## 3 Results and Discussion
### Phase Separation and Structural Transformation of Polymer Blends at the Nanoscale
interfacial area results in the decrease in the interfacial energy. The asymptotic power-low relation was proposed to explain the domain size of the droplets as in the following equation,  
\[d\approx(D\xi)^{1/3}t^{1/3}, \tag{2}\]  
where \(d\) is domain size of droplet, \(D\) is the diffusion coefficient, \(\xi\) is the correlation length, and \(t\) is the coarsening time. The second mechanism of the coarsening process is caused by the coalescence of the two droplets to form the larger droplet. The impinging of two droplets caused by the translational diffusion promotes the mass transfer, and then the larger single droplet is formed. The droplet domain size relates to time as in Equation (3)  
\[d\approx\left(\frac{k_{B}T}{\eta}\right)^{\frac{1}{3}}t^{\frac{1}{3}} \tag{3}\]  
where \(k_{B}\) is the Boltzmann constant, \(T\) is the temperature, and \(\eta\) is the viscosity. In this study, the viscosity of molten polymers used was reduced with increasing temperature referred to the viscosity Arrhenius model [11]. The third coarsening mechanism caused by the hydrodynamic flow of the fluid mixtures. The gradients of pressure along the axis of the cylindrical pore play the role of the flowability from a narrow to a wide region that induces the bi-continuous of the two polymers formed during the phase separation. The growth of the droplet domain is related linearly with time as in the following equation. Figure 10 simulates the phase separation caused by the coarsening behavior. \[d\approx\frac{\sigma}{\eta}t \tag{4}\]  
where \(\sigma\) is the surface tension. Figure 10: Formation of polymer droplets caused by surface–induced phase separation and coarsening behaviors. In the case of the PVA microdomain, Figure 7C,\(\alpha\) illustrates the morphologies of PS\({}^{1}\) nanostructured surfaces using PS\({}^{1}\)/PVA (70/30 wt%) blend precursor. After the removal of the PVA segment, we found PS\({}^{1}\) nanostructure arrays with microholes. The appearance of microholes is caused by the PVA microdomain size of the film precursor. At the microholes area, we found PS\({}^{1}\) nanostructures with nanorods and nanospheres (See Figure 11). The transformation of the PS\({}^{1}\) nanostructures is the result of the surface interaction between PS\({}^{1}\) and PVA in the AAO\({}^{2}\) templates. The PS\({}^{1}\) encapsulated by the PVA-rich phase (30 wt%) adjoined with the AAO\({}^{2}\) pore wall, and the interfacial interaction between PS\({}^{1}\) and PVA lead to the structural transformation of the polymer nanostructures, which was driven by the Rayleigh instability within AAO\({}^{2}\) templates. Rayleigh instability is the common transformation phenomena when the columns of water are falling and breakup into water droplets. The instability is the result of the undulation of the liquid cylinder surface at low surface tension. Herein, the influences of imprinting temperatures (120-180 \({}^{\circ}\)C) and imprinting time (30-120 min) have been investigated. It was found that the number of the spherical structures increased when increasing the imprinting temperature and imprinting time. With increasing the imprinting temperatures, Rayleigh instability caused by the decrease in viscosities that enhances the degree of structural transformation of the PS\({}^{1}\) nanocolumns and converted to the nanorods and nanospheres. The increased imprinting temperature also resulted in the increasing rate of mass transfer and the kinetic phenomenon of the transformation. The increase in the immiscibility of the polymer blends due to the rise in the temperature that influences the increasing heat of mixing. Therefore, it was found that the number of nanorods and nanospheres increased when elevating the imprinting temperatures. In terms of the influence of the imprinting time, we found the similarity in the structural transformation behaviors when increasing the imprinting temperatures.