Solid-state transition

As with other crystalline substances, on heating coordination compounds may melt, sublime, decompose, or undergo a solid phase transition. The greater complexity of the constituents present increases the number of types of bond redistribution processes which are, in principle, possible within and between the coordination spheres. The following solid-state transitions may be distinguished (i) changes in relative dispositions... 

Fig. 11. DSC-trace of cyclotetraeicosane showing the melting transition at 322 K and an additional solid state transition at 297 K. Heating rate 2.5 K. (Ref.7))...

Thermal transitions can be studied by DSC. The crystallization transition is usually sharp with a good baseline. The melting transition is more complex and often not a single transition (Fig. 3.19)48 as it depends on the thermal history of the sample and the structural changes that can take place upon heating. In warming, solid-state transitions can take place in the unit cell, the lamellae can thicken, and secondary crystallization can also take place. The heats of crystallization and... 

For a polymorphic drug, the polymorph obtained depends on the physical conditions, such as temperature, pressure, solvent, and the rate of desupersaturation. For a solvated drug, in addition to these conditions, the thermodynamic activity of the solvating solvent may also determine the solvate obtained. However, kinetic factors may sufficiently retard the crystallization of a stable form or the solid-state transition to the stable form that an unstable form may be rendered metastable. 

Monnerie, L., Laupretre, F. and Halary,. L. Investigation of Solid-State Transitions in Linear and Crosslinked Amorphous Polymers. Vol. 187, pp. 35-213. 

J. Aaltonen, K. Kogermann, C.J. Strachan and J. Rantanen, In-line monitoring of solid-state transitions during fluidisation, Chem. Eng. Sci., 62, 408 15 (2006). 

Equation 2.47 describes the interdependence of thermal expansion, compressibility, and heat capacity of a first-order transition and furnishes a precise tool for the evaluation of the internal consistency of experimental data in solid state transition studies (see Helgeson et al., 1978 for a careful application of eq. 2.47). 

The heat of vaporization varies slowly with temperature and eventually becomes zero at the critical temperature. In addition, the assumptions which were used to approximate AV (ideal gas behavior and negligible volume of the condensed phase) are inaccurate at high pressures. However, the assumptions are adequate for data of moderate precision (about 1%) in the 1-760-torr range, and in these cases the heat of vaporization may be determined from the A parameter as indicated in Eq. (3). Of course, different A and B parameters have to be determined for each particular phase (e.g., for the liquid, and for each solid phase, if more than one exists). IfA and if are known for one phase and the heat of transition (fusion or solid-state transition) is known, the heat of vaporization and its equivalent, the A value for the second phase, maybe calculated. The new value of B is then found by taking advantage of the fact that the vapor pressures for the two phases are identical at the transition temperature. 

Investigation of Solid-State Transitions in Amorphous Polymers... 

Any motion occurring within any polymer system leads to a change of the dynamic mechanical behaviour, in particular its mechanical loss. This makes the dynamic mechanical measurements the most appropriate technique for studying solid-state transitions. However, in order to assign the molecular motions involved in the considered transition from only the dynamic mechanical results, it is necessary to perform systematic studies on a large series of compounds with gradual modification of their chemical structure. Such an approach has been used in some cases, but it requires lots of effort in synthesising the various compounds. 

For amorphous polymers, the glass-rubber transition is usually referred as the a transition, the solid state transitions (frequently called sub-Tg or secondary transitions) being designated by /3, y, S,... A typical example is shown in Fig. 1 with the temperature dependence of the mechanical loss modulus, E", which exhibits several peaks corresponding to the various transitions. 

In order to represent the temperature dependence of the process frequencies corresponding to the various transitions, it is usual to consider a relaxation map, as it is called, in which the logarithm of the frequency is plotted as a function of 1/T, where T is the absolute temperature. A typical example is shown in Fig. 2 for a polymer exhibiting two solid state transitions (/I and y), in addition to the a transition. It is worth pointing out that the lower the transition temperature, the smaller the activation energy. 

Conclusion on the General Features of Solid-State Transitions... 

This example dealing with the precise identification of the ring motions involved in the y transition of poly(cyclohexyl methacrylate) clearly illustrates how convenient and powerful the MAS CP 13C NMR is for studying solid-state transitions of polymers. It is worth noting that, owing to the very low temperature at which the y transition occurs, the involved motions are very localised. 

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