Overall crystallization kinetics

Generally, the inverse of half-crystallization time decreases with the D-isomer content, as reported by Kolstad, who indicates that the reduction is approximately 45% with increasing 1% in meso-lactide content. On the other hand, the effect of the molecular weight and similar o-isomer concentration shows that the inverse of half-crystallization time decreased with molecular weight as a consequence of the low chain mobility. 

The data obtained during the isothermal crystallization experiments by DSC can be fitted by the Avrami equation, which can be expressed as follows  

Inverse of crystallization half-time as a function of crystallization temperature, for PLAs with different molecular weight and D-isomer 

Auliawan et al7 studied ternary polymer blends of PLLA, poly(methyl methacrylate) (PMMA) and poly(ethylene oxide) (PEO) as matrix for nanocomposites. Their conclusions were that nanoclays enhanced the non-isothermal crystallization of the blend, since this ternary polymer blend hardly crystallized when cooled from the melt. The addition of vermiculite at loadings larger than 1% by weight retarded the crystallization process, while montmorillonite enhanced the crystallization process to some extent before retarding it. 

Xiao et al prepared blends of PLA with poly(butylene adipate-co-terephthalate) (PBAT), and followed their isothermal crystallization. They showed that the Avrami exponent was almost unchanged. However, the crystallization rate increased with the PBAT content. 

Centre of Molecular and Macromolecular Studies, Polish Academy of Sciences, Lodz, Poland 

Primary nuclei, forming when thermal fluctuations overcome a free energy barrier, appear randomly in space and in time, at a rate fluctuating around the momentary mean value, dictated for a given polymer by its thermomechanical history and crystallization conditions. Quiescent crystallization of homopolymers from the melt occurs usually in the form of spherulites growing radially from primary nuclei, as illustrated by 

Handbook of Polymer Crystallization, First Edition. Edited by Ewa Piorkowska and Gregory C. Rutledge. 2013 John Wiley Sons, Inc. Published 2013 by John Wiley Sons, Inc. 

Irrespective of structures encountered, the overall crystallization kinetics is characterized by a degree of conversion and a conversion rate. 

The conversion of polymer melt into growing entities is described by the conversion degree, which is a ratio of transformed volume or mass to the entire volume or mass of a crystallizing polymer portion, whereas the conversion rate is an increment of the conversion degree in an infinitely small time interval. The theories of overall crystallization kinetics are being applied in numerous papers to analyze the crystallization, especially the nucleation. Those theories are also widely used for predictions of the overall crystallization kinetics during processing, which is very important from the practical point of view. 

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In order to study the overall crystallization kinetics of the PCL block within PPDX-fo-PCL diblock copolymers, Muller et al. [ 103] first crystallized the PPDX block until saturation by performing a special thermal procedure (it consisted of first cooling from the melt as in Fig. 6 to allow both blocks to crystallize, then the sample was heated to 62 °C and annealed at that temperature for 70 min, a temperature at which the PCL is molten, before quenching to a Tc where the PCL block isothermal crystallization was followed by DSC). With the use of such a procedure the overall isothermal crystallization of only the PCL block was determined in the diblock copolymers where the PPDX block was already crystallized. 

Now, knowing the strong influence of particles (nuclei-I) on the overall crystallization kinetics, the increase of the crystallization rate with the gel ageing at ambient temperature (6,12,13,44,45) can be explained by the increase in the number of nuclei-I and/or the number of nuclei-II, respectively, during the gel ageing (11,12). 

The overall crystallization kinetics of blends can often be described by the Avrami equation [Avrami, 1939] ... 

In the following part, a discussion on the crystallization behavior in immiscible polymer blends is given, including the nucleation behavior, spheiuhte growth, overall crystallization kinetics, and final semicrystalline morphology. Each topic is illustrated with several examples from the literature, to allow the reader to find enough references on the discussed subject for further information. 

X indicates that the influence of different T on the overall crystallization kinetics have been investigated in the article mentioned... 

The overall crystallization kinetics of molten blends were analyzed by differential scanning calorimetry with a Perkin-Elmer DSC 2 apparatus. Following melting, the samples were heated at 85° C for 5 min. and isothermally crystallized at various T recording the heat of crystallization as a function of permanence time. The fraction of the material crystallized after time t was determined by means of the relation - Qt/Qoo> where Q - is the heat generated at time t and Qoo is the total heat of crystallization for t = . 

The details of the polymer crystallization process can be quite complicated. Practically, one may not care about the details of crystal nucleation and the linear crystal growth rates, but just want to characterize the overall crystallization kinetics. The degree of crystallization process can be roughly defined as crystallinity, regardless of their detailed crystal morphologies. The conventional methods to characterize the crystallinity include DSC, X-ray diffraction and dilatometer. Depending on the measured quantity, crystallinity is also separated into the weight crystallinity... 

Ozawa proposed to study the overall crystallization kinetics from several simple DSC scanning experiments (Ozawa 1971). Assuming that when the polymer sample is cooled from To with a fixed cooling rate a = dT/dt, both the radial growth rate v T) of the spherulites and the nucleation rate 1(T) will change with temperature. For a sphemlite nucleated at time t, its radius at time t will be... 

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. 

A comparison between the polarized optical micrographs taken at temperatures where the PCL block is molten for both PPDX-6-PCL and PLLA-6-PCL diblock copolymers of similar compositions (compare Fig. 13.8c and Fig. 13.10a), lead to the conclusion that when stronger thermodynamic segregation is present (as in PPDX-6-PCL diblock copolymers), the phenomenon of break-out is more difficult. Concurrently, the overall crystallization kinetics is much more strongly depressed at equivalent supercoohngs for the PPDX block than for the PLLA block when in both cases they are covalently bonded to molten PCL blocks. 

Figure 3.15b shows the overall crystallization kinetics data for the PE block within PLLA-Z)-PE (after the PLLA block was crystallized until saturation), PDLA-Z)-PE and also for a corresponding homo-PE. The crystallization rate of the PE block is reduced, as compared to homo-PE, regardless of whether it is covalently linked to amorphous PLDA or to semicrystalline PLLA. However, in the case of PLLA-Z)-PE, since the PLLA block was crystallized to saturation first, a nucleation effect of the PLLA crystals on the PE block was observed. This is obvious if we compare the PE crystallization in both PLDA-Z>-PE and PLLA-Z)-PE block copolymers. As the result of this nucleating effect, even though the crystallization rate of the PE block is depressed in the PLLA-Z>-PE diblock copolymer, the nucleation effect compensates this rate reduction and, in the end, the PE block attached to the semicrystalline PLLA can crystallize faster than that attached to amorphous PLDA. ... 

The overall kinetic parameters of polymers crystallized isothermally from the melt can be measured by DSC. The overall crystallization kinetics follow the Avrami equation ... 

Another important application for DSC is in isothermal tests. They are performed at constant temperature and are useful to determine overall crystallization kinetics, but can also be used to determine curing kinetics or monitoring isothermal polymerization. Chapter 11 details the use of DSC in isothermal mode, so it is not treated in this chapter. 

In order to bypass such limitations, the overall crystallization kinetics may be determined by DSC. However, in this case, both primary nucleation and crystal growth will make a contribution to the overall isothermal crystallization rate [6,7,12]. Ideally, it would be better to determine both spherulitic growth rate and overall isothermal crystallization kinetics in separate experiments, if possible. In the literature, the most commonly reported [30] type of isothermal crystallization kinetic data is that measured by DSC, because it is the easier to obtain. The DSC experimental approach can be very useful and in some cases, the DSC data thus obtained can provide not only the overall crystallization rate but also the separation of the individual contributions of the primary nucleation and growth rate (more details to follow). 

When the isothermal crystallization is determined by spherulitic growth experiments, the energy barrier determined by applying the LH model refers exclusively to secondary nucleation or crystal growth. Instead, when the inverse of half-crystallization time (1/t5q%) values obtained from DSC isothermal overall crystallization kinetic data is considered, both primary nucleation and crystal growth are considered. Therefore, the energetic parameters that we obtained after applying any classical kinetic crystallization theory to DSC data will include contributions from both processes. 

A(7) is a measure for crystal growth (G(7), from PLOM), or a measure for the overall crystallization kinetics (1/750%, from DSC). 

Figure 11.8a shows how the LH theory was applied to fit overall crystallization kinetics data of 1/t5q% versus 7). for the PPDX . Here, we have also assumed that crystal growth occurs under Regime II and the values of all parameters employed for the LH theory calculation are listed as a footnote in Table 11.4. 

Figure 11.8a shows the overall crystallization kinetics of PPDX obtained by DSC for neat and self-nucleated samples. When the sample is self-nucleated, the isothermal DSC data contain information of crystal growth only (assuming the self-nucleation process applied was 100% efficient in creating all necessary nuclei previously). In fact, the acceleration of the overall crystallization kinetics caused by the self-nucleation treatment is evident in Figure 11.8a, because the rates are higher for the self-nucleated sample as compared to neat PPDX at identical crystallization temperatures and also crystallization at lower supercoolings can be achieved in the self-nucleated samples. 

Figure 11.20 shows crystallization rate data as a function of the crystallization temperature for both polyethylene copolymers and for the polyethylene component within the blends. The linear low-density-type PE-1 crystallizes at much lower supercoolings than the very low-density-type PE-3. In the case of the blends, a nucleation effect caused by the previously crystallized polyamide phases was reported (the PA phases crystallize at higher temperatures than the PE phases see Ref [69]). This nucleation effect accelerates the overall crystallization kinetics and therefore the polyethylene component in the blends crystallizes faster than the corresponding neat polyethylene material, as shown in Eigure 11.20. 

Refs [56,64,68,72]). Supernucleation accelerates the primary nucleation rate and contributes to increase the overall crystallization kinetics. 

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