Material Characterization for Quiescent Crystallization Kinetics

, (10.23)

with G₀= 7.5 × 10⁸µm/s.

10.1.5 Material Characterization for Quiescent Crystallization Kinetics

One of the major problems in using any kinetic model is the availability of enough experimen-tal data for fully describing the kinetics. In industrial applications, and especially for simu-lation, we need to collect the data efficiently. The experiments described below were mainly performed using differential scanning calorimetry (DSC), except for the crystal growth rate measurements, for which the shearing hot-stage Linkam CSS450 is employed. The Linkam cell was used in conjunction with an optical microscope and a computer-operated camera for im-age production at times of interest. The DSC experiments involve a switch from the cooling mode to the isothermal mode. If the crystallization starts too soon before reaching the isother-mal stage, the DSC cannot be reliable when applied to isotherisother-mal crystallization. Therefore, the experiments can only be performed in a limited temperature range, depending on the ma-terial to be tested. As an example to describe the experimental procedures, we choose an in-dustrial isotactic polypropylene (iPP), grade HD601CF, produced by Borealis, as the sample material. The iPP has Mw= 367 kg/mol, Mn= 74 kg/mol, and Mw/Mn= 4.96. The sample size in the DSC is approximately 5 mg, while for the Linkam cell 4 − 5 pellets are required for each run. The following experimental methods have been presented by Hadinata et al. [141].

10.1.5.1 Half-Crystallization Time

The half-crystallization time t1/2is defined as the time required to reach a relative crystallinity of 0.5. The sample is annealed first at 210^◦C for 5 minutes and then cooled to a desired crystal-lization temperature Tcwith a cooling rate of 30^◦C/min. Quiescent, isothermal crystallization occurs at Tc and is shown by the DSC as an exothermic peak. Figure 10.3 gives an example for the iPP sample at 132^◦C. The time-dependent relative crystallinity is calculated by integrat-ing the area inside the DSC crystallization curve. Various crystallization temperatures can be tested. The typical temperature range for iPP is 128–140^◦C. The range is chosen so that the crystallization times are not too long or too short, ensuring that the DSC signal can still be read clearly and no crystallization occur during cooling. The half-crystallization times at dif-ferent T_cs can then be obtained, which is also shown in Figure 10.3. The area under the peak is calculated to give the latent heat of crystallization.

10.1.5.2 Equilibrium Melting Temperature

The state of the semi-crystalline polymers in most cases is far from equilibrium, and therefore melting points (T_m) directly measured from DSC curves are almost always non-equilibrium

Figure 10.3 Isothermal crystallization curve of the Borealis iPP sample at 132^◦C. Inset: Variation of half-crystallization time with crystallization temperature

Figure 10.4 Heat flow curves for Borealis iPP

ones. The equilibrium melting temperature (T_m⁰) can be determined by extrapolations. A widely used method is the Hoffman-Weeks extrapolation method [158], which is described next, using the Borealis iPP sample as an example again. First, the sample is melted and an-nealed at 210^◦C for 5 minutes. Then the sample is cooled to the desired crystallization

tem-148 10 Crystallization

Figure 10.5 Determination of equilibrium melting temperature using Hoffman-Weeks method, for Borealis iPP. Melting point data measured on samples isothermally crystallized at different Tcs were used to determine the equilibrium melting temperature

perature (ranging between 128–140^◦C) with a cooling rate of 30^◦C/min. At this temperature, the sample is held until sufficiently crystallized. The sample is heated up again to 210^◦C to obtain the nominal melting point Tm. The above experiment is done for several crystalliza-tion temperatures. T_mvaries with T_c, as shown in Figure 10.4. The melting temperature T_m is plotted as a function of the crystallization temperature, T_c. A linear relationship between T_mand T_c is observed. The T_m= f (Tc) curve is extrapolated up to its intersection with the T_m= Tcstraight line. The intersection gives the value of T_m⁰ (Figure 10.5). The Hoffman-Weeks extrapolation method, however, is not very accurate. Improved experimental methods have also been discussed by Marand et al. [238] and Al-Hussein and Strobl [6].

For many crystalline polymers, the ratio Tg/Tmapproximately equals 2/3 [380]. This empirical rule is useful in the absence of data for T_g.

10.1.5.3 Crystal Growth Rate

For the crystal growth rate experiment, the Linkam cell is first heated up to the annealing tem-perature. Then, the sample (a few pellets) is put in, melted, and pressed to a thickness of 150µm. After placing the Linkam cell under the microscope, the temperature is cooled down to the desired crystallization temperature with cooling rate 30^◦C/min. The instant the Tc is reached is defined as t = 0. The development of structures is then monitored with the micro-scope, and photographs are taken at regular time intervals using the camera and the computer.

By measuring the radius of the spherulites at different times, the growth rate is known. Several

T_cs are tested to obtain the function G(T ). Figure 10.6 show the iPP spherulite growth at 132^◦C.

Figure 10.6 Isothermal crystal growth for Borealis iPP sample at 132^◦C under quiescent condition

For some industrial polymers, especially those having nucleating agents, the crystallization occurs too quickly for an observation of the spherulite growth under the microscope at the in-teresting temperature ranges. In these cases, one may use the van Krevelen equation (Equation 10.23) to estimate the thermal dependence of G(T ).

After t_1/2(T ) and G(T ) have been obtained, the nuclei number density can be evaluated by N₀= 3 ln 2±(4πG³t_1/2³ ). Here, we assume the nucleation is instantaneous in the quiescent crys-tallization.