Thermodynamics barrier to nucleation

Having described the equilibrium structure and thermodynamics of the vapor condensate we then re-examine homogeneous nucleation theory. This combination of thermodynamics and rate kinetics, in which the free energy of formation is treated as an activation energy in a monomer addition reaction, contains the assumption that equilibrium thermodynamic functions can be applied to a continuum of non-equilibrium states. For the purpose of elucidating the effects of the removal of the usual approximations, we retain this assumption and calculate a radially dependent free energy of formation. Ve find, that by removing the conventional assumptions, the presumed thermodynamic barrier to nucleation is absent. 

The onset of crystallization within the test tubes occurred wherever a nucleation site was available, typically on the inner wall or on the thermocouple rod. Large, feathery crystals were often observed growing into the sample. To control growth and circumvent the thermodynamic barrier to nucleation, we in some instances used a small bit of seed material with the same bulk composition as the solution. The density of the eutectic solid in all instances is less than that of the liquid solution. Thus, when the seed was deployed, it floated on the surface and crystal growth continued downward with a nearly planar solid-liquid interface. 

The first exponential term is sometimes referred to as the kinetic barrier to nucleation, whereas the second exponential term is known as the thermodynamic barrier to nucleation. And although it is not immediately obvious... 

Over-saturation is necessary to breakthrough the thermodynamic barrier of nucleation. According to the Ostwald-Freundlich equation, the concentration in a confined space CiCn = exp(2 aVm RTr). Figure 2 shows the dependence of... 

Although the Langelier index is probably the most frequently quoted measure of a water s corrosivity, it is at best a not very reliable guide. All that the index can do, and all that its author claimed for it is to provide an indication of a water s thermodynamic tendency to precipitate calcium carbonate. It cannot indicate if sufficient material will be deposited to completely cover all exposed metal surfaces consequently a very soft water can have a strongly positive index but still be corrosive. Similarly the index cannot take into account if the precipitate will be in the appropriate physical form, i.e. a semi-amorphous egg-shell like deposit that spreads uniformly over all the exposed surfaces rather than forming isolated crystals at a limited number of nucleation sites. The egg-shell type of deposit has been shown to be associated with the presence of organic material which affects the growth mechanism of the calcium carbonate crystals . Where a substantial and stable deposit is produced on a metal surface, this is an effective anticorrosion barrier and forms the basis of a chemical treatment to protect water pipes . However, the conditions required for such a process are not likely to arise with any natural waters. 

Ve see in Figure 7 that Tolman s representation of the radially dependent surface tension also leads to a vanishing thermodynamic barrier, at high but metastable supersaturations, when a value of 6 computed from solutions of the YBG equation on the planar interface is used. This value of the Tolman parameter is consistent with values obtained from simulation studies of the planar Lennard-Jones surface (28,29). It is apparent that the physical picture of nucleation is highly dependent upon the assumed radial dependence of the surface tension. 

Atomistic theory of nucleation — The theory applies to very small clusters, the size n of which is a discrete variable and the process of nucleus formation must be described by means of atomistic considerations. Thus, the thermodynamic barrier AG ( ) that has to be overcome in order to form an n-atomic nucleus of the new phase is given by the general formula [i-v]... 

Na is the Avagadro number). The nucleation process just described is known as homogenous nucleation and the nuclei formed are due to thermal fluctuation. The thermodynamic barrier, Wmax for the homogeneous nucleation can decrease significantly if the nucleation takes place on surfaces of other materials (particles) already present in the melt. 

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