Effect of Nanoparticle Geometry and Concentration

Compared to conventional microsized filler particles used in the foaming processes, nanoparticles offer unique advantages for enhanced nucleation. The extronely fine dimensions and large surface area of nanoparticles provide much more mtimate contact between the fillers, polymer matrix, and gas. Furthermore, a significantly higher effective particle concentration can be achieved at a low nominal particle concentration. Both could lead to improved nucleation efficiency. 

While the efficiency of nanoparticles for enhancing nucleation has been widely reported and superior to micron-sized particles, the effects of particle size and geometry in general (shape, aspect ratio, and surface curvature) require further elucidation. 

Fletcher (1958) ascertained the effects of particle geometry on the nucleation efficiency and this is briefly summarized below. 

Based on the classical nucleation theory (Abraham 1974 Laaksonen, Talanquer, and Oxtoby, 1995), the heterogeneous nucleation rate is expressed as 

The above analysis was first adopted by Shen, Zeng, and Lee (2005) to compare the nucleation efficiency of nanoparticles of different geometry (single-waUed carbon nanotubes, carbon nanofibers, and clay nanoparticles) in polystyrene foams. They found that consistent with the theoretical prediction, among the three nanoparticles studied, the single-walled carbon nanotubes exhibited the lowest nucleation efficiency because of the smallest size and curvature. Carbon nanofibers have the highest nucleation efficiency and nanoclays (with flat surface) have an efficiency in between. 

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