Kinetic modelling and simulation of gravimetric curves: application to the oxidation of bismaleimide and epoxy resins

https://doi.org/10.1016/S0141-3910(02)00230-6Get rights and content

Abstract

A simplification of a previously presented “closed-loop” kinetic scheme of radical chain oxidation consisting in taking into account the substrate consumption is applied to the thermal oxidation (in oxygen excess) of a polybismaleimide (BMI) and an amine crosslinked epoxy (ACE). The model fits gravimetric curves in the 0–12% mass loss range well, for both polymers and constitutes a noticeable progress compared to the previously established “steady-state” models. The qualitative difference between BMI (presence of an initial maximum) and ACE (continuous mass decrease), is explained by the fact that ACE hydroperoxides are considerably less stable than BMI ones, which can be mechanistically justified. A generalisation of these results leading to a classification of gravimetric oxidation curves according to their shape, is tentatively proposed.

Introduction

Thermosets such as epoxies or polyimides are often used as matrix for composite materials in structural applications involving exposure in air at relatively high temperatures. Typical examples are engine or body parts in supersonic aircraft. Indeed, durability is a key property in such domains, which explains the relatively large amount of literature devoted to degradation mechanisms and kinetics. It has been clearly shown [1], [2], [3] that, in most cases, oxidation is the predominant ageing process. Its kinetic study is especially difficult for many reasons:

  • (i)

    Oxidation is a branched radical chain process. There is not yet a consensus on a kinetic scheme.

  • (ii)

    Oxidation kinetics are diffusion controlled (for sample thicknesses typically higher than 0.1–0.5 mm). A realistic model must take into account the reaction-diffusion coupling.

  • (iii)

    Analytical investigations are especially difficult in thermosets (and in composites) owing to their insolubility and structural complexity. Since the most common experimental ageing data are gravimetric, it appears especially interesting to build a kinetic model of mass changes.

In recent years, it has been shown that mechanistic schemes of the “closed loop” type, in which initiation results only from hydroperoxide decomposition (i.e. the reaction generates its own initiator), are interesting bases for kinetic modelling of thermal oxidation of high glass transition temperature (Tg) networks such as poly(bismaleimide) (BMI) [4] and amine crosslinked epoxy (ACE) [5]. These schemes involve six elementary steps:

where λ, μ, η, γ and υ are stoichiometric coefficients, and V is an “average” volatile molecule of molar mass MV, formed with a yield υ in the initiation step. In a first approach, the following set of hypotheses was used in order to obtain an analytical solution of the kinetic scheme:

  • (a)

    There is only one type of reaction site (PH).

  • (b)

    Initiation is unimolecular: λ=1 so that μ=2 and η=0.

  • (c)

    At the temperatures under consideration, there is no significant induction period: the steady-state is reached almost immediately after the beginning of exposure.

  • (d)

    The termination rate constants obey to the following inequality [6]:k52>>4k4k6

  • (e)

    Volatile molecules are formed only in the initiation step. Their formation in termination steps could also be envisaged but it will just add an adjustable parameter without changing the mathematical form of the model.

  • (f)

    Kinetic modelling is limited to low conversion ratios, so that it can be considered that the substrate concentration is constant:PH=PH0

  • (g)

    The choice of the above model involves the implicit assumption that radical (and volatile) generation from polymer thermal decomposition is negligible, which can be checked from experiments in inert atmosphere.

According to hypothesis (f), the use of this model must be restricted to relatively low mass losses. In the case of BMI, it correctly fits the experimental curves until a mass loss of the order of 8%, which can be considered sufficient in most practical cases. The ability of the model to represent the non-monotonous character of gravimetric curves in their initial part is noteworthy. This behaviour can be explained as follows. In closed-loop schemes, the kinetic chain length decreases continuously in the early period of exposure and tends asymptotically towards unity when the steady-state is established. Since weight loss occurs only in initiation whereas mass gain due to oxygen incorporation occurs only in the propagation step, mass gain is expected to predominate during the initial period of exposure but mass loss becomes more and more important as the kinetic chain length decreases, to predominate in the steady-state as experimentally observed (Fig. 1a).

In the case of ACE, however, mass loss predominates as soon as exposure begins and is continuously autoretarded (Fig. 1b). This behaviour cannot be simulated by the above model which predicts, in principle, an initial acceleration (linked to hydroperoxide accumulation) until a steady-state (where POOH destruction equilibrates with POOH formation) is reached.

The first question which comes in mind is: why do BMI and ACE display a different behaviour? Is it possible to classify the gravimetric behaviours of polymers and, eventually, to predict this classification from their structure? This question is practically important because it is presumably an important element of the discussion on the validity of gravimetric criteria to compare the polymer thermal stabilities.

In this study we attempt to answer the above question in term of kinetics and this first needs us to solve another problem: how to modify the kinetic scheme to take into account the auto-retarded character of gravimetric curves beyond about 8% mass loss for BMI and for the whole reaction course in the case of ACE? The simplest explanation which comes in mind is the non-validity of the hypothesis (f): the whole reaction rate is obviously linked to the substrate (PH) consumption and decreases as soon as the reaction has reached its steady-state. It seemed to us interesting to study a modification of the kinetic scheme in which hypothesis (f) is suppressed. If, with this modification, good fits of experimental curves, as well for BMI as for ACE are obtained, we can attempt to explain the difference of shape of gravimetric curves. For the sake of simplicity, only the case of oxygen excess (thin samples) will be studied.

Section snippets

Experimental

Both networks selected for this study have been previously described elsewhere [4], [5] and their characteristics will be briefly recalled. ACE is a mixture of triglycidyl derivative of p-aminophenol and diglycidylether of bisphenol F crosslinked by diaminodiphenylsulphone and blended with about 30% by weight of polyethersulphone. Its Tg is about 210 °C.

BMI is a mixture of aromatic bismaleimides blended with a diallyl bisphenol A derivative and about 20% by weight of a linear polyimide. Its Tg

Analytical model

For the model described in the introduction, the steady-state oxygen consumption rate r(C) is given by [4], [5]:rC=2r0βC1+βC1−βC21+βCwhere r0=k32PH02k6 and β=k2k62k5k3PH0, C being the oxygen concentration in the polymer. The “zero-order” kinetic regime, in which oxidation rate is almost independent of the oxygen concentration [r(C)→r0 when C→∞], begins at:CC≈3β−1=6k5k3PH0k2k6

The values of CC are given in Table 1 in the “results section”. Since oxygen solubility S in the polymers is known [4],

Results

The problem is now to determine the model parameters. The following procedure can be proposed:

Some parameters are experimentally determined (C) or calculated from the theoretical network structure ([PH]0). The other parameters can be determined using the model as an inverse method but, from a theoretical study [14], it appears that k3 and k6 are sharply linked within the parameter r0=k32PH02k6 so that there is presumably an infinity of pairs of k3 and k6 values giving equally good results. Both

Conclusion

A kinetic model has been derived from a mechanistic scheme in which initiation is exclusively due to hydroperoxide decomposition. Mass loss results from volatile formation in the initiation step and oxygen is in excess. The main novelty, here, is the introduction, in the kinetic scheme, of an equation describing the substrate consumption. With this latter modification, it is now possible to simulate correctly the gravimetric curves of amine crosslinked epoxies, which was impossible with the

References (17)

  • X. Colin et al.

    Polym Testing

    (2001)
  • K.T. Gillen et al.

    Polym. Degrad Stab

    (1995)
  • K.J. Bowles et al.

    J. Adv. Mat.er

    (1994)
  • M.A.B. Meador et al.

    High Perform. Polym.

    (1996)
  • Colin X, Marais C, Favre JP. Proceedings of ICCM-12. Paris: AMAC...
  • X. Colin et al.

    J. Appl. Polym. Sci.

    (2001)
  • Kamiyam Y, Niki E. In: Jellinek HHG, editor. Aspects of degradation and stabilisation of polymers. New York: Elsevier;...
  • K.U. Ingold

    Acc. Chem. Res.

    (1969)
There are more references available in the full text version of this article.

Cited by (57)

  • Gamma irradiation influence on mechanical, thermal and conductivity properties of hybrid carbon nanotubes/montmorillonite nanocomposites

    2021, Radiation Physics and Chemistry
    Citation Excerpt :

    Nevertheless, beyond 150 kGy, the storage modulus value reduced back at the doses of 200 and 250 kGy. The reduction in the modulus is attributed to chain scission of the material (Ahmed et al., 2012; Colin et al., 2002) which contributed to the increase in the material brittleness (Ahmed et al., 2012; Perera et al., 2004). The values of the glass transition temperature (Tg) were evaluated and plotted as a function of the gamma irradiation dose as shown in Fig. 3.

  • Towards a general kinetic model for the thermal oxidation of epoxy-diamine networks. Effect of the molecular mobility around the glass transition temperature

    2020, Polymer Degradation and Stability
    Citation Excerpt :

    Indeed, this tool could help aeronautical manufacturers to take into account the possible alteration of the thermomechanical properties of composite structures from the moment of their design and sizing, but also to consider the use of these materials in more aggressive thermochemical environments. There is a large amount of literature works devoted to the thermal degradation mechanisms [1-9] and kinetics [10-17] of EPO-DA networks, showing that oxidation is clearly the predominant aging process. However, in these publications, each network is considered as a completely different material from other networks of the EPO-DA family, because it is assumed to be characterized by its own chemistry, its own oxidation mechanisms, its own degradation kinetics and its specific kinetic model.

View all citing articles on Scopus
View full text