b) The probe radius is in the range from 2.0 to 3.5 Â

Figure 4 shows radial distribution functions for the PE particles of 12,000, 30,000 and 60,000 atoms with a chain length of 100 beads at a temperature of 100 K. For the amorphous PE particles, the peak positions ofthe radial distributions are insensitive to the size in the diameter range 12.5 nm. By comparing the peak positions ofthe radial distributions ofthe particles with the bulk system, it is clear that the peak around 3.15 A corresponding to gauche configuration is very small for the particles. The reduction of gauche configuration in the radial distributions is believed to be due to alignments of the chains on the surface. In our previous study, we monitored the averaged end-to-end distances of the surface- and inner-chains for the particle of 12,000 atoms with a chain length of 100 beads. The average end-to-end distance of the surface chains is longer than that of the inner chains, and the inner chains have more gauche configurations than the surface.6

Several simulations have been applied to study the morphology of single or multiple chains with different chain length.2425 Since the surface chains of the PE nano-particles tend to straighten and aline at temperatures below the melting point, the preferential morphology for the small PE particle with a long chain length is a rod-like shape. This mechanism was also observed by Liu and Muthukumar in the simulations of polymer crystallization.25 This stretching of the chains leads to reduction ofthe cohesive energy and an increase in volume. Studies on the effect ofa chain length show that the particles with the shortest chain length (50 beads) have the most spherical shape.

Thermal Properties of PE Nano-particles

Thermal analysis provides a great deal of practical and important information about the

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I I I I I Mil I I I l"V I { I I I I | II I I | I I I ! | II I I pr T 1 I

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