^{1,2}, A. Mdarhri

^{3}, C. Prunier

^{2}, B. Haidar

^{4}and C. Brosseau

^{2,a)}

### Abstract

Multiple-walled carbon nanotube (CNT)-and carbon black (CB)-polymer composites have been fabricated by mechanical mixing with different loadings, the polymeric matrix being identical between the two series of samples. The main focus of this work is to report measurements of physical properties of these mixtures in ambient conditions and to discuss the origin of similarities and differences among them according the kind of carbonaceous filler. The uniform dispersion of the carbonaceous phase in the dielectric matrix was probed by high-resolution transmission electron microscopy. The good dispersibility of the filler particle is also reflected in the much lower conduction threshold observed for CNT-containing samples than in the CB composites. This is likely due to the high aspect ratio of the CNTs.Mechanical properties show that the storage modulus of the two kinds of samples is close to the modulus value of the neat styrene-butadiene rubber (SBR), independent of filler content over a wide range of compositions encompassing the percolation threshold. Microwave measurements show that the real part of the effective permittivity exhibits a flat frequency response, with the exception of the sample containing CB for which an inverse-power law is observed revealing a behavior that has been seen for many random heterogeneous soft materials. No resonant dielectric absorption is evidenced within the frequency range explored and for the filler concentrations investigated. The results were also compared with analytical effective (mean-field) models. The symmetric Bruggeman model is in very good agreement with the microwave effective permittivity once account is taken of the depolarization factor which is close to the value found for a three-dimensional (3D) random dispersion of monodisperse spherical conductive inclusions within a dielectric matrix. By combining microwave frequency-domain spectroscopy with uniaxial tension, we obtain the effective permittivity as a function of the elongation ratio. Our results indicate that the effective permittivity spectrum of the CNT-polymer samples and their CB-based counterparts is not very sensitive to the applied stress in the range of elongation ratios explored. For the sample containing CB, the relative variation in the effective permittivity as a function of the elongation ratio is well described by the Gaussian molecular network model. The experimentally determined mechanical and microwaveproperties of these nanocomposites is related to the change in the mesostructure, formed by the heterogeneous 3D interconnected network of polymer and of aggregates (or agglomerates) of filler particles, as the composite is stretched. The results of this study provide another insight and opportunities to the comprehension of multifunctional materials, including novel nanoelectronic components, and carbon-based systems.

One of the authors (B.J.-P.A.) gratefully acknowledges the hospitality and financial support of Université de Brest where part of this work was done. Lab-STICC is Unité Mixte de Recherche CNRS 3192. MATEIS is Unité Mixte de Recherche CNRS 5510. IS2M is Laboratoire Commun de Recherche LRC CNRS 7228.

I. INTRODUCTION

A. Background

B. Objectives

II. EXPERIMENT

A. Materials

B. Morphology

C. Mechanical experiments

D. dc conductivity characterization

E. Electromagnetic characterization

III. RESULTS AND DISCUSSION

A. Storage modulus

B. dc conductivity

C. Permittivity

D. Permittivity under uniaxial tension

IV. CONCLUDING REMARKS AND FUTURE DIRECTIONS

### Key Topics

- Carbon nanotubes
- 56.0
- Polymers
- 33.0
- Composite materials
- 23.0
- Permittivity
- 23.0
- Materials properties
- 19.0

## Figures

TEM micrograph of: (a) individual MWCNTs and (b) CB particles.

TEM micrograph of: (a) individual MWCNTs and (b) CB particles.

TEM images of ultracryomicrotomed samples of (a) CB-SBR for and (b) CNT-SBR for .

TEM images of ultracryomicrotomed samples of (a) CB-SBR for and (b) CNT-SBR for .

Storage modulus as a function of the filler volume fraction. The symbols used in this figure are: (○) CB and (◻) CNT. Room temperature. The curve is a fit to the Einstein equation, with .

Storage modulus as a function of the filler volume fraction. The symbols used in this figure are: (○) CB and (◻) CNT. Room temperature. The curve is a fit to the Einstein equation, with .

Dc conductivity of CB-(top) and CNT-(bottom) polymer samples plotted against . Room temperature. From these graphs, the conduction transition volume fraction is estimated to be for the CB-SBR samples and for the, respectively, CNT-SBR samples. More data points are necessary to determine the onset conductivity accurately.

Dc conductivity of CB-(top) and CNT-(bottom) polymer samples plotted against . Room temperature. From these graphs, the conduction transition volume fraction is estimated to be for the CB-SBR samples and for the, respectively, CNT-SBR samples. More data points are necessary to determine the onset conductivity accurately.

(a) Frequency dependence of the real part of the effective complex (relative) permittivity of SBR/CB composites for several filler volume fractions . The numbers in the inset are the filler volume fractions. Room temperature. (b) Same as in (a) for SBR/CNT composites.

(a) Frequency dependence of the real part of the effective complex (relative) permittivity of SBR/CB composites for several filler volume fractions . The numbers in the inset are the filler volume fractions. Room temperature. (b) Same as in (a) for SBR/CNT composites.

Comparison of measurements of the real part of the effective complex (relative) permittivity of the SBR/CB and SBR/CNT composites as a function of the filler volume fraction with the Bruggeman (solid line) and MG (dashed line) equations. The inset shows the low-volume fraction region of the figure (indicated by the arrow).

Comparison of measurements of the real part of the effective complex (relative) permittivity of the SBR/CB and SBR/CNT composites as a function of the filler volume fraction with the Bruggeman (solid line) and MG (dashed line) equations. The inset shows the low-volume fraction region of the figure (indicated by the arrow).

(a) The real part of the effective complex (relative) permittivity of SBR/CB composites as a function of the extension ratio for two filler volume fractions (indicated by the arrows). Room temperature. The numbers in the inset are the elongation ratios. (b) Same as in (a) for two SBR/CNT samples (c) Dependence of the thickness change (triangles), width change (squares) and length (circles) change in the SBR/CB composite (nominal CB volume fraction of ) normalized to the corresponding initial value, as a function of the extension ratio . The solid and dashed curves represent the and functions, respectively. (d) Same as in (c) for the SBR/CNT sample (nominal CNT volume fraction of ).

(a) The real part of the effective complex (relative) permittivity of SBR/CB composites as a function of the extension ratio for two filler volume fractions (indicated by the arrows). Room temperature. The numbers in the inset are the elongation ratios. (b) Same as in (a) for two SBR/CNT samples (c) Dependence of the thickness change (triangles), width change (squares) and length (circles) change in the SBR/CB composite (nominal CB volume fraction of ) normalized to the corresponding initial value, as a function of the extension ratio . The solid and dashed curves represent the and functions, respectively. (d) Same as in (c) for the SBR/CNT sample (nominal CNT volume fraction of ).

(a) Frequency dependence of the effective complex (relative) permittivity of the SBR/CB sample containing CB for two values of the extension ratio . (b) The relative difference of the real part of the complex (relative) permittivity as a function of the extension ratio . . The lines represent the function with different values of the constant . (c) Same as in (b) for the relative difference of the imaginary part .

(a) Frequency dependence of the effective complex (relative) permittivity of the SBR/CB sample containing CB for two values of the extension ratio . (b) The relative difference of the real part of the complex (relative) permittivity as a function of the extension ratio . . The lines represent the function with different values of the constant . (c) Same as in (b) for the relative difference of the imaginary part .

## Tables

The specifications of the filler materials examined in the current study from manufacturer product literature. Brunauer–Emmett–Teller (BET).

The specifications of the filler materials examined in the current study from manufacturer product literature. Brunauer–Emmett–Teller (BET).

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