Nucleation temperature dependence

Instantaneous boiling takes place only if the temperature of a liquid is higher than its supeiheat-limit temperature (also called the homogeneous-nucleation temperature), in which case, boiling occurs throughout the bulk of the liquid. This temperature is only weakly dependent on the initial pressure of the liquid and the pressure to which it depressurizes. As stated in Section 6.1., T has a value of about 0.89T,., where is the (absolute) critical temperature of the fluid. 

The temperature dependence of the spreading rate is generally small and can often be neglected against that of the nucleation rate (but see Sect. 3.6.3). 

A more detailed picture of the temperature dependence of the growth is given in Figure 2.4, where the island density is plotted as a function of temperature. It can be seen that only in the temperature range from 207 to 288 K the growth is perfectly template controlled and the number of islands matches the number of available nucleation sites. This illustrates the importance of kinetic control for the creation of ordered model catalysts by a template-controlled process. Obviously, there has to be a subtle balance between the adatom mobility on the surface and the density of template sites (traps) to allow a template-controlled growth. We will show more examples of this phenomenon below. 

Reid et al. [ 1.12] described the effect of 1 % addition certain polymers on the heterogeneous nucleation rate at-18 °C the rate was 30 times greater than in distilled, microfiltered water and at -15 °C, the factor was still 10 fold hogher. All added polymers (1 %) influenced the nucleation rate in a more or less temperature-dependent manner. However, the authors could not identify a connection between the polymer structure and nucleation rate. None the less it became clear that the growth of dendritic ice crystals depended on to factors (i) the concentration of the solution (5 % to 30 % sucrose) and (ii) the rate at which the phase boundary water - ice crystals moved. However, the growth was found to be independent of the freezing rate. (Note of the author the freezing rate influences the boundary rate). 

Turnbull and Cech [58] analyzed the solidification of small metal droplets in sizes ranging from 10 to 300 xm and concluded that in a wide selection of metals the minimum isothermal crystallization temperature was only a function of supercooling and not of droplet size. Later, it was found that the frequency of droplet nucleation was indeed a function of not only crystallization temperature but also of droplet size, since the probability of nucleation increases with the dimension of the droplet [76]. However, for low molecular weight substances the size dependence of the homogeneous nucleation temperature is very weak [77-80]. 

Another interesting implication of the data compiled in Fig. 4 is that when Tc is plotted as a function of the inverse of the sphere diameter, the limit where the sphere diameter tends to infinity should correspond to the crystallization temperature of homogeneously nucleated PEO in the bulk. In other words, this would be the maximum temperature at which homogeneous nucleation for PEO could ever be observed, for very large heterogeneity-free PEO phases or even bulk PEO. Such a temperature depends on the fitting expression employed however, it should correspond to a crystallization temperature close to - 5 °C or between - 10 and 0 °C. 

The temperature dependence of the reaction was studied, and the activation energy of the reaction was calculated to be approximately 100 kj mol The exponent n was found to lie in the range 1-2, which is consistent with a 2D diffusion controlled reaction mechanism with deceleratory nucleation. The rate of reaction increases markedly with the amount of water added to the LDH with very small amounts of water added, the deintercalation process does not go to completion. This effect is a result of the LiCl being leached into solution. An equilibrium exists between the LDH and gibbsite/LiCl in solution. The greater [LiCl], the further to the LDH side this lies. 

The nucleation rate increased from 65°C to 70°C and dropped from 70°C to 80°C. Thus 70°C seems to be the optimum temperature for maximum nucleation. Published work on alumina trihydrate by Misra and White (5) and Brown (9 10) revealed that the nucleation rate decreases with increasing temperature, at greater than 70 C by the former but from 50 to 75°C by the latter. This nucleation rate dependence on temperature differs with normal chemical reaction where the reaction rate increases with increase in temperature. It is not clear whether then-studies at different temperatures in the published work were conducted at constant initial absolute supersaturation (AC7C ) for all the temperatures studied or at constant initial concentration. The latter would account for the higher nucleation rates obtained at lower temperatures as the AC/C is higher at lower temperatures since C decreases with temperature. 

It is remarkable that the predictions of classical nucleation theory without any consideration of polymer connectivity are borne out in experiments. At higher supercooling, deviations are expected because of temperature dependence of the nucleation rate prefactor. 

Bertram, A. K., and J. J. Sloan, Temperature-Dependent Nucleation Rate Constants and Freezing Behavior of Submicron Nitric Acid Dihydrate Aerosol Particles under Stratospheric Conditions, J. Geophys. Res., 103, 3553-356f (f998a). 

The temperature dependence of the nucleation rate allows many critical nuclei to be formed on a time scale that is small relative to the growth time when the difference between the actual solution and equilibrium temperatures is greater than a critical value, ATc. If the temperature variations of liquid density are neglected, the critical super saturation, A Tc, will vary with... 

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