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Understanding the response of nanostructured polyaniline gas sensors
Accepted Manuscript Title: Understanding The Response of Nanostructured Polyaniline Gas Sensors Author: Zhe-Fei Li Frank D. Blum Massimo F. Bertino Chang-Soo Kim PII: DOI: Reference:
S0925-4005(13)00417-6 http://dx.doi.org/doi:10.1016/j.snb.2013.03.125 SNB 15350
To appear in:
Sensors and Actuators B
Received date: Revised date: Accepted date:
5-1-2013 28-3-2013 29-3-2013
Please cite this article as: Z.-F. Li, F.D. Blum, M.F. Bertino, C.-S. Kim, Understanding The Response of Nanostructured Polyaniline Gas Sensors, Sensors and Actuators B: Chemical (2013), http://dx.doi.org/10.1016/j.snb.2013.03.125 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
*Manuscript
Understanding The Response of Nanostructured Polyaniline Gas Sensors
a
ip t
Zhe-Fei Lia, Frank D. Blum*b, Massimo F. Bertinoc, Chang-Soo Kimd
Department of Mechanical Engineering, Purdue School of Engineering and Technology,
cr
Indiana University-Purdue University Indianapolis, Indiana 46202, USA
Department of Chemistry, Oklahoma State University, Stillwater, OK, 74078, USA
c
Department of Physics, Virginia Commonwealth University, Richmond, VA 23824, USA
d
Departments of Electrical and Computer Engineering, and Biological Sciences, Missouri
M
an
us
b
Ac ce p
te
d
University of Science and Technology, Rolla, MO 65409, USA
Abstract
Polyaniline/Ag nanocomposite gas sensors have been fabricated with a single-step technique. The current response of the sensors to triethylamine and toluene was monitored and analyzed. The time dependence of the response to the two gases of the sensors was found to be exponential and was fit to chemisorption and diffusion models. The equilibrium absorption amounts from the chemisorption model were found to obey a Langmuir isotherm. The results of the diffusion model to the data were consistent with a dual sorption process, i.e., diffusive and non-diffusive
Page 1 of 40
adsorption sites. The estimated diffusion coefficients were found to increase with the concentration of diluent, probably due to the swelling of the polymer by the organic vapors. Our
cr
ip t
results suggest that both models can be employed to mathematically fit the sensor response.
an
Sensor, Adsorption, Diffusion, Langmuir Isotherm.
us
Keywords: Nanostructured Polyaniline, Polyaniline/Ag Nanocomposites, Nanofibers, Gas
Ac ce p
te
d
M
* Corresponding Author
Page 2 of 40
1. Introduction
ip t
Gas sensors, sometimes denoted as electronic noses, have been widely studied ever since the design of a gas sensor was reported by Seiyama et al. in 1962.[1] Chemical methods for
cr
determining unknown species, such as gas chromatography/mass spectrometry (GC/MS), are
us
time-consuming, expensive, and require trained personnel. There is a need to develop miniature
an
devices for rapid and inexpensive analysis of volatile compounds. Significant research has been focused on conducting polymer–based gas sensors[2]. Polyaniline is a promising candidate for
M
gas sensing applications because of its relatively easy synthesis, low cost, high sensitivity, and
d
fast response[3,4]. In particular, nanostructured polyaniline-based gas sensors have shown
te
excellent performance because of their large surface areas and high porosity of nanostructured
Ac ce p
polyaniline[5-10]. Most methods of making polyaniline are multi-step and a facile one-step environmental-friendly method may overcome its poor processability. Our group has reported a novel method to synthesize polyaniline nanofibers and nanocomposites based on either gamma or ultra-violet radiation[11-13]. This technique can be utilized to fabricate nanostructured polyaniline-based electrochemical gas sensors in a single step. This type of sensor has shown a fast response to various organic vapors[9,10]. Although considerable research has been carried out in the development of novel conductingpolymer sensors, some basic problems still remain, especially with respect to nanostructured
Page 3 of 40
conducting-polymer sensors. The modeling of time-dependent sensor response is particularly relevant for understanding the sensing kinetics. The gas sensor response is basically controlled
ip t
by two factors. One is the transport process of gas molecules to or into the sensor film. The other
cr
is the interaction of the sensing material and gas molecules, i.e., a physical interaction or
us
chemical reaction. A few models have been proposed for bulk-conducting-polymer–based gas sensors[14-17].
an
Previous work from our group has shown how these sensitive materials can be made in a
M
single step. It was found that the incorporation of nanometals into the composite enhanced the
d
sensitivity of the sensors[9]. The incorporation of Ag, in particular, gave faster and more
te
sensitive responses to triethylamine than other metals because of the affinity of amines for Ag.
Ac ce p
We also showed that this enhancement was primarily due to the charge transfer to the Ag and that the sensor response of our polyaniline materials to triethylamine can be fit with an exponential decay as a function of time and gas concentration[9]. This paper reports the response of one-step polyaniline/Ag based sensors and interprets the response in terms of chemisorption and diffusion.
The chemisorption model is based on the de-doping (or swelling) of the conducting polymer when a guest molecule is adsorbed at or near the surface of that polymer. For nanostructures with high surface areas, such as in our PANI nanocomposites, this model embodies importance of the
Page 4 of 40
capture of the guest molecule by the polymer at active sites. It would be consistent with the limiting response factor being adsorption at the interface. The diffusion model is based on the
ip t
penetration of the polymer by the guest molecules. It assumes that the guest molecules go
cr
quickly to the surface, but the limiting step for sensing is diffusion into the polymer. We find that
us
both of these models fit the responses of the nanostructured polyaniline based gas sensors to organic vapors, probably because both fitting methods are consistent with exponential decay
an
functions. The chemisorption model was found to fit a Langmuir isotherm, while the diffusion
te
2. Experimental
d
M
model was consistent with a dual sorption mechanism.
Ac ce p
2.1. Synthesis of polyaniline/Ag nanocomposites To produce nanocomposites for the sensors, 0.1 M aniline (93 mg), 0.01 M AgNO3 (17 mg) and 0.1 M nitric acid were first dissolved in 10 mL distilled water. The aniline began to polymerize after the addition of 0.05 M ammonium persulfate (114 mg). After vigorous shaking, the solution was immediately irradiated with a low-pressure Hg-UV light source (Model: PASCO Scientific OS-9286A)[10].
2.2. Fabrication of polyaniline/Ag nanocomposite sensors
Page 5 of 40
Sensors were fabricated by placing a 10 µL drop of premixed precursor solution on the active area of an interdigitated microelectrode array. The precursor solution had the same composition
ip t
as described above. The drop was then illuminated with the UV lamp. After the reaction
us
room temperature before being used for measurements[10].
cr
(approximately 30 min), the polyaniline thin films were washed with distilled water and dried at
an
2.3. Characterization
M
The morphology of the polyaniline/Ag nanocomposites was characterized using a Hitachi S-
d
4700 scanning electron microscope (SEM) operated at accelerating voltages of 5 kV and a JEOL
te
JEM-2100 Transmission Electron Microscope (TEM). The changes in electrical current for
Ac ce p
polyaniline/Ag based thin film sensors were measured at room temperature as a function of time and exposure to organic vapors. The real-time current changes were monitored using a Keithley 4200 semiconductor analyzer operated at 0.1 V. To test the sensors, nitrogen gas was used as both the carrier and diluting gas. The carrier gas was passed through the neat liquids in a gas bubbler. The resulting gas mixtures were then diluted with additional diluting gas that was then directed to the sensor, which was kept at room temperature. The relative concentration (or volume fraction, measured in ppm) of gases in the carrier gas, c, was determined using: c = (M/ρ)/(M/ρ + L1 + L2)
(1)
Page 6 of 40
where M is the weight loss rate of the liquid sample (in g/min), ρ is the density of the vapor (in g/L), L1 is the nitrogen carrier gas flow rate (in L/min), and L2 is the nitrogen diluting gas flow
ip t
rate (in L/min). The flow rate of the nitrogen diluting gas was 1.5 L/min, and the total gas
cr
pressure was about 15 psi.
us
The mathematical fitting of experimental data was performed in Excel or Mathematica using least-squares method. The best fit was achieved when the sum of the squares of the
an
residuals was minimized. The standard deviation (SD) of the residuals, the square root of the
M
sum of the squares of the residuals divided by n-1 (n is the number of data points) was used to
d
estimate the uncertainty of the fit. The uncertainty in the fitting parameters was estimated by
te
varying each fitting parameter independently from the best-fit value until the SD increased to
Ac ce p
1.96 × SD, which corresponds to a 95% confidence interval[18,19].
3. Theory
3.1. Chemisorption model
This model is based on that originally developed for chemisorption, which states that the rate of adsorption is affected by the evaporation and condensation processes.[20-23]. The application of the model to our systems was based on the following assumptions[17,24]:
Page 7 of 40
1) The conductivity of the polyaniline is proportional to the number of conduction sites (dopant sites), N, which are uniformly distributed on the polymer surface. These sites can adsorb species
ip t
that affect the conductivity.
cr
2) All dopant sites are equivalent and the probability of a gas molecule adsorbing on any site is
us
the same. Each site can only adsorb one molecule. The adsorption process is described by the following equation: !! ! !!
A
an
A + dopant site
(2)
M
where A is the adsorbate, (A) is the adsorbate at an occupied site, k1 is the adsorption rate
!" !"
= !! !" ! − !!! !
(3)
Ac ce p
!=
te
the rate of desorption), R, equals
d
constant and k-1 is the desorption rate constant. The net adsorption rate (rate of adsorption minus
where θ is the fractional amount of surface coverage, c is the vapor concentration, and f(θ) is a surface coverage function. In this case f(θ) is given by M0 - θ, where M0 is the fractional coverage of the surface for the maximum adsorption of a monolayer. This definition of M0 accounts for the possibility that not all of the surface is accessible to the absorbant. The absorptions are normalized to their monolayer amounts and θ ranges from 0 to M0. Assuming that k1, k-1, and c are independent of θ, integrating Eq. 3 gives, for the boundary condition θ = 0 at t = 0:
Page 8 of 40
!! !! !
!!"# ! = !
! !!!!!
(1 − ! ! !! !!!!! ! )
(4)
Equation 4 describes the approach to equilibrium absorption, starting from when no initial
ip t
analyte is present and the amount adsorbed is referred to as θabs. Similarly, the approach towards
cr
complete desorption, given by θdes(t), when the material begins saturated with analyte and then is
us
exposed to an atmosphere with no analyte, can be similarly derived as:
(5)
an
!!"# ! = !! (1 − ! !!!! ! )
M
3.2. Langmuir adsorption isotherm
d
Langmuir, in 1918, suggested that the adsorption process is controlled by the rates of evaporation
Ac ce p
!! !" ! = !!! !
te
and condensation. At equilibrium, the rates of evaporation and condensation are equal[25]. Thus (6)
In order to account for the partial coverage of the surface, the surface coverage function is given by, f(θ) = M0 – θ. Therefore, Eq. 6 can be written as: !! !! !
!=!
! !!!!!
! !"
! = !"!!
(7)
with k1/k-1 = b, which is the Langmuir adsorption constant.
3.3. Diffusion model
Page 9 of 40
According to Fick’s first law[26], the rate of transfer of a diffusing substance through the unit area of a section is proportional to the concentration gradient that is normal to that section, i.e.: !"
!"
!"
! = −!(!" + !" + !")
ip t
(8)
cr
where J is the flux of diffusant, D is the diffusion coefficient, c is the concentration of diffusant,
us
and x, y, z are the spatial coordinates. Since the net flux into the element under consideration
obtained in the form of !"
!
!"
!
!"
!
!"
(9)
M
!" = !" ! !" + !" ! !" + !" (! !")
an
should be equal to the change in concentration (equation of continuity), Fick’s second law can be
d
For diffusion in a long circular cylinder where diffusion is radial[27], through substitution of x =
!"
!"
= ! !" (!" !")
(10)
Ac ce p
!"
! !
te
r cos θ and y = r sin θ, we can obtain,
In the cylinder of radius, a, the boundary conditions are c = c0, r = a, t ≥ 0,
c = 0, 0 < r < a, t = 0,
Solving Eq. 10 for the conditions when there is no dedopant initially (analyte in this case), for the cylinder, one can obtain a series solution (Crank's book, eq. 5.21)[27]: !
!(!, !) = c! (1 − !
!! !!! ! !!! ! ! !! ! ! !
exp −!!!! ! )
(11)
Page 10 of 40
where J0(x) is the Bessel function of the first kind of order zero, J1(x) is the Bessel function of
Integrating c(r,t) as a function of r from 0 to a gives[27]: ! ! !
!, ! !" = !! (1 −
! ! !!! ! ! ! !
!
exp −!!!! ! )
(12)
cr
!! =
ip t
the first kind of order one, and the αn's are roots of Bessel function of the first kind of order zero.
us
where Mt denotes the quantity of substance that diffuses into the cylinder in time t and M∞ is the
an
corresponding quantity after infinite time (i.e., equilibrium sorption amount).
M
3.4. Sorption
In 1958, Barrer et al. proposed a dual sorption model to describe the sorption isotherms of
te
d
small gas molecules in polymers[28]. In glassy polymers, there exists a distribution of "holes"
Ac ce p
frozen in the structure. These holes can immobilize some of penetrant molecules by entrapment or by binding various sites. Therefore, this model consists of two concurrent mechanisms of sorption: ordinary dissolution and "hole-filling". The equilibrium sorption uptake can be expressed by the following equation[29-31]: ! ! !"
! ! = !! + !! = !! ! + !!!"
(13)
where kD is the Henry’s law constant, P is the vapor pressure of the penetrant, cH' is the maximum uptake in holes, b is the hole affinity constant. The first term, cD, represents sorption of normally diffusible species, while the second term cH represents the sorption in holes.
Page 11 of 40
ip t
4. Results and Discussion
The scanning electron micrograph (SEM) and transmission electron micrograph (TEM) of
cr
polyaniline/Ag nanocomposite thin films grown on the interdigitated electrodes are shown in Fig.
us
1. These images clearly show a nanofiber structure with an average fiber diameter of about 51
an
nm, as analyzed by ImageJ[32]. The morphology was consistent with previous results for
Ac ce p
te
d
M
polyaniline made in this way[13].
Fig. 1. SEM (a) and TEM (b) images of polyaniline/Ag nanocomposites grown on interdigitated electrodes. The scale bar is 500 nm in (a) and 200 nm in (b).
Page 12 of 40
The change in current of the sensors in response to vapors was monitored. Fig. 2 displays the time-dependent change in the normalized current of the nanocomposite sensors upon exposure to
ip t
triethylamine at various concentrations. A valve allowing triethylamine to enter the chamber was
cr
opened to allow a sufficient amount to achieve a given concentration of vapor and then closed
us
allowing no triethylamine to pass. A fast current decrease was observed within 120 s as a result of the dedoping of polyaniline and decrease in the charge transfer by triethylamine. The
an
dedoping of polyaniline/Ag is generally a reversible process after replacing the triethylamine
M
vapor with pure N2. As shown in the figure, the current decreases very quickly in the early stage
d
and then tends to level off. At higher concentrations, complete recovery was not found in the
te
time frame measured. In our previous work, it was demonstrated that these decay curves
1
Normlized Current I/Io
0.9 0.8 0.7 0.6 0.5
Ac ce p
following nitrogen exposure could be fit to a single exponential function[9].
39 ppm
77ppm
0.4
116ppm
0.3
271ppm
543ppm
0.2
1100ppm
0.1 0 0
500
1000
1500
2000
2500
3000
3500
Time(s)
Page 13 of 40
Fig. 2. Sensor response and recovery curves of the polyaniline/Ag nanocomposite sensor to triethylamine. The sensor was exposed to the triethylamine vapor for 100 s and then exposed to
ip t
pure nitrogen until the current became stable before it was exposed to the next concentration of
us
cr
triethylamine.
4.1. Analysis based on the chemisorption model
an
The adsorption of nitrogen gas on or in the polyaniline film does not significantly affect the
M
conductivity of the polyaniline, especially compared to the response to triethylamine or toluene.
d
If the conductivity is proportional to the number of conductive sites, the normalized current
te
should be proportional to the fraction of unoccupied sites, or from equation (4): !! !! !
! !!!!!
(1 − ! ! !! !!!!! ! ) (14)
Ac ce p
!!"#$ ! = 1 − ! ! = 1 − !
where Mo is the fraction of occupied sites, and b = k1/k-1. The polyaniline/Ag composite sensor responses, as a function of time to triethylamine at various concentrations, are shown in Fig. 3. The y-axis is the normalized current monitored by the electrometer, and the x-axis is the gas exposure time. These decay curves were fit by minimization of the least-squares of the residuals to an exponential growth function: !!"#$ ! = 1 − !! ×(1 − ! !!/!! ) (15) where 1 - I∞ is the normalized final current in the presence of the dopant.
Page 14 of 40
39 ppm
0.7
77 ppm
0.6
150 ppm
0.5
271 ppm
0.4
543 ppm
cr
0.8
ip t
0.9
us
0.3
1100 ppm
0.2 0.1 0 0
20
40
60
an
Normalized current I(t)/Io
1
80
120
M
Time (s)
100
d
Fig. 3. Polyaniline/Ag nanocomposite sensor responses to triethylamine vapor with different
te
concentrations. The exponential decay curves are best fits from Eq. 15. The order of the curves
Ac ce p
in the figure is the same as shown in the figure legend.
The current changes followed exponential decays with the time constants decreasing with increasing concentrations of triethylamine. Comparing Eq. 14 and 15, the functional form becomes:
! !"
! !! = !"!! (16)
with !! = !
! ! !!!!!
(17)
Page 15 of 40
Similarly, the recovery curves were fit to an exponential growth or: !!"#$ ! = 1 − !! ! !!/!! (18)
ip t
For recovery, I∞ was taken as the value from the fitted decay curve, which varies from sample to
us
cr
sample. The recovery curves with the recoveries are shown in Fig. 4.
0.9
an
0.8 0.7 0.6
M
39 ppm
0.5
77 ppm
0.4
100 ppm
d
0.3 0.2 0.1 0 100
200
Ac ce p
0
te
Normalized current I(t)/Io
1
300
Time (s)
543 ppm
400
500
Fig. 4. Polyaniline/Ag nanocomposite decay and recovery curves for triethylamine vapor with different concentrations fit to exponential increases after the organic vapor was removed from the carrier gas. The curves are best fits from Eq. 15 until 100 s, (i.e., the end of the adsorption step), and then Eq. 18. The order of the curves in the figure is the same as shown in the figure legend.
Page 16 of 40
The decay and response curves for the polyaniline composite sensors shown in Figs. 3 and 4 show that the functions used provided good fits to the experimental data. The time constants
ip t
τa and τd are for adsorption and desorption, respectively. Table 1 shows the value of the fitting
cr
constants I∞, τa, and τd for these curves. As was evident from the curves, I∞ and τd increased with
us
the triethylamine concentration, while τa decreased with it. For the highest amount of
an
triethylamine there was a noticeable deviation from a single exponential for the recovery curve. For this curve, selections of single time constants, τa and τd, were unable to fit this data
M
satisfactory with Eq. 17. However, this data could also be fit to power laws with τa = 0.683c-0.33
d
and τd = 2655c0.43. A power law relationship was also previously observed for NO2 adsorbed on
te
polyaniline.[17,33] The reason for this deviation from simple exponential functions is currently
Ac ce p
unknown. One possible explanation is that τa and τd may not have been independent of concentration.
Table 1. Fitting constants for the polyaniline/Ag sensor exposed to triethylamine based on Eqs. 15 and 18. The uncertainties were estimated at the 95% confidence interval. Triethylamine
I∞
τa (s)
τd (s)
0.225 ± 0.008
18.3 ± 1.7
22.4 ± 2.1
Concentration (ppm) 39
Page 17 of 40
0.410 ± 0.009
16.7 ± 1.3
37.9 ± 3.6
116
0.486 ± 0.017
13.9 ± 1.4
48.6 ± 4.1
150
0.526 ± 0.011
12.5 ± 1.0
58.9 ± 5.1
271
0.570 ± 0.008
10.4 ± 0.79
94.1 ± 6.4
543
0.619 ± 0.012
7.5 ± 0.66
109 ± 12.2
1100
0.719 ± 0.019
5.9 ± 0.83
131 ± 11.8
us
cr
ip t
77
an
The polyaniline/Ag composite sensor response as a function of time exposed to toluene at
M
various concentrations is shown in Fig. 5. These curves were also fit using exponential decays. Recovery curves were not measured for the toluene system. Values of fitting constants I∞ and τa
te
d
shown in Table 2. Similar to that for triethylamine, I∞ also increased with the toluene vapor concentration and τa decreased with it. The time constants for toluene were larger (slower) than
Ac ce p
for triethylamine. The time constant τa was fit to a power law in concentration resulting in τa = 2.89c-0.25.
Page 18 of 40
0.9 0.8 0.7
ip t
29 ppm
0.6
67 ppm
0.5 0.3
296 ppm
0.2
500 ppm
cr
187 ppm
0.4
us
Normalized current I(t)/Io
1
0.1 0
20
40
an
0 60
80
100
120
140
M
Time (s)
Fig. 5. Polyaniline/Ag nanocomposite sensor responses to toluene vapor for different
d
concentrations fit to exponential decays. The curves are best fits from Eq. 15. The order of the
Ac ce p
te
curves in the figure is the same as shown in the figure legend.
Table 2. Fitting constants of the polyaniline/Ag sensor exposed to toluene from Eq. 15. Toluene
I∞
τa (s)
0.086 ± 0.0019
41.2 ± 1.9
67
0.135 ± 0.0097
32.9 ± 3.7
146
0.212 ± 0.0068
29.2 ± 5.9
187
0.248 ± 0.0092
25.0 ± 4.3
296
0.281 ± 0.010
20.2 ± 3.3
Concentration (ppm) 23
Page 19 of 40
500
0.325 ± 0.015
18.6 ± 4.2
ip t
In the chemisorption model, the fitting constant, I∞, was dependent on the adsorbed amount. Fig.
cr
6 is a plot of I∞ as a function of triethylamine and toluene concentrations. As shown in the figure,
us
these curves fit the Langmuir isotherm equation well. Based on equation 7, the normalized maximum adsorption amount, M0, was equal to 0.407 and 0.733 for toluene and triethylamine,
an
respectively. The Langmuir constant, b, for triethylamine and toluene were 1.48 × 104 atm-1 and
M
7.86 × 103 atm-1, respectively. The values of the Langmuir constants were higher with those values reported for triethylamine adsorbed on CdSe (380 atm-1) and toluene adsorbed on active
te
d
carbon (2845 atm-1) [34,35]. These larger values may be due to a stronger interaction of triethylamine and toluene with polyaniline/Ag composites.
Ac ce p
Page 20 of 40
0.9
Triethylamine
0.8
Toluene
0.7
ip t
I∞
1
0.6 4
0.5
4
cr
I = 0.733 x 1.48x10 c/(1+1.48x10 c) ∞
us
0.4 0.3
0.1 0 200
400
600
M
0
an
I∞ = 0.407 x 7.86x103c/(1+7.86x103c)
0.2
800
Concentration (ppm)
1000
1200
te
d
Fig. 6. Plot of the fitting parameter, I∞, as a function of toluene and triethylamine vapor
Ac ce p
concentrations fit to a Langmuir isotherm.
4.2 Analysis based on the diffusion model Adsorption normally only occurs at the surface of the adsorbate. In our work, the polyaniline consists of mainly interconnected networks of nanofibers. Diffusion in a cylinder may also be appropriate to describe the transport processes within the fibers. Therefore, the sensor response curves were also fit using a diffusion model for comparison. It has been reported previously that there is a charge transfer effect between polyaniline and Ag nanoparticles[10]. The response of
Page 21 of 40
polyaniline/Ag composite sensors to triethylamine was caused by both the dedoping of polyaniline and a reduction in the charge transfer. For simplicity, we assume that the effect of
ip t
charge transfer can be modeled in the same way as dedoping process. The conductivity through
cr
the polyaniline film should be linearly proportional to the concentration of the dopant, [DP],
us
which is equal to the initial dopant concentration, [DP]0, minus the reacted dopant[36]. As discussed in the previous section, the sensing mechanism of triethylamine is based on the
an
reaction between the triethylamine and the acid dopant. The enthalpy of reaction for the
M
protonation of triethylamine was determined to be about -43.4 kJ/mol, indicating that this
d
reaction is exothermic. Therefore, it was assumed that each triethylamine molecule that diffuses
Ac ce p
then be estimated as
te
into the polyaniline film will react with a dopant molecule. The conductivity of polyaniline can
! ∝ !" = [!"]! − [!"#$%h!"#$%&'](19) Based on this assumption, the normalized current can be expressed based on equation (12) as: !!"#$ t = 1 −
!"#$%!!"#$%&' !" !
=1−
!! !" !
1−
! ! !!! ! ! ! ! exp !
−! !!! ! (20)
The result of fitting the data from the polyaniline/Ag sensor exposed to gaseous triethylamine at concentrations of 39 to 1100 ppm is shown in Fig. 7 for the diffusion model. Two fitting constants, M∞/[DP]0 and D, were obtained from a least-square fit based on Eq. 20. The values of
Page 22 of 40
the fitting constants for these curves are shown in Table 4. It was apparent that M∞/[DP]0 and D increase with the toluene concentration. Since [H+]0 should be a constant for all of our sensors,
ip t
the fitting constant, M∞/[H+]0, then should be proportional to the final absorbed amount, M∞. It
cr
should also be noted that the diffusion in a cylinder fits the data significantly better that a
us
comparable fit for diffusion in a slab.
0.9
an
0.8 0.7
M
0.6 0.5 0.4 0.2 0.1
Ac ce p
0
0
20
40
60
Time(s)
77ppm 150ppm
543ppm
d
0.3
39ppm
271ppm
1100ppm
te
Normalized Current I(t)/Io
1
80
100
120
Fig. 7. Polyaniline/Ag nanocomposite sensor response to triethylamine vapor of various concentrations fit with the diffusion model. The curves are best fits from Eq. 20. The order of the curves in the figure is the same as shown in the figure legend.
Table 3. Fitting constants of the polyaniline/Ag sensor exposed to triethylamine Triethylamine
M∞/[DP]0
D x 1018 (m2/s)
Page 23 of 40
0.244 ± 0.022
3.14 ± 0.58
77
0.440 ± 0.029
4.01 ± 0.88
116
0.511 ± 0.036
4.71 ± 1.17
150
0.549 ± 0.029
5.57 ± 1.18
271
0.583 ± 0.030
7.02 ± 1.51
543
0.620 ± 0.021
10.4 ± 1.82
1100
0.727 ± 0.023
13.1 ± 2.34
M
an
us
cr
39
ip t
Concentration (ppm)
d
Toluene is a solvent that can swell the polymer and increase the polymer interchain distances;
te
consequently causing a conductivity decrease. The conductivity of a conducting polymer is
Ac ce p
dependent on the hopping distance, i.e., the interchain distance. This conductivity can be expressed with an exponential term[37-39]: ! = !! exp(−!")
(21)
where σ0 is the pre-exponential constant, β is the electron-tunneling coefficient, and δ is the hopping distance. The swelling of polymers generally results because of the diffusion of solvent molecules and then chain relaxation processes. The relaxation processes may be considerably slower than the diffusion and may take hours to occur[40]. If this is the case, the interchain distance would be expected to be only proportional to the uptake of a diffusing substance, or
Page 24 of 40
! ! !!! !∞ !!!
∝ !(!)
(22)
where δ1 stands for the initial interchain distance, δ∞ denotes the interchain distance when
ip t
swelling is at equilibrium. Thus, the normalized current of polyaniline during the swelling can be
cr
expressed as ! ! !!! ! ! ! ! !"# !
−!!!! ! ](23)
us
!!"#$ ! = !"# [− ∆!! !!! 1 −
where ∆δ is the maximum interchain distance change.
an
The sensor response upon exposure to toluene at various concentrations fit with the
M
diffusion model is shown in Fig. 8. The values of fitting constants, ∆δ∞βM∞ and D, are listed in
d
Table 4. Similar to the fitting constants for triethylamine, the quantity ∆δ∞βM∞ is considered as
Ac ce p
Normalized current I(t)/Io
te
the product for study of sorption uptake, because ∆δ∞, and β are constants.
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
29 ppm 67 ppm 146 ppm 187 ppm 296 ppm 500 ppm
0
20
40
60 80 Time (s)
100
120
140
Page 25 of 40
Fig. 8. Polyaniline/Ag nanocomposite sensor response to toluene vapor of various concentrations
cr
curves in the figure is the same as shown in the figure legend.
ip t
and the fits with the diffusion model. The curves are best fits from Eq. 23. The order of the
Table 4. Fitting constants of the polyaniline/Ag sensor exposed to toluene using Eq. 23 D x 1018 (m2/s)
29
0.150 ± 0.017
0.276 ± 0.18
67
0.209 ± 0.019
0.852 ± 0.14
146
0.307 ± 0.007
187
0.326 ± 0.019
1.90 ± 0.32
296
0.362 ± 0.021
2.59 ± 0.47
500
0.441 ± 0.021
2.96 ± 0.38
us
∆δ∞βM∞
Toluene
M
an
Concentration (ppm)
Ac ce p
te
d
1.23 ± 0.08
Plots of the fitting parameters M∞/[H+]0 and ∆δ∞βM∞ of triethylamine and toluene as a function of concentration are shown in Figs. 9 and 10. These data were fit with the dual sorption model and Langmuir isotherm. It was found that both curves fit the parameter M∞/[H+]0 of triethylamine very well. The standard deviation from the dual sorption model was only 5%, which was smaller than that from the Langmuir isotherm. However, for toluene, the fitting error from the dual sorption model was 76% smaller than that from Langmuir isotherm. Thus, the dual sorption
Page 26 of 40
model fits the toluene data better. Comparing the fitting equations with Eq. 22, we can determine that the normalized uptake in holes was equal to 0.336 and 0.701 for toluene and triethylamine,
ip t
respectively. The Langmuir constant for triethylamine was 1.86 x 104 atm-1, which was close to
cr
that estimated from the chemisorption model (Fig. 6). However, the Langmuir constant for
us
toluene was found to be 2.3 x 104 atm-1, much larger than that predicted by the chemisorption model. This larger value of Langmuir constant for toluene may result from the high swelling
an
effect of toluene in polyaniline. The Henry’s Law dissolution constant of triethylamine and
d
M
toluene was determined to be 39.3 and 259.4 atm-1, respectively.
te
0.7 0.6
Ac ce p
Fitting parameter M∞/[H+]0
0.8
0.5 0.4
Dual sorption Langmuir
M∞/[H+]0 = 0.701 x 1.86x104c/(1+1.86x104c) + 39.3c
0.3 0.2 0.1 0
0
200
400
600
800
1000
1200
Concentration (ppm)
Page 27 of 40
Fig. 9. Plot of fitting parameter M∞/[H+]0 of triethylamine as a function of concentration. The curves were fit by the dual sorption and Langmuir isotherm models. The equation shown is the
cr
ip t
result for the dual sorption model.
0.5
us
0.4
an
0.35 0.3
Dual sorption fit
M
0.25 0.2 0.15
Langmuir fit
∆δ∞βM∞ = 0.336 x 2.33x104c/(1+2.33x104c) + 259.4c
d
0.1 0.05 0
100
200
Ac ce p
0
te
Fitting parameter ∆δ∞βM∞
0.45
300
400
500
600
Concentration (ppm)
Fig. 10. Plot of sorption uptake of toluene as a function of concentration with the fit for the dual sorption model and Langmuir isotherm models. The equation shown is the result for the dual sorption model.
The diffusion coefficients of toluene and triethylamine are plotted as a function of concentration and shown in Fig. 11. The diffusion coefficients showed an increase with the vapor concentration
Page 28 of 40
and could be fit with an empirical power law or an exponential function. The results of the fitting determined that D = 273.5c0.44 or D = 12.7 x (1 – e-368c). For toluene, the fits yielded, D =
ip t
417c0.64 or D = 3.62 x (1 – e-3660c). Again, the increase in diffusion coefficient was probably due
us
cr
to the swelling effect of these organic vapors, which greatly increases the solubility.[41,42]
an
14 12 10
Triethylamine
M
8 6
Toluene
d
4 2 0 200
400
600
800
Concentration (ppm)
1000
1200
Ac ce p
0
te
Diffusion coefficient (m2/s)
16
Fig. 11. Diffusion coefficients of toluene and triethylamine as a function of concentration fit with a power law (curve) and an exponential function (dashed curve).
Although other measurements of the toluene and triethylamine diffusion coefficients are not available in polyaniline, one can estimate the diffusion coefficient of a gas in polymers from kinetic diameters using an empirical equation proposed by Michaels and Bixler [43,44]. From
Page 29 of 40
these parameters, the estimated values for vapor diffusion coefficients of toluene and triethylamine in polyaniline were on the order of 10-16 m2/s, which were larger than those
ip t
determined in this work. In the empirical models mentioned, the interaction of the gas molecules
cr
and the polymer was ignored. However, our diffusants showed strong interactions with the
us
polyaniline, which would be expected to lower the diffusion coefficients. Given this, the values
an
obtained in this work seem reasonable.
M
4.3. Reproducibility and fitting errors
d
The reproducibility of independent individual runs is illustrated in Fig. 12 for the sensor
te
response to 39 ppm triethylamine. The individual data points were averaged from four
Ac ce p
independent experiments at each time. From each of the 4 runs, the values of the uptakes and diffusion coefficients were calculated. The resulting means and standard deviations were also calculated and are shown in Table 5. A small standard deviation (about 1.4%) was found for the fitting constant M∞/[H+]0, and a larger error (about 6.7%) was attained for the diffusion coefficient.
Page 30 of 40
0.95
ip t
0.90 0.85
cr
0.80 0.75
us
Normalized Current I(t)/I0
1.00
0.70 20
40
60
Time (s)
80
an
0
100
M
Fig. 12. Sensor responses to 39 ppm triethylamine plotted with error bars representing the
d
averages of 4 runs from independent experiments. The curve is the best fit of the averaged data,
Ac ce p
te
using the diffusion model.
Table 5. Standard deviations from the fits to the parameters of the polyaniline/Ag sensor exposed to 39 ppm triethylamine from the diffusion model. Run
No. 1
No. 2
No. 3
No. 4
Average
Standard Deviation
M∞/[DP]0
0.248
0.246
0.244
0.239
0.244
1.43%
D x 1018 (m2/s)
3.26
3.14
3.55
3.05
3.24
6.7%
Page 31 of 40
In order to compare the results from the application of both kinds of models to the data, the standard deviation of the residuals is plotted for triethylamine in Table 6 and toluene in Table 7.
cr
ip t
For both systems, there was little difference in the quality of the fits from both models.
us
Table 6. Standard deviation of the residuals for the chemisorption and diffusion models of the sensor response to triethylamine at different concentrations. 39
77
116
Concentration (ppm)
0.010
271
543
1100
0.0079 0.0096 0.017
0.0075 0.0096 0.0085 0.011
0.011
0.012
Ave.
0.011 0.0098
te
d
Diffusion Model
0.0084 0.013
M
Chemisorption model 0.0076 0.013
150
an
Triethylamine
Ac ce p
Table 7. Standard deviation of the residuals for the chemisorption and diffusion models of the sensor response to toluene at different concentrations. Toluene
29
67
146
187
296
500
Ave.
Concentration (ppm)
Chemisorption model
0.0012 0.0081
0.0088
0.0094
0.0091
0.014
0.0084
Diffusion Model
0.0033 0.0031
0.0029
0.011
0.012
0.014
0.0077
5. Conclusions
Page 32 of 40
A chemisorption and diffusion model has been used to fit the responses of polyaniline/Ag nanocomposite sensors exposed to triethylamine and toluene at several different concentrations.
ip t
Both models can reproduce the sensor response as a function of time. As determined from the
cr
fitting constants, a Langmuir adsorption isotherm was used in the chemisorption fit, while a dual
us
sorption mechanism was required for the diffusion fit. In addition, the diffusion coefficients obtained from the diffusion fit was found to increase with the vapor concentration, probably due
an
to the swelling effect by organic vapors. Fitting errors from the two models were small, both
M
allowing reasonable mathematical forms for the time-dependent and concentration behavior. Our
d
results also show the potential for studying the adsorption or diffusion process of conducting
te
polymers based on conductivity measurements.
Ac ce p
It should be noted that in this case, both models are able to reproduce the functional form of the data as a function of time. This is because both models are capable of mimicking an exponential decay. The Langmuir model is inherently exponential and the diffusion model results in a series of exponentials. Since the functional form of the diffusion model is dependent on the root of the Bessel function squared in the denominator and also the negative exponential, the lower order terms dominate, making the form close to exponential. Thus, unfortunately, our work cannot make a definitive statement about which mechanism is dominant with both models yielding reasonable fitting parameters.
Page 33 of 40
6. Acknowledgements
ip t
The authors acknowledge Terry Colberg and Balika Khatiwada at Oklahoma State University for
cr
assistance in obtaining the TEM pictures. FDB acknowledges the financial support of the
us
Department of the Army Research Office under Award No. W911NF-10-1-0476 and of
M
an
Materials Research Center, Missouri S & T.
Ac ce p
te
d
Biographies Z.-F. Li received his Ph.D. degree in materials science and engineering at the Missouri University of Science and Technology in 2010. His graduate research interests have been focused on nanomaterials and conducting polymer-based sensors. Currently, he is a postdoctoral research fellow in the Department of Mechanical Engineering at Indian University-Purdue University Indianapolis working on graphene-based materials. F.D. Blum is the Harrison I. Bartlett Chair of Chemistry and Regents Professor at the Oklahoma State University. His research activities include conducting polymer nanocomposites and dynamics in interfacial materials. He is a Fellow of the American Chemical Society (ACS) and the Division of Polymer Chemistry, Inc,. and has been awarded the Distinguished Service Award and Special Service Award by the Division of Polymer Chemistry, Inc. of the ACS. M.F. Bertino is associate professor of physics at Virginia Commonwealth University. His research activities include photolithographic synthesis of metal, oxide and polymer nanoparticles. C.-S. Kim is an associate professor with joint appointment at the Departments of Electrical and Computer Engineering and Biological Sciences at Missouri University of Science and Technology. Dr. Kim’s current research interests include microsystem technologies for special applications to environmental, agricultural, and plant sciences.
Page 34 of 40
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ip t
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ip t
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us
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Page 40 of 40
S0925-4005(13)00417-6 http://dx.doi.org/doi:10.1016/j.snb.2013.03.125 SNB 15350
To appear in:
Sensors and Actuators B
Received date: Revised date: Accepted date:
5-1-2013 28-3-2013 29-3-2013
Please cite this article as: Z.-F. Li, F.D. Blum, M.F. Bertino, C.-S. Kim, Understanding The Response of Nanostructured Polyaniline Gas Sensors, Sensors and Actuators B: Chemical (2013), http://dx.doi.org/10.1016/j.snb.2013.03.125 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
*Manuscript
Understanding The Response of Nanostructured Polyaniline Gas Sensors
a
ip t
Zhe-Fei Lia, Frank D. Blum*b, Massimo F. Bertinoc, Chang-Soo Kimd
Department of Mechanical Engineering, Purdue School of Engineering and Technology,
cr
Indiana University-Purdue University Indianapolis, Indiana 46202, USA
Department of Chemistry, Oklahoma State University, Stillwater, OK, 74078, USA
c
Department of Physics, Virginia Commonwealth University, Richmond, VA 23824, USA
d
Departments of Electrical and Computer Engineering, and Biological Sciences, Missouri
M
an
us
b
Ac ce p
te
d
University of Science and Technology, Rolla, MO 65409, USA
Abstract
Polyaniline/Ag nanocomposite gas sensors have been fabricated with a single-step technique. The current response of the sensors to triethylamine and toluene was monitored and analyzed. The time dependence of the response to the two gases of the sensors was found to be exponential and was fit to chemisorption and diffusion models. The equilibrium absorption amounts from the chemisorption model were found to obey a Langmuir isotherm. The results of the diffusion model to the data were consistent with a dual sorption process, i.e., diffusive and non-diffusive
Page 1 of 40
adsorption sites. The estimated diffusion coefficients were found to increase with the concentration of diluent, probably due to the swelling of the polymer by the organic vapors. Our
cr
ip t
results suggest that both models can be employed to mathematically fit the sensor response.
an
Sensor, Adsorption, Diffusion, Langmuir Isotherm.
us
Keywords: Nanostructured Polyaniline, Polyaniline/Ag Nanocomposites, Nanofibers, Gas
Ac ce p
te
d
M
* Corresponding Author
Page 2 of 40
1. Introduction
ip t
Gas sensors, sometimes denoted as electronic noses, have been widely studied ever since the design of a gas sensor was reported by Seiyama et al. in 1962.[1] Chemical methods for
cr
determining unknown species, such as gas chromatography/mass spectrometry (GC/MS), are
us
time-consuming, expensive, and require trained personnel. There is a need to develop miniature
an
devices for rapid and inexpensive analysis of volatile compounds. Significant research has been focused on conducting polymer–based gas sensors[2]. Polyaniline is a promising candidate for
M
gas sensing applications because of its relatively easy synthesis, low cost, high sensitivity, and
d
fast response[3,4]. In particular, nanostructured polyaniline-based gas sensors have shown
te
excellent performance because of their large surface areas and high porosity of nanostructured
Ac ce p
polyaniline[5-10]. Most methods of making polyaniline are multi-step and a facile one-step environmental-friendly method may overcome its poor processability. Our group has reported a novel method to synthesize polyaniline nanofibers and nanocomposites based on either gamma or ultra-violet radiation[11-13]. This technique can be utilized to fabricate nanostructured polyaniline-based electrochemical gas sensors in a single step. This type of sensor has shown a fast response to various organic vapors[9,10]. Although considerable research has been carried out in the development of novel conductingpolymer sensors, some basic problems still remain, especially with respect to nanostructured
Page 3 of 40
conducting-polymer sensors. The modeling of time-dependent sensor response is particularly relevant for understanding the sensing kinetics. The gas sensor response is basically controlled
ip t
by two factors. One is the transport process of gas molecules to or into the sensor film. The other
cr
is the interaction of the sensing material and gas molecules, i.e., a physical interaction or
us
chemical reaction. A few models have been proposed for bulk-conducting-polymer–based gas sensors[14-17].
an
Previous work from our group has shown how these sensitive materials can be made in a
M
single step. It was found that the incorporation of nanometals into the composite enhanced the
d
sensitivity of the sensors[9]. The incorporation of Ag, in particular, gave faster and more
te
sensitive responses to triethylamine than other metals because of the affinity of amines for Ag.
Ac ce p
We also showed that this enhancement was primarily due to the charge transfer to the Ag and that the sensor response of our polyaniline materials to triethylamine can be fit with an exponential decay as a function of time and gas concentration[9]. This paper reports the response of one-step polyaniline/Ag based sensors and interprets the response in terms of chemisorption and diffusion.
The chemisorption model is based on the de-doping (or swelling) of the conducting polymer when a guest molecule is adsorbed at or near the surface of that polymer. For nanostructures with high surface areas, such as in our PANI nanocomposites, this model embodies importance of the
Page 4 of 40
capture of the guest molecule by the polymer at active sites. It would be consistent with the limiting response factor being adsorption at the interface. The diffusion model is based on the
ip t
penetration of the polymer by the guest molecules. It assumes that the guest molecules go
cr
quickly to the surface, but the limiting step for sensing is diffusion into the polymer. We find that
us
both of these models fit the responses of the nanostructured polyaniline based gas sensors to organic vapors, probably because both fitting methods are consistent with exponential decay
an
functions. The chemisorption model was found to fit a Langmuir isotherm, while the diffusion
te
2. Experimental
d
M
model was consistent with a dual sorption mechanism.
Ac ce p
2.1. Synthesis of polyaniline/Ag nanocomposites To produce nanocomposites for the sensors, 0.1 M aniline (93 mg), 0.01 M AgNO3 (17 mg) and 0.1 M nitric acid were first dissolved in 10 mL distilled water. The aniline began to polymerize after the addition of 0.05 M ammonium persulfate (114 mg). After vigorous shaking, the solution was immediately irradiated with a low-pressure Hg-UV light source (Model: PASCO Scientific OS-9286A)[10].
2.2. Fabrication of polyaniline/Ag nanocomposite sensors
Page 5 of 40
Sensors were fabricated by placing a 10 µL drop of premixed precursor solution on the active area of an interdigitated microelectrode array. The precursor solution had the same composition
ip t
as described above. The drop was then illuminated with the UV lamp. After the reaction
us
room temperature before being used for measurements[10].
cr
(approximately 30 min), the polyaniline thin films were washed with distilled water and dried at
an
2.3. Characterization
M
The morphology of the polyaniline/Ag nanocomposites was characterized using a Hitachi S-
d
4700 scanning electron microscope (SEM) operated at accelerating voltages of 5 kV and a JEOL
te
JEM-2100 Transmission Electron Microscope (TEM). The changes in electrical current for
Ac ce p
polyaniline/Ag based thin film sensors were measured at room temperature as a function of time and exposure to organic vapors. The real-time current changes were monitored using a Keithley 4200 semiconductor analyzer operated at 0.1 V. To test the sensors, nitrogen gas was used as both the carrier and diluting gas. The carrier gas was passed through the neat liquids in a gas bubbler. The resulting gas mixtures were then diluted with additional diluting gas that was then directed to the sensor, which was kept at room temperature. The relative concentration (or volume fraction, measured in ppm) of gases in the carrier gas, c, was determined using: c = (M/ρ)/(M/ρ + L1 + L2)
(1)
Page 6 of 40
where M is the weight loss rate of the liquid sample (in g/min), ρ is the density of the vapor (in g/L), L1 is the nitrogen carrier gas flow rate (in L/min), and L2 is the nitrogen diluting gas flow
ip t
rate (in L/min). The flow rate of the nitrogen diluting gas was 1.5 L/min, and the total gas
cr
pressure was about 15 psi.
us
The mathematical fitting of experimental data was performed in Excel or Mathematica using least-squares method. The best fit was achieved when the sum of the squares of the
an
residuals was minimized. The standard deviation (SD) of the residuals, the square root of the
M
sum of the squares of the residuals divided by n-1 (n is the number of data points) was used to
d
estimate the uncertainty of the fit. The uncertainty in the fitting parameters was estimated by
te
varying each fitting parameter independently from the best-fit value until the SD increased to
Ac ce p
1.96 × SD, which corresponds to a 95% confidence interval[18,19].
3. Theory
3.1. Chemisorption model
This model is based on that originally developed for chemisorption, which states that the rate of adsorption is affected by the evaporation and condensation processes.[20-23]. The application of the model to our systems was based on the following assumptions[17,24]:
Page 7 of 40
1) The conductivity of the polyaniline is proportional to the number of conduction sites (dopant sites), N, which are uniformly distributed on the polymer surface. These sites can adsorb species
ip t
that affect the conductivity.
cr
2) All dopant sites are equivalent and the probability of a gas molecule adsorbing on any site is
us
the same. Each site can only adsorb one molecule. The adsorption process is described by the following equation: !! ! !!
A
an
A + dopant site
(2)
M
where A is the adsorbate, (A) is the adsorbate at an occupied site, k1 is the adsorption rate
!" !"
= !! !" ! − !!! !
(3)
Ac ce p
!=
te
the rate of desorption), R, equals
d
constant and k-1 is the desorption rate constant. The net adsorption rate (rate of adsorption minus
where θ is the fractional amount of surface coverage, c is the vapor concentration, and f(θ) is a surface coverage function. In this case f(θ) is given by M0 - θ, where M0 is the fractional coverage of the surface for the maximum adsorption of a monolayer. This definition of M0 accounts for the possibility that not all of the surface is accessible to the absorbant. The absorptions are normalized to their monolayer amounts and θ ranges from 0 to M0. Assuming that k1, k-1, and c are independent of θ, integrating Eq. 3 gives, for the boundary condition θ = 0 at t = 0:
Page 8 of 40
!! !! !
!!"# ! = !
! !!!!!
(1 − ! ! !! !!!!! ! )
(4)
Equation 4 describes the approach to equilibrium absorption, starting from when no initial
ip t
analyte is present and the amount adsorbed is referred to as θabs. Similarly, the approach towards
cr
complete desorption, given by θdes(t), when the material begins saturated with analyte and then is
us
exposed to an atmosphere with no analyte, can be similarly derived as:
(5)
an
!!"# ! = !! (1 − ! !!!! ! )
M
3.2. Langmuir adsorption isotherm
d
Langmuir, in 1918, suggested that the adsorption process is controlled by the rates of evaporation
Ac ce p
!! !" ! = !!! !
te
and condensation. At equilibrium, the rates of evaporation and condensation are equal[25]. Thus (6)
In order to account for the partial coverage of the surface, the surface coverage function is given by, f(θ) = M0 – θ. Therefore, Eq. 6 can be written as: !! !! !
!=!
! !!!!!
! !"
! = !"!!
(7)
with k1/k-1 = b, which is the Langmuir adsorption constant.
3.3. Diffusion model
Page 9 of 40
According to Fick’s first law[26], the rate of transfer of a diffusing substance through the unit area of a section is proportional to the concentration gradient that is normal to that section, i.e.: !"
!"
!"
! = −!(!" + !" + !")
ip t
(8)
cr
where J is the flux of diffusant, D is the diffusion coefficient, c is the concentration of diffusant,
us
and x, y, z are the spatial coordinates. Since the net flux into the element under consideration
obtained in the form of !"
!
!"
!
!"
!
!"
(9)
M
!" = !" ! !" + !" ! !" + !" (! !")
an
should be equal to the change in concentration (equation of continuity), Fick’s second law can be
d
For diffusion in a long circular cylinder where diffusion is radial[27], through substitution of x =
!"
!"
= ! !" (!" !")
(10)
Ac ce p
!"
! !
te
r cos θ and y = r sin θ, we can obtain,
In the cylinder of radius, a, the boundary conditions are c = c0, r = a, t ≥ 0,
c = 0, 0 < r < a, t = 0,
Solving Eq. 10 for the conditions when there is no dedopant initially (analyte in this case), for the cylinder, one can obtain a series solution (Crank's book, eq. 5.21)[27]: !
!(!, !) = c! (1 − !
!! !!! ! !!! ! ! !! ! ! !
exp −!!!! ! )
(11)
Page 10 of 40
where J0(x) is the Bessel function of the first kind of order zero, J1(x) is the Bessel function of
Integrating c(r,t) as a function of r from 0 to a gives[27]: ! ! !
!, ! !" = !! (1 −
! ! !!! ! ! ! !
!
exp −!!!! ! )
(12)
cr
!! =
ip t
the first kind of order one, and the αn's are roots of Bessel function of the first kind of order zero.
us
where Mt denotes the quantity of substance that diffuses into the cylinder in time t and M∞ is the
an
corresponding quantity after infinite time (i.e., equilibrium sorption amount).
M
3.4. Sorption
In 1958, Barrer et al. proposed a dual sorption model to describe the sorption isotherms of
te
d
small gas molecules in polymers[28]. In glassy polymers, there exists a distribution of "holes"
Ac ce p
frozen in the structure. These holes can immobilize some of penetrant molecules by entrapment or by binding various sites. Therefore, this model consists of two concurrent mechanisms of sorption: ordinary dissolution and "hole-filling". The equilibrium sorption uptake can be expressed by the following equation[29-31]: ! ! !"
! ! = !! + !! = !! ! + !!!"
(13)
where kD is the Henry’s law constant, P is the vapor pressure of the penetrant, cH' is the maximum uptake in holes, b is the hole affinity constant. The first term, cD, represents sorption of normally diffusible species, while the second term cH represents the sorption in holes.
Page 11 of 40
ip t
4. Results and Discussion
The scanning electron micrograph (SEM) and transmission electron micrograph (TEM) of
cr
polyaniline/Ag nanocomposite thin films grown on the interdigitated electrodes are shown in Fig.
us
1. These images clearly show a nanofiber structure with an average fiber diameter of about 51
an
nm, as analyzed by ImageJ[32]. The morphology was consistent with previous results for
Ac ce p
te
d
M
polyaniline made in this way[13].
Fig. 1. SEM (a) and TEM (b) images of polyaniline/Ag nanocomposites grown on interdigitated electrodes. The scale bar is 500 nm in (a) and 200 nm in (b).
Page 12 of 40
The change in current of the sensors in response to vapors was monitored. Fig. 2 displays the time-dependent change in the normalized current of the nanocomposite sensors upon exposure to
ip t
triethylamine at various concentrations. A valve allowing triethylamine to enter the chamber was
cr
opened to allow a sufficient amount to achieve a given concentration of vapor and then closed
us
allowing no triethylamine to pass. A fast current decrease was observed within 120 s as a result of the dedoping of polyaniline and decrease in the charge transfer by triethylamine. The
an
dedoping of polyaniline/Ag is generally a reversible process after replacing the triethylamine
M
vapor with pure N2. As shown in the figure, the current decreases very quickly in the early stage
d
and then tends to level off. At higher concentrations, complete recovery was not found in the
te
time frame measured. In our previous work, it was demonstrated that these decay curves
1
Normlized Current I/Io
0.9 0.8 0.7 0.6 0.5
Ac ce p
following nitrogen exposure could be fit to a single exponential function[9].
39 ppm
77ppm
0.4
116ppm
0.3
271ppm
543ppm
0.2
1100ppm
0.1 0 0
500
1000
1500
2000
2500
3000
3500
Time(s)
Page 13 of 40
Fig. 2. Sensor response and recovery curves of the polyaniline/Ag nanocomposite sensor to triethylamine. The sensor was exposed to the triethylamine vapor for 100 s and then exposed to
ip t
pure nitrogen until the current became stable before it was exposed to the next concentration of
us
cr
triethylamine.
4.1. Analysis based on the chemisorption model
an
The adsorption of nitrogen gas on or in the polyaniline film does not significantly affect the
M
conductivity of the polyaniline, especially compared to the response to triethylamine or toluene.
d
If the conductivity is proportional to the number of conductive sites, the normalized current
te
should be proportional to the fraction of unoccupied sites, or from equation (4): !! !! !
! !!!!!
(1 − ! ! !! !!!!! ! ) (14)
Ac ce p
!!"#$ ! = 1 − ! ! = 1 − !
where Mo is the fraction of occupied sites, and b = k1/k-1. The polyaniline/Ag composite sensor responses, as a function of time to triethylamine at various concentrations, are shown in Fig. 3. The y-axis is the normalized current monitored by the electrometer, and the x-axis is the gas exposure time. These decay curves were fit by minimization of the least-squares of the residuals to an exponential growth function: !!"#$ ! = 1 − !! ×(1 − ! !!/!! ) (15) where 1 - I∞ is the normalized final current in the presence of the dopant.
Page 14 of 40
39 ppm
0.7
77 ppm
0.6
150 ppm
0.5
271 ppm
0.4
543 ppm
cr
0.8
ip t
0.9
us
0.3
1100 ppm
0.2 0.1 0 0
20
40
60
an
Normalized current I(t)/Io
1
80
120
M
Time (s)
100
d
Fig. 3. Polyaniline/Ag nanocomposite sensor responses to triethylamine vapor with different
te
concentrations. The exponential decay curves are best fits from Eq. 15. The order of the curves
Ac ce p
in the figure is the same as shown in the figure legend.
The current changes followed exponential decays with the time constants decreasing with increasing concentrations of triethylamine. Comparing Eq. 14 and 15, the functional form becomes:
! !"
! !! = !"!! (16)
with !! = !
! ! !!!!!
(17)
Page 15 of 40
Similarly, the recovery curves were fit to an exponential growth or: !!"#$ ! = 1 − !! ! !!/!! (18)
ip t
For recovery, I∞ was taken as the value from the fitted decay curve, which varies from sample to
us
cr
sample. The recovery curves with the recoveries are shown in Fig. 4.
0.9
an
0.8 0.7 0.6
M
39 ppm
0.5
77 ppm
0.4
100 ppm
d
0.3 0.2 0.1 0 100
200
Ac ce p
0
te
Normalized current I(t)/Io
1
300
Time (s)
543 ppm
400
500
Fig. 4. Polyaniline/Ag nanocomposite decay and recovery curves for triethylamine vapor with different concentrations fit to exponential increases after the organic vapor was removed from the carrier gas. The curves are best fits from Eq. 15 until 100 s, (i.e., the end of the adsorption step), and then Eq. 18. The order of the curves in the figure is the same as shown in the figure legend.
Page 16 of 40
The decay and response curves for the polyaniline composite sensors shown in Figs. 3 and 4 show that the functions used provided good fits to the experimental data. The time constants
ip t
τa and τd are for adsorption and desorption, respectively. Table 1 shows the value of the fitting
cr
constants I∞, τa, and τd for these curves. As was evident from the curves, I∞ and τd increased with
us
the triethylamine concentration, while τa decreased with it. For the highest amount of
an
triethylamine there was a noticeable deviation from a single exponential for the recovery curve. For this curve, selections of single time constants, τa and τd, were unable to fit this data
M
satisfactory with Eq. 17. However, this data could also be fit to power laws with τa = 0.683c-0.33
d
and τd = 2655c0.43. A power law relationship was also previously observed for NO2 adsorbed on
te
polyaniline.[17,33] The reason for this deviation from simple exponential functions is currently
Ac ce p
unknown. One possible explanation is that τa and τd may not have been independent of concentration.
Table 1. Fitting constants for the polyaniline/Ag sensor exposed to triethylamine based on Eqs. 15 and 18. The uncertainties were estimated at the 95% confidence interval. Triethylamine
I∞
τa (s)
τd (s)
0.225 ± 0.008
18.3 ± 1.7
22.4 ± 2.1
Concentration (ppm) 39
Page 17 of 40
0.410 ± 0.009
16.7 ± 1.3
37.9 ± 3.6
116
0.486 ± 0.017
13.9 ± 1.4
48.6 ± 4.1
150
0.526 ± 0.011
12.5 ± 1.0
58.9 ± 5.1
271
0.570 ± 0.008
10.4 ± 0.79
94.1 ± 6.4
543
0.619 ± 0.012
7.5 ± 0.66
109 ± 12.2
1100
0.719 ± 0.019
5.9 ± 0.83
131 ± 11.8
us
cr
ip t
77
an
The polyaniline/Ag composite sensor response as a function of time exposed to toluene at
M
various concentrations is shown in Fig. 5. These curves were also fit using exponential decays. Recovery curves were not measured for the toluene system. Values of fitting constants I∞ and τa
te
d
shown in Table 2. Similar to that for triethylamine, I∞ also increased with the toluene vapor concentration and τa decreased with it. The time constants for toluene were larger (slower) than
Ac ce p
for triethylamine. The time constant τa was fit to a power law in concentration resulting in τa = 2.89c-0.25.
Page 18 of 40
0.9 0.8 0.7
ip t
29 ppm
0.6
67 ppm
0.5 0.3
296 ppm
0.2
500 ppm
cr
187 ppm
0.4
us
Normalized current I(t)/Io
1
0.1 0
20
40
an
0 60
80
100
120
140
M
Time (s)
Fig. 5. Polyaniline/Ag nanocomposite sensor responses to toluene vapor for different
d
concentrations fit to exponential decays. The curves are best fits from Eq. 15. The order of the
Ac ce p
te
curves in the figure is the same as shown in the figure legend.
Table 2. Fitting constants of the polyaniline/Ag sensor exposed to toluene from Eq. 15. Toluene
I∞
τa (s)
0.086 ± 0.0019
41.2 ± 1.9
67
0.135 ± 0.0097
32.9 ± 3.7
146
0.212 ± 0.0068
29.2 ± 5.9
187
0.248 ± 0.0092
25.0 ± 4.3
296
0.281 ± 0.010
20.2 ± 3.3
Concentration (ppm) 23
Page 19 of 40
500
0.325 ± 0.015
18.6 ± 4.2
ip t
In the chemisorption model, the fitting constant, I∞, was dependent on the adsorbed amount. Fig.
cr
6 is a plot of I∞ as a function of triethylamine and toluene concentrations. As shown in the figure,
us
these curves fit the Langmuir isotherm equation well. Based on equation 7, the normalized maximum adsorption amount, M0, was equal to 0.407 and 0.733 for toluene and triethylamine,
an
respectively. The Langmuir constant, b, for triethylamine and toluene were 1.48 × 104 atm-1 and
M
7.86 × 103 atm-1, respectively. The values of the Langmuir constants were higher with those values reported for triethylamine adsorbed on CdSe (380 atm-1) and toluene adsorbed on active
te
d
carbon (2845 atm-1) [34,35]. These larger values may be due to a stronger interaction of triethylamine and toluene with polyaniline/Ag composites.
Ac ce p
Page 20 of 40
0.9
Triethylamine
0.8
Toluene
0.7
ip t
I∞
1
0.6 4
0.5
4
cr
I = 0.733 x 1.48x10 c/(1+1.48x10 c) ∞
us
0.4 0.3
0.1 0 200
400
600
M
0
an
I∞ = 0.407 x 7.86x103c/(1+7.86x103c)
0.2
800
Concentration (ppm)
1000
1200
te
d
Fig. 6. Plot of the fitting parameter, I∞, as a function of toluene and triethylamine vapor
Ac ce p
concentrations fit to a Langmuir isotherm.
4.2 Analysis based on the diffusion model Adsorption normally only occurs at the surface of the adsorbate. In our work, the polyaniline consists of mainly interconnected networks of nanofibers. Diffusion in a cylinder may also be appropriate to describe the transport processes within the fibers. Therefore, the sensor response curves were also fit using a diffusion model for comparison. It has been reported previously that there is a charge transfer effect between polyaniline and Ag nanoparticles[10]. The response of
Page 21 of 40
polyaniline/Ag composite sensors to triethylamine was caused by both the dedoping of polyaniline and a reduction in the charge transfer. For simplicity, we assume that the effect of
ip t
charge transfer can be modeled in the same way as dedoping process. The conductivity through
cr
the polyaniline film should be linearly proportional to the concentration of the dopant, [DP],
us
which is equal to the initial dopant concentration, [DP]0, minus the reacted dopant[36]. As discussed in the previous section, the sensing mechanism of triethylamine is based on the
an
reaction between the triethylamine and the acid dopant. The enthalpy of reaction for the
M
protonation of triethylamine was determined to be about -43.4 kJ/mol, indicating that this
d
reaction is exothermic. Therefore, it was assumed that each triethylamine molecule that diffuses
Ac ce p
then be estimated as
te
into the polyaniline film will react with a dopant molecule. The conductivity of polyaniline can
! ∝ !" = [!"]! − [!"#$%h!"#$%&'](19) Based on this assumption, the normalized current can be expressed based on equation (12) as: !!"#$ t = 1 −
!"#$%!!"#$%&' !" !
=1−
!! !" !
1−
! ! !!! ! ! ! ! exp !
−! !!! ! (20)
The result of fitting the data from the polyaniline/Ag sensor exposed to gaseous triethylamine at concentrations of 39 to 1100 ppm is shown in Fig. 7 for the diffusion model. Two fitting constants, M∞/[DP]0 and D, were obtained from a least-square fit based on Eq. 20. The values of
Page 22 of 40
the fitting constants for these curves are shown in Table 4. It was apparent that M∞/[DP]0 and D increase with the toluene concentration. Since [H+]0 should be a constant for all of our sensors,
ip t
the fitting constant, M∞/[H+]0, then should be proportional to the final absorbed amount, M∞. It
cr
should also be noted that the diffusion in a cylinder fits the data significantly better that a
us
comparable fit for diffusion in a slab.
0.9
an
0.8 0.7
M
0.6 0.5 0.4 0.2 0.1
Ac ce p
0
0
20
40
60
Time(s)
77ppm 150ppm
543ppm
d
0.3
39ppm
271ppm
1100ppm
te
Normalized Current I(t)/Io
1
80
100
120
Fig. 7. Polyaniline/Ag nanocomposite sensor response to triethylamine vapor of various concentrations fit with the diffusion model. The curves are best fits from Eq. 20. The order of the curves in the figure is the same as shown in the figure legend.
Table 3. Fitting constants of the polyaniline/Ag sensor exposed to triethylamine Triethylamine
M∞/[DP]0
D x 1018 (m2/s)
Page 23 of 40
0.244 ± 0.022
3.14 ± 0.58
77
0.440 ± 0.029
4.01 ± 0.88
116
0.511 ± 0.036
4.71 ± 1.17
150
0.549 ± 0.029
5.57 ± 1.18
271
0.583 ± 0.030
7.02 ± 1.51
543
0.620 ± 0.021
10.4 ± 1.82
1100
0.727 ± 0.023
13.1 ± 2.34
M
an
us
cr
39
ip t
Concentration (ppm)
d
Toluene is a solvent that can swell the polymer and increase the polymer interchain distances;
te
consequently causing a conductivity decrease. The conductivity of a conducting polymer is
Ac ce p
dependent on the hopping distance, i.e., the interchain distance. This conductivity can be expressed with an exponential term[37-39]: ! = !! exp(−!")
(21)
where σ0 is the pre-exponential constant, β is the electron-tunneling coefficient, and δ is the hopping distance. The swelling of polymers generally results because of the diffusion of solvent molecules and then chain relaxation processes. The relaxation processes may be considerably slower than the diffusion and may take hours to occur[40]. If this is the case, the interchain distance would be expected to be only proportional to the uptake of a diffusing substance, or
Page 24 of 40
! ! !!! !∞ !!!
∝ !(!)
(22)
where δ1 stands for the initial interchain distance, δ∞ denotes the interchain distance when
ip t
swelling is at equilibrium. Thus, the normalized current of polyaniline during the swelling can be
cr
expressed as ! ! !!! ! ! ! ! !"# !
−!!!! ! ](23)
us
!!"#$ ! = !"# [− ∆!! !!! 1 −
where ∆δ is the maximum interchain distance change.
an
The sensor response upon exposure to toluene at various concentrations fit with the
M
diffusion model is shown in Fig. 8. The values of fitting constants, ∆δ∞βM∞ and D, are listed in
d
Table 4. Similar to the fitting constants for triethylamine, the quantity ∆δ∞βM∞ is considered as
Ac ce p
Normalized current I(t)/Io
te
the product for study of sorption uptake, because ∆δ∞, and β are constants.
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
29 ppm 67 ppm 146 ppm 187 ppm 296 ppm 500 ppm
0
20
40
60 80 Time (s)
100
120
140
Page 25 of 40
Fig. 8. Polyaniline/Ag nanocomposite sensor response to toluene vapor of various concentrations
cr
curves in the figure is the same as shown in the figure legend.
ip t
and the fits with the diffusion model. The curves are best fits from Eq. 23. The order of the
Table 4. Fitting constants of the polyaniline/Ag sensor exposed to toluene using Eq. 23 D x 1018 (m2/s)
29
0.150 ± 0.017
0.276 ± 0.18
67
0.209 ± 0.019
0.852 ± 0.14
146
0.307 ± 0.007
187
0.326 ± 0.019
1.90 ± 0.32
296
0.362 ± 0.021
2.59 ± 0.47
500
0.441 ± 0.021
2.96 ± 0.38
us
∆δ∞βM∞
Toluene
M
an
Concentration (ppm)
Ac ce p
te
d
1.23 ± 0.08
Plots of the fitting parameters M∞/[H+]0 and ∆δ∞βM∞ of triethylamine and toluene as a function of concentration are shown in Figs. 9 and 10. These data were fit with the dual sorption model and Langmuir isotherm. It was found that both curves fit the parameter M∞/[H+]0 of triethylamine very well. The standard deviation from the dual sorption model was only 5%, which was smaller than that from the Langmuir isotherm. However, for toluene, the fitting error from the dual sorption model was 76% smaller than that from Langmuir isotherm. Thus, the dual sorption
Page 26 of 40
model fits the toluene data better. Comparing the fitting equations with Eq. 22, we can determine that the normalized uptake in holes was equal to 0.336 and 0.701 for toluene and triethylamine,
ip t
respectively. The Langmuir constant for triethylamine was 1.86 x 104 atm-1, which was close to
cr
that estimated from the chemisorption model (Fig. 6). However, the Langmuir constant for
us
toluene was found to be 2.3 x 104 atm-1, much larger than that predicted by the chemisorption model. This larger value of Langmuir constant for toluene may result from the high swelling
an
effect of toluene in polyaniline. The Henry’s Law dissolution constant of triethylamine and
d
M
toluene was determined to be 39.3 and 259.4 atm-1, respectively.
te
0.7 0.6
Ac ce p
Fitting parameter M∞/[H+]0
0.8
0.5 0.4
Dual sorption Langmuir
M∞/[H+]0 = 0.701 x 1.86x104c/(1+1.86x104c) + 39.3c
0.3 0.2 0.1 0
0
200
400
600
800
1000
1200
Concentration (ppm)
Page 27 of 40
Fig. 9. Plot of fitting parameter M∞/[H+]0 of triethylamine as a function of concentration. The curves were fit by the dual sorption and Langmuir isotherm models. The equation shown is the
cr
ip t
result for the dual sorption model.
0.5
us
0.4
an
0.35 0.3
Dual sorption fit
M
0.25 0.2 0.15
Langmuir fit
∆δ∞βM∞ = 0.336 x 2.33x104c/(1+2.33x104c) + 259.4c
d
0.1 0.05 0
100
200
Ac ce p
0
te
Fitting parameter ∆δ∞βM∞
0.45
300
400
500
600
Concentration (ppm)
Fig. 10. Plot of sorption uptake of toluene as a function of concentration with the fit for the dual sorption model and Langmuir isotherm models. The equation shown is the result for the dual sorption model.
The diffusion coefficients of toluene and triethylamine are plotted as a function of concentration and shown in Fig. 11. The diffusion coefficients showed an increase with the vapor concentration
Page 28 of 40
and could be fit with an empirical power law or an exponential function. The results of the fitting determined that D = 273.5c0.44 or D = 12.7 x (1 – e-368c). For toluene, the fits yielded, D =
ip t
417c0.64 or D = 3.62 x (1 – e-3660c). Again, the increase in diffusion coefficient was probably due
us
cr
to the swelling effect of these organic vapors, which greatly increases the solubility.[41,42]
an
14 12 10
Triethylamine
M
8 6
Toluene
d
4 2 0 200
400
600
800
Concentration (ppm)
1000
1200
Ac ce p
0
te
Diffusion coefficient (m2/s)
16
Fig. 11. Diffusion coefficients of toluene and triethylamine as a function of concentration fit with a power law (curve) and an exponential function (dashed curve).
Although other measurements of the toluene and triethylamine diffusion coefficients are not available in polyaniline, one can estimate the diffusion coefficient of a gas in polymers from kinetic diameters using an empirical equation proposed by Michaels and Bixler [43,44]. From
Page 29 of 40
these parameters, the estimated values for vapor diffusion coefficients of toluene and triethylamine in polyaniline were on the order of 10-16 m2/s, which were larger than those
ip t
determined in this work. In the empirical models mentioned, the interaction of the gas molecules
cr
and the polymer was ignored. However, our diffusants showed strong interactions with the
us
polyaniline, which would be expected to lower the diffusion coefficients. Given this, the values
an
obtained in this work seem reasonable.
M
4.3. Reproducibility and fitting errors
d
The reproducibility of independent individual runs is illustrated in Fig. 12 for the sensor
te
response to 39 ppm triethylamine. The individual data points were averaged from four
Ac ce p
independent experiments at each time. From each of the 4 runs, the values of the uptakes and diffusion coefficients were calculated. The resulting means and standard deviations were also calculated and are shown in Table 5. A small standard deviation (about 1.4%) was found for the fitting constant M∞/[H+]0, and a larger error (about 6.7%) was attained for the diffusion coefficient.
Page 30 of 40
0.95
ip t
0.90 0.85
cr
0.80 0.75
us
Normalized Current I(t)/I0
1.00
0.70 20
40
60
Time (s)
80
an
0
100
M
Fig. 12. Sensor responses to 39 ppm triethylamine plotted with error bars representing the
d
averages of 4 runs from independent experiments. The curve is the best fit of the averaged data,
Ac ce p
te
using the diffusion model.
Table 5. Standard deviations from the fits to the parameters of the polyaniline/Ag sensor exposed to 39 ppm triethylamine from the diffusion model. Run
No. 1
No. 2
No. 3
No. 4
Average
Standard Deviation
M∞/[DP]0
0.248
0.246
0.244
0.239
0.244
1.43%
D x 1018 (m2/s)
3.26
3.14
3.55
3.05
3.24
6.7%
Page 31 of 40
In order to compare the results from the application of both kinds of models to the data, the standard deviation of the residuals is plotted for triethylamine in Table 6 and toluene in Table 7.
cr
ip t
For both systems, there was little difference in the quality of the fits from both models.
us
Table 6. Standard deviation of the residuals for the chemisorption and diffusion models of the sensor response to triethylamine at different concentrations. 39
77
116
Concentration (ppm)
0.010
271
543
1100
0.0079 0.0096 0.017
0.0075 0.0096 0.0085 0.011
0.011
0.012
Ave.
0.011 0.0098
te
d
Diffusion Model
0.0084 0.013
M
Chemisorption model 0.0076 0.013
150
an
Triethylamine
Ac ce p
Table 7. Standard deviation of the residuals for the chemisorption and diffusion models of the sensor response to toluene at different concentrations. Toluene
29
67
146
187
296
500
Ave.
Concentration (ppm)
Chemisorption model
0.0012 0.0081
0.0088
0.0094
0.0091
0.014
0.0084
Diffusion Model
0.0033 0.0031
0.0029
0.011
0.012
0.014
0.0077
5. Conclusions
Page 32 of 40
A chemisorption and diffusion model has been used to fit the responses of polyaniline/Ag nanocomposite sensors exposed to triethylamine and toluene at several different concentrations.
ip t
Both models can reproduce the sensor response as a function of time. As determined from the
cr
fitting constants, a Langmuir adsorption isotherm was used in the chemisorption fit, while a dual
us
sorption mechanism was required for the diffusion fit. In addition, the diffusion coefficients obtained from the diffusion fit was found to increase with the vapor concentration, probably due
an
to the swelling effect by organic vapors. Fitting errors from the two models were small, both
M
allowing reasonable mathematical forms for the time-dependent and concentration behavior. Our
d
results also show the potential for studying the adsorption or diffusion process of conducting
te
polymers based on conductivity measurements.
Ac ce p
It should be noted that in this case, both models are able to reproduce the functional form of the data as a function of time. This is because both models are capable of mimicking an exponential decay. The Langmuir model is inherently exponential and the diffusion model results in a series of exponentials. Since the functional form of the diffusion model is dependent on the root of the Bessel function squared in the denominator and also the negative exponential, the lower order terms dominate, making the form close to exponential. Thus, unfortunately, our work cannot make a definitive statement about which mechanism is dominant with both models yielding reasonable fitting parameters.
Page 33 of 40
6. Acknowledgements
ip t
The authors acknowledge Terry Colberg and Balika Khatiwada at Oklahoma State University for
cr
assistance in obtaining the TEM pictures. FDB acknowledges the financial support of the
us
Department of the Army Research Office under Award No. W911NF-10-1-0476 and of
M
an
Materials Research Center, Missouri S & T.
Ac ce p
te
d
Biographies Z.-F. Li received his Ph.D. degree in materials science and engineering at the Missouri University of Science and Technology in 2010. His graduate research interests have been focused on nanomaterials and conducting polymer-based sensors. Currently, he is a postdoctoral research fellow in the Department of Mechanical Engineering at Indian University-Purdue University Indianapolis working on graphene-based materials. F.D. Blum is the Harrison I. Bartlett Chair of Chemistry and Regents Professor at the Oklahoma State University. His research activities include conducting polymer nanocomposites and dynamics in interfacial materials. He is a Fellow of the American Chemical Society (ACS) and the Division of Polymer Chemistry, Inc,. and has been awarded the Distinguished Service Award and Special Service Award by the Division of Polymer Chemistry, Inc. of the ACS. M.F. Bertino is associate professor of physics at Virginia Commonwealth University. His research activities include photolithographic synthesis of metal, oxide and polymer nanoparticles. C.-S. Kim is an associate professor with joint appointment at the Departments of Electrical and Computer Engineering and Biological Sciences at Missouri University of Science and Technology. Dr. Kim’s current research interests include microsystem technologies for special applications to environmental, agricultural, and plant sciences.
Page 34 of 40
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