A non‐linear Brownian dynamics (BD) model based upon the Rouse model is developed for unentangled polymer melts. The essence of the model is that it includes an equilibrium spring length b, a non‐linear force term that is not present in the equation of motion of the Rouse model. The equation of motion is solved numerically with the technique of proper orthogonal decomposition (POD) to obtain the dynamics information. To illustrate that the BD model can be readily implemented on polymers with different molecular structures, it is applied to polyethylene with linear, ring, and star structures. For comparison purpose, the corresponding molecular dynamics (MD) simulation is also carried out on molecules with the same sizes (N = 30–73). To characterize the dynamics, time correlation functions of the end‐to‐end vector, the m‐to‐n vector, and the arm vector of the linear, ring, and star polyethylene are determined respectively. It is found that the longest relaxation times (τ1s), the relaxation times of the vectors (τv s), as well as zero‐shear viscosity (η0s) obtained from the BD and MD simulations agree well with each other. The time correlation functions can be reasonably described using the eigenmodes.

Visualization of the chemical structures of two-dimensional (2D) materials and their interfaces at the virtually atomic scale is an imperative step toward devising highly efficient ultrathin optoelectronic devices. Herein, we demonstrate a universal method featuring time-of-flight secondary ion mass spectrometry (ToF-SIMS), coupled with the structure simplicity of 2D materials, as a versatile tool to reveal the vertical atomic layers of various two-dimensional (2D) materials including graphene, hexagonal boron nitride (h-BN), and transition metal dichalcogenides (TMDs). We demonstrated that the vertical atomic layers of those 2D materials can be unveiled layer-by-layer using a strategy of ToF-SIMS three-dimensional (3D) analysis developed in this work. Moreover, we found that the extreme surface sensitivity and chemical specificity of ToF-SIMS also enables the examination of the lateral uniformity of 2D materials. During this process, we first removed interference of adsorbed organic contamination by annealing, which allows the high quality signals specific to the 2D materials which were accumulated along the sputtering depth. The accumulated signal was found to be linearly proportional to the number of atomic layers in the z-direction, thus providing a chemical intensity contrast that can be directly used to reveal the number of atomic layers in the vertical direction. For the case of CVD-grown graphene, up to six individual adlayers have been resolved. The technique developed in this work is substrate-independent and can be directly applied to the grown substrate, which circumvents the time-consuming transfer process and avoids any potential hazard to the delicate 2D materials. Our approach provides an efficient characterization tool for analyzing the 2D materials and their heterostructures, with extensive implications toward preparation of high-quality 2D crystals for atomically thin optoelectronic devices.

A free volume theory for the crossover in diffusion coefficients of linear polymers from unentangled to entangled regimes is developed.