Size-dependent melting-point depression

Zhang M, Efremov MY, Schiettekatte F, Olson EA, Kwan AT, Lai SL, Wisleder T, Greene, JE, Allen LH. Size-dependent melting point depression of nanostructures Nanocalorimetric measurements. Phys. Rev. B 2000 62 10548-10557. 

In the calorimetric approach, it is necessary to know the heat of fusion of the totally crystalline polymer. This can be obtained from melting-point depression measurements, as described in the following section. The basic idea depends on the fact that the melting temperature is independent of the size of the system, since it is an intensive property. The extent to which it is depressed by the presence of solvent can be used to calculate a heat of fusion characteristic of the crystallites, irrespective of how many are present. This is therefore the heat of fusion of the 100% crystalline polymer. The fractional crystallinity in an actual sample is then the ratio of its calorimetrically measured heat of fusion per gram to that of the 100% crystalline polymer. For example, if the actual polymer has a heat of fusion of 7 cal per gram, and the 100% crystalline polymer a heat of fusion of 10 cal per gram, then the fractional crystallinity is 0.7, and the percentage crystallinity is 70%. 

Jahnert et al. (2008) showed that there are the pronounced differences in the magnitude and pore size dependence of the transition temperature T d) of water obtained by the spin-echo method due in part to the chosen delay time x (Figure 1.277). For instance, the X value (2-20 ms) plays an important role as the pore size of the silica samples decreases. The melting point depression of water in silica pores of nominal pore size 4 nm was found to be 14 K when measured with x=l ms, but only 6 K when measured with x=20 ms. This was attributed to a pore size dependence of the relaxation time T2 of the confined liquid (Jahnert et al. 2008). 

In order to explain the observed effects, different thermodynamic models have been developed, which establish the dependence of melting temperatures and enthalpy, Debye temperature, and atomic vibration amplitude on the crystal grain size (different models and the history of the question see in reviews [8,15,16]). The melting point depression for small crystals is described in the classical thermodynamic approach by the Gibbs-Thomson equation [17,18], For spherical particles,... 

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