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Figure 4 Radial distribution functions for several different polymer particles as compared to that ofthe bulk system.

molecular and materials world relating to equations of state, critical points and the other thermodynamics quantities. For our study of thermodynamic properties of nano-scale polymer particles, we have calculated temperature, volume, and total energy in the process of annealing the system by scaling the momenta at a constant rate. To determine the appropriate annealing schedule7, we have examined the melting point and glass transition temperature for the particle of 12,000 atoms with a chain length of 100 beads for different rates in the rage from 1.7 Wps to 29.5 K/ps. The transition temperatures were found to be rather insensitive ( within the error of 5 K ) to annealing rates slower than 6.0 Wps. In all subsequent simulations, we set the annealing rate at approximately 2.5 Wps so that the particle is thermally equilibrated for each sampling point. Computing the straight lines of total energy of the system or molecular volume vs. temperature with a least square fit, we take the points where those extrapolated straight lines meet, as the melting point, Tm , and the glass transition temperature, T g. Table 3 summarizes thermal properties of the PE particles with respect to size and various chain lengths.

Figure 5 shows dependence of melting point and glass transition temperature on the diameter of the particles. The dramatic reduction of the melting point for the fine polymer particles is a example of surface effects and shows the importance of size. Since the large ratio of surface atoms to the total number leads to a significant reduction of the non-bonded interactions, the melting point decreases with decrease of the total number of atoms. Figure 6 shows the effect of chain length on transition temperatures. A strong dependence of the melting point and the glass transition temperature on chain length is attributed to molecular weight and non-bonded energy of each chain.

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