Tunneling conductivity in composites of attractive colloids.

In conductor-insulator nanocomposites in which conducting fillers are dispersed in an insulating matrix, the electrical connectedness is established by inter-particle tunneling or hopping processes. These systems are intrinsically non-percolative and a coherent description of the functional dependence of the conductivity σ on the filler properties, and in particular of the conductor-insulator transition, requires going beyond the usual continuum percolation approach by relaxing the constraint of a fixed connectivity distance. In this article, we consider dispersions of conducting spherical particles which are connected to all others by tunneling conductances and which are subjected to an effective attractive square-well potential. We show that the conductor-insulator transition at low contents φ of the conducting fillers does not determine the behavior of σ at larger concentrations, in striking contrast to what is predicted by percolation theory. In particular, we find that at low φ the conductivity is governed almost entirely by the stickiness of the attraction, while at larger φ values σ depends mainly on the depth of the potential well. As a consequence, by varying the range and depth of the potential while keeping the stickiness fixed, composites with similar conductor-insulator transitions may display conductivity variations of several orders of magnitude at intermediate and large φ values. By using a recently developed effective medium theory and the critical path approximation, we explain this behavior in terms of dominant tunneling processes which involve inter-particle distances spanning different regions of the square-well fluid structure as φ is varied. Our predictions could be tested in experiments by changing the potential profile with different depletants in polymer nanocomposites.

Depletion-interaction effects on the tunneling conductivity of nanorod suspensions.

We study by simulation and theory how the addition of insulating spherical particles affects the conductivity of fluids of conducting rods, modeled by spherocylinders. The electrical connections are implemented as tunneling processes, leading to a more detailed and realistic description than a discontinuous percolation approach. We find that the spheres enhance the tunneling conductivity for a given concentration of rods and that the enhancement increases with rod concentration into the regime where the conducting network is well established. By reformulating the network of rods using a critical path analysis, we quantify the effect of depletion-induced attraction between the rods due to the spheres. Furthermore, we show that our conductivity data are quantitatively reproduced by an effective-medium approximation, which explicitly relates the system tunneling conductance to the structure of the rod-sphere fluid.

Tunneling and percolation transport regimes in segregated composites.

We consider the problem of electron transport in segregated conductor-insulator composites in which the conducting particles are connected to all others via tunneling conductances, thus forming a global tunneling-connected resistor network. Segregation is induced by the presence of large insulating particles, which forbid the much smaller conducting fillers from occupying uniformly the three-dimensional volume of the composite. By considering both colloidal-like and granular-like dispersions of the conducting phase, modeled respectively by dispersions in the continuum and in the lattice, we evaluate by Monte Carlo simulations the effect of segregation on the composite conductivity σ, and show that an effective-medium theory applied to the tunneling network reproduces accurately the Monte Carlo results. The theory clarifies that the main effect of segregation in the continuum is that of reducing the mean interparticle distances, leading to a strong enhancement of the conductivity. In the lattice-segregation case the conductivity enhancement is instead given by the lowering of the percolation thresholds for first and beyond-first nearest neighbors. Our results generalize to segregated composites the tunneling-based description of both the percolation and hopping regimes introduced previously for homogeneous disordered systems.

Cranklike conformational transitions in polyethylene.

Molecular dynamics simulations of a variety of polymeric systems provide the evidence for two different kinds of conformational transitions: independent single bond transitions and cranklike transitions (or correlated bond transitions). While single bond transitions can be rationalized according to standard theories of activated processes controlled by the saddle point crossing, a more complex description is required for the other type of transitions. In a recent work devoted to the analysis of the simplified chain model with three rotors [B. Nigro and G. J. Moro, J. Phys. Chem. B 106, 7365 (2002)], a theory has been proposed for cranklike transitions represented as a kinetic process between equilibrium states differing by two torsional angles (i.e., two bond transitions). Moreover their rate coefficients were estimated on the basis of a local expansion about the bifurcation of the separatrices departing from the potential function maximum. In the present work the same theory is applied to a model for long alkyl chains in solution, in order to rationalize the behavior of cranklike transitions in polyethylene and to recognize the molecular features controlling them. We obtain probabilities of occurrence of cranklike transitions in substantial agreement with simulation results. Furthermore, the theory is capable of explaining the dependence of the rate on the separation between the two reactive bonds, as well as the dependence on the conformational state of the starting configuration. In particular, selection rules for next-to-nearest neighbor transitions are recovered from the shape of the separatrices and the location of the corresponding bifurcations.