Employing impedance spectroscopy to investigate electrical conduction mechanism in polymer composite blends containing conductive masterbatch: PP/EVA/ (PP-g-MA/MWCNTS)

Impedance spectroscopy analysis has been employed to investigate the effect of melt mixing time on electrical conduction mechanism, direct contact or electron tunneling, of a polymer blend using a conductive masterbatch. A novel approach is proposed to correlate the dispersion/distribution states of conductive nanoparticles within the phases, achieved through kinetic control of the conductive masterbatch, and their impedance properties. A blend of polypropylene and ethylene-vinyl acetate copolymer (PP/EVA) was considered as a case study for the matrix. An electrically conductive masterbatch of multiwalled carbon nanotubes (MWCNTs) in polypropylene-grafted-maleic anhydride (PP-g-MA) was added to the blend. The masterbatch in varying amounts was mixed with PP/EVA in a range of 1 min–4.5 min. The co-continuous morphology of the ternary polymer blend was validated via scanning electron microscopy micrographs. The atomic force microscopy (AFM) results showed that as the mixing time of the masterbatch increases the interconnected structures within the conductive interphase decrease. Impedance spectroscopy using alternating current was employed to probe the conduction mechanism in the composite blends. The impedance spectroscopy results revealed that for samples with low mixing time, a dielectric relaxation peak occurs at high frequencies due to the existence of more conductive pathways as a consequence of the interconnected structures of the masterbatch phase. Also, the major contribution of conductance was direct contact in the samples with low mixing times while electron tunneling mechanism was considerable for the samples with high mixing times. Dielectric constant was increased as a result of interfacial polarization boosting with mixing time. The percolation threshold was considerably decreased from 0.95 v% for simultaneous direct mixing method to 0.16 v% for the masterbatch method. Graphical Abstract


Introduction
2][3][4][5][6][7] Antistatic property is the key factor in electrical/flammable/EMI packaging. 8The need of flexibility of material in antistatic packaging makes it very important to decrease percolation threshold.Because a large amount of conductive filler is required to make insulating polymers conductive which makes the polymer brittle. 9The development of material technologies in the packaging industry can help to preserve the products from damage during transportation, storage, and commercializing processes.Every year, a lot of time and energy is devoted to the enhancement of research and development in this area. 10,113][14] Electrical packaging is one of the main sections of the packaging industry.Antistatic discharge of electronic products, flammable bottles, and containers during transportation and storage due to the triboelectric effect can damage the products or causes fire.6][17] Blending these commercial polymers can improve the purposive properties for antistatic applications such as mechanical properties, film processing, and barrier ability properties. 18,19Also, in polymer blend nanocomposites the adjustability of morphology due to the segregated structure that is originated from the formation of disperse-matrix or co-continuous morphologies and the tendency of conductive nanoparticles for localization in favorite phase is desirable in academic and industry for fabrication of conductive polymer nanocomposites with widespread applications. 20,21n polymer blend nanocomposites, two important parameters that correlate with electrical conductivity and percolation threshold are first, blend morphology, i.e. cocontinuous or disperse-matrix and their domain size, and second, nanoparticles localization.The blend morphology can be altered by interfacial properties induced by several parameters such as nanoparticle localization, compatibilizer effect, mixing time, etc. [22][23][24]

Dadashi and Hashemi Motlagh
A lower percolation threshold is usually observed in co-continuous morphology as compared to disperse-matrix morphology on the condition that nanoparticles are predominantly distributed in one phase or at interphase. 22,23Liu et al. investigated Polylactic acid/Polycaprolactone/Multiwalled carbon nanotubes (PLA/PCL/MWCNTs) (70/30) blend nanocomposites.They found that electrical conductivity increases by an order of 10 and percolation threshold decreases from 0.14V% to 0.06V% when a transition from dispersed morphology to co-continuous morphology occurs.They embedded Silicone dioxide (SiO 2 ) particles in PLA to increase PLA viscosity for the development of cocontinuous morphology. 25he electrical percolation threshold dramatically decreases by the localization of nanoparticles at the interface for immiscible polymer blend nanocomposites with a cocontinuous morphology due to the confinement of a continuum electrical path.This is well known as double percolation. 26,279][30] Using an immiscible, but compatible, third polymer component as a favorable phase for nanoparticles and an interfacial agent with improved filler-polymer interactions is one of the most promising methods that has been used for changing the affinity of nanoparticles for localization at the interface. 31,32Chen et al. used acrylonitrile butadiene styrene grafted maleic anhydride (ABS-g-MA) as a compatibilizer for localizing MWCNTs at the interface of polycarbonate/acrylonitrile butadiene styrene (PC/ABS) blends.They reported an ultralow percolation threshold of 0.05 wt.% for the case of using compatibilizer as compared to 0.25 wt% without compatibilizer. 33In another study, Poothanari et al. 34 reported that the DC electrical conductivity of cocontinuous PC/PP blends is increased from 10 À12 S/cm without using compatibilizer to 0.33 S/cm using 10 wt% of PP-g-MA as compatibilizer.
PP/EVA blend is a good candidate for cost-effective antistatic films or dielectric films with a low percolation threshold.6][37] Also, PP-g-MA compatibilizer is an interfacial agent for controlling blend morphology, MWCNTs localization, and manipulating conduction properties. 38he effect of melt mixing time of a conductive composite masterbatch into a cocontinuous immiscible polymer blend on electrical behavior of the composite blend has not been reported.Also, the effect of the mixing time on mechanical and dielectric properties, at the same time, would be very useful.In this work first PP-g-MA/MWCNTs (3 v%) masterbatch is prepared through melt mixing.This masterbatch is added to PP/ EVA blend through melt mixing at varying mixing times for the masterbatch, after the complete melting of PP/EVA.The idea is to keep MWCNTs in the PP-g-MA phase, as a minor phase, which develops as a third phase in the ternary blend.The relationship between AC/DC electrical conductivity, dielectric constant, dielectric loss, rheological properties, blend morphology, MWCNTs dispersion/distribution, and tensile properties with masterbatch mixing time are investigated.For the first time the mechanism of conduction, either direct contact or electron tunneling is discussed and reported using impedance spectroscopy data.The effect of mixing time and therefore mixing state, MWCNTs distribution state, on these mechanisms are investigated.It is interesting to know how much is the power and benefits of impedance spectroscopy to address morphological changes of a polymer blend nanocomposite.Also a high electrical conductivity is expected to see for the blend with very short mixing time of masterbach but it is a question that how big is this increase and how would be its detrimental effect on mechanical properties due to poor mixing.

Sample preparation
The samples were mixed in a 60 cm 3 internal melt mixer, Misagh Afzar, Tehran, Iran, at 190°C and 60 rpm.PP-g-MA and CNT were mixed for 10 min in the internal mixer at 190°C and 60 rpm to prepare a masterbatch of PP-g-MA/CNT (3 v%).Then conductive polymer blends were prepared using this masterbatch.First PP and EVA (40/60 v%) were melt-blended at the same condition but for 6 min.Then the PP-g-MA/CNT masterbatch was added at 20 v% to the blend and mixing was continued for 1, 2.5, and 4.5 min to prepare PP/EVA/PP-g-MA/CNT (0.6 v%) blends.The nanocomposites were molded into 1.5 mm thick sheets or thin films using a hot press at 200°C, 5 min preheat, and 100 bar for 3 min.For comparison purposes a direct mixing sample was prepared by melt-mixing of all components which were added at the same time to the internal mixer and mixed for 10 min.

Characterization
Dynamic rheometry was carried out using MCR300 of Physica rheometer, Anton Paar, Austria at 190°C.First, a strain sweep test at a frequency of 1 HZ was performed on a blend composite sample to determine the linear viscoelastic region.Based on that, a strain of 1% was used for a frequency sweep of 0.1-600 HZ.The DC electrical resistivity of the samples with a conductivity of lower than 10 À4 S/cm was measured using a Keithley electrometer, model 610°C through a two-point probe method.For the samples with higher electrical conductivity, the measurements were performed by a four-point probe method (in-plane conductivity) using a DC supply IT6123 from ITECH company and a Mastech MS8050 Digital multimeter. 29,30,39A Hitachi S-4160 field emission scanning electron microscope (FE-SEM) at 10 kV accelerating voltage was used to characterize the morphology of the blends and localization of MWCNTs.The samples were immersed in liquid nitrogen for 5 min and then fractured immediately.Some of the fractured samples were etched by 1,2-Dichloroethane at 70°C.The cryo-fractured surfaces were coated with gold to make sure the surface is sufficiently electrically conductive.The tensile test was carried out by a 2 ton JJ universal testing machine, Jinjian Co, China, according to ASTM D638-10 at a crosshead speed of 20 mm/min.The static contact angle of the polymers was measured using a surface tension measurement device, CAG-20, Jikan Co at 25°C.To investigate the inductivecapacitive and dielectric properties of the samples, the impedance changes against frequency (0.1-1,000,000 (1/s)) were measured using a Sharif Solar potentiostat, Tehran, Iran, in EIS mode.An alternating voltage of 2000 mV was applied to the samples in frequency mode.A multifunctional atomic force microscopy (AFM), ARA-AFM, Ara Pajoohesh, Iran with a silicone tip was used to study the morphology and surface topology of the samples in both contact and tapping modes.The samples were cryogenically ultramicrotomed into 1 micron-thick sections using a HIS-2260 rotary microtome, mrc company, UK to obtain specimens with a smooth surface for AFM.The samples were etched with 1,2 dichloroethane at 70°C to mark the EVA phase.

MWCNTs localization in PP/PP-g-MA/EVA polymer blends
The preferred localization of MWCNTs in EVA, PP, and PP-g-MA was estimated using their surface energies.In Table 1 polar surface energy (γ p ), disperse surface energy (γ d ), total surface energy (γ) and rate of change in γ with temperature (dγ/dT) of all materials of this work at 25°C are given.Then according to equations ( 1) and (2), surface energies at 190°C were estimated by extrapolating the values at 25°C-190°C 39 : where, γ is surface energy at temperature of T, γ 0 , and T C are equation constants.
The interfacial tension of PP/MWCNTs, EVA/MWCNTs, and PP-g-MA/MWCNTs nanocomposites given in Table 2 was calculated using equation (3) (mean-geometric), and equation (4) (mean-harmonic) (3) where γ 12 , 1, 2, p, and d are interfacial tension, phase indices, polar, and dispersive part of surface energy. 40According to Table 2, EVA/MWCNTs shows the smallest interfacial tension of 2.6 mN/m.Thus, MWCNTs is thermodynamically selective toward EVA phase.PP-g-MA with an interfacial tension of 8.1 mN/m after EVA is the favorable phase for embedding the MWCNTs in itself.Therefore MWCNTs thermodynamically prefer to localize in EVA rather than PP-g-MA.Thus, MWCNTs were imbedded in PP-g-MA by using PP-g-MA/MWCNT masterbatch where the masterbatch develops as the compatibilizer at the interface of PP and EVA.In this way, conductive MWCNT particles would localize in the minor phase of compatibilizer at the interface.

Microstructure evaluation
Figure 1, shows FE-SEM micrographs of the nanocomposite blends containing PP-g-MA/ CNT masterbatch after 1 min, 2.5 min, and 4.5 min mixing.A co-continuous morphology is observed for the three samples.Also, the degree and quality of co-continuity has further developed by increasing the mixing time.A co-continuous morphology is known as the preferred morphology for lower percolation threshold in conductive polymer blends. 44,45igure 2(d), shows the AFM image of the sample with 1 min mixing time of the masterbatch.Due to the etching of EVA phase with 1,2, dicholoroethane, this phase has appeared in slightly dark color and the PP or PP-g-MA/MWCNTs phase has appeared in slightly bright color. 46According to Figure 2(d),(a) continuum structure of masterbatch with a bright color is observed for the sample with a short mixing time of 1 min.The topography images from AFM for the three mixing times of 1, 2.5 and 4 min are demonstrated in Figures 2(a)-(c).As seen a higher mixing time of masterbatch causes better homogeneity and therefore lower surface roughness.Briefly a successful co-continuous morphology of PP/EVA was developed in the samples with a continuous phase of PP-g-MA/MWCNTs masterbatch at their interface.
Further attention into AFM image in Figure 2(a) shows needle like particles i.e.MWCNTs in the PP-g-MA phase. 47The smooth bright areas are PP which is poor in CNT.The needle-like bright areas could be PP-g-MA or its interface with PP or EVA which is Dadashi and Hashemi Motlagh rich in CNT.Therefore, the wish of putting MWCNTs in a minor phase of PP-g-MA localized at the interface of PP/EVA has come true (further results are included in supplementary information, Supplementary Figure S1).

Electrical percolation threshold
Figure 3 shows the volume DC electrical conductivity versus volume fraction of MWCNT for the blends prepared through the masterbatch method with 1 min mixing time.By fitting equation ( 5), the universal percolation model, on the experimental results of Figure 3(a) percolation threshold of 0.16 v% was obtained. 48igure 4 shows the volume DC electrical conductivity versus volume fraction of MWCNT for the blends prepared through direct mixing protocol.By fitting equation ( 5) to the experimental results of Figure 4(a) percolation threshold of 0.95 v% was obtained.
Table 3 shows the parameters of the universal percolation model given in equation ( 5) for the blends prepared through masterbatch mixing or direct mixing method where, σ and σ 0 are electrical conductivity of composite and filler, P is filler volume fraction, P C is percolation threshold, and t is critical exponent.As seen by using the masterbatch method and a short mixing time the percolation threshold can be reduced up to 6 times.The exponent t is smaller for the masterbatch method which could be related to a better-developed conductive network.For example, t exponent is about 2 for a composite containing high surface area carbon black, which is smaller than t ∼ 3.5 of a composite with carbon fibers of about 3.5. 39,49,50ectrical and dielectric properties Figure 5 shows the electrical conductivity of the PP/EVA/PP-g-MA (MWCNTs 0.6 v%) blends prepared with the masterbatch method after 1, 2.5, and 4.5 min of mixing time for the masterbatch.As the mixing time has increased, the DC electrical conductivity of the samples has drastically decreased up to 4 orders of magnitude due to more distribution of the rich MWCNTs phase and probably more migration of MWCNTs from PP-g-MA to EVA.An increase in the mixing time leads to an improvement in the distribution and dispersion of compatibilizer in the PP/EVA blend and hence a decrease in the interconnected networks of MWCNTs localized in the compatibilizer.The resistance and reactance (loss factor) in a material are denoted as Z 0 for the real part and Z 00 for the imaginary part respectively, where the overall impedance (Z) is expressed as Z = Z 0 + jZ 00 , where j = √À1.Figures 6(a)-(c) shows the plots of impedance, its real part (Z 0 ), and imaginary part (Z 00 ) against frequency for the samples with 1 min, 2.5 min, and 4.5 min mixing time.Insulating materials are notable for their tendency to exhibit a significant decrease in Z 0 as the frequency of the electrical conductivity increases.The impedance and its real part have slightly decreased with an increase in the mixing time due to further dispersion/distribution of the compatibilizer as the conductive network.The frequency cutoff is the frequency at which impedance starts to decrease with frequency.Before this frequency, the major conduction mechanism is direct contact while after that the major mechanism is electron tunneling. 51As seen in Figure 6 the frequency cutoff has increased to higher frequencies as the mixing time has decreased meaning that the direct contact mechanism is more dominant at low frequencies for the sample with low mixing time.In fact, at low mixing time, a near continuous and conductive phase of PP-g-MA/ MWCNTs masterbatch exists.In Figure 6(c) a peak is observed for the storage impedance against frequency.Interestingly, there is a shift in the location of the peak for the sample with 1 min mixing time compared to the samples with 2.5 and 4.5 min mixing time.This shift can be assumed and used as an indication of a change in blend morphology or homogeneity.The peak for low mixing time occurs at a higher frequency but with less intensity.This could be due to the decrease in impedance and also the increase in the relaxation time of the polarizable dipoles to the applied AC electric field. 52Figure 6(d) shows the plot of Z 00 against Z 0 , Nyquist plot.The diameter of the Nyquist plot has increased from 0.75 × 10 6 V to 3 × 10 7 V by increasing the mixing time from 1 min to   4.5 min.Again there is a distinct difference between the size of the circle for the sample with short mixing times and that of the samples with longer mixing times.A smaller diameter is an indication of a more conducting network. 51,53The difference in the size of the circle in the Nyquist plot can be used as an indirect tool or quality control tool for morphology characterization in conductive polymer blends.
AC electrical conductivity for all the samples was calculated from equation (6).
Where, σ c , t, and A represent AC electrical conductivity of composite, thickness of specimen, and cross-sectional area of specimen, respectively. 54Figure 7 shows AC electrical conductivity versus frequency for the samples with 1 min, 2.5 min, and 4.5 min mixing time.As seen at low frequencies the sample with a short mixing time is more conductive while at high frequencies the samples with a longer mixing time are more    conducive.This is due to the more homogeneity and higher number of conductive islands in the samples with longer mixing time which have higher potential for electrical tunneling at high frequencies while their islands are not useful at low frequencies for the direct contact mechanism of conduction.In other words, the frequency cutoff for the onset of tunneling occurs faster in the samples with more homogeneity.According to Figure 6 and Figure 7, electrical conductivity decreases with increasing the mixing time, below a critical frequency, but after that frequency, the trend is the opposite.The samples with a high mixing time have a chance for better dispersion/ distribution.In this regard, more nanoparticles with less particle-particle distances will be expected and also, electron tunneling process is the most possible conduction mechanism in the systems with high mixing time.Based on Simmons approximation, when the applied electrical energy increases, as a consequence of increase in frequency, electron conduction mechanism boosts over direct contact mechanism due to increasing electron tunneling current, after a critical frequency. 55In other words, the samples with high mixing time and therefore a higher degree of dispersion/distribution are potentially able to start electron tunneling which becomes active after a critical frequency.
where, ε 0 is vacuum permittivity equal to 8.85 × 10 12 F.m À1 , ω is frequency (1/s), A is the cross section of specimen, and d is the thickness of specimen.Figure 8 shows the effect of mixing time on the dielectric properties of the samples. 56 improvement in masterbatch dispersion and therefore an increase in the number of nanocapacitor units.According to Maxwell-Wagner-Sillars theory, an increase in the interfacial polarization of polarizable dipoles occurs, and subsequently dielectric constant increases. 57In Figure 8(b) the slope of dielectric loss against frequency shows how electrons are conducted through the samples.Electron conduction is controlled by direct contact, as much as the slope of this graph is close to 1, otherwise, electron tunneling is dominant.By fitting the experimental data in Figure 8(b) with a linear equation, the slope of the graph was obtained as 0.56, 0.36, and 0.24 for 1 min, 2.5 min, and 4.5 min mixing time, respectively meaning that direct contact mechanism is more contributing for the sample with short mixing time. 58

Rheological assessments
0][61] In this way, Figure 9 shows the plots of storage modulus (G 0 ), loss modulus (G 00 ), and complex viscosity (η*) vs frequency for the samples with 1 min, 2.5 min, and 4.5 min of mixing time.As seen G 0 , G 00 and η* increase by increasing the mixing time due to more dispersion/distribution of CNTs in the blends.Han plot (log G 0 -log G 00 ) is a  well-known plot for investigating the miscibility of polymer blends and multiphase systems. 62igure 10 shows the Han plots for the samples with 1 min, 2.5 min, and 4.5 min mixing time.
The linearity trend of the plots at low frequencies is an indication of the homogeneity of the blends.As the mixing time has decreased to 1 min, a small deviation from linearity is observed at lower frequencies. 63Figure 11 shows Cole-Cole plots (ƞ 00 -ƞ 0 ) of the samples.The height of semi-arcs has increased with mixing time.A higher peak shows more homogenization which takes place with increased mixing time of the PP-g-MA compatibilizer. 64

3.6-Mechanical properties
Figure 12 shows the average tensile stress-strain curves of PP/EVA/PP-g-MA (MWCNTs 0.6 v%) at varying mixing times of 1 min, 2.5 min, and 4.5 min.As seen all the samples  are ductile and the short mixing time has not caused a severe effect on the tensile properties. 65It is interesting that a monotonic yield behavior is observed for the samples with longer mixing times while for the sample with the short mixing time a nonmonotonic yield behavior is observed.A nominal yield elongation of 40% can be assigned to the sample with 1 min mixing time.The results of tensile tests are tabulated in Table 4.
Tensile strength, elongation at break, and toughness have slightly improved with increasing mixing time due to the reduction of interfacial tension originating from the development of compatibilizer dispersion in the polypropylene phase and the migration of some of it towards the interface.

Conclusion
In this research, the effect of mixing time of PP-g-MA/MWCNTs masterbatch into a PP/EVA polymer blend on dielectric properties and electrical conductivity in AC and DC mode was studied.SEM and AFM results confirmed a co-continuous morphology for PP/EVA/PP-g-MA blends.A very low percolation threshold of 0.16 v% was obtained for the sample with a short mixing time of 1 min.For the direct method of mixing of all components at once, a percolation threshold of 0.95 v% was obtained.The results indicated that with an increase in the mixing time, the interfacial polarization increased which led to an increase in the dielectric constant due to a better distribution/dispersion of the masterbatch and an increase in the number of conductive nano-units according to Maxwell-Wagner-Sillars theory.Also, the results of impedance spectroscopy showed the interplay of the two electrical conduction mechanisms i.e. at low mixing time electrical contact was the main mechanism of conduction while at higher mixing time electron tunneling became the main mechanism of electrical conduction.It was interesting to also see that direct contact was the main mechanism for the sample with a low mixing time before the frequency cutoff.Before the frequency cutoff, the impedance decreased with a decrease in mixing time but after that, the trend was the opposite.The Nyquist plots revealed that as the particle distances decreases due to a higher degree of dispersion at a higher mixing time, the center of the semicircle shifts to a lower frequency.Therefore, this shift can be used as a tool to identify the dispersion/distribution state of a nanofiller in a matrix.The complementary results of rheology, mechanical properties, and microstructural examination validated the loss of interconnected conductive networks at a longer mixing time of the masterbatch.The use of impedance spectroscopy to investigate conduction mechanisam or conductive filler dispersion/distribution or blend morphology is applicable to all conductive nanocomposite materials with an insulating matrix.

Figure 2 .
Figure 2. AFM in tapping mode topography images of a) 1 min, b) 2.5 min, and c) 4.5 min samples, and d) AFM contact mode image of 1 min sample.

Figure 4 .
Figure 4. Log (volume electrical conductivity) vs MWCNTs volume fraction for simultaneous mixing of all components.

Figure 6 .
Figure 6.Plots of a) impedance, b) storage impedance, c) loss impedance versus frequency and d) Nyquist plots for mixing times of 1min, 2.5 min, and 4.5 min.

Figure 8 (
Figure 8. a) dielectric constant and b) loss dielectric for 1 min, 2.5 min, and 4.5 min samples.

Figure 9 .
Figure 9. Plots of a) complex viscosity, b) loss modulus and c) storage modulus versus frequency on the left with their magnified images on the right, for the mixing time of 1 min, 2.5 min and 4.5 min.

Figure 10 .
Figure 10.Han plots of a) 1 min, 2.5 min and 4.5 min samples and b) magnified image.

Figure 11 .
Figure 11.Cole-Cole plots of a) 1 min, 2.5 min and 4.5 min samples and b) magnified image.
*measured in this work.

Table 3 .
σ 0, pc, and t for prepared samples by masterbatch and direct mixing methods.

Table 4 .
Tensile strength, elongation at break, and toughness for 1 min, 2.5 min, and 4.5 min samples.