«CURE KINETICS OF WOOD PHENOL-FORMALDEHYDE SYSTEMS By JINWU WANG A dissertation submitted in partial fulfillment of the requirements for the degree of ...»
parameters obtained from individual peak 1 and 2 as indicated by the subscripts in Eqs. (19) and (20).
where wi is the fraction of each reaction. In this study peak deconvolution allowed an estimate of relative heat of reaction for the two main exotherms at around wi = 0.5.
Within E 698 method, predictions are compared with parameters (A, E) obtained for peak 1 and peak 2 respectively, and also compared with combinations of two distinct exotherms as described in Eqs (19) and (20). The predictions are best when two independent or consecutive reactions (Eq. (19)) are assumed as indicated by the lowest mean squared error of prediction (MSEP) (Rawlings et al. 1998).
Figure 3.2 shows the test data and predictions of reaction rate and degree of cure for both resins by parameters from each one of the E698, nth- BD and M-auto, which are best among each method as evidenced by the lowest MSEP in Table 3.
Clearly, the MF kinetic models studied predict the degree of cure for PF resins better than the reaction rate. The failure to accurately model reaction rate of PF cure likely stems from the limitation of most MF kinetics to one reaction and the fact that PF cure involves multiple reactions as evidenced by the multiple exotherms in the PF-low and PF-high thermograms. When two independent or consecutive reactions (Eq.(19)) are assumed with E 698 method, two peaks are captured for the reaction rate of PF-high (Figure 3.2c). This method also predicts PF-high degree of cure very accurately after 70% conversion (Figure 3.2d). Over the entire cure process however, the nth-BD method produces the best predictions of degree of cure as evidenced by the lowest MSEP (Table 3.4). This is true for both resins. As a conclusion, none of the models evaluated accurately predict the reaction rate of the PF cure studied. However, the degree of cure is accurately predicted with the nth-BD method. But the MSEP values for this method are higher than those obtained with the model-free kinetics Kissinger-Akahira-Sunose (KAS) method in a parallel study (Wang et al. 2005). This indicates that overall, model-free kinetics methods are better than MF method for dynamic predictions.
Table 3.4 Mean squared errors of prediction (MSEP) for both dynamic and isothermal conditions at specific degree of cure and data points (in parentheses).
Figure 3.3 Experimental degree of cure (α) at 120°C and MF predictions for (a) PF-low and (b) PF-high.
Predicting cure for isothermal conditions The ability to predict isothermal cure from dynamic scan data is significant because dynamic tests are more repeatable and easily conducted compared to isothermal tests. In addition, such predictions provide further validation of the models.
The predictions of isothermal cure development from all three models are compared to experimental data in Figure 3.3. For PF-low, nth-BD is more accurate than others (Figure 3.3a). However, for PF-high, the E698 with an assumption of two independent reactions (Eq. (19)) is more accurate during the early curing period while nth-BD predicts a little better towards the end of cure. Across the cure regime studied, the nth-BD model performs better as evidenced by MSEP (Table 3.4). Generally, nth-BD method is the best prediction model of isothermal cure. Comparing with model-free kinetics KAS method in a parallel study (Wang et al. 2005), the MSEP with nth-BD is the same order with that by KAS for PF-high, and higher for PF-low (Table 3.4);
supporting the notion that the model-free kinetics KAS model is more accurate for isothermal prediction than nth-BD method.
CONCLUSION The applicability of model-fitting kinetics for predicting cure development of PF resins is compared. The Auto-BD is inappropriate for kinetic modeling of commercial PF resins. The activation energy obtained by nth-BD, E698 and M-Auto methods are comparable. All methods give inaccurate predictions of reaction rate while providing reasonable predictions for degree of cure in both dynamic and isothermal conditions. For a high molecular weight PF resin the E698 independent method provides an excellent local prediction of degree of cure above 70% under dynamic conditions, and works better at the early curing period under isothermal conditions. Altogether, the nth-BD method performs better than the other methods. Yet, the nth-BD predictions are not as good as those by model-free kinetics. On the other hand, they can be easily incorporated in a complex hot-pressing model. Considering that nth-BD method requires only one single heating rate, this method is recommended for simple kinetic modeling of PF resins.
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Chapter 4 Comparison of Model-free Kinetic Methods for Modeling the Cure Kinetics of Commercial Phenol-formaldehyde Resins ABSTRACT For many industrial processes it is important to model the cure kinetics of phenol-formaldehyde resoles. Yet the applicability of common model-free kinetic algorithms for the cure of phenolic resins is not known. In this study the ability of the Friedman, Vyazovkin and Kissinger-Akahira-Sunose (KAS) model-free-kinetics algorithms to model and predict the cure kinetics of commercial resoles is compared.
The Friedman and Vyazovkin methods generate consistent activation energy dependences on conversion compared to the KAS method. In addition, the activation energy dependency on conversion is of higher amplitude with these two methods than with the KAS method. Hence, the Friedman and Vyazovkin methods are more adequate for revealing the cure steps of commercial PF resoles. Conversely, the KAS algorithm is easily amenable to dynamic cure predictions compared to the Friedman and Vyazovkin methods. Isothermal cure is equally well predicted with the three. As a result, the KAS algorithm is the method of choice for modeling and predicting the cure kinetics of commercial phenolic resoles under various temperature programs.
Key words: phenol-formaldehyde, model-free algorithms, differential scanning calorimetry (DSC), cure prediction.
INTRODUCTIONPhenolic resins are widely used as binders in the composites industry, for thermal insulation and molding compounds (Knop and Pilato 1985). As for any thermosets controlling the degree of cure and cure kinetics is critical to designing the manufacturing process and the performance of the end-product. For characterizing cure kinetics differential scanning calorimetry (DSC) is the technique of choice (Prime 1997). During a DSC temperature scan phenol-formaldehyde (PF) resoles typically exhibit two exotherms (Luukko et al. 2001; Holopainen et al. 1997).
Although a subject of controversy the first exotherm is often ascribed to hydroxymethylphenols (HMPs) formation and condensation while the second exotherm is attributed to dimethylene ether linkages decomposition into methylene linkages between phenolic moieties (Luukko et al. 2001; Holopainen et al. 1997). In addition, commercial PF resoles for wood-based composites are often modified with up to 20 % wt urea (Kim et al. 1996) such that their cure may not be adequately modeled with traditional model-fitting kinetic methods (Vyazovkin and Wight 1997).
On the other hand, model-free kinetics (MFK) is well suited to portray the kinetics of complex reactions such as the cure of PF resins (Vyazovkin and Wight 1997;