«CURE KINETICS OF WOOD PHENOL-FORMALDEHYDE SYSTEMS By JINWU WANG A dissertation submitted in partial fulfillment of the requirements for the degree of ...»
Sbirrazzuoli et al. 1997). MFK does not assume any definite form of the reaction and allows for variations in activation energy as the reaction progresses (Vyazovkin and Wight 1997). In fact, both PF and phenol-urea-formaldehyde (PUF) resins have been successfully characterized with MFK using the Kissinger-Akahira-Sunose (KAS) algorithm (Kissinger 1957; Sunose and Akahira 1971; He et al. 2003a; He and Riedl 2003). For PF resoles, changes in activation energy with degree of cure, Eα, helped distinguish two-stages in a highly condensed PF resin. In the first stage Eα increase with degree of cure was ascribed to consecutive and competitive reactions. Following this chemical regime, a decrease in Eα was ascribed to a diffusion-controlled regime (He et al. 2003a). The KAS algorithm could also be used to predict the isothermal cure of PF resins from dynamic tests (He et al. 2003a). Owing to additional cure reactions involving urea, PUF resins exhibited a more complex Eα curve than PF resins (He and Riedl 2003). Finally, the effects of water and wood on the cure kinetics of PF resins have also been examined with the KAS method (He et al. 2003b; He and Riedl 2004). While at low conversion water contributed to reversible cure reactions, it acted as a plasticizer at higher conversion and thus delayed the diffusion control regime enabling more complete cure (He et al. 2003a).
To date, all MFK studies on phenolic systems have utilized the KAS algorithm although isoconversional algorithms such as the Vyazovkin (1997; 2001) and Friedman methods (Friedman 1964) are also available. The objective of this research is to evaluate and compare the ability of the Friedman, Vyazovkin and KAS methods for 1) revealing the cure process and 2) predicting the dynamic and isothermal cure behavior of commercial PF resole resins from dynamic test data. In this objective, the cure kinetics of two commercial PF resoles that differ in molecular weight is evaluated with the three MFK methods.
EXPERIMENTALMaterials Two PF resoles, tailored as adhesives for oriented strand boards, were obtained from a commercial source. The resins were frozen and stored at -20oC until use. To determine molecular weights, the resins were acetylated with 1:1 pyridine and acetic anhydride (Yazaki et al. 1994) and analyzed by gel permeation chromatography (GPC) in tetrahydrofuran. The GPC system consisted of a Viscotek 270 coupled to a Waters HPLC unit and Jordi Gel polydivinylbenzene mixed bed column with triple detectors.
One resin had a weight-average molecular weight (Mw) of 621 g/mol and a polydispersity (Mw/Mn) of 1.41; it was labeled as PF-low. The other resin displayed an Mw = 6576 g/mol and Mw/Mn =1.72; it was labeled as PF-high. The resin solid contents were 54.5% and 45.0% for PF-low and PF-high respectively. In addition, elemental analysis (Nelson and Sommers 1982) showed the presence of 3.7 and 3.9 wt % nitrogen for PF-high and PF-low respectively, indicating the presence of urea in both resins.
Differential Scanning Calorimetry A Mettler-Toledo DSC 822e was used to perform dynamic and isothermal cure experiments. Approximately 13.5mg of resin was placed in a 30µl high pressure gold-plated crucible. Dynamic temperature scans were conducted at 5 heating rates 2, 5, 10, 20 and 25°C/min from 25°C to 250°C (He et al. 2003a). Nitrogen was used as a purge gas at a flow rate of 80 ml/min. For each heating rate six replicate measurements were performed. In addition the first replicate was scanned again at 10oC/min immediately after the first scan. This second scan ensured complete cure during the first heating scan as evidenced by the absence of residual cure. DSC thermograms were then processed with the Mettler-Toledo STARe V7.2 software to extract the degree of cure, α, reaction rate, dα/dt, and corresponding temperature, Tα, in the 0≤ α ≤0.99 range. Both α and dα/dt were determined at a specific cure time, t, by normalizing the partial heat of reaction, ∆H(t), and heat flow, dH/dt, respectively
by the total heat of reaction ∆H:
MATLAB programs using the linear least square method were then developed to extract cure kinetic parameters according to the Friedman, Vyazovkin and KAS algorithms. The experimental data obtained at 2, 5 and 10°C/ min was then processed with these three programs. Kinetic parameters measured with the KAS algorithm were used to develop and compare dynamic cure predictions with experimental data at 20 and 25°C/min. To further validate the three MFK methods for isothermal cure, isothermal DSC runs were conducted at 120°C for different periods of time. The cure temperature and the cure times were selected based on experimental facility and so as to span the complete cure process. Specifically, the DSC cell was preheated to 120°C and approximately 13.5 mg of PF resin was inserted and cured for different periods of time. The sample was then quickly removed from the DSC and quenched in liquid nitrogen. The residual heat of reaction of the partially cured samples, ∆HR, was
obtained from a subsequent ramp scan at 10°C/min from 25 to 250oC so that:
The total heat of reaction was taken as the average reaction heat previously measured in dynamic tests of fresh resins, 365 (± 5) kJ/kg for PF-high and 420 (± 9) kJ/kg for PF-low. The time dependence of the degree of cure at 120°C was compared with predictions from the three methods.
The phenomenological kinetics of cure can be generally described as:
where f(α) is the reaction model, T(K) the absolute temperature, A (s-1) the pre-exponential factor, E (kJ/mol) the activation energy and R the universal gas constant. The Friedman (1964), Vyazovkin (1997; 2001) and KAS algorithms (Kissinger 1957; Sunose and Akahira 1971) can then be used to determine the activation energy dependence on degree of cure Eα.
For various heating rates, βi, the Friedman method directly evaluates Eq. (24) at
a specific degree of cure α:
For a specific α value and several heating rates βi, pairs of (dα/dt)αi and Tαi are determined experimentally from the DSC thermograms. The parameters Eα and Cf (α) at this specific value of α are then estimated from plots of ln (dα/dt)αi versus 1/Tαi (Eq.
(26)) across at least three different heating rates. The procedure is repeated for many values of α yielding continuous functions of α for Eα and Cf (α). The interest of the Friedman method is that Eq. (26) does not introduce any approximations and the method is not restricted to the constant heating rate mode. However, as in the case of any kinetic methods involving the differential term dα/dt, the Friedman method is subject to significant numerical instability and noise interference (Sbirrazzuoli et al.
As a result, Vyazovkin proposed an alternative algorithm, which is summarized in the following equations. A detailed derivation of the algorithm is provided elsewhere (Vyazovkin 1997; 2001). In Vyazovkin method n scans are performed at different heating programs Ti(t). The activation energy at a specific
degree of cure is obtained by minimizing the function ϕ(Eα):
Eq. (28) can be solved numerically by integrating the experimental data within small time intervals ∆α. The I values are then substituted into ϕ(Eα), and this function is minimized by Brent’s method (Brent 1973) leading to Eα. Again the procedure is repeated for distinct values of α. A new parameter Cv(α) can also be created that
complements Eα in fully describing the cure kinetics:
Finally in the KAS method, Eα is evaluated by using Doyle’s integral approximations in Eq. (30) (Doyle 1961). In this case, Eq. (31) is derived for various heating rates. Again it can be rewritten into Eq. (32) by introducing a new parameter
Ck(α) =ln (RAα /Eα g(α)):
The experimental determination of Eα and Ck(α) is similar to that of the Friedman method. For each degree of cure α, a corresponding Tαi and heating rate are used to plot ln (βi/T2αi) against 1/Tαi. The parameters Eα and Ck(α) are then determined from the regression slope and intercept respectively.
The Friedman and Vyazovkin methods respectively solve the differential (Eq.
(24)) and the integral kinetic forms (Eq. (28)) without approximations. On the other hand, the KAS method utilizes a close-form approximation (Eq. (30)). As a result, the KAS method provides only an estimate of the activation energy compared to the Vyazovkin and Friedman methods (Budrugeac and Segal 2001). In addition, while the Friedman and Vyazovkin methods are applicable to different temperature programs, the KAS method only works for constant heating programs.
RESULTS AND DiSCUSSIONKinetic parameters from MFK methods As expected, the commercial PF resoles exhibit two major exotherms that shift to higher temperatures with increasing heating rate (Figure 4.1). In addition, PF-high displays a third intermediate exotherm of small intensity (Figure 4.1). Hence, PF-low has two discernable cure reactions while three reactions are evident during PF-high cure. Note also that a high degree of cure (54%) is required for PF-low to reach its highest reaction rate while the maximum reaction rate is achieved very early (22% degree of cure) for PF-high. To interpret the differences in stages in the cure of both resins, the Eα dependence on degree of cure can be examined (Sbirrazzuoli and Vyazovkin 2002).
Figure 4.1 DSC thermograms at 2oC/min for the PF-low and PF-high resins.
Insert highlights the influence of heating rate (2, 5, 10, and 20 oC/min) on the cure of the PF-high resin.
Friedman, Vyazovkin and KAS algorithms. The overall range of activation energies between 60 and 120 kJ/ mol is consistent with the values obtained from model fitting kinetics of PF resins (Ray and Westwood 1975; Park et al. 2002). Evident in Figure
4.2 is the superposition of the Friedman and Vyazovkin Eα curves. The KAS method yields similar ascending and descending pattern, yet variations in Eα are smaller and the activation energy curve is shifted to higher conversion (Figure 4.2). Such a consistency between the Friedman and Vyazovkin methods has been previously observed on simulated data of parallel reactions (Vyazovkin 2001). In contrast, the shift and low amplitude of Eα obtained with the KAS method likely stems from the approximation used in this algorithm. Recall that the Friedman and Vyazovkin methods use the point values of the overall reaction rate (Budrugeac and Segal 2001) or small time intervals (Vyazovkin 2001) while the KAS method uses Doyle’s approximation (Eq. 30) that describes the history of the system Budrugeac and Segal 2001). Yet Vyazovkin reported that the KAS method provides satisfactory E estimates as long as E/RT is greater than 13 (Vyazovkin and Dollimore 1996). In the case of the commercial PF resoles used in this study, despite an E/RT 13, the KAS method generates an activation energy curve that is shifted to higher conversion and reduced in amplitude. This discrepancy in the case of commercial PF resoles likely stems from violation of the Doyle’s assumption of a constant activation energy across the kinetic process (He and Riedl 2003). It results that the Vyazovkin and Friedman methods provide more consistent and accurate Eα functions. With these two methods, Eα is also more sensitive to changes in PF cure mechanisms. Therefore, to gain insight on the cure mechanism of PF resins, the Vyazovkin and Friedman methods are preferred over the KAS method.
and molecular weight dependency of PF cure kinetics. Indeed it is established that complex reactions involving multiple parallel reactions or changes in the limiting stage cause variations in Eα (Vyazovkin and Lesnikovich 1990; Flynn and Wall 1966;
Opfermann 2000). Specifically, an increasing Eα function reveals competition between parallel reactions (He et al. 2003a; Vyazovkin and Lesnikovich 1990).
Alternatively a concave decreasing Eα curve suggests a reversible stage reaction and a convex decreasing Eα function shows a change in limiting stage (Vyazovkin and Lesnikovich 1990). Therefore the shape of Eα can give some insight on the change in reaction steps (Vyazovkin and Wight 1997).
For PF-low, Friedman and Vyazovkin methods generate two Eα peaks at 45% and 88% degrees of cure (Figure 4.2) in accordance with two detected exotherms (Figure 4.1). Eα shape for PF-low suggests 4 cure stages. The increasing and then concave decreasing Eα curve suggests the presence of competitive reactions up to 45% conversion followed by a reversible stage intermediate up to 65% (Vyazovkin and Lesnikovich 1990; Vyazovkin and Wight 1997). At a degree of cure of 65% parallel reactions reconvene as indicated by the Eα increase until the cure changes from a kinetic to a diffusion-controlled process (Butt 1999) above 88% conversion where Eα decreases in a convex fashion (Vyazovkin and Lesnikovich 1990;
Vyazovkin and Wight 1997). This 4-stage cure is more complex than the 3-stage cure of PUF resins previously described based on the KAS algorithm (He and Riedl 2003).
Recall however that the KAS method is less sensitive to changes in Eα than the Vyazovkin and Friedman methods used in this study. In fact, the Eα curves obtained from the KAS method for PF-low and PF-high would also suggest a 3-stage cure. In addition in contrast to a single cure exotherm previously detected on PUF resins (He and Riedl 2003); two exotherm peaks are detected on these commercial PF resoles.