modelling and characterization of pmma

modelling and characterization of pmma
MODELLING AND CHARACTERIZATION OF PMMA-FILM
COATED IMPEDANCE PROBE DIPPED IN ADULTERATED MILK
1
SIULI DAS, 2B. GOSWAMI, 3KARABI BISWAS
1
RAIT, Nerul, Navi Mumbai, India
2
IEE, JU, Kolkata, India
3
Department of Electrical Engineering, IIT Kharagpur, India
Abstract- Impedance characterization and electrical equivalent circuit for the electrode-electrolyte interface of a capacitive
type probe dipped in adulterated milk is presented. The electrodes of the probe are coated with porous film of
poly-methyl-methaccrelate (PMMA ) where the diffusion of ions of the test solution through the porous surface is the mode of
sensing. In such measurement, it is very important to know the penetration depth of the ion into the porous surface. The vital
question is whether the ions reach the metal electrode surface which may contaminate the solution under test and also degrade
the sensor characteristics. In this study, the electrical equivalent circuit has been obtained by complex nonlinear least square
(CNLS) curve fitting of experimentally obtained impedance data. Then the parameters of the electrical equivalent circuit along
with the other experimental data are used to find the penetration depth of the ions through the porous surface of the coating
film. It has been observed that the penetration depth of the ions are less than the thickness of the porous film and hence, does
not reach the metal surface of the electrode. This is being validated with three probes of different thickness of the porous-film
used for sensing and four different types of test solution (pure milk, milk adulterated with urea, milk adulterated with
liquid-whey, and milk adulterated with tap-water). Hence, it is being concluded that measurement by the probes are free from
contamination when dipped inside the adulterated milk.
Index Terms- Penetration depth, porous-film, CNLS, LEVMW.
I. INTRODUCTION
Modelling of electrical equivalent circuit by fitting
EIS data has become a powerful tool in the field of
electrochemistry [1]-[5], biological sciences [6],
biomedical engineering [7]. It helps to understand the
underlying physical process [8]–[10] which is
otherwise difficult to intemperate or requires very
complex chemical kinetics [11] to explain. Hitz et. al
have used impedance spectroscopy to characterize
surface porosity [12]. In this work, porous
PMMA-film coated probes are used to detect milk
adulteration [13]-[15]. The probes are made up of
copper plated epoxy glass. The electrodes are coated
with porous film of poly-methyl-methaccrelate
(PMMA) [13]. For sensing purpose, the probe is
dipped inside the test medium and the ionic activity at
the surface of the electrode causes the impedance to
change across the two terminals of the probes as
shown in Fig. 1. The natural question comes whether
the ions travelling through the pores at all touches the
metal electrodes which may contaminate the milk
under test. In the study, the penetration depth is
calculated by the method presented by Hyun et. al [16]
based on R. de Levie [17]. To do so, first the
impedance data are fitted using CNLS curve fitting
using LEVMW software [18], and the electrical
equivalent circuit across the two terminal of the probe
dipped inside the test medium is obtained.
where, r is the radius of the pore in cm, k is the specific
conductivity in ohm-1cm-1, Cd is the electric double
layer capacitance at the electrolyte-electrode interface
in Farad/cm2 ω is the angular frequency in rad/sec.
The experimentation and subsequent calculation of
penetration depth have been carried out with three
different probes. The length, height and width of the
probes are same but the coating film thicknesses are
different. The coating film thickness decides the size
of the pore which again dictates the penetration depth.
The probe with coating film thickness of 6 µm (termed
as probe-1) has maximum pore diameter of 0.4 µm.
The other two probes has coating thickness of 8 µm
(termed as probe-2) and 18 µm (termed as probe-3)
with maximum pore diameters of 2 µm and 4 µm
respectively.
With the above three probes experiments are carried
out with four different test samples as described below
• pure milk (PM)
• pure milk adulterated with urea (PMU)
• pure milk adulterated with liquid-whey (PMW)
• pure milk with tap water (PMT)
Then the parameters obtained through the electrical
equivalent circuit are used to evaluate penetration
depth [16] using the following equation,
From the experimental impedance data, electrical
equivalent circuit of the probe have been evaluated
Proceedings of 8th IRF International Conference, 04th May-2014, Pune, India, ISBN: 978-93-84209-12-4
43
Modelling and Characterization of Pmma-Film Coated Impedance Probe Dipped In Adulterated Milk
using LEVMW [18] software. For all the cases one
particular electrical equivalent circuit shows the best
fit in least square sense. The fitting parameters of the
circuit are Cp, R1, RD, Q and α. It will be worth to
mention that though the structure of the electrical
equivalent circuit is same but the values of the
parameters (Cp, R1, RD, Q and α) are different for
different samples. As mentioned before, using the
fitting parameters and eqn. 1, penetration depth for
each case is calculated. It has been observed that the
penetration depth is at least 100 times less than the
thickness of the porous film coated on the electrodes.
inspection of the probes after testing more than 100
times over 15 to 20 days of continuous testing where
no degradation of the PMMA film is observed. The
paper is organized as follows: the curve fitting of the
EIS data and the electrical equivalent circuit is
discussed in section-II. Section-III gives the detailed
procedure to find out the penetration depth. Section-IV
provides the discussion on the results. Section-V is on
conclusion.
sample is evaluated and each one depicts the
equivalent circuit as shown in the Fig. 2. One
representative curve, for pure milk as a sample,
returned by LEVMW with the degree of fitting is
shown in the Fig. 3 and the parameters for pure milk
adulterated with urea are tabulated in the Table. I.
Hence it is concluded that the ions of the medium does
not reach metal surface of the electrodes and the
medium under test is free from contamination which
may arise due to chemical reaction. This is also
evident from the visual
II. THE ELECTRICAL EQUIVALENT CIRCUIT
Electrical equivalent circuit of the probe is obtained by
fitting the impedance data in LEVMW software. The
experimental setup to get the impedance data is shown
in Fig. 1. The two terminals of the probes are excited
with frequency 40 Hz to 4 MHz. The electrical
equivalent circuit is evaluated for the frequency zone
where best fitting is obtained. The phase angle and
magnitude of the impedance are noted by a precision
LCR meter (Impedance Analyzer: Agilent 4294A).
Fig. 1: Photograph of the experimental set up.
It has been observed that data obtained with different
test samples (pure milk, pure milk adulterated with
urea, pure milk adulterated with liquid-whey, pure
milk with tap water) always returned same electrical
equivalent circuit in least square sense using LEVMW
software [18]. The degree of fitting for each of the
Fig. 2: Equivalent circuit of the probe dipped in polarizing
medium.
Proceedings of 8th IRF International Conference, 04th May-2014, Pune, India, ISBN: 978-93-84209-12-4
44
Modelling and Characterization of Pmma-Film Coated Impedance Probe Dipped In Adulterated Milk
A. Validation of the equivalent circuit
To validate the model we have evaluated the
expression for the magnitude and phase of the
impedance across the two terminals of the equivalent
circuit denoted as ‘A’ and ‘B’. The impedance,
ZAB(s) can be written as
LEVMW software, CP is termed as double layer
capacitance, R1 as the pore resistance and RD, Q and α
is the parameters of the ZARC element [18]. The
presences of these circuit parameters are due to two
different types of ionic activity along the
liquid-coating film and electrode interface. When the
electrodes are excited by ac signal of peak to peak
amplitude 1V then the ions of the solution try to
change their states. Some of the ions forms dipole
layers and becomes immobile causing the capacitance
CP to arise as shown in the circuit. The other ions
become mobile and try to penetrate through the pores
of the coating film. As doing so they face a resistance
and denoted by R1 in the circuit. As will be shown in
the next section these ions does not reach the metal
surface of the electrode, rather after hopping from
outer layer with bigger pore to smaller pore in the
inner layer and settles down which can be modelled as
the ZARC (denoted by RD, Q and α here) element in
the circuit [18]. ZARC is the CPE (constant phase
element) with magnitude Q and exponent α, RD is the
parallel resistance to the CPE denoting the dc path
across the CPE [1], [19], [20].
Fig. 3: Complex plane plot of the probe dipped in test medium
(pure milk) for
the frequency range 13 kHz to 20 kHz. The fitness
quality factor FQF = -1139 as obtained from LEVMW
software.
The magnitude and phase angle of the impedance are
evaluated by substituting the parameter values
obtained from electrical equivalent circuit. These are
called estimated impedance. This estimated
impedance is then compared with the original
experimental data. Fig. 4(a) shows the comparison
between the estimated and experimental magnitude
where as Fig. 4(b) gives the error between them.
Similar curves are plotted for experimental and
estimated phase angle and shown in Figs. 5(a) and
5(b). It will be worth to mention here that different
electrical circuits available in LEVMW software are
tried to fit the experimental data. But the circuit shown
in Fig. 2 returns the best fitting for all the case. In
III. PENETRATION DEPTH
The aim to evaluate the penetration depth is to find
whether the mobile ions of the test medium reach the
metal surface of the electrodes, which may cause the
contamination of the test sample as well as
degradation of the sensor characteristics. Penetration
depth of the mobile ions from the solutions into the
pores of the coating film is evaluated using the
Proceedings of 8th IRF International Conference, 04th May-2014, Pune, India, ISBN: 978-93-84209-12-4
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Modelling and Characterization of Pmma-Film Coated Impedance Probe Dipped In Adulterated Milk
formula presented by Hyun et. al [16] as shown in eqn.
1.
Proceedings of 8th IRF International Conference, 04th May-2014, Pune, India, ISBN: 978-93-84209-12-4
46
Modelling and Characterization of Pmma-Film Coated Impedance Probe Dipped In Adulterated Milk
IV. DISCUSSIONS
The above result shows that the equivalent circuit of
the probe (coated with thin film of PMMA) dipped
inside different adulterated milk can be represented by
one circuit as shown in the Fig. 2. But the values of the
parameters (CP, R1, Q, α and RD) of the circuit are
different for different kind of adulterations and can be
an indicator of the adulterations. For all the cases the
circuit of the Fig. 2 gives best fitting parameters.
Table 1 summarizes the values of the different
parameters for the probe coated with 8 µm porous film
of PMMA and with the pore size of 2 µm as shown in
the Fig. 8. Column one shows the conductivity values
measured by the high resolution conductivity meter. Z
and θ are the magnitude and phase at the two terminals
of the probe measured by precision LCR meter. The
rest of the columns are the fitting parameter value
returned by the LEVMW software for each
adulteration. As mentioned all the time the model
circuit gives the best fit. Similar experiments are
conducted with two other different probes with
coating thickness (6µm and 18µm) and other test
samples. In every case it returned consistent result.
In the equation r is the radius of the pore in cm, and
this has been found out from the SEM picture of the
surface of the electrodes coated with porous film of
PMMA. Fig. 8 shows the SEM for probe-2 with pore
diameter 2 µm. It will be worth to mention here that
for calculation purpose radius of the biggest pore is
considered as it is more likely that ion will penetrate
deeper inside through the bigger pore. As mentioned
earlier ‘k’ is the specific conductivity in ohm-1cm-1.
The conductivity has been found for each sample sing
a precision conductivity meter (Systronics: Model
304). Table 1 shows the conductivity values for pure
milk and the urea adulterated milk.
To validate the circuit model analytical expression has
been evaluated and shown by the eqn. 2, 3, 4, and 5.
Then the values of the magnitude and phase at the two
terminal of the circuit is evaluated using the fitting
parameters (CP, R1, Q, α and RD) 6 returned by the
LEVMW software. These magnitude and phase are
then compared with the original experimental data and
shown in the Figs. 4(a), 5(a), 4(b) and 5(b). Next the
question of penetration depth is being investigated. To
do that, the equation presented in Eqn. 1 is being used.
The values of the conductivity are different for
different solutions. The second column of Table. 1
shows the conductivity values of the test samples for
urea adulteration. Similar measurement is being
conducted for all other type of test samples to measure
the penetration depth. The term r is the radius of the
pore and has been calculated from the SEM pictures.
Cd is the capacitance CP divided by the area of the
probe dipped inside the medium and ω is the angular
frequency. From the Figs. 6(a), 6(b), 6(c) and 7 that the
penetration depth is directly proportional to the pore
size of the coating film and inversely proportional to
the frequency. This is in agreement with the claim of
Hyun et. al. [9], [16].
In the Eqn. 1, Cd is the double layer capacitance at the
interface in Farad/cm2. From the electrical equivalent
circuit we get the value of CP in Farad which has been
shown in Table 1 for urea adulterated milk. Hence to
get Cd, CP is to be divided by the area of the probe
dipped inside the test medium. Here the width of the
probe is 6 mm and 2 cm of the probe is dipped inside
the test medium for optimum and stable result [13]. So
Cd is obtained by dividing Cp by 1.2 cm2 ω is the
angular frequency in rads-1. Penetration depth for
each of the probes is evaluated at every frequency in
the prescribed zone for different test samples. Fig. 6(a)
shows the penetration depth versus frequency for tap
water adulteration using Probe-2. As explained by
Hyun et. al, it is apparent from the figure that the
penetration depth decreases with the increasing
frequency. Figs. 6(b), 6(c) show the similar
characteristics with urea and whey adulteration.
Next the relation between the size of the pore and the
penetration depth of the ions through the pores are
evaluated. This is carried out by evaluating the
penetration depth for each of the probe. Fig. 7 shows
the penetration depth versus pore size. Here pure milk
is considered as this gives fitting for a wider zone (5
KHz to 20 kHz).
As reported in earlier works the phase angle and the
magnitude decreases (Table. 1) with increasing urea
adulterations [13], [14]. Further from Table. 1 it can be
seen that as the concentration of the adulterants
increases, more ions try to penetrate through the pores
hence, the resistance R1 decreases. Similarly the
double layer capacitance CP increases as more dipoles
are formed. The same phenomenon also have been
reflected in the parameters of the ZARC elements, i.e.
RD, Q and α.
The different curves of the Fig. 7 represent penetration
depth at different frequency. It is apparent from the
figure that as the pore size increases penetration depth
also increases as mentioned in [16].
Proceedings of 8th IRF International Conference, 04th May-2014, Pune, India, ISBN: 978-93-84209-12-4
47
Modelling and Characterization of Pmma-Film Coated Impedance Probe Dipped In Adulterated Milk
CONCLUSION
The aim of this study is to find the penetration depth of
the mobile ions through the pores to investigate
whether they reach the metal surface of the electrodes
or not. To do so, we need to know the double layer
capacitance across the electrode-electrolyte interface.
To find the double layer capacitance electrical
equivalent circuits of the probe used is evaluated using
LEVMW software which uses complex nonlinear
curve fitting. We have found double layer capacitance
for three different probes with four different test
samples. And at every case the structure of the
electrical equivalent circuit is same. The electrical
equivalent circuit returned by the LEVMW software is
validated using experimental data.The parameter of
the electrical equivalent circuit then used to find the
penetration depth of the mobile ions through the pores
of the coating film. In every case it was observed that
the penetration depth is at least hundred times less than
the coating film thickness. Hence, it can be concluded
that the ions from the test medium does not reach the
metals electrode surface, or in other way the electrode
does not contaminate the medium under test. Further
this type of probe is very simple to construct and being
rigid easy to install in a process, so can be used in
many biological applications.
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The authors would like to thanks to DST-PURSE
project and WB-DST sponsored project for their
financial support to our research work.
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Proceedings of 8th IRF International Conference, 04th May-2014, Pune, India, ISBN: 978-93-84209-12-4
48
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