Direct Measurement of the Percolation Probability in Carbon Nanofiber-Polyimide Nanocomposites

Abstract

We present the first experimental measurement of the geometric critical exponent beta associated with the percolation probability, the probability a metallic filler belongs to the conducting network, of an electrical composite. The technique employs conducting-tip atomic force microscopy to obtain a conducting areal density, and is demonstrated on polyimide nanocomposites containing different concentrations of carbon nanofibers. We find beta approximately 1 and t (the exponent for bulk conductivity) approximately 3. These values are consistent with the predictions for the Bethe lattice and larger than the values predicted in the 3D lattice percolation model. Hence, this electrical composite likely belongs to the same universality class as the Bethe lattice. The ability to measure geometric and transport critical exponents on the same material is critical to drawing this conclusion.

A facile assembly of polyimide/graphene core–shell structured nanocomposites with both high electrical and thermal conductivities

“…However, the low electrical and thermal conductivity limited the application of PI in aerospace and microelectronics industry [3,4]. Many efforts have been made to overcome this drawback by incorporation of carbon nanofiller into PI matrix, such as carbon black (CB) [5,6], carbon nanofiber (CNF) [7,8], carbon nanotube (CNT) [9,10] or graphene (GP) [11][12][13]. Among these nanoparticles, graphene is the most attractive one in recent years due to the excellent electrical and thermal conductivity, mechanical flexibility, optical transparency [14][15][16].…”

A percolation-based model for the conductivity of nanofiber composites

“…6 The appearance of an infinite network of connected particles at the threshold has been related to rapid growth in observables such as the conductivity (denoted σ ) for volume fractions that exceed φ c . Such growth (in the neighborhood of φ c ) is customarily modeled in terms of power-law behavior: σ (φ) ≈ σ 0 (φ − φ c ) t where the prefactor σ 0 and exponent t are treated [3][4][5] as being independent of φ. Mean-field and renormalization group theories for three dimensional systems suggest that the exponent t should equal 3 and 2, respectively. 5 The latter finding (namely, that t ≈ 2) also emerges from precise numerical studies performed upon resistor networks in three dimensions.…”

A model for the dependence of the electrical conductance with the applied stress in insulating-conducting composites

“…Nevertheless, nonuniversal behavior has been experimentally observed and theoretically predicted in the last years. 20,21,30,[43][44][45][46] The above definition ͓Eq. ͑8͔͒ holds for the whole range of percolation probabilities, that is, even for p not close to p c .…”