Non-isothermal crystallization rate

Gibbs-Thomson equation Hoffman-Weeks approach Isothermal crystallization Non-isothermal crystallization Rates of crystallization... 

The slope of the plots of the cooling crystallization function versus T has been suggested as a criterion for the overall non-isothermal crystallization rate. The non-isothermal crystallization of PPS is hastened by the presence of the VB phase, whereas, neither the type of nucleation nor the geometry of crystal growth changes, and no reduction of the PPS degree of crystallinity could be noticed. 

Choi WJ, Kim SC (2(X)4) Effects of talc orientation and non-isothermal crystallization rate on crystal orientation of polypropylene in injection-molded polypropyloie/ethylene-propylene rubber/talc blends. Polymer 45 2393-2401... 

Here, the non-isothermal crystallization rate, K T), is related to the isothermal crystallization rate, k T), by ... 

Equation 9.28 can be used to describe the kinetics of non-isothermal crystallization process imder quiescent conditiom However, the crystallization process in the spinning filament is non-quiescent, and the molecular orientation developed imder the tensile stress affects the crystallization rate. Therefore, the traditional non-isothermal crystallization rate, K T), must be replaced with the non-isothermal, stress-induced crystalhzation rate, K T,J), where / is the orientation factor. K T,J) also is called the total crystallization rate. With the total crystallization rate, Equation 9.28 can be rewritten to give ... 

The non-isothermal crystallization dynamics were performed using DSC, employing cooling rates of 2.5, 5, 10, 20, 25, 30, 35 and 40°C/min. The isothermal crystallization dynamics were studied for each sample heated to 290 °C, with a 5 min hold time, and cooled to the isothermal crystallization temperature using a cooling rate of 200°C/min, and then holding for 40 min to obtain the crystallization exotherm. 

The Ozawa equation of isothermal crystallization dynamics applied to non-isothermal crystallization assumes that the crystallization proceeds under a constant cooling rate, from the valid mathematical derivation of Evans [47], In... 

To applying Eq. (2.47) to non-isothermal problems, it is necessary to generalize it by introducing temperature-dependent constants. The basic approach was proposed by Ziabicki94,95 who developed a quasi-static model of non-isothermal crystallization in the form of a kinetic rate equation ... 

The observations of Campos etal. (2002) showed that in non-isothermal crystallization, the slow reduction of temperature results in a lower crystal volume containing larger crystals and a more heterogeneous spatial distribution of the mass. This gives a softer fat compared to when milk fat is crystallized at a faster rate. In laboratory experiments using a Bohlin rheometer as a crystallizer, Breitschuh and Windhab (1998) demonstrated that compound crystals were formed during supercooling and that less compositionally differentiated fractions were produced. 

Rtx Rate of change of temperature during non-isothermal crystallization. 

PLA crystallizes usually between 83 and 150°C but its fastest rate of crystallization occurs between 95 and 115°C [83]. The value of the crystallization half time (t, j) varies according to author. In the temperature range 95-115 °C the tj 2 of PLLA for crystallization from the melt varies between 1.5 min to 5 min [45, 79, 84]. Nevertheless the optimum, 1.5 min, is obtained at around 110°C for isothermal crystallization from melt (Figure 8.6) [45]. Not only does the tj of PLA depend widely on the crystallization temperature, but it is also linked to the crystallization type (isothermal or non-isothermal, from cold or melted state). So upon isothermal crystallization from the cold state, t is below 2 min [79, 85, 86]. Eventually, upon non-isothermal crystallization, t also lies around 2 min [85,87,88]. The further the isothermal crystallization is from this optimum, the more tj increases. For isothermal crystallization below 90°C or above 130°C, tj can be beyond 10 min [45, 69]. 

Upon non-isothermal crystallization the Avrami exponent takes on values between 2.1 and 4.82, whereas the Avrami crystallization rate constant are found between 0.0104 and 0.685 [85,87]. 

Abstract A number of theories for predicting non-isothermal crystallization of polymers have been proposed (1-5). Some are based on Avrami solution (2,3), others were derived independently (1,4,5). All are based on an "additivity" principle which states that the rate of crystallization at a time, t, depends on the extent of crystallization at time t, but not on the previous history (i.e., it is path independent). In this paper we present experimental results which show that, within a certain regime of cooling rates, the additivity principle applies to isotactic polystyrene. In a previous publication we have shown the same to be true for polyethylene (6). 

In blends of PPS with hyperbranched PPS, the crystallization temperature of PPS decreases by the addition of the hyperbranched PPS [77]. Also the rate of non-isothermal crystallization decreases as the energy of activation increases. 

From a technological point of view non-isothermal crystallization is important since many processing procedures are carried out under non-isothermal conditions. There are quite a number of approaches to non-isothermal crystallization. We restrict the discussion to non-isothermal conditions with constant cooling rate s. The Avrami equation serves as starting point for generahzations to non-isothermal conditions. We will discuss two approaches in detail that have been successfully applied. 

FIGURE 10 Non-isothermal crystallization of PTMS under various cooling rates s const, data after Chong et al. (2004), to the curve referring to T = 72 °C see below. 

Overall rate constants j for isothermal crystallization is given by Equation (3). In analogous way, one may define a rate constant for non-isothermal crystallization on base of Equation (34). This is done by replacing half time under T = const by half time of crystallization under condition s = const, (ATIs It follows ... 

Jeziomy directly applied Avrami equation to treat the non-isothermal crystallization peak in DSC scanning measurement (Jeziomy 1971). He obtained the Avrami index n and made a correction to K with the cooling rate a, as... 

Hu WB (2005) Molecular segregation in polymer melt crystallization simulation evidence and unified-scheme interpretation. Macromolecules 38 8712-8718 Hu WB, Cai T (2008) Regime transitions of polymer crystal growth rates molecular simulations and interpretation beyond Lauritzen-Hoffman model. Macromolecules 41 2049-2061 Jeziomy A (1971) Parameters characterizing the kinetics of the non-isothermal crystallization of poly(ethylene terephthalate) determined by DSC. Polymer 12 150-158 Johnson WA, Mehl RT (1939) Reaction kinetics in processes of nucleation and growth. Trans Am Inst Min Pet Eng 135 416-441... 

For non-isothermal crystallization, the process can be described by the modified Avrami equation in which the crystallization temperature is converted to time through heating or cooling rate,, by dividing crystallization temperature into infinity small [Equation (3)]. 

Non-isothermal crystallization during cooling is a cooling rate-dependent process. Ozawa extended the isothermal crystallization analysis to the non-isothermal case of controlled cooling rate [20,21]. This method accounts for the effect of cooling rate,, on crystallization from the melt by replacing t in equation (A) with T/ as Equation (5) ... 

The non-isothermal crystallization activation energy can be derived by the combination of cooling rate and exothermic peak temperature (Tp), shown as the Kissinger method [22] in Equation (6). 

Differential scanning calorimetry was used to study the non-isothermal crystallization behavior of blends of poly(phenylene sulfide) (PPS) with the thermotropic liquid-crystalline copoly(ester amide) Vectra-B950 (VB) [126], The PPS crystallization temperature and the crystallization rate coefficient increased significantly when 2-50% VB was added. The Ozawa equation was shown to be valid for neat PPS as well as for the blends. The values of the Avrami exponents matched well against those determined previously using isothermal analysis, and they are independent of the concentration of VB. 

Fig. 16.9. Phase distribution in high pressure non-isothermal crystallization experiments. The solidiflcations were carried out at a cooling rate of 5K/s 200° C...

The exfoliated graphite dramatically modified the non-isothermal crystallization behavior of the PP matrix, increasing the crystalhzation temperatirre, crystalhzation rate,... 

Dihthium hexahydrophthalate is an efficient nucleating agent of the non-isothermal crystallization of poly(lactic acid). The crystallization rate of PLA/0.5 wt% nucleator was faster than that of PLA/0.2 wt% nucleator, while AE of the former was lower than that of the latter. ... 

Isothermal and non-isothermal crystallization studies showed that the presence of nanofiller (multiwall carbon nanotubes, silver nanoparticles, nanodiamonds and copper-nanofibers) caused enhancement of crystallization rates and that the most effective nucleation was achieved using MWCNT. The crystals of a-type dominated, except in case of the sPS/MWCNT nanocomposite in which mairdy P-type crystals appeared. ... 

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