Free energy for formation of a nucleus

Since Jo and C are proportional to the diffusion coefficient (D) and activation free energy for formation of a critical nucleus (AG ), respectively, it is concluded that the Z dependence of J is mainly determined by the diffusion process of the polymer chain and not by the formation process of a critical nucleus. 

Crystallization occurs in two stages - nucleation and growth. The free energy of crystallization involves the sum of (1) the free energy for formation on a stable nucleus embryo (AG ) and (2) the free energy for... 

Let us consider a simple model in order to get an idea about the pertinent features of the nucleation process. We assume that the nucleus contains n molecules and has a spherical shape. It can be shown that the Gibbs free energy for formation of such a nucleus with n molecules is given by the following ... 

Hong et al. [21] also observed for sPS/aPS blends melted at rmax = 300°C for tm x = 5 min, and then rapidly cooled, a decrease in G with addition of aPS. However, as the Tg values of sPS and blends are very close, the influence of the transport energy is explicitly ruled out, while it is suggested that the dilution of sPS in aPS increases the free energy associated with the formation of a nucleus of critical dimensions. 

It is clear from Equations (9.1) to (9.4) that the free energy of formation of a nucleus and the critical radius r, above which the cluster formation grows spontaneously, depend on two main parameters, namely a and (S/S ), both of which are influenced by the presence of surfactants, a is influenced in a direct way by the adsorption of surfactant onto the surface of the nucleus this adsorption lowers y and this in turn reduces r and AG in other words, spontaneous cluster formation will occur at a smaller critical radius. In addition, surfactant adsorption stabilises the nuclei against any flocculation. The presence of micelles in solution also affects the processes ofnucleation and growth, both directly and indirectly. For example, the micelles can act as nuclei on which growth may occur, and may also solubilize the molecules of the material this can affect the relative supersaturation and, in turn, may have an effect on nucleation and growth. 

AG is estimated by minimizing the sum of the two free energies the volume free energy decrease characteristic of a crystal volume increase and the surface free energy increase associated with the formation of fresh crystal surface. Mathematically, for an assumed spherical nucleus,... 

Mendelkem [42] noted that there are three different interfacial free energies that are characteristic of crystallites. One, is for the equilibrium extended chain crystallite, a second one a c represents the mature, but nOTi-eqiulibrium crystallite, and the third one is Uen is the interfacial free energy involved in forming a nucleus. These quantities caimot be identified with one another. Because only portions of the polymeric chains participate in the formations of crystallites, the section or sections of the chains of x length that participate in crystallite formation can be designated as (e and the sections of the chains that remain in disorder and amorphous, as x — Ce -... 

The reverse could be observed in a compatibilized blend. Because in these blends a serious decrease of the spheruhte size was observed, the authors concluded that the compatibihzer acted as a nucleating agent for the PP phase. However, due to the increase of the melt viscosity upon compatibilization, the overall crystallization kinetics was retarded. Additionally, they observed experimentally that AF (free energy for the formation of a nucleus of critical size) and (surface free energy of folding) in compatibilized blends were larger than in PA-6 homopolymer. An opposite trend was observed for the physical PA-6/EPR blends. No further investigations have been dmie to elucidate this phenomenon. 

In crystallizable dispersed droplets, several different nucleating heterogeneities (type i) can be present, each having a typical free energy for the formation of a nucleus of critical size, AF, at an undercooling ATc/. 

If the nucleation is a thermally activated process, then the rate of nucleation will depend exponentially upon the free energy of formation of a nucleus of the critical size for growth to occur. The Gibbs-Thomson relation ... 

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