Isothermal crystallization curve

Figure 7. Dynamic shear response (expressed as G, G , J" and tanS) of isotactic polypropyienes of varying crystallinity (torsion pendulum, 1Hz, ref 6). O 65%, O 56%, A 50%, achieved by annealing of quenched specimen ( 45%) + 68%, isothermally crystallized. Curves are calculated from parameterized equation (8).

Crystallization Kinetics. Typical isothermal crystallization curves, which were measured using cast films of both types of copolymers, are presented in Figures 9 and 10. At the early stage of crystallization, the effect of the noncrystalline PS block on the rate curves was only shifts of the degree of crystallinity [1 — A(t)] vs. time curve along the time axis. However, the extent of shift does not correspond to PS content in the block copolymers. The change in crystallization temperature also causes the crystallization curves to shift. At the initial stage of crystallization, these rate curves could be superimposed on the rate curve of the homo-PTHF (Mn = 6 X 104), and an Avrami exponent... 

From DSC data the degree of crystallization is estimated by plotting the fractional area of the isothermal crystallization curve as a function of time. The rate of nucleation as a function of crystallization temperature is shown schematically in Figure 5.4. The isothermal crystallization temperature should be chosen so that the crystallization proceeds at a rate which can be accurately measured. A practical difficulty is to determine the true zero time (to ) from which the isothermal... 

A) DSC isothermal crystallization curves of carbon fibre-reinforced nylon 6 composite. At the lowest isothermal crystallization temperature nucleation occurs too rapidly to be accurately measured and must be inferred from the shape of the crystallization exotherm (dashed line). (B) The corresponding log-log plot, based on equation 5.28, from which the coefficient n can be calculated... 

The relationship between B, and log t can be established from Figure 4.16 and equation (4.26) (isothermal crystallization curve). Generally, 0 may be expressed as a function of f according to the Avrami equation ... 

Ning (2007) have studied i-PP loaded with 1 and 10 % w/w of Halloysite nanotubes with diameters reported to be in the range of 50-300 nm and a length/diameter ratio of 3-10. As the non-isothermal crystallization curves (Fig. 3.19) show there is a clear but small nucleation effect from the halloysite nanotubes. Despite this the larger scale morphology was reported to remain the same for samples containing halloysite nanotubes as displayed for the i-PP alone. 

Fig. 3.19 Non-isothermal crystallization curves for i-PP and i-PP/HNT composites. Cooiing rate is 10 C/min. Reproduced from Polymer 48 (2007) 7374-7384 with permission from Elsevier— Ning (2007)...

Figure 2.40 shows an isothermal crystallization curve of a high-density polyethylene sample recorded by a Perkin-Elmer DSC7 (see Fig. 2.41 for Avrami plots). In the study of isothermal crystallization, the power compensation DSC is the preferred instrument among the presently available commercial DSCs, because the temperature difference between the sample and the reference cells is negligible, as described in Section 2.3. 

Figure 2.40. An isothermal crystallization curve of high-density polyethylene (courtesy of Perkin-Ehner). The area calculation is shown for the Avrami evaluation. Exotherm is down.

Figure 6. Non-isothermal crystallization curves of (a) PEN and (b) the PEN/CNT 0.1 nanocomposites at various cooling rates.

Figures shows the bulk isothermal crystallization curves for H84, which is typical for all the copolymers. The relative crystallinity Xt, is defined as, ...

Figure 4 DSC melting endotherms of P7MB after isothermal crystallization at 135°C, starting from the isotropic melt [10]. The curves correspond to 0, 3,6, and 35 min of crystallization time, from bottom to top. Scanning rate 5°C/min.

Fig. 11 Monomer distributions of 32-mers with Ef/Ec = 0.1 at Ec/k /T =0.174 vs. variable crystalline-stem lengths changing with time during isothermal crystallization at a specific temperature. The evolution time is denoted by the numbers (times 1000 Monte Carlo cycles) near the curves. The curves are shifted vertically with an interval of 300 for clarity. We can see that with time the peak shifts from one third to half of the chain length [56]...

The term /mux denotes the time needed to attain the maximum rate of crystallization. The time for this situation to occur is the tmax from the isothermal DSC curves as follows ... 

Figure 3. Isothermal DSC curves showing crystallization of polymethoxy-benzalazine ether, VII-Cg crystallization temperature is indicated for each curve. (Reprinted with permission from ref. 8. Copyright 1986 Sen-i Gakkaishi.)...

Fig. 8. Superheating of polyethylene extended chain crystals. Curves 1) at 421.7 K, 2) at 419.2, 3) at 417.7 K, 4) at416.7K, 5) at 414.7 K. The equilibrium melting temperature is 414.6 K. Drawn after Ref.40). "w is the weight fraction molten, obtained by isothermal calorimetry...

Figure 1. Isothermal magnetization curves of TbFe6Co5Ti single crystal for magnetic field along the main symmetry directions at different temperatures.

FIGURE 6.1 Solubility curves for various types of crystallization systems Curve A, isothermal solubility curve B, positive temperature coefficient of solubility curve C, negative temperature coefficient of solubility. 

Figure 18.7 Time evolution of degree of crystallinity of SPS of various Mw. Isothermal crystallization temperature T = 245 °C. Numbers on curves represent M of SPS...

From this analysis it is clear that the trade-off between kinetics and thermodynamics is not at all obvious. Consider a monotropic, dimorphic system (for simplicity) whose solubility diagram is shown schematically in Fig. 2.10. It is quite clear that for the occurrence domain given by solution compositions and temperatures that lie between the form II and I solubility curves only polymorph I can crystallize. However, the outcome of an isothermal crystallization that follows the crystallization pathway indicated by the vector in Fig. 2.10 is not so obvious since the initial solution is now supersaturated with respect to both polymorphic structures, with thermodynamics favouring form I and kinetics (i.e. supersaturation) form II. 

Fig. 1. Differential scanning calorimetry (DSC) isothermal analysis curves of fat A. blank sample, B. sample with DK F-10, C. sample with P-170, D. sample with S-170 (Emulsifier concentration is 0.5%). Isothermal crystallization at 17°C (right side), and heating curves (left side), start at about 20°C at a rate of 5°C/min (rapidly cooled at a rateof 80°C/min). (Continued)...

Isothermal crystallization of the oil or fat was monitored by a Perkin Elmer DSC 7 differential scanning calorimeter. Sample sizes range from 5 to 10 mg. The oil sample is heated to a temperature of 80°C at a heating rate of 5°C/min from ambient and held at that temperature for at least 10 min in order to totally erase all past crystallization memories. The sample was then cooled at a rate of 5°C/min until the desired crystallization temperature had been reached. The sample temperature was then maintained at this crystallization temperature for 2 h to monitor the complete crystallization behavior of the sample. Partial areas under the thermal curve were determined by means of the Perkin Elmer Pyris partial area analysis software. 

Figure 8. SAXS curves recorded during isothermal crystallization of PEO fraction Mn = 3000 at 43 °C. The initial NIF peak (first order) at t = 2 min gives way to extended and F2 peaks at approximately 5 x 10-3 and 10 x 10 3 A-1, respectively (from ref 58 by permission of John Wiley Sons).

Indicated in Fig. 9 are temperature ranges of supercooled, stable and superheated water at atmospherie pressure. Ibidem one can see curves representing the temperature dependenee of the logarithm of the homogeneous nucleation rate for crystallization (curve 1) and boiling-up (curve 2). The maximum rate of formation of vapor nuclei is attained at the approach of the spinodal determined by condition (3). Fig. 9 also shows how the inverse isothermal eompressibility =-v(5p/5v) changes with temperature (curve 3). An arrow shows the temperature of the spinodal of superheated water. 

Fig. 7. Small-angle X-ray scattering curves of polyethylene terephthalate after different times of isothermal crystallization from the amorphous state at 125 °C...

Another method for the determination of polymer crystallinity was discussed by Duswalt (159). It is based on the ability of the instrument to cool a molten sample rapidly and reproducibJy to a reselected temperature where isothermal crystallization is allowed to occur. A number of crystallization curves for polyethylene obtained isothermalJy at different, preset crystallization temperatures are shown in Figure 7.57. Differences in polymer crystallizability that may be caused by branching, nucleation, or molecular weight effects can be observed. The sensitivity and speed of the method allow pellet-to-pellet variations in a lot of polymer to be examined. 

Figure 7.14 Structural evolution of 10/90 iPP/POE isothermally crystallized at 130°C showing both the sectorized curved single crystal and crosshatched structure of iPP.

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