Free-standing time to reach the most thermodynamically

Free-standing Au NRs monolayered nanosheets with different orientations can be fabricated through the drying-mediated self-assembly process at the air-water interface.84 The Au NRs nanosheets can be either horizontally (H-sheets) or vertically (V-sheets) aligned as shown in Figure 2.6a. In the free-standing NR assemblies, the assembly pattern is mainly affected directly by operating temperature and ligand length. For example, the majority of the sheets are H-sheets at ambient temperatures while the yield of V-sheets improves as the temperature or annealing time under the chloroform atmosphere is increased. The annealing time of nanosheets was controlled by sealing and capping the beaker with a lid immediately to build a slow solvent evaporation environment. The formation mechanism of nanosheets with different orientations could be explained by both the application of Tirado’s model and entropy-driven self-assembly.89-91 According to the Tirado’s model, the ratio of temperature to shear viscosity is a key parameter which can affect the rotational and translational diffusion behaviors of cylindrical objects. To obtain vertical alignment of nanoparticles, the temperature needs to be increased to decrease the shear viscosity, resulting a smaller diffusion constant. Therefore, the system would gain more time to reach the most thermodynamically stable state by correcting the disordered structures.84 An entropy-driven self-assembly also attributed to the formation of different orientated Au NR nanosheets, which can be explained by Onsager’s model. According to Onsager’s model, there is a competition between rotational and translational entropy during the assembly of hard rods.90, 92 Rotational entropy increased as the orientation possibility of the rods increased, which decreases as alignment increases. Translational entropy increased as the excluded volume decreased. In a dilute solution, the rods are possible to take on arbitrary orientations and positions to maximize entropy. However, in a high-concentration solution, both the translational and rotational freedom is restricted, some of their orientational freedom was sacrificed to maximize the translational freedom, so a vertical structure is formed.

In addition to Au NR, other plasmonic anisotropic nanoparticles such as Ag nanoprisms (Figure 2.6b)93 and copper sulphide nanodisks94 can also form two kinds of assembled structures with fact-to-face or parallel alignments. For the former, the anisotropic orientation was obtained by controlling the attractive force between nanoparism faces and nanoparticle face and substrate. For the latter, besides the substrate, the orientation of the nanodisks mainly depends on the composition.  Specifically, the CuS tend to lay face-down alignment on the substrate while Cu2S normally orient face-to-face on the substrate.

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