Interdisciplinary Applied Mathematics

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2 n2 + m2 + nm


Zigzag and armchair nanotubes correspond to в = 0° and в = 30°, respectively; 0 < в < 30° corresponds to chiral nanotubes.


Single-walled and multiwalled nanotubes have excellent mechanical properties, since the two-dimensional arrangement of carbon atoms in a graphene sheet allows large out-of-plane distortions. The strength of carbon-carbon in-plane bonds keeps the graphene sheet exceptionally strong against any in-plane distortion or fracture. For example, the Young’s modulus of a (10, 10) SWNT is estimated to be ж 0.64 TPa. The density-normalized modulus and strength of a (10, 10) SWNT are, respectively, ж 19 and ж 56 times that of a steel wire and, respectively, ж 2.4 and ж 1.7 times that of silicon carbide nanorods. The measured room temperature thermal conductivity for an individual MWNT (>3000 W/mK) is greater than that of natural diamond. Because of their excellent structural and material characteristics, carbon nanotubes are being explored for a wide variety of applications including nanoelectronics, microscopy, sensors, and actuators, field emission, nanotube-polymer composites, and many others. It is not surprising that carbon nanotubes are also being explored for applications in nanoflows. In particular, the transport of liquids, gases, and electrolytes through carbon nanotubes have many applications including biomimetics, sensors, nanofluidic interconnects, and many others.

13.2.2 Ion Channels in Biological Membranes


Ion channels are proteins in cell membranes (lipid bilayers) that are crucial for shaping electrical signals and controlling diffusion and flow of ions and fluids across cells. They provide a high conducting, hydrophilic pathway across the hydrophobic interior of the membrane. The key features of ion channels that give rise to their extraordinary range of biological functions include variations in:

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