Polypropylene–graphene – a nanocomposite that can be converted into a meta-material at desired frequencies

Abstract

Meta material (having negative dielectric constant) characteristics were observed in polymeric nanocomposites consisting of polypropylene and graphene. By varying the concentration of graphene the frequency at which the meta material was converted into a positive dielectric material was controlled. At percolation thresholds the dielectric constant had maximum negative values at low frequencies and high positive dielectric constant values at high frequencies. The dielectric measurements reveal that low concentrations of graphene affect the relaxation behavior greatly due to the modifications in the internal field in the nanocomposites by graphene. Also at low concentrations of graphene (less than 5%) the electrical conductivity and thermal loss decreased indicating that graphene acts as trappers of mobile charges and phonons. The dielectric loss at high frequencies near the percolation threshold was also less, indicating that this nanocomposite can also be potentially used as a high dielectric constant material for micro electronics. The dielectric constants obeyed a power law and the percolation was found to be at about 35 weight percent of graphene. A model is proposed for the dielectric behavior of the polypropylene–graphene nanocomposites. We hope that by tuning the frequency of conversion of positive dielectric constant material to meta material we can create new materials that have the advantages of both meta materials and high dielectric constant materials. Also, this conducting nanocomposite is made of polypropylene which is a corrosion resistant polymer and graphene. Therefore, it is hoped that this nanocomposite will have applications in batteries where preventing corrosion is essential. This research may benefit metamaterials research and polymeric nanocomposites for batteries.

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1. Introduction

Meta materials are materials with a negative refractive index.^1,2 Meta materials have properties such as negative refractive index, reversed Doppler effect, and reversed Cherenkov radiation that do not exist in natural materials. Meta materials have various applications such as in cloaking, wave filters and improvement of antenna performance.^3–6 Meta materials have been formed structurally^7–12 and by using conducting metallic nanoparticles.^13–15 Recently polymeric materials have also been used to make meta materials.^16–18 Polymeric nanocomposites attract great interest due to its advantages such as light weight, tunable mechanical, magnetic and electrical characteristics. Having a conducting and corrosion resistant polymer nanocomposite as electrodes will be of great benefit in batteries. Polypropylene has the advantage of having high corrosion resistance while it has poor conductivity. We reasoned that the inclusion of graphene in polypropylene would make the nanocomposite a good conductor. Recently Graphene has received wide attention as fillers. Graphene has a fascinating two-dimensional, honeycomb lattice arrangement made of carbon atoms and has very unique properties.^19–22 Graphene has several applications such as in composites, sensors and electronics.^23–25 Recently response of graphene oxide and Ni nanoparticles to electromagnetic waves in the microwave regime has been examined using permittivity and permeability.^26,27

We have in this article investigated the effect of incorporation of graphene in polypropylene matrix by using dielectric relaxation spectroscopy in the frequency range 0.1–1 M Hz. The study of modifications in the electrical characteristics of polymer nanocomposites due to incorporation of graphene would greatly benefit the field of nanocomposites. Dielectric relaxation spectroscopy (DRS) has been found to be a very useful tool in studying polymer dynamics.^28,29 It can help us understand the various relaxations that occur in polymers subjected to an AC field. Recently Jiahua Zhu et al.¹⁸ have shown that the switching frequency (the frequency at which the dielectric constant changes signs) depended upon the concentration of graphene in polyaniline (PANI) nanocomposites. In our research we have used SEM and also studied the dielectric parameters such as dielectric constant, dielectric loss, loss tangent, electric modulus, impedance and conductivity from 0.1 to 1 MHz. In this research Meta material formation in polypropylene–graphene nanocomposites by controlling the graphene concentration has been investigated. We have controlled the switching frequencies in these nanocomposites by varying the concentration of graphene. We have also studied the dependence of dielectric constant upon the frequency at high frequencies and have observed that these nanocomposites can also have high dielectric constant values with low values of loss tangent making these polypropylene–graphene nanocomposites as potential materials for batteries and microelectronics as they have less loss at high frequencies. We have proposed a model for the dielectric behavior of polypropylene–graphene nanocomposites.

2. Experimental section

2.1. Reagents

Graphene nano platelets – grade H25 were obtained from XG sciences, USA. The nano platelets have an average thickness of approximately 15 nanometers and a typical surface area of 60–80 m² g⁻¹. The average particle diameter is 25 μm. Polypropylene was purchased from Sigma Aldrich, USA.

2.2. Preparation of samples for dielectric measurements

Polypropylene and graphene were mixed in appropriate weight proportions using plasti-corder (brabender). The samples were then hot pressed between brass electrodes. The samples were made in the shape of disc of 1 mm thickness and 2 cm diameter.

2.3. SEM measurements

The morphology was studied by using SUPRA 55 FESEM/EDX, Carl Zeiss, Germany. The electron gun was operated at 30 kV. The instrumental resolution was 1.4 nm at 15 kV.

2.4. Dielectric and conductivity measurements

The dielectric and conductivity measurements were obtained using the broadband dielectric spectrometer (BDS) Novo control technology (Germany) concept 80 at 1 V AC signal. The frequency range was from 0.1 Hz to 1 MHz. The samples were placed between two gold electrodes for measurements. The measurements were made at room temperature.

3. Results and discussions

3.1. SEM measurements

Fig. 1 shows the SEM images of fractures surfaces (parallel to direction of pressing in the hot press for sandwiching the samples between the electrodes) of polypropylene–graphene nanocomposites containing 0, 5, 20 and 30% graphene. It is observed that pure polypropylene is nearly smooth (Fig. 1A). For 5% graphene dents are observed at several regions and they are well separated (Fig. 1B). The graphene can be identified by their sharp edges (shown using arrows). As the concentration is increased to 20% and higher the surface becomes rough. For 30% graphene several sheets touch each other (Fig. 1D). This indicates that percolation can happen for the nanocomposites with ∼30% graphene.

Fig. 1 SEM images of (A) pure polypropylene (B) polypropylene–5% graphene (C) polypropylene–20% graphene and (D) polypropylene–30% graphene nanocomposites. Scale bar is 10 μm.

3.2. Dielectric measurements

The results of the dielectric measurements involving dielectric constant, loss, tangent, loss tangent, Nyquist plot and electric modulus are discussed us under.

3.2.1. Dielectric constant (ε′). Fig. 2 shows the dependence of dielectric constant of pure polypropylene and polypropylene–graphene nanocomposites on frequency. Fig. 2A shows the dependence of ε′ upon frequency for all the samples. Fig. 2B–D shows the various sections in Fig. 2A for clarity as the spectra for 30% and 40% graphene nanocomposite dominate and mask the spectras of other nanocomposites with lesser graphene contents. It is observed from Fig. 2A (inset) that the ε′ changes from positive to negative at ∼1800 and 480 Hz for polypropylene–40% graphene and polypropylene–30% graphene. It is observed that the dielectric constant decreases rapidly to ∼−10⁷ as the frequency decreases to 0.1 Hz. Fig. 2B shows that that ε′ also changes from positive to negative at ∼2.8 and 0.5 Hz for polypropylene–20% graphene and polypropylene–10% graphene. It is observed that the ε′ becomes more negative as the graphene concentration is increased. Hence polypropylene–graphene nanocomposites with more than 10% graphene are metamaterials at low frequency regimes. The huge negative dielectric constant of the nanocomposite composite membranes in the low frequency region is attributable to the combination of interfacial polarization effects and space charge polarization effects as a result of huge electric charge accumulation around graphene and structural defects in the polymer matrix.¹⁶

Fig. 2 Dependence of dielectric constant of pure polypropylene and polypropylene–graphene nanocomposites on frequency at room temperature.

Fig. 2C shows the dependence of ε′ upon frequency for pure polypropylene and polypropylene–graphene nanocomposites with (1, 2 and 5% graphene). It is observed that the ε′ is positive for all frequency (0.1–10⁶ Hz). Fig. 2C shows that ε′ for pure polypropylene lies in the range 3–2.5 for frequency range from 0.1–10⁶ Hz. Inclusion of graphene (1%) reduced ε′ to 2.5. Also ε′ increased to 3.1 and 3.6 with increase in graphene concentrations (2 and 5%). Interestingly it is observed that the profile of the spectra is almost constant from 1–10⁶ Hz for polypropylene–graphene nanocomposites when compared to that of pure polypropylene which decreases and shows a peak in the (10⁴–10⁶ Hz). This indicates that the relaxation of polypropylene is highly influenced by the presence of graphene. Fig. 2D shows that ε′ increases as graphene concentration increased to 30% and then it decreases. The ε′ for nanocomposites with graphene concentrations of 10, 20, 30 and 40% in the frequency range from 10⁴–10⁶ Hz are 12–7.6, 14.4–7.2, 193–174 and 71–52. This indicates that polypropylene–graphene nanocomposites are high dielectric constant materials at high frequencies (greater than 10⁴ Hz). Interestingly the dielectric constant decreased when the concentration of graphene was increased to 40%. This indicates that there must be an optimum ratio between the concentrations of the polymer and graphene for it to be a high dielectric constant material. The high dielectric values for the nanocomposites occur at insulator – conductor percolation threshold.^30–33 Since the dielectric constant value is highest at high frequencies for polypropylene–30% graphene nanocomposites, this indicates that percolation occurs at ∼30% graphene concentration.

3.2.2. Dielectric loss (ε′′). Fig. 3 shows the dependence of loss upon applied frequency. The dielectric loss is a measure of the energy loss in the material.³⁴ It is observed that pure polypropylene has two relaxation peaks in the range 100–1000 Hz and 10⁴–10⁶ Hz. Inclusion of graphene affected the relaxations. A broad and very less intense relaxation was observed for polypropylene–1% graphene at ∼1000 Hz. Relaxations were completely absent for higher concentrations of graphene. Since the relaxations are absent for concentrations of graphene as low as 2%, this indicates that the local field has got modified due to the presence of graphene and therefore the response of the field sensitive groups to the applied filed in polypropylene has been affected. It is also observed that as the concentration of graphene increased the ε′′ decreased initially (till 2% graphene) and then increased. For all graphene concentrations less than 5%, the dielectric loss values for all frequencies were lesser than that of pure polypropylene. This reduction in dielectric loss is due to the reduction in heat loss indicating that at low concentrations (less than 5% graphene) the graphene acts as phonon trappers. As the concentration of graphene increases to 10% and more, the ε′′ increases rapidly. The profile is nearly a straight line for graphene concentrations greater than 10%. The high values of ε′′ for higher concentrations of graphene indicates heat loss through dissipation. Hence when the graphene concentration reaches the percolation threshold (30%), the localized phonons get delocalized leading to higher heat dissipation.

Fig. 3 Dependence of dielectric loss of pure polypropylene and polypropylene–graphene nanocomposites on frequency at room temperature.

3.2.3. Loss tangent (tan δ). Fig. 4 shows the dependence of loss tangent of pure polypropylene and polypropylene graphene nanocomposites upon frequency. It is observed that polypropylene has peaks in the range 10²–10⁴ Hz and 10⁴–10⁶ Hz. It is observed that the peaks disappear as the concentration of graphene increases to 5% (Fig. 4A). As the concentration of graphene is further increased peaks appear. Sharp negative peaks followed by positive peaks are observed for the nanocomposites with graphene concentrations greater then 10%. The switching frequencies are at 0.4, 385 and 1470 Hz for nanocomposites with 20, 30 and 40% graphene. The appearance of the peak in the tan δ is attributed to the resonance effect for which the system tends to oscillate with greater amplitude than others at certain frequencies. This is especially for the negative permittivity values.³⁵

Fig. 4 Dependence of loss tangent of pure polypropylene and polypropylene–graphene nanocomposites on frequency at room temperature.

The frequencies corresponding to the shift in loss tangent values from negative values to positive values coincide with those frequencies for which the dielectric constant changes from negative (meta material region) to positive values. The inset in Fig. 4B shows the dependence of loss tangent upon frequency for the nanocomposites at high frequency range (10⁵–10⁷ Hz). It is observed that the loss vale is very less at high frequencies for all the nanocomposites suggesting that this material can be used in microelectronic devices.³⁶ This indicates that by varying the concentration of graphene, the switching frequencies below which the material acts as a meta material and above which it acts as a high dielectric constant material can be controlled.

3.2.4. Electric modulus. Fig. 5 shows the dependence of M′ and M′′ upon frequency for polypropylene–graphene nanocomposites at room temperature. It is observed that the M′ drastically decrease as the concentration of graphene increases. It is also observed that as the graphene concentration increases from 1 to 5% the M′ become more plateau like from ∼1 Hz to 1 M Hz when compared to that of pure polypropylene. This is because since both ε′ and ε′′ become plateau like due to modification of the internal field due to graphene. M′ is a maximum at 1% graphene and then it decreases with increasing graphene concentrations. At graphene concentrations of 30% and above, the M′ is nearly non existent. Since the dielectric constant values are high at high concentrations of graphene the electric modulus (M′) becomes less for high concentrations of graphene. For M′′ it was observed that peaks were present for pure polypropylene between the frequency ranges of 0.1 to 1, 10² to 10³ and 10⁴ to 10⁶ Hz respectively. Upon addition of graphene till 5% the peaks vanished for higher frequencies. The peak at lower frequency range (between 0.1 to 1 Hz) shifted to lower values as the concentration decreased to 5%. This lowering indicates reduction in the DC conductivity.¹⁶ The reduction in the conductivity for low concentrations of graphene implies that graphene traps some of the charges. For graphene concentrations of 10% and more, new peaks are formed at frequencies different from that of pure polypropylene. This indicates that new relaxations formed. This relaxation is attributable to Maxwell–Wagner–Sillars (MWS) effect. The MWS relaxations occur due to the transfer of free charges towards the polypropylene–graphene interface under the effect of an AC electric field. This is caused due to difference in the dielectric properties between graphene and polypropylene which causes interfacial polarization. As the concentration of the graphene increases from 10 to 40%, the position of the peaks shifts to higher frequencies. This indicates enhancement in DC conductivity.¹⁶ Also, the M′′ peaks for nanocomposites with 30 and 40% are lesser in intensity when compared to that of nanocomposite with 10 and 20% graphene. This indicates that the MWS relaxations become weak indicating that the charges migrate from the polymer–graphene interfaces. This is attributable to percolation that leads to transport of charges through the conducting graphene channels.

Fig. 5 Dependence of (A) M′ and (B) M′′ upon frequency for polypropylene–graphene nanocomposites at room temperature.

3.2.5. Conductivity measurements. The AC conductivity usually consists of a frequency independent plateau at low frequencies and dispersive phenomena at high frequency in variety of ionic materials. This behavior follows Jonscher's universal power law³⁷

σ(ω) = σ_dc + Aωⁿ (1)

where, σ_dc is the dc conductivity at low frequency, A is the pre-exponential factor and n is the fractional exponent between 0 and 1. Jonscher also attributed the frequency dependence ac conduction mechanism to hopping process between the charge carriers in the polymer matrix. Fig. 6A shows the dependence of conductivity upon frequency for polypropylene–graphene nanocomposites at room temperature. It is observed that the conductivity is more linear for samples containing graphene when compared to pure polypropylene. As the concentration of graphene is increased from 0 to 5%, the conductivities of the nanocomposites is lesser at all frequencies when compared to that of pure polypropylene. As the concentration is further increased, the conductivity increases and reaches a maximum for nanocomposites with 40% graphene. Fig. 6B shows the dependence of conductivity measured at 0.1 Hz for the nanocomposites at room temperature. This corresponds to DC conductivity³⁷ as the frequency is low and the spectras have constant values at low frequency ranges for all these nanocomposites. It is observed that for low concentration of graphene the conductivity seems to get lesser while for graphene concentrations greater then 10% the conductivity increases drastically by several orders of magnitude and it reaches a steady value for polypropylene–graphene nanocomposites with 30% graphene. The percolation concentration can be considered as the minimum concentration of the filler at which the conductivity reaches a saturation value. Therefore the percolation concentration is ∼30%. The initial decrease in the conductivity shows the same trend as observed for dependence of M′′ on the frequency for the nanocomposites.

Fig. 6 (A) Dependence of conductivity upon frequency for polypropylene–graphene Nanocomposites and (B) dependence of conductivity (at 0.1 Hz) upon concentration graphene in polypropylene–graphene nanocomposites at room temperature.

3.2.6. Nyquist plots. In the conductivity plots the values for conductivity for low concentration of graphene is very close. Hence for greater clarity the Nyquist plots were plotted. Fig. 7 shows the Nyquist plots for the polypropylene–graphene nanocomposites. The bulk resistance (R_b) can be found by knowing the intercept of the semi circle. Since the plots are arcs of semi circles it implies that the conduction is through ions. From the plots in Fig. 7A it is inferred that the bulk resistance increases as the concentration of graphene increases from 0 to 5%. As the concentration of graphene further increases it is observed that the resistance decreases. Fig. 7B shows the Nyquist plots for the nanocomposites with 10 and 20% graphene where both the x and y axis were plotted using log scales as the differences between their resistance is large and both spectra could not be shown clearly in the same graph when both axis were plotted in linear scale as in Fig. 7A and C. When plotted separately using linear scales for x and y axis the spectras for nanocomposites with 10% graphene did looks as arcs of circles as in Fig. 7A and C. Fig. 7C shows the Nyquist plots for nanocomposite with 30 and 40% graphene. It is observed from Fig. 7b and C that when the concentration of graphene is increased from 10 to 40%, the intercepts decrease indicating that the bulk resistance decreases. Hence from the Nyquist plots it is clear that the conductivity decreases when the concentration of graphene in the polypropylene–graphene nanocomposites increases from 0 to 5% and then the conductivity increases when the concentration of graphene increases from 10 to 40%. The results are in agreement with the inferences made using M′′ and conductivity studies.

Fig. 7 Nyquist plots for polypropylene–graphene nanocomposites at room temperature.

3.2.7. Complex plane for the electric modulus. Fig. 8 shows the complex plane of the electric modulus for the polypropylene–graphene nanocomposites. The formation of a semi circle implies idealized Debye model with a single relaxation time. Also, the radius of the arc of the complex planes diagram is dependent upon the electrical conductivity of the material. If the radius of the arc is small then the material has higher electrical conductivity.^38,39 It is observed that the plot for polypropylene has two semi circles indicating that there are two relaxations. With addition of graphene from 1 to 5%, only one semi circle is observed. Also the radius of the arcs increases as the concentration of graphene increases to 5%. This indicates that the electrical conductivity is less for the nanocomposites with graphene concentrations of upto 5%. It is also observed that for the nanocomposites with 10% graphene concentration two semi circles are formed indicating the formation of new relaxation. This is in agreement with the results obtained using electric modulus. As the concentration is further increased it is observed that not complete semi circles are formed and that their arc radius decreases indicating that the conductivity increases. These results are in agreement with the inferences made earlier using other dielectric parameters.

Fig. 8 Complex plane of the electric modulus for polypropylene–graphene nanocomposites at room temperature.

3.2.8. Determination of concentration of graphene at percolation. The percolation threshold can be calculated according to the power law⁴⁰

K_eff ∝ K_{polypropylene}(fc − f)^−s for f < fc (2)

where K_eff represents the dielectric constant of the composites, K_{polypropylene} is the dielectric constant of polypropylene, f is the volume fraction of the filler (graphene), fc is the percolation threshold and s is the critical exponent. Taking logarithm on both sides of the eqn (1) gives log(K_eff/K_{polypropylene}) = log C − s log(fc − f) where C is the proportionality constant. The volume fraction of graphene in the nanocomposites for 1,2,5,10,20 and 30 wt% of graphene were calculated to be 0.42, 0.86, 2.19, 4.53, 9.65 and 15.4% respectively by taking the density of graphene as 2.2 g cm⁻³ and the density of polypropylene as 0.94 g cm⁻³. Numerical fitting of the experimental data gives a threshold value of 35% graphene. Also, to further verify the result log(K_eff/K_{polypropylene}) was plotted against log(fc − f) (Fig. 9). The data could be fitted with a straight line with negative slope and R value of 0.94. This indicates that the power law indeed could be used for our nanocomposites and that the percolation happens at a graphene concentration of ∼35%. This is in close agreement with results obtained using conductivity measurements.

Fig. 9 The dependence of the ratio of the dielectric permittivity of the nanocomposites and pure polypropylene on the volume fraction of graphene measured at room temperature and 10⁵ Hz.

4. Conclusions

Based on the results above the following model is proposed for dielectric behavior of poly-propylene graphene nanocomposites. When small amount of graphene (less than 5 wt%) is added to polypropylene, the graphene traps phonon and mobile charges. This leads to decrease in the heat loss and conductivity of the polypropylene–graphene nanocomposites. The presence of graphene also modifies the local electric field and therefore affects the response of the field sensitive groups to the applied AC field. As the concentration of graphene is further increased, due to interfacial polarization effect and space charge polarization effect caused due to accumulation of charges at the interface between graphene and polypropylene the dielectric constant becomes negative at low frequencies leading to meta material formation (Fig. 10B and C). Also, the conductivity increases due to percolation effects. As the graphene concentration approaches percolation threshold the dielectric constant increases and becomes a high dielectric constant material. By changing the concentration of graphene it is possible to control the frequency to make the material as a meta material.

Fig. 10 Model for dielectric behavior of poly-propylene graphene nanocomposites.

Acknowledgements

This research was made possible due to funding provided by University Grants Commission – INDIA under Raman fellowship for Postdoctoral Studies in USA under Indo-US 21^st Century Knowledge Initiative to one of the authors (Radha Perumal Ramasamy) and the NSF-Inspire program – USA.

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