Nucleation rate energy barrier

Nucleation. The energy barrier and the nucleation rate depend critically on the supersaturation. 

The central quantity of interest in homogeneous nucleation is the nucleation rate J, which gives the number of droplets nucleated per unit volume per unit time for a given supersaturation. The free energy barrier is the dommant factor in detenuining J J depends on it exponentially. Thus, a small difference in the different model predictions for the barrier can lead to orders of magnitude differences in J. Similarly, experimental measurements of J are sensitive to the purity of the sample and to experimental conditions such as temperature. In modem field theories, J has a general fonu... 

Polymer crystallization is usually initiated by nucleation. The rate of primary nucleation depends exponentially on the free-energy barrier for the formation of a critical crystal nucleus [ 110]. If we assume that a polymer crystallite is a cylinder with a thickness l and a radius R, then the free-energy cost associated with the formation of such a crystallite in the liquid phase can be expressed as... 

Interestingly, this barrier does not depend on chain length. This result coincides with experimental observations on the primary nucleation rate of bulk polymers [128-130]. For secondary nucleation of crystallization on a smooth growth front, a similar free-energy expression can be obtained for 2D nucleation ... 

Shear enhancement effects in foam formation can be understood through the modified cavity model. Shear force behaves as catalyst to reduce energy barrier to allow a quik path from stable gas cavity to unstable bubble phase. It can be concluded that both shear rate and viscosity contribute to foam nucleation in the continuous foam extrusion process. Therefore, proper die opening and process conditions will help to optimise the foam product. 11 refs. 

Discontinuous transformations In this type of transformation, there is a free-energy barrier to infinitesimal variations and the system is initially metastable. However, a sufficiently large variation can cause the free energy to decrease. The transformation therefore can be initiated at a finite rate only by a variation that is large in degree but small in extent (i.e., nucleation is required). Examples include the formation of B-rich precipitates from a supersaturated A-B solution. 

Solution. Important assumptions include that the interfacial free energy is isotropic, that elastic strain energy is unimportant, and that the nucleation rates mentioned are for steady-state nucleation. The critical barrier to nucleation, AQe, can be calculated for the 0.3 atomic fraction B alloy using the tangent-to-curve construction on the curves in Fig. 19.18b to provide the value Aga = —9 x 107 Jm-3 for the chemical driving force for this supersaturation at 800 K. AQc is given for a spherical critical nucleus by... 

In both cases, the nucleation rate is a very strong function of the driving force. Essentially, the rate of nucleation is very low until some critical value of the driving force is reached. At this critical point, massive nucleation is then observed. This very sharp delineation in nucleation at some critical driving force leads to observation of a metastable zone, and is often related to the energy barrier that must be overcome for nucleation to occur. 

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