Ministeriales en contexto.
4.3. La Reforma Educacional de 1981.
4.3.2. Revisión de los Programas Ministeriales de esta reforma.
We then derived the following expression for the rate of degradation:
!!!""#!!
!" ! !! ! !!!! (Eq. 2.3.1)
This differential equation was solved numerically using built-in integrators of the
MathCAD package,4 and details of the modelling can be found in Appendix 2:
Additional Material for Chapter 2.
Several scenarios of polyester degradation were considered. First, we modelled degradation on the polymer surface where the oxygen is continually replenished from
air. In the case of a ‘perfect’ polyester, i.e. with no defect units and only fully-saturated
chains, the degradation is extremely slow, with a half-life time of the material equal to
ca. 200 years (Figure 2.3.1A). On the other hand, in the worst-case scenario where
every single chain has a defect the damage is so rapid that it only takes 20 days to break down 50% of the polymer (Figure 2.3.1B). Obviously, these models are simplified and extreme, however they vividly illustrate the detrimental effect of the defect units,
concentration of which in polyester depends strongly on the curing conditions.5
However, apart from the defects, there is another likely source of facilitated degradation – reactive alkoxyl radicals, RO•. Specifically, given the low reactivity of peroxyl radicals towards H-abstraction, these are instead more likely to accumulate in concentrations, sufficiently high for two ROO• to ‘meet’ and disproportionate, producing alkoxyl radicals, i.e. 2ROO• " [ROOOOR] " 2RO• + O2.6 The latter, in
contrast, are much more reactive and able to abstract hydrogens virtually non- selectively.7
RO2 + RH ROOH + R
2 RO2 products
RO2 + R products
Figure 2.3.1 Results of a preliminary kinetic modelling of polyester degradation under various scenarios.
The second scenario considered is that of the degradation inside the polymer matrix.
Diffusion of O2 inside the polymer is considered to decay quickly, effectively
disappearing at depths over 10 mm.8 Therefore, the only oxygen available to react with
R• is that initially dissolved in the polymer. For polyethylene terephthalate (PET) the concentration of such oxygen is ca. 10-3 mol L-1.9 Under these conditions our kinetic
model (Scheme 2.3.1) predicts that the degradation proceeds only until all of the oxygen is consumed, and the total amount of damaged polymer is consequently equal to the
initial O2 concentration (Figure 2.3.1C). In other words, less than 0.02% of polyester is
degraded. This is not, unfortunately, a realistic prediction, because our simplified kinetic model does not account for one other important damage event – transfer of C-
centred radicals from one chain to another, i.e. R• + RH " RH + R•. While kinetically
this is a ‘null’ reaction (which makes it conceptually difficult to model it), on a molecular level R• can undergo various transformations (e.g. fragmentations and rearrangements), ultimately yielding a defected chain. According to our calculations, the rate of this reaction is almost 100 times higher than even the thermodynamically favourable H-abstraction from the defect units by ROO•. Thus, it is likely that inside the
concentration. In the absence of O2 a more severe damage propagates via the
aforementioned ‘null’ reaction instead (Figure 2.3.1D).
Although these conclusions are based upon an admittedly over-simplified kinetic model, they allow explaining intriguing differences in the rates of degradation occurring in the air vs. that in an inert N2 atmosphere.10 Specifically, when the oxygen is
eliminated as the atmosphere is changed from air to N2, polymer degradation is
significantly accelerated (Figure 2.3.2), quite counter intuitively considering that the
very name of the damage process – autooxidation – implies the leading role of O2 in it.
But according to our results, oxygen converts more reactive carbon-centred radicals into less reactive peroxyl radicals, and in essence acts as an inhibitor of the degradation, or an antioxidant!
Figure 2.3.2 Thermo-gravimetric analysis (TGA) curve showing the effect of switching of gaseous atmospheres between air and nitrogen on the thermal degradation of poly(methyl) methacrylate (PMMA) at 200 °C. Reproduced from Ref. 10a.
In summary, both the findings of the Paper 1 and of the subsequent kinetic modelling illustrate the mechanistic complexity of the thermo- and photo-oxidative damage of organic materials, in particular suggesting that the degradation pathways vary depending on a number of factors: the chemical structure of the material, the presence of oxygen, the temperature, etc. On one hand, this knowledge is now being applied to design new monomers affording more stable polyesters and acrylates in the course of another industry-funded project. On the other hand, understanding of the degradation chemistry is pertinent for its effective minimisation and prevention, as shown in the next Chapter.
temperature of degradation. In other words, the stabilizing effect of oxygen has already reached its saturation in air. The use of an oxygen-nitrogen mixture containing 21% oxygen gives rise to a TGA curve that is very similar to that obtained for degradation under air. For technical reasons (the maximum gas flow should not exceed 200 mL min-1), we could not obtain
an oxygen-nitrogen mixture with an oxygen concentration lower than 1.6%. Even at this level, oxygen has a profound stabilizing effect on PMMA degradation.
Effect of Switching between Air and Nitrogen on Degra-
dation.Figure 5 shows how switching of gaseous atmospheres
between air and nitrogen affects the thermal degradation of PMMA. Degradation was started in the atmosphere of air. This process is characterized by a slow rate. Upon switching to a nitrogen atmosphere, the degradation rate increases significantly. Switching back to air causes the reaction rate to immediately slow down. This switching of reaction atmospheres was repeated at regular intervals until a 9% mass loss was achieved. The effect appears to be reversible.
Visual Analysis of Partially Degraded Samples. Several
experiments run under air and nitrogen were stopped at 20% mass loss and analyzed visually. Note that this extent of degradation is reached at practically the same temperature for degradations performed under nitrogen and air (Figure 4). Visually, the sample degraded in air was a single chunk of clear glassy material that contained a few bubbles. The sample decomposed in nitrogen, however, was a white powder material similar to the original PMMA sample.
Kinetic Analysis of TGA Data. The kinetics of heteroge-
neous decompositions is traditionally described by the basic kinetic equation
whereRrepresents the extent of reaction (R )0-1),tis time,
k(T) is the rate constant, andf(R) is the reaction model, which
describes the dependence of the reaction rate on the extent of reaction. The value ofRis experimentally determined from TGA as a relative mass loss and from DSC as a fractional peak area. In most cases the temperature dependence of k(T) can be satisfactorily described by the Arrhenius equation, whose substitution into eq 1 yields
whereEis the activation energy and Ais the preexponential factor. To evaluate a dependence of the effective activation energy on the extent of conversion, we used an advanced isoconversional method,36 which is based on the assumption
that the reaction model is independent of the heating program,
T(t). According to this method, for a set ofnexperiments carried out at different heating programs, the activation energy is determined at any particular value of R by finding ER that minimizes the function
where the subscriptsiandjrepresent oridinal numbers of two experiments performed under different heating programs. Hence- forth, the subscriptRdenotes the values related to a given extent of conversion. In eq 3, the intgeral
is evaluated numerically for a set of experimentally recorded heating programs,Ti(t). The minimization procedure is repeated for each value ofR to find the dependence of the activation energy on the extent of conversion. An advantage of the advanced isoconversional method is that it can be applied to study the kinetics under arbitrary temperature programs (e.g., under a linear heating program distorted by self-heating).36
Figure 6 shows theERdependencies evaluated for the thermal degradation of PMMA under nitrogen and air. Under nitrogen, the initial activation energy required to initiate decomposition was about 60 kJ mol-1. As the reaction approaches 30%
conversion, the activation energy increases to a maximum value of about 190 kJ mol-1. This is followed by a decrease from
190 to ∼60 kJ mol-1 in the region 0.3 < R < 0.55. This
decrease falls in the transition region between the first and second step in the mass loss. Further degradation (R >0.55) is characterized by an increase in the activation energy from 60 to∼230 kJ mol-1near completion.
In air the thermal degradation of PMMA gives rise to a parabolicERdependence that decreases from about 220 kJ mol-1 to a minimum value of 160 kJ mol-1atR≈0.55 degradation.
Then the activation energy rises to about 200 kJ mol-1 at
completion. Discussion
Degradation in Nitrogen. In the absence of oxygen, the
thermal degradation of radically polymerized PMMA usually Figure 5. TGA curve showing the effect of switching of gaseous
atmospheres between air and nitrogen on the thermal degradation of PMMA at 200°C. dR dt )k(T)f(R) (1) dR dt )Aexp
(
-E RT)f(R) (2)Figure 6. ER-dependencies obtained by isoconversional analysis of TGA data for degradations under nitrogen (squares) and air (circles).
Φ(ER))
!
i)1 n!
j*1 n(
J[ER,Ti(tR)] J[ER,Tj(tR)]-1)
2 (3) J[ER,Ti(tR)]≡∫
0tRexp[
-ER R Ti(t)]
dt (4)2.4 References
1 Private communication with Dr. Philip Barker of the Bluescope Steel.
2 Unpublished experimental results by A/Prof. Uta Wille, University of Melbourne. 3 Gillen, K. T.; Wise, J.; Clough, R. L. Polym. Degrad. Stab. 1995, 47, 149-161. 4 MathCAD 14.0 by PTC#.
5 Kelsey, D. R.; Kiibler, K. S.; Tutunjian, P. N. Polymer 2005, 46, 8937-8946.
6 (a) Nangia, P. S.; Benson, S. W. Int. J. Chem. Kinet. 1980, 12, 29-42. (b) da Silva, G.; Bozzelli, J. W. J. Phys. Chem. A 2007, 111, 12026-12036.
7 (a) Ingold, K. U. Acc. Chem. Res. 1969, 2, 1-9. (b) Griller, D.; Ingold, K. U. J. Am. Chem. Soc. 1974, 96, 630-632. (c) Carstensen, H.-H.; Dean, A. M. P. Combust. Inst. 2005, 30, 995- 1003.
8 Stuetz, D. E.; Diedwardo, A. H.; Zitomer, F.; Barnes, B. P. J. Polym. Sci., Polym. Chem. Ed. 1980, 18, 987-1009.
9 The solubility of oxygen in PET is taken equal to 0.098 cc(STP) cm-3 atm-1, partial pressure of oxygen in the atmosphere at STP is equal to 0.2095 atm (from Dalton’s law). From this, volume solubility of oxygen in PET is equal to 0.098$0.2095 = 2.0531$10-2 L per L of PET. Assuming the ideal gas behaviour, the molar concentration of oxygen is calculated equal to 9.16$10-4 mol L-1. See (a) Sekelik, D. J.; Stepanov, E. V.; Nazarenko, S.; Schiraldi, D.; Hiltner, A.; Baer, E. J. Polym. Sci., Part B: Polym. Phys. 1999, 37, 847-857. (b) Zoller, P.; Walsh, D. J. Standard pressure-volume-temperature data for polymers; Technomic: Basel, 1995. (c) Polyakova, A.; Connor, D. M.; Collard, D. M.; Schiraldi, D. A. Hiltner, A.; Baer, E. J. Polym. Sci., Part B: Polym. Phys. 2001, 39, 1900-1910.
10 (a) Peterson, J. D.; Vyazovkin, S.; Wight, C. A. J. Phys. Chem. B 1999, 103, 8087-8092. (b) Peterson, J. D.; Vyazovkin, S.; Wight, C. A. Macromol. Chem. Phys. 2001, 202, 775-784. (c) Azimi, H. R.; Rezaei, M.; Abbasi, F.; Thermochim. Acta 2009, 488, 43-48.