Nucleation energy barrier

When 0= 0° this means that the liquid completely wets the solid, [(AGT)max]heterogeneous equals zero, and spontaneous heterogeneous nucleation occurs with no super-saturation at the equilibrium temperature. When 6 = 90° then [(AGT)max]heterogeneous is half the homogeneous value, and when 6= 180° both homo- and heterogeneous nucleation energy barriers are equal. 

Keywords polymer nanofibers, nanospider, nucleation, energy barrier. 

Heterogeneous nucleating agent improves cell morphology of the polymer foams made from poly(lactic acid) by microcellular extrusion. Mesoporous sihca was surface modified with heptadecafluoro-l,l,2,2-tetradecyl trimethoxy silane to decease nucleation energy barrier. The modified silica was found to be excellent nucleating agent for PLA foam production. ... 

Nucleation energy barriers depend upon the surface and volume energies associated with the reaction. A critical radius for the nucleus exists beyond which the new phase may grow spontaneously. 

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... 

Fig. 3. Curve ihustrating the activation energy (barrier) to nucleate a crystalline phase. The critical number of atoms needed to surmount the activation barrier of energy AG is n and takes time equal to the iacubation time. One atom beyond n and the crystahite is ia the growth regime.

The catalytic effect of solid particles (as ia heterogeneous nucleation) is to reduce the energy barrier to formation of a new phase. This, in effect, can reduce the interfacial energy O significantly. 

Spontaneous (Homogeneous) Nucleation This process is quite difficult because of me energy barrier associated with creation of the interfacial area. It can be treated as a kinetic process with the... 

The validity of mean field theory for N —y oo has striking consequences for the initial stages of phase separation. " In a metastable state slightly inside the coexistence curve, the nucleation free energy barrier is due to spherical droplets with a radius R The free energy excess of a droplet is written in terms of bulk and surface terms " "... 

For N x 1 the free energy barrier hence is very large and homogeneous nucleation is suppressed. Very close to T, where Eq. (10) does not hold, Eq. (15) is replaced by fm/kaTc... 

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... 

Equation 20 predicts a free-energy barrier for primary crystal nucleation (i.e., the free-energy difference between the top of the barrier and the initial coil state) as... 

Surface energetics and thermodynamic driving force thus define the energy barrier for nucleation as shown in Fig. 2.13b. For heterogeneous nucleation,... 

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