metals
Article
Leaching Kinetics of Zinc from Metal Oxide Varistors
(MOVs) with Sulfuric Acid
Youngjin Kim and Jaeryeong Lee *
Department of Energy & Resources Engineering, Kangwon National University, Chuncheon 24341, Korea;
yjcokr@kangwon.ac.kr
* Correspondence: jr-lee@kangwon.ac.kr; Tel.: +82-33-250-6252
Academic Editor: Hugo F. Lopez
Received: 22 July 2016; Accepted: 17 August 2016; Published: 19 August 2016
Abstract: The leaching kinetics of zinc from zinc oxide-based metal oxide varistors (MOVs) was
investigated in H2 SO4 at atmospheric pressure. Kinetics experiments were carried out at various
agitation speeds, particle sizes, initial H2 SO4 concentrations, and reaction temperatures. It was
determined that the leaching rate of zinc was independent of agitation speed above 300 rpm and
also independent of particle size below 105 µm, whereas it dramatically increased with an increasing
H2 SO4 concentration. Except for when the H2 SO4 concentration was varied, the m-values were almost
constant at varying agitation speeds (m-values: 0.554–0.579), particle sizes (m-values: 0.507–0.560) and
reaction temperature (m-values: 0.530–0.560) conditions. All of the m-values in these experiments were
found to be below 0.580. Therefore, it is proposed that the extraction of zinc is a diffusion-controlled
reaction. The leaching kinetics followed the D3 kinetic equation with a rate-controlling diffusion
step through the ash layers, and the corresponding apparent activation energy was calculated as
20.7 kJ/mol in the temperature range of 313 K to 353 K.
Keywords: leaching kinetics; zinc leaching; metal oxide varistors (MOVs); sulfuric acid
1. Introduction
Many researchers have recovered metals from waste printed circuit boards (WPCBs) due to the
dramatic increase in the amount of WPCBs. There are many papers reporting on the recovery of
high content metals (Cu, Al, Sn) or precious metals (Au, Ag) from WPCBs using physical, chemical,
or biological methods, or a combination of these approaches [1–12]. However, these processes are
very difficult to perform and are expensive not only for the concentration of minor metals but also for
their individual recovery. For these reasons, few studies have focused on the recovery of metals that
have low concentrations of electric/electronic components (EECs) due to the diversity of mounted
EECs in WPCBs, such as in varistors, condensers, inductors, resistors, diodes, and so on. These EECs
consist of various metals, such as zinc, copper, cobalt, and nickel, as well as toxic substances [12].
Among these EECs, metal oxide varistors (MOVs) are widely used in electronic devices. Due to
their excellent nonlinear coefficient, low leakage current, and high energy absorption capacity, they
have been used as surge absorbers in small current electrical circuits, as well as in transmission lines,
for many years [13,14].
MOVs are made by sintering a mixture of zinc oxide with small amounts of other oxides,
such as Bi2 O, Sb2 O3 , Co2 O3 , Cr2 O3 , among others [13,14]. Therefore, wasted MOVs, if separated
from other types of waste components, could be good starting materials for the recovery of various
metals [15]. Gutknecht et al. [15] investigated the leaching of MOVs using four acid solutions, including
acetic acid, hydrochloric acid, nitric acid and sulfuric acid. However, this study was not sufficient
from an industrial point of view. Similar investigations have been carried out by other research
groups [16–18]. However, these studies focused on zinc leaching from electric arc furnace dust (EAF
Metals 2016, 6, 192; doi:10.3390/met6080192
www.mdpi.com/journal/metals
Metals 2016, 6, 192
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dust) or zinc ores. More importantly, except for the Gutknecht study [15], our research group has not
found any literature on the recycling of MOVs.
For these reasons, a basic study of the leaching kinetics of the metals from MOVs is important to
develop recycling routes for various metals, such as Zn, Bi, Sn, and Co, among others.
The main objective of this work is to provide information on the leaching kinetics of zinc from
MOVs. Factors influencing zinc extraction, including the agitation speed, particle size, initial H2 SO4
concentration, and reaction temperature, were studied in detail.
2. Experimental Section
2.1. Materials
The MOVs with dimensions of 15 mm × 25 mm × 4.5 mm (produced by Thinking Electronic
Industrial Co., Ltd., Kaohsiung, Taiwan) were used in the present study. MOVs were ground to
a particle size less than 210 µm by using a rod mill, and screened into different sized fractions with
Tyler sieves. The −210 µm fraction, containing various metals with chemical compositions, as shown in
Table 1, was used as the sample for this study. The chemical composition of MOVs was analyzed using
inductively coupled plasma spectrometer (ICP) after these were completely dissolved in aqua regia
at 383–393 K. These results are summarized in Table 1. The undersized fraction of MOVs contained
70.97% Zn, 2.76% Sb, and 1.83% Bi as major elements. The analysis of the zinc content of different
particle sizes and mass fractions of the MOVs, as presented in Table 2, indicates an increase in the
percentage of the zinc content with decreasing particle size. Typical X-ray diffraction (XRD) patterns
of the MOVs, prepared by rod milling and sieving, are shown in Figure 1. Major intensity peaks
correspond to zinc oxide (ZnO), while minor intensity peaks corresponding to zinc cobalt antimony
Sb0.67 )O4 ) and antimony oxide (Sb4 O6 ) were also detected.
oxideMetals 2016, 6, (Zn(Co1.33192 3 of 14 ZnO (079-0206)
ZnO (079-0205)
Zn(Co1.33Sb0.67)O4 (089-6004)
Intensity (a.u.)
Sb4O6 (076-1717)
10
20
30
40
50
60
2 /° (Cu-Kα)
70
Figure 1. XRD patterns of the MOVs used in this research. Figure
1. XRD patterns of the MOVs used in this research.
2.2. Procedures Table 1. Chemical composition of the metal oxide varistors (MOVs) used in this study.
The leaching experiments were carried out in a 1‐L four‐neck thermostatic Pyrex reactor with a heating mantle. The hole at the center of the reactor was fitted with a stirrer, and three side holes Metal
Zn
Sb
Bi
Co
Al
Ni
Sn
Ag
Ca
Mn
were fitted with a reflux condenser, a temperature controller, and a glass cap to collect leach liquor wt. %
70.97
2.76
1.83
0.77
0.58
0.44
0.43
0.41
0.33
0.33
samples. H2SO4 (0.5 L) was poured into the reactor and allowed to reach thermal equilibrium. Five grams of the samples was added to the reactor and, in all experiments, the solid/liquid ratio was kept constant at 10 g/L. Following this, 2 mL of leach liquor samples were taken periodically (between 0.5 min and 60 min). At selected time intervals, approximately 2 mL of slurry samples were withdrawn and quickly separated by vacuum filtration. All of the aqueous solutions were prepared using distilled water, and reagent grade H2SO4 (95%–97%, Merck, Darmstadt, Germany) was used as Metals 2016, 6, 192
3 of 13
Table 2. Zn contents in different size fractions of MOVs used in this study.
Particle Size
105–210 µm
53–105 µm
−53 µm
wt. %
63.80
72.01
72.73
2.2. Procedures
The leaching experiments were carried out in a 1-L four-neck thermostatic Pyrex reactor with
a heating mantle. The hole at the center of the reactor was fitted with a stirrer, and three side holes were
fitted with a reflux condenser, a temperature controller, and a glass cap to collect leach liquor samples.
H2 SO4 (0.5 L) was poured into the reactor and allowed to reach thermal equilibrium. Five grams of
the samples was added to the reactor and, in all experiments, the solid/liquid ratio was kept constant
at 10 g/L. Following this, 2 mL of leach liquor samples were taken periodically (between 0.5 min
and 60 min). At selected time intervals, approximately 2 mL of slurry samples were withdrawn and
quickly separated by vacuum filtration. All of the aqueous solutions were prepared using distilled
water, and reagent grade H2 SO4 (95%–97%, Merck, Darmstadt, Germany) was used as the solvent.
For quantitative analysis, the chemical digestion method was used for each of the samples.
The zinc content was analyzed by using an inductively coupled plasma spectrometer (ICP, Optima
7300 DV, PerkinElmer, Waltham, MA, USA), and the samples were characterized by the high-resolution
X-ray diffraction (HRXRD) analysis (X’pert-pro MPD, PANalytical, Almelo, The Netherlands) method.
3. Results and Discussion
3.1. Effect of Agitation Speed
The effect of the agitation speed on zinc leaching was studied using fine particles of 53 to 105 µm
and agitation speeds of 100 to 400 rpm. Within the series of experiments, the reaction temperature,
initial H2 SO4 concentration, and solid-to-liquid ratios were kept constant at 333 K, 0.1 M, and 10 g/L,
Metals 2016, 6, 192 2 shows the effect of the agitation speed on the leachability of zinc.
4 of 14 respectively.
Figure
100
Leachability / %
80
60
40
400 rpm
300 rpm
200 rpm
100 rpm
20
0
0
10
20
30
40
Time / min.
50
60
70
Figure
2. Effect of agitation speed on zinc leaching (initial H2SO
Figure 2. Effect of agitation speed on zinc leaching (initial H
4 concentration: 0.1 M; temperature: 2 SO
4 concentration: 0.1 M; temperature:
333 K;333 K; particle size: 53–105 μm; pulp density: 10 g/L). particle size: 53–105 µm; pulp density: 10 g/L).
As shown in Figure 2, the leachability of zinc increased with increasing agitation speed and As shown in Figure 2, the leachability of zinc increased with increasing agitation speed and
leaching time due to the decreasing thickness of the mass transfer boundary layer on the surface of leaching
time due
to the[19]. decreasing
thickness
of the
mass
transfer
boundary
on the surface
of the
the MOV particles However, it was also found that the leachability of layer
zinc remained almost MOVconstant over 300 rpm. These results indicate that the dissolution process is not controlled by mass particles [19]. However, it was also found that the leachability of zinc remained almost constant
over transfer through the liquid boundary layer at agitation speeds of or above 300 rpm. 300 rpm. These results indicate that the dissolution process is not controlled by mass transfer
An liquid
agitation speed of 300 atrpm can provide particle suspension. Therefore, all through the
boundary
layer
agitation
speedsadequate of or above
300 rpm.
subsequent runs were performed at 300 rpm [17,18,20]. An agitation speed of 300 rpm can provide adequate particle suspension. Therefore, all subsequent
runs were performed at 300 rpm [17,18,20].
3.2. Effect of Particle Size A plot of the leachability of zinc against time using different sized fractions (105–210, 53–105, −53 μm) is presented in Figure 3. In this leaching test, the leaching temperature and initial H2SO4 concentration were fixed at 333 K and 0.1 M, respectively. The results indicate that the leachability of zinc is almost independent of particle size below 105 μm. Thus, for further experiments, particles in As shown in Figure 2, the leachability of zinc increased with increasing agitation speed and leaching time due to the decreasing thickness of the mass transfer boundary layer on the surface of the MOV particles [19]. However, it was also found that the leachability of zinc remained almost constant over 300 rpm. These results indicate that the dissolution process is not controlled by mass Metals 2016,
6, 192
4 of 13
transfer through the liquid boundary layer at agitation speeds of or above 300 rpm. An agitation speed of 300 rpm can provide adequate particle suspension. Therefore, all subsequent runs were performed at 300 rpm [17,18,20]. 3.2. Effect of Particle Size
A3.2. Effect of Particle Size plot of the leachability of zinc against time using different sized fractions (105–210, 53–105,
−53 µm) isA plot of the leachability of zinc against time using different sized fractions (105–210, 53–105, presented in Figure 3. In this leaching test, the leaching temperature and initial H2 SO4
−53 μm) presented in Figure 3. In 0.1
this test, the leaching temperature and initial H
2SO4 concentration is were
fixed at 333 K and
M,leaching respectively.
The results
indicate that
the leachability
of
concentration were fixed at 333 K and 0.1 M, respectively. The results indicate that the leachability of zinc is almost independent of particle size below 105 µm. Thus, for further experiments, particles in
zinc is almost independent of particle size below 105 μm. Thus, for further experiments, particles in the size range of 53 to 105 µm were chosen to minimize the effect of particle size on leaching [20].
the size range of 53 to 105 μm were chosen to minimize the effect of particle size on leaching [20]. 100
Leachability / %
80
60
40
- 53 μm
53 - 105 μm
105 - 210 μm
20
0
0
10
20
30
40
50
60
70
Time / min.
FigureFigure 3. Effect
particle
size on size zinc on leaching
(agitation(agitation speed: 300
rpm;300 initial
H2 SO
3. of
Effect of particle zinc leaching speed: rpm; initial H2SO4 4 concentration:
0.1 M;concentration: 0.1 M; reaction temperature: 333 K; pulp density: 10 g/L). reaction temperature: 333 K; pulp density: 10 g/L).
3.3. Effect of H
4 Concentration 3.3. Effect
of H2 SO42SO
Concentration
The
effect on zinc extraction was studied by varying the initial H2 SO4 concentration from 0.05 M
to 1 M while the leaching temperature was kept constant at 333 K. The results are shown Figure 4.
The leachability of zinc increased with the increasing initial H2 SO4 concentration and zinc leaching
was typically found to be fast in the initial period up to 10 min, but slowed to a lower rate with further
increases in leaching time. It is obvious that the initial H2 SO4 concentration had a pronounced effect
on the extraction of zinc.
Metals 2016, 6, 192 5 of 14 After 60 min, the leaching ratio reached 100% in the H2 SO4 concentration range of 0.5 to
1 M, whereas
the leaching rate was 83.5% at a H2 SO4 concentration
0.1 M. The effect of H2 SO4
The effect on zinc extraction was studied by varying the initial H
2SO4of
concentration from 0.05 M to 1 M while the leaching temperature was kept constant at 333 K. The results are shown Figure 4. concentration
found in these investigations agrees well with the results of other investigators [15,16,18].
The leachability of zinc increased with the increasing initial H
2SO4 concentration and zinc leaching If all of
the zinc in the MOVs is leached, the total zinc concentration
will be 0.11 M in the leaching
was typically found to be fast in the initial period up to 10 min, but slowed to a lower rate are
with solution because the mole ratio of H2 SO4 to zinc ions is 1. The
experimental
results
almost
further increases in leaching time. It is obvious that the initial H2SO4 concentration had a consistent with the fundamental analysis [21].
pronounced effect on the extraction of zinc. 100
Leachability / %
80
60
40
1 M H2SO4
0.5 M H2SO4
0.1 M H2SO4
0.05 M H2SO4
20
0
0
10
20
30
40
Time / min.
50
60
70
FigureFigure 4. Effect of initial 4. Effect of initial H2 SO
on zinc zincleaching leaching
(agitation
speed:
300 rpm;
reaction
H2SO
4 concentration on (agitation speed: 300 rpm; reaction 4 concentration
temperature: 333 K; particle size: 53–105 μm; pulp density: 10 g/L). temperature:
333 K; particle size: 53–105 µm; pulp density: 10 g/L).
After 60 min, the leaching ratio reached 100% in the H2SO4 concentration range of 0.5 to 1 M, whereas the leaching rate was 83.5% at a H2SO4 concentration of 0.1 M. The effect of H2SO4 concentration found in these investigations agrees well with the results of other investigators [15,16,18]. If all of the zinc in the MOVs is leached, the total zinc concentration will be 0.11 M in the Metals 2016, 6, 192
5 of 13
3.4. Effect of Reaction Temperature
The Figure 5 shows the extent of zinc leaching at different reaction temperatures between 313 K
and 353 K while all of the other parameters were kept constant. The results show that the reaction
temperatures do not have a noticeable effect on the zinc extraction. The leachability of zinc initially
rose very sharply over approximately 15 min. After 15 min of treatment, the leachability of zinc
increased slowly with an increase in reaction time. The molecular collisions, mass transfer co-efficient,
and reaction constant are improved with increasing temperature [19]. However, when the reaction
temperature increased from 313 K to 353 K, the leachability of zinc increased from 80.48% to 86.8%
after 60 min in 0.1 M H2 SO4 . This weak temperature dependence indicates that the dissolution process
6 of 14 does Metals 2016, 6, not seem to192 be controlled by a chemical reaction [22].
100
Leachability / %
80
60
40
353 K
333 K
313 K
20
0
0
10
20
30
40
50
Time / min.
60
70
Figure
5. Effect
of leaching
temperature
on zinc
(initial(initial H2 SOH
0.1 M;
4 2concentration:
Figure 5. Effect of leaching temperature on leaching
zinc leaching SO4 concentration: 0.1 agitation
M; speed:
300 rpm; particle size: 53–105 µm; pulp density: 10 g/L).
agitation speed: 300 rpm; particle size: 53–105 μm; pulp density: 10 g/L). 3.5. Kinetic Analysis 3.5. Kinetic
Analysis
The leaching process of zinc oxide in a sulfuric acid solution is described by the following The leaching process of zinc oxide in a sulfuric acid solution is described by the following chemical
chemical reaction [16]: reaction [16]:
2SO4 → ZnSO4 + H2O (1) (1)
ZnOZnO + H
+ H2 SO
4 → ZnSO4 + H2 O
On the basis of the above reaction, the effects of the temperature, agitation speed, initial H2SO4 On the basis of the above reaction, the effects of the temperature, agitation speed, initial H2 SO4
concentration, and particle size on the kinetics of zinc extraction in a sulfuric acid solution are concentration, and particle size on the kinetics of zinc extraction in a sulfuric acid solution are analyzed
analyzed below. Hancock and Sharp [23] inferred the reaction mechanism through m‐values, as per below.
Hancock and Sharp [23] inferred the reaction mechanism through m-values, as per the following
the following equation. This method was reported by Sharp et al. [24] and Hancock and Sharp [23]. equation.
This method was reported by Sharp et al. [24] and Hancock and Sharp [23]. Baik et al. [25]
Baik et al. [25] also used this equation to describe the dissolution of tungsten in NaOH solution. also used this equation to describe the dissolution of tungsten in NaOH solution.
−ln[ln(1 − a)] = lnk + mlnt (2) where a = Fraction of reaction, k = rate constant, t = reaction time. −ln[ln(1 − a)] = lnk + mlnt
(2)
Kinetic equations for different reaction mechanisms and m‐values are presented in Table 3. The wherem‐values of diffusion‐controlled reactions are in the range of 0.54 to 0.62, while reaction‐controlled a = Fraction of reaction, k = rate constant, t = reaction time.
reactions show an m‐value of approximately 1.0 [23]. Kinetic equations for different reaction mechanisms and m-values are presented in Table 3.
The m-values of diffusion-controlled reactions are in the range of 0.54 to 0.62, while reaction-controlled
Table 3. Reaction mechanisms and equations with changing m‐values. reactions show an m-value of approximately 1.0 [23].
The
data presented in Figures
2–5 are plotted according to Equation
(2) in Figure 6a–d, respectively.
Notation Reaction Mechanism Equation m The m-values
were
determined
from
the
straight
lines
plotted
in
Figure
6a–d.
2
D1 Diffusion a = kt 0.62 Figure
6c shows that the m-values
increased with an increasing
initial H2 SO4 concentration
D2 Diffusion (1 − a)ln(1 − a) + a = kt 0.57 from
0.578 to 0.689.
that the diffusion mechanism
changes
1/3]2with
D3 These results suggest
Diffusion [1 − (1 − a)
= kt the initial
0.54 H2 SO4
concentration
[25].
However,
the
m-values
were
almost
constant
under
variable
agitation
2/3
D4 Diffusion 1 − 2a/3 − (1− a) = kt 0.57 speed
(m-values:F0 0.554–0.579), particle Zero order size (m-values: 0.507–0.560) and reaction
(m-values:
a = kt temperature 1.24 F1 First order reaction −ln (1 − a) = kt 1.00 R2 Interface reaction (contracting area) 1 − (1 − a)1/2 = kt 1.11 1/3
R3 Interface reaction (contracting volume) 1 − (1 − a) = kt 1.07 A2 Nucleation and growth [−ln (1 − a)]1/2 = kt 2.0 A3 Nucleation and growth [−ln (1 − a)]1/3 = kt 3.0 The data presented in Figures 2–5 are plotted according to Equation (2) in Figure 6a–d, Metals 2016, 6, 192
6 of 13
0.530–0.560) conditions. Further, all of the m-values in these experiments were below 0.70, indicating
that the mechanisms for all of these reactions may be diffusion-controlled.
Table 3. Reaction mechanisms and equations with changing m-values.
Notation
D1
D2
Metals 2016, 6, 192 D3
D4
Reaction Mechanism
Diffusion
Diffusion
Diffusion
Diffusion
Equation
a2
= kt
(1 − a)ln(1 − a) + a = kt
[1 − (1 − a)1/3 ]2 = kt
1 − 2a/3 − (1− a)2/3 = kt
m
0.62
0.57
0.54
0.57
7 of 14 Figure 6c shows that the m‐values increased with an increasing initial H2SO4 concentration Zero
order that the diffusion mechanism a = kt changes with 1.24
from 0.578 F0
to 0.689. These results suggest the initial F1
First
order
reaction
−
ln
(1
−
a)
=
kt
1.00agitation H2SO4 concentration [25]. However, the m‐values were almost constant 1/2
under variable R2
Interface reaction (contracting area)
1.11
1 − (1 − a)
= kt
speed (m‐values: 0.554–0.579), particle size (m‐values: 0.507–0.560) and reaction temperature R3
Interface reaction (contracting volume)
1.07
1 − (1 − a)1/3 = kt
(m‐values: A2
0.530–0.560) conditions. Further, all of the m‐values in these 1/2
experiments were below Nucleation and growth
2.0
[−ln (1 − a)]
= kt
0.70, indicating that the mechanisms for all of these reactions may be diffusion‐controlled. 1/3
A3
Nucleation and growth
3.0
[−ln (1 − a)]
= kt
Figure
6. −ln[ln(1 − a)] vs. lnt plot for estimating the mechanism of zinc leaching in a 2H
2 SO
4 solution.
Figure 6. −ln[ln(1 − a)] vs. lnt plot for estimating the mechanism of zinc leaching in a H
SO
4 solution. (a)(a) Plot of the results from Figure 2 according to Equation (2); (b) plot of the results from Figure 3 Plot of the results from Figure 2 according to Equation (2); (b) plot of the results from Figure 3
according
to Equation (2); (c) plot of the results from Figure 4 according to Equation (2); (d) plot of the
according to Equation (2); (c) plot of the results from Figure 4 according to Equation (2); (d) plot of results
from
Figure 5 according to Equation (2).
the results from Figure 5 according to Equation (2). To investigate the relation between m‐values and correlation coefficients (R2), zinc extraction at varying agitation speeds, initial H2SO4 concentrations, particle sizes, and temperatures were analyzed according to kinetic equations D1, D2, D3, and D4, respectively, which are shown in Table 3. These expressions were plotted with respect to the reaction time, and the dependence of these diffusion models on the kinetic data was evaluated from R2. The plots of each kinetic equation, that Metals 2016, 6, 192
7 of 13
To investigate the relation between m-values and correlation coefficients (R2 ), zinc extraction at
varying agitation speeds, initial H2 SO4 concentrations, particle sizes, and temperatures were analyzed
according to kinetic equations D1, D2, D3, and D4, respectively, which are shown in Table 3. These
expressions were plotted with respect to the reaction time, and the dependence of these diffusion
models on the kinetic data was evaluated from R2 . The plots of each kinetic equation, that is, D1, D2,
Metals 2016, 6, 192 8 of 14 D3, and D4, versus reaction time under various conditions are shown in Figures 7–10, respectively.
1.0
0.8
(1-a) ln (1-a) + a
0.8
1.0
(a)
R2 = 0.974
R2 = 0.969
R2 = 0.913
R2 = 0.960
400 rpm
300 rpm
200 rpm
100 rpm
a2
0.6
0.4
0.6
0.4
10
20
30
40
50
60
0.0
0
70
10
20
0.20
[ 1- (1-a)1/3 ]2
1 - 2a/3 – (1– a)2/3
400 rpm
= 0.997
300 rpm R2 = 0.995
200 rpm R2 = 0.982
100 rpm R2 = 0.989
0.10
0.05
0
10
20
30
40
Time / min
40
50
0.20
(c)
R2
0.00
30
60
70
Time / min
Time / min
0.15
(b)
R2 = 0.989
R2 = 0.985
R2 = 0.952
R2 = 0.976
0.2
0.2
0.0
0
400 rpm
300 rpm
200 rpm
100 rpm
50
60
70
400 rpm
300 rpm
200 rpm
100 rpm
0.15
(d)
R2 = 0.993
R2 = 0.989
R2 = 0.964
R2 = 0.981
0.10
0.05
0.00
0
10
20
30
40
50
60
Time / min
Figure 7. Plots of the diffusion equations vs. time for different agitation speeds according to Figure 2.
Figure 7. Plots of the diffusion equations vs. time for different agitation speeds according to Figure 2. (a) Plot of the results from Figure 2 according to Equation D1; (b) plot of the results from Figure 2
(a) Plot of the results from Figure 2 according to Equation D1; (b) plot of the results from Figure 2 according to Equation D2; (c) plot of the results from Figure 2 according to Equation D3; (d) plot of the
according to Equation D2; (c) plot of the results from Figure 2 according to Equation D3; (d) plot of results from Figure 2 according to Equation D4.
the results from Figure 2 according to Equation D4. 70
Metals
2016, 6, 192
Metals 2016, 6, 192 89 of 14 of 13
1.0
a2
0.6
0.4
0.6
0.4
0.2
0.2
0.0
0
5
10
15
20
0.0
25
0
5
0.20
1 - 2a/3 – (1– a)2/3
[ 1- (1-a)1/3 ]2
0.10
0.05
0
5
10
15
Time / min
15
20
0.20
(c)
- 53 μm
R2 = 0.989
53 - 105 μm R2 = 0.995
105 - 210 μm R2 = 0.983
0.15
10
25
Time / min
Time / min
0.00
(b)
- 53 μm
R2 = 0.970
53 - 105 μm R2 = 0.985
105 - 210 μm R2 = 0.968
0.8
(1-a) ln (1-a) + a
0.8
1.0
(a)
- 53 μm
R2 = 0.946
53 - 105 μm R2 = 0.969
105 - 210 μm R2 = 0.950
20
25
(d)
- 53 μm
R2 = 0.978
53 - 105 μm R2 = 0.989
105 - 210 μm R2 = 0.974
0.15
0.10
0.05
0.00
0
5
10
15
20
Time / min
Figure 8. Plots of the diffusion equations vs. time for different particle sizes according to Figure 3.
Figure 8. Plots of the diffusion equations vs. time for different particle sizes according to Figure 3. (a) (a) Plot of the results from Figure 3 according to Equation D1; (b) plot of the results from Figure 3
Plot of the results from Figure 3 according to Equation D1; (b) plot of the results from Figure 3 according to Equation D2; (c) plot of the results from Figure 3 according to Equation D3; (d) plot of the
according to Equation D2; (c) plot of the results from Figure 3 according to Equation D3; (d) plot of results from Figure 3 according to Equation D4.
the results from Figure 3 according to Equation D4. 25
Metals
2016, 6, 192
Metals 2016, 6, 192 1.0
9 of 13
10 of 14 1 M H2SO4
0.5 M H2SO4
0.1 M H2SO4
0.05 M H2SO4
1.0
(a)
a2
0.6
0.4
0.2
0.0
1 M H2SO4
0.5 M H2SO4
0.1 M H2SO4
0.05 M H2SO4
0.8
(1-a) ln (1-a) + a
0.8
R2 = 0.988
R2 = 0.995
R2 = 0.969
R2 = 0.979
0.6
0.4
0.2
0
5
10
15
0.0
20
0
5
Time / min
[ 1- (1-a)1/3 ]2
0.3
0.2
0.1
0
5
10
Time / min
15
0.4
(c)
R2 = 0.992
R2 = 0.968
R2 = 0.995
R2 = 0.994
[1 – (2a/3)] – (1– a)2/3
1 M H2SO4
0.5 M H2SO4
0.1 M H2SO4
0.05 M H2SO4
10
20
Time / min
0.4
0.0
(b)
R2 = 0.998
R2 = 0.993
R2 = 0.985
R2 = 0.987
15
20
1 M H2SO4
0.5 M H2SO4
0.1 M H2SO4
0.05 M H2SO4
0.3
(d)
R2 = 0.998
R2 = 0.987
R2 = 0.989
R2 = 0.990
0.2
0.1
0.0
0
5
10
15
Time / min
Figure 9. Plots of the diffusion equations vs. time for different initial H2 SO4 concentrations according
Figure 9. Plots of the diffusion equations vs. time for different initial H
2SO4 concentrations according to
Figure 4. (a) Plot of the results from Figure 4 according to Equation D1;
(b) plot of the results from
to Figure 4. (a) Plot of the results from Figure 4 according to Equation D1; (b) plot of the results from Figure 4 according to Equation D2; (c) plot of the results from Figure 4 according to Equation D3;
Figure 4 according to Equation D2; (c) plot of the results from Figure 4 according to Equation D3; (d) (d)
plot of the results from Figure 4 according to Equation D4.
plot of the results from Figure 4 according to Equation D4. 20
Metals
2016, 6, 192
Metals 2016, 6, 192 10
of 13
11 of 14 1.0
a2
0.6
0.4
0.6
0.4
0.2
0.2
0.0
0
5
10
15
20
0.0
25
0
5
0.4
1 - 2a/3 – (1– a)2/3
[ 1- (1-a)1/3 ]2
0.2
0.1
0
5
10
15
Time / min
15
20
0.20
(c)
353 K R2 = 0.998
333 K R2 = 0.995
313 K R2 = 0.998
0.3
10
25
Time / min
Time / min
0.0
(b)
353 K R2 = 0.996
333 K R2 = 0.985
313 K R2 = 0.996
0.8
(1-a) ln (1-a) + a
0.8
1.0
(a)
353 K R2 = 0.979
333 K R2 = 0.969
313 K R2 = 0.989
20
25
(d)
353 K R2 = 0.999
333 K R2 = 0.989
313 K R2 = 0.997
0.15
0.10
0.05
0.00
0
5
10
15
20
Time / min
25
Figure 10. Plots of the diffusion equations vs. time for different temperatures according to Figure 5.
Figure 10. Plots of the diffusion equations vs. time for different temperatures according to Figure 5. (a) Plot of the results from Figure 5 according to Equation D1; (b) plot of the results from Figure 5
(a) Plot of the results from Figure 5 according to Equation D1; (b) plot of the results from Figure 5 according to Equation D2; (c) plot of the results from Figure 5 according to Equation D3; (d) plot of the
according to Equation D2; (c) plot of the results from Figure 5 according to Equation D3; (d) plot of results from Figure 5 according to Equation D4.
the results from Figure 5 according to Equation D4. The
plots of D1, D2, D3, and D4 versus reaction time at different H22SO
concentrations show
The plots of D1, D2, D3, and D4 versus reaction time at different H
SO44 concentrations show that
reaction time
a good linear
H22SO
concentrations of 0.5 of 0.5 M
and 11 M
that D1
D1 versus
versus reaction time has
has a good linear relation
relation at
at H
SO44 concentrations M and M (m-values:
0.645
and
0.689,
respectively)
(Figure
9a).
However,
the
leaching
data
for
0.05
M
and
0.1 M
(m‐values: 0.645 and 0.689, respectively) (Figure 9a). However, the leaching data for 0.05 M and 0.1 H
(m-value:
0.578 and 0.560, respectively) did not fit well to D1 versus reaction time, as shown in
M 2 SO
H24SO
4 (m‐value: 0.578 and 0.560, respectively) did not fit well to D1 versus reaction time, as Figure
9a.
shown in Figure 9a. 2
Generally,
Equations
D2D2 and
D4D4 versus
reaction
timetime are similar
(Figure
7b,d,
Generally, the
the RR2values
values for
for Equations and versus reaction are similar (Figures Figure
8b,d, Figure
9b,d
and Figure
Equations
D2 and D4
have the same
m-values.
7b,d–10b,d), because Equations D2 10b,d),
and D4 because
have the same m‐values. In addition, D3 provided a In
addition,
D3
provided
a
better
fit
for
the
kinetic
data
compared
to
Equations
D1,
D2,
and
D4.
On the
better fit for the kinetic data compared to Equations D1, D2, and D4. On the other hand, Figures 7–
other
hand,
Figures
7–10 had
smaller
R2 values
for equation
versus
reaction
of D2,
D3,
10 had smaller R2 values for equation D1 versus reaction D1
time those of D2, time
D3, those
and D4 versus and
D4
versus
reaction
time
for
the
case
of
zinc
leaching.
This
may
be
because
the
m-values
that
reaction time for the case of zinc leaching. This may be because the m‐values that were calculated were
calculated using D2, D3, and D4 are in the range of 0.507 to 0.579, which is close to the m-values
using D2, D3, and D4 are in the range of 0.507 to 0.579, which is close to the m‐values determined determined
by D2, D3, and D4, as shown in Table 3.
by D2, D3, and D4, as shown in Table 3. Metals 2016, 6, 192
Metals 2016, 6, 192 11 of 13
12 of 14 These results indicate that D2 and D4 provide better fits to the kinetic data than D1. However, These
results indicate that D2 and D4 provide better fits to the kinetic data than D1. However,
the model provided by D3 showed the best fit in all of the experiments. Therefore, this model was the model provided by D3 showed the best fit in all of the experiments. Therefore, this model was
chosen to describe the zinc extraction from MOVs during H
SO4 leaching. chosen
to describe the zinc extraction from MOVs during H22SO
4 leaching.
The Arrhenius plot constructed with the rate constant value, k,
k, calculated
calculated from data is
is The Arrhenius plot constructed with the rate constant value,
from the the data
presented in Figure 10c. The activation energy of zinc leaching by 0.1 M H
2SO4 is 20.7 kJ/mol is in presented in Figure 10c. The activation energy of zinc leaching by 0.1 M H2 SO4 is 20.7 kJ/mol is in the
the temperature range of 313 K to 353 K (Figure 11). temperature
range of 313 K to 353 K (Figure 11).
Depending on
on the activation energy value, the heterogeneous mechanism can be Depending
the
activation
energy
value,
the heterogeneous
reactionreaction mechanism
can be diffusion
diffusion controlled or chemical reaction controlled. Activation energy values lower than 20 kJ/mol controlled
or chemical reaction controlled. Activation energy values lower than 20 kJ/mol usually
usually a diffusion‐controlled process, whereas energy
the activation energy of chemical indicate aindicate diffusion-controlled
process, whereas
the activation
of chemical
reaction-controlled
reaction‐controlled processes is approximately 50 to 100 kJ/mol [16,17]. The activation energy value processes is approximately 50 to 100 kJ/mol [16,17]. The activation energy value obtained in this study
obtained in this study tofor Zn leaching is close to 20 kJ/mol, suggesting diffusion‐controlled for
Zn leaching
is close
20 kJ/mol,
suggesting
a diffusion-controlled
process.a This
confirms that the
process. This confirms that the leaching mechanism is controlled by ash layer diffusion. leaching mechanism is controlled by ash layer diffusion.
-4.0
lnk (min-1)
-4.5
Ea= 20.7 kJ/mol
-5.0
R2 = 0.995
-5.5
2.8
2.9
3.0
3.1
1000/T (K-1)
3.2
3.3
Figure 11. Arrhenius plot of the apparent rate constant.
Figure 11. Arrhenius plot of the apparent rate constant. 4. Conclusions 4.
Conclusions
The leaching
leaching kinetics of zinc zinc based
oxide metal
based metal oxide (MOVs)
varistors (MOVs) were The
kinetics
of zinc
fromfrom zinc oxide
oxide
varistors
were
investigated
investigated as a function of the H
2
SO
4
concentration, reaction time, agitation speed, and as a function of the H2 SO4 concentration, reaction time, agitation speed, and temperature. It was
temperature. was found that an agitation speed above 300 rpm was the
sufficient eliminate found
that an It agitation
speed
above
300 rpm was
sufficient
to eliminate
effect ofto this
variablethe on
effect of this variable on the leaching rate and that the extent of zinc extraction increased with the the leaching rate and that the extent of zinc extraction increased with the H2 SO4 concentration.
H2SOIn
4 concentration. the plots of −ln[ln(1 − a)] versus lnt, the m-values increased with increasing initial H2 SO4
In the plots of −ln[ln(1 a)] versus lnt, the suggest
m‐values with mechanism
increasing changes
initial Hwith
2SO4 concentrations,
from
0.578 to − 0.689.
These results
thatincreased the diffusion
concentrations, from 0.578 to 0.689. These results suggest that the diffusion mechanism changes with the H2 SO4 concentration. Except when the H2 SO4 concentration was used as the varying condition,
the H
2SO4 concentration. Except when the H
2SO4 concentration was used as the varying condition, the
m-values
remained almost constant at varying
agitation speeds (m-values: 0.554–0.579), particle
the m‐values remained almost constant at varying agitation speeds (m‐values: 0.554–0.579), particle sizes
(m-values: 0.507–0.560), and reaction temperatures (m-values: 0.530–0.560). It is reasonable
sizes (m‐values: 0.507–0.560), and reaction temperatures (m‐values: 0.530–0.560). It is reasonable to to
conclude that the extraction of zinc seems to be a diffusion-controlled process because all of the
conclude in
that the experiments
extraction of zinc seems to be a diffusion‐controlled process because all of the m-values
these
were
below
0.70.
m‐values in these experiments were below 0.70. The experimental data agreed quite well with the model described by the D3 kinetic equation:
The experimental data agreed quite well with the model described by the D3 kinetic equation: [1 − (1 − a)1/3
]2 = kt
[1 − (1 − a)1/3]2 = kt The
thethe leaching
kinetics
experiments
show show that thethat zincthe leaching
controlled
The results
results ofof leaching kinetics experiments zinc process
leaching is process is by
ash
layer
diffusion
with
an
activation
energy
of
20.7
kJ/mol.
controlled by ash layer diffusion with an activation energy of 20.7 kJ/mol. Acknowledgments:
Thiswork workwas wassupported supportedby by
Korea
Institute
of Energy
Technology
Evaluation
Acknowledgments: This the the
Korea Institute of Energy Technology Evaluation and and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea
Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. (No. 20165010100810).
20165010100810). Metals 2016, 6, 192
12 of 13
Author Contributions: Jaeryeong Lee and Youngjin Kim conceived and designed the experiments; Youngjin Kim
performed the Leaching experiments and analyzed the ICP data; Youngjin Kim wrote the paper; Jaeryeong Lee
modified the paper before submission.
Conflicts of Interest: The authors declare no conflict of interest.
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