Supercooled systems

The first way has been followed in what has become known as Car-Parrinello molecular dynamics (CPMD) (9). A solute and 60-90 solvent molecules are considered to represent the system, and the QM calculations are performed with density functionals, usually of generalised gradient approximation type (GGA), such as the Becke-Lee-Young-Parr (BLYP) (10) or the Perdew-Burke-Enzerhofer (PBE) (11,12) functionals. It is clear that the semiempirical character of concurrent density functional theory (DFT) methods and the use of these simple functionals imply a number of error sources and do not really provide a method-inherent control procedure to test the reliability of results. Recently it has been shown that these functionals even do not enable a correct description of the solvent water itself, as at ambient temperature they will describe water not as liquid but as supercooled system... 

Corezzi, S., Lucchesi, M., Rolla P. A., Capaccioli, S., Gallone, G. (1999) Temperature and pressure dependences of the relaxation dynamics of supercooled systems explored by dielectric spectroscopy, Phil. Mag. B 79, 1953-1963... 

Although a number of at least apparent exceptions to Ostwald s law have been found, it may nevertheless be accepted as a very useful generalisation which sums up very frequently observed phenomena. Of these factors, the most important, according to Tammann, is the readiness with which spontaneous formation of nuclei of the metastable and stable phases takes place in the supercooled system. 

Many reported cases of spontaneous (homogeneous) nucleation are found on careful examination to have been induced in some way. Indeed, it is generally accepted that true homogeneous nucleation is not a common event. For example, a supercooled system can be seeded unknowingly by the presence of atmospheric dust which may contain active particles (heteronuclei). Aqueous solutions as normally prepared in the laboratory may contain >10 solid particles per cm of sizes <1 pm. It is virtually impossible to achieve a solution completely free of foreign bodies, although careful filtration can reduce the numbers to <10 cm and may render the solution more or less immune to spontaneous nucleation. 

As soon as stable nuclei, i.e. particles larger than the critical size (section 5.1.1), have been formed in a supersaturated or supercooled system, they begin to grow into crystals of visible size. The many proposed mechanisms of crystal growth may broadly be discussed under a few general headings. 

SUpercooHns The slow cooling of a system, reaching a temperature below that at which a change in phase (liquid to solid or gas to liquid) would normally take place. A supercooled system is in a metastable state. 

However for the other cases in Table 2 it is possible that the high frequency process may be of a different character, since the local motions relax such a substantial part of . Warchol and Vaughan (73) proposed a model of small-step diffusion in a cone to account for limited motions in such supercooled systems. Their model has been extended by Wang and Pecora (74). The essential result of this model (73, 74) is that for motions of a dipole vector limited within a cone of cone-angle 0, where 0Q < 40 , we have... 

Classic nucleation theory must be modified for nucleation near a critical point. Observed supercooling and superheating far exceeds that predicted by conventional theory and McGraw and Reiss [36] pointed out that if a usually neglected excluded volume term is retained the free energy of the critical nucleus increases considerably. As noted by Derjaguin [37], a similar problem occurs in the theory of cavitation. In binary systems the composition of the nuclei will differ from that of the bulk... 

The formation of ECC is not only an extension of a portion of the macromolecule but also a mutual orientational ordering of these portions belonging to different molecules (intermolecular crystallization), as a result of which the structure of ECC is similar to that of a nematic liquid crystal. After the melt is supercooled below the melting temperature, the processes of mutual orientation related to the displacement of molecules virtually cannot occur because the viscosity of the system drastically increases and the chain mobility decreases. Hence, the state of one-dimensional orientational order should be already attained in the melt. During crystallization this ordering ensures the aggregation of extended portions to crystals of the ECC type fixed by intermolecular interactons on cooling. 

As compared to ECC produced under equilibrium conditions, ECC formed af a considerable supercooling are at thermodynamic equilibrium only from the standpoint of thermokinetics60). Indeed, under chosen conditions (fi and crystallization temperatures), these crystals exhibit some equilibrium degree of crystallinity at which a minimum free energy of the system is attained compared to all other possible states. In this sense, the system is in a state of thermodynamic equilibrium and is stable, i.e. it will maintain this state for any period of time after the field is removed. However, with respect to crystals with completely extended chains obtained under equilibrium conditions, this system corresponds only to a relative minimum of free energy, i.e. its state is metastable from the standpoint of equilibrium thermodynamics60,61). 

Similar methods to the above can be used to determine the 7-weight of a system composed of N molecules of vapor and N molecules of supercooled liquid. In this case, however, an exceedingly important difference arises when we consider the number of ways of arranging the molecules which make up the liquid phase. 

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