Avrami plot

Figure 20.24 Avrami plots of P(HB60-ET20)/PET (weight ratio, 4 3) T, 202.5 °C A, 205.0°C , 207.5°C , 210.0°C [44], From Park, J. K Park, Y. H Kim, D. J. and Kim, S. H., Crystallization kinetics of TLCP with polyester blends, J. Korean Fiber Soc., 37, 69-76 (2000). Reproduced with permission of The Korean Fiber Society...

Fig. 6. Avrami plots of the increase in volume fraction crystallinity as a function of time for Avrami exponents n from 1 to 6 (see Eq. (7)). For partial crystallization vc would be normalized to the ultimate crystallinity reached. K represents the geometry and time constants and nucleation terms19)...

Fig. 7. Double logarithmic Avrami plots for the crystallization of liquid crystalline poly(oxy-2 -dimethylazoxybenzene-4,4 -diyloxydodecanedioyl) to the fully ordered state between 322 and 362 K. Average of the Avrami exponent 3.5 0.3. Diagram courtesy J. Wiley and Sons27 ...

Fig. 535 Avrami plots showing the growth of the relative degree of crystallinity (

Figure 6.3 Avrami plot (Eq. 6.2) for different of PB- 1/HOCP 70/30 blend.

A series of non-isotherms with 5 = const is in that way characterized by an isothermal eqnivalent. There is a different law of conversion for each period of time. An example is given in Figure 10 for T=12 °C. Only a selected number of nonisotherms contributes to the Avrami-like relationship, from 5 = 7.5 to 30 K/min. As in isothermal Avrami plots (see Figure 2), deviations occnr at high conversions. The quasi-isothermal approach is depicted in Fignre 14 for non-isothermal ciystallization of PHBV. 

Rearrangement of Equation (1) arrives at Equation (2), and the calculation of estimated half-time crystallization from Avrami plot is shown in Equation (3). 

K " and n can be extracted from the intercept and the slope of Avrami plot, lg[-ln(l-.A0] versus lg(f-f ), respectively. The prime requirement of Avrami model is the ability of spherulites of a polymer to grow in a free space. Besides, Avrami equation is usually only valid at low degree of conversion, where impingement of polymer spherulites is yet to take place. The rate of crystallization of polymer can also be characterized by reciprocal half-time (/ 5). The use of Avrami model permits the understanding on the kinetics of isothermal crystallization as well as non-isothermal crystallizatioa However, in this chapter the discussion of the kinetics of crystallization is limited to isothermal conditions. 

FIGURE 18 Avrami plots for PEO/PiBMA 50/50 blends at T = 42 and 46 °C. Modified from Katime and Cadenato, (1995). 

Thus a plot of lg[-ln(l-A)] against Ig(t-tp) gives a linear curve, the slope of which gives the Avrami exponent and the y intercept gives the rate constant The values of and n are indicative of the crystallization mechanism. PTT with = 22,500 g mol and PI = 2.5 was subjected to isothermal crystallization at 205°C for 65 min. The corresponding Avrami plot is illustrated in Figure... 

FIGURE 11 Avrami plot for PTT after isothermal erystallization at T of 205 "C. Solid eurve represents the regression eurve after Eq. (3) (f- = 0.9967). 

Fig. 22. Avrami plots of melt-spun amorphous YojjFeo. v corresponding to various annealing temperatures.

Fig. 18 Avrami plot of the reduced scattering invariant IPhighW normalized to the extrapolated value of the scattering invariant at infinite time IPhighCt °o) for solutions with PVA volume fraction pva of 0.086 circles) and 0.042 squares). The Avrami exponents n are indicated. (Reproduced with permission from [77]. Copyright 2008 by the American Chemical Society)...

The numbers indicate thickness of PODMA lamellae or diameter of PODMA cylinders estimated based on i oDMA values from NMR. Peak maxima from scans with rates of dT/At = 10 K/min. Dynamic glass temperatures from c -maxima in TMDSC scans (time period tp = 60s, temperature amplitude Ta=0.4K, underlying heating rate - -2 K/min). Taken from scans with rates of 10 K/min ( 1 K/min). Taken from Avrami plots (Fig. 12.12). The uncertainty is about 0.2. The width of the transformation interval can be estimated from Alogtc = 1.253/n (cf. [37]). 

Fig. 12.12. Avrami plots for (a) two P(S—6—ODMA) block copolymers (Lam-9 nm,Cyl-ll nm) and a PODMA homopolymer and (b) block copolymers containing PODMA cylinders with different diameters (Cyl-11 nm,Cyl-16 nm,Cyl-24 nm) constructed based on master curves as shown in Fig. 12.11. Fits to the Avrami equation are indicated by solid lines. The fit parameters are given in Table 12.2...

Kinetics of crystallisation of the blends have also been studied by following crystallisation isotherms using DSC. Figure 7 presents an Avrami plot (16) for PA 66 and for the nylon matrix blends containing either EPR or functionalised EPR. From these data, half-times for crystallisation at 240 deg C were calculated. For PA 66, the half time is 1.6 minutes. Unmodified EPR in the nylon lowers this to 1.4 minutes, while with functionalised EPR in the blend, the value is 1.3 minutes. As reproducibility is only +/- 0.1 minutes, the difference between the two blends may be insignificant. However, it appears that the presence of EPR may increase the crystallisation rate of the nylon matrix. 

The two-dimensional condensation of bases proceeds by nucleation and growth mechanism, which can be analyzed by Avrami plot from the measurements of the capacitance-time curves [19, 28-32, 67]. 

Wandlowski and Pospisil [23, 86] have observed substantial deviations from the Avrami plot during the formation of compact layers of uracil at a hanging mercury drop electrode for long-time transients. They have found that compact layers of uracil are characterized by the fractal dimension which evolves with time. 

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 2.41. Avrami plots of the crystallization isotherms for biaxially oriented polypropylene after erasing the thermal history of the samples by heating them to 250 °C, which is much higher than the equilibrinm melting point of polypropylene...

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