«CURE KINETICS OF WOOD PHENOL-FORMALDEHYDE SYSTEMS By JINWU WANG A dissertation submitted in partial fulfillment of the requirements for the degree of ...»
during cure processes; respectively. The normalized mechanical cure under linear and isothermal heating regimes are shown as in Figure 8.2(c) and (d); respectively.
It is generally assumed that the heat evolution by DSC is proportional to the molecular network formation, but the elastic modulus is only proportional to the molecular network density if the entire curing process proceeds in the rubbery state (Malkin et al. 2005). This assumption only holds for the PF-wood system when the curing temperature is always greater than the glass transition temperature of forming polymer. In order to investigate the relationship of mechanical degree of cure with chemical degree of cure, the chemical cure kinetics was obtained by DSC with small discs taken from DMA samples. The evolution of α at linear heating rates (Figure 8.2a) was determined by the Mettler-Toledo DSC STARe software. Due to difficulty and accuracy problems of the isothermal DSC scans (Wang et al. 2005), the evolution at isothermal temperature (Figure 8.2b) was predicted according to the model-free Vyazovkin method (Wang et al. 2005). By comparing α to the prevailing time or temperature with the corresponding β (as shown by arrows in Figure 8.2), the relationship between chemical cure and mechanical cure was obtained in Figure 8.3. It was observed that the mechanical cure changed with chemical cure following a sigmoid.
Figure 8.2 The evolution of degree of cure at different cure conditions: (a) Chemical cure by DSC at 2, 3, 4, 5, 10, and 15 °C/min from left to right, (b) Predicted chemical cure at isothermal temperature 90, 100, 110, 120, 130, 140, and 160 °C bottom up by Vyazovkin model-free kinetics from DSC ramp data in (a), (c) Mechanical cure by DMA at 2, 3, 4, and 5 °C/min from left to right for aluminum foil-wrapped PF bonded wood joints, and (d) Mechanical cure by DMA at 90, 100, 110, 120, 130, 140, and 160 °C bottom up for aluminum foil-wrapped PF bonded wood joints.
Figure 8.3 Relationship between mechanical cure (β) and chemical cure (α) from aluminum foil-wrapped PF bonded wood joints under isothermal temperature (a) and linear heating rate (b).
Under both isothermal and linear heating regimes, a comparison of mechanical cure with chemical cure includes: (1) a slow rate increasing or delay period of front tail; (2) a rapid increase in mechanical properties with medium to high levels of α; (3) a decreasing rate of mechanical property development leading to a cessation of mechanical cure. At low isothermal temperatures, the onset of mechanical cure was almost identical to the onset of chemical cure; however the sensitivity of mechanical cure development at the early stages of chemical cure was low. For these conditions, the cessation of mechanical cure occurred at a low chemical cure of around 0.6. With increasing isothermal temperature, the onset of mechanical cure was delayed until substantially high amounts of chemical cure accumulated. When the curing temperature was 160 °C, the mechanical cure did not start until the chemical degree of cure reaches 0.7 and the cessation of mechanical cure approached fully chemical cure.
These observations indicate that the initial stages of chemical cure did not increase viscosity or shear modulus proportionally. When the curing temperature is high, the resin needs to attain substantial chemical cure to resist the softening effects of temperature. One might have expected that β depends only on the state of α and is independent of the time and cure regimes. The observations from the present study clearly indicated that although the β under the different cure conditions followed the same trend, the effect of cure temperature on the E’ was clearly discernable. While the mechanical stiffness was influenced by chemical advancement, the cured materials are in a state of expansion and under the influence of temperature. Therefore, with an increasing heating rate or isothermal temperature, a higher degree of cure is required to achieve an equivalent modulus observed at a lower temperature. Hence, the cure curve shifted to the higher degree of chemical cure as the cure temperature increased.
The curing temperatures (peak temperature at tan δ peak) at heating rate 2 and 3 °C /min were ca. 128.5 and 137.0 °C (Wang et al. 2007). It is noted that relation of β−α curves developed from the ramp heating experiments at 2 and 3 °C /min were coincidently located in the same region as those from the isothermal temperatures of 130 and 140 °C (Figure 8.3). Similarly, the β-α curves under 4 and 5 °C /min heating ramps were located between the curves for 140 and 160 °C (Figure 8.3) since curing windows at these heating rates were around 150 °C.
In Figure 8.4, it is shown that the wood/PF system has a glass transition temperature around 145 °C by DSC. However, it is more appropriate to think of glass transition temperature as a region with an onset, a midpoint and an associated breadth.
When the cure development was investigated in this region (130-160 °C), mechanical cure did not begin until substantial chemical cure occurred. However, regardless of the beginning, final mechanical and chemical cure occurred at similar points (Figure 8.3).
Figure 8.4 DSC thermgram at 10 °C/min showing glass transition temperature for a sample with two small pieces of basswood discs bonded by PF, trimmed from the DMA specimen after scanned from room temperature to 240 °C at 5 °C/min.
summarized in Table 8.1and Table 8.2. The gelation point defined by second peak on tan δ curve (Figure 8.1) was very close to the onset of mechanical cure as evidenced by small value for β. It has been reported that gelation occurs at a constant conversion, which is independent of cure regimes for a given thermosetting material (Prime 1997).
In this study, the average value of α at gelation was ca. 0.51 and was relatively constant across heating rates (Table 8.1). There were other reports that gelation was not iso-conversional under different cure regimes suggesting the heterogeneity of the curing process, as shown by Han and Lem (1983), and Malkin et al. (2005). Gelation was only recorded for the linear heating regime with aluminum foil-wrapped PF bonded wood joints because this event was not consistently evident in other samples.
The value for α at the vitrification point increased with heating rate or isothermal temperature. That is, vitrification occurred at higher degrees of cure with increasing cure temperatures, which was in agreement with the report for an epoxy resin (Yu et al. 2006). Such a result was reasonable since at high temperature, the resin needed to reach a high degree of cure required to achieve a glass transition to exceed the cure temperature. For example, at 90 °C, the α of 0.22 rendered a glass transition temperature for the system beyond the 90 °C, while at 160 °C, the α of 0.95 are required to achieve a glass transition temperature of forming polymer to exceed the cure temperature for vitrification. In this sense, Table 8.2 also provides the relationship of α and the Tg, which was linear in the studied temperature region.
Table 8.1 Corresponding mechanical and chemical degree of cure at gelation and vitrification points under the linear heating regime for aluminum foil-wrapped PF bonded wood joints.
Table 8.2 Corresponding mechanical and chemical degree of cure at the vitrification points under the isothermal heating regime for foil-wrapped PF bonded wood joints.
where k and m are fitting parameters obtained with nonlinear regression. When investigating these parameters (Table 8.3) under different isothermal and linear heating regimes, it was noted that both were dependent on the isothermal cure temperature or heating rate (Figure 8.5). The sensitivity of β to changes in α, is defined by dβ/dα. This derivative is directly defined by the slope in plot of β versus α (Figure 8.3) and can be directly calculated from Eq. (66). Also note that when (kα)m = (m-1)/m, dβ/dα reaches a maximum.
Experimental data of dβ/dα are presented in Figure 8.6 under isothermal heating regime and in Figure 8.7 under linear heating regime. By comparing the α defining the maximum of dβ/dα, it was found that the peak slope coincided with vitrification; i.e. in the vicinity of the vitrification point, small changes in chemical advancement promoted a large mechanical increment. Mechanical properties are mainly related to molecule mobility and therefore, relaxation time.
It was concluded that mechanical cure changed with chemical cure following a sigmoid. Both the initial α and final curing stages contributed little to the state of mechanical cure. The chemical cure and mechanical cure are not equivalent and β changed with the curing regime at specific chemical degree of cure.
Table 8.3 Parameters for the relationship equation of mechanical and chemical cure
Figure 8.5 Temperature dependence of parameters for the relationship equation of the mechanical and chemical degree of cure under isothermal temperatures, T in Celsius degree.
Figure 8.6 Sensitivity of mechanical property development to chemical advancement at designated isothermal temperature computed from experimental data.
Figure 8.7 Sensitivity of mechanical property development to chemical advancement at designated linear heating rates.
Model-free kinetics of the mechanical cure development
al. 2005; 2006). The relationship between chemical and mechanical degree of cure has been described by Eq.(65). In the following, model-free kinetics is used to describe the mechanical cure development by DMA. Using this approach, either α or β can be computer using a kinetics approach and then related to the other through Eq.
(65). The basic assumption of the model-free methods is that activation energy is dependent on the development of the reaction. The MFK Friedman, Vyazovkin, KAS and time event algorithms can then be used to determine the activation energy dependence on the advancing degree of cure. The basic kinetic model formulated for
The direct use of Eq. (67) gave rise to the differential method of MFK Friedman ((68)) that could be applied to isothermal as well as to ramp data (Wang et al. 2005).
where Cf (β) and Eβ are MFK Friedman complex parameter and activation energy;
respectively (subscripts β and i refer to specific mechanical degree of cure and a series of heating regimes hereafter). For isothermal conditions, integration and
rearrangement of Eq. (67) yields:
the time required to reach a specified conversion, β, at an iso-temperature, Ti. Let Ct(β) = ln(g(β)/Aβ), then Eβ and Ct(β) was evaluated from the slope and intercept of the plot ln∆tβi against reciprocal of temperature 1/Ti. This method was thereafter referred as the time-event model-free kinetics.
For ramp conditions, the model-free KAS method uses Eq. (70) (Wang et al.
Likewise, the model-free Vyazovkin method can be applied to isothermal and ramp data to obtain two set of parameters. In the Vyazovkin method, n scans are performed at different heating regimes Ti(t). The activation energy at a specific degree of cure is
obtained by minimizing the function ϕ(Eβ) (Wang et al. 2005):
Figure 8.8a depicts the activation energy curves for PF bonded wood joints wrapped with foil.
The parameters are calculated from isothermal data using the time-event and Vyazovkin methods; from ramp data by the KAS, Friedman and Vyazovkin methods.
As Wang et al. (2005) demonstrated that the activation energy curves were overlapped by Friedman and Vyazovkin methods from DSC data, the activation energy curves were also overlapped by these two methods from DMA data. To simplify the graphs, the activation energy curves by the Friedman method are not plotted in Figure 8.8a. It was observed that the activation energy computed from ramp data by the KAS method nearly overlapped with that from isothermal data by time–event method. The most notable exceptions are at a low degree of cure. In this case, the activation energy obtained from both ramp and isothermal data with the Vyazovkin method followed a similar pattern. Average activation energies are 52.6 and 49.4 kJ/mol from isothermal data by Vyazovkin and time event, and are 50.1, 47.8 and 52.2 kJ/mol from ramp data by Vyazovkin, Friedman and KAS methods; respectively. They are in general agreement with those obtained by model-fitting kinetic approaches (Wang et al. 2007).
The MFK combined parameters C(β) are shown in Figure 8.8b. Their physical meanings are not obvious and can be used with activation energy to fully describe cure development.
Figure 8.8 Activation energy dependence of mechanical cure (a) and combined parameters (b) obtained by KAS, time event, and Vyazovkin methods for aluminum foil-wrapped PF bonded wood joints.