«CURE KINETICS OF WOOD PHENOL-FORMALDEHYDE SYSTEMS By JINWU WANG A dissertation submitted in partial fulfillment of the requirements for the degree of ...»
Although the specific reactions underlying the four stages cannot be identified solely based on this study, this cure behavior is in line with the individual cure reactions of urea-modified PF resins. PF cure involves a set of parallel reactions with HMPs formation, condensation and the various crosslinking chemistries (Detlefsen 2002). With the addition of urea, condensation of phenol and urea with formaldehyde as well as co-condensation between phenol and urea derivatives are also taking place (He and Yan 2004). The changing contribution of each reaction to the overall activation energy explains the constant change in activation energy as cure progresses (He and Riedl 2003). Since water is remains in the crucible during cure, the cure process is further complicated (He et al. 2003b). At low conversion water contributes to reversible reactions (He et al. 2003b). At high conversion, water plasticizes the PF network thus delaying diffusion control and allowing for more complete cure (He et al.
For PF-high an even more complex cure mechanism is observed with the presence of 2 highest Eα peaks at 10% and 77% conversion but also two small Eα peaks at 40% and 90% degree of cure. The greater complexity likely stems from the detection of 3 exotherms on the DSC thermogram for PF-high (Figure 4.1). In all case PF-high likely exhibits a similar 4-steps pattern as PF-low does. That is competitive condensation reactions occur up to 10%; they are followed by a reversible intermediate stage up to 27 % degree of cure. Competing crosslinking reactions then resume until diffusion rate control occurs at 77 % degree of cure as previously observed on phenolic systems (He et al. 2003a; He and Riedl 2003). The Eα peaks shoulders at 40% and 90% may arise from a mathematical artifact.
combined complex parameter C(α). The degree of cure dependence of this parameter with all three methods also reflects the changing cure mechanism as shown for PF-high (Figure 4.3). Because this parameter is a modeling tool deprived of distinct physical meaning no inferences are made from its pattern. Next C(α) and Eα obtained from the 3 methods are utilized for assessing MKF predictions during dynamic and isothermal cure of PF resins.
Prediction of dynamic cure of PF resins
cure (He et al. 2003a). Therefore only the KAS method was used to predict the dynamic cure of PF resins. At a selected heating rate Ck(α) and Eα were substituted into Eq. (32) to predict the temperature associated with discrete values of α. An algorithm based on the Powell dogleg method (Powell 1970) was developed with MATLAB to solve Eq. (32). Relationships between temperature and degree of cure were thus obtained and were easily converted to reaction rate-temperature relationships at specific heating rates. Figure 4.4 compares experimental reaction rate and degree of cure with the KAS predictions for PF-high and PF-low respectively.
Recall that the model was built from data at 2, 5, and 10oC/ min only whereas predictions are also made at 20 and 25oC/ min for model validation. Mean squared errors of prediction (MSEPs) (Rawlings et al. 1998) were calculated for both dynamic and isothermal MFK predictions (Table 4.1). The MSEP is the average squared difference between independent experimental observations and model predictions for the corresponding values of the independent variable (Rawlings et al. 1998). The MSEP values of the KAS predictions for temperature and reaction rate are small, both one order of magnitude lower than those obtained with the best model-fitting kinetics in a parallel study (Wang et al. 2006). The KAS method therefore provides excellent dynamic predictions compared to model-fitting kinetics. This is further evidenced in Figure 4.4, where the KAS algorithm succeeds in capturing the complexity of PF-high thermogram.
α(%) Figure 4.4 Comparisons of experimental data and KAS predictions for dynamic conditions at 2, 5, 10, 20 and 25 oC/min for (a) the reaction rate of PF-high and (b) the degree of cure of PF-low.
Table 4.1 Mean squared errors of prediction for both dynamic and isothermal conditions at specific degree of cure and data points (in parentheses).
Prediction of isothermal cure of PF resins Prediction of isothermal cure from dynamic scans is of scientific and practical interest. First, good prediction of isothermal cure from parameters obtained during dynamic cure clearly validates the models. Second, isothermal cure characterization is notoriously challenging from the experimental standpoint (Widmann 1975). In this study, Friedman, Vyazovkin and KAS algorithms were used to predict the isothermal cure behavior of the two PF resins at 120°C. The premise of isothermal prediction is that pairs of α and the corresponding f(α), g(α), Eα and A values are identical for dynamic and isothermal conditions (Doyle 1962). Hence, MFK parameters can be used to develop a prediction model of the cure time needed to achieve a specific degree of cure, tα, at a given temperature (Tiso).
At each small ∆α, the left integral is evaluated numerically with the trapezoid integration rule and the corresponding ∆t is calculated. This calculation is reiterated from time 0 on. Thus at an arbitrary isothermal temperature a relationship between tα and α is established.
Finally, the KAS parameters are used to reorganize Eqs. (24) and (32) into:
Isothermal cure predictions from all three MFK algorithms are compared with experimental data for PF-low and PF-high in Figure 4.5. The small MSEP values (MSEP 19.4) for both resins and all three models (Table 4.1) indicates the quality of the models compared to those determined in another study (Wang et al. 2006) from n-order kinetics (MSEP 33). Analysis of variance (ANOVA) at an α level of 0.05 detected no differences in the isothermal prediction ability of the three MFK algorithms. Overall, the cure of PF-low and PF-high resins is equally well predicted with MFK methods. Yet, locally the isothermal data for PF-low does not capture the complexity of the cure prediction in the 10-20 minutes range (Figure 4.5).
Figure 4.5 Comparison of experimental data with the Friedman, Vyazovkin and KAS predictions of degree of cure of PF-low and PF-high during isothermal cure at 120°C.
CONCLUSION The cure development of two commercial PF resoles was analyzed by the Friedman, Vyazovkin and KAS model-free kinetics. The three algorithms were compared in their consistency and ability to perform dynamic and isothermal predictions. The Friedman and Vyazovkin methods generated consistent and accurate activation energy dependences on degree of cure. These two algorithms were also the most sensitive to changes in activation energy. Higher consistency and accuracy of the Friedman and Vyazovkin methods compared to the KAS algorithm were ascribed to the use of a close-form approximation of the kinetic equation in the latter algorithm.
On the other hand, the KAS algorithm was more amenable to dynamic cure predictions. For isothermal cure predictions the three MFK algorithms provided equally good predictions. In all cases, predictions with MFK were significantly better than those measured in a parallel study with model-fitting methods. Hence, the Friedman and Vyazovkin methods are best suited for activation energy measurement.
These two methods are the most appropriate for gaining insight on the cure mechanisms of commercial PF resoles. Alternatively, the KAS method is best suited for modeling and prediction purposes.
REFERENCES Brent, R. P. Algorithms for minimization without derivatives. Englewood Cliff, N.J., Prentice-Hall, 1973.
Butt, J. B. Reaction Kinetics and Reaction Design, second ed., Marcel Dekker, Inc., New York, 1999.
Budrugeac, P.; Segal, E. Some methodological problems concerning nonisothermal kinetic analysis of heterogeneous solid-gas reactions. International Journal of Chemical Kinetics (2001), 33(10), 564-573.
Detlefsen, W.D. Phenolic resins: Some chemistry, technology, and history, in: M.
Chaudhury, A.V. Pocius (Eds.), Surfaces, chemistry and applications, Elsevier, Amsterdan, 2002, pp. 869-945 Doyle, C. D. Kinetic analysis of thermogravimetric data. Journal of Applied Polymer Science (1961), 5, 285-92.
Doyle, C. D. Estimating isothermal life from thermogravimetric data. Journal of Applied Polymer Science (1962), 6(No. 24), 639-42.
Flynn, J. H.; Wall, L. A. General treatment of the thermogravimetry of polymers.
Journal of Research of the National Bureau of Standards, Section A: Physics and Chemistry (1966), 70(6), 487-523..
Friedman, H. L. Kinetics of thermal degradation of char-forming plastics from thermogravimetry-application to a phenolic resin. Journal of Polymer Science (1964), Volume Date 1963, No. 6(Pt. C), 183-95.
He, G.; Riedl, B.; Ait-kadi, A. Model-free kinetics: Curing behavior of phenol formaldehyde resins by Differential Scanning Calorimetry. Journal of Applied Polymer Science (2003a), 87, 433 -440.
He, G.; Riedl, B.; Ait-kadi, A. Curing process of powdered phenol formaldehyde resol resins and the role of water in the curing systems. Journal of Applied Polymer Science (2003b), 89, 1371-1378.
He, G.; Riedl, B. Phenol-urea-formaldehyde cocondensed resol resins: their synthesis, curing kinetics, and network properties. Journal of Polymer Science, Part B: Polymer Physics (2003), 41(16), 1929-1938.
He, G.; Riedl, B. Curing kinetics of phenol formaldehyde resin and wood-resin interactions in the presence of wood substrates. Wood Science and Technology (2004), 38(1), 1432-5225.
He, G.; Yan, N. 13C NMR study on structure, composition and curing behavior of phenol-urea-formaldehyde resole resins. Polymer (2004), 45(20), 6813-6822.
Holopainen, T.; Alvila, L.; Rainio, J.; Pakkanen, T. T. Phenol formaldehyde resol resins studied by 13C NMR spectroscopy, gel permeation chromatography, and differential scanniong calorimetry. Journal of Applied Polymer Science (1997), 66, 1183-1193.
Kay R.; Westwood, A. R. Differential scanning calorimetry (DSC) investigations on condensation polymers. I. Curing. European Polymer Journal (1975), 11( 1), 25-30 Kim, M. G., Watt, C.; Davis, C. R. Effects of urea addition to phenol-formaldehyde resin binders for oriented strandboard. Journal of Wood Chemistry Technology (1996), 16, 21-29.
Kissinger, H. E. Reaction kinetics in differential thermal analysis. Analytical Chemistry (1957), 29, 1702-1706.
Knop, A.; Pilato, L. A.; Phenolic Resins, Springer-Verlag, New York, 1985.
Luukko, P.; Alvila, L.; Holopainen, T.; Rainio, J.; Pakkanen, T. T. Effect of alkalinity on the structure of phenol-formaldehyde resol resins. Journal of Applied Polymer Science (2001), 82(1), 258-262.
Nelson, D. W.; Sommers, L. E. In Methods of soil analysis, Part 2. Chemical and microbiological properties, second ed., Page, A.L., Ed.; American Society of Agronomy, Madison, WI, 1982, Chap. 29.
Opfermann, J. inetic analysis using multivariate non-linear regression: I. Basic concepts. Joural of Thermal Analysis and Calorimetry (2000), 60(2), 641-658.
Park, B.-D.; Riedl, B.; Kim, Y. S.; So, W. T. Effect of synthesis parameters on thermal behavior of phenol-formaldehyde resol resin. Journal of Applied Polymer Science (2002), 83(7), 1415-1424.
Powell, M. J. D. in: P. Rabinowitz, (Ed.), Numerical Methods for Nonlinear Algebraic Equations, Gordon and Breach Science Publishers, London, 1970, pp. 87-114 Prime R. B. Thermosets. In: Turi EA, editor. Thermal characterization of polymeric materials. New York: Academic Press, 1997:435–569.
Rawlings, J. O.; Pantula, S. G.; Dickey, D. A. Applied Regression Analysis, second ed., Springer, New York, 1998.
Sbirrazzuoli, N.; Girault, Y.; Elegant, L. Simulations for evaluation of kinetic methods in differential scanning calorimetry. Part 3 - Peak maximum evolution methods and isoconversional methods. Thermochimica Acta (1997), 293(1-2), 25-37.
Sbirrazzuoli, Nicolas; Vyazovkin, Sergey. Learning about epoxy cure mechanisms from iso-conversional analysis of DSC data. Thermochimica Acta (2002), 388(1-2), 289-298.
Sunose, T.; Akahira, T. Method of determineing activation deterioration constant of electrical insulating materials. Research Report, Chiba Inst. Tecnol. (Sci. Tecnol.) (1971), 16, 22-23.
Vyazovkin, S. V.; Lesnikovich, A. I. An approach to the solution of the inverse kinetic problem in the case of complex processes. 1. Methods employing a series of thermoanalytical curves. Thermochimica Acta (1990), 165(2), 273-280.
Vyazovkin, S.; Dollimore, D. Linear and Nonlinear Procedures in Isoconversional Computations of the Activation Energy of Nonisothermal Reactions in Solids.
Journal of Chemical Information and Computer Sciences (1996), 36(1), 42-45.
Vyazovkin, S. Evaluation of activation energy of thermally stimulated solid-state reactions under arbitrary variation of temperature. Journal of Computational Chemistry (1997), 18(3), 393-402.
Vyazovkin, S.; Wight, C. A. Kinetics in solids. Annual Review of Physical Chemistry (1997), 48, 125-149.
Vyazovkin, S.; Sbirrazzuoli, N. Kinetic methods to study isothermal and nonisothermal epoxy-anhydride cure. Macromolecular Chemistry and Physics (1999), 200(10), 2294-2303.
Vyazovkin, S. Modification of the integral isoconversional method to account for variation in the activation energy. Journal of Computational Chemistry (2000), Volume Date 2001, 22(2), 178-183.
Wang, J., M.-P. G. Laborie, and M. P. Wolcott. Comparison of model-fitting kinetic methods for modeling the cure kinetics of commercial phenol–formaldehyde resins.
Journal of Applied Polymer Science (2006), Accepted.
Widmann, G. Quantitative isothermal DTA studies. Thermochimica Acta (1975), 11(3), 331-333.
Chapter 5 The Influence of Wood on the Cure Kinetics of