Dual-Transmission Line Modeling of Electrochemical Processes in

Article pubs.acs.org/JPCB

Dual-Transmission Line Modeling of Electrochemical Processes in Polyaniline−Cellulose Ester Composite Porous Membranes Asif A. Qaiser* Department of Chemical and Materials Engineering, The University of Auckland, Private Bag 92019, Auckland, New Zealand S Supporting Information *

ABSTRACT: The charge transport processes in polyaniline (PANI) composite porous membranes have been elaborated in this study using dual-transmission line impedance model conventionally used for macroscopically homogeneous (nanoporous) membranes. Mixed cellulose ester (ME)-PANI porous membranes were prepared using various in situ chemical polymerization techniques including solutionand vapor-phase polymerizations, and two-compartment cell diaphragmatic polymerization. Each technique yielded different PANI deposition site and content in the membranes. As a result, the modeling of electrochemical impedance spectroscopy (EIS) data yielded different model parameters that have been correlated with the PANI content and deposition site (i.e., surface layering versus in-bulk deposition) in the membranes. The modeling results showed that PANI deposition enhanced charge transport by shifting the interfacial transfer mechanism at pore walls from simple double layer charging to the charge transfer involving oxidation of PANI molecular chains deposited at the pore walls of the composite membranes. In addition, in-bulk PANI deposition in the membranes by means of two-compartment cell polymerization showed several orders of magnitude faster charge transport as compared to the membranes where PANI deposited only at the surface. This study shows that porecontrolled diffusion in PANI composite porous membranes can be satisfactorily modeled using dual-transmission line model and correlated with PANI deposition site in the membranes.

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INTRODUCTION Intrinsically conducting polymers (ICPs) have drawn special attention of researchers because of their interesting electrochemical and charge conduction properties. Based on these properties, ICPs find applications in various fields such as capacitors, protective coatings, electrochromic displays, and electrochemical sensors.1 Charge conduction in ICPs takes place by the movement of both electronic (polarons) and ionic charge carriers. The involvement of ions in charge conduction process originates ICPs’ application as ion exchange films and membranes. However, in contrast to the conventional ion exchange membranes, the ionic transport in ICP membranes takes place coupled with the electronic charge transport. Due to their unique transport properties, electrochemical impedance spectroscopy (EIS) has been used as a useful characterization technique.2−14 To study the charge transport and interfacial charge transfer phenomena of ICPs in asymmetric (i.e., a coated electrode) and symmetric (i.e., a free-standing film) configurations using EIS, various models have been proposed.8,10,15 These models differ in the consideration of the nature of ICP film, which is either homogeneous or heterogeneous composed of nanosized pores.16 The heterogeneous models stem from the nodular or fibrillar morphology of ICP films that gives rise to nanopores in the bulk film. Additional differences arise from different viewpoints on whether to include or not the interfacial charge transfer in the model and the nature of the conduction process © 2014 American Chemical Society

(i.e., Faradaic versus Non-Faradaic double layer charging). Vorotynstev et al.16 proposed a homogeneous film model based on diffusion−migration phenomena representing the electron (polaron) and (counter) ion transport in ICP film coated on a metallic electrode. The model has some specific features that had not been considered in the previous homogeneous film models. These features include the incorporation of interfacial double layer charging phenomenon and unequal diffusivities of electrons and ions in the film (i.e., De ≠ Di). This model was used in various subsequent studies to investigate the effects of various cations and anions on the diffusivities and interfacial charging of ICP films.17−19 Deslouis et al.8 used Vorotynsetev’s model for a free-standing membrane configuration and compared the EIS results with that of modified electrode geometry. On the other hand, Albery et al.7,20,21 developed a transmission line model for ICP coated electrodes by assuming two-phase heterogeneous film morphology. In this model, the electronic charge passes through the polymeric film, whereas ions are transported through the electrolyte present in the nanopores of the film. Both the electronic and ionic charges are represented by the separate transmission lines which are interconnected by a charge transfer capacitance that arises from Received: September 29, 2013 Revised: June 30, 2014 Published: July 14, 2014 9686

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the electrolyte present in nanopores (Figure 1). Many researches later used this model to study the electrochemical

Article

EXPERIMENTAL SECTION

Membrane Synthesis. Mixed cellulose esters (ME)-PANI composites membranes were synthesized using various in situ chemical polymerization techniques given elsewhere.30,31 These techniques include solution-phase and vapor-phase polymerizations for PANI surface layering, and two-compartment cell diaphragmatic polymerization for in-bulk PANI deposition. In two-compartment cell polymerization, microporous ME membranes (nominal pore diameter: 0.22 μm, thickness: 180 μm) were inserted between the two compartments of the cell with an exposed area of 4.5 cm2 to the reactants. The monomer solution (0.8 M aniline in 1 M HCl) and the oxidant (0.3 M FeCl3 in 1 M HCl) were taken in the two compartments separately that counter-diffused through the membrane for varying time periods. PANI deposited mainly in the bulk of the membrane along with some surface deposition. In solutionphase polymerization, the base ME membrane was treated with a polymerizing mixture of aniline solution (0.8 M in 1 M HCl) and oxidant (0.3 M ammonium persulfate in 1 M HCl) for various time periods. In vapor-phase polymerization, ME membranes were first soaked in anilinium solution (0.8 M aniline in 1 M HCl) and then treated with oxidant’s vapors generated by heating a strong acidic solution (0.8 M ammonium persulfate in 4 M HCl) in a sealed bottle for 2 min. The membranes were subsequently washed with 1 M HCl to remove adhering PANI particles and stored in desiccators for further characterization. Membranes Characterization. PANI fraction in the membranes was measured using gravimetric technique. After PANI deposition from various employed techniques, the composite membranes were dried in desiccators for more than 7 days and then weighed. The weight difference between PANI modified and bare ME membranes yielded PANI fraction in the membranes. Scanning electron microscope (SEM) images were captured using an environmental SEM (ESEM; FEI Quanta 200F) and an SEM (Philips XL30S FEG), both equipped with energy dispersive spectroscopy (EDS) detectors. EIS was conducted in a free-standing membrane configuration by sandwiching the membranes between the two compartments of a permeation cell (exposed area: 1.13 cm2) using 1 M HCl as electrolyte on both sides. Two Pt wire electrodes were used to acquire EIS data that were attached to membranes’ surfaces in the cell. The details of the experimental setup are discussed elsewhere.29,33 A perturbation signal of 100 mV was used to excite the membranes in a wide frequency range (0.1 to 100 000 Hz) and in-phase and out-of-phase impedance components were recorded. The EIS data were converted into Bode graphs and used in the following text. The numerical modeling of the EIS data was conducted using ZSimpWin software (version 3.21). The model fitting quality was shown by recording χ2 values of the data for each curve. Membrane Notation. In the subsequent text, the membranes are denoted by membrane (ME), polymerization technique (Poly: solution-phase, P1: two-compartment cell, and Vap: vapor-phase polymerization), oxidant used (Fe or APS), polymerization time (h or min).

Figure 1. Transmission line model for modified electrode, R1 and R2 represent two resistive paths, whereas C is the capacitance.7

properties of ICP and their composites.9,22,23 However, Albery’s model does not include the interfacial phenomena taking place at the polymer/electrolyte interface. Deslouis et al.9 used the same model for a free-standing PANI membrane by changing the boundary conditions, but they also neglected the interfacial charge transfer processes. Paasch et al.24 developed an improved transmission line model for macroscopically homogeneous porous modified electrodes. They extended the dual transmission line model by incorporating short-range diffusive resistances originating from the charge transfer reactions at the walls of the nanosized pores. Additionally, these charge transfer resistances are considered distributed in nature because of the spatially distributed oxidation−reduction transitions in the bulk of the film. Rossberg et al.25,26 used the same model to study polyaniline (PANI) modified electrodes at various potentials and pH of the electrolyte. Ehrenbeck et al.10 extended the model developed by Paasch et al.24 and investigated the electrochemical processes in polypyrrole free-standing membranes using EIS. In their earlier studies, Ehrenbeck and Juttner27,28 used an older version of the model for heterogeneous films to interpret the EIS response of free-standing polypyrrole membranes with mobile and immobilized dopants. In the present study, the charge transfer/transport processes of mixed cellulose ester-polyaniline (ME-PANI) microporous membranes are elaborated using dual transmission line model originally developed and used for macroscopically homogeneous (i.e., nanoporous) membranes. These membranes were synthesized using various in situ PANI polymerization techniques. Each technique yielded specific composite membrane morphology, where PANI was either deposited on the surface and/or inside the pores of the base ME membrane. The EIS data of these composite membranes showed strong effects of the morphology on charge transport characteristics of the composite membranes as previously given for cellulose ester (CA) membranes using lumped (static) parameters modeling.29 It was anticipated that PANI deposition inside the microsized pores of ME-PANI composite membranes could show pore-controlled permeability. To elaborate this porecontrolled permeation of the ions through strong interaction between these ions and the pore walls, the dual transmission line model seemed to best fit the EIS results. The model fitting parameters showed strong influence of PANI deposition site and the extent not only on the resistance levels of both ionic and electronic transports but also on various electrochemical charge transfer processes in the composite porous membranes.

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RESULTS AND DISCUSSION Effects of Polymerization Conditions on PANI Fraction in the Membrane or on Its Deposition at the 9687

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External Surface of the Membrane. The fraction of PANI content in the composite membranes is shown in Table 1. The PANI fraction showed the following trend,

extent remained same on both sides of ME membranes in the solution- and vapor-phase polymerization techniques. X-ray photoelectron spectroscopy (XPS) and FTIR characterization of ME-PANI membranes using the employed polymerization techniques showed PANI deposition in its emarldine salt sate doped with counterions, i.e., dominantly with Cl− and up to some extent with HSO4− ions.29,30,32 However, the extent of protonation of imine sites and association of the doping anion remained highly polymerization technique and time dependent. The Bode plots of EIS data of ME-PANI membranes synthesized using various techniques are shown in Figures 3 and 4. In these plots, the (absolute) impedance and phase angle are shown as the function of frequency. The former shows the impedance to the combined (i.e., electronic and ionic) charge transport process whereas the latter shows the contribution of imaginary (capacitive) impedance to the overall impedance value (maximum at 90 deg with no real impedance component). These PANI composite membranes were doped with HCl that was also used as electrolyte in EIS studies. Figure 3 shows the Bode plots of unmodified ME and ME-PANI composite membranes synthesized using two-compartment polymerization technique whereas Figure 4 shows the plots of ME-PANI membranes synthesized using solution- and vaporphase polymerizations. These plots show significant effects of the synthesis techniques on the charge transport characteristics of the ME-PANI membranes. To visualize the change in resistive impedance component (i.e., real impedance vector) versus capacitive component (i.e., imaginary impedance vector) as a function of frequency, same data are also given in Nyquist plots (see the Supporting Information). The overall charge transport process in a porous membrane can be visualized as a combination of a charge transfer resistance (R) and a capacitance (C) where the former represents the overall resistance of the electrolyte and membrane phase and the latter can be attributed to the double layer capacitive charging of the electrolyte in the pores. However, as the result of the incorporation of electrochemically active PANI in the membranes, the pseudocapacitance of oxidation−reduction transition of PANI phase during charge transfer becomes significant and dominates the overall capacitance of the membrane. For an R−C parallel combination, the characteristic time of a charge transfer process can be defined as

Solution‐phase < Vapor‐phase < Two‐compartment cell polymerization

Table 1. PANI Fraction in ME-PANI Membranes membrane identification two-compartment cell polymerization for 2 h (ME, P1, Fe, 2 h) two-compartment cell polymerization for 6 h (ME, P1, Fe, 6 h) two-compartment cell polymerization for 22 h (ME, P1, Fe, 22 h) vapor-phase polymerization for 2 min (ME, Vap, APS, 2 min) solution-phase polymerization for 6 h (ME, Poly, Fe, 6 h) solution-phase polymerization for 24 h (ME, Poly, Fe, 24 h)

PANI fraction in ME-PANI membranes (%) 1.9 33.9 50.1 19.5 5.9 12.6

These values show that PANI fraction in the membranes strongly depends on the polymerization technique and time within a specific technique. These trends can be correlated with the membranes morphologies in terms of PANI deposition site in the base ME membranes as shown by scanning electron microscopy (SEM) discussed elsewhere.29,30,33 Briefly, PANI was deposited as a thin and discontinuous layer at the surface by solution-phase and vapor-phase polymerizations (Figure 2a−c). However, the latter technique showed some subsurface deposition, as well (up to 9 μm).30 Contrary to the solutionand vapor-phase polymerizations, PANI was deposited inside the pores of base ME membrane where it was deposited on the pore-walls in the two-compartment cell polymerization technique (Figure 2d−e). Figure 2e shows PANI deposition around the structural fibers of cellulose ester forming the pores of base ME membrane. The deposition extent of PANI in the pores increased by increasing polymerization time in the twocompartment cell along with the surface layer that more uniformly covered the surface of the base membranes and grew in thickness, as well. The cross-sectional image of the composite membrane at 22 h polymerization in the twocompartment cell clearly shows that along with the completely covering the skeleton fibers of the base membrane, PANI protruded in the form of nanotubes from one skeleton fiber to another thus forming highly interconnected layering in the pores. It is also evident that the pores remained unfilled and PANI was deposited either as a discontinuous layer at the surface along with some in-bulk deposition or it was deposited as a layer on the pore walls of the base membrane. The cross-sectional images of the membranes synthesized using two-compartment cell polymerization coupled with Fourier-transform infrared (FTIR) spectroscopy data presented previously showed that PANI was deposited asymmetrically on the both faces of the base ME membranes.29,30 PANI deposition on the aniline side of the membrane was more uniformly layered with polyaniline as compared to the opposite oxidant (FeCl3 in this case) side in the two compartment cell. For prolonged polymerization (i.e., > 22 h), both faces showed almost equal layering extent.30 In contrast, PANI layering

τ=

1 = R·C f

(1)

where τ, R, C, and f are characteristic time, resistance (Ohm), capacitance (F), and frequency (cycles/s), respectively. The characteristic frequencies (f = 1/τ) in Figures 3 and 4 are indicated by peak frequency of phase angle curve as well as by a transition in the overall absolute impedance (|Z|) curve. Both of these parameters (τ and |Z|) signify the rate and the nature of the charge transfer processes taking place in these electrochemical membranes.34 The broad phase angle peak spanning the medium-to-low frequency range for an unmodified ME membrane (Figure 3a) shows slow charge transfer processes (with large τ values) as also indicated by high impedance values (|Z|). For a highly porous and electrically insulating ME membrane, these can be attributed to the dominant diffusional charge transfer processes involving electrolyte anions in membrane pores where the high 9688

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Figure 2. SEM surface images (Magnification: 5000 X) of (a) Bare ME, (b) ME, Vap, APS, 2 min, (c) ME, Poly, Fe, 6 h, (d) ME, P1, Fe, 6 h, and (e) cross-sectional image of ME, P1, Fe, 22 h.

impedance values represent insulating nature of the membrane matrix and low-frequency represent double layer charging at pore-walls electrolyte interface. PANI fraction in the membranes synthesized by the two-compartment cell polymerization at shorter time (i.e., 2 h), introduced an additional peak at high frequency where these two peaks are widely separated in different frequency ranges (Figure 3b). The appearance of the second peak indicates two different charge transfer processes taking place in ME-PANI membranes. The high frequency peak (i.e., with lower characteristic time) coupled with the lower impedance value may be attributed to the faster electronic charge transfer in PANI phase incorporated in the composite membrane. The lower frequency peak may be assigned to slower charge transfer process taking place between the porewalls of the membranes and the electrolyte. The significant drop in the impedance value indicated the presence of PANI layer at the pore-wall that resulted in faster charge transference with the electrolyte anions. As the PANI fraction increases for longer polymerization times in the two-compartment cell polymerization (i.e., 6 and 22 h, Figure 3c,d), the impedance of ME-PANI membranes decreases and the transfer processes show two-time constant curves similar to that of 2 h

polymerization. The decrease in the impedance for both peaks shows the effects of conducting PANI phase in the composite membranes on the charge transfer rates. Figure 4 shows Bode plots of ME-PANI membranes synthesized by solution-phase and vapor-phase polymerizations of aniline. The impedance curves of the solution-phase polymerization (at 6 and 24 h polymerization) signify slow ionic charge transfer as the peaks appear at low frequencies. However, the solution-phase polymerization shows a significant drop in impedance on increasing the polymerization time from 6 to 24 h (Figure 4a,b). The impedance decreases about 1 order of magnitude due to higher PANI content in these composite membranes (Table 1). The impedance decrease shows the effect of PANI layering at the surface of the base ME membrane. The lower impedance values on prolonged polymerization times may be attributed to the combined effect on the charge transfer in solid matrix and inside the pores of the composite membranes. Vapor-phase polymerization shows two distinctive peaks indicating a two-time constant charge transfer process. However, the incomplete peak formation (half peak) at lower frequencies shows highly hindered diffusion processes 9689

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Figure 3. Bode plots of (a) unmodified ME membrane and (b,c,d) membranes synthesized using two-compartment cell polymerization for different polymerization times; (ME, P1, Fe, 2h), (ME, P1, Fe, 6h), and (ME, P1, Fe, 22h), respectively.

This impedance may be considered as a parallel combination of a double-layer capacitance (C) and charge transfer conductivity (gct). The value of gct depends on various membrane parameters, as given by

with much larger characteristic time probably due to the presence of a thick PANI layer at the surface.30,35 The charge transfer processes in pristine PANI membranes have been modeled using well-known porous membrane model by assuming PANI film morphology as nanoporous film.27,28 In this study, this model has been employed for first time for microporous PANI composite membranes. The model is based on two transmission lines, each representing electronic and ionic conduction paths, and both are linked with an interfacial capacitance and a distributed charge transfer resistance both combined to form frequency-dependent impedance (Figure 5). The transmission lines represent electronic conduction in solid ME-PANI membrane phase and ionic conduction through the electrolyte present in the pores of these membranes. The pores, either uncoated or coated with PANI, are highly multiconnected thus form a two phase membrane system comprising solid membrane matrix and electrolyte-filled pores. The linking capacitance and frequency-dependent resistance are responsible for the charge transference in the pores involving pore-walls and electrolyte ions. This charge transference is highly dependent on PANI deposition on the pore-walls as the transference mechanism is shifted from double-layer charging to the transference involving oxidation of PANI molecular chains. In Figure 5, dR1 and dR2 represent resistive lines for two types of charges, i.e., electronic and ionic, respectively, and dG represents a distributed impedance connecting these two transmission lines (here letter “d” represents ‘differential’).

gct = i0SA

F RT

(2)

where i0 is charge transfer current density, S is pore surface area per unit volume of the membrane, A is the surface area, F is Faraday’s law constant, R is the general gas law constant, and T is absolute temperature. The charge transport in ME-PANI membranes takes place by oxidation−reduction coupling of microdomains of PANI by the incorporation of ions from the electrolyte (i.e., HCl solution). Since this oxidation front progresses gradually within the membrane, the charge transfer conductivity (gct), in addition to pore surface transference also accounts for this in-homogeneous charge transport in the membrane phase.10 This charge transport in the bulk membrane phase is considered distributed instead of being a constant resistance. The charge transfer conductivity is opposed by the diffusion hindrance so the local conductivity value is modified with a frequency-dependent admittance (Y), as follows:

gct → gct Y (jω)

(3)

where Y(jω) is a dimensionless admittance, defined as 9690

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Figure 4. Bode plots of ME-PANI membranes synthesized by (a) and (b) solution-phase polymerization at various times (ME, Poly, Fe, 6 h and ME, Poly, Fe, 24 h, respectively) and (c) vapor-phase polymerization (ME, Vap, APS, 2 min).

pore length. The exponent α in eq 4 accounts for the pore length distribution (i.e., 1 − α) in the film. This leads to the final expression for the membrane impedance (Z), 2

(Z − R 0) Figure 5. Dual-transmission line model for charge transfer in microporous membranes.

⎛ jω ⎞α /2 ⎛ ω2 ⎞1/2 1 = 1 + ⎜ ⎟ coth⎜ ⎟ Y ⎝ jω ⎠ ⎝ ω3 ⎠

ρ1ρ2 ρ2 2λ A d tanh = + 2λ d ρ1 + ρ2 ρ1 + ρ2 d

(5)

where R0 is electrolyte resistance; ρ1 and ρ2 are the resistivity of ME-PANI membrane matrix and electrolyte, respectively; A and d are the area and thickness, respectively, whereas λ represents the decay length. In addition to ω2 and ω3, which represent the characteristic ionic diffusion in pores and its variation due to the pore length, two other characteristic frequencies, ω0 and ω1 have been included in the model. The ω0 represents the characteristic frequency of the charge transfer processes involving the charge

(4)

Here ω stands for the angular frequency (radians·s−1), ω2 and ω3 are the characteristic frequencies representing (anions) diffusion hindrance and space limitations due to the available

Table 2. Model Parameters of Dual Transmission Line Model for the Membranes (χ2 Values ∼10−3) membranes ME, ME, ME, ME, ME,

P1, Fe, 2 h P1, Fe, 6 h P1, Fe, 22 h Vap, APS, 2 min Poly, APS, 24 h (χ2: 3.65 × 10−2)

ρ1 (Ω)

ρ2 (Ω)

ωo (s−1)

ω1 (s−1)

ω2 (s−1)

ω3 (s−1)

467.5 42.1 54.3 1709 2.01 × 1011

2.1 3.4 2.68 1.67 0.03

584.8 1497 3508 3312 9.42 × 1014

8.0 155.8 329 0.83 7.73 × 10−7

42.9 0.07 2.9 19.55 2.72 × 10−3

0.09 1.08. 0.17 2.87 6.2 × 107

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The frequencies ω1, ω2, and ω3 represent the characteristics of electrical charge propagation through the membranes phase, ionic diffusion through the membrane and pore size limited diffusion, respectively.10 The ω1 shows a strong dependence on PANI content resulted from various specific techniques where it increases by increasing PANI content in the two-compartment cell polymerization. As discussed previously, the PANI content in the membranes coupled with the deposition site resulted from a specific polymerization technique may indicate continuity of conductive PANI network in the composite membranes. The vapor-phase polymerization yields lower ω1 value though it has higher PANI content as compared to the smaller polymerization time (2 h) in the two-compartment cell. This lower value may be explained by considering that PANI deposited in the membrane bulk in the latter technique whereas it mainly deposited on the surface in the former technique. The ionic diffusion, being a slower process, gives frequency resolution (ω2 and ω3) at lower frequencies. The ω3 has weak dependence on polymerization technique and polymerization time. However, the ω2 decreases by increasing PANI content in the bulk membrane probably due to the higher hindrance offered by the deposited PANI in the membrane. The vapor-phase polymerization also shows higher ω2 as PANI was only deposited at the surface, and there was very small inbulk deposition.

transfer conductivity (gct) and the capacitance of the double layer (Cdl) at the pore wall of the ME-PANI membrane, ωs =

CdlSA gct

(6)

whereas the charge conduction through the solid ME-PANI membrane phase is characterized by ω1,

ω1 =

K d2

(7)

Here K represents a diffusion coefficient describing the propagation of the potential in ME-PANI membrane phase whereas d has the usual meanings as described earlier. The values of various frequencies computed by applying abovediscussed dual transmission line model are given in Table 2. ME-PANI membranes with low PANI incorporation levels resulting from the shorter polymerization time (