Relationship of Extensional Viscosity and Liquid Crystalline Transition to Length Distribution in Carbon Nanotube Solutions

TLDR

We demonstrate that CNT length can be determined simply and accurately from extensional viscosity measurements of semidilute CNT solutions. The authors measure extensional viscosity of CNT solutions in chlorosulfonic acid with a customized capillary‑thinning rheometer, determine aspect ratio from the theoretical viscosity–aspect‑ratio relation for rigid rods, measure diameter by TEM, and use these data to calculate CNT length, demonstrating the method works for lengths from 0.4 to at least 20 μm and that the isotropic–nematic transition concentration scales as d/L. The method accurately determines CNT length, works for lengths 0.4–20 μm, shows the isotropic–nematic transition concentration scales as d/L, yields length distributions that match cryo‑TEM, and reveals CNTs have relatively low polydispersity compared to polymers but higher than colloidal particles.

Abstract

We demonstrate that the length of carbon nanotubes (CNTs) can be determined simply and accurately from extensional viscosity measurements of semidilute CNT solutions. The method is based on measuring the extensional viscosity of CNT solutions in chlorosulfonic acid with a customized capillary thinning rheometer and determining CNT aspect ratio from the theoretical relation between extensional viscosity and aspect ratio in semidilute solutions of rigid rods. We measure CNT diameter d by transmission electron microscopy (TEM) and arrive at CNT length L. By studying samples grown by different methods, we show that the method works well for CNT lengths ranging from 0.4 to at least 20 μm, a wider range than for previous techniques. Moreover, we measure the isotropic-to-nematic transition concentration (i.e., isotropic cloud point) φiso of CNT solutions and show that this transition follows Onsager-like scaling φiso ∼ d/L. We characterize the length distributions of CNT samples by combining the measurements of extensional viscosity and transition concentration and show that the resulting length distributions closely match distributions obtained by cryo-TEM measurements. Interestingly, CNTs appear to have relatively low polydispersity compared to polymers and high polydispersity compared to colloidal particles.