## 3 Results and Discussion
### Dispersion of Functionalized Silica Micro- and Nanoparticles by Ultrasound Micro-Moding Technology
It should be pointed out that the ratio between the two kinetic constants decreased (_i.e._, between 2.5 and 1.4) as crystallization temperature decreased, which justifies further studies on nucleation and crystal growth processes. Optical Microscopy Studies on the Influence of Functionalized Silica Nanoparticles on the Isothermal Crystallization of Poly(nonamethylene Azelate)  
Crystallization kinetics from the melt state was also studied for micro-molded samples with and without functionalized silica nanospheres by optical microscopy. Spherulite radii grew linearly with time until impingement in both cases, as shown in Figure 12. Crystal growth rates were clearly higher for the nanocomposite at high crystallization temperatures, whereas differences were minimal when this temperature decreased. The relatively high growth rate allowed for collecting experimental data only over a narrow temperature range where crystallization was mainly governed by secondary nucleation (_i.e._, the typical bell curve of crystal growth rate _versus_ temperature could not be obtained). The increase in the crystal growth rate for the nanocomposite is peculiar and suggests favored deposition of molecules onto existing crystal surfaces, as will be discussed. At lower temperatures, this effect seems to be counterbalanced by reduced chain mobility in the presence of silica nanoparticles and spatial constraints imposed by confinement [29, 30]. Figure 12: Variation of PE99 (**garnet**) and PE99-N 3 (**blue**) spherulite radii with time for isothermal crystallizations performed at the indicated temperatures. Pristine polyester and nanocomposite spherulites with similar morphological features were formed (Figure 13). Thus, both samples crystallized from the melt into ringed spherulites with negative birefringence. The spacing between rings decreased significantly with decreasing crystallization temperatures (_i.e._, 13 \(\upmu\)m at 60 \({}^{\circ}\)C and 5 \(\upmu\)m at 56 \({}^{\circ}\)C) and decreased slightly upon incorporation of nanospheres (_i.e._, 5 \(\upmu\)m as opposed to 4 \(\upmu\)m for crystallizations at 56 \({}^{\circ}\)C). A more confusing texture of less defined rings was detected at an intermediate temperature (_i.e._, 59 \({}^{\circ}\)C) for both samples. Note that pristine polyester and nanocomposite spherulites fill the field of view and have a relatively uniform size, suggesting athermal nucleation (_i.e._, the number of nuclei remains constant during crystallization). More interestingly, this result indicates good dispersion of silica nanoparticles in the polyester matrix. In fact, adsorption of PE99 molecules onto the functionalized surface of silica nanoparticles may hinder particle-particle agglomeration and enhance colloidal stability. Figure 13: Optical micrographs of PE99 (**a**,**c**,**e**) and PE99-N 3 (**b**,**d**,**f**) spherulites isothermally grown at 60 \({}^{\circ}\)C (**a**,**b**); first step at 59 \({}^{\circ}\)C and second step at 54 \({}^{\circ}\)C (**c**,**d**); and 56 \({}^{\circ}\)C (**e**,**f**). Well-defined rings with interspacing between 3 and 2 \(\upmu\)m were detected (see arrows) in the outer part of spherulites grown at 54 \({}^{\circ}\)C.  
Despite the morphological similarities, great differences were detected in the primary nucleation (Figure 14). They were more remarkable at low crystallization temperatures; for example, nucleation densities of 60 and 20 nucleus/mm\({}^{2}\) were determined from the optical micrographs taken at 57 \({}^{\circ}\)C. Note that crystal growth rates were similar at this temperature; consequently, the differences determined for the overall crystallization rate (e.g., 0.01284 and 0.00589 s\({}^{-1}\) for PE99 and PE99-N 3 at 57 \({}^{\circ}\)C, respectively) were mainly attributed to a nucleation effect. On the contrary, nucleation densities were similar at high temperatures, while crystal growth rates were clearly different.