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Sodium-ion batteries (SIBs) are promising candidates for the replacement of lithium-ion batteries (LIBs) because of sodium's abundant reserves and the lower cost of sodium compared to lithium. This is a topic of interest for developing novel anodes with high storage capacity. Owing to their low cost, high stability, and conductivity, carbon-based materials have been studied extensively. However, sp2-C based carbon materials have low-rate capacities. Intensive density functional theory calculations have been implemented to explore the applicability of α, β, and γ graphyne nanotubes (αGyNTs, βGyNTs, and γGyNTs, respectively) as SIB anodes. Results suggest that (3, 0)-αGyNT, (2, 2)-βGyNT, and (4, 0)-γGyNT have, respectively, maximum Na storage capacities of 1535, 1302, and 1001 mAh/g, which exceeds the largest reported value of carbon materials (N-doped graphene foams with 852.6 mAh/g capacity). It was determined that αGyNTs have the largest storage capacity of the three types because they possess the largest specific surface area. Moreover, the larger pores of αGyNTs and βGyNTs allow easier diffusion and penetration of Na atoms compared to those of γGyNTs, which could result in better rate capacity. [ABSTRACT FROM AUTHOR]