Melting first-order phase transitions

An intrinsic surface is built up between both phases in coexistence at a first-order phase transition. For the hard sphere crystal-melt interface [51] density, pressure and stress profiles were calculated, showing that the transition from crystal to fluid occurs over a narrow range of only two to three crystal layers. Crystal growth rate constants of a Lennard-Jones (100) surface [52] were calculated from the fluctuations of interfaces. There is evidence for bcc ordering at the surface of a critical fee nucleus [53]. 

Let us first consider a network immersed in a melt of polymer chains with degree of polymerization p. In the athermal case, the network should be swollen. As polymer-network interaction parameter Xnp increases, the volume of the network decreases until a practically complete segregation of the gel from polymer melt occurs. It has been found [34, 35] that two qualitatively different regimes can be realized either a smooth contraction of the network (Fig. 8, curve 1) or a jumpwise transition (Fig. 8, curve 2). The discrete first order phase transition takes place only for the networks prepared in the presence of some diluent and when p is larger than a critical value pcr m1/2. The jump of the... 

Figure 13.2 Heat capacities of (a), Hg near the melting temperature of 234.314 K showing the abrupt nature of the change in heat capacity for this first-order phase transition at this temperature [from R. H. Busey and W. F. Giauque, J. Am. Chem. Soc., 75, 61-64 (1953)] and (b), MnO showing the continuous magnetic transition (note inset). (Data obtained from Professor Brian Woodfield and co-workers at Brigham Young University.) The dashed line is an estimate of the lattice heat capacity of MnO.

Figure 3 Changes at a first-order phase transition (drawn for the melting of ice).

The temperature dependence of the thickness of foam bilayers shows the occurrence of a first-order phase transition of melting of hydrocarbon tails of the phospholipid molecules. This melting is realised at a temperature very close to the temperature of the corresponding phase transition in fully hydrated water dispersions of phosphatidylcholines. This result is in agreement with the theoretical considerations of Nagle [436] for the decisive role of van der Waals attractions between hydrocarbon chains of phospholipid molecules for the chainmelting phase transition in bilayer systems. 

Between temperatures of 28 and 29 K the rms bond length fluctuations of the 13-particle system increase dramatically. Similar results have been obtained for all the other clusters N = 5, 6, and 7) for which S(T) is cal-culated. - The curves of S T) for these systems are similar to those occurring with first-order phase transitions of macroscopic systems.Lindemann s criterion states that melting occurs for such systems when rms fluctuations reach 10%.For the small clusters studied, the rise in this function occurs at values of S slightly below 10%—an effect that can be attributed to the large ratio of surface to core atoms. 

Fig. 2. Isobaric relationship between enthalpy and temperature in the liquid, glassy, and crystalline states. is the melting temperature, and Fg the glass transition temperature. The lower diagram shows the behavior of the isobaric heat capacity. The arrow indicates the -function singularity due to latent heat at a first-order phase transition. (From Debenedetti, 1996.)...

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