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Abstract

The effect of annealing on the electrical and rheological properties of polymer (poly (methyl methacrylate) (PMMA) and polystyrene (PS)) composites filled with carbon black (CB) was investigated. For a composite with CB content near the electrical percolation threshold, the formation of conductive pathways during annealing has a significant impact on electrical conductivity, complex viscosity, storage modulus and loss modulus. For the annealed samples, a reduction in the electrical and rheological percolation threshold was observed. Moreover, a simple model is proposed to explain these behaviors. This finding emphasizes the differences in network formation with respect to electrical or rheological properties as both properties belong to different physical origins.

Keywords

Conductive polymer composites electrical properties rheology compression molding

Introduction

The filler network in the bulk polymer has a significant role in the electrical conductivity of the conductive polymer composites (CPCs).^1-11 With increasing conductive filler content, a drastic transition from an electric insulator to a conductor can be clearly observed when the critical filler content is reached, which is called percolation. The critical fillers content is known as the electrical percolation threshold corresponding to the formation of a conductive filler network in the polymer host. On the other hand, the rheological properties of CPCs are also influenced by the formation of filler network, and the filler network of composites can be detected by the dynamic rheological measurements.^2-6 It has been proved that the solid-like behavior of composite melt at low frequencies reveals the existence of a rheological network.

Much research efforts have been devoted to study the difference between the two percolation behaviors.^12,13 To the best of our knowledge, most researches mainly focus on the carbon nanotube (CNT) filled polymer composites.^14-17 It is well established that the rheological threshold of CNT filled polymer composites is smaller than that of electrical percolation threshold.^17-20 The difference in the percolation threshold is understood in terms of the smaller nanotube-nanotube distance required for electrical conductivity as compared to that required to impede polymer mobility. However, for carbon black (CB) filled polymer composites, some studies suggested that the rheological percolation is more difficult to achieve than the electrical percolation.^2,3 Huang et al. demonstrated that the time to form a rheological network is longer than that to form a conductive network. The CB/HDPE composites have a low electrical percolation threshold of 0.5 vol% after melt annealing at 200°C for 120 min and the rheological percolation threshold is greater than 3.1 vol%.³

Thermal annealing is proved to be a simple and efficient way to regulate the morphology and properties. For example, it is crucial to affect the filler network and electrical performance of the CPCs.^21-29 To our knowledge, there are some publications available for polymers filled with CB,^30-38 but studies on the electrical conductivity and rheological properties of carbon black based polymer composites prior to and after annealing are rare in the open literature. Therefore, it is still an interesting subject needed to be further investigated how the two percolations take place when the CB network formation before and after annealing. Accordingly, in this work, two different polymer composites composed of CB have been prepared and studied with the aim of understanding the effect of annealing on the electrical and rheological properties of the CB based polymer composites.

Experimental section

In this work, amorphous thermoplastic polymers, poly (methyl methacrylate) (PMMA) and polystyrene (PS), were used as the polymer matrix. Commercial PMMA Plexiglas 6N and PS 158N were provided by Evonik Röhm GmbH, Germany and Styrolution Group GmbH, Germany respectively. Material properties of PS and PMMA used in our work are summarized in Table 1. The carbon black used in this work was Printex® XE2 from Evonik industries. The specific surface area of the CB is about 886 m²/g as measured by the Brunauer–Emmett–Teller method and Dibutyl phthalate absorption is 380 ml/(100 g). The mean diameter of the primary particles is around 35 nm and the density at room temperature is 2.13 g/cm³. Due to strong attractive forces leads to secondary aggregates, the size of the CB aggregates is in the range of approximately 50∼200 nm.^39,40

Table 1.

Material properties of the PS and PMMA used in this study.

Polymer	T_g (°C)	Density (g/cm³)	M_w (kg/mol)	M_w/M_n
PMMA	101	1.19	85	2.07
PS	105	1.05	268	2.50

The polymer matrix and CB were mixed in an internal kneader (Haake PolyDrive, Thermo Scientific, Germany) for 8 min (200°C and 60 rpm). The PMMA/CB and PS/CB composite materials with different volume fractions is prepared (0, 1, 2, 4, 6 and 8 vol.%). Then, the samples were compression molded at 100 bars and 200°C to 2 mm thick disk-shape plates with a diameter of 25 mm. The compression times for the unannealed and annealed (AN) samples are 2 min and 2 h, respectively. Prior to the sample preparation and the measurements, the materials were dried at 80°C under vacuum for at least 12 h.

The electrical resistance of the samples was measured at room temperature for a constant voltage of 1 V using a Keithley 6487 picoammeter based on our self-made device.^6,7 The electrical conductivity $σ$ was estimated using the following equation:

σ = d / R π r^{2}

where d and r are the thickness and radius of the sample, respectively. The lower detection limit of our measurements is 10⁻¹¹ S/cm. The rheological measurements were performed at 200°C under a nitrogen atmosphere by stress-controlled rheometer (TA-ARG2, TA, USA) using a plate-plate geometry. The oscillatory frequency dependence of the complex viscosity was investigated in a frequency range between 0.01 and 100 rad/s at a stress amplitude of 100 Pa.

Results and discussion

It is well known, that the formation of conductive pathways in a composite are increased by increasing the volume concentration of conductive fillers. Accordingly, three different scenarios in a CB composite were proposed. During the annealing, we assume that (1) the free CB aggregates become mobile and are able to be connected to the existing conductive pathways to enhancement the electrical conductivity because of the effect of dynamic percolation^7,8; (2) some unstable conductive pathways were interrupted due to the Brownian motion (thermal diffusion); (3) the CB particles or primary CB aggregates tend to form secondary aggregates.^6,41 Therefore, take into account the composites after annealing, the situation is expected to become different. Herein, the CB content in Scenario II is around the electrical percolation threshold. In the Scenario I, due to the low CB content, even after annealing, there is no conductive pathways formation; nevertheless, considerable the formation of CB agglomerates, some unstable conductive pathways will be broken down after annealing in the Scenario III, leading to the decrease of the electrical conductivity. Accordingly, the electrical and rheological properties in those three situations will be different.

To investigate the percolation threshold, the electrical conductivity measurements were carried out and are plotted in Figure 1. It is observed that the electrical conductivities of the composites strongly depend on CB content and show a typical percolation behavior. According to the classical percolation theory, the relationship between electrical conductivity σ and the percolation threshold $ϕ_{c}$ is described as

σ = σ_{0} {(ϕ - ϕ_{c})}^{t} for ϕ > ϕ_{c}

where, $σ_{0}$ is the electrical conductivity of CB aggregates in the CPCs and t is the critical exponent. The percolation thresholds have been estimated from the two curves as shown in the insert of Figure 2, which are ca. 2.5 vol.% CB (2.5CB) for PS/CB composites, whereas only ca. 1.9CB for PMMA/CB composites, which is in accordance with the test results reported in previous studies.³⁴

Figure 1.

Electrical conductivity as a function of the CB loading for PMMA/CB and PS/CB composites. Insert: The log-log plot of σ versus ( $ϕ - ϕ_{c}$ ) for the composites.

Figure 2.

van Gurp-Palmen plots of phase angle (δ) vs. complex modulus (|G*|) for the neat polymers and their composites.

van Gurp-Palmen plot is commonly used to detect the rheological percolation. Therefore, this method is usually used to roughly estimate the rheological percolation of the composites. Figure 2 shows the phase angle vs. the complex modulus (|G*|). It was found that δ values of PMMA composites all below 45^o with addition of 4CB, indicating that the liquid-to-solid transitions probably occurred between 2CB and 4CB, whereas this transition occurred between 4CB and 6CB for PS composites. Above results indicate that the rheological percolation threshold of PMMA/CB and PS/CB composites is between 2CB to 4CB and between 4CB to 6CB, respectively (Table S1), and the rheological percolation threshold is higher than the electrical percolation threshold. Accordingly, for a brevity purpose, we have investigated the annealed sample composites with 1CB, 2CB and 4CB in the follow study.

Figure 3 shows the electrical conductivity as a function of the CB loading before and after annealed 2 h for CPCs. Note that, after annealing, the electrical percolation threshold is shift to a low value, which is 0.98CB for PMMA/CB composites (Figure S1) and ca. 2CB for PS/CB composites. Moreover, as shown in Figure 3, the different electrical conductivity behaviors were found for the annealed PMMA and PS composite samples with the different CB contents. According to the proposed model in Figure 4 and the results in Figure 3, the electrical conductivity of PMMA and PS composite samples can be classified as three groups: PS/CB composites with 1CB (Scenario I); PS/CB composites with 2CB and PMMA/CB composites with 1CB and 2CB (Scenario II); PS/CB and PMMA/CB composites with 4CB (Scenario III). It is therefore interesting to make a comparison between the unannealed and annealed samples for the better understanding of the conductive pathways evolved. For the Scenario I, due to the PS/CB composites have a high percolation threshold (2.5CB), 1CB in this case is hard to form conductive pathways even annealed 2 h, therefore, it is still an electric insulator. In Scenario II, it is interesting to find that electrical conductivity increases dramatically due to annealing. For example, after 2 h annealing, the electrical conductivity increased by more than 1 order of magnitude from 3.8 × 10⁻⁷ to 8.5 × 10⁻⁶ S/cm for the PMMA with 2CB; and for the PMMA with 1CB and PS with 2CB, the composites from an electric insulator become to a conductor (more than four orders of magnitude). Herein, the increase of electrical conductivity of CPCs can be attributed to the formation of new conductive pathways during the annealing treatments.^4-7 However, the electrical conductivity of both two composites slightly decreases after annealing in Scenario III. The decrease of electrical conductivity of CPCs can be attributed to breakdown of the unstable conductive pathways and the formation of secondary CB aggregates during the annealing treatments, which is in good agreement with our speculation.

Figure 3.

Electrical conductivity as a function of the CB loading for PMMA/CB and PS/CB composites without and with annealing (200°C, 2 h).

Figure 4.

Schematics of CB conductive pathways in (a) before and (b) after annealing for various scenarios. The CBs in gray spheres are originally freely individual CB particles, while the CBs in the black spheres are the separated agglomerates and/or original effective conductive pathways.

Dynamic rheology is a sensitive probe of the percolated network formed in polymer composites. The complex viscosities of the PMMA and PS with various CB loadings at 200°C before and after annealing are given in Figure 5. It is apparent from Figure 5 that annealing has a dramatic effect on the complex viscosity of the composites, especially for the CB content around the electrical percolation threshold. For example, the viscosity curve for 2CB reveals a Newtonian plateau at low frequencies for both composites, similar to the neat polymer behavior (0CB). However, the viscosity curves for the annealed samples with 2CB exhibit much steeper slope at the low frequency region.

Figure 5.

Changes in complex viscosity of the (a) PMMA and (b) PS composites with various CB contents without and with annealing for 2 h.

It is well known that a plateau of $G^{'}$ observed in the region of low frequency manifests the presence of a network or network-like structure formed in the melt.⁴² Figure 6 shows the dynamic rheological properties at 200°C for selected PMMA/CB samples prior to and after annealing at 200°C for 2 h. The results are especially notable for the 2CB sample. As shown in Figure 6(a), there does not exist a $G^{'}$ plateau at low frequencies for the unannealed sample, which implies that there is no percolated CB network in this sample. However, after annealing, the $G^{'}$ plot levels off at low frequencies, suggesting that a sample-spanning CB network has been established. Thus, the results demonstrated the formation of rheological network in the composites was shift to low content after annealing. This also provides evidence for the connection of CBs into a network. However, due to the network connectivity is primarily reflected in the elastic properties of the sample, therefore, $G^{″}$ shows less remarkable changes than $G^{'}$ during annealing. Similar increases in low frequencies $G^{'}$ and $G^{″}$ are also seen for the PS/CB composites. The rheological data are summarized in Figure 7, which shows $G^{'} / G^{″}$ before and after annealing as a function of the CB concentrations. The shifts in these results are consistent with a reduction in the percolation threshold due to annealing. Those results further indicate that the rheological percolation threshold is higher than the electrical percolation threshold regardless of unannealed or annealed samples.

Figure 6.

Effect of annealing on the storage modulus $G^{'}$ (triangles) and the loss modulus $G^{″}$ (circles) at 200°C of PMMA/CB composites containing (a) 2CB and (b) 4CB. Unannealed sample: open symbols; annealed sample: filled symbols.

Figure 7.

Effect of annealing on PS/CB and PMMA/CB composites firmness $G^{'} / G^{″}$ .

It is known that viscosity of a polymer melt filled with CBs is given by three factors: (A) entanglements of polymer chains, (B) CB aggregates and/or network,⁴³ and (C) interaction between polymer entanglements and CB aggregates and/or network.⁶ Considering the proposed model, the influence of conductive pathways on the rheological properties of CPCs is clear. (1) If there are not CB conductive pathways formation (only small CB aggregates) after annealing, the factor A is still the dominating effect, so annealing could not influence the viscosity, such as PMMA and PS composites with 1CB; (2) nevertheless, if there are conductive pathways formation, the factor B becomes the dominating effect, so the formation of new conductive pathways could influence the viscosity greatly (because they are the main macroscopic expression of factor B); (3) As the CB contents further increased, the contribution of factor C to the increase in viscosity is large (due to formation more and secondary CB aggregates), so the conductive pathway makes a negligible contribution to the viscosity. Also, note from our data (Figure 3) that the composites with 4CB concentrations restrain their conductivity after annealing. This is because, at high concentration, the primary CB aggregates can form interconnects quite easily. However, after annealing, considerable numbers of secondary CB agglomerates are formed, through thermal diffusion of primary CB aggregates. Therefore, some unstable conductive pathways will be breakdown, leading to the decreasing of electrical conductivity. Those results indicate that the situations in rheological behaviors are different form the electrical conductivity behaviors. This is attributed to those two networks are from different physical origins.

Conclusions

In this work, the evolutions of rheological and electrical conductivity properties under annealing for PMMA/CB and PS/CB composites were investigated, with particular attention given to the formation of conductive pathways. It is found that different electrical conductivity behaviors were found for the annealed samples with the different CB contents. Additionally, it was found that annealing leads to the increase of complex viscosity, storage modulus and loss modulus at low frequencies. The different situations in rheological and electrical conductivity behaviors are attributed to their networks are from different physical origins.

Supplemental material

Supplemental Material, sj-docx-1-ppc-10.1177_09673911211001277 - Electrical conductivity and rheological properties of carbon black based conductive polymer composites prior to and after annealing

Supplemental Material, sj-docx-1-ppc-10.1177_09673911211001277 for Electrical conductivity and rheological properties of carbon black based conductive polymer composites prior to and after annealing by Qingsen Gao, Jingguang Liu and Xianhu Liu in Polymers and Polymer Composites

Footnotes

Acknowledgment

We express our great thanks to the National Natural Science Foundation of China and National Key Research and Development Program of China for financial support.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (51803190) and National Key Research and Development Program of China (2016YFB0101602).

ORCID iD

Xianhu Liu

Supplemental material

Supplemental material for this article is available online.

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Supplementary Material

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