Finite-size effects in continuum percolation

Finite-size effect on the percolation and electromechanical behaviors of liquid metal particulate composites

Liquid metal particulate composites (LMPCs) are super-stretchable conductors with promising applications in soft electronics. Their conductance originates from the percolation networks of liquid metal particles. This work aims at elucidating the effect of finite-size and sample shape on the percolation and electromechanical properties of LMPCs, given that their dimensions range from microns to centimeters. It is found that their percolation threshold is dominated by the smallest dimension of the samples, not the shape or aspect ratio. A smaller sample size increases the percolation threshold and makes it harder to activate the conductance. In addition, smaller samples are more sensitive to local defects, which adversely impair the electromechanical properties or even undermine the conductance. Finally, this work considers the influence of finite-size on the piezoresistance effect, i.e., strain-dependent resistance. It is found that the piezoresistance effect and finite-size effect are uncorrelated, if the samples are above the percolation threshold. The findings provide not only fundamental insights on the finite-size effect of percolation but also guidance on the design-fabrication process for LMPCs to achieve more reliable electromechanical performance.

Rheology of crystallizing polymers: The role of spherulitic superstructures, gap height, and nucleation densities

A longstanding goal in polymer rheology is to develop a physical picture that relates the growth of mechanical moduli during polymer crystallization to that of a structure. Here, we utilize simultaneous mechanical rheology and optical microscopy, with augmentation by deterministic reconstruction and stochastic simulations, to study isothermal crystallization in isotactic polypropylene. We observe the nucleation and growth of the surface and bulk spherulites, which are initially isolated and then impinge to form clusters and superstructures that eventually span the gap. We find that spherulitic superstructures play a critical role in the rheology, especially in the characteristic sharp upturn in moduli. Both the rheology and the spherulitic superstructures show pronounced gap dependencies, which we explain via finite-size effects in percolation phenomena and via surface-induced nucleation. The modulus-crystallinity relationship can be described through a general effective medium theory. It indicates that for thicker gaps, the viscoelastic liquid to solid transition can be described via percolation, whereas for our thinnest gap, it is best described by the linear mixing rule. We describe our results in terms of dimensionless nucleation rates and spherulite size, which enable the estimation of when gap-dependent superstructure effects can be anticipated.

Emergent Electrical Properties of Ensembles of 1D Nanostructures and Their Impact on Room Temperature Electrical Sensing of Ammonium Nitrate Vapor

Ammonium nitrate is an explosive agent that has a very low vapor pressure, which makes airborne detection very challenging. Detection of ammonium nitrate vapor has been achieved by using silica nanospring mats coated with a thin semiconducting layer of zinc oxide. The sensor was operated at room temperature and under ambient conditions in air. Lock-in amplification was employed to measure the change in electrical resistance of the sensor upon exposure to the said target gas analyte. The sensor showed fast detection, only taking ∼15 s to reach its peak response, and exhibited a moderate recovery time of approximately 0.5 min/20 ppm for <40 ppm exposures. A comparison between the ZnO coated nanospring sensor and ZnO thin film sensor demonstrated that the nanospring sensor has superior sensitivity and responsiveness over the thin film sensor. A percolation-based model is proposed to explain the greater sensitivity at low analyte concentrations of the ZnO-nanospring sensor, as compared to a ZnO thin film sensor.

Percolation of binary disk systems: Modeling and theory

The dispersion and connectivity of particles with a high degree of polydispersity is relevant to problems involving composite material properties and reaction decomposition prediction and has been the subject of much study in the literature. This work utilizes Monte Carlo models to predict percolation thresholds for a two-dimensional systems containing disks of two different radii. Monte Carlo simulations and spanning probability are used to extend prior models into regions of higher polydispersity than those previously considered. A correlation to predict the percolation threshold for binary disk systems is proposed based on the extended dataset presented in this work and compared to previously published correlations. A set of boundary conditions necessary for a good fit is presented, and a condition for maximizing percolation threshold for binary disk systems is suggested.

Nonuniversal conductivity exponents in continuum percolating Gaussian fractures

We study the electrical and hydraulic conductivity percolation exponents in a Gaussian fracture using the method proposed in Plouraboué [Phys. Rev. E 73, 036305 (2006)]. Nonuniversal conductivity percolation exponents are found: they differ from the theoretical predictions for infinite system size for frozen power-law distributions of local conductivities, as with their finite size corrections. In the hydraulic case, we also find that the probability density function of the conductivity follows a power-law distribution near the percolation threshold.