title: On the equilibrium of helical nanostructures with ordered mesopores.
abstract: Helical conformation exists universally at different length scales. We present a new model to explain the energetics of a helical structure with ordered mesopores and successfully predict their equilibrium state. The formation of the helical structure, which is composed of twisted and hexagonally arrayed one-dimensional pore channels, should be understood at the macromorphology level through the competition between surface free energy reduction and torsion strain energy increase. Our model is established by first reverting a helical rod with experimentally defined parameters to a conjectured straight rod without intrinsic pore channel twisting, and then quantitatively calculating the variation of two competitive energies as a function of twist angle in the torsion process starting from the reverted straight rod. Through our model, a free energy curve is achieved, so that the equilibrium state and the helical structural parameters can be predicted, which are in good agreement with experimental results for helical rods synthesized by different surfactant templates. Moreover, our model can be successfully applied to explain the pitch-radius relationships in previous observations. Our achievement provides unique and fundamental understandings for the spontaneous mesoscopic helix formation, which are different from the microscopic helical structures such as DNA chains.
authors.affiliation: Department of Chemistry and Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Fudan University, Shanghai, 200433, P. R. China.
authors.forename: Lingzhi
authors.initials: L
authors.lastname: Zhao
authors.forename: Pei
authors.initials: P
authors.lastname: Yuan
authors.forename: Nian
authors.initials: N
authors.lastname: Liu
authors.forename: Yifan
authors.initials: Y
authors.lastname: Hu
authors.forename: Yang
authors.initials: Y
authors.lastname: Zhang
authors.forename: Guangfeng
authors.initials: G
authors.lastname: Wei
authors.forename: Liang
authors.initials: L
authors.lastname: Zhou
authors.forename: Xufeng
authors.initials: X
authors.lastname: Zhou
authors.forename: Yunhua
authors.initials: Y
authors.lastname: Wang
authors.forename: Chengzhong
authors.initials: C
authors.lastname: Yu
mesh_terms: D008956:Models, Chemical; D008958:Models, Molecular; D049329:Nanostructures / Q000737:chemistry*; D013816:Thermodynamics; D014961:X-Ray Diffraction