Nucleation thermal

Of course (as always in a delicate subject like the present one) I have my own critiques on certain points in the presentation for instance, in Section 5.3.1, coalescence is attributed to the thermal nucleation of a pore between two adjacent droplets. For me, discussing this channel is like discussing the sex of angels. Nucleation, in most physical systems, does not occur via plain thermal fluctuations. It involves external defects a cosmic ray in a bubble chamber, or a dust particle in a condenser. I believe that the same holds for emulsions dust particles (or small surfactant aggregates) control coalescence. 

The number of nuclei is assumed to be either constant (athermal nucleation) or varying with time (thermal nucleation). 

The average values n are indicative of thermal and/or athermal nucleation followed by a three-dimensional crystal growth. Indeed, for spherulitic growth and athermal nucleation, n is expected to be 3. In the case of thermal nucleation, it is expected to be 4 [2], However, complications in the Avrami analysis often arise because several assumptions, not completely applicable to polymer crystallization, are involved in the derivation. A comparison of some crystallization kinetics parameters is summarized in Table 3.5 [70-80]. 

In a first-order phase transition, the low-temperature (massive) phase would appear via thermal nucleation, which is a truly far-from-equilibrium process. Inside the bubbles of the new phase the baryon number-violating processes are stopped. So the question is this What is the net baryon concentration frozen ... 

As can be seen from Table 2.3, in the case of athermal nucleation the Avrami exponent equals the dimension of the geometry of the growing crystal entities 1 for fibrillar crystals, 2 for lamellar crystals, and 3 for spherulites. In the case of thermal nucleation, the Avrami exponent equals the geometry of the growing entities plus 1 (however, this is not true for diffusion-controlled processes). 

Another nucleation type is thermal nucleation, in which new crystals appear until all the melt is used up by crystal growth, as could occur in homogeneous nucleation. Often, thermal nucleation is described by the linear expression of Eq. (10) in Fig. 2.11. As can be seen from the top graph in Fig. 2.10, it is again necessary to introduce an induction time, t. After the induction time the indicated straight line describes the continuing nucleation. Nucleation stops in this case only when all material has been crystallized. 

A slightly more complex case involves thermal nucleation. The nuclei are here formed at a constant rate both in space and time, similar to normal rain. Let us select the case of three-dimensional growth at a constant linear rate. The number of waves (d ) which pass the arbitrary point (P) for nuclei within the spherical shell confined between the radii r and r + dr is given by ... 

The model of thermal nucleation of screw dislocations by Peterson [143, 144] and Young [150,151] has been shown to account fairly well for the plastic behavior of PE [152,153] and PP [154] and for the yield stress dependency on crystal thickness. Elastic line energy calculations indicate that nucleation of screw dislocations is more favorable than that of edge dislocations [155,156]. Glide is also easier for the former [157]. It has been shown that screw dislocations pai-allel to the chain stems may be nucleated firom the lateral surface of thin polymer crystal platelets upon coupled thermal and stress activation [143,144,158]. 

Table 14.4 shows the values of half-crystallization time and Avrami exponent n and rate constant k. The values of n around 1.4-1.5 suggest the rod-shaped crystal geometry and thermal nucleation type. Results show that rate constant k has been significantly changed due to inclusion of the carbon nanotubes. This suggests that carbon nanotubes restrict or interfere with the growth of the crystals that are around the vicinity of the carbon nanotubes. 

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