Temperature and time dependence of conductive network formation: Dynamic percolation and percolation time

Percolation in Carbon Nanotube-Reinforced Polymers for Strain-Sensing Applications: Computational Investigation on Carbon Nanotube Distribution, Curvature, and Aggregation

The present article investigates the possibility of simulating the electrical conductivity of carbon nanotube-reinforced polymer composites by numerical methods. Periodic representative volume elements are generated by randomly distributing perfectly conductive reinforcements in an insulating matrix and are used to assemble an electrical network representative of the nanocomposite, where the nanotube-nanotube contacts are considered equivalent resistors modeled by means of Simmons' equation. A comparison of the results with experimental data from the literature supports the conclusion that a random distribution of reinforcements is not suitable for simulating this class of materials since percolation thresholds and conductivity trends are different, with experimental percolation taking place before the expectations. Including nanotube curvature does not solve the issue, since it hinders percolation even further. In agreement with experimental observations, the investigation suggests that a suitable approach requires the inclusion of aggregation during the volume element generation to reduce the volume fraction required to reach percolation. Some solutions available in the literature to generate properly representative volume elements are thus listed. Concerning strain sensing, the results suggest that representative volume elements generated with random distributions overestimate the strain sensitivity of the actual composites.

Poly(lactic acid)-Based Ink for Biodegradable Printed Electronics With Conductivity Enhanced through Solvent Aging

Biodegradable electronics is a rapidly growing field, and the development of controllably biodegradable, high-conductivity materials suitable for additive manufacturing under ambient conditions remains a challenge. In this report, printable conductive pastes that employ poly(lactic acid) (PLA) as a binder and tungsten as a conductor are demonstrated. These composite conductors can provide enhanced stability in applications where moisture may be present, such as environmental monitoring or agriculture. Post-processing the printed traces using a solvent-aging technique increases their conductivity by up to 2 orders of magnitude, with final conductivities approaching 5000 S/m. Such techniques could prove useful when thermal processes including heating or laser sintering are limited by the temperature constraints of typical biodegradable substrates. Both accelerated oxidative and hydrolytic degradation of the printed composite conductors are examined, and a fully biodegradable capacitive soil moisture sensor is fabricated and tested.

Percolation behaviors of model carbon black pastes

The percolation behaviors of a series of high-structured carbon black (CB) pastes (CB weight fractions 10-25 wt%, ethyl cellulose as the binder, α-terpineol as the solvent) were systematically investigated using analyses of rheology and impedance spectra together with characterization via small-angle X-ray scattering (SAXS) and scanning electron microscopy (SEM). When the CB concentration was near the static percolation threshold (∼20 wt%), the permittivity, ac conductance, and elastic modulus of the paste displayed notable increases, whereas the SAXS profile revealed the prevalence of isolated CB aggregates (mean radius of gyration ∼40 nm). Upon further aging at 25 and 40 °C (up to 6 h), two CB pastes near the static percolation threshold (i.e., 20 and 25 wt%) exhibited prominent temporally evolving responses, including more than tenfold increases in their ac conductance and elastic modulus, as well as a pronounced upturn in the low-q SAXS profile (q < 0.03 nm-1) and the formation of a (partially) interconnected cluster network in SEM observations of the morphologies of screen-printed films. In this case, we provide the first evidence of "(aging) Time-(relaxation) Time-Temperature-Concentration Superposition (TTTCS)" for the dynamic modulus data over a frequency range of seven orders of magnitude. This suggests that prolonged aging time imparted to CB aggregate interaction and restructuring (or gelation) may work in tandem with the known effects of the system temperature and concentration to further extend the accessible range of dynamic modulus data, in a similar way to recent reports on the effect of the curing (crosslinking) time on a carbon nanotube suspension and caramel. In combination with existing (three) master curves for two different colloidal materials, we show that there is a reasonable superposition of all the dynamic modulus data over a frequency range of 12 orders of magnitude.

Effect of phase coarsening under melt annealing on the electrical performance of polymer composites with a double percolation structure

The effect of phase coarsening on the evolution of the carbon black (CB) nanoparticle network under quiescent melt annealing and the electrical performance of polypropylene/polystyrene/carbon black (PP/PS/CB) composites with a double percolation structure was investigated. The results showed that when the CB content is low, the coarsening process of PP/PS/CB blends can be divided into two stages. In the first stage, the coarsening rate is fast before the formation of the CB nanoparticle network, and after annealing for a certain time, the evolution of the co-continuous morphology can drive the CB nanoparticles to self-assemble into a complete nanoparticle network. In the second stage, the coarsening rate is slow after the formation of the CB nanoparticle network. When the CB content is high, the CB nanoparticle network can be maintained throughout the whole annealing process, so that the conductivity and morphology of the PP/PS/CB composites are stable. Moreover, the electrical conductivity of the PP/PS/CB composites greatly increases after annealing for a certain time, and a percolation threshold as low as 0.07 vol% can be obtained. These results reveal the relationship between the evolution of the morphology and the conductivity in the conductive polymer composites with a double percolation structure, and provide a more in-depth and comprehensive understanding of the double percolation structure.

Flexible Dielectric Nanocomposites with Ultrawide Zero-Temperature Coefficient Windows for Electrical Energy Storage and Conversion under Extreme Conditions

Polymer dielectrics offer key advantages over their ceramic counterparts such as flexibility, scalability, low cost, and high breakdown voltages. However, a major drawback that limits more widespread application of polymer dielectrics is their temperature-dependent dielectric properties. Achieving dielectric constants with low/zero-temperature coefficient (L/0TC) over a broad temperature range is essential for applications in diverse technologies. Here, we report a hybrid filler strategy to produce polymer composites with an ultrawide L/0TC window of dielectric constant, as well as a significantly enhanced dielectric value, maximum energy storage density, thermal conductivity, and stability. By creating a series of percolative polymer composites, we demonstrated hybrid carbon filler based composites can exhibit a zero-temperature coefficient window of 200 °C (from -50 to 150 °C), the widest 0TC window for all polymer composite dielectrics reported to date. We further show the electric and dielectric temperature coefficient of the composites is highly stable against stretching and bending, even under AC electric field with frequency up to 1 MHz. We envision that our method will push the functional limits of polymer dielectrics for flexible electronics in extreme conditions such as in hybrid vehicles, aerospace, power electronics, and oil/gas exploration.

Conductivity and phase morphology of carbon black-filled immiscible polymer blends under creep: an experimental and theoretical study

The simultaneous evolution of conductivity and phase morphology of blend composites was investigated under shear and in the quiescent state.

The effect of DBP of carbon black on the dynamic self-assembly in a polymer melt

Three types of carbon black with different dibutyl phthalate (DBP) absorption have been used to study the electrical percolation behavior in thermoplastic polyurethane.

Effect of multi-walled carbon nanotubes on the morphology evolution, conductivity and rheological behaviors of poly(methyl methacrylate)/poly(styrene-co-acrylonitrile) blends during isothermal annealing

MWNTs migrate and aggregate in SAN-rich phase to form the double percolated structure with thermal-induced phase separation of blend matrix.

Molecular dynamics simulation of the conductivity mechanism of nanorod filled polymer nanocomposites

We adopted molecular dynamics simulation to study the conductive property of nanorod-filled polymer nanocomposites by focusing on the effects of the interfacial interaction, aspect ratio of the fillers, external shear field, filler-filler interaction and temperature. The variation of the percolation threshold is anti N-type with increasing interfacial interaction. It decreases with an increase in the aspect ratio. At an intermediate filler-filler interaction, a minimum percolation threshold appears. The percolation threshold decreases to a plateau with temperature. At low interfacial interaction, the effect of an external shear field on the homogeneous probability is negligible; however, the directional probability increases with shear rate. Moreover, the difference in conductivity probabilities is reduced for different interfacial interactions under shear. Under shear, the decrease or increase of conductivity probability depends on the initial dispersion state. However, the steady-state conductivity is independent of the initial state for different interfacial interactions. In particular, the evolution of the conductivity network structure under shear is investigated. In short, this study may provide rational tuning methods to obtain nanorod-filled polymer nanocomposites with high conductivity.

Considerable different frequency dependence of dynamic tensile modulus between self-heating (Joule heat) and external heating for polymer--nickel-coated carbon fiber composites

Dynamic tensile moduli of polyethylene--nickel-coated carbon fiber (NiCF) composites with 10 and 4 vol % NiCF contents under electrical field were measured by a homemade instrument in the frequency range of 100--0.01 Hz. The drastic descent of the storage modulus of the composite with 10 vol % was verified in lower frequency range with elevating surface temperature (T(s)) by self-heating (Joule heat). The composite was cut when T(s) was beyond 108 °C. On the other hand, the measurement of the composite with 4 vol % beyond 88 °C was impossible, since T(s) did not elevate because of the disruption of current networks. Incidentally, the dynamic tensile moduli by external heating could be measured up to 130 and 115 °C for 10 and 4 vol %, respectively, but the two composites could be elongated beyond the above temperatures. Such different properties were analyzed in terms of crystal dispersions, electrical treeing, and thermal fluctuation-induced tunneling effect.

Styrene-butadiene-styrene copolymer compatibilized carbon black/polypropylene/polystyrene composites with tunable morphology, electrical conduction and rheological stabilities

We report a facile kinetic strategy in combination with styrene-butadiene-styrene (SBS) copolymer compatibilizers for preparing carbon black (CB) filled immiscible polypropylene (PP)/polystyrene (PS) (1/1) blends with finely tuned morphologies and show the important role of location and migration of CB nanoparticles in determining the electrical conductivity and rheological behaviour of the composites. A novel method of mixing a SBS/CB (5/3) masterbatch with the polymers allowed producing composites with CB aggregates dispersed partially in the unfavorable PP phase and partially in the PP side of the interface to exhibit diverse phase connectivity and electrical conductivity depending on the compounding sequences. A cocontinuous morphology with CB enrichment along the interface was formed in the composite prepared by mixing the SBS/CB masterbatch with the premixed PP/PS blend, giving rise to a highest electrical conductivity and dynamic moduli at low frequencies. On the other hand, mixing the masterbatch with one and then with another polymer yielded droplet (PS)-in-matrix (filled PP) composites. The composites underwent phase coalescence and CB redistribution accompanied by marked dynamic electrical conduction and modulus percolations as a function of time during thermal annealing at 180 °C. The composites with the initial droplet-in-matrix morphology progressed anomalously into the cocontinuous morphology, reflecting a common mechanism being fairly nonspecific for understanding the processing of filled multicomponent composites with tailored performances of general concern.

Mapping the electrical conductivity of poly(methyl methacrylate)/carbon black composites prior to and after shear

In this letter, the electrical conductivity of disklike poly(methyl methacrylate)/carbon black composite samples was investigated prior to and after a shear process. Novel electrical conductivity maps of the samples as a function of the position were obtained. It was found that the electrical conductivity after angular averaging of the static (nonsheared) sample is, as expected, independent of the radius. However, for the sheared sample, the electrical conductivity is decreasing from the center to the outer rim of the sample. This is attributed to the interplay of destruction and buildup effects of the applied linear shear stress on the agglomerate network.

Thermal annealing induced enhancements of electrical conductivities and mechanism for multiwalled carbon nanotubes filled poly(ethylene-co-hexene) composites

Thermal annealing-induced enhancements of electrical conductivities at the temperature higher than the melting point of poly(ethylene-co-hexene) matrix for multiwalled carbon nanotubes filled poly(ethylene-co-hexene) (MWCNTs/PEH) composites were investigated by electrical conductivity measurements. Two types of MWCNTs with low and high aspect ratios (4 and 31) were added as fillers into PEH matrix, respectively for comparison study purpose. The morphological changes due to annealing for MWCNTs/PEH composites were observed by SEM. The formation of MWCNT networks in the composites were clearly demonstrated by rheological measurements. It is surprisingly found that the electrical conductivity for MWCNTs/PEH composites with high MWCNT concentrations increases obviously with annealing time of 40 min and the maximum increment approaches about 3 orders of magnitude with annealing time of 120 min. The increase of electrical conductivity of MWCNTs/PEH composites depends on MWCNT content, MWCNT aspect ratio and annealing time. SEM results clearly reveal that micrometer-sized MWCNT aggregates are broken down and more loosely packed MWCNT networks form due to annealing. Different types of networks in the composites are responsible for the evolutions of rheological (MWCNT network and PEH chain-MWCNT combined network) and electrical conductivity properties (tube-tube contacting MWCNT network). The reconstruction of MWCNT network during annealing is attributed to rotational diffusion of MWCNTs in PEH matrix at high temperature and the length of MWCNTs shows significant effect on this. The obvious enhancements of electrical conductivities can be ascribed to the thermal annealing-induced formation of loosely packed more homogeneous networks through non-Brownian motions.