Kinetic Percolation Research Articles

Synergistic effect of CNT/CB hybrid mixture on the electrical properties of conductive composites

Nanocomposites are advanced engineering materials with multifunctional characteristics and numerous applications in the packaging, automotive, construction, and energy sectors. In this work, the effects of nanofiller geometry on the processing behavior, interfacial interaction, and electrical percolation behaviors of melt-mixed polystyrene (PS) nanocomposites were investigated. This paper also reports on the synergistic influence of incorporating multi-nanofiller mixture on the electrical resistivity of polymer nanocomposites. Two nanofillers of different geometries and electrical conductivities, namely carbon nanotubes (CNTs) and high-structure carbon black (CB), were used to prepare the nanocomposites. CNTs have a rod-like (1D) shape, whereas CB is characterized by an irregular-branched shape. Because CNTs have higher aspect ratio and electrical conductivity than CB, the CNT-based composites exhibited lower electrical resistivity and electrical percolation threshold than the CB-based composites. The analysis of the percolation behaviors showed that the network formation in the CNT/PS and CB/PS composites can be attributed to the kinetic percolation rather than the statistical percolation. Most interestingly, the CNT:CB/PS composites with a CNT:CB mass ratio of 75:25 showed higher electrical conductivity than the CNT-based and the CB-based composites, revealing a synergetic effect on the electrical properties at this nanofiller ratio.

Kinetic percolation.

We demonstrate that kinetic aggregation forms superaggregates that have structures identical to static percolation aggregates, and these superaggregates appear as a separate phase in the size distribution. Diffusion limited cluster-cluster aggregation (DLCA) simulations were performed to yield fractal aggregates with a fractal dimension of 1.8 and superaggregates with a fractal dimension of D=2.5 composed of these DLCA supermonomers. When properly normalized to account for the DLCA fractal nature of their supermonomers, these superaggregates have the exact same monomer packing fraction, scaling law prefactor, and scaling law exponent (the fractal dimension) as percolation aggregates; these are necessary and sufficient conditions for same structure. The size distribution remains monomodal until these superaggregates form to alter the distribution. Thus the static percolation and the kinetic descriptions of gelation are now unified.

Self-assembly of carbon nanotubes in polymer melts: simulation of structural and electrical behaviour by hybrid particle-field molecular dynamics.

Self-assembly processes of carbon nanotubes (CNTs) dispersed in different polymer phases have been investigated using a hybrid particle-field molecular dynamics technique (MD-SCF). This efficient computational method allowed simulations of large-scale systems (up to ∼1 500 000 particles) of flexible rod-like particles in different matrices made of bead spring chains on the millisecond time scale. The equilibrium morphologies obtained for longer CNTs are in good agreement with those proposed by several experimental studies that hypothesized a two level "multiscale" organization of CNT assemblies. In addition, the electrical properties of the assembled structures have been calculated using a resistor network approach. The calculated behaviour of the conductivities for longer CNTs is consistent with the power laws obtained by numerous experiments. In particular, according to the interpretation established by the systematic studies of Bauhofer and Kovacs, systems close to "statistical percolation" show exponents t ∼ 2 for the power law dependence of the electrical conductivity on the CNT fraction, and systems in which the CNTs reach equilibrium aggregation show exponents t close to 1.7 ("kinetic percolation"). The confinement effects on the assembled structures and their corresponding conductivity behaviour in a non-homogeneous matrix, such as the phase separating block copolymer melt, have also been simulated using different starting configurations. The simulations reported herein contribute to a microscopic interpretation of the literature results, and the proposed modelling procedure may contribute meaningfully to the rational design of strategies aimed at optimizing nanomaterials for improved electrical properties.

Galvanic function of zinc-rich coatings facilitated by percolating structure of the carbon nanotubes. Part II: Protection properties and mechanism of the hybrid coatings

Innovative zinc-rich hybrid paint coatings were developed using nano-size particles composed of alumina hydrate modified with polystyrene-sulfonate (PSS) doped polypyrrole (PPy) and either purified or functionalised multi-walled carbon nanotubes (MWCNTs). General properties of the particles and their dispersions were characterised in 1st part of the work. Corrosion protection characteristics of the hybrids were examined on low-carbon steel panels by immersion and salt-spray chamber tests. Immersion tests were monitored by electrochemical impedance spectroscopy (EIS). Primers were analysed by glow-discharge optical emission spectroscopy (GD OES) and surface of the steel substrates was investigated by X-ray photoelectron (XPS) and FT-Raman spectroscopy. Improved barrier and galvanic function of the hybrids over traditional zinc-rich paints (ZRPs) were evidenced by performance metrics. Optimal protection characteristics were found when content of the particles was close to the statistical and kinetic percolation thresholds. Advanced protection mechanism of the hybrids is discussed on function of the nano-size filler benefiting the utilisation of sacrificial current output of the anodic zinc along with taking into account aspects of the multiple percolation theory. The interpretation given in this work is intended to facilitate design of next generation of corrosion protecting metal-rich coatings.

On the influence of nanotube properties, processing conditions and shear forces on theelectrical conductivity of carbon nanotube epoxy composites

We analyse statistical and kinetic percolation thresholds and maximum electrical conductivitiesof carbon nanotube epoxy composites as a function of shear forces, processing conditions,nanotube type and dimensions. Entangled and non-entangled nanotubes of different lengths(15–100 µm) and thicknesses (12–80 nm) have been obtained with three different synthesismethods based on catalytic or plasma enhanced chemical vapour deposition. Thedispersions were processed either solely with a dissolver disk or additionally with athree roll calender. Care was taken to prevent unintentional shearing (e.g. throughconvection) in all samples that were not subject to deliberate shearing. It wasfound that shear forces have a similar influence on kinetic percolation thresholdsand composite conductivities independent of nanotube types and dimensions.

Oscillatory phenomena in kinetic antipercolation.

We observe growth oscillations in our Monte Carlo simulations of kinetic antipercolation that have no analog in regular percolation. A mean-field theory that explains the existence of these oscillations is presented. The kinetic critical exponent obtained in our simulations is close to the corresponding exponent for regular percolation. This suggests that kinetic antipercolation may be in the same universality class as kinetic percolation.

New kinetic percolation model with diffusion-limited growth.

A new kinetic percolation model which exhibits diffusion-limited growth is studied. The model is a modification of the (site-) percolation model of Alexandrowicz in the sense that sites connected to the growing polymer are not incorporated at random but according to their probability of being reached by a monomer diffusing from far away. The critical exponents differ from those for random percolation, diffusion-limited aggregation, and Bethe lattice percolation.

Kinetic percolation with mobile monomers and solvents as a model for gelation

AbstractWe discuss the results of Monte Carlo simulations of a recent kinetic percolation model applicable to free radical initiated copolymerization of bifunctional and tetrafunctional units in the presence of a solvent. We find that the critical exponent for gelation and the critical amplitudes are unchanged by the inclusion of solvent and mobility. We also obtain relations for the dependence of the critical conversion and the maximum value of the suscepiibility on the fraction of tetrafunctional monomers, solvent concentration, and initiator concentration.

Computer simulation of a model for irreversible gelation

A random mixture of bifunctional and tetrafunctional units is placed on a simple cubic lattice. Permanent bonds between these units are then formed by the random motion of active centres (radicals) resulting in a model for the gelation of polyacrylamide and similar processes. The largest of the clusters formed by this kinetic percolation process is identified with the gel fraction, the 'mean cluster size' with the weight-average degree of polymerisation. The critical exponent gamma of the mean cluster size is roughly the same as for random percolation, that is, different from that of the 'classical' theory of Flory (1941) and Stockmayer (1943), but the corresponding amplitude ratio, that is, the ratio of average molecular weight on both sides of the gel point, differs strongly from its value in random percolation. Thus, this kinetic gelation model seems to belong to a universality class of its own, different from both that of random percolation and that of classical gelation theories.