
6 


1- 2 
2
2
q eq
 n 1
9  9  q n 
(12a)
qn non-zero roots of the equation:
tan q n 
with
3 qn
(12b)
3   q 2n
q
1

VC o 1  
and r being the radius of the particle
(12c)
The equation (11a,b,c) was used with the Mathematica® package for the determination of the
intraparticle diffusion coefficient.
9
Annex A: Influence of HCl concentration and IL loading on Fe(III) distribution coefficient
using Cyphos IL101 immobilized on Amberlite XAD-7 – Slope analysis
Table A1: Linearization of log D versus log [L+Cl-)] R for different HCl concentrations
C(HCl)
(M)
0.5
1
2
3
4
5
6
7
8
Slope
(y)
1.78
1.65
1.99
1.76
1.53
1.24
1.57
1.31
1.48
Ordinate Intercept
log Ky + w log CHCl
2.31
3.06
4.00
4.09
4.28
4.17
4.92
4.94
5.25
R2
0.99
0.96
0.98
0.97
0.92
0.81
0.95
0.92
0.99
Table A2: Linearization of log D versus log aHCl for different IL loadings (HCl concentration:
2-8 M)
qIL
(mg IL g-1 EIR)
102
149
193
310
402
487
579
Slope
(y)
1.85
2.14
2.03
2.38
2.36
2.36
2.22
Ordinate Intercept
log Ky + w log CHCl
1.81
2.15
2.36
2.82
3.22
3.07
3.32
R2
0.99
0.99
0.99
0.99
0.99
0.99
0.99
Table A3: Linearization of log D versus log aHCl for different IL loadings (HCl concentration:
2-8 M)
qIL
(mg IL g-1 EIR)
25
50
88
102
149
194
Slope
(y)
1.13
1.17
1.16
1.20
1.05
1.14
Ordinate Intercept
log Ky + w log CHCl
1.07
1.43
1.86
2.03
2.57
2.60
R2
0.99
0.99
0.98
0.97
0.96
0.99
References
10
[1] V. Gallardo, R. Navarro, I. Saucedo, M. Avila, E. Guibal, Sep. Sci. Technol., 2008,43, 910, 2434.
[2] R.-S. Juang, Proc. Natl. Sci. Counc. ROC(A), 1999,23, 3, 353.
[3] G.-X. Li, C.-Z. Yan, D.-D. Zhang, C. Zhao, G.-Y. Chen, Can. J. Chem. Eng., 2013,91, 6,
1022.
[4] M.R. Moghaddam, S. Fatemi, A. Keshtkar, Chem. Eng. J., 2013,231, 294.
[5] C. Tien, Adsorption Calculations and Modeling, Butterworth-Heinemann, Newton, MA,
1994, p. 243.
[6] R.-S. Juang, C.-Y. Ju, Ind. Eng. Chem. Res., 1998,37, 8, 3463.
[7] R.-S. Juang, H.-C. Lin, J. Chem. Technol. Biotechnol., 1995,62, 132.
[8] R.-S. Juang, H.-C. Lin, J. Chem. Technol. Biotechnol., 1995,62, 141.
[9] Y. Liu, Sep. Purif. Technol., 2008,61, 3, 229.
[10] Y.S. Ho, Water Res., 2006,40, 1, 119.
[11] T. Furusawa, J.M. Smith, Ind. Eng. Chem. Fundam., 1973,12, 2, 197.
[12] J. Crank, The Mathematics of Diffusion, 2nd ed., Oxford University Press, Oxford, G.B.,
1975, p. 414.
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