Kinetic analysis for cyclic CO2 capture using lithium orthosilicate sorbents derived from different silicon precursors

Article abstract of DOI:10.1039/c8dt01617h

A series of Li₄SiO₄ was synthesized using LiNO₃ and six different silicon precursors. The precipitated-silica-derived Li₄SiO₄ presented the highest CO₂ capacity in a 10 h sorption test, and ZSM-5-derived Li₄SiO₄ demonstrated the most rapid CO₂ sorption. The CO₂ sorption kinetics predominantly followed the nucleation mode and could be accurately described by the Avrami-Erofeev model. The Avrami-Erofeev model provided an in-depth analysis of correlation between sorption performance and material properties. Both the nucleation speed and nucleation dimensionality affected the overall sorption kinetics. The kinetics and pore-size distribution suggest that the sorption kinetics was dependent on the quantity of ～4 nm-pores which favors nucleation dimensionality. For the cyclic tests, the precipitated-silica-derived sample presented the poorest performance with the capacity decreasing from 31.33 wt% at the 1^st cycle to only 11.52 wt% at the 30^th cycle. However, the sample made from fumed silica displayed an opposite trend with the capacity increasing from 19.90 wt% at the 1^st cycle to 34.23 wt% at the 30^th cycle. The radically distinct behaviour of samples during cycles was on account of the alternation of sorption kinetics. The decrease in ～4 nm-pores after cycles was responsible for the decrease of nucleation dimensionality for the precipitated-silica-derived sample. The rearrangement during cycles could enrich the pores of ～4 nm for the fumed silica-derived sample, which improved the nucleation growth, thus enhancing the kinetics with cycles.

Full text of DOI:10.1039/c8dt01617h

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ISSN 1477-9226
PAPER
Joseph T. Hupp, Omar K. Farha et al.
Efficient extraction of sulfate from water using
framework
a Zr-metal–organic
rsc.li/dalton

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Kinetic analysis for cyclic CO capture using lithium orthosilicate
2
sorbents derived from different silicon precursors
Received 00th January 20xx,
Accepted 00th January 20xx
a, b
a
a
a
a
a
Ming Zhao , Hanlu Fan , Feng Yan , Yinqiang Song , Xu He , Muhammad Zaki Memon , Suresh
c
, a
K. Bhatia , Guozhao Ji *
DOI: 10.1039/x0xx00000x
A series of Li
presented the highest CO
sorption. The CO
4
SiO
4
was synthesized using LiNO
3
and 6 different silicon precursors. The precipitated-silica-derived Li
4
SiO
4
2
www.rsc.org/
2
capacity in a 10-h sorption test, and ZSM-5-derived Li
4
SiO demonstrated the most rapid CO
4
2
sorption kinetics predominently followed the nucleation mode and could be accurately described by
Avrami-Erofeev model. Avrami-Erofeev model previded an in-depth analysis of correlation between sorption performance
and material property. Both nucleation speed and nucleation dimensionality affected the overall sorption kinetics. The
kinetics and pore-size distribution suggest that the sorption kinetics was dependent on the quantity of ~4-nm-pores which
favors nucleation dimensionality. For the cyclic tests, precipitated-silica-derived sample presented the poorest
st
th
performance with a capacity decreasing from 31.33 wt.% at the 1 cycle to only 11.52 wt.% at the 30 cycle. However the
st
sample made from fumed silica displayed the opposite trend with a capacity increasing from 19.90 wt.% at the 1 cycle to
th
3
4.23 wt.% at the 30 cycle. The radically distinct behaviour of samples during cycles was on account of the alternation of
sorption kinetics. The decrease in ~4-nm-pores after cycles was responsible for the decrease of nucleation dimensionality
for precipitated-silica-derived sample. The rearrangement during cycles could enrich the pores of ~4-nm for the fumed
silica-derived sample, which improved the nucleation growth, thus enhancing the kinetics with cycles.
addition to such pre-combustion capture applications, solid
1
. Introduction
sorbents could also serve as acceptor of CO after combustion
2
8
, 9
of fossil fuels . The post-combustion goal can be fulfilled by
using two parallel fluidized beds serving as carbonator and
regenerator, respectively, or by setting up fixed-bed reactors
Flue gas from fossil fuel combustion has been known as one of
the significant contributors of anthropogenic CO leading to
2
1
climate change. Traditional fossil fuels such as oil, coal and
1
0, 11
with swinging carbonation/calcination reactions
regenerations, the carbonated solid sorbents would release
concentrated CO which is valuable source for
photosynthesis and production of useful chemicals such as
. During
natural gas are still the major sources of energy for industrial
processes; hence, reducing fossil fuels usage and their harmful
impacts on the environment is critical to mitigate climate
change. This necessitates the development of alternative clean
energy source with the advantages of low pollutant emissions
2
a
1
2
2
urea, methane and methanol . Furthermore, CO sorbents
could also be employed to enhance the efficiency of natural
and more energy per mass. Hydrogen (H ) production from
2
gas, coal bed gas, shale gas and landfill gas by removing the
1
CO content and concentrating the combustible components.
2
sorption enhanced steam reforming (SESR) seems a feasible
solution to this issue, but SESR requires in-situ CO capture at
2
2
high temperatures (400~700 ºC) to elevate the H yield . This
-4
In closed environments such as spacecraft, space station,
submarine which are isolated and lack of gas exchange with
2
is a typical pre-combustion CO capture process. Traditional
2
2 2
surroundings, restraining the CO concentration by CO
CO2 capture techniques such as amine-scrubbing and
sorbents is an effective way to ensure the life safety of human
beings.
cryogenic distillation are unable to be applied in-situ under the
5
conditions for SESR . Developing high temperature solid
-7
sorbents is thus of increasing importance for H production. In
2
One such sorbent which has been widely used is CaO-based
material due to its high theoretical sorption capacity (78 wt.%
-1
or 17.7 mmol g ) and low cost. However, it has been well
known to suffer from rapid decays over multiple cycles of
sorption and desorption due to sintering-related deactivation
1
3-16
.
In order to minimize the sintering effect and improve the
cyclic stability, sacrifice of the sorption capacity was accepted
by incorporating high-melting-point inert materials such as
1
7
18
19
19
20
Ca
9
Al
6
O
18 , Ca
2
Al
2
SiO
7
, CaZrO
3
, Ca
2
SiO
4
, MgO
and
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2
1, 22
-1
47
Al
complexity and potential cost increment by making such Ca-doped Li
hybrid’ type sorbents, it is motivated to develop more (or 8.0 mmol g ). Si precursor also plays a role in affecting the
2
O
3
into CaO as a stabilizer (or ‘spacer’). To avoid the 27 wt.% (or 6.1 mmol g ). Chen and co-workers synthesized
4
4 2
SiO which reached a CO capacity of 35.1 wt.%
-1
‘
4
8
efficient alternative sorbents that can be used over repeated performance of Li
cycles. Recently, alkali metal oxide CO sorbents such as performance of Li
Li SiO Li ZrO and Na ZrO
attentions for their good CO
4
SiO
4
sorbents. Shan et al. compared the
derived from diatomite and pure SiO
SiO reached
chemisorption capacities and 28.62 wt.% (or 6.5 mmol g ) which was higher than that for
2
4
SiO
4
2
.
4
4
,
2
3
2
3
have attracted increasing The sorption capacity of diatomite-derived Li
4
4
-1
2
2
3, 24
-1
excellent cyclic stability
form carbonate as demonstrated in Eqs. 1-3
Li Li SiO3(s), ∆H298=-142 kJ mol
Li Li
Na Na
The theoretical capacities of Li-based sorbents (36.7 wt.% or 56.1 mg g min . Pan et al.
. They could react with CO
2
to pure SiO
2
-derived Li
al. prepared Li SiO
(1) precursors: LiOH, LiNO
(2) LiOH was identified as the best in their study, showing a CO
2
4
SiO
by fumed silica with three different Li
and Li CO . The sorbent made from
4
(22.08 wt.% or 5.0 mmol g ). Kim et
2
3, 25, 26
40
4
4
-1
4
SiO4(s)+CO2(g)
ZrO3(s)+CO2(g)
ZrO3(s)+CO2(g)
⇌
⇌
⇌
2
CO3(s)+Li
CO3(s)+ZrO2(s), ∆H298=-160 kJ mol
2
3
2
3
-1
2
2
-1
-1
2
2
CO3(s)+ZrO2(s), ∆H298=-149 kJ mol
(3) capacity of 29.8 wt.% (or 6.8 mmol g ) and sorption rate of
-1
-1
49
developed Li
4 4
SiO from very
-1
-1
8
.3 mmol g for Li
Li ZrO ) are higher than the corresponding Na-based one (23.8 capacity (36.3 wt.% or 8.3 mmol g ) in open literatures so far.
wt.% or 5.4 mmol g for Na
why Li species were reasonably more attractive for during the cyclical sorption-desorption. Almost all the reported
researchers. From an industrial prospective, Li SiO is cyclic capacity of Li SiO declined during cycles with different
advantageous over Li ZrO because silicon (Si) is the second levels, and the mechanistic reason of this decline is still yet to
4
SiO
4
and 28.7 wt.% or 6.5 mmol g for porous silicon precursor SBA-15, and reported the highest CO
2
-1
2
3
-1
2
3 4 4
ZrO ). This was likely the reason Another important concern of Li SiO is the decay of capacity
4
4
4
4
2
3
most abundant element on the earth’s surface and silicon be disclosed.
oxide (silica) as precursor is more widely available compared to
zirconium oxide (zirconia). In addition to the materials above, a However, Li-based sorbents have been criticized for their slow
2
number of newly developed Li-based ceramics were also CO sorption kinetics which limits their development and
2
7-29
30
50-53
investigated for CO
3
2
capture, such as Li
33-36
2
CuO
2
, Li
2
38
TiO
3
,
application
. Since kinetics is the limiting factor of the
1, 32
37
Li
5
AlO
4
, Li
5
FeO
4
, Li
2
O–Bi
2
O
3
and LiNiO
2
. Current application of Li-based sorbents, theoretical investigation of
research on those materials focuses on the improvement of sorption kinetics is of great importance for interpreting the
sorption capacity. Even though some of them showed higher reaction mechanism and improving material design. The
2 4 4
CO capacity than Li SiO , the material cost still remains as an double exponential model, being a popular data fitting tool,
issue. Moreover, further investigations on the cyclic stability of has been frequently used to fit the kinetic sorption profile for
3
9, 43, 44, 48, 54
those newly developed material are still needed.
alkali metal ceramics
a common model for solid-fluid interaction, has also been used
sorbent, a number in studying the CO sorption kinetics using alkali metal based
. The shrinking core model, as
In view of the potential of Li
of studies have been conducted to optimize the performance sorbents
of cyclic sorption. Li SiO is commonly prepared by solid state double exponential model as well as the Avrami-Erofeev
reactions between Li and Si precursors
that smaller particle size of the precursor results in more Li
complete reaction during synthesis and thus higher purity of to explain the reaction mechanism and give reasonable fitting.
Li SiO , which naturally leads to greater CO capture capacity
4 4
Romero-Ibarra et al. deployed post-treatment of Li SiO As discussed above, Li SiO sorbents developed from diverse
4
SiO
4
as a CO
2
2
55, 56
57
. Zhang et al. applied the shrinking core model,
4
4
3
9, 40
. It has been found nucleation model to interpret the CO
2
sorption kinetics in
4
SiO , and found that only the Avrami-Erofeev model is able
4
4
4
2
4
1
42
.
4
4
by mechanical ball-milling and succeeded in reducing crystal precursors resulted in different sorption performances. This
size and increasing surface area of the material. The work aims to model and interpret the sorption kinetics of
-1
consequent CO
wt.%) to 4.3 mmol g (18.9 wt.%). Venegas et al. employed a develop the correlation of sorption kinetics with the textual
precipitation method to achieve small particle size of Li SiO property of the material. Since cyclic sorption-desorption
being around 3 μm as opposed to 36 μm via solid-state generally alters the performance of CO capture, to the best of
reaction, and the smaller particles lowered the reaction our knowledge, there has not been any theoretical study to
2 4 4
capacity was increased from 2.0 mmol g (8.8 Li SiO samples made from 6 different Si precursors and
-1
43
4
4
,
2
4
4
activation energy by half. Subha et al.
prepared via sol-gel routes showed improvements over the cycles. This work applied Avrami-Erofeev model, which has
solid-state samples in terms of both CO capacity (30 wt.% or been proved a reasonable model of CO sorption in Li SiO , to
.8 mmol g for sol-gel and 17 wt.% or 3.8 mmol g for solid gain an insight of the kinetic change caused by cycles.
found that Li
4
SiO
4
explain the mechanism of this performance change during
2
2
4
4
-
1
-1
6
-
1
-1
state) and sorption kinetics (22.5 mg g min for sol-gel and
-
1
-1
3.2 mg g min for solid state). It was believed that doping
1
2
. Experiment and Methodology
hetero elements may create lattice vacancies which accelerate
2
-
45
O
hopping, thus favouring CO
incorporated Al and Fe in Li SiO
rate from 0.01 to 0.12 and 0.15 wt.% min . Seggiani et al.
developed K CO -doped Li SiO and achieved a CO capacity of
2
sorption. Gauer et al.
2
.1 Material synthesis
SiO -based sorbents were prepared by using the solid-
with pure SiO with a molar ratio of
4
4
and promoted the sorption
-1
46 The Li
state reaction of LiNO
4
4
3
2
2
3
4
4
2
2
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n
Li:nSi = 4:1. Six types of pure SiO
Nanjing, China), MCM-41 (JCNANO, Nanjing, China), ZSM-5
JCNANO, Nanjing, China), fumed silica (S5130; Sigma-Aldrich,
2
, namely SBA-15 (JCNANO,
mmax,i − mmin,i
Q =
×100%
i
m0
(4)
(
USA), precipitated silica (Sipernat-306; Evonik, Essen,
Germany) and waste-derived silica, were selected as the Si
where mmax,i, and m
are the maximum mass and initial
min,i
th
mass at the i cycle, and m is the minimum mass of the
0
precursors. The waste-derived SiO
the hydrolysis of SiCl (99 wt %; LDK Solar Ltd., Xinyu, China) at
50 °C and was collected and dried at 105 °C for 2 h. Initially,
.0666 mol LiNO (Fengshun Fine Chemicals Ltd., Shanghai,
2
was synthesized through
sample during the entire test. The total capacity (Qtotal) over
4
the entire 30 cycles was also calculated in Eq. 5
1
0
30
3
Qtotal
=
Qi
∑
China) was dissolved in 40 ml of absolute ethanol (99.8 %,
Beijing Chemical works) and then sonicated for 20 min until
i=1
(
5)
2
completely dissolved. Then, 0.0166 mol pure SiO was added
4 4
Since the only difference among these Li SiO samples is the Si
to the solution and the mixture was stirred for 24 h with 300
rpm at 60 °C until evaporated completely. After drying in the
vacuum oven at 60 °C for 8~12 h, the mixed powders were
precursors, the Si precursor’s names are used to represent the
samples investigated in this study. For instance, LS-SBA-15
4 4
means the Li SiO made from SBA-15 precursor.
-1
calcined at 750 °C for 2 h with a ramping rate of 10 °C min .
After the calcination process, the products were ground to
powder again in the agate mortar for later use.
3. Results and Discussion
3
.1 Characterization results
Fig. 1 shows the XRD patterns of the samples developed from
the 6 different Si precursors. The presence of Li SiO was
2
.2 Material characterization
Powder X-ray diffraction (XRD) was carried out on a
Dmax/2500 X-ray diffractometer (Rigaku, Japan) with a 2θ
range of 10 - 90º (Cu Kα radiation, λ = 0.1542 nm).
Morphological properties of samples were detected using
scanning electron microscopy (SEM, Zeiss MERLIN VP
Compact). All the sorbents for SEM were sputter-coated with a
4
4
confirmed in all the samples. No impurities were observed
from the samples of LS-SBA-15, LS-MCM-41, LS-Precipitated
and LS-Waste at least at the XRD detection level. As for the
samples made from ZSM-5 and fumed silica, some Li
phase was shown as minor peaks which indicated the
existence of slight amount of Li SiO . The grain sizes of crystal
2 3
SiO
layer of platinum (~5 nm). N physisorption was conducted on
2
2
3
a Quantachrome autosorb iQ-C instrument. Prior to analysis,
the sorbent was degassed at 300 °C until the pressure
increment rate in the sample chamber was less than 20 μmHg
could not be provided by Scherrer equation because the sizes
of all the samples were beyond 100 nm. As such, only the full
width at half maximum (FWHM) was reported here to indicate
a qualitative comparison of grain sizes. The FWHM was 0.152
for LS-SBA15, 0.155 for LS-MCM41, 0.155 for LS_ZSM5, 0.160
for LS-Fumed, 0.147 for LS-Precipitated and 0.146 for LS-
Waste. These numbers of FWHM could possibly imply the
order of grain size as: dLS-Waste > dLS-Precipitated > dLS-SBA15 > dLS-
-1
min . The Brunauer-Emmett-Teller (BET) surface area was
estimated based on the N adsorption isotherms with a P/P
2
0
range of 0.05 ~ 0.3. Total pore volume and pore size
distribution were calculated from the according to the Barrett-
Joyner-Halenda (BJH) method.
MCM41 = dLS_ZSM5 > dLS-Fumed
.
2
.3 CO
2
sorption tests
CO sorption capacity of the sorbents was tested using a
2
thermogravimetric analyser (METTLER, TOLEDO, TGA/DSC 2).
In each test, ~10 mg of sample was first subject to purification
-
1
in a pure N
2
flow of 60 ml min with a ramping rate of 30 ºC
min to remove the pre-sorbed substances such as H O and
CO . Then the chamber temperature was controlled to 650 °C
under a stream of pure CO
-1
2
2
-1
2
at 60 ml min for 10 h.
Cyclic sorption/desorption tests were also carried out to
evaluate long term stability of CO capture performance. After
pre-calcination in a 60 ml min flow of pure N at 650 °C, the
sample was kept at 650 °C under a stream at 60 ml min
periodically switched between pure CO and pure N for 30
times. The duration of purging the CO stream in a cycle was
0 min and for the N purging it only lasted for 10 min.
2
-1
2
-1
2
2
2
6
2
2 i
The CO capacity of each cycle (Q ) is defined in Eq. 4
4 4
Fig. 1 XRD patterns of Li SiO samples derived from different Si precursors
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presented hysteresis in the adsorption-desorption isotherms.
The shape of the hysteresis (Type B, based on D. Duong)
5
9
suggested that the pores had slit shape . Therefore the
scanty pores were most likely formed by the gaps between
particles or the cracks in the particles. The pore size
distributions (PSD) of the 6 samples in Fig. 2b all exhibited a
narrow unimodal distributions with peaks at ~4 nm. Close to
this pore size, LS-ZSM-5 contained the most pores, followed by
LS-precipitated, LS-MCM-41, LS-Waste, LS-Fumed and LS-SBA-
1
5.
(a)
Fig. 3 SEM images of synthesized samples.
The SEM images in Fig. 3 show the morphology of the 6
samples. LS-SBA-15 presented some macro-pores (visible
holes) inside the solid. This was consistent with the measured
2
-1
surface areas in Table 1. The BET surface area (1.09 m g ) of
2
LS-SBA-15 was much more than external area (0.45 m g )
-1
2
-1
suggesting that part of the surface area (0.64 m g ) is
attributed to internal marco-pores. For dense material, the
(b)
BET surface area should be equal to the external area because
Fig. 2 (a) N
2
adsorption-desorption isotherms of Li
4
SiO
4
samples derived from different there is no internal pore to contribute surface area. Remaining
Si precursors; (b) Pore size distributions of Li
precursors.
4
SiO
4
powders derived from different Si materials were composed of dense agglomerate particles with
various sizes. The agglomeration was very evident for LS-MCM-
4
1 material, and the size of the particle clusters was ~60 μm.
2
The N physisorption isotherms of the 6 samples were plotted
LS-Fumed and LS-Waste also agglomerated but the cluster size
was relatively smaller, ranging from 30 to 50 μm. Only LS-ZSM-
5
8
in Fig. 2a. All of them exhibited type II isotherms . The
information of BET surface area, external area, average pore
size and pore volume were summarized in Table 1. The highest
surface area and pore volume were observed for LS-ZSM-5,
closely followed by LS-precipitated. Generally, all the samples
possessed rather low surface area and small pore volume. The
calculated BET surface areas were equal to the external areas
for all the sorbents except LS-SBA-15, which meant that most
of these materials were barely porous. Every material also
5
and LS-Precipitated were shown as separated participles
with average size about 10 μm.
4
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Table 1. Surface area, pore size and pore volume of as-prepared samples.
The CO
2
sorption kinetics of the freshly calcined samples in 10
BET
surface
area
External
area
Average
Pore size
Pore
h at 650 ºC was plotted as CO
the CO capture rate (Fig. 5b) which is defined as the first
order derivative of CO uptake with respect to time. The
sample derived from precipitated silica presented the highest
2
uptake versus time (Fig. 5a) and
Volume
Samples
2
2
-1
2
-1
3
-1
2
(
m g )
1.09
0.99
1.46
1.05
1.43
1.06
(m g )
0.45
0.99
1.46
1.05
1.43
1.06
(nm)
3.94
4.18
3.94
3.94
3.95
3.94
(cm g )
0.009
0.008
0.012
0.007
0.009
0.006
LS-SBA-15
LS-MCM-41
LS-ZSM-5
-1
2 2
CO capacity over 10 h, namely, 0.35 g-CO g-sorbent . The
capacities of LS-ZSM-5 and LS-Fumed almost converged to the
-1
same value being ~0.34 g-CO
than the capacity of LS-precipitated. This was likely owing to
the minor quantity of Li SiO in LS-ZSM-5 and LS-Fumed (Fig.
). The capacity order was then followed by LS-Waste, LS-
2
g-sorbent , which is slightly less
LS-Fumed
LS-Precipitated
LS-Waste
2
3
1
3
.2 Sorption kinetics
MCM-41 and LS-SBA-15. The uptakes of these samples were
still growing after 10 hours. The trend is especially evident for
LS-SBA-15. This indicated that the poor capacity of SBA-15-
derived sample was mainly due to the slow kinetics. Fig. 5b
The mechanistic assumption of CO2 sorption procedure in
Li SiO sorbent has been proposed as three steps (Fig. 4). The
4
4
first step of CO capture started from the external surface of
2
further confirmed this point as the CO capture rate of LS-SBA-
2
the Li SiO particles to form Li CO and Li SiO nucleus. This
3
4
4
2
3
2
1
5 was the lowest through the 10-h test.
surface reaction is very rapid and almost requires no time. The
further nucleation had to evolve from the existing nucleus on
the surface. Hence, the CO capture rate in the second step
2
partially relies on how much nuclei formed in the first step.
The second step lasts until the formation of an outer shell
consisting of Li
2 3 2 3
CO and Li SiO grains. During the third stage,
diffusion resistance is significantly increased and thus diffusion
7
5
becomes the rate limiting factor . In the third stage, several
studies proposed that two separative product layers were
formed with Li
2
SiO
3
as internal layer and Li
. However, the surface of the fully chemisorbed
sorbent presented Si element in the EDX mapping in this study
Fig. S1) indicating Li SiO was also present on the external
surface. Therefore as shown in Fig. 4, Li CO and Li SiO
more likely to be mixed together than to be separated.
2 3
CO as external
4
0, 41, 47, 60
layer
(
2
3
were Fig. 4 CO
during a single cycle test (in pure CO
2
uptake profile (a) and CO
2
capture rates (b) of as-prepared Li
at 650 ºC for 10 h).
4 4
SiO samples
2
3
2
3
2
2 4 4
Fig. 5 The illustration of CO sorption process in Li SiO
LS-ZSM-5 performed the most rapid CO
stage with a maximum sorption rate of 21.14 wt.% min , underwent a peak at around 20 s after which the sorption
followed by LS-precipitated, LS-MCM-41, LS-Waster, LS-Fumed rate suddenly declined. The acceleration of CO sorption in the
and LS-SBA-15. This order did not demonstrated any initial stage was a typical behaviour of nucleation growth
2
sorption in the initial Fig. 5b shows that the sorption rates of all the samples
-1
th
2
6
1
correlation with BET surface area, external area, pore volume processes . The CO
2
sorption process could be regarded as a
SiO phase to the phase of Li CO and
(
Table 1) or FWHM, but it was in agreement with the sequence transformation from Li
4
4
2
3
of the pore surfaces around 4 nm (Fig. 2). This strongly Li
suggested that the sorption kinetics was predominantly
determined by the number of pores of ~4 nm.
2 3
SiO .
To interpret the kinetic behaviour further and deeply, Avrami-
Erofeev model which has been used to express solid-gas
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reactions was employed in this study. The nucleation could be The reduction of germ nuclei due to the transformation from
homogeneous or heterogeneous. Homogeneous nucleation germ nuclei to growing nuclei is proportional to the number of
starts from a nuclei which is randomly and homogeneously available germ nuclei remaining in the material
generated over the untransformed portion of the material.
dN ' = −k ' Nd
τ
(13)
&
dN = VNd
τ
(6)
The second term dN′′ which refers to the inoperative germ
6
nuclei ingested by growing product is given by
2
where dN is the number of nucleus in volume
V
is the nuclei generation rate.
generated
&
during time
d
τ
, and
N
N
dN '' = −
d
α
(14)
1−α
The second assumption is that growth rate of nuclei size is
independent of the transformation. So the radius of a nuclei is
only a function of time.
Where α is the conversion. The Eqs. 12, 13 and 14 leads to Eq.
1
5 by integrating from τ=0 to τ=t,
r = r&
(
t −
τ
)
(7)

1
2
1
6
3

−
ln(1−
α
) = 6k '' N0 exp(−k '
τ
) −1+ k 't − t +
t




2
where r& is the radius growth rate, τ is the time when nuclei is
generated and t is the time of growth (so t>τ).
(15)
By assuming k=k′′N
0
and omitting lower order terms provided t
is large, the final expression of Eq. 15 is
The ideally converted volume of solid is then expressed as:
3
−
ln(1−
α
) = kt
(16)
4
π
3
ideal
convert
&
dV
=
r&
(
t −
τ
)
 VNd
τ
(8)


3
Eq. 11 for homogeneous nucleation and Eq. 16 for
heterogeneous nucleation presented similar format for 3-
dimensional nucleation but heterogeneous nucleation showed
lower order for time term.
However, with the evolution of transformation, the possibility
that some of the ideal converted volume lies on previously
converted material, and this part should not be counted
repeatedly. The real nuclei increment dVconvert is only based on
the untransformed portion of the material as indicated by Eq.
The above deductions were based on the assumption that
nuclei performs three dimensional growth, which leads to the
power exponent of t as 4 and 3 for homogeneous and
heterogeneous nucleation, respectively. For the situation
where the nuclei evolves in other number of dimensionalities
9.
ideal
dVconvert
dV
convert
=
V −Vconvert
V
(
9)
(
n), a general format of the nuclei growth model for
homogeneous and heterogeneous nucleation should be:
Upon integration and by defining α = Vconvert/V, Eq. 9 yields:
n+1
ideal
convert
−ln(1−
α
) = kt
(17)
(18)
V
π
3
3
4
&
ln(1−
α
) = −
= − r& Nt
(10)
V
n
−
ln(1−
α) = kt
Therefore Eq. 10 can be simplified as:
ln(1−α) = kt
Eqs. 17 and 18 imply that the reaction kinetic depends on the
constant k and nucleation dimensionality n+1 (or n). k
indicates the speed of nucleation, and the nucleation
4
−
(11)
3
where πṙ Ṅ/3 is lumped as k. Eq. 11 described the relation of dimensionality number indicates the available dimensions for
conversion and time for homogeneous nucleation. But a nuclei to grow. Taking logarithm for both side, Eqs. 17 and 18
sometimes nucleation is not absolute homogeneous. For provide,
heterogeneous nucleation, the nucleation growth starts from a
ln[−ln(1−
α
)] = ln k + (n +1)lnt
)] = ln k + nlnt
number of germ nuclei in the material. At the commencement
of the nucleation, there are a number of N germ nuclei. With
(19)
(20)
0
ln[−ln(1−
α
the progression of nucleation, the number of germ nuclei
available for nucleation declines due to two possible
phenomena: the first is that nucleation already occurred from
some germ nuclei and this part of nuclei is no longer available;
the second effect comes from the heterogeneity of the
reaction as some germ nuclei might be incorporated or
ingested by the actively growing growth nuclei. Hence, the rate
of disappearance of germ nuclei is given by
Plotting ln[-ln(1-α)] vs ln(t) yields a straight line with slope = n
1 or n. The magnitude of n implies the reaction mechanism.
+
When n > 1, the model is known as ‘nucleation and nuclei
growth model’ which means the reaction rate is determined by
5
the rate of nuclei growth . For the situation when n < 1, the
7
6
3
reaction generally proceeds by diffusion control
.
dN = dN '+ dN ''
(12)
6
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Reaction (1) can be regarded as a transformation from Li
to Li CO and Li SiO , so Li CO and Li SiO are the nucleus. Fig. by CO
displayed the plot of ln[-ln(1-α)] to ln(t) in the first cycle for is governed by Eq. 22
4
SiO
4
However, in the second scenario where the reaction is limited
2
3
2
3
2
3
2
3
2
diffusion across Li
2
SiO
3
2 3
and Li CO shell, the conversion
6
the six as-prepared samples. Two distinct stages were
observed for all the samples as a fast and slow periods,
respectively. By comparing with the data of pore size
distribution in Fig. 2, the slopes of the initial fast stages in Fig.
2
2
)3 1−
(1−α0 )3 1−α0
(
1−
2
α
α
3
−
−
+
= k(t −t0 )
2
3
(22)
6
performed a consistent order with the order of ~4 nm pores
2/3
A straight line of [(1/2)(1-α) -(1/3)(1-α)] against t should be
expected if the reaction in the second stage is limited by
diffusion.
(nLS-ZSM5 > nLS-Precipitated > nLS-MCM41 > nLS-Fumed ≈ nLS-Waste >
nLS-SBA15). This strongly implied that ~4 nm pores have a
positive effect on the sorption kinetics. A possible reason
might be that pores in this size allow rapid penetration of CO
2
gases into the interior of sorbent particles, and therefore some
germ nucleus grow from the core with all the dimensionalities
available to propagate. On the contrary, without these pores,
germ nucleus were only generated from particle surface. The
available direction for surface germ nuclei to grow is only
towards the particle centre. The nucleation dimensionality was
then significantly reduced. The existence of ~4 nm pores
tended to proceed the nucleation more homogeneously,
leading to higher value of kinetic slope (growth
dimensionality).
With the evolution of the product shell, the nucleus were
more likely to grow into the converted volume, but growth in
this manner did not contribute to the total CO capture. When
2
the product shell became even thicker, some germ nucleus
may be fully surrounded by converted volume, so it had no
available dimensionality to grow. Consequently, the kinetics
would eventually shift to a much slower stage (ln(t)>3) as
shown in Fig. 6. Since the kinetics in the second stage seem to
be different from the stage prior to the inflection point, forcing
it to fit Avrami-Erofeev model to get a slope value does not
have any physical sense. It is more appropriate to examine
what the reaction mechanism of this stage is. The first possible
cause of the reduced reaction kinetics is that nucleation can
only proceed towards the centre of a particle after the
continuous product shell is formed. Hence, the nucleation rate
is limited by the geometry of the particle. This type of process
could be described by reaction-controlled-shrinking-core-
model (or known as contracting model); the second possibility
is that the product shell inhibits the contact of reactants,
therefore CO2 has to diffuse though the product shell for
further reaction. This type of process can be generally
described by diffusion-controlled-shrinking-core-model.
Fig. 6 The kinetic correlation between ln[-ln(1-α)] and ln(t) for the six samples in the
first cycle.
For reaction controlled model (contracting model), if the
nucleation proceed towards the centre at a constant speed,
6
1
the conversion with time is expressed as
1
3
1
3
−
(1−
α
) + (1−α0 ) = k(t − t )
(21)
0
where k is a constant and α
0
is the conversion at time t
0
. So if
1
/3
the plot of -(1-α) against t follows a straight line, the second
stage after the inflection point corresponds to reaction
controlled model.
Fig. 7 The comparison between contracting model and diffusion controlled model for
the slow reaction stage
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Fig. 7 showed that diffusion controlled model gave a better the 30-cycled precipitated silica was further test with 5
fitting to the experimental data than reaction controlled additional sorption-desorption cycles. But the desorption time
model, indicating the slow kinetics in the second stage is more of in each additional cycle was extended to 30 mins to achieve
likely to be diffusion limited.
more complete desorption. Remarkable improvement of
sorption capacity was observed after more complete
desorption (Fig. S2), but the capacity was still much lower than
the theoretical value. This indicated that incomplete
desorption did not solely result in the poor cyclic capacity. The
uptake slopes at the end of each cycle were still steep for
these three samples, suggesting 60 min were insufficient to
reach their CO
2
uptake ceiling. Surprisingly, the sorbent
cycle
derived from fumed silica captured more and more CO
2
by cycle until the end of Cycle No. 30. At the last cycle, the CO2
uptake was 34.23 wt.%, corresponding to 93.27% conversion
of Li SiO . It seemed the slope of CO uptake was nearly flat at
4
4
2
the end of each cycle, indicating 60-min sorption was sufficient
for a full carbonation.
Fig. 9 CO
2
capture capacities for the 30 cycles. (a) Capacity of individual cycle; (b) Total
capacity over the 30 cycles.
Fig. 8 Sorption and desorption performance in 30 cycles. Conditions: sorption in pure
2 2
CO for 60 min and desorption in pure N for 10 min at 650 °C.
3
.3 Cyclic sorption-desorption performance
It seems that the sample from precipitated silica was the most
favourable sorbent for the 10-h sorption test (Fig. 5). However,
solid sorbents were not designed to be one-off in practical
applications. The cyclic sorption/desorption stability of
sorbents is of greater importance for both pre- and post-
combustion applications. Therefore, all the samples were
further subject to a 30-cycle test in this study. Fig. 8 suggested
that all samples underwent self-activation in the initial a few
cycles. Except the sample developed from fumed silica, all the Fig. 10 XRD patterns of LS-Fumed and LS-Precipitated samples after 30 cycles.
other sorbents experienced performance decay after reaching
The cyclic capacity in the 30 cycles was summarized in Fig. 9.
The order of total uptake over the 30 cycles (Fig. 9b) was: LS-
Fumed > LS-ZSM-5 > LS-SBA-15 > LS-MCM-41 > LS-Waste > LS-
Precipitated, which is identical to the order of the individual
a peak value of capture capacity. Not only the sorption uptake
did not reach the same value of previous cycle, but also the
desorption process failed to come back to the original base
line. This incomplete sorption and desorption resulted in poor
reversibility of Reaction (1). This kind of negative phenomenon
was especially evident for samples made from precipitated
silica, MCM-41 and waste silica. To inspect the effect of
desorption extent on the sorption capacity of following cycle,
th
capacity at the 30 cycle (Fig. 9a). That means the capacity at
the last cycle was more important than the initial capacity at
st
the 1 cycle. The sample derived from precipitated silica,
which was identified as the best sorbent based on the single
8
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10-h test (Fig. 5a), exhibited the most disappointing particle sizes were smaller after cycles, there must be more
performance for the long term cyclic test. Its individual particles. In turn, there were more gaps between them,
capacity for Cycle No. 30 was 11.52 wt.%, which was only 1/3 causing an enhancement of pores. Since the first step is the
of that at Cycle No. 3 (the cycle it peaked in term of individual rapid surface reaction, the enlarged surface area might
2 2
cycle uptake). Its total CO captured all over 30 cycles was as correlate to the increased k value in the initial stage of CO
-
1
low as 5.46 g-CO
2
g-sorbent . Contrastingly, the sorbent made sorption. This correlation needs to be further examined for the
from fumed silica presented the opposite trend. It showed the LS-Fumed material.
st
second lowest CO capacity in the 1 cycle (19.90 wt.%), but its
2
capacity grew with cycles until approaching to the theoretical The slope for LS-Precipitated sample during the nucleation
maximum. During the following cycles, the capacity did not stage continuously decreased from slope = 2.31 for the first
th
th
present any observable decline, sustaining at a constant level cycle, to slope = 2.25, 1.52, 1.11, 0.99 and 0.82 for the 5 , 10 ,
th
until the last cycle (34.23 wt.%). Owing to such stable 15 , 20 and 30 cycles, respectively (Fig. 11). Since the slope
th
th
th
performance, it captured the most CO through the total 30 value for the 20 and 30 cycles was less than 1, it was even
th
2
-1
cycles, namely, 10.03 g-CO g-sorbent .
2
barely reasonable to refer to this stage as nucleation. An
exceptional phenomenon of pore size distribution after 30
The morphological transformations of the 6 samples before cycles in Fig. 12 was that a decrease of pores occurred for pore
and after the 30-cycle tests are displayed in Fig. S3. For all the size of ~4 nm. As discussed above (Fig. 2b and 6), the
samples, an evident change caused by the cycles was the nucleation dimensionality was sensitive to the number of ~4
reduction of particles sizes. This phenomenon was consistent nm pores, its reduction might be the reason of the decayed
with reports for other similar sorbents. It was likely due to the kinetics with cycles.
structure rearrangements during sorption and desorption
6
4
processes . To further confirm the change of materials, the
0-cycled LS-Fumed and LS-Precipitated samples which
3
performed the most contrasting behaviours were selected for
XRD test. Both samples still preserved the Li SiO phase after
4
4
3
1
0
0 cycles with observable minor peaks of Li SiO phase (Fig.
2 3
0). The FWHM of cycled LS-Fumed and LS-Precipitated were
.178 and 0.179, respectively. According to Scherrer equation,
these values implied the grain sizes reduced after cycles. But
not all samples demonstrated better sorption kinetics with the
th
st
finer particle size at the 30 cycle than at the 1 cycle. Only
the LS-SBA-15 and LS-Fumed ones did so.
As shown above, LS-Precipitated sample and LS-Fumed sample
displayed the most striking contrast in the cyclic test. In order
to interpret the contrasting behaviour, the kinetic data for the
st
1
th
th
th
th
th
, 5 , 10 , 15 , 20 and 30 cycle were plotted as ln[-ln(1-
α)] vs ln(t) for the two samples. Since ln[-ln(1-α)] is a single
increasing function of α, a higher value of ln[-ln(1-α)] also
indicates a higher value of α. k indicates how fast the
nucleation proceeds. The intercept value (lnk) for LS-
Precipitated sample in Fig. 11 increased with cycles, suggesting
the nucleation proceeded at a faster rate at the very beginning
compared to that in previous cycles. This might be due to the
incomplete regeneration of previous cycle. The remaining
2 3 2 3
Li CO and Li SiO from the previous cycle provided more
seeds for the heterogeneous nucleation of the next cycle, thus
giving a higher k value. Another possible cause could be the
st th
th
th
Fig. 11 The kinetic correlation between ln[-ln(1-α)] and ln(t) at the 1 , 5 , 10 , 15 ,
2
morphological change caused by cycles. The N physisorption
th
th
2
0 and 30 cycles.
test of 30-cycled LS-Precipitated sorbent was conducted to
evaluate the change of porous property (Fig. S4) and
compared with that of the fresh sample. After 30 cycles, the
enlarged surface area and pore volume (Table 3) indicated that
the material became more porous. The derived pore size
distribution by BJH method also confirmed that there was an
enrichment of pores for most pore sizes (Fig. 12). The enriched
pores stemmed from the reduced particle sizes. Since the
As for the LS-Fumed sample in Fig. 11, the value of ln[-ln(1-α)]
th
at ln(t) = 0 (or lnk) was almost constant all over the 30 cycles,
which was on account of the complete regeneration in each
cycle (Fig. 8). The enlarged pore volume and surface area after
cycles (Fig. 12 and Table 3) did not show a higher starting point
(lnk) for LS-Fumed, hence proved the starting point was
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irrelevant to the material morphology. The slope during the Table 2. The Li SiO4 conversion when CO2 sorption mode switched from nucleation
4
nucleation stage was promoted with cycles for the LS-fumed stage to diffusion controlled stage.
sorbent. The slope value started from 2.05 for the initial cycle
Conversion after nucleation - α (%)
and reached at 2.88 for the last cycle. This strongly suggested
Cycles
2
that the improved CO capacity with cycles was ascribed to the
LS-Fumed
LS-Precipitated
increment of dimensionality for growing during the nucleation
growth stage. Fig. 12 reported an enrichment of ~4 nm pores
after 30 cycles. Since the nucleation kinetics was mainly
dependent on the ~4 nm pores, the enrichment of such pores
was responsible for this improved cyclic kinetics.
1
5
7
17
29
27
25
23
20
42
61
72
71
71
1
0
5
0
0
1
2
3
Table 3. Surface area, pore size and pore volume of LS-fumed and LS-Precipitated
samples before and after 30 cycles.
BET surface
Average
pore size
Pore
Fig. 12 The comparison of pore size distribution for LS-Fumed and LS-Precipitated
samples before and after 30 cycles.
[
a]
area
volume
Samples
2
-1
3
-1
(
m g )
(nm)
(cm g )
With higher cycle numbers (>10), the evident distinction
between LS-Precipitated and LS-Fumed was that LS-
Precipitated started from a higher conversion value but grew
with lower number of dimensionality afterwards. The higher
starting conversion value of LS-Precipitated came from the
LS-Fumed before 30
cycles
1
3
1
3
.05
.65
.44
.17
3.94
0.007
LS-Fumed after 30
cycles
3.94
3.95
3.94
0.034
0.009
0.036
LS-Precipitated
before 30 cycles
LS-Precipitated after
uncalcined Li
Since heterogeneous nucleation is more favourable than
homogeneous nucleation, the uncalcined Li CO and Li SiO
2 3 2 3
CO and Li SiO in the previous cycle (Fig. 8).
3
0 cycles
2
3
2
3
[
a]
could act as seeds for heterogeneous nucleation and formed
larger clusters during the nucleation. The large clusters were
very likely to interfere each other and reduce the number of
growing dimensionality. That is why the cycled LS-Precipitated
BET surface area equals external area
sample showed higher
k value and lower nucleation
dimensionality value. As for LS-Fumed, since the calcination in
previous cycle was more complete (Fig. 8), it had to generate
2 3 2 3
new Li CO and Li SiO nucleus from zero in the new cycle. So
the commencement of LS-Fumed sample to nucleate is more
homogeneous. That was why it showed lower starting point or
intercept (Fig. 11). But the newly generated nucleus were
more dispersed. So the chance of interfering each other is
relatively lower and growth dimensionality was thus relatively
higher. Eq. 17 and 18 indicate homogeneous nucleation had
one more order (n+1) than heterogeneous nucleation (n) in
the time term (t), which also confirmed the nucleation of
cycled LS-Fumed was more homogeneous and that of cycled
LS-Precipitated was more heterogeneous.
Fig. 13 The schematic of nucleation of samples with different pore sizes
The quantity of ~4 nm pores seemed to have a reasonable
correlation to the dimensionality of nucleation. This could be
further explained by Fig. 13. When gas was switched from N
to CO , the contact between CO and the surface of Li SiO
2
2
2
4
4
initiated the nucleation. In this regard, smaller pores were
advantageous over lager pores as smaller pores provide more
1
0 |Dalton Trans., 2018
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surface area to start nucleation. However, the material will found that the sorption kinetics had a positive correlation to
swell after being converted from Li SiO to Li SiO and Li CO the quantity of ~4 nm pores. As such, LS-ZSM-5 which had the
because the molar volume of Li SiO and Li CO (35.542 cm most amount of ~4 nm pores exhibited the most rapid
mol and 35.019 cm mol ) is higher than the molar volume of sorption kinetics. The cyclic performance of these sorbents
4
4
2
3
2
3
,
3
2
3
2
3
-
1
3
-1
-1
3
Li
volumetric expansion would close the narrow pore as depicted cycles, all the materials presented smaller particle size due to a
in Fig. 13, thus causing the blockage of CO transfer. In this self-rearrangement effect with cycles. Only the sorbent made
4
SiO
4
(50.146 cm mol ). If the pores are too small, the was tested for 30 cycles of sorption/desorption. After 30
2
small pore scenario, nucleation can only commence from the from fumed silica presented outstanding cyclic stability with its
external part of the sorbent. The experimental observation capacity growing from 19.90 wt.% for Cycle No. 1 to 34.23
and theoretical analysis in this study indicated that ~4 nm was wt.% for Cycle No. 30. Even though the cycles reduced particle
highly likely the optimum size for Li
size were highly possible from the minor cracks of particles, capacity with cycles, especially for the sorbent made from
which allowed CO diffuse rapidly into the interior of particle precipitated silica. The diverse cyclic behaviours of different
4 4
SiO sorbents. Pores of this size, all the other sorbents showed deteriorated sorption
2
without being blocked when product was generated. In such a sorbents were attributed to the sorption kinetics after cycles.
manner, the nucleation could commence from anywhere of The Avrami-Erofeev model was used to interpret the rates of
the particle. Hence, the nuclei had many dimensionalities to nucleation for the cycled LS-Fumed sorbent. The kinetics was
grow. However, the nucleation only started from the particle boosted due to more homogeneous nucleation which might be
surface if the pores are too small. Once the product shell was related to the enrichments of ~4 nm pores after 30 cycles. The
formed, the inner part did not have a chance to be converted cycled LS-Precipitated sample only showed improved starting
2 3 2 3
by nucleation mechanism, instead, the inner part could only be point due to the remaining Li CO and Li SiO from the
converted via the diffusion limited mode. The favourable incomplete regeneration in previous cycle. But the decrease of
sorption kinetics by ~4 nm pores was also evident in a number ~4 nm pores in the cycled LS-Precipitated sample reduced the
6
5-67
of other Li
4
SiO
4
studies
.
dimensionality of nucleation, thus slowed down the overall
sorption kinetics.
The Li SiO
4
4
conversion at inflection point from the nucleation
stage to the diffusion-controlled stage denoted the extent of
sorption via nucleation growth. As shown in Table. 2, the
conversion ratio at the inflection point increased with cycle
numbers for fumed silica derived sorbents. In the first cycle,
Nomenclature
2
-1
D
Diffusion coefficient in product shell, m s
k
Constant
the sorbent conversion was only α
≈
7% in the nucleation
SiO had
k′
m
m
Rate of germ nuclei disappearance
stage. After the inflection point, all the remaining Li
4
4
0
Minimum mass of the sample during the entire test, g
to be converted in the diffusion limited mode. With increasing
cycle numbers, the conversion after nucleation stage climbed
th
max,i
Maximum mass at the i cycle, g
th
th
42% at the 5 cycle, 61% at the 10 cycle, 72% at mmin,i
th
up to α
th
≈
Minimum mass at the i cycle, g
th
th
the 15 cycle, 71% at the 20 cycle and 71% at the 30 cycle,
respectively. Although the slow diffusion would limit further
N
Number of nucleus
-1
Ṅ
Generation rate of nucleus, s
CO
2
capture, the diffusion limited stage only accounted for a
sorption. This implied that
N′
N′′
N
Reduction of germ nuclei due to transformation
Reduction of germ nuclei due to ingestion
minor portion of the total CO
2
nucleation growth played a progressively important role in a
cyclic sorption test, especially with higher cycle numbers. For
the precipitated silica derived sample, nucleation stage
Number of dimensions
th
Q
Q
R
ṙ
i
CO
Total CO
Radius of nuclei, m
2
capture capacity at the i cycle, wt.%
converted 17% of the Li
rather a low conversion. But the diffusion controlled stage
demonstrated a decent rate of CO capture in the first cycle, so
this material performed great CO capacity initially. With
increasing cycle numbers, the conversion by nucleation growth
4 4
SiO at the first cycle, which is still
total
2
capture capacity, wt.%
2
-1
Growth rate of nuclei radius, m s
2
t
Time for sorption, s
th
th
3
kept declining from the 5 cycle to the 30 cycle for the LS-
Precipitated sample. Likewise, the sorption rate in the
diffusion controlled stage also deteriorated with cycles, thus
leading to a declining trend of sorption capacity.
V
Volume, m
ideal
3
V
V
α
τ
convert
Ideally converted volume, m
3
convert
Real converted volume, m
Sorbent carbonation conversion
Time when nuclei is generated, s
4
. Conclusions
Six different Si precursors were used to synthesize Li
4 4
SiO
Conflicts of interest
sorbents. The sorbent derived from precipitated silica
-
demonstrated the highest CO
1
2
capacity (0.35 g-CO
g-sorbent There are no conflicts to declare.
2
)
in a 10-h sorption test in a pure CO stream at 650 ºC. It was
2
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2
5.
M. Z. Memon, X. Zhao, V. S. Sikarwar, A. K.
Vuppaladadiyam, S. J. Milne, A. P. Brown, J. Li and M.
Zhao, Environ. Sci. Technol., 2017, 51, 12-27.
Acknowledgements
Authors thank for the support by the National Natural Science
Foundation of China (grant number: 51506112). Dr. Ji is 26.
grateful for China Postdoctoral Science Foundation (grant
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Table of contents entry:
2 4 4
The illustration of CO sorption process in Li SiO