Nanocomposites consist of nanofillers and matrices, thus allowing one to design novel materials with desirable properties of both nanofillers and matrices. The percolating network formation of nanofillers in matrices is critical to such desired properties. Some nanofillers such as carbon nanotubes and graphene nanosheets are so flexible that they become either wavy or crumpled. Such a variability in the nanofiller conformation may affect the percolating network formation but has been often (but not always) ignored in the theoretical and computational investigation. In this work, we investigate how the flexibility of different kinds of nanofillers influences the formation of the percolating network by performing extensive Langevin dynamics simulations. We consider three kinds of nanofillers of different shape: nanospheres, nanorods, and nanoplates. When the sizes of nanofillers (or the radius of gyration, $R_g$) are comparable, nanorods form a percolating network at a lower volume fraction than nanoplates while nanofillers require the highest volume fraction to form the percolating network, which is consistent with previous experiments. The percolation threshold concentration $\left({\varphi }_c\right)$ of nanospheres increases with an increase in their $R_g$, while ${\varphi }_c$ of nanorods and nanoplates decrease with $R_g$. However, the effect of flexibility on the percolation threshold volume fraction is much more significant for nanoplates than nanorods. We also estimate the electric conductivity and find that the electric conductivity follows a scaling relation faithfully but with different critical exponents depending on the shape and flexibility.

Cell migration, an essential process for normal cell development and cancer metastasis, differs from a simple random walk: the mean-square displacement (〈(Δr)²(t)〉) of cells sometimes shows non-Fickian behavior, and the spatiotemporal correlation function (G(r, t)) of cells is often non-Gaussian. We find that this intriguing cell migration should be attributed to heterogeneity in a cell population, even one with a homogeneous genetic background. There are two limiting types of heterogeneity in a cell population: cellular heterogeneity and temporal heterogeneity. Cellular heterogeneity accounts for the cell-to-cell variation in migration capacity, while temporal heterogeneity arises from the temporal noise in the migration capacity of single cells. We illustrate that both cellular and temporal heterogeneity need to be taken into account simultaneously to elucidate cell migration. We investigate the two-dimensional migration of A549 lung cancer cells using time-lapse microscopy and find that the migration of A549 cells is Fickian but has a non-Gaussian spatiotemporal correlation. We find that when a theoretical model considers both cellular and temporal heterogeneity, the model reproduces all of the anomalous behaviors of cancer cell migration.

We report Brownian dynamics simulations of tracer diffusion in regularly crosslinked polymer networks in order to elucidate the transport of a tracer particle in polymer networks. The average mesh size of homogeneous polymer networks is varied by assuming different degrees of crosslinking or swelling, and the size of a tracer particle is comparable to the average mesh size. Simulation results show subdiffusion of a tracer particle at intermediate time scales and normal diffusion at long times. In particular, the duration of subdiffusion is significantly prolonged as the average mesh size decreases with increasing degree of crosslinking, for which long-time diffusion occurs via the hopping processes of a tracer particle after undergoing rattling motions within a cage of the network mesh for an extended period of time. On the other hand, the cage dynamics and hopping process are less pronounced as the mesh size decreases with increasing polymer volume fractions. The interpretation is provided in terms of fluctuations in network mesh size: at higher polymer volume fractions, the network fluctuations are large enough to allow for collective, structural changes of network meshes, so that a tracer particle can escape from the cage, whereas, at lower volume fractions, the fluctuations are so small that a tracer particle remains trapped within the cage for a significant period of time before making infrequent jumps out of the cage. This work suggests that fluctuation in mesh size, as well as average mesh size itself, plays an important role in determining the dynamics of molecules and nanoparticles that are embedded in tightly meshed polymer networks.