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Novel architecture of carbon nanotube decorated poly(methyl methacrylate)
microbead vapour sensors assembled by spray layer by layer†
J. F. Feller,*
a
J. Lu,
a
K. Zhang,
b
B. Kumar,
a
M. Castro,
a
N. Gatt
a
and H. J. Choi
b
Received 4th November 2010, Accepted 17th December 2010
DOI: 10.1039/c0jm03779f
For the first time vapour sensors were made by assembling multi-wall carbon nanotube (CNT)
decorated poly(methyl methacrylate) microbeads (PMMAmB) by spray layer by layer (sLbL). This
combination of materials and technique resulted in an original hierarchical architecture with
a segregated network of CNT bridging PMMAmB. The chemo-resistive behaviour of these conductive
polymer nanocomposite (CPC) sensors was studied in terms of sensitivity and selectivity towards
standard volatile organic compounds (VOC), as well as quantitativity and reproducibility of responses
A
r
to methanol, water, toluene and chloroform. Results show that 3D sLbL assembly allows boosting
CNT network sensitivity by a factor 2 and selectivity for methanol vapour by a factor of 5. Additionally
CNT-PMMAmB sensors gave responses proportional to vapour molecules content that could easily be
fitted by the Langmuir–Henry-clustering model. Such sensors are thus expected to be good candidates
for implementation in electronic noses.
1. Introduction
By definition, materials can be ‘‘smart’’ if they are able to respond
to external stimuli of their environment.
1
Although this character
can rarely reveal itself without external input, there has been
many successful utilisations of smart behaviours in the field of
sensors under different forms, fibres
2–5
or coatings. This last
category particularly concerns vapour sensors that drew some
interest since the discovery of electronic noses (e-noses).
6–9
The
cleverness of e-noses results from the fact that they are composed
of partly selective sensors associated in array. Only the compu-
tation of all signals through pattern recognition algorithms will
provide full selectivity and allow vapour identification, like in
mammal’s sense of olfaction.
10,11
During the last decades both
algorithms
12,13
and materials
14–18
have progressed contributing to
the improvement of sensors performances. Mainly two families
of materials (ceramics and polymers) are competing for vapour
sensors design, metal oxides (MOx),
19–23
intrinsically conducting
polymers (ICP) and conductive polymer nanocomposites
(CPC).
24–33
From the sensing principle point of view the classi-
fication is different as (MOx) and ICP electrical response results
from variations of their work function
34,35
whereas for CPC it is
related to changes in quantum tunnelling conduction,
36–39
although they can be combined when ICP is part of the CPC
composition.
40
The recent discovery of CNT
41–44
found to be
sensitive to vapour
45,46
particularly when functionalized with
COOH,
47
has provided a new impulsion in the development of
new CPC for sensing.
48–54
The versatility of properties by simple
adjustment in their formulation, their easy processing in the melt
or in solution, the variety of shapes they can take, and their
operability at room temperature make CPC attractive to design
sensors able to detect volatile organic compounds (VOC),
24–27,46–48
explosives,
28
nerves agent
29
or to diagnose lung cancer from the
presence of biomarkers in patients breath.
30–33
However some issues such as reproducibility and durability of
sensing properties still remain, due to the high interdependency
between the percolation state, dispersion/aggregation balance,
shape factor and interactions.
55–57
Thus it appears useful to take
benefit from tools that proved their effectiveness; first in
controlling conducting nanofillers dispersion such as surfac-
tants,
58,59
functionalization of filler
52,60,61
and second in struc-
turing a conducting architecture such as decoration,
62–70
double
filler percolation,
71,72
segregated networks,
73,74
self-assembly by
electrostatic LbL
5,63,75
or spray LbL.
25–27,52–54,76,77
In the present study, we made vapour sensors by assembling
multi-walled carbon nanotube (CNT) decorated poly(methyl
methacrylate) microbeads (PMMAmB) stabilized by poly(vinyl
pyrrolidone) (PVP) and structured by spray layer by layer
(sLbL). This process led to an original architecture built from
a segregated network of CNT bridging PMMAmB that gave
quantitative and reproducible responses A
r
to VOC such as
methanol, water, toluene and chloroform. Hierarchically struc-
tured CNT-PMMAmB sensors allowed increasing CNT sensi-
tivity by a factor 2 and selectivity for methanol vapour by
a factor 5. Additionally all responses could easily be fitted by the
Langmuir–Henry-clustering model.
a
Smart Plastics Group, European University of Brittany (UEB),
LIMATB—UBS, Lorient, France. E-mail: jean-francois.feller@univ-ubs.fr
b
Department of Polymer Science and Engineering, Inha University,
Incheon, 402-751, Korea
† Electronic supplementary information (ESI) available: TGA curves of
CNT-d-PMMAmB. See DOI: 10.1039/c0jm03779f
4142 | J. Mater. Chem., 2011, 21, 4142–4149 This journal is ªThe Royal Society of Chemistry 2011
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2. Experimental
2.1. Synthesis of CNT decorated PMMA mbeads
Azoisobutyronitrile used as initiator was obtained from Junsei
Chemicals (Japan) and purified three times by recrystallization
from methanol before use. Poly(vinyl pyrrolidone) used as
a stabilizer had a molar mass of M
w
¼55 000 g mol
1
and was
obtained from Sigma-Aldrich (USA). Methanol used as
a medium in the polymerization and methyl methacrylate were
both obtained from Duksan Chemical (Korea). Type CM95
multi-walled nanotubes (CNT) from Iljin Nanotec Co. (Korea)
used to decorate PMMAmB have a diameter ranging from 10 to
20 nm and a purity of ca. 95%. These CNT are prepared via
thermo-chemical vapour deposition method. Prior to use they
were treated with 3 M H
2
SO
4
(98%) and 1 M HNO
3
(70%) at
60 C for 30 min in an ultrasonic bath, and then refluxed for 12 h.
After that, the mixture was filtered through 0.2 mm Millipore
poly(carbonate) membrane, and washed with distilled water until
the pH value of the filtrate was 7.0. The acid treated CNT were
dried under vacuum oven at 60 C for 24 h, thus obtaining
carboxylic acid-functionalized CNT (CNT-f-COOH). Concur-
rently, once mono-dispersed PMMAmB with 2 mm diameter were
prepared by dispersion polymerization, they were dispersed in
DI-water with CNT–COOH under ultrasonication with
a Kyungil Ultrasonic Co. (Korea) generator, at 28 KHz and
600 W for 8 h at 20 C. The fabricated mbeads were dried in
a vacuum oven at 60 C. Finally, PMMA microbeads decorated
with CNT-f-COOH (CNT-d-PMMAmB) are obtained as
described in Fig. 1 and also in a previous paper.
67
2.2. Characterization techniques
(a) FTIR characterization of CNT functionalisation. Fig. 2
shows Fourier transform infrared (FTIR) spectra of CNT before
and after functionalization, obtained with a PerkinElmer System
2000 spectrometer. The characteristic adsorption peak at
3440 cm
1
found in functionalized CNT (CNT–COOH) spec-
trum is attributed to hydroxyl group. The band observed at 1718
cm
1
is associated with the stretching vibration of carbonyl
groups, while no obvious characteristic bands can be found in the
raw CNT spectrum. (The peak with low intensity at 3440 cm
1
in
the raw CNT spectrum is believed to be the stretching of O–H
groups of the adsorbed water.) This is because dangling bands
exist at the head end and some defects lie on the side wall of
nanotube, which are oxidized to carboxylic acid, carbonyl or
hydroxyl groups in the concentrated acid mixture.
(b) Composition checking by TGA. The thermal behaviour of
carbon nanotubes before and after functionalization is illustrated
in Fig. 3 by thermo-gravimetric analysis (TGA) with a Polymer
Lab (TGA1000, UK) device. The main body of CNT cannot be
decomposed below 600 C in nitrogen atmosphere. Therefore the
weight loss in the curve of CNT–COOH is due to the decom-
position of organic groups on its sidewall. The estimated
attachment content of organic groups is 13% according to the
residual weight of CNT–COOH at 600 C. Moreover, the
content of CNT in CNT-d-PMMAmB was also quantitatively
determined by this technique. Samples were heated up to 600 C
under nitrogen atmosphere with a heating rate of 20 C min
1
.
Fig. 1 a) Process of PMMAmB decoration by CNT–COOH, SEM
picture of PMMAmB (b) before and (c) after decoration by CNT–
COOH.
18
Fig. 2 FTIR spectra of raw (down) and COOH functionalised (up)
CNT.
18
Fig. 3 TGA curves of raw (up) and COOH functionalised (down)
CNT.
19
This journal is ªThe Royal Society of Chemistry 2011 J. Mater. Chem., 2011, 21, 4142–4149 | 4143
After PMMA degradation, between 180 and 430 C, the weight
loss curve stabilized and the residual weight of 4.4% which was
assumed to correspond to the amount of CNT in PMMAmBas
the same experiment made with PMMAmB alone led to almost
no residue (see Fig. 11 in the ESI†).
(c) Optical microscopy (OM). The microstructure of sprayed
layers of CNT-d-PMMAmB in Fig. 4 was observed using a Leica
DMLP optical microscope in non-polarized monochromatic
light at 200 magnification coupled with a tri CCD video
acquisition device. For optimal observation the solution was
sprayed onto methanol cleaned glass blades and interdigitated
electrodes (IDE) at the same time. Although the magnification of
OM is quite low, this technique allows to control that the
aggregation of mbeads by sLbL is progressive and homogeneous,
not leading to supermicronic agglomerates.
(d) Scanning electron microscopy (SEM). Scanning Elec-
tronic Microscopy (SEM) was further performed to characterize
the CNT-d-PMMAmB surface morphology at higher magnifi-
cations. SEM images of Fig. 1 and 8 were obtained with a Jeol
JSM-6031F with conventional tungsten cathode at 12 kV accel-
erating voltage in secondary electron image (SEI) mode.
(e) CNT-d-PMMAmB chemo-resistive sensor preparation.
CNT-d-PMMAmB chemo-resistive sensors were assembled using
a two step process: firstly 50 mg CNT-d-PMMAmB were added
to 10 ml of ethanol and sonicated for 2 hours at 25 C to obtain
a homogeneous dispersion. Secondly the CNT-d-PMMAmB
suspension was sprayed layer by layer (sLbL) onto interdigitated
electrodes (IDE) obtained by cleavage of capacitors.
7,40
The
shape of conducting tracks is clearly visible in Fig. 4 and 5.
Spraying was done with a homemade device,
25
allowing to
precisely control spraying conditions such as nozzle flow rate
(index 2), air pressure (p
s
¼0.20 MPa), sweep speed (V
s
¼10 cm
s
1
) and target to nozzle distance (d
tn
¼8 cm). In order to obtain
reproducible transducers with relatively low resistance, the LbL
process was monitored by following the evolution of electrical
resistance as a function of layers deposition. After spray depo-
sition, samples were vacuum dried at room temperature for
24 hours prior to chemical vapour testing.
(f) Dynamical vapour sensing measurement. Chemo-electrical
properties of CNT-d-PMMAmB sensors were investigated by
recording their electrical responses when subjected to 10 min
successive cycles of dry nitrogen and vapours streams. The
dynamic system consisting in mass flow controllers, solvent
bubblers and electrical valves is controlled by LabView software.
Bubbling dry nitrogen in liquid solvent provides a saturated
vapour stream, which was in turn diluted by dry nitrogen flow to
the desired concentration at room temperature. The sensing
device is presented in Fig. 5 and samples were placed in 9 cm 3
cm 3.5 cm chamber. The design of the device allows to keep
constant the total flow rate at Q
v
¼100 cm
3
min
1
, where the
analyte flow rate is set to Q
v
¼10 cm
3
min
1
,50cm
3
min
1
or
100 cm
3
min
1
to investigate the effect of analyte’s concentration.
Electrical characteristics of the CPC transducer were recorded
with a Keithley 6517A multimeter.
3. Results and discussion
3.1. Characterization of PMMAmB-CNT thin film
morphology by microscopy
SEM was performed to make a fine analysis of the meso-struc-
ture of sprayed thin films. Fig. 1b shows that PMMAmB are
monodispersed with an average diameter of 2 mm diameter. The
initial smooth character of PMMAmB surface becomes fuzzy in
Fig. 1c evidencing the effectiveness of PMMAmB decoration by
COOH-functionalized CNT according to the process described
in Fig. 1a. It is clear from these pictures that carbon nanotubes
are entangled at microbeads surface, almost completely wrap-
ping them and also making possible their bridging. At lower
magnification optical microscopy (OM) allows us to image both
IDE dimension and CNT-d-PMMAmB microstructure. In
Fig. 4a the distance between two consecutive conducting tracks is
found to be about 30 mm whereas Fig. 4b shows the mparticles
density in one single sprayed layer at a comparable magnification
(scale bar is 30mm). Due to the low magnification accessible by
OM, the core–shell structure of PMMAmB-CNT cannot be
observed, but instead this technique evidence that spray allows to
well disperse CNT-d-PMMAmB on the substrate. However at
this step only a small amount of mbeads is aggregated showing
Fig. 4 Microstructure of (a) IDE mcapacity, (b) Single spayed layer of
CNT-d-PMMAmB observed by optical microscopy (OM), and (c) scheme
of sLbL 3D architecture.
19
Fig. 5 Scheme of chemo-resistive vapour sensing device.
20
4144 | J. Mater. Chem., 2011, 21, 4142–4149 This journal is ªThe Royal Society of Chemistry 2011
the necessity for additional layers to complete the conducting
network in 3D. The assembly of successive layers on the IDE is
followed by the evolution of the CPC film resistivity that must be
comprised between 900 and 1000 kUfor optimal sensing prop-
erties. At this level of conductivity the thickness of the film is
about 2.5 mm (measured by SEM). Finally the transducer’s
conducting architecture obtained is based on a 2D segregated
network of entangled CNT coating and interconnecting
PMMAmB (not expected to be welded by more than a tiny
tangential surface due to their rather high rigidity at room
temperature), which in turn will be packed in 3D. The PMMAmB
interparticle distance is necessarily comprised between 0 (hard
sphere contact) and a couple of 100 nm as on the one hand CNT–
CNT junctions need to be separated by less than 10 nm (due to
the necessity for tunnel conduction) and on the other hand CNT
length characterized by AFM (see Fig. 12 in the ESI†) is
comprised between 500 and 900 nm. So, given that their entan-
gled structure will tend to decrease their effective length by
a factor of 3 or more, CNT must not be able to connect
PMMAmB on distances larger than some hundreds of nm as
assumed from Fig. 8. This process was found reliable for the
fabrication of chemo-resistive sensors with regular structure and
controlled thickness.
3.2. Vapour sensing properties of CNT-d-PMMAmB
transducers
(a) Chemo-resistive behaviour. In a first step the chemo-
resistive behaviour of CNT-d-PMMAmB-based sensors was
investigated by exposing them to a standard set of polar (meth-
anol, water) and dispersive (toluene and chloroform) saturated
vapours (concentration of 100%) for which solubility parameters
are given in Table 1. The resistance changes recorded during
experiments were converted into relative amplitude A
r
, calcu-
lated from eqn (1), which allows us to quantify the sensor’s
performance more easily, as it is a more sensitive and normalized
parameter.
Ar¼RvRini
Rini
(1)
where R
v
is the resistance of sensor when exposed to vapour and
R
ini
is the initial resistance in dry nitrogen at room temperature.
25
Fig. 6 shows that all sensors exhibit a strong positive vapour
coefficient (PVC) effect meaning that their resistivity increases
with analyte’s sorption and decreases with their desorption in dry
nitrogen. Such behaviour is classically obtained in percolated
CPC when solvent molecules diffusion results in the disconnec-
tion of the conducting network as described in a previous work.
54
This phenomenon generates large resistance variations as the
energy required for electrons circulation by tunnelling is
increasing exponentially with the gap at CNT–CNT junctions
according to the quantum resistive sensing (QRS) model
expressed by eqn (2).
DR
R0
¼aebDZ(2)
where DR/R
0
is the tunnel relative resistance variation, aand
bare positive constants and DZthe gap variation between two
vicinal CNT.
39
Qualitatively, Fig. 6 shows that CNT-d-PMMAmB electrical
responses are reproducible with short response time, suggesting
an easy disconnection of the conductive network and thus high
potential for the fabrication of highly sensitive sensors. A
r
instantly increases in the presence of vapours to reach a plateau
within a few seconds for all vapours except methanol for which
no equilibrium is observed within the experiment time.
(b) Selectivity of sensors towards VOC. More quantitatively,
comparing the evolution of A
r
with vapour nature shows that
methanol gives a response 5 times larger than the three other
vapours that have quite the same amplitude. This high selectivity
towards alcohols contrasts with the predictions of eqn (3) (with
n¼1) used for conventional CPC that would be obtained by
dispersing the same amount of CNT, i.e., 4 wt%, in a PMMA
matrix (Table 2). For instance assuming A
r
¼1 for chloroform
will only give A
r
¼0.155 methanol.
Table 1 Solubility parameters of solvent vapours and PMMA
17
d
T
/
(J cm
3
)
1/2
d
d
/
(J cm
3
)
1/2
d
p
/
(J cm
3
)
1/2
d
h
/
(J cm
3
)
1/2
V
molar volume
/
cm
3
mol
1
Water 47.90 15.50 16.00 42.40 18.10
Methanol 29.61 15.10 12.30 22.30 40.70
Toluene 18.16 18.00 1.40 2.00 106.30
Chloroform 18.95 17.80 3.10 5.70 79.70
PMMA 22.2 17.02 5.8 9.20
Fig. 6 Chemo-resistive response of CNT-d-PMMAmB sensors exposed
to methanol, water, toluene and chloroform vapour.
20
Table 2 c
12
Flory–Huggins interaction parameter and A
r
relative
amplitude of CNT based transducers
17
c
12[PMMA]
calculated
A
r[CNT-d-PMMAmB]
measured
A
r[CNT]
measured
A
r[PMMA-4%CNT]
calculated
Water 5.6 0.18 0.14 0.15
Methanol 1.4536 1 0.42 0.155
Toluene 0.1777 0.21 0.15 0.25
Chloroform 0.0504 0.19 0.14 1
This journal is ªThe Royal Society of Chemistry 2011 J. Mater. Chem., 2011, 21, 4142–4149 | 4145
Ar¼aebðc12Þn(3)
Flory–Huggins interaction parameter c
12
values are calculated
with eqn (4) and summarized in Table 2, a,band nare constants.
This equation is derived from
49,79
and has been successfully used
in
54
c12 ¼VmdTpoldTsol 2
RT (4)
where V
m
is the solvent molar volume, d
Tsol
and d
Tpol
are the
global Hildebrand solubility parameters for solvent and polymer
calculated with d
2
T
¼d
2
d
+d
2
p
+d
2
h
from data of Table 1.
To better understand the reason for this deviation from
eqn (3), we have sprayed a solution of CNT-f-COOH onto IDE
using experimental protocol as for CNT-d-PMMAmB and
sensors to the same set of saturated vapour. Interestingly (Fig. 7)
the fact that A
r
for methanol is only 4 times higher than other
vapours shows that CNT-f-COOH have the same selectivity as
CNT-d-PMMAmB. Nevertheless CNT-f-COOH sensors are
more than twice less sensitive than CNT-d-PMMAmB sensors
taking for instance the response to methanol, A
r
is only 0.42
against 1 respectively. Moreover CNT were found to have some
affinity for methanol and ethanol
78
which has also been
confirmed in a forthcoming paper in which we show that func-
tionalizing CNT with COOH groups also results in the
enhancement of their sensitivity to methanol vapour. Hence, it
can be concluded that PMMAmB have almost no influence on
CNT-d-PMMAmB selectivity, which is mainly driven by CNT
affinity for analytes. Thus the most important input of building
a CNT-d-PMMAmB sensor with hierarchical architecture is the
boost in sensitivity (about 240%) it generates, due to the larger
specific surface of CNT network accessible to solvent molecules
clearly understandable when comparing Fig. 8b and c. But on the
contrary of techniques allowing to enhance transducers specific
surface by the creation of porosities resulting from solvent
evaporation,
25
the use of hard spheres (such as PMMAmB in the
present case) allows a better control of specific surface expansion
and final morphology. Moreover no contribution of PMMAmB
expansion due to solvent swelling has been evidenced, since this
would have changed the sensor’s selectivity. Fig. 8a and b show
the importance of CNT bridging between PMMAmB that can
explain the easy disconnection of the conducting network.
Bridges appear to be obliged paths for the delivery and amplifi-
cation of all sensing information through the transducer.
(c) Sensitivity of sensors to analytes concentration. Apart
from being selective towards chemical nature of VOC, CNT-d-
PMMAmB sensors give responses proportional to the amount of
organic molecules in their surrounding. Fig. 9 shows the
dependence of A
r
towards methanol concentration when it is
varied from 10% to 50% and finally to 100% (a concentration of
100% corresponds to the saturated vapour). Summarizing
maximum responses of CNT-d-PMMAmB sensor for all vapour
concentrations and types leads to curves in Fig. 10. The main
feature of this graph is that only methanol curve fits the classical
shape of the Langmuir–Henry-Clustering (LHC) model,
27,52–54
which is recalled in Fig. 10 inset. This empirical model which is
derived from classical sorption models describes quite well as
Fig. 7 Compared selectivity of CNT-d-PMMAmB and CNT random
network when exposed to methanol, water, toluene and chloroform
vapours.
21
Fig. 8 Compared CNT architectures in CNT-d-PMMAmB (a) observed
by SEM and (b) schematized (black rectangles show bridging of
PMMAmB), and (c) in CNT random network (small dots symbolize
analyte molecules).
21
Fig. 9 Effect of vapour concentration of methanol vapour on CNT-d-
PMMAmB sensor response amplitude A
r
.
22
4146 | J. Mater. Chem., 2011, 21, 4142–4149 This journal is ªThe Royal Society of Chemistry 2011
which diffusion regime takes place in the CPC sensor: simple
adsorption, diffusion, clustering, corresponding, respectively, to
the three terms of the equation recalled in Fig. 10 inset. A look at
LHC fitting parameters summarized in Table 3 makes it possible
to finely analyse the different electro-sorption behaviours
depending on vapour chemical nature. All vapour have the same
Langmuir affinity constant that corresponds to the first step of
analytes diffusion of b
L
¼6, except methanol which differentiates
even at low vapour concentration by a larger value of b
L
¼7.7.
During the next step no big change in Henry’s solubility coeffi-
cient is observed, k
H
is close to 1, but the range of Henry’s
diffusion defined by the relative values of f00 (end of Langmuir
adsorption) and f0(beginning of clustering regime) is much larger
for water, toluene and chloroform than for methanol. In fact the
latter is the only vapour to exhibit a clustering with an average
number of analyte molecules per cluster of n0¼4. Finally LHC
parameters analysis makes it easier to understand why CNT-d-
PMMAmB reaches instantaneously equilibrium for water,
toluene, and chloroform whereas for methanol more time is
needed. In fact the clustering mode, although giving signal of
larger amplitude, also results in larger macromolecular confor-
mational changes relaxing the stresses accumulated during pro-
cessing. Thus when designing transducers for e-noses this is
a parameter to take into account when looking for the right
balance between sensitivity and stability.
4. Conclusion
For the first time vapour sensors have been fabricated by spray
layer by layer (sLbL) assembly leading to an original hierarchical
architecture with a segregated network of CNT bridging
PMMAmB multi-wall carbon nanotube (CNT) decorated poly-
(methyl methacrylate) microbeads (PMMAmB). The main trend of
this morphology is to develop in 3D the 2D CNT network
wrapping PMMAmB surface or located at their interface. This
increase in specific surface results in a boosting of conducting
network sensitivity of 240%. Interestingly PMMAmB behaved as
hard spheres not being much affected by solvents used for
sensing and consequently preserving native CNT selectivity. The
resulting discrimination ability of CNT-PMMAmB was excellent
since A
r
was five times larger for methanol than for the three
other vapours, i.e., water, toluene and chloroform. Additionally
CNT-PMMAmB sensors gave responses proportional to vapour
molecules content that could easily be fitted by the Langmuir–
Henry-clustering model. Such sensors are thus expected to be
good candidates for an implementation in e-noses.
Acknowledgements
The authors are grateful to Herv
e BELLEGOU for his contri-
bution to this work. This research was financed by a STAR
Franco-Korean collaboration program together with INTEL-
TEX European Integrated Project supported through the Sixth
Framework Program for Research and Technological Develop-
ment of European Commission (NMP2-CT-2006-026626).
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Fig. 10 Effect of analyte concentration on CNT-d-PMMAmB response
amplitude A
r
for methanol, water, toluene and chloroform vapours.
Curves are fitted with LHC electro-sorption model described in the
inset.
22,27,51
Table 3 Fitting parameters of LHC electro-sorption model for CNT-d-
PMMAmB
17
Water Methanol Toluene Chloroform
k
H
0.99 0.93 1.06 0.99
n’0 4 0 0
f’ 1 0.27 1 1
b
L
6 7.7 6 6
f00 0.04 0.25 0.02 0.06
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